The hydraulic transport of wood chips
by John Leonard Gow
A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Civil Engineering
Montana State University
© Copyright by John Leonard Gow (1971)
Abstract:
The hydraulic transport of wood chips in pipelines has been examined. Experimental head-loss data
were recorded from mixtures of wood chips and water flowing in smooth pines of 4-in. and 6-in.
nominal diameters with concentrations of solids ranging up to 20 percent by volume. Fanning friction
factors were calculated from these head-loss data. Two distinct modes of transporting solids,
"pseudo"-laminar and "pseudo"-turbulent, were defined from an analysis of the experimental data.
The "pseudo"-!aminar mode occurs in the sliding bed regime. The head-loss data in this mode were
correlated by the non-Newtonian model developed by Metzner and Reed.
The "pseudo"-turbulent mode occurs in the saltation and heterogeneous flow regimes. The head-loss
data in this mode were correlated by a model similar to Prandtl's smooth pipe friction equation for
Newtonian fluids in smooth pipes. A slurry Reynolds' Number was defined for this correlation using a
pseudo-viscosity for the mixture of wood chips and water calculated from the experimental data. The
pseudo-viscosity appears to be a function of concentration only.
Error analyses for both modes of flow showed that all experimental data points were within 5 percent
of values predicted by the proposed correlation models. THE.HYDRAULIC TRANSPORT OF WOOD CHIPS
by
JOHN LEONARD GOW
A t h e s is s u b m itte d t o th e Graduate F a c u lty i n p a r t i a l
f u l f i l l m e n t o f th e re q u ire m e n ts f o r th e degree
of
D o ctor o f P h ilo s o p h y
in
C iv il
E n g in e e rin g
Chairman, Examining Committee
MONTANA STATE UNIVERSITY
Bozeman, Montana
December, 1971
Iii
ACKNOWLEDGEMENTS
The a u th o r wishes t o express h is s in c e r e a p p r e c ia t io n t o
Dr. W illia m A. Hunt under whose guidance t h i s i n v e s t i g a t i o n was
made. • In a d d i t i o n , th e most h e l p f u l a s s is ta n c e o f Mr. Jay B i llm a y e r
i s g r a t e f u l l y acknowledged.
The p r o j e c t was sponsored by th e F o r e s t E n g in e e rin g Research
Branch o f th e I n te rm o u n ta in F o re s t Range Experim ent S t a t i o n , U n ited
S ta te s F o r e s t S e r v ic e , Department o f A g r i c u l t u r e , as p a r t o f a
c o o p e r a tiv e a id agreement w i t h th e Department o f C i v i l
E n g in e e rin g
and E n g in e e rin g Mechanics o f Montana S ta te U n i v e r s i t y .
T h is d i s s e r t a t i o n i s d e d ic a te d t o th e a u t h o r 's w i f e Jean, and
c h i l d r e n E r ic and J a n e t.
■ S
iv
TABLE OF CONTENTS
CHAPTER
PAGE
V I T A ..............................................................................................................
ii
ACKNOWLEDGEMENTS ....................................................................................
iii
LIST OF TA B LE S ......................
v
LIST OF F I G U R E S ....................................................................................
ABSTRACT . . .
...............
. . . . .
.................................................
NOMENCLATURE .............................................................................................
I
INTRODUCTION................................... ....................................................
II
vi
v iii
ix
.
I
REVIEW OF HYDRAULIC TRANSPORT OF SOLIDS
...............................
I
III
EXPERIMENTAL INVESTIGATION...................... ....
. ...........................
24
IV
CORRELATION METHOD AND ANALYSIS
.................................................
48
V '
CONCLUSIONS AND RECOMMENDATIONS
................................................
82
REFERENCES CITED ...................................
87
APPENDICES.........................................................
90
Appendix A
Appendix B
........................................................................................
91
.................................
'100
•
•
■ .
■
. V
l is t
No.
of
■
,
Table 's
.
Page
3.1
S ize G ra d a tio n o f Wood Chips . . .................................. 31
3 .2
Weight D i s t r i b u t i o n o f I n d i v i d u a l Sizes
. . . .
31
3 .3
Bed Form ation V e l o c i t i e s - 4 . - i n .
. . . .
46
4.1
"Pseudo11-L a m in a r Index Parameters
4 .2
E r r o r A n a ly s is o f Measured and P r e d ic te d
F r i c t i o n Facto rs f o r "Pseudo-Laminar
R e g i o n ............................................ ..............................
4 .3
"P s e u d o "-T u rb u le n t Flow Parameters ........................... 73
4 .4
E r r o r A n a ly s is o f Measured and P re d ic te d
F r i c t i o n F a cto rs f o r "P s e u d o "-T u rb u le n t
Region ............................................ ..................................
Pipe .
. . . . . . .
54
; 54
73
vi
LIST OF FIGURES
F ig u re
Page
3.1
M acroscopic C o n tro l Volume For Two-Phase Flows . .
25
3 .2
C le a r Water F r i c t i o n F acto rs
33
3 .3
M ix tu re Wood-Chip Head-Loss Data . . . . . .
i . .
35
3 .4
. 8 7 5 - in . Wood-Chip Head-Loss D a t a ...................... ■ . .
36
3 .5
0 . 5 0 - i n . Wood-Chip Head-Loss Data
37
3 .6
0 . 3 7 5 - i n . Wood-Chip Head-Loss Data ...............................
38
3 .7
F a d d ic k 's Wood-Chip Head-Loss Data . . .
..................
40
3 .8
Soucy's Wood-Chip Head-Loss Data ...................................
41
3 .9
E l l i o t e t a i Wood-Chip Head-Loss D a t a ...................... 42
4.1
F r i c t i o n F a c to r Comparison ...............................
4 .2
F r i c t i o n F a c to r Comparison ................................................
59
4 .3
"P s e u d o "-T u rb u le n t Head-Loss Data f o r
M ix tu r e Sample ............................... ....
68
4 .4
"P s e u d o "- T u r b u le n t Head-Loss Data f o r
0 . 8 7 5 - i n . Sample ..................................................................
69
4 .5
" P s e u d o "-T u rb u le n t Head-Loss Data f o r
0 . 5 0 - i n . Sample
. . .........................................................
70
4 .6
llPseudoll- T u r b u le n t Head-Loss Data f o r
0 . 3 7 5 - i n . Sample ..................................................................
71
4.7a
" P s e u d o "-T u rb u le n t C o r r e l a t i o n Parameters M ix tu r e Sample .................................................................
74
4.7b
............................................
. . . . . . . .
. . . .
llPseudoll- T u r b u le n t C o r r e l a t i o n Parameters M ix tu r e Sample ......................................................................
59
.
74
vi i
F ig u re
Page
4.8a
llPseudoll- T u r b u le n t C o r r e l a t i o n Parameters 0 . 8 7 5 - i n . Chip S ize
. . . .
4.8b
"Pseudo11- T u r b u le n t C o r r e l a t i o n Parameters 0 . 8 7 5 - i n . Chip S iz e
. . . . . . .
..................
75
,
75
4 .9a
"Pseudon- T u r b u l e n t C o r r e la t i on Parameters 0 . 5 0 - i n . Chip S ize . . . . .
76
4.9b
"P s e u d o "- T u r b u le n t C o r r e l a t i o n Parameters 0 . 5 0 - i n . Chip S ize . . . . .
76
4.10a
llPseudoll- T u r b u le n t C o rre l a t i on Parameters 0 . 3 7 5 - i n . Chip S ize
. . . .
77
4.10b
"Pseudon- T u r b u le n t C o r r e l a t i o n Parameters 0 . 3 7 5 - i n . Chip S ize
. . . .
77
A -I
Schematic o f E xp e rim e n ta l System
. ...................... ....
A -2
Wood-Chip I n j e c t i o n and S e p a ra tio n Equipment
. .
93
96
v iii
ABSTRACT
The h y d r a u lic t r a n s p o r t o f wood ch ip s i n p i p e l i n e s has been
examined.
E xp erim e ntal h e a d -lo s s data were recorded from m ix tu re s
o f wood c h ip s and w a te r f lo w in g i n smooth pines o f 4 - i n . and 6- i n .
nominal d ia m e te rs w i t h c o n c e n tr a t io n s o f s o l i d s ra n g in g up to 20
p e r c e n t by volume.
Fanning f r i c t i o n f a c t o r s were c a l c u la t e d from
these h e a d -lo s s d a ta .
Two d i s t i n c t modes o f t r a n s p o r t i n g s o l i d s ,
" p s e u d o " - la m in a r and " p s e u d o " - t u r b u le n t , were d e fin e d from an
a n a ly s is o f the e xp e rim e n ta l d a ta .
The " p s e u d o " - ! am inar mode occurs i n th e s l i d i n g bed regim e. The
h e a d -lo s s data i n t h i s mode were c o r r e l a t e d by th e non-Newtonian
model developed by M etzner and Reed.
The " p s e u d o " - t u r b u le n t mode occurs i n th e s a l t a t i o n and
heterogeneous f lo w regim es. The h e a d -lo s s data i n t h i s mode were
c o r r e l a t e d by a model s i m i l a r to P r a n d t l 's smooth p ip e f r i c t i o n
e q u a tio n f o r Newtonian f l u i d s i n smooth p ip e s .
A s l u r r y Reynolds'
Number was d e fin e d f o r t h i s c o r r e l a t i o n using a p s e u d o - v is c o s it y f o r
th e m ix t u r e o f wood c h ip s and w a te r c a l c u la t e d from th e expe rim e n ta l
d a ta .
The p s e u d o - v is c o s it y appears t o be a f u n c t i o n o f c o n c e n tr a t io n
o n ly .
E r r o r analyses f o r both modes o f f lo w showed t h a t a l l e x p e rim e n ta l
data p o in t s were w i t h i n 5 p e rc e n t o f va lu e s p r e d ic t e d by th e proposed
c o r r e l a t i o n models.
' ix
NOMENCLATURE
S.ymbol
D e s c r ip t io n
A,a
E m p iric a l c o n s ta n ts
V o lu m e tric p a r t i c l e
c o n c e n tr a t io n
Pipe d ia m e te r, f t
Wood c h ip s iz e parameter
E
E m p iric a l c o n s t a n t
f
Fanning f r i c t i o n
fa c to r
C le a r w a te r h y d r a u lic
g ra d ie n t, f t / f t
S l u r r y h y d r a u lic g r a d i e n t ,
ft/ft
K
F l u id c o n s is te n c y in d e x ,
dim ensions c o n s i s t e n t w i t h
d e f i n i n g e q u a tio n
L
Pipe le n g t h , f t
m
E m p iric a l c o n s ta n t
n
F l u id b e h a v io r in dex
P
S t a t ic pressure, psf
S l u r r y f lo w r a t e , c f s
^ m
i x
^cw
R
Reg
■
v
C le a r w a ter f l o w r a t e , c f s
Pipe i n t e r n a l
ra d iu s , f t
G e n e ra lize d Reynolds number,
Reg=V2- n DnPZSn" 1K
X
S l u r r y Reynolds number,
Res=VDpsZps
C le a r w a te r Reynolds number,
RV
VDp/yo
S p e c ific g r a v it y .
Tem perature, 0 F
S lu rry v e lo c ity , ft/s e c
a
E m p iric a l C onstant
3
E m p iric a l c o n s t a n t
AP
S t a t i c p re s s u re decrem ent,
p s f/ft
Dim ensionless param eter
(D u ra n d )'
V is c o s ity r a t i o
Water d e n s i t y , s l u g s / f t
3
<3
S lu rry d e n s ity , s l u g s / f t
Wall shear s t r e s s , p s f
Water v i s c o s i t y ,
lb s e c / ft ^
S lu rry v is c o s it y ,
lb s e c /ft^
a
Dim ensionless param eter
(Durand)
CHAPTER I
. INTRODUCTION
The h y d r a u l i c t r a n s p o r t o f wood c h ip s i n p i p e l i n e s o f f e r s one
method f o r conveying low v a lu e f o r e s t p ro d u c ts o ver lo n g d is ta n c e s
which can be c o m p e t it iv e w i t h c o n v e n tio n a l t r u c k and r a i l r o a d t r a n s ­
p o rta tio n .
b ility
The r e s u l t s o f s t u d ie s i n d i c a t i n g th e economic f e a s i ­
o f p i p e l i n e t r a n s p o r t prompted th e p re s e n t i n v e s t i g a t i o n o f
th e hydrodynam ic aspects o f pumping m ix tu re s o f wood c h ip s and w a te r.
HISTORICAL BACKGROUND
For many y e a rs pulpwood and paper i n d u s t r i e s have been faced w i t h
in c r e a s in g demands f o r w o o d - f ib e r p r o d u c ts .
Vast amounts o f pulpwood
and r e s id u e from th e m a nufacture o f f o r e s t p ro d u cts are r e q u ir e d to
s a t i s f y t h i s demand.
F u tu re s u p p lie s may w e ll r e l y on f o r e s t stands
w h ic h , because o f t h e i r s iz e o r q u a l i t y , are n o t s u i t a b l e f o r com­
m e rc ia l grade lumber and on w o o d - f ib e r a v a i l a b l e in th e lo g g in g
s la s h now l e f t as r e s id u e i n th e f o r e s t .
The lo d g e p o le p i n e , which abounds i n Montana i n t h i c k e t s so dense
t h a t tr e e s r i v e r a t t a i n useable s i z e , p re s e n ts an example o f such a
re s o u rc e f o r pulpwood m a t e r i a l .
In th e p a s t , th e f u l l
r e a liz e d .
economic v a lu e o f these re s o u rc e s was n o t
The c o s t o f o b t a i n in g th e wood and p ro c e s s in g i t ,
as com­
pared t o th e v a lu e o f th e f i n i s h e d p r o d u c t , in d ic a t e d a m a r g in a l.
2
if
any, p r o f i t .
One area where c o s ts appear p r o h i b i t i v e i s the
t r a n s p o r t a t i o n o f th e wood from th e f o r e s t o r saw m ill t o th e in d u s ­
tria l
p ro c e s s o r.
*1
S tu d ie s o f th e c o s t o f t r a n s p o r t a t i o n
(I)
(2) have in d ic a t e d
th e p o s s ib le use o f p i p e l i n e s f o r conveying wood p a r t i c l e s .
No
i n d u s t r i a l w ood-chip p i p e l i n e s a re known t o e x i s t , a lth o u g h p i p e l in e s
have been s u c c e s s f u l l y employed t o t r a n s p o r t many s o l i d m a t e r i a ls
such as c o a l , m in e ra l ore's, and sewage.
Three s p e c i f i c i n d u s t r i a l
a p p l i c a t i o n s o f s o l i d s t r a n s p o r t i n p i p e l i n e s bear m e n tio n .
In 1957, th e P i t t s b u r g C o n s o lid a te d Coal Company used a p ip e ­
l i n e t o d e l i v e r 3400 to n s o f coal p e r day from Georgetown, Ohio to
C leve la n d ( 3 ) .
.
A ls o in 1957, th e American G i l s o n i t e Company (23) began o p e r a tio n
o f 72 m ile s o f 6- i n c h d ia m e te r p i p e l i n e t o d e l i v e r 1100 to n s p e r day
o f g i l s o n i t e to Grand J u n c t io n , Colorado.
T h e ,B la ck Mesa p i p e l i n e
( 5 ) , p r e s e n t l y th e lo n g e s t co a l p i p e l i n e
i n th e n a t i o n , t r a n s p o r t s coal 273 m ile s from K ayenta, A riz o n a to
B u llh e a d C i t y , A r iz o n a .
The 1 8 - in . d ia m e te r p i p e l i n e w i l l
d e liv e r
th e e q u iv a l e n t o f 200 r a i l r o a d cars o f coal each day.
These and o t h e r examples i l l u s t r a t e
t h a t th e h y d r a u l i c t r a n s ­
p o r t o f v a r io u s s o l i d s i n p i p e l i n e s i s e c o n o m ic a lly and t e c h n o l o g i c a l l y
^Numbers i n parentheses r e f e r t o numbered r e fe re n c e s i n th e
References C ite d .
3
f e a s i b l e , and t h a t th e a p p l i c a t i o n t o w o od-chip t r a n s p o r t a t i o n
r e q u ir e s a d e t a i l e d i n v e s t i g a t i o n .
WOOD-CHIP PIPELINE RESEARCH AT MONTANA STATE UNIVERSITY
In 1961, th e conce pt o f h y d r a u l i c a l l y conveying wood chips
prompted r e s e a rc h e rs a t Montana S ta te U n i v e r s i t y , in c o o p e r a tio n w i t h
th e In te rm o u n ta in F o re s t and Range Experim ent S t a t io n o f th e U n ited
S ta te s F o r e s t S e rv ic e i n Ogden, U ta h , t o i n i t i a t e
in v e s tig a tio n
an e x te n s iv e
i n t o th e economic and t e c h n o lo g ic a l aspe cts o f the
h y d r a u l i c t r a n s p o r t o f wood c h ip s i n p i p e l i n e s .
D u ring th e course o f
t h i s p r o j e c t , th e economic analyses and e x p e rim e n ta l i n v e s t i g a t i o n s
necessary f o r th e d e sign and o p e r a tio n o f w ood-chip p i p e l i n e s have
been conducted and p re s e n te d .
Economic Analyses
Hoffman ( 6 ) , f o l l o w i n g an e x t e n s iv e re v ie w o f a v a i l a b l e l i t e r a ­
t u r e on two-phase f lo w by Dr. W. A. H u nt, P r o j e c t P r i n c i p a l
In v e s ti­
g a t o r , developed a method f o r d e te r m in in g optimum p ip e d iam e te rs and
v o l u m e t r ic w ood-chip c o n c e n tr a t io n s f o r p i p e l i n e networks and a p p lie d
th e te c h n iq u e t o a h a r v e s t area i n Montana.
H o ffm a n 's r e p o r t showed
t h a t p i p e l i n e networks f o r conveying wood chip s c o u ld be c o m p e t it iv e
w i t h t r u c k t r a n s p o r t a t i o n i n many a p p l i c a t i o n s .
From H o ffm a n's work and an e a r l i e r economic a n a ly s is by Hunt ( I )
which i l l u s t r a t e d
th e economic a t t r a c t i v e n e s s o f th e p i p e l i n e t r a n s p o r t
•4
o f wood c h i p s , i t was concluded t h a t l a b o r a t o r y re s e a rc h on a model
p i p e l i n e was w a rra n te d .
L a b o r a to ry I n v e s t i g a t i o n s
P r i o r t o c o n s t r u c t i o n o f th e model p i p e l i n e , Schmidt (3) con­
ducted e x p e rim e n ta l i n v e s t i g a t i o n s on th e e f f e c t s o f p re s s u re and
tim e on m o is tu r e c o n t e n t , volume change, and s p e c i f i c g r a v i t y o f
lo d g e p o le p in e wood c h ip s submerged i n w a te r .
The i n v e s t i g a t i o n
showed t h a t wood c h ip s i n w a t e r , when s u b je c te d t o p re ssu re s such as
those encountered d u r in g h y d r a u l i c t r a n s p o r t , s a t u r a t e e x p o n e n t ia lly
as a f u n c t i o n o f t i m e , and t h a t th e s p e c i f i c g r a v i t y o f th e s a tu r a te d
wood c h ip s t e s t e d was a p p ro x im a te ly 1 . 1 .
A model p i p e l i n e was c o n s tr u c te d i n the E n g in e e rin g L a b o r a to r ie s
o f Montana S ta te U n i v e r s i t y .
The e x p e rim e n ta l f a c i l i t y was designed
t o p e r m it th e i n v e s t i g a t i o n o f th e f o l l o w i n g problem s:
1)
m in o r p re s s u re lo sse s due t o v a lv e s and f i t t i n g s
2)
perform ance o f c e n t r i f u g a l pumps f o r h a n d lin g h ig h woodc h ip c o n c e n t r a t i o n s , and
3)
fric tio n a l
p r e s s u r e - lo s s c o r r e l a t i o n s f o r lo n g p i p e l i n e s .
C h a rle y (7) i n v e s t i g a t e d th e e f f e c t s o f h ig h c o n c e n tr a t io n s o f
wood c h ip s on th e p re s s u re drop caused by enlargem ents i n th e pipe
cro ss s e c t i o n , and found t h a t p r e s s u re l o s s e s , f o r a p a r t i c u l a r
v e l o c i t y , decreased as th e c o n c e n t r a t io n o f s o l i d s was in c re a s e d .
'
5
Johnson ( 8 ) conducted an e x t e n s iv e s e rie s ' o f t e s t s t o determ ine
th e e f f e c t s o f c h ip -sh a p e d p a r t i c l e s on th e h e a d -lo ss and o p e r a tin g
c h a r a c t e r i s t i c s o f f i v e types o f v a lv e s
and b a l l ) .
( w e i r , p in c h , p l u g , v e e - b a l l ,
These t e s t s in d ic a t e d t h a t h e a d -lo s s c o e f f i c i e n t s f o r
each v a lv e in c re a s e d as th e c o n c e n tr a t io n o f s o l i d s was in c re a s e d .
Page (9) conducted perform ance t e s t s w i t h t h r e e d i f f e r e n t
c e n t r i f u g a l pumps t h a t were s u p p lie d by the m a n u f a c t u r e r s .
These
t e s t s in d i c a t e d t h a t pump e f f i c i e n c y decreased as s o l i d s c o n c e n tr a t io n
was in c re a s e d .
^An e x p e rim e n ta l program t o dete rm in e the e f f e c t s o f v a r io u s
v o l u m e t r ic c o n c e n tr a t io n s o f s o l i d p a r t i c l e s in w a te r on f r i c t i o n a l
p re s s u re lo s s e s i n smooth p ip e s conducted by Faddick (TO). . P l a s t i c
c h i p s , 1 /2 in c h x 3 /8 in c h x 1/10 i n c h , w i t h s p e c i f i c g r a v i t i e s o f
.92 and I .045 were t r a n s p o r t e d w i t h w a te r th ro u g h 3 - in c h and 4 - in c h
d ia m e te r pipes t o i n v e s t i g a t e th e param eters f o r th e development o f
a h e a d -lo s s c o r r e l a t i o n .
A d im en sion al a n a ly s is by Faddick (10) o f a two-phase f lo w
system produced f i v e p a ra m e te rs :
m ix t u r e f r i c t i o n f a c t o r , Reynolds
number based on p ip e d ia m e te r and w a te r v i s c o s i t y , s p e c i f i c g r a v i t y ,
and a param eter r e l a t i n g p a r t i c l e s iz e and shape t o th e p ip e d ia m e te r.
H ead-loss data showed t h a t th e m ix t u r e f r i c t i o n
f a c t o r s were
g r e a t e r than those f o r c l e a r w a te r flo w s and t h a t th e d i f f e r e n c e
between them in c re a s e d .
PRESENT INVESTIGATION
The purpose o f th e p re s e n t i n v e s t i g a t i o n , i n i t i a t e d
in 1969, was
t o o b t a i n and c o r r e l a t e e xp e rim e n ta l h e a d -lo s s data f o r m ixture s, o f
wood c h ip s and w a te r o v e r a range o f m ix t u r e v e l o c i t i e s , p ip e diam­
e t e r s , c h ip s i z e s , and c h ip c o n c e n t r a t io n s .
Real wood c h i p s , p r i m a r i l y
lo d g e p o le p in e , were used.
The w ood-chip h e a d -lo s s data o f o t h e r i n v e s t i g a t i o n s , c o l le c t e d
by Faddick ( 1 0 ) , t o g e t h e r w i t h th e h e a d -lo s s data o f th e p re s e n t s tu d y
were employed t o a id i n th e e x p la n a tio n o f q u a l i t a t i v e r e s u l t s , and
t o f o r m u la t e a q u a n t i t a t i v e e m p ir ic a l c o r r e l a t i o n e q u a tio n .
The l a b o r a t o r y p i p e l i n e system employed by Faddick (10) f o r
p l a s t i c c h ip s was m o d if ie d t o accommodate wood c h ip s .
T h is system
and th e e x p e rim e n ta l procedures used t o o b t a in th e h e a d -lo s s data
are p re se n te d i n APPENDIX A.
k
CHAPTER I I
REVIEW OF HYDRAULIC TRANSPORT OF SOLIDS
Research has been conducted i n th e f i e l d o f t r a n s p o r t i n g s o l id s
by p i p e l i n e s s in c e about 1850 ( 4 ) , however hydrodynamic th e o r y s t i l l
la g s p r a c t i c e .
Head-loss data from v a r io u s i n v e s t i g a t i o n s , w h ile
showing s y s t e m a tic q u a l i t a t i v e t r e n d s , have n o t been q u a n t i t a t i v e l y
c o r r e l a t e d i n t o a gen eral e x p r e s s io n .
Thus, design e n g in e e rs have
been f o r c e d to conduct model p i p e l i n e s t u d ie s f o r n e a r ly e very d i f f e r e n t
a p p lic a tio n .
P resented i n t h i s s e c t io n i s a d is c u s s io n o f p r e v io u s i n v e s t i g a ­
t i o n s w hich p e r t a i n t o th e h y d r a u l i c t r a n s p o r t o f wood c h i p s .
In c lu d e d
a re d e s c r i p t i o n s o f two-phase f lo w re g im e s , t h e i r hydrodynamic s i g n i f i ­
cance and some methods f o r p r e d i c t i n g th e occurrence o f a p a r t i c u l a r
f lo w regim e.
Two p o p u la r methods f o r c o r r e l a t i n g h e a d -lo s s data are
p re s e n te d , and t h e i r a p p l i c a t i o n t o wood c h ip s d is c u s s e d .
Previous
re s e a rc h on th e h y d r a u l i c t r a n s p o r t o f wood c h ip s i s p re se n te d w i t h
p r im a r y emphasis placed on c o r r e l a t i n g h e a d -lo ss w i t h v e l o c i t y ,
s p e c i f i c g r a v i t y , p a r t i c l e s i z e , and p a r t i c l e c o n c e n t r a t io n .
FLOW REGIMES
S a tu r a te d wood c h i p s , l i k e many o t h e r s o l i d p a r t i c l e s have a
s p e c i f i c g r a v i t y g r e a t e r than w a te r .
The h y d r a u lic t r a n s p o r t o f such
s o l i d s - i n - w a t e r m ix tu r e s can be c l a s s i f i e d i n t o two f lo w re g im e s.
8
a) homogeneous, o r b ) heterogeneous.
The c l a s s i f i c a t i o n depends on
th e mode o f t r a n s p o r t o f th e s o l i d p a r t i c l e s .
Homogeneous m ix tu r e s occu r when th e d i s t r i b u t i o n o f th e sus­
pended s o l i d p a r t i c l e s i s n e a r ly u n ifo rm o ver th e c r o s s - s e c t i o n o f
th e p ip e .
I f th e p a r t i c l e s
by Brownian movement.
are s m a ll , th e y are held i n suspension
However, f o r l a r g e p a r t i c l e s , such as wood
c h i p s , w i t h a s p e c i f i c g r a v i t y g r e a t e r than t h a t o f th e conveying
medium, a f o r c e must be c o n t i n u a l l y e x e r te d on th e p a r t i c l e s t o o v e r­
come th e f o r c e o f g r a v i t y .
In la m in a r f l o w such fo r c e s do n o t e x i s t ,
and th e p a r t i c l e s s e t t l e t o th e bottom o f th e p ip e .
T u r b u le n t f lo w
i n p ip e s , however, does p r o v id e a mechanism t o g en erate f o r c e s capable
o f m a in t a in in g la r g e p a r t i c l e s i n suspe nsio n.
The random v o r t e x m o tio n o f t u r b u l e n t f lo w i n p ip e s im p a rts
s u f f i c i e n t i n e r t i a l f o r c e s t o th e s o l i d p a r t i c l e s t o h o ld them in
suspension i n homogeneous f lo w s .
I f th e p a r t i c l e s are a p p ro x im a te ly
th e same s iz e as th e l a r g e r t u r b u l e n t e d d ie s , the p a r t i c l e s w i l l
f o l l o w th e la r g e s c a le m otion o f th e t u r b u l e n t f l u i d .
As long as
s u f f i c i e n t tu r b u le n c e i s g e n e ra te d , th e p a r t i c l e s w i l l
be tr a n s p o r te d
as a homogeneous m ix t u r e .
.
Babcock (19) has p o in te d o u t t h a t low c o n c e n tr a t io n s o f p a r t i c l e s
w ill
be e n t r a in e d in th e f lo w and c a r r i e d in suspension by th e t u r b u ­
l e n t v o r t e x m otion causing l i t t l e
o r no in c re a s e i n th e f r i c t i o n a l
r e s is t a n c e o ver t h a t produced by th e c l e a r f l u i d
its e lf.
However, a t
9
h ig h e r c o n c e n t r a t io n s , p a r t i c l e - p a r t i c l e and p a r t i c l e - p i p e w a ll
i n t e r a c t i o n s i n f l u e n c e th e f lo w c h a r a c t e r i s t i c s .
The i n e r t i a and
r i g i d i t y o f s o l i d p a r t i c l e s a l t e r th e s t r u c t u r e o f th e t u r b u le n c e and
supress th e g e n e r a tio n o f t u r b u le n c e .
As th e c o n c e n t r a t io n in c re a s e s
a n d /o r m ix t u r e v e l o c i t y de cre a se s, th e s c a le and i n t e n s i t y o f the
tu r b u le n c e decrease t o th e p o i n t t h a t th e p a r t i c l e s cann ot be main­
t a in e d i n s u s p e n s io n , g r a v i t a t i o n a l f o r c e s p r e v a i l , and th e p a r t i c l e s
begin t o s e t t l e t o th e p ip e i n v e r t .
T h is r e s u l t s i n n o n -u n ifo rm
d i s t r i b u t i o n s o f th e p a r t i c l e c o n c e n t r a t io n s , and more and more
p a rtic le s s lid e or r o l l
r e s is t a n c e .
along th e i n v e r t in c r e a s in g th e f r i c t i o n a l
T h is n o n - u n if o r m i t y i n c o n c e n tr a t io n d i s t r i b u t i o n
c h a r a c t e r iz e s a heterogeneous f lo w regim e.
During heterogeneous f l o w , th e s o l i d s are t r a n s p o r t e d by two
d i s t i n c t p rocesse s.
The f i r s t i s due t o a non-uni form suspension o f
th e p a r t i c l e s i n th e f l o w , and th e second i s du.e t o th e s l i d i n g o r
r o l l i n g o f th e p a r t i c l e s along th e p ip e i n v e r t .
A c o m b in a tio n o f these t r a n s p o r t p ro c e s s e s , c a l l e d s a l t a t i o n
heterogeneous f l o w , i s c h a r a c t e r iz e d by suspension and s l i d i n g - b e d
modes.
B ed-load f l o w occurs when a l l
th e p a r t i c l e s have s e t t l e d - o u t ,
and th e t r a n s p o r t mode i s one o f pure s l i d i n g along th e p ip e i n v e r t .
During s l i d i n g bed t r a n s p o r t t h e r e i s a c o n tin u o u s c o n t a c t between
th e p ip e w a ll and th e s o l i d p a r t i c l e s , and thus a g r e a t e r amount o f
I
1 10
energy i s r e q u ir e d t o move th e p a r t i c l e s than w i t h suspension f lo w s .
Carstens (11) and Zandi and Govatos (12) have s t a t e d t h a t i f a
homogeneous m ix t u r e e x h i b i t s ' Newtonian c h a r a c t e r i s t i c s , th e f lo w can
be analyzed as a s in g le - p h a s e " p s e u d o - f l u i d " w i t h d e n s it y and v i s ­
c o s i t y dependent on c o n c e n tr a t io n as w e ll as te m p e ra tu re .
S a lta tio n
and bedload flo w s are co n s id e re d by Carstens and Zandi and Govatos t o
be two-phase f l u i d s
in which th e s o l i d and l i q u i d phases should be
analyzed s e p a r a t e l y .
In c o n t r a s t t o th e above d e s c r i p t i o n o f homogeneous and h e t e r o ­
geneous f lo w re g im e s , Faddick (10) d e s c rib e s homogeneous f lo w s as those
comprised o f v e r y sm all p a r t i c l e s h e ld i n suspension s o l e l y by
Brownian movement.
suspended by f l u i d
He d e s c rib e s th e t r a n s p o r t o f l a r g e r p a r t i c l e s ,
t u r b u le n c e , as heterogeneous susp e n sio n s.
Uniform
c o n c e n tr a t io n p r o f i l e s c h a r a c t e r iz e h i s d e s c r i p t i o n o f both homogeneous
and heterogeneous s u s p e n s io n s ; th e o n ly app a re n t d i f f e r e n c e being th e
s iz e o f p a r t i c l e s a p p li c a b le t o each f l o w regim e.
PREDICTION OF FLOW REGIME
Methods f o r p r e d i c t i n g the p a r t i c u l a r f lo w regime f o r a given
■'S
c o m b in a tio n o f f l u i d p r o p e r t ie s and p a r t i c l e p r o p e r t ie s f o r two-phase
flo w s have n o t been s a t i s f a c t o r i l y e s t a b l is h e d .
may be s i g n i f i c a n t i n th e o p e r a tio n a l
tra n s p o rtin g p ip e lin e .
Such d e te r m in a tio n s
f e a s ib il it y o f a s o lid s -
For example, th e minimum h e a d -lo sse s f o r
' 11
g iv e n c o n c e n tr a t io n s o f p a r t i c l e s a p p a r e n t ly may o c c u r ( 10) in the
s l i d i n g - b e d regim e.
However, p lu g g in g c o n d it io n s are a ls o imminent
i n t h i s regim e.
'
.
G r o v ie r and C harles (13) atte m pted t o s i m p l i f y th e f lo w regimes
by c l a s s i f y i n g m ix tu re s as s e t t l i n g o r n o n - s e t t l i n g .
The s e t t l i n g
m i x t u r e , as d e f in e d , i s e q u iv a l e n t t o th e heterogeneous s a l t a t i o n and
b e d -lo a d regimes d e s c rib e d ' p r e v io u s ly .
The n o n - s e t t l i n g m ix t u r e was
d e fin e d as e q u iv a l e n t t o th e homogeneous regim e.
They employed th e s e t t l i n g v e l o c i t y , o r t h a t v e l o c i t y which a
p a r t ic le a tta in s in f r e e - f a l l
th ro u g h an i n f i n i t e medium o f the
t r a n s p o r t i n g f l u i d , t o d i s t i n g u i s h between th e two c l a s s i f i c a t i o n s .
G r o v ie r and C harles r e a l i z e d t h a t th e s e t t l i n g v e l o c i t y i n c o r ­
p o ra te d f l u i d
p r o p e r t ie s as w e ll as th e e f f e c t s o f p a r t i c l e s i z e ,
shape, and s p e c i f i c g r a v i t y and was chosen as the c r i t e r i a f o r
d i f f e r e n t i a t i n g th e f l o w regim es.
Zandi and Govatos (12) a ls o used th e s e t t l i n g v e l o c i t y t o d e t e r ­
mine a d im e n s io n le s s param eter which c l a s s i f i e d two-phase flo w s as
e i t h e r heterogeneous s a l t a t i o n o r b e d -lo a d .
This param eter was
d e fin e d as ■v
,
I
. yI 2 i cd
" Cv D g (S -I)
where Vffl = m ix t u r e v e l o c i t y , f t / s e c
( 2 . 1)
12
Cd = d im e n s io n le s s p a r t i c l e drag c o e f f i c i e n t ,
Cd = 4 /3 S d C S d l
vS
S = s p e c i f i c g r a v i t y o f s o l i d p a r t i c l e s , d im e n s io n le s s
g = g r a v ita tio n a l a c c e le ra tio n , f t / s e c
D = i n t e r n a l p ip e d ia m e te r , f t
Vg= s e t t l i n g v e l o c i t y , f t / s e c
d = e q u iv a l e n t s p h e r ic a l p a r t i c l e , d ia m e te r based oh
volume, f t
From a l a r g e d ata bank com piled by Zandi and G ovatos, th e c r i t i c a l
v a lu e o f N-J appeared t o be a p p ro x im a te ly 40.
va lu e s le s s than 40
d e fin e d a c o n d i t i o n o f b e d -lo a d f l o w .
As m entioned p r e v i o u s l y , knowledge o f th e f lo w regime t o be
encountered f o r a g iv e n s e t o f f lo w c o n d it io n s co u ld be e x tre m e ly
v a lu a b le t o th e design e n g in e e r.
But e q u a ll y im p o r t a n t , i f
the
d i f f e r e n t regimes c o u ld be d e s c rib e d as la m in a r , t u r b u l e n t , o r '
secondary f lo w t y p e , a p l a u s i b l e approach t o hea d -lo ss c o r r e l a t i o n s
m ig h t be p o s s i b l e .
HEAD-LOSS CORRELATION MODELS
Since th e mechanisms o f h y d r a u lic t r a n s p o r t o f s o l i d s in p ip e ­
l i n e s have n o t been f u l l y e s t a b l i s h e d , a general c o r r e l a t i o n method
13
f o r p r e d i c t i n g h e a d -lo s s does n o t e x i s t .
Several e m p ir i c a l methods
have been p re s e n te d ; th e most p o p u la r are those o f Durand (10) and
Dodge and M etzner ( 1 4 ) .
Al I o t h e r methods seem t o have t h e i r r o o ts
i n e i t h e r one o r th e o t h e r o f th e se .
Durand's C o r r e l a t i o n Model
From e x t e n s iv e i n v e s t i g a t i o n s o f t r a n s p o r t i n g sands and g r a v e ls
w i t h w a te r i n p i p e s , Durand (10) proposed th e e m p ir ic a l c o r r e l a t i o n
e q u a tio n
$ = KYm ----------------------------------------------------------- ( 2 .2 )
where
$ = ( i m- i ) / C
Y = Vm^
‘i,
Cj
2
Cj= g d/V s (S-T)
d im e n s io n le s s
/ g D ( S - l ) , d im e n s io n le s s
2
, a d im e n s io n le s s p a r t i c l e drag c o e f f i c i e n t
i = m ix t u r e h y d r a u l i c g r a d i e n t , f t / f t
i = h y d r a u l i c g r a d i e n t f o r c l e a r w a te r f l o w , f t / f t
Cy= v o l u m e t r ic c o n c e n t r a t io n o f s o l i d p a r t i c l e s ,'
d im e n s io n le s s
dn= e q u iv a l e n t s p h e r ic a l p a r t i c l e d ia m e te r , based on
volum e, f t
14
Vm= average v e l o c i t y o f m i x t u r e , f t / s e c
Vs = p a r t i c l e s e t t l i n g v e l o c i t y , f t / s e c
D = in te rn a l
p ip e d ia m e te r , f t
g = g r a v ita tio n a l a c c e le ra tio n , f t/ s e c
2
K and m = e m p ir ic a l c o n s ta n ts
K and m were dete rm in e d e m p i r i c a l l y by G i l b e r t (10) f o r sands and
g r a v e ls
( s p e c i f i c g r a v i t y 2 .6 5 ) t o be 180 and - 1 . 5 r e s p e c t i v e l y .
Durand and CondoTios (15) m o d if ie d Equation 2 .2 t o accommodate
s o l i d s o f d i f f e r e n t s p e c i f i c g r a v i t y as f o l l o w s :
1 .5
$ = 124
g D ( S - l)
v, 2
(2 .3 )
/g d ( S - l)
A p p l i c a t i o n o f Durand's E q uation t o Wood-chip Research
In 1957, th e Pulp and Paper I n s t i t u t e o f Canada, (PPRIC) i n i t i a t e d
f e a s i b i l i t y s t u d ie s co n c e rn in g th e t r a n s p o r t o f wood c h ip s w i t h w a te r
in p ip e lin e s .
McColl
(16) i n v e s t i g a t e d th e h y d r a u lic t r a n s p o r t , o f
w ood-chips i n a 2 - in c h d ia m e te r copper p ip e .
He concluded t h a t
wood c h ip s were amenable t o p i p e l i n e t r a n s p o r t b u t he d id n o t a tte m p t
an a n a l y t i c a l
c o r r e l a t i o n between h e a d -lo s s and f lo w r a t e .
E l l i o t and deMontmorency (4 ) a ls o o f PPRIC i n v e s t i g a t e d th e
h y d r a u l i c t r a n s p o r t o f wood chips p r i m a r i l y t o d e te rm in e th e e f f e c t s
15
o f pumping on th e paper-m aking q u a l i t y o f t h e wood c h ip s .
They have
prese n te d h e a d -lo s s d a ta f o r m ix tu re s o f wood c h ip s and w a te r pumped
th ro u g h an 8 - i n c h d ia m e te r aluminum p ip e .
They d id n o t express a
c o r r e l a t i o n e q u a tio n f o r t h e i r h e a d -lo s s d ata a n a l y t i c a l l y .
Fad dick (10) r e p o r t s t h a t S t e p a n o f f , employing th e Durand m odel,
'I
as p r e v i o u s l y d e s c r ib e d (Eq. 2 . 2 ) , p re se n te d th e e q u a tio n s
$ = 4gD/Vm2 ...................................... ............. .......... ( 2 .4 )
and
$ = 1.25
4gD/Vm2
1*0 3 ........................... - ( 2 . 5 )
as th e e m p ir i c a l e q u a tio n s o f b e s t - f i t f o r th e data o f McColl and o f
E l l i o t and deMontmorency, r e s p e c t i v e l y .
Fad dick ( 1 7 ) , i n h is work a t Queen's U n i v e r s i t y , p resen ted headlo s s d a ta f o r wood c h ip s t r a n s p o r t e d w i t h w a te r in a 4 - in c h dia m e te r
aluminum p ip e by th e e q u a tio n
$ = 2.51
4gD/V m2
1 , 4 2 -------------------------- ( 2 . 6 )
T h is e q u a tio n re p re s e n te d h is d a ta f o r c o n c e n tr a t io n v a r y in g from
5 p e r c e n t t o 17 p e r c e n t by volume.
Soucy, o f Laval U n i v e r s i t y , has p ro v id e d th e p r o j e c t a t Montana
S t a te U n i v e r s i t y w i t h h e a d -lo s s d a ta he c o l l e c t e d fro m th e f lo w o f
m ix tu r e s o f wood c h ip s and w a te r i n a 6- in c h d ia m e te r p ip e f o r concen
t r a t i o n s v a r y in g from 5 p e r c e n t t o 20 p e r c e n t by volume.
16
F a d d ic k ' ( 1 0 ) , i n h is work a t Montana S ta te U n i v e r s i t y , c o l l e c t e d
and compared th e w ood-chip d ata o f M c C o ll, F a d d ic k , Soucy and E l l i o t
and deMontmorency i n 2 - , 4 - , 6- , and 8- i n c h d ia m e te r p ip e s , re sp e c­
t i v e l y , em ploying a s i m p l i f i e d v e r s io n o f th e Durand e q u a tio n (Eq. 2 . 2 )
$ = K f ------------------------------------ -------- ------------( 2 . 7 )
where as b e fo re
$ = Um-I )/C v-
i - .........................................- — (2 .7 a )
and
'i' = 4gD/V m2 ................ .............................. - .............(2 .7 b )
w i t h K and m = e m p ir i c a l c o n s ta n ts .
A n a ly s is o f Durand C o r r e l a t i o n Model
F a d d ic k 's comparison o f th e h e a d -lo s s data f o r m ix tu r e s o f wood
c h ip s and w a te r o f M c C o ll, F a d d ic k , Soucy and E l l i o t and deMontmorency,
showed t h a t th e c o e f f i c i e n t K v a r ie d 200 p e rc e n t and th e exponent m
v a r ie d 40 p e r c e n t.
Faddick (10) has s t a t e d t h a t , s in c e th e wood-chips
,used i n th e f o u r d i f f e r e n t i n v e s t i g a t i o n s were b a s i c a l l y th e same
s i z e , th e Durand model a p p a r e n t ly n e g le c t s th e e f f e c t s o f c h ip s iz e
as compared t o p ip e d ia m e te r.
A lth o u g h th e i n d i v i d u a l c o r r e l a t i o n s presented by Faddick f o r
th e d a ta o f each o f th e i n v e s t i g a t o r s may be v a l i d f o r th e s p e c i f i c
c o n d it io n s under which th e p a r t i c u l a r d ata were o b t a in e d , th e
r
/
■
.
c o r r e l a t i o n ' e q u a tio n s cannot be employed t o c a l c u l a t e h ea d-losses f o r
m ix t u r e s o f wood c h ip s and w a te r i n p ip e s o f d i f f e r e n t d ia m e te rs .
Faddick (18) has a ls o s t a te d t h a t E q uation 2 .7 does n o t r e f l e c t
th e r o l e o f th e m ix t u r e Reynolds number (Re
= V
Dp/p ) which he
s t a t e s i s th e r a t i o o f i n e r t i a l t o v is c o u s fo r c e s f o r m ix t u r e f lo w s .
However, th e t r a n s p o r t f l u i d v i s c o s i t y , Pq , which d e f in e s Rem, cannot
be i n t e r p r e t e d as a measure o f th e v is c o u s fo r c e s p r e s e n t in two-phase
f l o w s , because i t
s o lid s .
does n o t r e f l e c t th e b e h a v io r o f a m ix t u r e c o n t a in in g
I t a ls o n e g le c t s th e e f f e c t s o f p a r t i c l e - p i p e w a ll c o n ta c t
on th e . v e l o c i t y g r a d i e n t a t th e boundary.
The r a t i o o f th e w a ll shear
s t r e s s t o th e v e l o c i t y g r a d i e n t a t th e boundary i s a f u n c t i o n o f the
v i s c o s i t y o f th e two-phase f l u i d .
Babcock (19) e x t e n s i v e l y in v e s t i g a t e d th e use o f Durand's c o r ­
r e l a t i o n model and showed t h a t th e e x t r a p o l a t i o n o f h e a d -lo s s d ata t o
p ip e s o f d ia m e te rs d i f f e r e n t from those employed i n o b t a i n in g the
2
data cannot be accounted f o r by th e param eter Vm
va lu e s o f Vffl
2
/ gD, and equal 2
/ gD do n o t produce equal va lu e s o f ¥ i n d i f f e r e n t s iz e
p ip e s .
For th e Durand E q u a tio n 2 .2 t o c o r r e l a t e a v a i l a b l e hea d -lo ss data
s u c c e s s f u l l y , th e param eter ¥ must be independent o f th e v o lu m e tr ic
c o n c e n t r a t io n , Cy .
However, Babcock has shown t h a t ¥ appears t o be
in dependent o f Cy under some c ir c u m s ta n c e s , w h ile under o th e rs i t
c l e a r l y n o t in depe nden t o f C ..
is
T h is f a c t a lo n e , as Babcock p o in t s o u t .
18.
can account f o r much o f th e s c a t t e r which i s noted i n d a ta c o r r e la t e d
by th e Durand model.
I f th e param eters t h a t com prise th e Durand Equa­
t i o n 2.2 are t o c o r r e l a t e th e h e a d -lo s s d a ta s u c c e s s f u l l y f o r two-phase
f l o w s , n o n -d im e n sio n a l g ro u p in g s d i f f e r e n t from those proposed, and
perhaps a c o m p le te ly new method o f app ro ach, must be examined.
M etzner and Dodge C o r r e l a t i o n Method
M etzner and Reed (2.0) have developed a s e m i - t h e o r e t i c a l c o r r e l a ­
t i o n method f o r a n a ly z in g h e a d -lo s s d a ta o f la m in a r non-Newtonian
f l u i d s w h ich has been s u c c e s s f u l l y a p p lie d t o s e v e ra l s o l i d - l i q u i d
m ix t u r e f lo w s .
M etzn er and Dodge (14) have extended t h i s method to
in c lu d e t u r b u l e n t non-Newtonian f l u i d s
as w e l l .
Based on e a r l i e r developments by R a bin ow itsch (21) and Mooney ( 2 1 ) ,
M etzner and Reed proposed t h a t the w a ll shea r s t r e s s f o r non-N ew tonian,
as w e ll as N ew tonian, p ip e f lo w s be g iv e n as
Tw = K( 8V /D )n — ............ — ...........- ................. - ( 2 . 8 )
where
Tw = f X
and
...............................................- ............... ( 2 . 8a)
n = f l o w b e h a v io r in d e x
K = flu id
c o n s is te n c y in d e x .
R a bin ow itsch and Mooney d e r iv e d E q uation 2 .8 w i t h b u t one s t i p u l a t i o n :
th e w a ll shear s t r e s s must be a unique f u n c t i o n o f th e r a t e o f s t r a i n
a lo n e .
For Newtonian la m in a r f l o w s , K = y Q, th e a b s o lu te v i s c o s i t y o f
19
th e f l u i d
pha se, and n - I .
These values g iv e the f a m i l i a r Newtonian
r e l a t i o n s h i p between shear s t r e s s and r a t e o f s t r a i n e v a lu a te d a t th e
w a ll:
v
( 2 . 9)
' a r1
r = R
Employing th e d e f i n i t i o n o f th e Fanning f r i c t i o n
fa c to r
f = z-rypv
( 2 . 10 )
and s u b s t i t u t i n g E q uation 2 .8 i n t o th e d e f i n i t i o n o f th e Fanning
fric tio n
fa c to r fo r
t
, th e e x p re s s io n f o r f becomes
« _ iefs"-1) K
(2. 11)
V2- nDnp
L e t t i n g f = 16 /R e , as f o r Newtonian f l u i d s
i n la m in a r f l o w ,
E q uation 2.11 d e f in e s a g e n e r a liz e d Reynolds number
,
_ DnV2- nP
"9
(2.
12 )
Sn- 1K
E q uation 2.11 shows t h a t a l l f l u i d s
i n la m in a r f l o w , s u b j e c t t o the
s t i p u l a t i o n g iv e n b e f o r e , must f o l l o w th e usual f versus Re r e l a t i o n ­
s h ip
f
16
(2 . 13 )
%
as long as th e g e n e r a liz e d Reynolds number i s used.
K and n are d e te rm in e d from v is c o m e te r t e s t s .
On a l o g a r i t h m i c
20
graph o f r w versus 8V/D, n i s th e s lo p e , and K can be a f u n c t io n o f
tw,
8V/D, o r c o n s t a n t .
I f th e p l o t o f Ty versus 8V/D i s n o t a
s t r a i g h t l i n e o v e r a wide range o f 8 V/D v a lu e s , M etzner and Reed
p o i n t o u t t h a t care must be e x e r c is e d i n u sin g th e v is c o m e te r data
f o r d e s ig n .
K and n sh o u ld be v a l i d f o r th e 8V/D v a lu e s encountered
i n d e s ig n .
For many ty p e s o f s o l i d - l i q u i d m ix t u r e f lo w s , th e parameters
K and n can be ta ke n as c o n s ta n ts f o r a wide range o f 8V/D values as
shown by S k e lla n d
(2 2 ).
Such m ix tu re s in c lu d e many p o ly m e rs , c l a y -
w a te r s u s p e n s io n s , and d i l u t e c o n c e n tr a t io n s o f paper p u lp i n w a te r.
Dodge and M etzner (14) have extended t h i s la m in a r f lo w a n a ly s is
t o t u r b u l e n t f lo w s .
They concluded t h a t th e f lo w param eters n and K
shou ld be th e same f o r t u r b u l e n t f lo w s as f o r la m in a r f l o w s , j u s t
as th e v i s c o s i t y o f a Newtonian f l u i d
i s d e fin e d under la m in a r con­
d i t i o n s , b u t used i n th e t u r b u l e n t r e g io n as w e l l .
An e m p ir i c a l e q u a tio n r e l a t i n g Fanning f r i c t i o n
g e n e r a liz e d Reynolds number was developed.
f a c t o r t o the
The d e r i v a t i o n o f t h i s
e q u a tio n was modeled a f t e r P r a n d t V s u n iv e r s a l law o f f r i c t i o n f o r
t u r b u l e n t p ip e f lo w
— = 4 Iog(RewZF) - . 4
ZF
----------------------------------( 2 .1 4 )
and was based on an a x is y m m e tric v e l o c i t y p r o f i l e .
For non-N ew tonian f l u i d s , th e c o n v e n tio n a l Reynolds number, Rew
21
i n E q ua tio n 2 .14 wais r e p la c e d . by th e g e n e r a liz e d Reynolds number to
produce a non-Newtonian e q u iv a l e n t t o Equation 2 .14 as:
( 2 .1 5 )
An and Cfi were c o n s id e re d f u n c t io n s o f th e b e h a v io r in d e x n and were
determ ined e x p e r i m e n t a lly from data o b ta in e d w i t h aqueous C a rb o p o l.
The r e s u l t i n g r e l a t i o n s h i p between f r i c t i o n f a c t o r and g e n e r a liz e d
Reynolds number i s expressed i n terms o f th e b e h a v io r in d e x as
E q uation 2 .16 reduces t o E q uation 2.13 f o r Newtonian f l u i d s where
n = I , and k = u .
Dodge and M etzner have a ls o p ro v id e d an approxim ate e m p ir ic a l
e q u a tio n r e l a t i n g f r i c t i o n
f a c t o r s f o r t u r b u l e n t non-Newtonian flo w s
t o th e g e n e r a liz e d Reynolds number w i t h th e f o l l o w i n g e q u a tio n :
f = ----- 9—
(Reg) 6
T his e q u a tio n modeled a f t e r B l a s i u s 1 f r i c t i o n
(2 .1 7 )
f a c t o r e q u a tio n f o r
t u r b u l e n t f lo w o f Newtonian f l u i d s i n sm oo th -w a lle d p ip e s , i s u s e fu l
because i t
is e x p l i c i t in f .
The terms a and 3 were determ ined as
f u n c t i o n o f th e f lo w in d e x param eter n by Dodge and M etzner (14) and
p re se n te d by S k e lla n d ( 2 2 ) .
22
E q ua tio n 2.17 i s a p p ro x im a te ly v a l i d between g e n e r a liz e d Reynolds
numbers o f 5000 and 100,000.
For th e t u r b u l e n t f lo w o f Newtonian
f l u i d s , w i t h n = I and K = Jjq , a = .0791 and g = .25.
S u b s t i t u t i o n o f the se values i n t o E q uation 2.17 r e s u l t s in
t h e B la s iu s e q u a tio n
f =
.0791
( 2. 18)
A n a ly s is o f Metzner-Dodqe C o r r e l a t i o n Model
The s e m i - t h e o r e t i c a l method proposed by Dodge and M etzner has
some sh ortcom ings when a p p lie d t o m ix tu r e s w i t h s o l i d s o f s p e c i f i c
g r a v i t y g r e a t e r o r le s s than t h a t o f th e conveying f l u i d .
The assum ption t h a t th e param eters n and K have th e same
num erica l v a lu e f o r t u r b u l e n t and la m in a r flo w s seems unfounded.
However, M etzner and Dodge have shown t h a t f o r a v a r i e t y o f s o l i d l i q u i d m ix tu r e s i n v e s t i g a t e d , th e a n a ly s is appears v a l i d and th e
c o r r e l a t i o n between th e h e a d -lo s s and th e f lo w b e h a v io r and f l u i d
c o n s is te n c y in d ic e s g iv e s re p e a ta b le r e s u l t s .
The f l u i d - s o l i d s
m ix tu r e s used seem t o be c h a r a c t e r iz e d as homogeneous ( o r n o n - s e t t l i n g )
suspensions o f f i n e l y - s i z e d p a r t i c l e s .
The apparent v i s c o s i t i e s o f
these suspensions are r e a d i l y o b ta in e d by c o n v e n tio n a l v is c o m e t r ic
t e c h n iq u e s .
A ls o , E q ua tio n 2 .8 was developed assuming an a x is y m m e tric
v e l o c i t y p r o f i l e , which o b v io u s ly does n o t e x i s t f o r s e t t l i n g m ix t u r e s .
23
A tte m p ts t o use th e Metzner-Dodge c o r r e l a t i o n by t h i s w r i t e r
f o r w o od-chip and w a te r m i x t u r e s , in d i c a t e d t h a t K and n both were
f u n c t io n s o f c o n c e n tr a t io n and v e l o c i t y .
E v a lu a tio n o f n and K
f o r w o o d -ch ip and w a te r m ix t u r e flo w s was attem pted from .Equation
2 . 1 6 , s in c e la m in a r f l o w c o n d it io n s c o u ld n o t be a c h ie v e d .
The
method r e q u i r e d an i t e r a t i v e r e g r e s s io n a n a ly s is f o r n and K w i t h a
le a s t- s q u a r e s b e s t - f i t o f e x p e rim e n ta l h e a d -lo s s data used as the
convergence c r i t e r i a .
The a n a ly s is proved h i g h l y u n s t a b l e , and the
method was abandoned in f a v o r o f o t h e r c o r r e l a t i o n m odels.
C o r r e l a t i o n A tte m p ts Using a Pseudo V i s c o s i t y
The b a s ic d i f f i c u l t y
i n a n a ly z in g th e hydrodynamic p r o p e r t ie s
o f two-phase f lo w s o f l a r g e , ir r e g u l a r - s h a p e d s o l i d s w i t h s p e c i f i c
g r a v i t i e s d i f f e r e n t from th e t r a n s p o r t i n g f l u i d , i s f i r s t d e f i n i n g
and then e x p e r im e n ta lI y measuring m ix t u r e v i s c o s i t i e s .
Such m ix tu re s
are n o t amenable t o any known v is c o m e t r ic t e s t .
Employing th e p ro p e r d e f i n i t i o n o f a p s e u d o - v is c o s i t y , based
on p h y s ic a l c o n d it io n s o f th e f l o w , h e a d -lo s s c o r r e l a t i o n models
may be proposed.
CHAPTER I I I
EXPERIMENTAL INVESTIGATION
The p r e s e n t i n v e s t i g a t i o n was conducted t o e x p e r im e n t a lly
measure th e f r i c t i o n a l
h e a d -lo s s encountered d u r in g th e h y d r a u lic
t r a n s p o r t o f wood c h ip s w i t h w a t e r , and t o c o r r e l a t e th e hea d -lo ss
v a lu e s observed t o p ip e d ia m e te r , s l u r r y v e l o c i t y , p a r t i c l e s i z e ,
and v o l u m e t r ic c o n c e n t r a t io n .
The c o r r e l a t i o n model pre se n te d in
CHAPTER IV was developed a f t e r th e h e a d -lo s s data o f th e p re s e n t
i n v e s t i g a t i o n and p r e v io u s w o o d -ch ip i n v e s t i g a t i o n s were c a r e f u l l y
a n a ly z e d .
A h e a d -lo s s p r e d i c t i o n model was developed w i t h due
c o n s i d e r a t io n o f th e f o l l o w i n g two c o n d i t i o n s :
1.
The a n a l y t i c a l model must be c o n s i s t e n t w i t h p h y s ic a l
c o n d it io n s observed d u r in g th e f lo w o f wood chip s and w a te r s l u r r i e s
i n p ip e s , and
2.
The a n a l y t i c a l model must be. d e s c rib e d i n term s o f parameters
t h a t may be d e te rm in e d by s im p le f i e l d
la b o r a t o r y t e s t s and a p p lie d
by th e o p e r a tin g person nel 'o f th e p i p e l i n e system.
Thus an e x a m in a tio n o f th e p h y s ic a l c o n s id e r a t io n s and the
a c tu a l h e a d -lo s s d a ta i s necessary to. e s t a b l i s h th e c o r r e l a t i o n
m odel.
ANALTYI CAL CONSIDERATIONS
The energy s u p p lie d t o a lo ng d is ta n c e p i p e l i n e i s p r i m a r i l y t o
overcome f r i c t i o n a l
h e a d - lo s s .
For s in g le -p h a s e f l u i d s ,
th e parameters
used to p r e d i c t h e a d -lo s s are based on a n a ly z in g the f l u i d
geneous medium.
homogeneous, i t
as a homo­
A lth o u g h a m ix t u r e o f wood chip s and w a te r is noni s p o s s ib le to d e s c r ib e the f lo w o f such a m ix tu re
i n terms o f the v a r ia b le s which d e f in e the energy r e q u ir e d to pump the
s lu rr y .
F r ic tio n a l
h e a d - lo s s , measured as th e d i f f e r e n c e i n p ie z o m e tric
head between any two p o in t s along a h o r iz o n t a l
p ip e , may be expressed
in terms o f the average v e l o c i t y o f th e s l u r r y , s l u r r y p r o p e r t ie s
( v i s c o s i t y and d e n s i t y ) , s o l i d s c o n c e n t r a t io n , and p ip e c h a r a c t e r i s t i c s
( le n g t h , d ia m e te r, and i n t e r n a l s u r fa c e roughness).
The form o f th e f r i c t i o n a l
h e a d -lo s s e x p re s s io n i s o b ta in e d by
a p p ly in g th e m acroscopic c o n t r o l volume p r i n c i p l e f o r s te a d y , f u l l y developed f lo w o f a s l u r r y o f wood c h ip s and w a te r i n a c i r c u l a r p ip e .
For an elem ent o f pipe le n g th L and d ia m e te r D, w i t h a f lo w
r a t e o f wood chips and w a te r o f Qm^x » th e tim e averaged e q u a tio n o f
Jw _____
p]
F ig u re 3.1
M acroscopic C o n tro l Volume
26
m otion reduces t o
= TwTrDL
------------------------------- (3.1)
or
Tw = DaP/4 1
--------------------------------------------------- ( 3 .2 )
where
P^-Pg = s t a t i c p re s s u r e lo s s o ver le n g t h L 5 p s f
T 1,
= w a ll sh e a r s t r e s s , p s f
Since th e f lo w was assumed t o be f u l l y - d e v e l o p e d
w i t h r e s p e c t t o L ) , th e h y d r a u l i c g r a d i e n t
aP/L
(i.e .
u n ifo rm
i s measureable w i t h
p ie z o m e t r ic in s tr u m e n t s .
N o n -d im e n s io n a li z in g th e w a ll shea r s t r e s s tw w i t h th e s p e c i f i c
O
k i n e t i c energy PgV / 2 , th e Fanning f r i c t i o n f a c t o r i s d e fin e d as
f = 2 tw
= APD
P^V2
------------------------------------ ( 3 .3 )
L2pgV2
where pg i s th e d e n s it y o f th e m ix t u r e .
One o f th e o b j e c t i v e s o f t h i s
a fric tio n
i n v e s t i g a t i o n i s t o dete rm in e i f
f a c t o r - Reynolds number r e l a t i o n f o r w o o d -ch ip and w a te r
s l u r r i e s c o u ld be deve lop ed.
The s i m p l i c i t y o f th e r e l a t i o n s h i p
and ease o f a p p l i c a t i o n are o f prim e im p o rta n c e .
Head-loss in
Newtonian p ip e f lo w i s p r e d i c t a b l e in both th e la m in a r and t u r b u l e n t
re g io n s .
The Newtonian f u n c t i o n a l r e l a t i o n s h i p s between f r i c t i o n
f a c t o r and Reynolds number suggest a s i m i l a r approach f o r non-Newtonian
27
flo w s such as m ix tu re s o f wood c h ip s and w a te r .
T his may be expressed
as
f = f (Res ) ---------------------------------------------------- — ( 3 .4 )
where Reg i s a s l u r r y Reynolds number d e fin e d as
Re. =
where
VD
ps — .................— ------------- r ..................... ( 3 .5 )
i s th e v i s c o s i t y o f th e s l u r r y .
The s l u r r y d e n s i t y , pg , i s a f u n c t i o n o f v o l u m e t r ic c o n c e n tr a t io n
o f wood c h i p s , th e d e n s it y o f th e wood f i b e r ,
and d e n s it y o f w a te r .
The s l u r r y d e n s it y can be expressed i n f u n c t i o n a l form as
ps
ps ^ ,pwood, p ^
Wood-chip p a r t i c l e s c o n t a in le s s than 50 p e rc e n t s o l i d . m a t e r i a l by
volume ( 1 0 ) .
The re m a in in g volume i s v o id which f i l l s
upon s a t u r a t i o n .
w i t h w a te r
For a v o lu m e t r ic c o n c e n tr a t io n o f 30 p e r c e n t,
s a t u r a te d wood c h ip s have.a s p e c i f i c g r a v i t y a p p ro x im a te ly equal to
1 . 1 , g i v i n g a s l u r r y d e n s i t y , p , equal t o a p p ro x im a te ly 1.015 tim es
t h a t o f w a te r .
T h is 1 .5 p e rc e n t r e p r e s e n ts the maximum s l u r r y d e n s it y
v a r i a t i o n p o s s ib le and i s co n s id e re d t o be s u f f i c i e n t l y c lo s e to t h a t
o f w a te r t o p e r m it a l l
c a l c u l a t i o n s based on the s p e c i f i c g r a v i t y o f
w a te r .
The s l u r r y v i s c o s i t y i s n o t a p r o p e r t y o f the m ix t u r e which can
28
r e a d i l y be measured.
S l u r r i e s o f wood chips and w a te r are n o t
amenable to e x p e rim e n ta l v is c o m e t r ic te c h n iq u e s .
Wood c h ip s are
la r g e i n comparison to a llo w e d to le r a n c e s i n in s tr u m e n ts such as the
c a p i l l a r y - t u b e v is c o m e te r o r th e cone and p l a t e v is c o m e te r .
In
a d d i t i o n wood f i b e r i s h e a v ie r than w a te r , and wood c h ip s s e t t l e
i n w a te r unless th e m ix t u r e i s a g i t a t e d .
By s u i t a b l y d e f i n i n g a " p s e u d o - v i s c o s i t y , " and making i t a
param eter to be determ ined e x p e r i m e n t a lly r a t h e r than measured
d ire c tly ,
th is
problem i s a l l e v i a t e d .
The " p s e u d o - v is c o s i t y " o f
th e s l u r r y i s r a t i o n a l i z e d to be a f u n c t i o n o f th e average v e l o c i t y
o f th e s l u r r y , p a r t i c l e s i z e , p a r t i c l e c o n c e n t r a t io n , and tem p era ture
I n s i g h t i n t o r e l a t i o n s h i p s which c o u ld d e s c r ib e two-phase
f lo w s o f wood chips and w a te r r e q u ir e s an e x a m in a tio n o f e x p e rim e n ta l
data and p h y s ic a l
in te r p r e t a tio n o f t h e ir s ig n ific a n c e .
EXPERIMENTAL DATA
H ead-loss data o f w o od-chip and w a te r s l u r r i e s were o b ta in e d
em ploying th e e x p e rim e n ta l system and t e s t procedures o u t l i n e d i n
APPENDIX A.
Pipe s i z e , f lo w r a t e , w ood-chip c o n c e n t r a t io n , and
w ood-chip p r o p e r t ie s were th e c o n t r o l l e d v a r i a b l e s .
Pipe C h a r a c t e r i s t i c s
Pipes o f two s i z e s , nominal 4 - i n .
nominal 6- i n .
d ia m e te r a c r y l i c p l a s t i c and
d ia m e te r aluminum were connected i n s e r i e s .
F ric tio n a l
29
p r e s s u r e - lo s s e s were recorded from t e s t s e c tio n s in each s im u lta n e o u s ly .
The a c tu a l i n t e r n a l d ia m e te rs were 3.930 i n . and 5.864 i n . ,
re s p e c tiv e ly .
Flow Rate Range
The e x p e rim e n ta l system l i m i t e d th e f l o w - r a t e range from 250 t o
450 gpm.
The range o f s l u r r y v e l o c i t i e s o b ta in e d in th e 4 - i n .
d ia m e te r p ip e was a p p ro x im a te ly 5 .5 fp s t o 11 f p s , and i n th e 6- i n .
d ia m e te r p ip e th e range was a p p ro x im a te ly 2 .5 fps t o 4 .5 f p s .
250 gpm, p lu g g in g o c c u rre d i n th e t r a n s i t i o n from th e 6 - i n .
Below
d iam e te r
p ip e t o th e 4 - i n . d ia m e te r p ip e f o r v o l u m e t r ic c o n c e n tr a t io n s above
15 p e r c e n t.
The e l e c t r i c a l c a p a c it y o f th e s o l i d s - h a n d l i n g pump was
exceeded f o r f lo w r a te s above 450 gpm.
V o lu m e tr ic C o n c e n tra tio n Range
The v o l u m e t r ic c o n c e n tr a t io n o f wood c h ip s was v a r ie d i n
5 p e r c e n t in crem en ts t o a p p ro x im a te ly 20 p e rc e n t.
In one in s ta n c e
27 p e r c e n t c o n c e n t r a t io n was a t t a i n e d .
Wood Chip P r o p e r t ie s
■’
S
Four d i f f e r e n t g r a d a tio n s o f wood c h ip s were used.
Ungraded
c h i p s , p r i m a r i l y o f lo d g e p o le p in e s p e c ie s , were o b ta in e d from a
lo c a l s a w m i ll , and were segregated i n t o t h r e e d i f f e r e n t s iz e s using
screens o f 0 . 8 7 5 - i n . , 0 . 5 - i n . , 0 . 3 7 5 - i n . , and 0 . 2 5 - i n . mesh.
The
30
t h r e e d i f f e r e n t s iz e s employed were as f o l l o w s :
1.
tho se passing th e 0 . 8 7 5 - i n . mesh screen and r e t a in e d
on 0 . 5 - i n .
2.
screen,
tho se passin g th e 0 . 5 - i n . mesh screen and r e t a in e d
on 0 . 3 7 5 - i n . s c r e e n ,
3.
tho se passin g th e 0 : 3 7 5 - i n . mesh screen and r e t a in e d
on 0 . 2 5 - i n . s c r e e n , and
4.
c h ip s which passed th e 0 . 2 5 - i n . mesh screen are r e f e r r e d
t o as f i n e s .
In a d d i t i o n , a m ix t u r e o f a l l s iz e s i n c l u d i n g f i n e s was employed.
The ungraded sample o f chip s w i l l
sample.
be r e f e r r e d t o as th e m ix tu re
The samples r e f e r r e d t o i n T . , 2 . , and 3. above w i l l be
r e f e r r e d t o as 0 . 8 7 5 - i n . , 0 . 5 0 - i n . , and 0 . 3 7 5 - i n . samples.
. Table 3.1 i l l u s t r a t e s
in d iv id u a l
th e s iz e d i s t r i b u t i o n o f th e th r e e
c h ip s iz e s employed and Table 3 .2 i l l u s t r a t e s
d i s t r i b u t i o n o f samples o f th e agg re gate m ix t u r e .
as th e maximum dim ension p a r a l l e l
th e w e ig h t
Length was taken
t o th e wood g r a i n , and w id th as
th e maximum dim ension p e r p e n d ic u la r t o th e wood g r a i n .
The data
i n d i c a t e t h a t th e t h r e e s iz e g r a d a tio n s are n e a r ly th e same average
le n g th and t h ic k n e s s .
Chip w id th i s th e o n ly dim ension which
d i s t i n g u i s h e s th e i n d i v i d u a l s iz e s .
31
Table 3.1
S ize G ra d a tio n o f Wood Chips
. 8 7 5 - in . Sample
0 . 5 0 - i n . Sample
. 3 7 5 - in . Sample
Average Length
1.12 i n .
1 .11 i n .
Average W idth
0 .6 4 i n .
0 .4 4 i n .
.317 i n .
Average T hickness
0 .15 i n .
0.11 i n .
.092 i n .
Table 3 .2
1.14 i n .
W eight D i s t r i b u t i o n o f I n d i v i d u a l Sizes
Wood Chip Size
% o f Batch Weight
+0.875 i n .
8%
+ 0.50 i n .
27%
+0.375 i n .
18%
+0.25 i n .
31%
- 0 .2 5 i n .
(F in e s )
16%
HEAD-LOSS DATA
As w i t h most i n v e s t i g a t i o n s o f t h i s ty p e w a te r te m p e ra tu re
was n o t a c o n t r o l l e d v a r i a b l e .
in d iv id u a l f r i c t i o n
th e f r i c t i o n
The method f o r d e t e r m in in g th e
f a c t o r va lu e s c o r r e c te d t o 60° F assumed t h a t
f a c t o r f o r a s l u r r y o f wood c h ip s and w a te r v a r ie d w i t h
te m p e ra tu re i n th e same manner as th e v i s c o s i t y o f w a te r v a r ie s
w i t h te m p e ra tu re .
E v a lu a tin g th e f r i c t i o n
f a c t o r f o r 60° F from E q u a tio n 2 .1 4 ,
1 / / f 60 = 4 l 1 o g ^
/ f 60) " A
------------------- ( 3 '6 )
32
and f o r the. measured te m p e ra tu re I ,
I //F y = 4 . l o g ( ^ 6. y^ r )
-.4
-----------------------( 3 .7 )
an e x p r e s s io n f o r th e te m p e ra tu re c o r r e c te d f r i c t i o n
fa c to r (fo r
a g iv e n v e l o c i t y , p ip e d ia m e te r , and d e n s it y ) was found by sub­
t r a c t i n g th e two e q u a tio n s :
! / / T 6O = ! / / F
t
+ 4. lo g (V
fSO)
-------------------------------- ( 3 .8 )
yGoV
S ince f y , Py,
ite r a tiv e
were known, f 6Q was c a l c u la t e d em ploying an
p ro ce d u re .
The te m p e ra tu re c o r r e c te d f r i c t i o n
fa c to rs
are l i s t e d i n APPENDIX B.
F r i c t i o n f a c t o r s f o r c l e a r w a te r f lo w were measured b e fo re wood
ch ip s were i n j e c t e d i n t o th e system.
A comparison o f these c a lc u la t e d
va lu e s w i t h s ta n d a rd c l e a r w a te r f r i c t i o n
f a c t o r va lu e s f o r smooth
pipes in d i c a t e d the a ccu ra cy o f th e in s t r u m e n t a t io n c a l i b r a t i o n .
The c l e a r w a te r f r i c t i o n
f a c t o r values f o r the 4 - i n .
and 6- i n .
d ia m e te r pipes are shown as f u n c t io n s o f v e l o c i t y in F ig u re 3 .2 .
The
s o l i d l i n e s r e p r e s e n t P r a n d t l 's u n iv e r s a l e q u a tio n f o r t u r b u l e n t
p ip e f lo w f r i c t i o n
(Eq. 2 .1 4 ) f o r th e 4 - i n . and 6- i n .
d ia m e te r p ip e s .
F r i c t i o n f a c t o r va lu e s o b ta in e d from t h e 4 - i n . d ia m e te r and 6- i n .
d ia m e te r p ip e s f o r s l u r r i e s o f wood c h ip s and w a te r c o n t a in in g the
m i x t u r e , th e 0 . 8 7 5 - i n . , the 0 . 5 0 - i n . , and the 0 . 3 7 5 - i n . wood c h ip
.02
Fanning F r i c t i o n
F a c to r
O - 3 .9 3 0 -in .
a - 5 . 8 6 4 - in .
S l u r r y V e lo c i t y - V , f t / s e c
Figure 3.2
Clear Water F rictio n Factors
I . D . Pipe
I.D . Pipe
samples are pre se n te d i n Figures 3 . 3 , 3 . 4 , 3 . 5 , and 3 . 6 , r e s p e c t i v e l y
Fanning f r i c t i o n
f a c t o r i s p l o t t e d versus s l u r r y v e l o c i t y on
lo g a r i t h m i c s c a le s f o r each v o l u m e t r ic c o n c e n tr a t io n in c re m e n t.
These h e a d -lo s s data are a ls o p resen ted i n APPENDIX B i n t a b u l a r
form .
P r a n d t l 's r e s is t a n c e e q u a tio n , E q uation 2 .1 4 , i s shown on
each graph f o r both p ip e s iz e s based on c l e a r w a te r flo w s a t 60° F.
DISCUSSION OF EXPERIMENTAL RESULTS
Head-loss data f o r th e h y d r a u lic t r a n s p o r t o f m ix tu re s o f wood
c h ip s and w a te r was pre se n te d i n th e p re v io u s s e c t io n .
To avoid
cumbersome w o rding i n l a t e r s e c t io n s , th e wood-chip s l u r r y w i l l
be
used to mean the m ix tu re s o f wood ch ip s and w a te r.
C le a r w a te r f r i c t i o n f a c t o r s were measured b e fo re each run w it h
w ood-chip s l u r r i e s
t o dete rm in e the accuracy o f th e in s tr u m e n t
c a lib r a tio n .
F ig u re 3 .2 i l l u s t r a t e s
these c l e a r w a te r f r i c t i o n
compared to P r a n d t l 's u n iv e r s a l f r i c t i o n
f a c t o r s as
law, E q u a tio n 2 .1 4 .
The
average d e v i a t io n between measured and accepted c l e a r w a te r f r i c t i o n
fa c to rs is
1.6 p e r c e n t, and th e maximum d e v i a t io n i s 3 .4 p e rc e n t.
■S
Fig u re s 3 . 3 , 3 . 4 , 3 . 5 , and 3 .6 show t h a t th e d i f f e r e n c e between
fric tio n
f a c t o r s f o r w ood-chip s l u r r i e s and those o f c l e a r w a te r
in c re a s e s w i t h d e c re a s in g v e l o c i t y , and in c r e a s in g c o n c e n t r a t io n .
For c o n c e n tr a t io n s le s s than 15 p e r c e n t, s l u r r y f r i c t i o n f a c t o r s
approach th e c l e a r w a te r f r i c t i o n
f a c t o r values a s y m p t o t i c a l l y f o r
5 .8 6 4 -in .
Fanning F r i c t i o n
F a c to r
Chip s iz e = M ix tu re sample
0 - 5 % cone.
□
A
3 .9 3 0 -in .
O
□
0=3.930 i n .
0=5.864 i n .
l / / f = 4 . lo g (RewZ f ) - . 4
S lu rry V e lo c it y - V , f t / s e c
F ig u re 3 .3
M ix tu re Wood-Chip Head-Loss Data
Chip s iz e = 0.875 i n .
O - 5% cone.
5 .8 6 4 -in .
O - 10% "
F a c to r
A - 15%
"
Fanning F r i c t i o n
3 .9 3 0 -in .
0=3.930
0=5.864
J -L -L
S lu rry V e lo c it y - V ,f t/ s e c
Figure 3.4
0.875-in. Wood-Chip Head-Loss Data
.02
4-
Fanning F r i c t i o n
O-
.01
A
F a c to r
I
Chip s iz e = 0.50 i n .
5 .8 6 4 -in .
Pipe
O
5% cone.
□ -
10% "
A -
15%
"
O -
20%
"
CO
.005
0=3.930 i n .
0=5.864 i n .
l//f= 4 .1 o g (R e / f ) - . 4
.002
j _________I
2.
i
5.
I
i
i
i
i
10.
j ________ I
20.
30.
S l u r r y V e lo c i t y - V , f t / s e c
Figure 3.5
0.50-in. Wood-Chip Head-Loss Data
Chip s iz e = 0.375
0 - 5 % cone.
5 .8 6 4 -in .
D - 10% "
A - 15%
"
F a cto r
O - 20% "
Fanning F r i c t i o n
3 .9 3 0 -in .
- 0=3.930 i n .
- 0=5.864 i n .
l / / r = 4 . Iog(RewZ f ) - . 4
S lu rry V e lo c it y - V , f t / s e c
Figure 3.6
0.375-in. Wood-Chip Head-Loss Data
39
v e lo c itie s
i n th e v i c i n i t y o f - 10 f p s .
th e s l u r r y f r i c t i o n
For h ig h e r c o n c e n t r a t io n s ,
f a c t o r s appear to converge to those f o r c l e a r
w a te r a t v e l o c i t i e s h ig h e r than 10 f p s .
F igures 3 . 3 , 3 . 4 , 3 . 5 , and 3 .6 i n d i c a t e an a b r u p t change in
th e t r e n d o f th e f r i c t i o n
f a c t o r data f o r c o n s ta n t c o n c e n tr a tio n s
occurs o v e r a v e l o c i t y range o f ,5.5 t o 7 .5 f p s .
which t h i s
change o f s lo p e occurs w i l l
The v e l o c i t y a t
be c a l l e d th e " c r i t i c a l "
v e l o c i t y because a t t h i s v e l o c i t y v a lu e th e r e appears to be a
change i n the mode o f t r a n s p o r t o f wood c h ip s .
v e lo c ity w i l l
be discu sse d more f u l l y
The c r i t i c a l
c o n c e n t r a t io n .
4 - in .
The c r i t i c a l
i n l a t e r s e c t io n s .
v e l o c i t y in c re a s e s w i t h in c r e a s in g w ood-chip
A lth o u g h hea d -lo ss data were n o t recorded from the
d ia m e te r p ip e a t v e l o c i t i e s
below 5 f p s , th e gen eral
tren ds are
expected t o be th e same as shown by th e data o b ta in e d fro m the 6- i n .
d ia m e te r p ip e .
An i n s p e c t io n o f s i m i l a r d a t a , F ig u re 3 . 6 , presented
by Faddick (17) f o r w ood-chip and w a te r f lo w s i n a 4 - i n . d ia m e te r
p ip e , bears o u t t h i s assum ption.
Because th e v e l o c i t y range i n v e s t i g a t e d was l i m i t e d by the
e x p e r im e n ta l system, h e a d -lo s s data from p re vio u s i n v e s t i g a t i o n s
was employed to a id i n d e s c r ib in g the q u a l i t a t i v e t r e n d s .
COMPARISON WITH PREVIOUS INVESTIGATIONS
Head lo s s data o b ta in e d by Faddick ( 1 7 ) , Soucy ( 2 4 ) , and
E l l i o t and deMontmorency (4) are shown i n Figures 3 . 7 , 3 . 8 , and
Fanning F r i c t i o n
F a c to r
Faddick (Queens)
0=4.026 i n .
o - 5 % cone.
D - 10% "
A - 15% "
O - 20% "
0=4.026 i n .
l / / f =4. Iog(RewZ f) - .4
S l u r r y V e lo c i t y - V , f t / s e c
F ig u r e 3 .7
F a d d ic k ‘ s Wood-Chip Head-Loss Data
Soucy ( L a v a l )
D=6.0 i n .
0-5%
Fanning F r i c t i o n
F a c to r
□ -
A - 15%
"
O - 20%
"
- 0=6.0 i n .
l/ / f = 4 . 1 o g ( R e / f ) - .4
S lu rry V e lo c it y - V , f t / s e c
Figure 3.8
cone.
10% "
Soucy's Wood-Chip Head-Loss Data
E l l i o t e t al_ (PPRIC)
0=8.412 i n .
Fanning F r i c t i o n
F a c to r
0 - 5 % cone.
D - 10% "
A - 20% "
O - 30% "
- 0=8.412 i n .
l//r= 4 .
I og(Rew/ f ) - . 4
J_ I l l l
S lu rry V e lo c it y - V ,f t/ s e c
Figure 3.9
E llio t et al_ Wood-Chip Head-Loss Data
43
3 . 9 , r e s p e c t i v e l y ..
Faddick (10) has s t a t e d t h a t th e data o f these
th re e i n v e s t i g a t o r s were o b ta in e d from ungraded w ood-chip samples.
Thus, t h e i r head lo s s d ata sho u ld be q u a l i t a t i v e l y s i m i l a r t o t h a t
o b ta in e d from the m ix t u r e sample o f the p re s e n t i n v e s t i g a t i o n .
The
dashed l i n e s on Fig u re s 3 . 7 , 3 . 8 , and 3 .9 r e p r e s e n t th e data o f
th e p r e s e n t i n v e s t i g a t i o n c o r r e c te d t o 60° F.
S tr a ig h t lin e s
r e p r e s e n t these data w i t h a maximum d e v i a t i o n o f ± 3 p e r c e n t.
Temperature c o r r e c t i o n was n o t a p p lie d to th e data o f th e o t h e r
i n v e s t i g a t o r s s in c e measured te m p era tures were n o t a v a i l a b l e .
Fig u re s 3 . 7 , 3 . 8 , and 3 .9 i n d i c a t e a s i m i l a r a b r u p t change
i n th e s lo p e o f th e f r i c t i o n f a c t o r versus v e l o c i t y curves f o r
c o n s ta n t c o n c e n t r a t io n .
As b e f o r e , th e v e l o c i t y a t which t h i s
a b r u p t change i n s lo p e occurs depends on c o n c e n t r a t io n .
Below 10 p e r c e n t c o n c e n t r a t io n , f r i c t i o n f a c t o r va lu e s approach
th e c l e a r w a te r values a s y m p t o t i c a l l y i n th e v i c i n i t y o f 10 f p s .
T h is was a ls o i n d ic a t e d by th e data o f th e p re s e n t i n v e s t i g a t i o n .
For c o n c e n tr a t io n s above 10 p e r c e n t, th e f r i c t i o n f a c t o r values
appear to approach th e f r i c t i o n
w a te r a t v e l o c i t i e s
f a c t o r - v e l o c i t y curves f o r c le a r
l a r g e r than 10 f p s .
S oucy's d a ta . F ig u re 3 . 8 , which was o b ta in e d from a 6 . 0 - i n .
in te rn a l
d ia m e te r p ip e can be q u a l i t a t i v e l y compared to th e data
o b ta in e d from th e 5 . 8 6 4 - i n . d ia m e te r p ip e .
For 10, 15, and 20
p e r c e n t c o n c e n tr a t io n s these dashed l i n e s appear to r e p r e s e n t Soucy's
44
d ata v e r y w e l l .
The d is c re p a n c y between the two s e ts o f d ata f o r
5 p e r c e n t c o n c e n t r a t io n cannot be e x p la in e d .
A q u a n t i t a t i v e com­
p a r is o n i s n o t p o s s i b l e , however, s in c e Soucy d id n o t in c lu d e w a te r
te m p e ra tu re v a lu e s w i t h h is h e a d -lo s s d a ta .
F a d d ic k ' s w o od-chip d a t a . F ig u re 3 . 7 , i s d i r e c t l y comparable
to the data o b ta in e d d u r in g th e p r e s e n t i n v e s t i g a t i o n from the
m ix t u r e w o od-chip sample in th e 4 - i n . d ia m e te r p ip e .
The dashed l i n e s
i n F ig u re 3 .7 r e p r e s e n t t h i s data o f the p re s e n t i n v e s t i g a t i o n .
A lth o u g h th e r e appears t o be some s c a t t e r in F a d d ic k 's d a t a , i t
tre n d s tow ard th e dashed l i n e s .
E l l i o t and deMontmorency's d a ta was o b ta in e d from a 8 . 4 1 2 - i n .
i n t e r n a l d ia m e te r p ip e and i s n o t d i r e c t l y comparable to th e data
o f th e p r e s e n t i n v e s t i g a t i o n .
However, th e data from th e f o u r
i n v e s t i g a t i o n s do show a s y s te m a tic tr e n d which w i l l
i n a n a ly z in g these d ata in CHAPTER IV :
fric tio n
be o f s i g n i f i c a n c e
The tre n d o f d a ta shows the
f a c t o r s f o r c o n s ta n t c o n c e n t r a t io n in c re a s e in magnitude
w i t h in c r e a s in g c o n c e n t r a t io n .
In th e lo w er v e l o c i t y r e g io n s , Fig u re s
3 . 7 , 3 . 8 , and 3 .9 show th e r e l a t i o n s h i p between f r i c t i o n
v e l o c i t y does depend on th e pipe d ia m e te r.
f a c t o r and
F r i c t i o n f a c t o r decreases
w i t h in c r e a s in g p ip e d ia m e te r f o r a g iv e n v e l o c i t y and a given
c o n c e n t r a t io n .
T h is dependence o f f r i c t i o n
f a c t o r on p ip e dia m e te r
i s n o t a l i n e a r f u n c t i o n o f p ip e d ia m e te r because th e f r i c t i o n f a c t o r v e l o c i t y cu rves appear t o converge t o one c u r v e , in d e p e n d e n t o f
45
p ip e d ia m e te r f o r h ig h e r c o n c e n t r a t io n s .
The dependence o f f r i c t i o n
f a c t o r on pipe d ia m e te r i s n o t as
s i g n i f i c a n t in the h ig h e r v e l o c i t y r e g io n as in th e lo w e r v e l o c i t y
r e g io n .
FLOW REGIME DELINEATION
As m entioned in th e p re v io u s s e c t io n , the h e a d -lo s s data o f the
f o u r w ood-chip p i p e l i n e i n v e s t i g a t i o n s show an a b r u p t in c re a s e in
th e s lo p e o f th e f r i c t i o n
f a c t o r versu s v e l o c i t y curves i n the
range o f v e l o c i t y from 5 . 5 - 7 . 5 f t / s e c .
T h is " c r i t i c a l " v e l o c i t y
i s a f u n c t i o n o f c o n c e n t r a t io n .
One p l a u s i b l e e x p la n a tio n o f t h i s phenomena i s th e t r a n s i t i o n
from heterogeneous s a l t a t i o n f lo w to b e d -lo a d f lo w .
V is u a l measure­
ments were made to a s c e r t a in th e v e l o c i t y range in w hich th e bed-load
fo rm e d .
T a b le 3 .3 shows th e measurements observed i n th e 4 - i n .
d ia m e te r p ip e .
I t was n o t p o s s ib le to o b t a in s i m i l a r v a lu e s f o r th e
6- i n . d ia m e te r p ip e s in c e aluminum i r r i g a t i o n pipe was used th ro u g h ­
o u t th e 9 0 - f t t e s t s e c t io n .
The average v e l o c i t i e s , based on s l u r r y f lo w r a t e , a t which the
b e d -lo a d formed f o r v a r io u s c o n c e n tr a t io n s o f each c h ip s iz e are
lis te d
in T ab le 3 .3 as "F o rm a tio n V e l o c i t y . "
The v e l o c i t i e s which
c h a r a c t e r iz e th e a b r u p t change in s lo p e o f the f r i c t i o n
curves are l i s t e d as " C r i t i c a l
V e lo c ity ."
fa c to r- v e lo c ity
The maximum p e rc e n t
Table 3 .3
Chi p
Size
C o n c e n tra tio n
%
• 8 7 5 - in .
Bed Form ation V e l o c i t i e s - 4 . - i n .
Form ation
V e lo c ity
• fp s
Pipe
C r itic a l
V e lo c ity
■ fp s
Bed
V e lo c ity
fps
5 .0
5 .9
10.0
6.1
5 .10
5.5
1 5.0
7.1
6.2
5.67
5 .98
6.91
.50 - i n .
15.0
6.6
6.8
6.32
.3 7 5 -in .
. 10.0
6.25
6.22
6.14
10.0
6.58
7.1
7 .5 4
6 .5
6 .9
7 .3
6.32
6.91
7.13
M ix t u r e
15.0
"
20.0
47
d e v ia tio n .b e tw e e n b e d -fo r m a tio n v e l o c i t y and c r i t i c a l
v e lo c ity is
13 p e r c e n t.a n d the average d e v i a t i o n i s 3 .5 p e r c e n t.
Table 3 .3
a ls o l i s t s
th e v e l o c i t y o f th e s l i d i n g bed o f wood c h ip s as "Bed
V e l o c i t y . 11 The "Bed" v e l o c i t i e s were observed a t th e same tim e the
"F o rm a tio n " v e l o c i t i e s were measured.
The d i f f e r e n c e between the
average v e l o c i t y o f th e s l u r r y and th e v e l o c i t y o f th e s l i d i n g bed
i s a p p ro x im a te ly 3 p e r c e n t, w i t h a maximum d e v i a t i o n o f 5 .5 p e rc e n t
o c c u r r in g f o r th e 20 p e r c e n t c o n c e n tr a t io n o f th e m ix t u r e sample.
In t h i s c h a p te r th e hea d -lo ss data o f th e p r e s e n t i n v e s t i g a t i o n
have been p r e s e n te d , d is c u s s e d , and q u a l i t a t i v e l y compared t o data
o f p re v io u s i n v e s t i g a t i o n s .
The d ata were presen ted i n such a
manner as t o i l l u s t r a t e th e p h y s ic a l phenomena o c c u r r in g d u r in g
tra n s p o rt.
CHAPTER IV
CORRELATION METHOD AND ANALYSIS
A method f o r a n a ly z in g h e a d -lo ss data o f w ood-chip and w a te r
s l u r r i e s i s pre se n te d i n t h i s c h a p te r .
The p h y s ic a l phenomena are
examined and analyzed i n accordance w i t h th e data pre se n te d in
CHAPTER I I I .
The c o r r e l a t i o n model i s developed on th e b a s is o f
the e x p e rim e n ta l h e a d rlo s s data and e x i s t i n g t h e o r y .
CORRELATION MODEL DEVELOPMENT.
In CHAPTER I I ,
th e p h y s ic a l phenomena o f the h y d r a u l i c t r a n s p o r t
o f l a r g e p a r t i c l e s in p i p e l i n e s were d is c u s s e d .
P a r t i c l e s , such as
wood c h ip s , w i t h s p e c i f i c g r a v i t i e s g r e a t e r than th e conveying
medium are acted upon by g r a v i t a t i o n a l
fo rc e s and i n e r t i a l
fo rc e s
im p a rte d by the t u r b u l e n t v e l o c i t y f l u c t u a t i o n s in p ip e f lo w .
These f l u c t u a t i o n s a r is e from the random v o r t e x m o tio n generated
by the t u r b u l e n t shea r.
. In homogeneous s l u r r y f l o w s , th e t u r b u l e n t s t r u c t u r e i s o f
s u f f i c i e n t i n t e n s i t y to overcome the g r a v i t a t i o n a l fo r c e s a c t in g
on the p a r t i c l e s and t o m a in ta in a u n ifo rm c o n c e n tr a t io n p r o f i l e
o v e r th e p ip e c r o s s - s e c t i o n .
damped due to th e r i g i d i t y ,
When th e i n e r t i a l
However, th e t u r b u l e n t s t r u c t u r e is
i n e r t i a , and s iz e o f the p a r t i c l e s .
fo rc e s im parted to th e s o l i d p a r t i c l e s by th e
49
t u r b u l e n t m o tio n are n o t s u f f i c i e n t t o overcome g r a v i t a t i o n a l
fo rc e s ,
th e p a r t i c l e s s e t t l e t o th e bottom o f th e p ip e .
S a l t a t i o n heterogeneous f lo w i s c h a r a c t e r iz e d by suspended
p a r t i c l e s as w e ll as p a r t i c l e s which have s e t t l e d t o th e p ip e
i n v e r t and are r o l l e d o r dragged along th e p ip e by a c o m b in a tio n o f
sh e a r and l i f t
fo rc e s induced by the f l u i d medium.
A b e d -lo a d f lo w
( o r s l i d i n g bed) c o n d i t i o n e x i s t s when a l l
p a r t i c l e s have s e t t l e d t o the p ip e i n v e r t .
is not s u f f i c i e n t to l i f t
Since th e f l u i d
tu rb u le n c e
th e s o l i d p a r t i c l e s from th e p ip e i n v e r t '
f o r t h i s ty p e o f f l o w , a "p s e u d o " - la m in a r c o n d it io n appears t o e x i s t .
The term "pseudo" i s employed to d i s t i n g u i s h t h i s phenomena from
c la s s ic a l
la m in a r p ip e f l o w .
T h is i n v e s t i g a t i o n in d i c a t e s t h a t the
"p s e u d o " - la m in a r c o n d i t i o n occurs in th e b e d -lo a d f lo w regime
d e s c r ib e d in CHAPTER I I .
S a l t a t i o n f l o w s , w hich were d e s c rib e d e a r l i e r i n t h i s c h a p te r
and in CHAPTER I I ,
appear t o be a ty p e o f t u r b u l e n t f l o w .
Since
th e t u r b u l e n t s t r u c t u r e o f the f lo w i s a l t e r e d by th e presence o f
th e s o l i d p a r t i c l e s , th e t u r b u l e n t s t r u c t u r e i s n o t th e same as
c l a s s i c a l t u r b u l e n t p ip e f lo w and th e term " p s e u d o " - t u r b u le n t i s
employed t o d e s c r ib e t h i s
c o n d itio n .
The s l u r r y v e l o c i t y a t w h ich a pronounced b e d -lo a d f lo w
developed was pre se n te d i n Table 3 .3 i n CHAPTER I I I .
These c r i t i c a l
v e l o c i t i e s were shown t o agree t o w i t h i n 13 p e rc e n t w i t h v e l o c i t i e s
50
where th e a b ru p t change in s lo p e o f th e f r i c t i o n f a c t o r - v e l o c i t y
curves o c cu rs f o r each d i f f e r e n t c o n c e n t r a t io n i n F ig u re s 3 . 3 , 3 . 4 ,
3 . 5 , and 3 . 6 .
Based on th e above c o n s id e r a t io n s o f p l a u s i b l e f lo w regim es,
th e h e a d -lo s s o f w ood-chips and w a te r s l u r r i e s w i l l
be analyzed
as "pseudo“ - l a m i n a r , o r " p s e u d o " - t u r b u le n t , depending on the
m agnitude o f th e param eters V and
a P /L.
PSEUDO-LAMINAR ANALYSIS
The Metzner-Reed a n a ly s is f o r la m in a r non-Newtonian flo w s was
found t o be s u f f i c i e n t f o r a n a ly z in g th e h e a d -lo ss d a ta f o r s l u r r i e s
o f w ood-chips and w a te r t r a n s p o r te d i n what appeared t o be a
"p s e u d o " - la m in a r f l o w c o n d i t i o n .
This h e a d -lo ss p r e d i c t i o n model
i s d e s c r ib e d i n terms o f th e param eters s e t f o r t h i n CHAPTER I I I .
A n a ly s is D e s c r ip t io n
R e i t e r a t i n g th e p r e s e n t a t io n o f th e Metzner-Reed a n a ly s is o f
CHAPTER U", th e c o r r e l a t i o n model i s based on th e prem ise t h a t
Tw = K( 8V /D )n
-------- ------------- ---------------------- ( 4 .1 )
where
T 11
W
= w a ll shear s t r e s s , d e fin e d by Eq. 3 . 2 , I b f / f t
V = average s l u r r y v e l o c i t y , f t / s e c
D = i n t e r n a l p ip e d ia m e te r , f t
T
2
51
n. = f l u i d
b e h a v io r in d e x , d im e n sio n le ss
K = flu id
c o n s is te n c y in d e x , u n i t s c o n s i s t e n t w i t h Eq. 4.1
In th e d e f i n i t i o n o f th e Fanning f r i c t i o n
2 T
f - - mJ
fa c to r.
----------------------------- ------------ - ...............( 4 . 2 )
V
th e s l u r r y d e n s i t y , p , i s taken t o be t h a t o f w a te r as e x p la in e d
e a r lie r.
S u b s titu tin g th is f r i c t i o n
f a c t o r d e f i n i t i o n i n t o Equation 3.1
f o r th e w a ll shear s t r e s s , r , th e f o l l o w i n g e q u a tio n r e s u l t s :
f = IS (S 11- 1K)
( 4 .3 )
V2- n Dnp
I f a g e n e r a liz e d Reynolds number i s d e fin e d as
V2 - n Dnp
nn - l „
( 4 .4 )
E q uation 4 .3 reduces t o
f = 16 / Reg
.......... .................................... ...............( 4 .5 )
which i s th e non-Newtonian e q u iv a l e n t o f th e P o i s e u i l l e e q u a tio n
f = 16 / Re,
W
where Re , = VDp/u
E q uation
4 .5
------ r ................................................. ( 4 .6 )
i s th e c o n v e n tio n a l Reynolds number.
reduces t o e q u a tio n
4 .6
f o r Newtonian la m in a r
p ip e f l o w s in c e n = I and K = Hq .
The param eters n and K o f E q uation 4 .3 were determ ined from
-
52
w ood-chip h e a d -lo ss d ata o f th e p r e s e n t i n v e s t i g a t i o n as f u n c t io n s
o f p a r t i c l e c o n c e n t r a t io n .
The param eter n i s th e s lo p e o f the
ta n g e n t drawn a t any p o i n t on a l o g a r it h m ic p l o t o f w a ll shear s t r e s s
versus th e param eter 8V/D.
where l o g ( 8 V/D) equals z e r o .
K i s th e i n t e r c e p t o f t h a t ta n g e n t
Both n and K may va ry w i t h v e l o c i t y ,
b u t are assumed to be in dependent o f p ip e d ia m e te r.
W ith n and K values d e te rm in e d , f r i c t i o n
c a l c u la t e d knowing th e v e l o c i t y ,
c o n c e n t r a t io n .
f a c t o r s can be
p ip e d ia m e te r, and p a r t i c l e
-
E q uation 4 .5 o f f e r s th e advantage o f p r e d i c t i n g hea d-losses f o r
pipes whose d iam e te rs are d i f f e r e n t fro m those used i n the o r i g i n a l
c o r re la tio n .
For a g iv e n v e l o c i t y and v o lu m e tr ic c o n c e n t r a t io n ,
the r a t i o o f two e q u a tio n s f o r d i f f e r e n t p ip e d iam e te rs
and Dg
g ives
f,
= (D2ZD1) 11---------- ----------------------------------- - ( 4 . 7 )
s in c e th e v e l o c i t y , d e n s i t y , and f l u i d
c o n s is te n c y in d e x values are
id e n tic a l.
Thus, th e r a t i o o f f r i c t i o n f a c t o r s f o r two d i f f e r e n t p ip e s iz e s
i s equal to th e r e c ip r o c a l r a t i o o f th e p ip e diam eters to the "n"
power.
A knowledge o f n and K values as f u n c t io n s o f c o n c e n tr a t io n
a llo w s th e c a l c u l a t i o n o f hea d -lo ss values f o r v a r io u s p ip e s iz e s
53
o v e r th e " p s e u d o " - ! am inar v e l o c i t y range.
A p p l i c a t i o n t o Head-Loss Data
The h e a d -lo s s d ata o f t h i s i n v e s t i g a t i o n which appeared t o be
i n th e " p s e u d o "- !a m in a r r e g io n were analyzed a cc o rd in g t o the
Metzner-Reed c o r r e l a t i o n m o d e l.
from th e 6- i n .
Al I data i n t h i s re g io n were o b ta in e d
d ia m e te r p ip e and were c o r r e c te d f o r te m p e ra tu re
a c c o rd in g t o th e te c h n iq u e d e s c rib e d i n CHAPTER I I I .
flu id
b e h a v io r in d e x , n , and th e f l u i d
Values o f the
c o n s is te n c y in d e x , K, were
o b ta in e d em ploying l e a s t squares c u r v e - f i t t i n g te c h n iq u e s .
The
v a lu e s o f n and K p re se n te d i n Table 4.1 i n d i c a t e t h a t both are
dependent on c o n c e n t r a t io n and c h ip s i z e .
g e n e r a liz e d Reynolds (based on the c r i t i c a l
The v a lu e o f th e c r i t i c a l
v e l o c i t y ) number i s
a p p ro x im a te ly 3,000.
The r e s u l t s o f an e r r o r a n a ly s is t o compare th e measured f r i c t i o n
f a c t o r s t o those p r e d ic t e d from E q uation 4 .3 using th e e x p e r im e n ta lI y determ ined va lu e s o f n and K are shown in Table 4 . 2 .
Maximum and
average p e r c e n t d e v i a t io n s f o r each c o n c e n tr a t io n in c re m e n t and ch ip
s iz e g r a d a tio n are shown.
-\
For th e m ix t u r e sample o f wood c h ip s the maximum d e v i a t io n was
.
3 p e rc e n t and th e average d e v i a t io n was le s s than I p e r c e n t.
For
th e 0 . 8 7 5 - i n . , 0 , 5 0 - i n . , and 0 . 3 7 5 - i n . , w ood-chip samples th e
maximum d e v i a t i o n was 4 p e r c e n t and th e average d e v i a t i o n was le s s
than 0.1 p e r c e n t.
54
T ab le 4.1
Chip Sample
"Pseudo11-L a m inar Index Parameters
Index
Parameter
5%
M ix tu re
n
K
.831
.00274
0 .8 7 5 -in .
n
K
0 .5 0 -in
.
0 .3 7 5 -in .
C o n c e n tra tio n
10%
15%
20%
.756
.00447
.358
.0299
.288
.052
1.043
.000915
.980
.00101
.741
.00338
*
*
n
K
1 .00
.979
.00157
.524
.0121
*
*
n
K
1 .01
.927
.001996
.606
.00894
*
*
.00123
.00073
*1 data p o i n t
Table 4 .2
Chip Sample
D e v ia tio n s
%
M ix tu re
0 .8 7 5 -in .
0 .5 0 -in .
0 .3 7 5 -in .
E r r o r A n a ly s is o f Measured and P r e d ic te d
F r i c t i o n Fgctors f o r "Pseudo"- Laminar Region
./
5%
C o n c e n tra tio n
15%
10%
Avg. Dev.
Max. Dev.
±1 .5%
3 .0
A vg. Dev.
Max. Dev.
1 .7
2.2
.6
2.2
4 .0
.9
A vg. Dev.
Max. Dev.
.3
.5
.4
.5
2 .5
Avg. Dev.
Max. Dev.
.0
.7
.5
1.4
1.2
1.0
± 1 . 1%
2.3
± .5%
20%
±0%
.8
0
—
1.0
—
———
55
E q uation 4 .3 shows t h a t f r i c t i o n
t o th e v e l o c i t y t o th e " n - 2 “ power.
curves o f f r i c t i o n
f a c t o r i s d i r e c t l y p r o p o r t io n a l
The s lo p e o f th e l o g r i t h m i c
f a c t o r versus s l u r r y v e l o c i t y
3 . 5 , and 3 . 6 ) p re se n te d i n CHAPTER I I I
(F ig u re s 3 . 3 , 3 . 4 ,
are then equal t o n - 2 .
Since
n decreases w i t h in c r e a s in g c o n c e n t r a t io n , th e q u a n t i t y n -2 a ls o
decreases a l g e b r a i c a l l y , b u t th e m agnitude (a b s o lu te v a lu e ) o f n -2
in c r e a s e s , which i s i n d ic a t e d by th e s te e p e n in g o f th e slo p e s o f
th e c u r v e s .
This i s c o n s i s t e n t w i t h th e q u a l i t a t i v e d e s c r i p t i o n o f
th e h e a d -lo s s data p re se n te d i n CHAPTER I I I .
From th e d a ta o f Table 4 . 1 , th e energy re q u ire m e n ts f o r pumping
th e v a r io u s c h ip s iz e g r a d a tio n s can be e s t a b l is h e d .
The va lu e s o f
n decrease w i t h in c r e a s in g c o n c e n tr a t io n and K va lu e s in c re a s e w it h
in c r e a s in g c o n c e n t r a t io n .
During th e p re s e n t i n v e s t i g a t i o n v a lu e s o f th e param eter 8V/D
were c o n s i s t e n t l y g r e a t e r than I .
T h u s, as n decreases w i t h
c o n c e n t r a t i o n , th e q u a n t i t y ( 8V /D )n a ls o decreased.
E q uation 4 . 1 , th e w a ll shear s t r e s s ,
t
A c c o rd in g to
, should decrease w i t h
d e c re a s in g n ; however th e in c re a s e i n K a s s o c ia te d w i t h d e crea sing
n va lu e s more than overcomes th e e f f e c t s o f decrease i n n.
th e w a ll shea r s t r e s s ,
t
Thus,
, in c re a s e s w i t h in c r e a s in g c o n c e n t r a t io n ,
which in c re a s e s th e energy re q u ire m e n ts t o pump th e s l u r r y .
The r e s u l t s g iv e n i n Table 4.1 show t h a t th e n v a lu e s o b ta in e d
from th e m ix t u r e sample are c o n s i s t e n t l y s m a lle r than those f o r the
56
t h r e e ' i n d i v i d u a l s iz e g r a d a t i o n s .
The r e s p e c t iv e K v a lu e s are a ls o
l a r g e r . . T h is i n d i c a t e s more energy i s r e q u ir e d t o pump th e m ix tu r e
samples a t a g ive n c o n c e n t r a t io n than any o f th e t h r e e i n d i v i d u a l
s iz e g r a d a tio n s a t t h a t c o n c e n t r a t io n .
One p l a u s i b l e e x p la n a t io n f o r t h i s phenomena i s as f o l l o w s :
The m ix t u r e sample i s comprised o f a l l s iz e g r a d a tio n s
in c lu d in g f i n e s .
The ch ip s are l y i n g on th e p ip e i n v e r t ,
bein g dragged by th e f l u i d medium.
Some w a te r passes
th ro u g h t h i s s l i d i n g bed and th e s m a lle r p a r t i c l e s can
be moved t o some e x t e n t th ro u g h th e v o id s between
in d iv id u a l c h ip s .
E v e n tu a lI y the se vo id s become plugged
and th e bed a c t u a l l y moves as a s o l i d mass in c o n t a c t
w i t h th e p ip e s u r f a c e .
The c h ip s o f u n ifo rm s iz e p r o v id e a s e r ie s o f p o i n t masses
i n c o n t a c t w i t h th e , s u r fa c e as no f i n e s are p r e s e n t t o
fill
th e v o id s .
W ater passes th ro u g h th e u n ifo rm s iz e
c h ip bed more e a s i l y than th ro u g h the m ix t u r e sample.
The d i f f e r e n c e among n values f o r th e th re e i n d i v i d u a l g ra d a tio n s
is not s ig n if ic a n t.
However, th e K- va lu e s do in c re a s e w i t h d e crea sing
p a r t i c l e s iz e and in c r e a s in g c o n c e n t r a t io n .
The v a lu e K = .0121 f o r
th e 0 . 5 0 - i n . c h ip s iz e i s th e o n ly v a lu e t h a t does n o t f i t
p a tte rn .
-
« '
'
th is
57
An e x p la n a tio n s i m i l a r to t h a t g ive n above f o r d i f f e r e n c e s
i n n and K values f o r th e m ix t u r e sample and i n d i v i d u a l s iz e
g r a d a tio n s a p p lie s to d i f f e r e n c e s among K values f o r th e th re e
s iz e g r a d a tio n s .
From v is u a l o b s e r v a t io n s , the i n d i v i d u a l chips
do n o t assume a p r e f e r r e d o r i e n t a t i o n i n the bed.
The s m a lle r
chip s form a c l o s e r packed m a t r i x and th e r e i s more p a r t i c l e - p i p e
w a ll c o n t a c t than w i t h l a r g e r p a r t i c l e s .
Thus more energy i s
r e q u ir e d t o overcome drag between th e p a r t i c l e s and p ip e w a l l .
The l a r g e r values o f K f o r s m a ll e r c h ip s iz e r e f l e c t th e in cre a se d
energy r e q u ire m e n t o f pumping.
A p p l i c a t i o n t o O ther I n v e s t i g a t i o n s
The h e a d -lo s s d a ta o b ta in e d from t e s t s conducted w i t h th e 6 - i n .
d ia m e te r p ip e i n t h i s i n v e s t i g a t i o n were shown to be r e p r e s e n t a t iv e
o f S oucy's d a t a , which were a ls o o b ta in e d from a 6 - i n . d ia m e te r
p ip e .
The data f o r the two i n v e s t i g a t i o n s i n the " p s e u d o "- la m in a r
r e g io n f o r 10, 15, and 20 p e rc e n t c o n c e n tr a tio n s l i e w i t h i n a p p r o x i­
m a te ly 10 p e r c e n t o f one a n o th e r.
A d e t a i l e d q u a n t i t a t i v e a n a ly s is
cann ot be made s in c e w a te r te m p e ra tu re values f o r S oucy's data are
•
\
n o t known.
F a d d ic k 's w ood-chip hea d -lo ss d a ta and E l l i o t and deMontmorency's
w ood-chip h e a d -lo s s data were o b ta in e d from 4 - i n . and 8 - i n . d ia m e te r
p ip e s , r e s p e c t i v e l y .
I t has been shown i n a p re v io u s s e c t io n t h a t
d a ta o b ta in e d from two d i f f e r e n t p ip e s iz e s should f o l l o w the
58
•>) .
r e la tio n s h ip
f
f
1 = (D2ZD1 ) n
( 4 .7 )
2
f o r th e same v e l o c i t i e s and values o f n and K.
The v a l i d i t y o f t h i s e q u a tio n was t e s te d by c a l c u l a t i n g the
f r i c t i o n f a c t o r s f o r th e 4 . 0 6 2 - i n . and th e 8 . 4 1 2 - i n . d ia m e te r pipes
u sin g th e va lu e s o f n from Table 4.1 f o r th e m ix t u r e sample and the
f r i c t i o n f a c t o r - v e l o c i t y d ata f o r th e 5 . 8 6 4 - i n . d ia m e te r p ip e o f t h i s
in v e s tig a tio n .
These c a l c u la t e d va lu e s were compared w i t h th e data
o f Faddick and E l l i o t and deMontmorency a lth o u g h th e v e l o c i t i e s in
t h e . p r e s e n t s t u d ie s were n o t i d e n t i c a l w i t h those o f th e i n v e s t i g a t o r s
c i t e d above.
S ince t h e r e i s no o v e r la p between th e sets o f data f o r d i r e c t
com parison, s t r a i g h t l i n e s o f s lo p e n -2 shou ld f i t
th ro u g h th e p o in t s
f o r each c o n c e n t r a t io n .
F ig u re 4.1 shows th e comparison w i t h F ad dic k 's d a ta on a
l o g a r i t h m i c graph o f f r i c t i o n
f a c t o r versus v e l o c i t y .
A c co rd in g to
E q uation 4 . Si a l o g a r i t h m i c curve o f f r i c t i o n f a c t o r versus s l u r r y
■\
v e l o c i t y s h o u ld be a s t r a i g h t l i n e .
These s t r a i g h t l i n e s re p r e s e n t
th e d a ta t o w i t h i n 5 p e rc e n t i n d i c a t i n g e x c e l l e n t agreement.
F ig u re 4 .2 shows th e same comparison w i t h E l l i o t and deMontmorency
h e a d -lo s s d a ta .
However, E q uation 4 .7 does n o t s a t i s f a c t o r i l y p r e d i c t
59
F a c to r
15% cone.
Fanning F r i c t i o n
A - Faddick (Queens)
O - P r e d ic te d from
Eq. 4 .7
S l u r r y V e lo c i t y - V , f t / s e c
Fanning F r i c t i o n F a c to r - f
F ig u re 4 .1 F r i c t i o n F a c to r Comparison
A - E l l i o t e t al(PPRIC)
o - P r e d ic te d from
20% cone
S l u r r y V e lo c i t y - V , f t / s e c
F ig u r e 4 .2
F r i c t i o n F a c to r Comparison
60
th e f r i c t i o n
f a c t o r values o f E l l i o t and deMonttporency.
Maximum
p e r c e n t d e v i a t io n s are o f th e o r d e r o f 30 p e rc e n t f o r th e lo w e r
c o n c e n tr a t io n v a lu e s .
In CHAPTER I I I ,
i t was noted t h a t th e f r i c t i o n
f a c t o r values
from th e f o u r i n v e s t i g a t i o n s become n e a r ly in dependent o f p ip e
d ia m e te r f o r c o n c e n tr a t io n s o f 20 p e r c e n t and g r e a t e r .
This
phenomenon i s a ls o f u l l y e x p la in e d by E q uation 4 . 7 .
The f r i c t i o n
f a c t o r r a t i o f o r two d i f f e r e n t p ip e s iz e s i s
equal t o th e r e c ip r o c a l r a t i o o f th e p ip e d iam e te rs t o th e "n "
power.
As n decreases t o z e r o , the d ia m e te r r a t i o t o th e "n"
power approaches I ,
and f r i c t i o n
f a c t o r r a t i o become independent
o f p ip e s i z e .
A t 20 p e rc e n t c o n c e n t r a t i o n , th e v a lu e o f n f o r th e m ix t u r e
sample i s 0 .2 8 8 .
A lth o u g h t h i s v a lu e i s s i g n i f i c a n t l y d i f f e r e n t
from z e r o , the d ia m e te r r a t i o s f o r th e d ata o f F ig u re s 4.1 and 4 .2
(4 .0 2 6 /5 .8 6 4 f o r F a d d ic k 's data and 8 .4 1 2 /5 .8 6 4 f o r E l l i o t and
deMontmorency's d a ta ) are n e a r ly equal t o I when r a is e d t o the
0.288 power.
■ \
Summary o f llPseudoll-Lam ina r A n a ly s is
The c o r r e l a t i o n model proposed by MetZner and Reed f o r " la m in a r "
non-Newtonian flo w s was shown t o s a t i s f a c t o r i l y c o r r e l a t e th e headlo s s d ata o f the p re s e n t i n v e s t i g a t i o n .
In a d d i t i o n , th e model
61
a llo w s h e a d -lo s s c a l c u l a t i o n s f o r pipes w i t h d iam e te rs o t h e r than
those employed t o o b t a in th e c o r r e l a t i o n param eters.
The model
s t i p u l a t i o n s g ive n a t th e b e g in n in g o f CHAPTER I I I a re a ls o s a t i s f i e d
th e model s a t i s f i e s t h i s
p h y s ic a l phenomena and i s expressed in
terras o f param eters w h ich are r e a d i l y o b ta in e d i n th e la b o r a t o r y .
In CHAPTER I I ,
i t was shown t h a t th e Metzner-Dodge c o r r e l a t i o n
model f o r t u r b u l e n t non-Newtonian flo w s i s an e x te n s io n o f th e
la m in a r non-Newtonian model o f M etzner and Reed.
The success i n
u s in g th e Metzner-Reed model f o r th e "p s e u d o " - la m in a r r e g io n led
t o an e x a m in a tio n o f th e c o r r e l a t i o n model proposed by M etzner and
Dodge f o r th e " p s e u d o " - t u r b u le n t r e g io n .
The f l u i d b e h a v io r in d e x , n , and f l u i d
c o n s is te n c y in d e x , K,
were assumed t o be th e same v a lu e f o r t u r b u l e n t flo w s as f o r la m in a r
flo w s as s t a t e d by M etzn er and Dodge ( 1 4 ) .
The t u r b u l e n t c o r r e l a t i o n model o f Metzner and Dodge,
l//f
4 lo g _
n - 75
(Ren f 1" 11/ 2 ) 9
.4
(4 .8 )
n1-2
i s s i m i l a r t o E q uation 2 . 1 4 , P r a n d t l 1s u n iv e r s a l p ip e f r i c t i o n
law,
e xce p t th e c o n v e n tio n a l Reynolds number Rew i s r e p la c e d by the
g e n e r a liz e d Reynolds number Re , and c o n c e n tr a t io n e f f e c t s
are
9
75
1 2
in c lu d e d i n th e c o n s ta n t terms 4 /n *
and - . 4 / n ' .
However, as w i l l
be e x p la in e d i n th e f o l l o w i n g s e c t i o n , t h i s
t u r b u l e n t non-Newtonian model was n o t s a t i s f a c t o r y f o r c o r r e l a t i n g
62
th e w ood-chip h e a d -lo s s d ata o f th e " p s e u d o " - t u r b u le n t re g io n o f
th e p re s e n t i n v e s t i g a t i o n .
PSEUDO-TURBULENT ANALYSIS
The h e a d -lo s s d a ta o f th e p r e s e n t i n v e s t i g a t i o n f o r th e "p seu do"t u r b u l e n t r e g io n was e x t e n s i v e l y ana lyzed em ploying th e c o r r e l a t i o n
model p re s e n te d by Dodge and M etzner ( 1 4 ) , which i s an e x te n s io n o f
th e M e tz n e r- Reed a n a ly s is f o r th e la m in a r f lo w o f non-Newtonian f l u i d s
Dodge and M etzner propose t h a t n and K are th e same va lu e f o r
t u r b u l e n t f lo w s as f o r la m in a r f l o w s .
To check t h i s a ssum ptio n,
n and K were c a l c u l a t e d from E q uation 4 .8 using th e data which
appeared t o be in th e " p s e u d o " - t u r b u le n t range i n t h i s i n v e s t i g a t i o n .
A n o n - l i n e a r r e g r e s s io n a n a ly s is was employed.
The n and K v a lu e s o b ta in e d d id n o t agree w i t h th e values
c a l c u l a t e d from th e "p s e u d o " - !a m in a r d a ta .
The d i f f e r e n c e s between
n v a lu e s f o r th e same c o n c e n tr a t io n and c h ip s iz e reached 30 p e rc e n t.
I t was found t h a t n and K values were f u n c t io n s o f v e l o c i t y , con­
c e n t r a t i o n , and p a r t i c l e s i z e .
T his f u n c t i o n a l r e l a t i o n s h i p was
c o n s id e re d to o cumbersome t o be o f v a lu e i n design problem s.
Based on th e p h y s ic a l c o n d it io n s observed i n th e f l o w s , one
would n o t e x p e ct n and K t o be th e same f o r " p s e u d o " - t u r b u le n t flo w s
as f o r " p s e u d o " - ! aminar flo w s o f wood c h ip s i n w a te r .
In "pseudo"-
t u r b u l e n t f l o w s , some o r a l l o f th e p a r t i c l e s are suspended in the
f l u i d medium; i n
"p s e u d o "- !a m in a r f l o w s , n e a r ly a l l
th e c h ip s have
63
s e t t l e d t o th e p ip e i n v e r t and are. dragged' o r r o l l e d a long the p ip e .
These c o n d it io n s g iv e two d i f f e r e n t d i s t r i b u t i o n s o f th e v e l o c i t y
and th e c o n c e n t r a t io n o f p a r t i c l e s .
The param eter K i s a measure o f th e v is c o u s fo r c e s p re s e n t a t
th e p ip e w a l l ,
tw
i n " la m i n a r " f lo w s .
p ip e w a ll
= K(8V /D )n
-------- ---------- ...........- ...............( 4 .1 )
Since more p a r t i c l e s are i n c o n t a c t w i t h the
i n "p s e u d o " - la m in a r flo w s than i n " p s e u d o " - t u r b u le n t f lo w s ,
K. s h o u ld n o t be expected t o be th e same f o r both modes o f t r a n s p o r t .
' The v a lu e o f n f o r Newtonian la m in a r p ip e flo w s i s o n e ; whereas
n f o r Newtonian t u r b u l e n t flo w s i s a p p ro x im a te ly 1.75 as in d ic a t e d by
th e d is c u s s io n i n CHAPTER I I f o l l o w i n g Equation 2 .1 7 .
Thus, the
va lu e s o f n shou ld be dependent on th e v e l o c i t y p r o f i l e o f th e f l u i d ,
/
w hich i n th e case o f wood c h ip s and w a te r i s a f u n c t io n o f th e average
s l u r r y v e l o c i t y and c o n c e n t r a t io n .
For th e se reasons a n o th e r c o r r e l a t i o n model was proposed f o r
th e " p s e u d o " - t u r b u le n t r e g io n .
The model was based on th e equ a tio n
— = A lo g (Re / f ) + E
/f
s
-------------------------:-------( 4 .9 )
where
f = Fanning f r i c t i o n
f a c t o r , d im e n s io n le s s
Res = Reynolds number o f s l u r r y , d im e n sio n le ss
65
: Rtg.= vopg
'
X
"
.
•
'
.
Ps = p s e u d o - v is c o s it y o f s l u r r y , I b f s e c / f t 2
Ps = d e n s it y o f s 1 u r r y - - ( t a k e n t o be w a te r d e n s it y f o r
O
c o n v e n ie n c e ) , s l u g / f t
A and E = e m p ir ic a l v a lu e s , d im e n s io n le s s .
E q uation 4 .9 i s modeled a f t e r P r a n d t l 1s u n iv e r s a l
law o f pipe
f r i c t i o n . E q uation 2 . 1 4 , j u s t as th e Metzner-Dodge model.
There were
t h r e e reasons f o r assuming a model o f t h i s form .
1.
The h e a d -lo s s d ata f o r th e " p s e u d o " - t u r b u le n t re g io n
o f a l l w o od-chip i n v e s t i g a t i o n s d e f in e curves s i m i l a r
t o th e c l e a r w a te r l i n e s defined: by Equation 2 .1 4 .
Curves p l o t t e d from th e h e a d -lo s s d ata f o r s l u r r i e s
o f wood c h ip s and w a te r approach th e c l e a r w a te r
curves a s y m p t o t i c a l l y w i t h in c r e a s in g v e l o c i t y .
2.
The e q u a tio n can be fo rc e d t o f i t
th e c l e a r w a te r
boundary c o n d i t i o n s , i f A and E are 4. and - . 4 ,
r e s p e c t i v e l y , f o r zero p e r c e n t c o n c e n t r a t io n .
3.
S l u r r i e s o f wood c h ip s and w a te r do n o t le nd them­
s e lv e s , t o c o n v e n tio n a l v is c o m e t r ic t e s t i n g .
In
o r d e r t o d e f in e a Reynolds number i n terms o f a
s l u r r y v i s c o s i t y , th e s l u r r y Reynolds number was
d e f in e d .
S ince th e s l u r r y v i s c o s i t y i s a d e fin e d
_________________________ ____________________ ___ ________ -
-
66
,
v a r i a b l e i t was one o f th e parameters t o be
o b ta in e d by an a n a ly s is o f th e d a ta .
Since t h r e e unknowns, A, E, and p , are p re s e n t i n E q uation 4 . 9 ,
two assum ptions were made:
1.
The r a t i o o f s l u r r y v i s c o s i t y t o th e c l e a r w a te r
v i s c o s i t y c o u ld be re p re s e n te d as a f u n c t i o n o f
c o n c e n t r a t io n , d e n s it y o f th e f l u i d , v e l o c i t y o f
th e f l o w , p ip e d ia m e te r and c h ip s i z e ,
UsZ r 0 = $•, ( C ,V ,D ,p s ,d )
------------------------------ (4 .1 0 )
and,
2.
The v a lu e s A, E, and
must be such t h a t e q u a tio n
( 4 . 1 ) reduces t o th e t u r b u l e n t c l e a r w a te r e q u a tio n .
E q uation 2 . 1 4 , f o r zero p e r c e n t c o n c e n t r a t io n .
The s l u r r y Reynolds number i s d e fin e d by
Reg - VDps
(4 .1 1 )
The s l u r r y o e n s it y pg i s taken t o be th e w a te r d e n s i t y , p , as e x p la in e d
i n CHAPTER I I I ,
and th e s l u r r y v i s c o s i t y i s d e fin e d by E q uation 4 .1 0 .
S u b s t i t u t i o n o f E q uation 4.10 i n t o E q uation 4.11 g iv e s th e e q u a tio n
Re
= VDl
---------------------------------------------------- (4 .1 2 )
67
E q u a tio n 4 .9 then becomes
-^Z
= A lo g (Rew / f ) + E - A Io g s 1 ..............................- ( 4 . 1 3 )
i n w hich Rew, th e e q u iv a l e n t c l e a r w a te r Reynolds number, and f are
measured v a lu e s .
Thus, a p l o t o f l / / f versus Iog(R ewZ f ) g iv e s A and
th e q u a n t i t y (E-A I o g s 1 ) as th e s lo p e and o r d in a t e i n t e r c e p t ,
re s p e c tiv e ly .
Employing th e second a s s u m p tio n , A i s fo r c e d t o th e v a lu e 4 . 0 ,
and lo g S1 t o zero f o r zero p e rc e n t c o n c e n t r a t io n .
S ince t h r e e unknowns, A, E, and S1 , a re in v o lv e d i n Equation
4 . 1 3 , E was a r b i t r a r i l y fo rc e d to be - . 4 f o r a l l
A cu rv e f i t t i n g
c o n c e n t r a t io n s .
procedure was employed to f i n d va lu e s o f A
and s-j f o r the h e a d -lo s s d ata o f th e p r e s e n t i n v e s t i g a t i o n .
E v a lu a tio n o f Parameters
F ig u re s 4 . 3 , 4 . 4 , 4 . 5 , and 4 .6 show th e h e a d -lo ss d a ta o f the
p r e s e n t i n v e s t i g a t i o n f o r the m ix t u r e sample, 0 . 8 7 5 - i n . , 0 . 5 0 - i n . ,
and 0 . 3 7 5 - i h .
c h ip g r a d a t i o n s , r e s p e c t i v e l y .
as 1 / Z f as a f u n c t i o n o f Iog(RewZ f ) .
W
The d a ta are p l o t t e d
S o lid l i n e s are shown to
e x h i b i t th e dependence o f 1 / Z f on I o g (RewZ f ) a t v e l o c i t i e s o f 10,
9, 8 , 7 , and 6 f t / s e c and 0 , 5, TO, 15, and 20 p e r c e n t c o n c e n tr a ­
tio n s .
The zero p e r c e n t c o n c e n t r a t io n l i n e re p re s e n ts P r a n d t l l s
u n iv e r s a l p ip e f r i c t i o n e q u a t io n . E q u a tio n 2 .1 4 .
The c l e a r w a te r
- 1 7. 0
1 6 . 0 h-
l//f
o
1 5 .0 cn
CO
14.0 “
1 3 . 0 t-
4
Figure 4.3
11Pseudo11-Turbulent Head-Loss Data fo r Mixture Sample
17.0
l//f
16.0
15.0
Chip s iz e = 0 .8 7 5 - in .
0 - 0 % cone.
O - 5%
"
14.0
10% "
A - 15% "
□
-
13.0 L
4
-
i — l __ I
4.05
4 .1
4.15
4 .2
Iog(R ew^T)
Figure 4.4
"Pseudon-Turbulent Head-Loss Data fo r 0.875-in. Sample
4.25
1 //F
0 - 5 % cone.
O
-
10%
A - 15%
"
"
O - 20% "
Iog(RewZ f)
Figure 4.5
"pseudo"-Turbulent Head-Loss Data fo r 0.50-in. Sample
l//f
Chip s iz e = 0 . 3 7 5 - in .
0 - 5 % cone.
10%
"
A - 15%
"
□
-
O - 20% "
l o g (Rew /T )
Figure 4.6
"Pseudon-Turbulent Head-Loss Data fo r 0.375-in. Sample
72
fric tio n
f a c t o r va lu e s o b ta in e d from the 3 . 9 3 - i n .
i n t e r n a l d ia m e te r
p ip e are shown i n F ig u re 4 . 4 .
An e x a m in a tio n o f F ig u re s 4 . 3 , 4 . 4 , 4 . 5 , and 4 .6 shows t h a t
l//f
i s a l i n e a r f u n c t i o n o f l o g ( R e y T ) , and t h a t A, th e slo p e o f
each c u r v e , and (.E-A l o g $ ^ ) , th e o r d in a t e i n t e r c e p t where
Iog(RewV f ) equ als z e r o , are both f u n c t io n s o n ly o f c o n c e n t r a t io n .
A lth o u g h th e r e i s a l i m i t e d amount o f e x p e rim e n ta l d a t a , th e s o l i d
l i n e s o f c o n s ta n t c o n c e n t r a t io n r e p r e s e n t th e measured data w i t h a
maximum d e v i a t i o n o f a p p ro x im a te ly 4 p e r c e n t.
The slo pes o f c o n s ta n t c o n c e n tr a t io n l i n e , A, in c re a s e w it h
in c r e a s in g c o n c e n t r a t io n from a magnitude o f 4 f o r c l e a r w a te r to
a p p ro x im a te ly 20 f o r 20 p e rc e n t c o n c e n tr a t io n depending on th e
c h ip s i z e .
F igures, 4 . 7 - a , 4 . 8 - a , 4 . 9 - a , and 4 .1 0 -a e x h i b i t A as
a f u n c t i o n o f c o n c e n t r a t io n f o r th e m ix t u r e sample, 0 . 8 7 5 - i n . ,
0 . 5 0 - i n . , and 0 . 3 7 5 - i n . c h ip s iz e g r a d a t io n s .
The v a lu e s o f Iogo^
c o rre s p o n d in g t o these A values are p l o t t e d in F ig u re s 4 . 7 - b ,
4 . 8 - b , 4 . 9 - b , and 4 . 1 0 - b .
Both A and ^
are l i s t e d in Table 4 .3 .
F r i c t i o n f a c t o r values were c a l c u la t e d from E q uation 4.13
u sin g th e Ve1Ues o f A and
l i s t e d i n T ab le 4 .3 and c l e a r w a te r
Reynolds numbers c o rre s p o n d in g to" each e xp e rim e n ta l d ata p o i n t o f
th is in v e s tig a tio n .
A comparison o f these c a lc u la t e d f r i c t i o n f a c t o r s
i s shown i n Table 4 . 4 .
Maximum and average p e rc e n t d e v i a t io n s
between these values a re shown' f o r each d a ta p o i n t o f each concen-
73
Table 4 .3
Chip Size
"Pseudo11- T u r b u le n t Flow Parameters
Parameter
M ix tu re
5%
C o n c e n tra tio n
15%
10%
20%
A
• $
5.87
20.71
6.81
53.48
9 .6 2
287.20
0 .8 7 5 -in .
A
$
6.09
29.7
8.82
231.7
12.51
835.60
0 . 5 0 - i n.
A
O
6.1
30.0
8 .02
142.56
10.20
434.7
13.80
1221.8
0 .3 7 5 -in .
A
$
5.43
14.08
7.51
99.77
11 .30
582.6
15.09
1445.40
Table 4 .4
Chip Sample
17.00
1970.15
E r r o r A n a ly s is o f Measured and P r e d ic te d
F r i c t i o n F acto rs f o r " P s e u d o "-T u rb u le n t Region
D e v ia t io n
%
5%
C o n c e n tra tio n
10%
15%
20%
± .2
.5%
M ix tu re
Avg. Dev.
Max. Dev.
± .3
.6%
± .1
.2%
± .2
.3%
0 .8 7 5 -in .
A vg. Dev.
Max. Dev.
.1
.2
.1
.3
.1
.3
0 .5 0 -in .
Avg. Dev.
Max. Dev.
.9
3.1
.1
.3
.1
.3
.2
.5
0 .3 7 5 -in .
Avg. Dev.
Max. Dev.
.0
.1
.1
.3
. .1
.2
.2
.4
—
74
30.
25.
Chip s iz e = M ix tu r e sample
A - d im en sion less
20 .
o
15.
10.
-
o
o
_L
5.
O
I
10.
J _ _ _ _ _ _ _ _ _ _ _ I___________ L
15.
20.
30.
C o n c e n tra tio n - %
F ig u re 4 . 7 - a
"Pseudo11- T u r o u l e n t C o r r e l a t i o n Parameters
Chip s iz e = M ix tu re sample
o
3.
lo g $
o
2.
o
o
I.
0.
£
J____________I____________I____________ I___________ I
5.
10.
15.
20.
25.
C o n c e n tra tio n - %
Figuer 4.7-b
"Pseudon-Turbulent Correlation Parameters
A - dim e n sio n le ss
Chip s iz e = 0 . 8 7 5 - i n .
C o n c e n tra tio n - %
F ig u re 4 . 8 - a
P s e u d o "-T u rb u le n t C o r r e l a t i o n Parameters
4.
Chip s i z e - 0 . 8 7 5 - i n .
o
lo g $
3.
o
2.
O
I.
J__________ I__________ I_________ I___________ L
5.
10.
15.
20.
C o n c e n tr a tio n - %
Figure 4.8-b
"Pseudo"-Turbulent Correlation Parameters
25.
76
30.
A - dim e n sio n le ss
25.
Chip s i z e = 0 . 5 0 - i n .
20 .
15.
o
10 .
o
o
o
5",
0.
J_________ I_________ I_________ I_________ i
5.
10.
15.
20.
25.
C o n c e n tra tio n - %
F ig u re 4 . 9 - a
"Pseudo11- T u r b u le n t C o r r e l a t i o n Parameters
Chip s i z e = 0 . 5 0 - i n .
3.
I og $
0
0
I.
'
0. m0.
I____________I____________I____________I___________ I
5.
10.
15.
20.
C o n c e n tr a tio n - %
Figure 4.9-b
"Pseudo11-Turbulent Correlation Parameters
25.
A - d im en sion less
Chip s iz e = 0 . 3 7 5 - i n .
C o n c e n tra tio n - %
F ig u re 4 .1 0 - a
"P s e u d o "- T u r b u le n t C o r r e l a t i o n Parameters
4.
Chip s iz e = 0 . 3 7 5 - i n .
lo g
3.
o
2.
o
O
I.
0. &0.
JL
J __________ I_________ I___________ L
5.
10.
15.
20.
C o n c e n tra tio n - %
Figure 4.10-b
"Pseudo"-Turbulent Correlation Parameters
25.
78
t r a t i o n in cre m e n t f o r th e f o u r w ood-chip s iz e g r a d a tio n s '.
The
maximum p e r c e n t d e v i a t i o n i s le s s than 4 p e rc e n t and th e maximum
average p e rc e n t i s le s s than I p e r c e n t.
Values o f A and j>^ in c re a s e w i t h in c r e a s in g c o n c e n t r a t io n as
shown i n Table 4 . 3 .
Values o f 3>-j in c re a s e from I a t zero p e rc e n t
c o n c e n tr a t io n t o a p p ro x im a te ly 2,000 f o r 20 p e rc e n t c o n c e n t r a t io n .
The values o f A and
a ls o show a t r e n d which in d i c a t e s t h a t A and
$1 decrease w i t h p a r t i c l e s i z e .
va lu e s o f A and ^
A t 15 p e rc e n t c o n c e n t r a t io n th e
f o r th e 0 . 8 7 5 - i n . c h ip s iz e a re a ls o a p p ro x im a te ly
10 p e rc e n t l a r g e r than th e e q u iv a l e n t va lu e s f o r th e 0 . 3 7 5 - i n . and
0 .5 0 -in .
c h ip s iz e .
T h is tr e n d i n d ic a t e s t h a t th e s l u r r y v i s c o s i t y , as d e fin e d by
E q uation 4 . 1 0 , in c re a s e s w i t h in c r e a s in g c o n c e n tr a t io n and has a
l a r g e r m agnitude f o r the l a r g e r c h ip s iz e s .
A p o s s ib le e x p la n a tio n
f o r t h i s phenomena i s as f o l l o w s :
The s l u r r y v i s c o s i t y f o r w ood-chips and w a te r in c re a s e s
w i t h in c re a s e d c o n c e n tr a t io n because more p a r t i c l e s come
i n t o c o n t a c t w i t h th e pipe w a ll a t h ig h e r c o n c e n tr a t io n s
■ S
and f r i c t i o n a l r e s is t a n c e between c h ip s and w a ll
in c re a s e s .
A ls o as c o n c e n tr a t io n in c re a s e s th e t u r b u l e n t s t r u c t u r e i s
damped due t o th e i n e r t i a and r i g i d i t y o f th e wood c h ip s .
The dependence o f s l u r r y v i s c o s i t y on c h ip s iz e can
p ro b a b ly b e s t be e x p la in e d by th e e f f e c t o f a s i n g l e c h ip
79
on th e t u r b u l e n t m o tio n .
T u r b u le n t f lo w i s c h a r a c t e r iz e d by v o r te x m otions
(e d d ie s ) o f v a r io u s s i z e .
I f a s o l i d p a r t i c l e i s s m a lle r
than th e . l a r g e s t e d d ie s , i t
sho u ld n o t c o m p le te ly dampen
th e t u r b u l e n t s t r u c t u r e .
The l a r g e s t eddies e n g u lf the
p a r t i c l e and t r a n s p o r t i t
as p a r t o f th e eddy.
Only the
s m a lle r edd ies would be a f f e c t e d by th e presence o f the
p a rtic le .
However, as th e p a r t i c l e s iz e in c re a s e s more
and more o f th e l a r g e r eddies are a f f e c t e d .
Thus, as
th e t u r b u l e n t s t r u c t u r e i s damped, g r a v i t a t i o n a l
fo r c e s
p r e v a i l , and p a r t i c l e s s e t t l e t o th e bottom o f th e
p i p e , and a d d i t i o n a l energy i s r e q u ir e d t o m a in ta in th e
flo w .
The e x p la n a tio n g iv e n above f o r th e dependence o f s l u r r y
v i s c o s i t y i s s p e c u l a t i v e , based on. observed p h y s ic a l c o n d it io n s o f
th e a c t u a l t r a n s p o r t o f wood c h ip s w i t h w a te r and on p re v io u s
e x p e rie n c e w i t h p ip e f lo w t u r b u le n c e .
Summary, o f "P s e u d o "- T u r b u le n t A n a ly s is
The c o r r e l a t i o n model proposed by M etzner and Dodge f o r
" t u r b u l e n t " non-Newtonian f l o w s , w h ic h i s an e x te n s io n o f th e
" la m i n a r " model o f M etzner and Reed, was n o t s a t i s f a c t o r y f o r
a n a ly z in g th e h e a d -lo s s data o f th e " p s e u d o " - t u r b u le n t r e g io n .
.8 0
The atte m p te d use o f t h i s model was based on th e s a t i s f a c t o r y
' a p p l i c a t i o n o f th e " la m i n a r " non-Newtonian model o f M etzner and
Reed t o " p s e u d o " - ! am inar h e a d -lo ss d a ta .
In s te a d a s i m i l a r model based on a s l u r r y v i s c o s i t y was
proposed.
S ince w o od-chip and w a te r s l u r r i e s
are n o t amenable to
c o n v e n tio n a l v is c o m e t r ic t e c h n iq u e s , th e s l u r r y v i s c o s i t y was
d e fin e d i n terms o f th e c l e a r w a te r v i s c o s i t y and c a l c u la t e d from
th e e x p e rim e n ta l d a ta .
The s l u r r y v i s c o s i t y , as d e f in e d , was
found t o v a r y fro m th e c l e a r w a te r v i s c o s i t y v a lu e , Jjq , f o r zero
p e r c e n t c o n c e n t r a t io n , t o more than 1000 tim es th e c l e a r w a te r
v i s c o s i t y f o r 20 p e r c e n t c o n c e n t r a t io n s .
The model s t i p u l a t i o n s g iv e n a t th e b e g in n in g o f CHAPTER I I
are a ls o s a t i s f i e d .
The " p s e u d o " - t u r b u le n t model i s re p re s e n te d
by th e p h y s ic a l phenomena and i s expressed in terms o f parameters
(fr ic tio n
f a c t o r , s l u r r y v e l o c i t y ) which are r e a d i l y o b ta in e d in
th e l a b o r a t o r y .
A lth o u g h th e model i s i m p l i c i t i n f , th e f r i c t i o n
f a c t o r , these v a lu e s o f f can be determ ined by an i t e r a t i v e
p ro c e d u re .
In a d d i t i o n . F ig u re s 4 . 3 , 4 . 4 , 4 . 5 , and 4 .6 c o n ta in
s u f f i c i e n t i n f o r m a t i o n t o be a p p lie d d i r e c t l y i n th e use o f the
d a ta f o r d e sig n p ro b le m s .
A comparison w i t h p r e v io u s w ood-chip i n v e s t i g a t i o n s , o t h e r
than th e q u a l i t a t i v e d e s c r i p t i o n g iv e n i n CHAPTER I I I ,
a tte m p te d .
was n o t
Water te m p e ra tu re d ata f o r th e i n v e s t i g a t i o n s o f
81
Soucy5 F a d d ic k 5 and E l l i o t and deMontmorency are n o t a v a i l a b l e ,
and f r i c t i o n
f a c t o r values co u ld n o t be c o r re c te d t o 60° F f o r a
d e t a i l e d q u a n t i t a t i v e comparison w i t h th e f r i c t i o n
o f th e p r e s e n t i n v e s t i g a t i o n .
f a c t o r values
CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
The h y d r a u l i c t r a n s p o r t o f wood c h ip s w i t h w a te r has been
examined.
E xp erim e ntal h e a d -lo s s data were recorded from f lo w
i n two p ip e s i z e s , 4 - i n . and 6 - i n .
nominal d ia m e te rs , f o r concen­
t r a t i o n in c re m e n ts t o 20 p e r c e n t by volume f o r f o u r d i f f e r e n t
w ood-chip g r a d a t i o n s .
Fanning f r i c t i o n
f a c t o r values were
c a l c u l a t e d and c o r r e c t e d t o 60° F f o r a n a ly s is purpo ses.
Based
on p h y s ic a l c o n s id e r a t io n s o f two-phase flo w s and an a n a ly s is
o f th e e x p e rim e n ta l d a t a , two d i s t i n c t modes o f t r a n s p o r t were
d e fin e d as "p s e u d o " - la m in a r and " p s e u d o " - t u r b u le n t .
The mode o f t r a n s p o r t i n th e " p s e u d o " - ! aminar r e g io n i s
s t r i c t l y one o f a s l i d i n g bed.
The v e l o c i t y a t which t h i s s l i d i n g
bed forms i s c h a r a c t e r iz e d as th e c r i t i c a l v e l o c i t y .
g r e a t e r than th e c r i t i c a l
v e l o c i t y th e t u r b u l e n t le v e l i n th e f l u i d
i s s u f f i c i e n t t o m a in ta in some, o r a l l ,
p e n s io n .
For v e l o c i t i e s
o f th e p a r t i c l e s i n sus­
T h is regime has been termed " p s e u d o " - t u r b u le n t .
'i Pseudoii - L a m in a r
model
The Metzner-Reed (20) a n a ly s is f o r la m in a r nonr-Newtonian flo w s
was employed t o c o r r e l a t e h e a d -lo s s d a ta from th e "pseu do"-Tam ina r
r e g io n .
The Metzner-Reed correlation equation
83
f = IGZReri
9
where
- V2-nP
a
Sn- 1K
c o n ta in s two f lo w p a ra m e te rs , n and K, w h ich c h a r a c t e r iz e th e f lo w
o f non-Newtonian f l u i d s .
and K, th e f l u i d
Values o f n, th e f l u i d b e h a v io r in d e x ,
c o n s is te n c y in d e x , were c a lc u la t e d from th e e x p e r i ­
mental h e a d -lo s s d a ta o f th e " p s e u d o " - ! aminar r e g io n .
Values o f n
decrease from a p p ro x im a te ly I f o r zero and 5 p e rc e n t t o a p p ro x im a te ly
0 .3 f o r 20 p e r c e n t c o n c e n t r a t io n s .
Values o f K in c re a s e from
th e c l e a r w a te r v i s c o s i t y , f o r zero p e r c e n t c o n c e n tr a t io n to
a p p ro x im a te ly 0.05 f o r 20 p e rc e n t c o n c e n t r a t io n .
F r i c t i o n f a c t o r va lu e s were c a l c u la t e d from th e Metzner-Reed
model and th e c a l c u la t e d va lu e s o f n and K f o r comparison w i t h
measured f r i c t i o n
f a c t o r v a lu e s .
The maximum p e rc e n t d e v i a t i o n
between c a l c u la t e d and measured va lu e s was 4 p e rc e n t and th e average
d e v ia tio n o f a l l
values i s c o n s id e r a b ly le s s than I p e r c e n t.
Thus,
an e x c e l l e n t c o r r e l a t i o n r e s u lt e d from the a p p l i c a t i o n o f th e .
Metzner-Reed model t o the h e a d -lo ss d ata o f the " p s e u d o "-!a m in a r
r e g io n .
The " p s e u d o " - ! aminar model and th e data o b ta in e d from the
6 - i n . d ia m e te r p ip e o f t h i s
fric tio n
i n v e s t i g a t i o n were employed t o p r e d i c t
f a c t o r values f o r f lo w in a 4 - i n . d ia m e te r p ip e f o r which
s i m i l a r e x p e rim e n ta l d ata were developed.
C o rre la tio n to w ith in
84
±4 p e rc e n t o f th e f r i c t i o n
p ip e r e s u l t e d .
f a c t o r s measured from th e 4 - i n .
dia m e te r
A s i m i l a r a n a ly s is o f d a ta from a n o th e r i n v e s t i g a t i o n
f o r 8 - i n . d ia m e te r p ip e f l o w d id n o t y i e l d s a t i s f a c t o r y r e s u l t s as
d e v i a t io n s o f th e o r d e r 30-50 p e r c e n t were noted between c a l c u la t e d
and e x p e rim e n ta l f r i c t i o n
fa c to rs .
A d e t a i l e d q u a n t i t a t i v e a n a ly s is
o f th e d a ta o f w o od-chip i n v e s t i g a t i o n s was n o t co n d u cte d .
Because
t h e i r w a te r te m p e ra tu re d ata were n o t a v a i l a b l e , and f r i c t i o n
fa c to rs
c o u ld n o t be c o r r e c te d t o 60° F f o r d i r e c t com parison.
The t r a n s i t i o n
from “ pseudo11- ! am inar f lo w occurs i n th e v e l o c i t y
range 5 . 5 - 7 . 5 f t / s e c f o r v o lu m e t r ic c o n c e n tr a t io n s t o 20 p e rc e n t
i n th e two p ip e s iz e s i n v e s t i g a t e d .
The c o rre s p o n d in g c r i t i c a l
g e n e r a liz e d Reynolds number i s a p p ro x im a te ly 3000.
"PSEUUOn-TURBULENT MODEL
An o r i g i n a l
c o r r e l a t i o n model was proposed f o r a n a ly s ts o f
h e a d -lo s s d ata o f th e l,p s e u d o " - t u r b u le n t r e g io n .
The model e q u a tio n
l / / f = A Iog(R e 5 Z f ) + E
was p a tte r n e d a f t e r P r a n d T t1s e q u a tio n f o r f r i c t i o n a l
p ip e f l o w .
r e s is t a n c e in
T h is model i s based on a s l u r r y Reynolds number d e fin e d as
Reg = VDp5Zp5
where P5 i s a s l u r r y v i s c o s i t y .
The v a lu e E was fo r c e d t o be - . 4 f o r a l l c o n c e n tr a t io n s to
s a t i s f y th e c l e a r w a te r boundary c o n d i t i o n s t i p u l a t e d by P r a n d t l 1s
e q u a tio n f o r t u r b u l e n t p ip e f lo w .
85
Since w o od-chip and water, s l u r r i e s
are n o t amenable t o con­
v e n t io n a l v is c o m e t r ic te c h n iq u e s , th e s l u r r y v i s c o s i t y was d e fin e d
as
jjS = ^ V l ( V ' D , C , d )
and c a l c u la t e d from th e e x p e rim e n ta l d a t a .
The s l u r r y v i s c o s i t y ,
as d e f in e d , was found t o be a d e f i n i t e f u n c t i o n o f w ood-chip
c o n c e n t r a t io n and a le s s e r f u n c t i o n o f c h ip s iz e .
The s l u r r y
v i s c o s i t y in c re a s e s from n , th e c l e a r w a te r v i s c o s i t y , f o r zero
p e r c e n t c o n c e n t r a t io n t o b e t t e r than 1000 tim es th e c l e a r w a te r
v i s c o s i t y f o r 20 p e rc e n t c o n c e n t r a t io n .
C orresponding values o f th e param eter A were found t o v a ry w i t h
c o n c e n tr a t io n from th e v a lu e 4 .0 f o r zero p e rc e n t c o n c e n tr a t io n
t o a p p ro x im a te ly 20 f o r 20 p e rc e n t w ood-chip c o n c e n t r a t io n .
F r i c t i o n f a c t o r v a lu e s c a l c u la t e d from th e t a b u la t e d values
o f A and ^
and th e model e q u a tio n i n d i c a t e a maximum p e r c e n t
d e v i a t i o n from measured f r i c t i o n
p e r c e n t.
f a c t o r values o f le s s than 4
The average d e v i a t io n among these values i s
le s s than
I p e r c e n t, i n d i c a t i n g an e x c e l l e n t c o r r e l a t i o n .
Thus,
i t can be concluded t h a t h e a d -lo s s values f o r the
h y d r a u l i c t r a n s p o r t o f wood chips w i t h w a te r are s a t i s f a c t o r i l y
analyzed by s e p a r a tin g o f th e data i n t o a " p s e u d o " - ! am inar re g io n
and a "p s e u d o " - tu .r b u le n t r e g io n , both from th e a n a l y t i c a l s ta n d ­
p o i n t and fro m th e s t a n d p o in t o f observed t r a n s p o r t c o n d i t i o n s .
-
86
RECOMMENDATIONS
. Based on th e r e s u l t s o f t h i s
i n v e s t i g a t i o n , th e f o l l o w i n g
recommendations are made:
1.
That f u r t h e r i n v e s t i g a t i o n s be made in p ip e s iz e s 8 - i n .
and l a r g e r t o s o lv e th e p ip e d ia m e te r dependence
problem i n th e " p s e u d o " - t u r b u le n t re g io n and t o check
■the v a l i d i t y o f th e proposed " p s e u d o - tu r b u le n t
c o r r e l a t i o n a n a ly s i s .
2.
That f u r t h e r i n v e s t i g a t i o n s be made w i t h i n d i v i d u a l
c h ip s iz e s t o dete rm in e s p e c i f i c a l l y th e r o l e o f c h ip
s iz e on h e a d -lo s s and t o c o r r e l a t e i n d i v i d u a l c h ip
s iz e e f f e c t s t o h e a d -lo ss va lu e s observed f o r c o n g lo ­
m erate m ix t u r e samples.
3.
That an i n v e s t i g a t i o n be und ertaken t o d e te rm in e th e
/
a c t u a l t u r b u le n c e i n t e n s i t y o f th e f l u i d phase as a
f u n c t i o n o f s l u r r y v e l o c i t y and c o n c e n t r a t io n .
A lth o u g h seem in gly academ ic, such an i n v e s t i g a t i o n would i n d i c a t e
th e a c tu a l t r a n s p o r t mechanism, and show how t h i s mechanism is
a f f e c t e d by th e presence o f wood c h ip s .
This i n v e s t i g a t i o n would
a ls o be o f im p o rta n c e f o r a l l two-phase f lo w s .
REFERENCES CITED
H u n t, W. A . , "Economic A n a ly s is o f a Wood-Chip P i p e l i n e , "
F o re s t P rodu cts J o u r n a l , V o l . 17, No. 9 , September,
1967, p p . 6 8-74 .
Wasp, E. J . , "Economics o f Chip T r a n s p o r t a t i o n , " TAPPI,
2 1 s t E n g in e e rin g C o nfe re nce, B o ston , M assa ch u se tts,
O c to b e r, 1966.
S ch m id t, R. E . , An I n v e s t i g a t i o n o f th e E f f e c t s o f Pressure
and Time on th e S p e c i f i c G r a v i t y , M o is tu r e Content and
Volume o f Wood Chips i n a Water S l u r r y , M.S. T h e s is ,
C i v i l E n g in e e rin g D e p t . , Montana S ta te U n i v e r s i t y , Bozeman,
1965.
E l l i o t , D. R ., and W. H. deMontmorency, "The T r a n s p o r t a t io n
o f Pulpwood Chips i n P i p e l i n e s , " Pulp and Paper Research
I n s t i t u t e o f Canada, T e c h n ic a l R e p o rts , 334 s e r i e s ,
A u g u st, 1963.
" P i p e l i n e to C a rry Coal from A riz o n a to Nevada," ASCE CE, News
B r i e f s , March 1967, page 103.
Hoffman, I . C ., A Method f o r O p tim iz in g a Network o f P ip e lin e s
f o r T r a n s p o r t in g Wood C h ip s , M.S. T h e s is , C i v i l E n g in e e rin g
D e p t . , Montana S ta te U n i v e r s i t y , Bozeman, 1966.
C h a rle y , R. W., The E f f e c t o f Chip-Shaped S o lid s on Energy
Losses i n A x is y m m e tric Pipe E xp a n sio n s, M.S. T h e s is ,
C i v i l E n g in e e rin g D e p t . , Montana S ta te U n i v e r s i t y , Bozeman,
1966.
Johnson, D. A . , The E f f e c t o f Chip-Shaped S o lid s on Valve
Head-Loss C h a r a c t e r i s t i c s , M.S. T h e s is , C i v i l E n g in e e rin g
D e p t . , Montana S ta te U n i v e r s i t y , Bozeman, 1968.
Page, K. L . , The E f f e c t o f Chip-Shaped P a r t i c l e s on Pump
Performance C h a r a c t e r i s t i c s , M.S. T h e s is , C i v i l E n g in e e rin g
D e p t . , Montana S ta te U n i v e r s i t y , Bozeman, 1966.
88
10.
F a d d ic k , R. R ., The H y d r a u lic T r a n s p o r t a t io n o f S o lid s
in P i p e l i n e s , R h.D.' D i s s e r t a t i o n , C i v i l E n g in e e rin g
D e p t. , Montana. S ta te U n i v e r s i t y , Bozeman, 1970.
11.
C arste ns, M. R ., "A Theory f o r Heterogeneous Flow o f
S o lid s i n P ip e s , " ASCE J o u rn a l o f H y d ra u lic s D i v i s i o n ,
V o l . 95, No. H Y l, Proc. paper 6154, Jan. 1969,
p p . 275-285.
12.
Z a n d i, I . and G. G ovatos, "Heterogeneous Flow o f S o lid s
i n P i p e l i n e s , " ASCE J o u rn a l o f th e H y d ra u lic s D i v i s i o n ,
Paper No. 5244, V o l . 93, No. HY3, May, 1967, pp. 145-59.
13.
G r o v i e r , G. W. and M. E. C h a r le s , "The H y d r a u lic s o f th e
P i p e l i n e Flow o f S o l i d - L i q u i d M i x t u r e s , " The E n gin e e r. in g J o u r n a l , A u gust, 1961, pp. 50-57.
14.
Dodge, D. W., and M e tzn e r, A. B . , " T u r b u le n t Flow o f NonNewtonian S ystem s," A .I.C H .E . J o u r n a l , V o l . 5 , No. 2,
June, 1959, pp. 189-203.
15.
Durand, R. and E. Condoli o s , "The H y d r a u lic T r a n s p o r t o f
Coal and S o l i d M a t e r i a ls i n P ip e s , " Proc. o f a
C o lloquium on the H y d r a u lic T r a n s p o rt o f C o a l, S c i e n t i f i c
D e p t . , N a tio n a l Coal Board o f G reat B r i t a i n , Nov. 1952.
16.
M c C o ll, B. j . , Data s u p p lie d t o p r o j e c t by Pulp and Paper
Research I n s t i t u t e o f Canada.
17.
. F a d d ic k , R. R ., "The Aqueous T r a n s p o r t a t io n o f Pulpwood
Chips i n a F o u r-In c h Aluminum P i p e l i n e , M.S. T h e s is ,
Queen's U n i v e r s i t y a t K in g s to n , O n t a r io , 1963.
18.
F a d d ic k , R. R ., " L i g h t Plate-S haped P a r t i c l e s and th e
Durand E q u a t io n ," paper p resen ted a t I n t e r n a t i o n a l
Conference on H y d r a u lic T r a n s p o rt o f S o l i d s , B r i t i s h
Hydromechanics Research A s s o c ia t io n , C o v e n try , England,
September, 1970.
19.
Babcock, H. A . , "Heterogeneous Flows o f Heterogeneous
S o l i d s , " Paper p resen ted t o th e I n t e r n a t i o n a l Sym­
posium on S o l i d - L i q u i d Flow i n Pipe and i t s A p p l i c a t i o n
t o S o lid -W a s te C o l l e c t i o n and Removal, U n i v e r s i t y o f
P e n n s y lv a n ia , P h i l a d e l p h i a , P a . , March 4 - 6 , 1968.
89
20.
M e tz n e r, A. B. and J . C; Reed, "Flow o f Non-Newtonian
F lu id s — C o r r e la tio n o f th e L am in ar, T r a n s it io n , and
.T u rb u le n t-flo w . R e g io n s ," A .I.C H .E . J o u r n a l, V o l. I ,
No. 4 , December, 1955, pp. 431-440.
21.
M iddlem an, S ta n le y , The Flow o f High P o lym e rs, In te rs c ie n c e
P u b lis h e r s , New Y o rk, 1968.
22.
S k e lland, A .H .P ., Non-Newtonian Flow and Heat T r a n s f e r ,
J . W ile y & Sons, In c .., New Y o rk, 1967.
23.
F u lk e rs o n , E. F. and J . E. R inne , " G ils o n it e S o lid s Pipe
L in e , " ASCE J o u rn a l o f th e P ip e lin e D iv is io n , V o l. 85,
No. P L l, Jan. 1959, P a rt I .
24.
Soucy, A.. Data s u p p lie d to p r o je c t by Laval U n iv e r s it y ,
Quebec C it y , Quebec, D e c ., 1968.
25.
Knudsen, J . G. and D. L. K a tz , F lu id Mechanics and Heat
T r a n s f e r , M cG raw -H ill Book Company, New Y o rk , 1958.
A P P E-N D I C E S
■APPENDIX A
EXPERIMENTAL SYSTEM AND TEST PROCEDURES
The a c q u is it io n o f h e a d -lo s s d a ta f o r any in v e s t ig a t io n such
as th e p re s e n t one r e q u ire s t h a t th e p ip e lin e t e s t lo o p f u n c tio n
p r o p e rly and r e li a b l e t e s t procedures be e s ta b lis h e d .
The fo llo w in g
is an o u t lin e o f th e e x p e rim e n ta l system and t e s t p roced ure s used
in th e p re s e n t in v e s t ig a t io n .
A more d e ta ile d d e s c r ip tio n o f th e
b a s ic e x p e rim e n ta l system can be found in F a d d ic k 's .P h .D .
( 10 ) .
d is s e r t a t io n
EXPERIMENTAL SYSTEM
The b a s ic model p ip e lin e t e s t f a c i l i t i e s
o f 4 - in . d ia m e te r p ip e and 160 f t o f 6- i n .
in s e r ie s w ith s u ita b le t r a n s it io n s .
c o n s is te d o f 500 f t
d ia m e te r p ip e connected
An assembly o f m echanical
and e l e c t r i c a l equipm ent was employed to i n j e c t th e wood c h ip s
in t o th e p ip e lin e , pump th e s lu r r y o f w a te r and wood c h ip s , and
s e p a ra te th e wood c h ip s from th e tr a n s p o r tin g w a te r.
A schem atic
diagram o f th e p h y s ic a l system is shown in F ig u re A - I .
■
\
P ip e lin e
The 5 0 0 -f t t e s t lo o p o f 4 - in . d ia m e te r p ip e c o n ta in e d 2 0 - f t
s e c tio n s o f aluminum p ip e , 18 to 20- f t s e c tio n s o f tra n s p a r e n t
a c r y li c p ip e , and 6- f t s e c tio n s o f a c r y li c p ip e connected by
92
V ic ta u T ic and D re sse r c o u p lin g s ..
The t e s t s e c tio n f o r th e 4 - in .
d ia m e te r p ip e , shown in F ig u re A - I , c o n s is te d o f a p p ro x im a te ly
230 f t o f s t r a i g h t , 'h o r i z o n t a l a c r y li c p ip e .
A 6 0 - f t s e c tio n was
used f o r e n tra n c e le n g th to a llo w th e s lu r r y flo w t o deve lop
c o m p le te ly a f t e r p a s s in g th ro u g h bends in th e p ip e lin e upstream
o f th e e n tra n c e s e c tio n .
Four p ie z o m e te r r in g s , spaced a p p ro x im a te ly 55 f t a p a rt
o v e r th e 2 3 0 - f t t e s t le n g th p ro v id e d p re s s u re taps f o r h e a d -lo ss
measurem ents.
in F ig u re A - I .
The lo c a tio n o f th e se p ie zo m e te r r in g s are shown
Each p ie z o m e te r r in g c o n s is te d o f f o u r , 1 / 8 - in .
d ia m e te r, h o le s spaced 90° a p a rt around th e c irc u m fe re n c e o f th e
p ip e .
M e rc u ry -w a te r manometers were employed to measure f r i c t i o n
p re s s u re lo s s v a lu e s .
The average in t e r n a l d ia m e te r o f th e 2 3 0 - f t t e s t s e c tio n was
3.9 3 in .
Measurements were made a t b o th ends o f th e in d iv id u a l
p ip e le n g th s a t f o u r a n g u la r p o s itio n s and averaged.
The 160 f t o f 6- i n .
d ia m e te r p ip e c o n ta in e d 90 f t o f
h o r iz o n t a l, s t r a i g h t t e s t s e c tio n f o llo w in g 60 f t o f e n tra n c e
le n g th as shown in F ig u re A - I .
The 160 f t o f 6- i n . d ia m e te r pipe
c o n s is te d o f f i v e 3 0 - f t le n g th s and one 1 0 - f t le n g th .
Three p ie z o m e te r r in g s p ro v id e d p re s s u re taps f o r h e a d -lo ss
measurements o v e r 6 0 - f t and 9 0 - f t le n g th s .
shown in F ig u re A - I .
The p o s itio n in g is
Each p ie zo m e te r r in g c o n s is te d o f f o u r , l/S - ^ in .
5.
6.
7.
8.
9.
C le a r w a te r li n e
W ood-chip hopper
Auger d r iv e m otor
Conveyer b e lt
W ood-chip s to ra g e
F ig u re A - I
14.
15.
16.
17.
6- i n . t e s t s e c tio n
Reducer
4 - i n . t e s t s e c tio n
P ressure taps
Schem atic o f E xp e rim e n ta l System
94
d ia m e te r, h o le s spaced 90° a p a rt around th e c irc u m fe re n c e o f th e p ip e .
Manometers c o n ta in in g c a r b o n te tr a c h lo r id e and w a te r were employed
t o measure f r i c t i o n a l p re s s u re lo s s v a lu e s .
The in t e r n a l d ia m e te r o f th e nom inal 6- i n . d ia m e te r p ip e was
5.864 i n .
Measurements were made a t b o th ends o f each p ip e le n g th
a t f o u r a n g u la r p o s itio n s and averaged.
To a d e q u a te ly d e s c rib e th e m echanical system in c y c lin g th e
wood c h ip s th ro u g h th e t e s t lo o p , i t
is nece ssary t o f o llo w th e
pa th o f th e c h ip s and w a te r s te p - b y - s te p .
F ig u re A -2 i l l u s t r a t e s
th e equipm ent w h ich in je c t e d th e wood c h ip s in t o th e w a t e r - f i l l e d
p ip e lin e and s e p a ra te d th e wood c h ip s fro m th e w a te r.
Wood-Chip and W ater S torage
Wood c h ip s were s to re d in a dual purpose ta n k , h a l f f o r w a te r
s to ra g e and h a l f f o r th e s to ra g e o f wood c h ip s when th e system was
n o t in o p e ra tio n .
Wood-Chip I n je c t io n
The system was s t a r t e d w ith c le a r w a te r pumped th ro u g h the
p ip e lin e .
Wood c h ip s were removed fro m th e s to ra g e hopper in 3 0 -g a l
b a r r e ls and ra is e d a p p ro x im a te ly 12 f t where th e y were em ptied onto
a conve yor b e l t w h ich t r a n s fe r r e d them t o a r e te n tio n h op per.
The
r e te n tio n hopper h e ld a p p ro x im a te ly 9 c u b ic f e e t o f lo o s e ly -p a c k e d
wood c h ip s and p ro v id e d a b u f f e r s to ra g e once th e system had
95
s t a b iliz e d a t a d e s ire d c o n c e n tr a tio n .
The wood ch ip s were conveyed
v e r t i c a l l y downward w ith a 9 - in . g r a in auger from th e r e te n tio n
hopper in t o a n o th e r ta n k where th e wood ch ip s and w a te r were m ixed.
T h is auger was d r iv e n by a 1 /2 hp a lt e r n a t in g c u r r e n t m o to r,
coupled th ro u g h a v a r ia b le speed g ea r re d u ce r to p ro v id e a c o n tr o lle d
q u a n tity o f wood c h ip s in t o th e m ix - ta n k .
The m ix -ta n k was a c y l i n d r ic a l ta n k , 3 f t in d ia m e te r, equipped
w ith a c o n ic a l s e c tio n w hich was th e i n l e t o f th e s u c tio n li n e o f
th e s o lid s - h a n d lin g ' pump.
Wood c h ip s were d is c h a rg e d fro m th e auger
housing near th e to p o f t h is
c o n ic a l i n l e t .
T his was a p p ro x im a te ly
10 to 12 i n . below th e w a te r le v e l m a in ta in e d in th e m ix -ta n k .
C le a r w a te r was pumped from th e w a te r s to ra g e ta n k th ro u g h a
s h o r t s e c tio n o f 4 - in . d ia m e te r p ip e , w hich co n ta in e d a 3 - in .
m a g n e tic flo w m e te r, in t o th e m ix -ta n k u s in g a 4 - in . c e n t r if u g a l
pump d r iv e n by a 15 hp, 2 2 0 - v o lt , d i r e c t c u r r e n t m o to r.
C le a r
w a te r flo w ra te s were c o n t r o lle d by th e v a r ia b le speed o f th e
d i r e c t c u r r e n t m oto r and by a t h r o t t l i n g
v a lv e lo c a te d in th e lin e
between th e f lo w m ete r and th e m ix - ta n k .
The j e t o f w a te r e n te re d
th e m ix -ta n k t a n g e n t ia lly and c re a te d a fo rc e d v o r te x w ith a
d ir e c t io n o f r o t a t io n o p p o s ite to t h a t o f th e auger.
T h is a c tio n ,
p ro v id e d s u f f i c i e n t a g it a t io n to c o m p le te ly d is p e rs e th e wood c h ip s
in th e w a te r.
The s lu r r y was th e n drawn in t o th e s u c tio n li n e o f th e
s o lid s - h a n d lin g pump.
drum m otor
s e p a ra tio n drum
auger d r iv e
VD
CM
m ix tank
F ig u re A-2
Wood-Chip I n je c t io n and S e p a ra tio n Equipment
97
S o lid s -H a n d lin q Pump
The s u c tio n li n e
d ia m e te r a c r y li c p ip e .
in t o th e s o lid s - h a n d lin g pump was a 4 - in .
A lth o u g h t h is pump had a 5 - in . d ia m e te r
i n l e t , a 4 - in . s u c tio n p ip e was used to m a in ta in a v e l o c it y s u f f i c i e n t
to keep th e wood c h ip s d is p e rs e d in th e w a te r.
Dry wood, i n i t i a l l y
in je c t e d in t o th e system , tended t o c o l le c t a t th e to p o f a 5- i n .
d ia m e te r s u c tio n li n e because o f th e lo w e r v e lo c it ie s and lo w e r
le v e l o f tu rb u le n c e .
The s o lid s - h a n d lin g pump was a H a ze lto n
5 - in . CTL c e n t r if u g a l pump w ith a 1 2 - in . im p e lle r s p e c i f i c a l l y
c o n s tru c te d f o r pumping la rg e s o lid p a r t ic le s .
The pump was d riv e n
by a 25 hp, 2 4 0 - v o lt , d i r e c t c u r r e n t m o to r w ith v a r ia b le speed
c o n tr o l t o p ro v id e v a r ia b le s lu r r y flo w r a te s .
Flow M eters
S lu r r y flo w ra te s were measured w ith a 4 - in .
Foxboro m agnetic
flo w m ete r p o s itio n e d .a p p r o x im a te ly 10 f t downstream o f th e s o lid s h a n d lin g pump.
C le a r w a te r flo w ra te s were measured w ith a 3 - in .
Foxboro m a g n e tic flo w m e te r.
Each flo w m eter was equipped w ith
r e c o r d e r s , and flo w ra te s were p e rm a n e n tly re c o rd e d .
The v o lu m e tr ic c o n c e n tra tio n o f wood c h ip s was d eterm ined
fro m th e d iff e r e n c e in th e flo w ra te s o f s lu r r y and c le a r w a te r and
c a lc u la te d from th e f o llo w in g r e la t io n :
% C o n c e n tra tio n
, Q M - J c w xloo
98
The w o o d -ch ip and w a te r s lu r r y was pumped th ro u g h th e t e s t loop
p ip e lin e where h e a d -lo s s measurements were made.
S e p a ra tio n o f Wood Chips From W ater
A t th e end o f th e p i p e lin e , th e s lu r r y o f wood .ch ip s and w a te r
was d is c h a rg e d in t o an in c lin e d , r o t a t in g c y l i n d r i c a l screen open to
th e atm osphere to s e p a ra te th e wood c h ip s fro m th e w a te r.
The wood
c h ip s tum b led th ro u g h th e le n g th o f th e c y li n d r ic a l scre e n onto th e
co nve yor b e l t w h ich t r a n s fe r r e d them back to th e r e te n tio n hopper f o r
r e - c y c lin g .
W ater d ra in e d from th e ch ip s in th e screen and was c o lle c te d
in th e e le v a te d w a te r s to ra g e ta n k and a ls o r e - c y c le d .
When a p a r t ic u l a r t e s t was c o m p le te d , th e wood c h ip s were
d iv e r te d o f f th e conve yor b e l t in t o th e w o od-chip s to ra g e ta n k
in s te a d o f r e tu r n in g to th e r e te n tio n hopper.
The t e s t procedure
e s ta b lis h e d to p ro v id e th e a c q u is it io n o f a c c u ra te h e a d -lo s s da ta
is p re se n te d in th e f o llo w in g s e c tio n .
TEST PROCEDURE
C le a r w a te r was pumped th ro u g h th e system p r io r t o in je c t in g
th e wood c h ip s .
D u ring t h is p e rio d h e a d -lo s s measurements and flo w
r a te s were re co rd e d and. used to c a lc u la t e c le a r w a te r f r i c t i o n
fa c to rs .
These were compared to va lu e s c a lc u la te d fro m Drew 's E q u a tio n (2 5 ).
f = .0014 + .125/Re
(A. I )
99
T h is com parison p ro v id e d a check o f th e in s tru m e n ta tio n
c a lib r a tio n
b e fo re wood c h ip s were added t o th e flo w .
Wood ch ip s were in je c t e d in t o th e system a t a slo w r a te u n t i l
th e d e s ire d c o n c e n tra tio n was a t ta in e d .
W ith th e system f u l l y
s t a b il iz e d , th e f o llo w in g da ta were re c o rd e d :
Qmix, Qcw, manometer
re a d in g s , and w a te r te m p e ra tu re .
A d a ta a c q u is it io n run c o n s is te d o f m easuring f r i c t i o n a l
p re s s u re lo s s e s f o r a range o f s lu r r y flo w ra te s a t a p a r t ic u la r
w o o d -ch ip c o n c e n tr a tio n .
C o n c e n tra tio n was v a r ie d in 5 p e rc e n t,
by volum e, in cre m e n ts to 20 p e rc e n t.
APPENDIX B
TABLE B .1
PIPE INTERNAL DIAMETER = 5.864 in .
PIPE MATERIAL = ALUMINUM
CHIP SIZE = MIXTURE SAMPLE
C o n c e n tra tio n
C-%
S lu r r y
V e lo c it y
V -ft/s e c
W ater
Temp.
0F
F r ic t io n
F a c to r
fT
F r ic t io n
F a c to r
Reynolds
Number
f 60
5.0 0
5.10
5.00
5.00
4 .9 7
■ 4.193
3.896
3.564
3 .124
2.756
5 2.3
52.3
52.3
52.3
52.3
.00565
.00612
.00655
.00783
.00931
.00548
.00593
.00634
.00755
.00897
168240
156326
142980
125340
110570
9.8 0
4.253
3.872
3.480
3.041
52.7
52.7
52.7
52.7
.00655
.00736
.00819
.01006
.00635
.00712
.00792
.00969
170624
155372
139645
13.7
14.7
15.5
4.074
3.730
3.421
53.8
53.8
53 .8
.00859
.01007
.01148
.00833
.00974
.01109
163475
149654
137262
20.0
4.158
3 .504
55.5
55.5
.01074
.01445
.01047
.01403
166811
140598
.00597
.00610
.00578
.00602
.00617
.00474
.00458
.00482
.00470
.00442
118198
120104
130113
130113
120104
152036
167764
152036
152513
167764
11.8
9.2 0
8.90
20.3
122010
CHIP SIZE = 0 . 8 7 5 - in .
*
5.14
5.06
6.7 3
6.7 3
5.00
6.5 7
6 .6 2
6.57
6.9 3
6 .6 2
2.946
2.993
3.243
3.243
2.993
3.789
4.181
3.789
3.801
4.181
75.7
64.1
64 .8
64 .8
64.1
65.2
81.1
■ 6 5.2
. 65 .2
81.1
.00568
.00605
.00571
.00595
.00612
.00469
.00431
.00476
.00464
.00416
IOl
C o n c e n tra tio n
W ater
Temp.
C-%
S lu r r y
V e lo c ity
V -ft/s e c
10.7
9 .9 5
9 .9 5
10.7
10 .7
1 0.7
1 0 .7
11.9
8 .8 7
8 .8 7
11.9
2.993
4.169
4.169
2.993
2.993
3.552
3.552
3.718
3 .267
3.267
3.884
66 .3
63.4
6 3.4
62 .3
6 2 .3
62 .7
62 .7
61 .6
62.1
62.1
63.1
.00857
.00571
.00561
.00842
.00829
.00648
.00670
.00640
.00714
.00720
.00586
13.4
14.10
14.1
14.1
14 .7
14.63
3.243
3 .5 5 2
3 .552
3 .5 5 2
4.039
3.991
66.1
66.1
66.1
66.1
.00822
.00733
,00735
.00746
.00639
.00641
of
66 .4
6 6 .4
F r ic t io n
F a c to r
fT
.
F r ic t io n
F a c to r
Reynolds
Number
f 60
Rew
.00860
.00574
.00564
.00845
.00832
.00651
.00673
.00641
.00716
.00721
.00589
120104
167288
167287
120104
120104
142504
142504
149176
131066
131066
155849
.00837
.00746
.00748
.00759
.00651
.00653
130113
1.42504
142504
142504
162045
160139
CHIP SIZE = 0 . 5 0 - in .
C
V
6,00
V
fT
f 60
3.849
4.110
3.279
3.564
61.6
61.6
63.1
61.6
.00488 '
.00459
.00641
.00590
.00488
.00459
.00645
.00590
154419
164905
131543
142981
9 .8 7
10.3
1 0 .5
9.8 6
4 .356
4.253
3 .2 7 8
3 .278
3.861
52.1
51.9
51.9
5 2.2
52.7
.00574
.00585
.00772
.00767
.00652
.00556
.00566
.00744
.00740
.00632
174914
170604
131543
131543
154896
15.0
15.5
15 .0
13 .8
13.8
3 .3 8
4.015
3 .338
3.600
3.600
58 .8
58 .8
5 8.8
58 .8
58 .8
.00922
.00685
.00932
.00823
.00831
.009.12
.00679
.00922
.00815
.00823
133926
161096
133926
144411
144411
5.23
5.6 2
5.0 0
10.1
Rew
102
C
V
yo
fT
f 60
13.8
15.5
15.2
3.706
4.015
4.253
58.8
58.8
57.1
.00784
.00697
.00666
.00776
.00690
.00655
20.0
4.110
61.6
.0103
.0103
Rew
•
148700
161092
170624
164905
CHIP SIZE = 0 .3 7 5 - in .
C
V
5.60
4 .9 3
5.3 0
4 .9 5
4.003
4.336
3 .600
3.124
52.1
52.1
52.0
52.0
.00494
.00478
.00565
.00641
.00480
.00464
.00547
.00620
160616
173960
144411
125347
9 .9 2
9 .9 4
10.3
9 .8 0
10.0
2.875
4.183
3.801
3.290
2.875
51.4
52.1
52.1
52.1
52.1
.00917
.00616
. .00677
.00791
.00935
.00880
.00596
.00654
.00762
.00896
115338
167764
152513
132019
115338
15.0
15.0
14.7
14.7
15.3
15.4
15.4
4.098
4.098
4.371
4.371
3.813
3.457
3.457
58.5
58.5
57.8
57.8
57.1
57.1
57.1
.00708
.00703
.00653
.00655
.00790
.00905
.00914
.00700
.00696
.00644
.00646
.00780
.00889
.00897
164428
164428
175390
175390
152989
138692
138692
20 .
3 .2 7
61.6
.0106
.0106
131070
T
fT
f 60
Rew
103
TABLE B.2
PIPE INTERNAL DIAMETER = 3 .9 3 0 - in .
PIPE MATERIAL = ACRYLIC
C o n c e n tra tio n
C-%
S lu r r y
V e lo c ity
V -ft/s e c
W ater
Temp.
0F
F r ic t io n
F a c to r
f
I
F r ic t io n
F a c to r
f
60
R eynolds
Number
Rew
CHIP SIZE = MIXTURE SAMPLE
C
5 .0 5
5.3 0
5 .8 0
V
fT
f 60
Re„
8 .9 1 2
9 .468
7.749
6.400
5.210
54.6
55 .5
55.7
55.7
55.7
.00383
.00373
.00392
.00408
.00445
.00376
.00367
.00385
.00401
.00437
239656
254590
208366
172097
140096
1 0.7
10.4
9 .6 0
9.8 5
8.833
7.405
8.146
6.612
5.739
56.6
56.5
56.5
56.6
56 .5
.00379
.00408
.00399
.00425
.00441
.00374
.00402
.00394
.00419
.00435
237523
199121
219033
177786
154319
15.2
14 .8
14 .8
8.146
7.167
6.268.
57.5
57.6
57.6
.00401
.00426
.00449
.00396
.00421
.00444
219033
192720
168542
19.9
20.9
20.3
8.886
57.6
57.6
57.6
.00443
.00505
.00534
.00438
.00499
.00534
238945
204099
179209
6.20
5.08
10.2
7.590
6.665
CHIP SIZE = 0 .8 7 5 - in .
C
5.1 0
5.20
5.26
4 .9 2
6.6 0
7 .5 0
V
T
8.833
8.146
7.035
5.924
7.220
8 .833
54.6
55.5
55.7
55.7
55.5
' 51.4
.
fT
.00397
.00406
.00421
.00445
.00447
.00396
f 60
Rew
.00389
‘ .00400
.00414
.00438
.00439
.00385
237522
219033
189165
159297
194143
237523
C
6.16
4.50
4 .9 0
V
T
8.146
7.035
5.924
52.0
5 3.5
54.3
11.9
11.9
8.6 3
9 .9 5
7.669
6.136
8.278
8.463
9.362
9.283
14.6
13.9
14.8
8.807
7.590
7.141
10.3
11.6
fT
8*
104
Rew
.00406
.00421
.00445
.00396
.00411
.00436
219033
189165
159297
59.8
59.8
6 1.6
61.6
63.0
63 .4
.00426
.00480
.00414
.00409
.00396
.00400
.00424
.00477
.00414
.00411
.00401
.00402
206233
164986
222589
227567
251746
249612
58 .2
58.2
6 0 .2 .
.00412
.00439
.00473
.00408
.00435
.00472
236812
204099
192009
.
CHIP SIZE = 0 . 5 0 - in .
C
V
.
T
5.6 2
5.58
4 .33
5.32
4 .9 5
3 .7 0
4 .0 8
7.09
5.87
5.11
5.32
5.23
7.300
8.595
9.071
7.960
7.908
10.37
9.89
11.03
6.850
6.744
7.008
7.008
66.8
66.8
66.8
66.6
9.7 6
8.146
8.595
8.251
8.357
11.45
9.468
7.300
57.1
56.4
67.3
67.0
6 7 .3
58.0
56.4
10.2
10.9
11.0
9.4 7
8 .3 8
9 .7 8
fT
62.5
6 1.8
61.4
6 1.8
6 5.8
63 .8
66.8
67 .5
.
'
f 60
Rew
.00414
.00395
.00389
.00404
.00390
.00375
.00380
.00363
.00416
.00418
.00423
.00418
.00415
.00396
.00389
.00404
.00395
.00377
.00386
.00370
.00423
.00425
.00430
.00425
196276
231122
243923
214055
212633
278769
265969
295648
184187
181342
188453
.188453
.00417
.00408
.00390
.00384
.00354
.00395
.00432
.00411
.00402
.00397
.00391
.00360
.00391
.00425
219033
231122
221878
224722
307926
254590
196276
105
G
V
T
15.2
15.5
13.2
14,6
9.468
8.939
8.013
7.432
59.8
60 .2
60.6
60.6
19.2
9.124
8.199
7.458
62 .4
51.4
51.4
20.0
20.2
CHIP SIZE
C
5.00
5.00
5.28
6 .9 2
4.71
4 .9 6
5,0 0
5.87
4 .8 7
V
9.653
8.913
10.50
10.76
10.44
9.600
6.955
6.850
7.405
I
61.1
61.1
67.9
fT
f 60
Rew
.00415
.00423
.00440
.00452
.00413
.00422
.00439
.00451
254590
240367
215477
199832
.00449
.00474
.00502
.00450
.00460
.00487
245346
220455
20543
0 .3 7 5 - in .
fT
f 60
Rew
61.3
.00380
.00390
.00369
.00367
.00371
.00381
.00424
.00416
.00404
.00380
.00390
.00376
.00374
.00377
.00388
.00424
.00423
.00404
259568
239656
282325
289437
280903
258146
187031
184187
199121
10.8
9.309
7.326
8.463
6.400
10.92
11.00
11.13
10.34
10.42
9.336
52.1
52.1
52.1
52.2
■ 63.8
63 .8
6 3 .8
64.1
64.4
64.1
.00391
.00434
.00395
.00456
.00363
.00362
.00362
.00376
.00370
.00388
.00381
.00422
.00384
.00444
.00366
.00365
.00365
.00378
.00373
.00392
250323
196987
227566
172097
293703
295837
299393
278058
280192
251035
15.0
15.0
15.0
14.6
15.0
13.4
14.6
14 .6
9.124
9.732
8.489
6.876
7.696
10.05
10.74
11.03
6 1 .2
61 .0
61.0
.00398
.00387
.00417
.00474
.00439
.00390
.00369
.00362
.00398
.00386
.00416
.00482
.00438
.00396
.00373
.00367
245345
261702
228278
184898
206944
270236
288726
296548
10.0
10.0
10.0
10.0
8 .5 8
10.0
10.3
10.1
9.19
68.0
67 .8
67 .8
61.1
66.8
66.8
61.0
66.8
66 .3
66 .3
106
C
V
T
20.0
20.0
7.458
8.198
51 .4
51.4
.00502
.00474
22 .4
23.9
23 .5
9.124
8.516
8.198
53.0
53 .0
53 .0
.00431
.00461
.00482
fT
dfM
f 60
.
Rew
.00487
.00460
200543
220455
.00420
.00449
.00469
245235
228989
220455
MONTANA STATE UNIVERSITY LIBRARIES
7 6 2 1001 0791 9
4• '
D378
GT1+?
cop. 2
Gow, John L .
The h y d r a u lic tra n s p o rt
o f wood chips
____________________ ^
iJ V
MAY
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