Experiments on the free shear layer between adjacent supersonic streams
by Timothy L Brower
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Mechanical Engineering
Montana State University
© Copyright by Timothy L Brower (1983)
Abstract:
A closed-form analytical theory has been developed to predict the flow field of two-dimensional,
laminar, non-equilibrium free shear layers, shed from the trailing edge of a thin flat plate serving as a
partition separating two dissimilar parallel flows. A Mach 3 supersonic nozzle in combination with
either a Mach 1.6 or a Mach 2 supersonic nozzle were used to produce a free shear layer. The
investigation was designed to provide experimental evidence by which free shear layer theories may be
checked. A comparison of theoretical/experimental mean flow properties in the laminar,
non-equilibrium region of the free shear layer were made. The theory showed good agreement
qualitatively, but poor agreement quantitatively when compared to experimental data. The theoretically
assumed initial velocity profile showed a 35 % difference in thickness compared to the experimental
thickness. The theory predicts free shear layer thickness and minimum velocity growth rates that
parallel the experimental results, although a quantitative error of between 20-50 % exists. EXPERIMENTS ON TEE FREE SHEAR LAYER
BETWEEN ADJACENT SUPERSONIC STREAMS
by
Timothy
L Brower
A t h e s i s subm itted in p a r t i a l f u l f i l l m e n t
of the r e q u i r e m e n t s f o r the degree
of
Master
of
Science
in
Mechanical
Engineering
MONTANA STATE UNI VE R S I T Y
Bozeman, Montana
March
1983
m a in
l ib
.
1439%
Ccp-A
APPROVAL
of
a
thesis
Timothy
submitted
by
L Brower
T h i s t h e s i s h a s b e e n r e a d by e a c h m em b er of t h e t h e s i s
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s t y l e , and c o n s i s t e n c y , and i s r e a d y f o r s u b m i s s i o n to the
C o l l e g e of G r a d u a t e S t u d i e s .
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Date
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for
the
Major
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Studies
iii
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V
ACKNOWLEDGEMENT
The
author
contribution
Eis
to
with
Anthony
the
Rompel
Harry
and
Barry
committee
members
Research
and
for
Special
c h ild re n
for
the
his
machine
wind
tunnel
Glenn
for
and
the
McCullough
thanks
during
his
his
shop
their
guidance
and
crew
for
their
m odifications .
for
their
p articip atio n
and
Bob
reviewed
U.S.
Air
in
W arrington
this
Engineering
financial
V ic to ria
encouragement
for
investigation.
and
Townes
Mechanical
U niversity
follow ing
assistance
equipment.
Townes,
design.
The
of
laboratory
the
Demetriades,
the
Williamson
construction
to
investigation.
throughout
Gordon
John
indebted
this
advisor,
cooperation
expert
is
the
nozzle
served
as
thesis.
Department
Force
of
Office
Montana
of
State
S cientific
assistance.
go
to
his
and
Skylar
this
graduate
wife
for
Cindi
th e ir
program.
and
his
two
support
and
vi
TABLE OF CONTENTS
Page
L I S T OF T A B L E S .............................................. ................................................... .....
LIST
,viii
OF F I G U R E S ...................................................................................................... i x
NOMENCLATURE
xiii
1.
I N T R O D U C T I O N ...............................................................
2.
THEORETI CAL REVI EW
3.
EXPERI MENTAL A P P R O A C H ...........................................................................
11
4.
EXPERI MENTAL APPARATUS AND P R O C E D U R E ....................... ..... .
Wind T u n n e l
...................................................................................... ..... .
P i t o t P r o b e ............................
S c h lie re n O p tical System. . . . . .
....................................
S t a ti c P re ssu re Probe
. .
. . ..........................................
T o tal T em perature Probe
...................................
H ot-F ilm Anemometer
.....................
Probe
P ositioning
................................................ . . . . . .
Data C o l l e c t i o n
. . . . . . . .................................................... 2 0
12
12
12
17
17
18
19
19
5.
EXPERI MENTAL DES I GN
.................................................................................
23
W i n d T u n n e l M o d i f i c a t i o n ...............................................................
23
Configuration I
........................................................................................ 26
C o n f i g u r a t i o n 1 1 ........................................................................................ 26
C o n f i g u r a t i o n I I I .................................................................................. 2 9
C o n f i g u r a t i o n I V ........................................................................................ 3 1
D iffuser M odification
. ...............................................................
35
6.
RESULTS
. . . . . . . . . . . . . . . . . . . . .
40
T r a i l i n g Edge B o u n d a r y L a y e r . . . . . . . . . . .
42
F r e e S h e a r L a y e r Me a n F l o w M e a s u r e m e n t s
. . . . .
49
T r a n s i t i o n D e t e r m i n a t i o n .............................
58
C o m p a r i s o n w i t h T h e o r y .......................................................................... 7 1
C o n f i g u r a t i o n I I I .............................................
72
C o n f i g u r a t i o n I V ........................................................................................ 75
7.
C O N C L U S I O N S ....................................................
.
.
.
.
.
.
.
.
.
I
.
.
.
.
.
............................ .....
.
.
4
78
vii
TABLE OF CONTENTS— Continued
Page
A P P E N D I C E S ......................................................................................................................... 81
AP PENDI X A
- Transition
AP P ENDI X B
- Tunnel
AP PENDI X C
—Wa v e
S t r u c t u r e s .......................................................................... 88
AP PENDI X D
- Data
Layer
R eduction Program ForBoundary
P r o f i l e s .....................................................................
90
- Data
Layer
Reduction
Profiles
93
AP PENDI X E
REFERENCES
CI TED
.
Theory
Vibration
Comparison
...........................
82
.............................................................
86
Program For Free Shear
.........................................................
96
viii
L I S T OF TABLES
Page
1.
Nozzle
configurations
2.
Nozzle
c o o r d i n a t e s .................................................... .....
3.
Optimum
4.
Boundary
layer
laminar
5.
Boundary
layer
8/6,
6.
Boundary
layer
and
7.
Summar y
operating
of
......................................................................
conditions
region
measured
edge
transition
.
34
..............................................
41
...............................................
42
v .
theory
.
.
25
. . . .
45
p r o p e r t i e s .................................... 51
determination
.............................
71
ix
L I S T OF F I GURES
Page
1.
Nomenclature
2.
FSL
development
3 .
FSL
development
4.
5.
6.
and
definitions
of
the
r
= 0
...........................
7
r
=
6^
= ©2 . .
7
T h e o r e t i c a l FSL d e v e l o p m e n t a t r = I a n d
r = . 5 .................................................... ...............................................................
9
at
at
y ' = 0 and
y'
= 0
and
T h e o r e t i c a l FSL d e v e l o p m e n t
v e l o c i t y g r o w t h a t y' = 0
2
major
13
Photograph
8.
Pitot
9.
S t a t i c p r e s s u r e v. d o w n s t r e a m d i s t a n c e p l o t
used to i n t e r p o l a t e unknown p r e s s u r e v a l u e s
c l o s e t o t h e T . E ..........................................................................................18
static
probe
collection
wind
10
7.
and
modified
I,
. . . .
a t r = 0 and minimum
. . . .....................................
Diagram of t h e wind t u n n e l showing
c o m p o n e n t s .........................................................
of
FSL
t u n n e l .............................
14
s c h e m a t i c .....................................
10.
Data
11.
Schematic
12.
Nomenclature
13.
S c h l i e r e n p h o t o g r a p h of C o n f i g u r a t i o n s I I and
I I a ................................................................................................................................ 2 8
14.
Photograph
15.
Schlieren
16.
Configuration
pieces 'butted'
IV s
slow -side
design.
together to form nozzle
17.
Photograph
Configuration
18.
Schlieren
of
block-diagram
tunnel
for
of
of
.
22
..................................
24
F S L ...........................................
27
m odification
deflected
Configuration
Photograph
photograph
................................ .....
15
of
of
III
..................................
Configuration
III
. . .
IV
32
Two
. . . .
I V ............................... ....
Configuration
30
. . .
33
.
33
.
36
X
LIST OF FIGURES— Con tinued
Page
19.
Configuration
20.
Configuration
21.
Schematic
22.
P q v . RMS B . L . t r a n s i t i o n t r a c e
Configuration III
.............................
23.
of
III
flow
IV
uniform ity
flow
variable
uniform ity
................................
37
. . . . . . . . .
37
d i f f u s e r ..................................... .....
39
for
........................
43
P q v . RMS B . L . t r a n s i t i o n t r a c e f o r
C o n f i g u r a t i o n I V . . .......................................................................
24.
Experim ental
25.
E x p e r i m e n t a l B.L.
5
v.
theory
. ... .....................................
46
26.
E x p e r i m e n t a l B.L.
G
v.
theory
............................................
46
27.
E x p e r i m e n t a l B. L .
comparison
to
Blasius
p r o f i l e ............................................................................................................47
28.
G r a p h i c a l c o m p a r i s o n o f t h e o r e t i c a l v.
experim ental p r o p e r t ie s e n te r in g the i n te g r a l
d e f i n i n g 0 ..................................................................................................
.
48
29.
Configuration
.
50
30.
Configuration
31.
Mach
No.
v.
downstream d istan ce
in
FSL
32.
Velocity
v.
downstream d istan ce
in
F S L .....................
52
33.
Reynolds
No.
in
53
34i
C onfiguration I I I ty p ical p ro p ertie s through
F S L ............................................................................................
55
C o n f i g u r a t i o n IV t y p i c a l
F S L ...................................................
55
35.
36.
37.
Velocity
I I I
B.L.
43
p r o f i l e s ................................................
III
pressure
IV p r e s s u r e
v.
gradients
gradients
downstream
distance
properties
. .
44
. . .
............................
. . . . .
FSL. . .
v.
y-position
in
FSL
52
through
p l o t v . y - p o s i t i o n i n FSL C o n f i g u r a t i o n
..............................................................................
Velocity plot
IV . . . .
50
56
Configuration
56
xi
LIST OF FIGURES— Continued
Page
3 8.
h v.
...........................
57
39.
S c h l i e r e n p h o t o g r a p h of C o n f i g u r a t i o n I I I
t r a n s i t i o n d e t e r m i n a t i o n ................................................................
60
Edge and p l a n v i e w of a low s p e e d
( incom pressible) mixing la y e r.
Scale:
s t r e a m w i s e d i m e n s i o n o f p i c t u r e i s 15 c m.
.
61
.............................................
64
40.
x for
Configurations
41.
Configuration III
Spectra
42.
C o n f i g u r a t i o n IV
Spectra
43.
Configuration III
RMS
44.
C o n f i g u r a t i o n IV
RMS v .
45.
Configuration III
175
46.
C o n f i g u r a t i o n IV
17 5 KHz .
47.
48.
III
v.
v.
x
KHz .
and
x
v .
x
x
.
IV
.
.
........................................................65
.................................................
66
...................................................................67
signal
.........................
68
4
.
69
G rap h ic a l r e s u l t s showing C o n f ig u ra tio n I I I
h o t - f i l m t r a n s i t i o n a l p o i n t s ................................................
70
G r a p h i c a l r e s u l t s s h o w i n g C o n f i g u r a t i o n IV
h o t - f i l m t r a n s i t i o n a l p o i n t s ....................................................
70
signal
v. x
v.
x
.
.
.
49.
T h e o r e t i c a l v . e x p e r i m e n t a l mini mum v e l o c i t y
g r o w t h i n F S L o f C o n f i g u r a t i o n I I I .......................................... 73
50.
T h e o r e t i c a l v . e x p e r i m e n t a l FSL d e v e l o p m e n t
a t x ' = 0 o f C o n f i g u r a t i o n I I I ...............................................74
51.
T h e o r e t i c a l v . e x p e r i m e n t a l FSL d e v e l o p m e n t
a t x ' = 0 . 0 5 6 and x ' = 0 . 1 1 2 of C o n f i g u r a t i o n
I I I ......................................................................................................................... 7 5
52.
T h e o r e t i c a l v . e x p e r i m e n t a l mi ni mum v e l o c i t y
g r o w t h i n F S L o f C o n f i g u r a t i o n I V ...........................................76
53.
T h e o r e t i c a l v . e x p e r i m e n t a l FSL d e v e l o p m e n t
a t x '
= O a n d x '
= 0 . 0 5 9 ................................................................
54.
Experimental tr a n s itio n point for
C o n f i g u r a t i o n I I I ................................................................................. 84
77
x ii
LIST OF FIGURES— Continued
Page
55 .
56.
57 .
Experimental tr a n s itio n point
C o n f i g u r a t i o n IV
.............................
Frequency v . in te n s ity
accelerometer attached
for
85
s p e c t r a from
above the t e s t
N o n - d i m e n s io n a l graph showing
w a v e l e n g t h t o be p r o p o r t i o n a l
t h i c k n e s s ....................................................
section
.
.
87
.
89
t h e wave s t r u c t u r e
t o t h e FSL
Xiii
NOMENCLATURE
Symbol
D e s c r i p t i on
DSL
:
Dividing
f
:
Frequency
FSL
:
Free
stream
shear
h
FSL
M
Ma c h n u m b e r
line
layer
thickness
P
:
Mo me n t u m
P0
:
Stagnation
Ps
:
Static
r
:
Speed
Re
:
Reynolds
Re '
:
Unit
Re '
:
(R ef1 + R e ' 2 ) /2
SWT
:
Supersonic
T
:
Temperature
T0
=
Stagnation
T.E.
:
Trailing
U
:
Velocity
Us
:
Velocity
x
:
D i s ta n c e from the T.E.
(x p o s i t i v e downstream)
:
Sa me
:
Non-dimensional
x
*
x '
thickness
ratio
/©2
pressure
pressure
ratio
U2 / U J
Number
Reynolds
as
Number
Wind T u n n e l
,
Temperature
Edge
on
the
DSL
x
x
*
x iv
NOMENCLATURE— Continue d
Symbol
:
y
De s c r i p t i o n
Distance
normal
to
y
Compressible
y '
Non-dimensional
y
a
Deflected
of
5
Boundary
layer
6
Mo me n t u m
thickness
P
©i
P
Density
X
Non-dimensional
( U^ + U2 ) , a l s o
FSL
transformed
angle
y
FSL
thickness
at
at
T.E.
T»E.
+ e2
s p e e d r a t i o ( U^ ~ U2 ) /
w av elen g th in Appendix
(
)l
:
F a s t —s i d e
property
(
^2
:
Slow-side
property
(
>e
=
Free
stream
property
XV
ABSTRACT
A c l o s e d - f o r m a n a l y t i c a l t h e o r y has been d e ve lope d to
p r e d i c t the flow f i e l d of t w o - d i m e n s io n a l , l a m i n a r , nonequilibrium free shear layers,
shed from the t r a i l i n g edge
of a t h i n f l a t p l a t e s e r v i n g as a p a r t i t i o n s e p a r a t i n g two
dissim ilar parallel
flows.
A Mach 3 s u p e r s o n i c n o z z l e i n
c o m b i n a t i o n w i t h e i t h e r a Mach 1.6 or a Mach 2 s u p e r s o n i c
nozzle
were
used
to
produce
a free
shear
layer.
The
i n v e s t i g a t i o n was d e s i g n e d t o p r o v i d e e x p e r i m e n t a l e v i d e n c e
by w h ic h f r e e
shear layer theories
may b e c h e c k e d .
A
c o m p a r i s o n of t h e o r e t i c a l / e x p e r i m e n t a l mean f l o w p r o p e r t i e s
in th e l a m i n a r , n o n - e q u i l i b r i u m r e g i o n of th e f r e e s h e a r
la y e r were
made.
The t h e o r y
showed
good
agreem ent
q u alitativ ely ,
but poor
agreement
q u an titativ ely
when
compared to e x p e rim e n tal data.
The t h e o r e t i c a l l y a s s u m e d
in itia l
velocity
profile
showed
a 35 % d i f f e r e n c e
in
th ic k n e s s compared to the e x p e rim e n ta l th ic k n e s s.
The
theory p red icts
f r e e s h e a r l a y e r t h i c kn e s s and minimum
velocity
growth
rates
that
p arallel
the
experim ental
r e s u l t s , a l t h o u g h a q u a n t i t a t i v e e r r o r of b e t w e e n 2 0 -5 0 %
exists.
I
CHAPTER I
INTRODUCTION
An a n a l y t i c a l
{ 11 ^
to
theory
predict
the
non-equilibrium
tra ilin g
edge
separating
two
shear
(FSL)
by
layer
solid
I.
diagram
nozzle
applied
The
theory
region
Figure
and
also
of
I
a
combination
of
the
p ro files
of
the
two
p r o file
in
trough
depth
progressively
decreases
with
until
the
the
finally
equilibrium
^The
References
trough
as
is
the
coalesce
greatest
increasing
disappears
(self-sim ilar)
and
in
at
shown
in
of
a
5 and
6.
velocity
into
a single
region
the
the
distance
the
confined
diagram
Chapters
(T.E.),
decrease)
free
nomenclature
n o n -e q u ilibrium
(velocity
term
not
layer
in
the
non-equilibrium
general
detail
flows
The
is
the
from
a p a rtitio n
The
schem atic
edge
p arallel
trough
The
in
to
a
as
flow
shear
of
tra ilin g
a
profile.
free
shed
flows.
the
applies
the
two-dim ensional,
serving
q u alitativ e
F SL .
by
since
by D e m e t r i a d e s
layers,
p arallel
consists
the
identified
plate
described
Downstream
of
shear
flat
is
developed
field
free
d issim ilar
(n o n - s i m il a r )
Figure
a thin
walls.
been
flow
laminar,
of
has
is
velocity
T.E.
and
downstream
profile
becomes
profile.
symbol
{ } w i l l ’ denote
refe re n c e s
cited .
c i t e d are found fo llo w in g the a p p e n d ic e s.
2
GENERAL
TROUGH
FREE SHEAR
LAYER
" I * r 02
^T02
SLOW-SIDE
PARTITION
FAST-SIDE
pOl • mI
NON-EQUILIBRIUM
REGION
CONFIGURATION
TE.
IV
INITIAL
PROFILE
EQ U IL IB RIU M /SEL F-SIM IL A R
REGION
FSL
DEVELOPMENT
EQUILIBRIUM
PROFILE
NON-EQUILIBRIUM
PROFILE
\
x inchlcm)
Figure
I.
Nomenclature
l a y e r (FSL).
1.0(2.54)
and
2.0(5.08)
definitions
of
the
3 .0(7.62)
FSL
free
shear
3
Two-dimensional
injection
engines,
is
system s,
as
well
d e sira b le
addressing
shear
high
the
have
mentioned
in
shear
flows
power
half
closed-form
using
jets
optim ization
of
and
region
and
jet
It
so lu tio n s
of
the
free
interest
has
been
or n u m e ric a l
gas-dynamic
mass
wakes.
a n a ly tic
Particular
th eo retical
in
systems
non-equilibrium
abovei
appear
laser
classical
laminar,
shown
design
as
to
the
layers
recently
for
free
and
methods
chemical
laser
systems„
The
State
following
U niversity
provide
the
A
shear
in
layer
the
of
performed
Wind T u n n e l ,
evidence
comparison
properties
free
Supersonic
experim ental
validated.
flow
investigation,
by
be
was
the
Montana
designed
theories
can
theoretical/experim ental
lam inar,
will
which
at
made.
n o n - e q u i l ibrum
to
be
mean
region
of
4
CHAPTER 2
THEORETICAL REVIEW
Investigation
1879,
as
Lord
other
fluid
to
FSL
near-wake
initial
and
a
addressed,
lim ited
velocity
an
was
laminar
compressible
stream
of
Denison
case where
to
num erical
form
In
in
{6}
extended
the
= 0.
solution
Kubota
method
m ixing
Denison
with
velocity
in
for
layer
and Baum's
the
and
Dewey
{7}
the
constant
with
a
fin ite
mean
{3}
a
assumed
Blasius
profile
a
{4},
the
{5}
flow
in
far
proposed
zero
a
boundary
of
an
air
model.
analysis
to
thickness
at the
are
layer
developed
in itia l
flow
incompressible
results
pressure,
and
solved
n e a r —w a k e
shear
as
numerically
profiles
Chapman's
of
jets
Tollm ien
Chapman
tem perature
in
Goldstein
be
(starting
the
the
predicting
1950
theory
for
to
x
early
were
equations
problem.
at
as
Goldstein
profiles
predict
separation.
equation.
free
time
1930
the boundary la y e r had a f i n i t e
of
integral
to
Baum
point
a
that
noted
plate.
arb itrary
and
until
distribution
a
thickness)
not
U2 = 0)
began
instabilities
differential
asym ptotic
flat
layers
noted
velocity
behind
layer
At
flow
sin g u larity
used
{2}
shear
but
(h alf-jet,
the
1931
Rayleigh
governing
compute
free
m otions,
properties
the
of
a
the
lim ited
momentum
momentum-
two-dimensional,
thickness.
Two
5
d ifferent
expressions
above
one
I),
a
and
therefore
single
below
the
theory
by D e m e t r i a d e s
without
{I },
the
boundary
parallel
velocity
dealt
{1},
with
theory
of
the
were
and
streams.
The
shear
not
layer,
(DSL,
one
Figure
represented
by
is
( G^
on
/
imposed
are
constant,
that
and
the
that
reacting.
Prandt I
theory
the
The
(0
that
the
fluid
flow
Number
two
As
linear
p r o file
detailed
flow
by
profile
exponential.
fields
two
merging
jo in in g
velocity
The
the
at
to
have
little
provides
an
analytical
two
the
shape
said
entire
the
the
62’
com pressibility
profiles.
solution
T .E .
of
the
affect
at
distance).
including
re stric tio n s
symmetry
initial
proposed
analytical
generated
FSL
profiles
to
investigation,
flow
flow
be
Dem e t r i a d e s '
I,
the
to
(downstream
closed-form
in
the
assumed
large
this
a closed-form
wake
velocity
x
in
superposes
lay ers
arbitrarily
Figure
the
stream line
profiles
gives
initial
in
for
dividing
discontinuities
consisting
is
the
used
expression.
The
in
were
of
/
<
of
I^),
M
<
x
heat
00
).
the
pressure
flow
is
is
must
I.
flow
equilibrium
range
^i
lam inar
A
transfer
is
be
Tq2 ) or
everywhere
two-dim ensional,
homogeneous
com puter
no
restric tio n s
assumed
laminar,
are
in
distance),
(Tq^ /
only
and
shown
There
(downstream
p arallel
also
field
region.
The
chem ically
expression
steady
code,
and
and
non­
have
prepared
a
by
6
Demetiriade s
y, with
{I } ,
inputs
provides
of
P =
The
non-dim ensional
the
physical
Reynolds
mean
flow
/ D2 » r = ^ 2 ^
downstream
downstream
Number
distributions
distance
distance
and
the
^Ol ^
x,
square
of
x and
an^ x'•
02
x ' is
divided
in
defined
by
the
both
as
average
momentum
thickne sses.
x ' = x * /p^Re'
where
P = ©^
distance.
the
fast
just
The
and
of
cases
r
= O and
= O (base
flow,
#
is
the
the
the
tra ilin g
edge.
and
total
and
is
of
the
present
r = I
are
shown
near-wake)
and
the
momentum-integral
TJ s
The
( TJ s
defined
= TJ/ Uj )
p resen t
agreem ent
solution.
compares
Kuriki
on
the
from
compared
the
{10}
r
= I
theory
using
to
(wake)
with
Figure
for
of
and
also
case.
Figure
experimental
{11}
and
Number.
The
from
a n d Ba u m
and
Dewey,
uses
a
{5} .
shows
(taken
r
{1}),
Chapman
Ti g ,
points
also
3.
theory
Baum's
3
lim iting
Denison
Kubota
Chapm an’s
and
Mach
the
from
free
Tq ^ and
2 (taken
of
I,
U^,
2 and
Dem etriades'
Denison
and D e m e tr ia d e s
are
of
Figure
adjacent
Figures
method
{8}
in
fast-side
solution
DSL.
M ills
theory,
The
(exact)
thicknesses
The
theory
in
case.
numerical
= O is
the
downstream
shown
tem peratures
the
y'
momentum
layers,
presents
also
dim ensional
boundary
respectfully,
Comparisons
2
©2 a r e
slow-side
v elo cities
T ^
an^
6 ^ and
upstream
stream
©2 ,
+ ©2
good
num erical
from
taken
by
{9}),
Sato—
G oldstein's
{12
I
SYMBOL
METHOD
SOURCE
------------ NUMERICAL DENNISON - BAUM
.................
MOMENTUM DEWEY-KUBOTA
INTEGRAL
(QUADRATIC)
T
T
T
T
PRESENT THEORY [l]
-GOLDSTEIN (INCOMPRESSIBLE) -
ALL M 1
r «0
0 6 9 2 (MILLS)
O 5 9 (CHAPMAN)__ T
PRESENT
THEORY
Ue-U(O)
: MILLS u , - I CHAPMAN u ,
.1 -
O
Figure
2.
FSL d e v e l o p m e n t
and r = O.
at
y '
= O
Figure
• SATO-KURIKI, M=O
O DEMETRIADES' SERIES 100, M*4
ADEMETRIADES' SERIES 200, M=4
— I------- 1--------- 1_____ I_____ I_____L_
.2
4
.6
.8
I
1.2
x'
3.
FSL d e v e l o p m e n t a t
and r = I , 6 = 0 .
y'
= O
8
and
13}
shown
incompressible
in
Figures
Aside
l i t t l e
from
or
no
3
theory
as
such
follow ing
two
to
cases
the
of
ratio
A brief
at
need
r
this
time
of
shows
p ro files
in
r
= I
late ra l
compressible
r
y '
layers
are
shear
to
validate
Dem etriades.
to
verify
ratio
~ I.
Dem etriades
be
the
—
)
case
ratio
divided
by
and
is
both
theory
momentum
is
in
by way of
of
the
also
two
velocity
in
plotted
distance
the
a
The
predicts
accom plished
development
Th e U/
(y),
the
temperature
what
=
of
shown
by
cases,
properties
the
non-dim ensional
y
theory
and/or
w ith
( D^
the
so lu tio n s
.9
and w i l l
4
to
lim iting
free
attem pt
and
the
( U2 = . 5 U^ ) c a s e .
of
therefore
w ill
Figure
the
flow
region
.8
example
mean
presented
graphs.
(the
a c c e ssib le
one
P and
agreement
aforem entioned
is
=
The
evident.
the
experiments
thickness
.5
is
n o n -e q u ilibrium
The
order
the
data
available.
using
2 and
re a d ily
experim ental
lam inar,
theory.
the
against
defined
as
r
=
y'
the
momentum
thicknesses),
also
FSL
= y / ( 0 1 + @2 )
f
y =
p/pg
dy
0
Figure
5
velocity
r
= .5
shows
growth
and
r
the
at
r
y'
=
0
case
and
= 0 progressing
= 0 cases.
the
downstream
minimum
for
r
= I,
9
t • .9 9
Figure
4.
Theoretical
F SL d e v e l o p m e n t
at
r
I
and
r
10
Figure
5.
T h e o r e t i c a l FSL d e v e l o p m e n t
v e l o c i t y gr o wt h at y ' = 0.
at
r
= 0 and
mi ni mum
11
CHAPTER 3
EXPERIMENTAL APPROACH
The
code,
the
latter
developed
flow
field
equilibrium
necessary
The
Wind
at
local
various
mean
stream
the
FSL
the
such
in
campus
fully
layer
describes
its
non­
provide
this
a
Mach
of
code
the
and
( i .e * U/U^)
the
State
profiles
momentum
through
the
T.E.
as
well
the
provided
as
free
M ^ , Re ' ^ > R e ' 2 > U ^ a n d
Finally,
a
Supersonic
layer
traverses
of
3
M ontana
supplied
furnished
and
into
computer
in
w ill
Boundary
as
a
validity.
downstream
properties
curves
which
shear
V ertical
region.
references
inputs
edge
©2 ) •
measurements
th e o r e tic a l
as
Montana.
properties
laminar
pre sented
on
x stations
flow
flow
Transition
and
free
conducted
tr a ilin g
(0^
{1}
experimental
were
lo cated
2
investigation
needed
their
the
thicknesses
the
of
This
Bozeman,
at
Chapter
a lam inar
experiments
U niversity,
taken
of
parameters
Tunnel
of
by D e m e t r i a d e s
region.
justification
FSL
portion
evidence
graphical
of
the
U2 •
lim its
of
comparisons
of
experim ental
p o in ts
are
12
CHAPTER 4
EXPERIMENTAL APPARATUS AND PROCEDURE
W ind T n n n e l
The
Montana
(MSU/ SWT)
as
continuous
The
seen
is
Numbers
o
14 5 F
o
(605
control
The
of
high
336
with
are
about
18
x
(46
optical-quality
th ro a t
to
description
of
+1
a
8.13
from
can
be
pressures
abs.
at
up
and
to
and
+1
autom atically
cross
cm.)
o
F
from
sectional
and
a
upstream
A
found
of
of
made
of
the
more
in
area
length
sid e w alls
en tran ce.
( MS U/ S WT)
hours
area.
Rem ovable
stretch
several
fluid.
tem peratures
or
has
Tunnel
circu it,
working
mm E g .
test
section
d iffu s e r
the
for
Wind
open
stagnation
at
x
an
the
supply
the
(7.87
is
as
manually
in
cm.).
glass
the
and
points
test
in.
air
Supply
located
3.2
in.
4
K).
7
operating
controlled
console
in.
as
Supersonic
6 and
using
of
set
rectangular
3.1
Figures
tunnel
as
R or
respectively,
U niversity's
capable
tem peratures,
a
in
flow,
MSU/ SWT
Mach
State
nozzle
d e ta ile d
{14}.
P L t ojt P r o b iC
The
mean
used,
p ito t
flow
one
probe
was
m easurem ents.
for
the
the
principal
Two d i f f e r e n t
tra ilin g
edge
instrum ent
pitot
boundary
in
probes
layer
the
were
profiles
13
EXHAUST
S IL E N CE R
PUMPS
MOTOR
MOTOR CONTROL
y -----DESSICANT BED
Z
/ ----- DRYER
_.
Z / — T H R O T T L E VALVE
Z -A IR
BELLOWS
\
T E S T AREA
INLET
/
/
STILLING TANK
SUBSONIC D I F F U S E R - Z
CONTROL CONSOLE
T E S T SECTION
Figure
6.
(shown
as
shear
Diagram
of
components .
probe
layer
no.
were
diam eter
0.004
of
to
0.003
measurements
o u tside
and
(spanw ise)
rationale
response
(probe
(0.01
(0.008
taken
of
time
using
of
two
a 0.003
cm.)
0.005
probe
for
with
at
in.
the
probes
would
be
(B.L.)
outside
layer
cm.)
an
a
(FSL)
initial
which
to
(0.013
free
chem ically
with
tip
the
an
was
probe
major
layer
shear
(0.02
d ifferen t
in.
probe
Free
in.
etched
other
which
a pitot
0.008
showing
Boundary
a pitot
with
of
the
2).
cm.).
chem ically
tunnel
8),
no.
in.
dim ension
for
Figure
with
in.
were
wind
taken
diam eter
flattened
in
p ro files
measurements
etched
I
the
was
lateral
cm.).
The
was
that
the
too
slow
and
Figure
7.
Photograph
of
modified
wind
tunnel.
15
PITOT
PROBE
NO. I
.57
Figure
8.
Pitot
and
static
probe
schematic.
16
not
appropriate
p ro files.
The
response
time
resolution
This
in
is
In
profile
p ito t
0.04
c m. )
where
the
was
less
than
200.
the
actual
to
account
The
larger
into
for
p ito t
for
an
to
by
immersed
the
outside
15.7
v o lts
dynam ically
converter.
is
in
discussed
a
Number
low
the
reading
low
data
were
tubes
and
the
of
Model
flow
the
before
the
latter
100
part
to
and
data
of
this
a
the
< y
<
diameter
of
this
overestimate
curve
into
{16}
was
program
progressively
a
bullet-shaped
transducer
The
tim es
an
(Kulite
transducer
leads
transducer
connected
Th e A/D c o n v e r t e r
in
The
in
to
(0
flows
to
{15 }
affect.
electrical
a m p lified
being
wall
X T E-1-190-5A ).
and h a d
made
computer
to
pressure
tunnel.
d. c.,
reduction
attached
= 30}.
used
on p r o b e
known
Number
lateral
observed.
was
Number
telescoped
encapsulated
C o rp .,
was
A correction
Reynolds
probes
were
the
based
is
the
Demetriades
sizes
to
Reynolds
B .L .
dia.)
to
FSL
reduced
(probe
correction
close
the
a
0.005
probe
up
afforded
interference
readings
reading.
the
Semi-conductor
was
{16},
pressure
diam eter
housing
with
Reynolds
p ito t
incorporated
p ito t
probe
In
and
/
making
probe
according
and
pressure
pitot
half
width)
varying
accordance
the
than
(FSL
points
flattened
adequate
B .L .
type,
data
in.
more
{0.15
where
flow
many
0.005
by
of
the
considered
a study
single
for
was
and
extending
energized
damped
analog/digital
collecting
Chapter.
process
17
S ch lleren
O ^ tleal
An 8 - i n c h
the
quality
such
as
of
System
portable
Schlieren
the
and
flow
transition
continuous
strobe,
to
investigation.
in h eren t
detailed
bulb,
viewing
shear
flow s,
exposures,
light
other
showing
using
of
Schlieren
the
the
flow
one
speed
13
a
spark
throughout
the
differences
continuous
Figures
verify
sources,
density
in
to
of
a high
the
appear
explanation
used
details
Two
the
was
cap ab ilities
Photographs
to
photograph
photograph
turbulence.
illum ination
provided
System
and
and
spark
15.
System
is
A more
given
in
{14} .
Static
Pressure
Static
in.
its
cm.)
0 .0 1 5
the
hole
of
as
that
For
shown
of
the
in
shown
0.10
was
the
less
probe
in
pitot
(0.254
9.
probe.
0.35
tip.
cm.)
in.
this
region,
from
Signal
with
around
of
one
(0,89
cm.)
This
in.
a 0.02
8,
d rilled
0.35
interpolated
Figure
with
Figure
holes
in.
than
taken
in
d rille d
profiles
were
were
diam eter
w ith in
edge
edge.
values
downstream
as
f ir s t
tube,
cm.)
m easurements
trailing
pressure
same
(0.038
leading
prohibited
the
in.
The
measurements
diam eter
circum feren ce
another.
from
pressure
(0.051
three
Probe
distance
downstream
the
known
recording
of
static
values
was
the
18
I
Ps (mm hg)
I
~T~
CONFIGURATION
Jil
IV
EXPERIMENTAL
I
I
ESTIMATES
(INTERPOLATED)
A
O
0
SL
-
A
Z
Z
^
3L
%
T
|
I
Figure
T olal
9.
I
3
(x)
S t a t i c p r e s s u r e v. downstream d i s t a n c e p l o t
used
to
interpolate
unknown p r e s s u r e
values
clo se to the T.E.
Temper i i u r£
The
total
thermocouple
connected
tunnel.
I
2
in.
4 cm.
6
DOWNSTREAM DISTANCE
2
I
to
The
includes
originally
a
PffihA
tem perature
bead,
0.005
a d ig ital
data
in.
consisted
(0.013
tem perature
reduction
tem perature
documented
probe
in
v.
in
indicator
program,
Reynolds
(17).
cm.)
of
shown
in
Number
a
type
K
diam eter,
outside
Appendix
the
E,
calibration
19
H o t - F J liI m AniCmomiCtiiCiT
A hot-film
anemometer
indications
of
provided
means
to
in
flow
a
fluctuations
its
tip.
0.002
The
in.
deposited
of
0.02
probe
was
1213
x
the
in.
in.
to
amplifier
for
measurements
and
500
limit,
and
since
300
Zrobe,
KHz .
KHz ,
of
of
x
edge
of
500
a range
heat
transfer
0.05
in
cm.)
dimension
glass
a Transmetrics
used
The
frequency
setting
in
in
was
was
{18}
or
The
a n ADP
with
window
used
between
3 Hz
as
range
and
tip
rod.
series
used
to
ground
6401
and
experiment
seen
from
approximately
signals.tended
also
away
platinum,
Kimax
this
film
temperatu re / veIocity
diameter
KHz
turbulence
The
wedge
combinations.
The
qualitative
double
circuit
in
give
a
either
heating
various
all
way
to
turbulence.
the
(0.005
cm. )
connected
hot-wire
by
leading
(0.05
to
measure
consisted
0.02
the
used
tran sitio n
film
on
a
the
was
an
upper
between
50
{19}.
P o s i t i o n i ng
All
probes
immersed
electromechanical
section
in
Figure
ceiling
of
the
hollow
shaft
leads.
The
v e rtica lly
horizontal
7.
Four
struts,
the
system
was
were
system,
horizontally
positioning
flow
provided
supported
actuating
and
the
actuating
tunnel,
that
in
seen
above
extending
vertical
probe,
the
same
mechanically
the
positioning
the
by an
test
through
transducer
enabled
in
positioned
probes
plane.
adjusted,
the
of
a
and
wire
to
move
While
vertical
20
positioning
is
was
explained
fully
as
automated.
follows,
taken
The
from
vertical
{1}
positioning
(Section
6.3.6).
For t he mean f l o w m e a s u r e m e n t s t he d a t a wer e
o b t a i n e d i n t h e f o r m of p r o f i l e s , i . e . t r a v e r s e s
a l o n g y a t c o n s t a n t x.
T h e SWT e l e c t r o m e c h a n i c a l
a c t u a t o r s y s t e m a l l o w e d t h i s t r a v e r s e t o be done
fully
autom atically.
The v e r t i c a l
motion
is
geared
to
a flywheel
with
adjustable
spoke s
p r o tr u d in g from i t s p e ri p h e ry which p e r i o d i c a l l y
i n t e r r u p t a p h o t o d e t e c t o r beam, ea ch i n t e r r u p t i o n
t r a n s m i t t i n g a n e l e c t r i c r e a d c o m m a n d t o t h e SWT
Data System.
Ey a d j u s t i n g t h e a n g u l a r s e p a r a t i o n
o f t h e s p o k e s a r o u n d t h e f l y w h e e l , a r e a d c omma nd
a t each of t he v e r t i c a l s t e p s m e n t i o n e d above is
obtained.
In a d d i t i o n , and to e n s u r e a d e q u a t e
response
time
for
the
sensor,
the
system
a u to m a tic a lly produces a pause between sensor
arrival
a t a hew v e r t i c a l
point
and the r e a d
c ommand a t t h a t p o i n t ,
the pause being t y p i c a l l y
15 s e c o n d s i n l e n g t h .
The
use
of
pitot,
provided
all
the
mean
theory.
In
taking
positioned
=
0)
and
reading
other
within
probes
to
this.
I)
and
flow
FSL
downstream
This
positive
until
temperature
needed
the
the
the
taken
negative
y
at
to
pitot
the
probe
was
total
y
in
probes
verify
trailing
became
electronically
were
to
of
position
positioned
FSL p r o f i l e s
from
total
properties
v e rtic a lly
minimized.
were
and
measurements,
7 mils
adjusted
was
static
edge
(x
pressure
= 0
and
all
relationship
increasing
x (Figure
always.
DjsLtjL C o l l e c t i o n
The
relayed
leads
signals
of
the
electro n ically
outside
the
by
pitot
way
tunnel
and
of
to
static
probes
the
transducer
an
a m p lifie r.
and
were
its
Upon
21
a m p l i f i c a t i o n ,
the
s ig n a l
was
resistance/capacitance
( E C)
unsteadiness,
analog
(Spectral
was
in
then
Dynamics
counts
Recording
S ile n t
to
700
available),
Corp.
and
was
AS R
circu it
Mo d e l
to
to
digital
SD-133).
( A/ D)
The
d ig itally
displayed
on
cassettes
via
computer
5-inch
disks
via
of
the
transducer
before
and
after
converter
and
output
recorded.
Instruments
(hard
an
a
signal
latters
a Texas
term in a l
on
th ro u g h
dampen
was
done
and
an
p a sse d
copy
Intertek
also
Superbrain
microcomputer.
The
signal
frequently,
using
a linear
corresponded
regression
to
pressure
P( mm E g )
where
A and B were
y-intercept
were
an
of
input
into
Appendices
D and
collection
approach
Data
replaced
The
E.
by
h o t-film
magnetic
tape
by
a latter
time
for
in
the
following
A being
the
reduction
shown
the
Type
diagram
in
the
sig n als
a H o n e y w e l l .7600
analysis.
The
constants
the
given
in
above
data
probe
was
arrangement
was
10.
temperature
Digital
were
count
and B the
programs
transducer
2809
Each
slope
showing
Figure
total
measurements,
+ B
the
is
of
calibrated
wa y:
calibration.
data
was
routine.
pressure
only
a n Ome g a
series
= A * (counts)
by
stored,
counts
calculator
A block
acquired
sim ilarly
each
constants,
the
in
Thermometer.
recorded
Recorder
on
and
0.5-inch
replayed
at
POWER
SUPPLY
SENSING
PROBE
PITOT/STATIC
POWER
SUPPLY
_____________ I __________
Y-ACTUATOR
POSITIONING
TRANSDUCER
A
AMPLIFIER
PHOTO
DETECTOR/
FLYW HEEL
DAMPER
A /D
CONVERTER
'
ELECTRONIC
TIM ER
Figure
10.
Data
STORAGE*
5-IN C H DISC
collection
block-diagram.
STORAGE=
CASSETTE/
HARD COPY
23
CHAPTER 5
EXPERIMENTAL DESIGN
TunnjiJL M o d j . f ^ c . a J : . i o n
In
the
dimensional
The
M S U / S WT
DeLaval
present
parallel
joining
therefore,
s o me
(10.2
channel,
tunnel's
the
and
11),
tunnel
a
4
for
in.
gate
Figure
and
of
11
creating
a
ceiling
this
forming
its
principal
referred
axis,
to
subscripted
The
3 nozzle
as
air
on
a flat
forming
with
its
s l o w —s i d e
a
Ma c h
3
was
The
in
the
upper
top
of
ceiling.
channel
and
(FSL),
7
manually
Figure
to
is
its
wind
machined
3
11.
channel
consisted
s p litte r
It
in.
(Figures
Ma c h
parallel
two
stagnation
channel
the
flow.
the
controlled
The
plate,
of
throat
shown
3
A 4
a hole
stream.
two-
layer
top
at
a
for
required.
splitting
the
called
the
as
Ma c h
shear
was
at
stream
nozzles.
and
the
air
positioned
surface
floor
a free
the
a plate
half
uniform
terminating
above
second
shows
contoured
and
second
valve,
two
form
modification
tank
a
a
mode,
investigation
originating
provided
pressure
op eratin g
provides
to
tunnel
stagnation
into
by
Nozzle
experimental
flows
cm. )
normal
the
plate
S WT ’ s
hereafter
properties
are
"2" .
lower
channel
block
for
its
consisted
floor
and
of
half
the
the
flat
original
s p litte r
Ma c h
plate
4
4
GATE
VALVE
DIA.
O 2 4 6 8 IO
SECONDARY
AIR
INCH
SPLITTER
PLATE"^
STAGNATION
UPPER
(SLOW-SIDE)
NOZZLE
TANK
PRIMARY
AIR
Figure
11.
Schematic of tunnel modification.
LOWERz
(FAST-SIDE)
NOZZLE
25
for
its
c e ilin g .
properties
(spanwise)
edge
are
line
(T .E.) of
Four
called
These
The
subscripted
at
which
the
fast/slow -side
nozzle
and
flow
a
two
,
"I"
flows
(or
.
The
join
is
f a s t-s id e )
horizontal
the
trailing
plate.
nozzle
combinations
their
channel
by
the
s p litte r
"Configurations"
sections
lov/er.
were
combinations,
used
are
in
this
described
parameters
are
in
hereafter
investigation.
the
following
summarized
in
Table
I .
TABLE
I.
NOZZLE
I
CONFIGURATIONS.
II
M1 d e s i g n
3
3
actual
3
3
3
3
Nozzle I co n to u r 3
contour3
design
1.56
1.6
1.47
Mj a c t u a l
Nozzle 2
straight
contour
X1 , i n ( c m ) 1 0 . 4 ( 2 6 . 4 ) 1 0 ( 2 5 . 4 )
Xj , i n ( c m ) 4 . 2 ( 1 0 . 5 ) 3 . 7 ( 9 . 4 )
1.
2.
3.
4.
IIa
2.7
contour3
1.6
1.74
contour
5(12.7)
3.7(9.4)
III
IV
2.7
2.7
2.65
2.8
contour3
contour3
2.25
1.6
2.15
1.67
contour3
contour3
6.$5(16.9) 6.71(17)
4.8(12.2)
3 .76(9,5)
Conventional v e rtic a l mill
C o n v e n t i o n a l v e r t i c a l m i l l , m o d i f i e d by hand sanding
Numerically controlled mill
D i s t a n c e measur ed downstream from noz zl e t h r o a t
26
C o n f j.£ura..t_ion. %
Configuration
shake-down
model
slow-side
1.5
with
The
the
overall
were
to
f a s t —s i d e
the
design
tunnel
flow
problems
attributed
to
the
Configu r a t ion
ch aracteristics
aiding
code
the
A conventional
flow
II
12)
Mg -
achieved
tap
a flow
were
design
at
as
already
and
readings
observations
associated
nozzle
give
measurements
pressure
above
to
was
a
(straight)
nozzle
quantitative
consisted
give
Mg
was
used
as
that
of
Mach
1.5
of
the
deflection
with
the
thought
that
FSL.
to
be
time.
1.5
mill
by.
slow-side
flow.
method
in
the
the
used
The
{20}
to
Configuration,
code.
nozzle
Although
the
13.
a
nozzles.
the
quality
seen in the
Figure
of
coordinates
machine
achieved,
as c a n b e
develop
contoured
computer
was
to
nozzle
subsequent
was
flow
a contoured
outlined
and
acceptable
this
=
of
provided
this
generated
of
3
flow
and
was
combination,
Mach
problems
to
{21}
was n o t
photograph
this
Schlieren
Figure
vertical
approximately
the
flow.
straight
design
coordinates
in
7,
II
designed
computer
designed
static
mentioned
Configuration
nozzle
ratio
No
in Figure
non-contoured
the
ceiling
in
seen
Supersonic
choking
(defined
a
was
checked^
from
a
nozzle
tunnel.
supersonic
noted
of
area
ones,
was
aside
confirm
angle
The
in
made
flow
havi ng, an
following
installed
c a n be
consisting
nozzle
flow.
I , which
of
Schlieren
Small
shock
/
/
EXPANSION
FAN
/
/
Re e 2
/
/
/
pO 2
DEFLECTED
FREE
SHEAR
LAYER
PARTITION
M l l Re
SHOCK
WAVE
Figure
12.
Nomenclature
for deflected F S L .
S)
-J
Figure
13.
Schlieren
photograph
of
Configurations
II
and
IIa.
29
waves
emanating
form
a
well
ceiling
cut
downstream
of
the
of
and
F SL .
The
throughout
bottom
to
the
nozzle
assure
I
a laminar
B. L.
would
(i.e.
Using
as
^Q^/P^)
shock
a
stated
from
c m. )
by
nozzle
problems
also
which
( a = 0)
id e n tif ie d
be
a
Configuration
at
T.E.
bottom
in the
in
l im it a ti o n
5 in.
the
up s t r e a m
mismatched
downstream
the
must
was
in
exist
waves
arrived
are
r a t ^c
slow-side
nozzle
was
as
a
it
a
This
Controled
on
11 a ,
the
(12.7
c m. )
channel.
by
Mill,
wind
Figure
that
tunnel
a
6).
** q I ^
I
ratio
before
diffuser
{23}.
M2 = 2 . 2 5
a Bridgeport
in
I>o 2 /f^ I
pressure
condition,
time
ratio
in
thought
the
theoretical
the
driving
supersonic
minimum
after
shown
was
swallowed
chosen.
Numerically
as
A minimum
in
at
dependence
{22},
flow.
I>0 2 ^ 1
Special
milled
moved
pressure,
the
II
c m. )
respective
to
tunnel
(1.9
a horizontal
seen
In
tunnel
inlet
dominate
normal
III
showed
pump
Originally,
achieve
be
(20.3
choking
was
in.
was
the
the
to
III
calculations
the
w ill
was
Configuration
(Pj»
to
off
created
along
experiment.
block
Confie u ra t ion
loads
problem
and
in.
coalesced
0.75
nozzle
8
exhibited
able
choking
C o n fig u ratio n
almost
distributions
being
about
the
under
surface
reflected
FSL
Since
tunnel
in not
The
T.E.
nozzle
that
the
deflected
pressure
resulted
shock
through
the
it
channels.
upper
cantilevered
T .E .,
static
the
defined
and
aluminum
from
Series
conjunction
with
30
a CNC B a n d i t
nozzle.
Table
2
shown
in
measured
cm. )
and
11
Micro-computer,
The
slow-side
and
a
photograph
Figure
4.82
the
nozzle
in.
14.
From
(12.2
tra ilin g
used
coordinates
of
this
nozzle
cm.),
edge
were
the
used
nozzle
throat
width
thickness
to
was
s hown
trailin g
3 .1 0
0.015
cm.).
Figure 14.
are
the
combination
to
was
contour
Photograph of Configuration III.
in.
in.
in
is
edge
(7.87
(0.038
31
Tunne I
choking
configuration
Schlieren
plate
for
and
the
at
no
of
flow
velocity
Confi g u r a t ion
that
the
used
In
as
shown
pieces
mentioned
T.E.
was
butted
in
th is
shown
was
this
added
support
II.
observed.
nozzle
I % (Figure
in
sp litte r
Configuration
was
the
of
The
combination
19).
3.71
c m. ) .
The
a FSL
(Numeric-Control) Mill
was
m illin g
nozzle,
of
the
of
steel
use
from
of
(9.4
c m. ) .
the
deflection
2.
flow
From
(a),
width,
of
made
fashion
was
the
a ffe c t
II.
Figure
nozzle
choking
the
prevented
thickness
angle
was
Configuration
in
the
and
c a n tile v e r
The
T.E.
steel
streamwise
provided
in.
of
the
for
latter
The
in Table
problem
for
a
is
II,
aluminum
machinability
are
and
versus
in
nozzle
cm. )
used
Configuration
v e r t i c a l
description
this
of
together
nozzle
the
(7.87
and
noted
the
of
in.
however,
the
16.
measured
(0.038
of
machine
coordinates
3.1
provided
t h e , N.C.
Figure
in
photograph
as
increased
throat
a redesign
steel
and
to
and
in
d e fle c tio n
nozzle
1018
view
needed
two
The
from
w ith
obtained
deflection
conventional
contouring.
in
15.
within
IV was
material
versus
accuracy
se v ere
IV
h o t —r o l l e d
nozzle
plate
emerging
Configuration
in
affect
uniformity
as
a ~ 0 was
nozzle
splitter
the
not
Figure
the
cantilever
Therefore
shows
a FSL o f
photography
thickness
quality
was
17,
throat
as
A
and
to
before,
was
0.015
not
corrected
about
10
in.
degrees
33
FLOW
Figure
Figure
16.
17.
C o n f i g u r a t i o n IV s I o w - s i d e d e s i g n .
Two
p i e c e s ' b u t t e d ' t o g e t h e r t o form n o z z l e .
Photograph of Configuration IV.
34
TABLE
2 .
NOZZLE COORDINATES.
MACB = 1 . 6
(Configurations II,
IIa ,
I V)
MACH = 2 . 2 5
(Configuration III)
X(inch)
Y( i n c h )
X( i n c h )
Y( i n c h )
0.0000
0.6805
0.8880
1.0546
1.1526
1.2547
1.4253
1.5865
1.6775
1.8853
2.0942
2.4740
2.8414
3.2729
3 .7 1 1 7
0.3500
0.2571
0.2298
0.2081
0.1954
0.1822
0.1607
0 .1 4 1 1
0.1303
0.1069
0.0852
0.0512
0.0263
0.0076
0.0000
0.0000
0.5222
0.6402
0.7571
0.8269
0.9019
0.9769
1 .1 0 1 8
1.1687
1.3457
1.6859
2.2734
3.0805
4.8184
5.3578
0.8786
0.7239
0.6889
0.6544
0.6339
0.6120
0.5902
0.5543
0.5354
0.4867
0.3991
0.2703
0.1392
0.0068
0.0000
35
was
present*
A deflected
well
defined
the
T.E.
shock
to
respectively,
Configuration,
provided
stated
for
an
in
the
assumption
just
As
shown
The
in
the
theory
in
of
is
exit
Figure
{23}
in
the
plane
the
after
plot
that
the
of
velocity
the
this
no
way
as
The
only
8 measured
shock/expans ion.
to
is
of
parameters
th ick n ess
assumption
from
since,
locally.
is
a
tu n n e l
in
a.
governing
regard
this
of
experiment
this
a
exhibits
extending
resulting
properties
s a me
a,
photograph
flow
be
versus
valid.
again
The
within
I %
20.
arrangement
show
that
was
experimented
Experimental
the
diffuser
with
evidence
plays
an
and
early
on
diffuser
important
role
choking.
solid-block
varying
respect
Therefore,
Schlieren
theoretical
35,
shows
fan
c e i l i n g
The
the
investigation.
changes.
plate
in
Figure
diffuser
Various
with
address
the
expansion
continuing
the
positive
Modificalion
tunnel
placed
in
2,
distance
in
Diffuser
18.
T.E.
in
uniformity
shown
Figure
only
the
downstream
as
in the
obstacle
with
and
seen
considered
before
and
f lo o r
Chapter
FSL
wave
the
as
FSL,
to
This
combinations
stagnation
proved
a variable
attached
diffusers
to
the
time
diffuser
ceiling
were
and
on
hand.
the
flow
pressure
and
consuming
was
of
designed
the
They
was
were
observed
temperature
and
using
tunnel
by
tedious.
a hinged
a
spring
Figure
18.
Schlieren
photograph
of
Configuration
I V.
FLOW ACROSS NOZZLE EXITS
CEILING OF TUNNEL
. -------------- O,O—
CEn_,NG 0 F TUNNEL B L
CEILING
/
OF TUNNEL
'CEILING OF TUNNEL B.L.
plane of interest
O
O
O
O
O
O
O
O
O
O
O
O
g
O
=SS^-TS -I
O
O
O
O
O
2r
O
y
O
I(CM)
O
O SLOW-SIDE BL ON TE.
Ih
O
Z te5 Z
FAST-SIDE BL ON TE.
b f - A 7 lr -o ~ ° ~
O
O
O
-Ih
O
O
O
O FLOOR OF TUNNEL
O
O
Z
I r --------------------- o T T C ? -------------
i
I (cm)
SLOW-SIDE B L ON TE.
LE-_
U
03cm
X
FFLOOR OF TUNNEL
~
19.
CT- O0 -
TUNNEL
SOO
600
700
VELOCITY (M/S)
Configuration
uniformity.
B.L.
OFLOOR OF
_L
Figure
O
O
O
O
O
O
O
O
O
BL
• FLOOR OF TUNNEL
500
O-r,
-O
FAST-SIDE B.L. ON TE.
VELOCITY
III
flow
Figure
20.
(M /S )
Configuration
uniformity.
IV f l o w
38
assembly,
varied
in
(lowered
The
Figure
and
diffuser
a
straight
bottom
the
tunnel
ceiling
far
as
might
use
flow,
the
noted
the
tunnel.
possible,
be
of
flow
of
and
thus
that
a modified
quality.
as
hindered
The
seen
the
in
21.
raised)
final
was
of
seen
by
variable
one
of
combination,
diffuser
variable
The
block
of
photographs
process.
in
Figure
to
was
diffusion
the
did
diagnostic
Figures
the
14
21,
floor
to
the
raised
as
area.
It
diffuser
block
was
struts.
attached
diffuser
increasing
diffuser
immersion
attached
the
diffuser
actuator
diffuser
maximizing
bottom
the
sketched
variable
further
diffusion
The
area
by
not
help
the
probes
into
the
and
15,
also
WIRE
HOLE THROUGH TUNNEL CEILING
SPRING
/
STRUT
HINGE
VARIABLE DIFFUSER
FINAL POSITION
POSSIBLE "VARIABLE"
POSITION
FLOW
TUNNEL
FLAT BOTTOM
DIFFUSER
Figure
21.
Schematic
of
variable
diffuser
FLOOR
TUNNEL TEST
S E C TIO N
40
CHAPTER 6
RESULTS
General
In
which
{1} ,
the
Demetriades
theory
summarized
as
could
A large
2;
A laminar
X ( U2 - U 2 / U J + U 2 )
3.
4.
B .L .
shed
A long
laminar
FSL.
A flow
field
coming
the
side
nozzle
off
above
in
the
quality
verified.
which
is
conditions
combinations
phase
1,
of
judgements
far
from
T.E.,
Configurations
shakedown
be
desirable
The
conditions
conditions
at
are
follows:
I.
With
discusses
the
were
from
the
that
of
wake
flows.
T. E.
the
a,
deflection
of
the
FSL
0.
as
guidelines,
were
11
tried
and
as
IIa
and
III
and
noted
were
experiment,
made
various
in
used
where
diagnostic
fast/slowChapter
only
5.
as
overall
a
flow
expertise
wa s
acquired.
In
Configurations
conditions
These
optimum
function
along
Si
were
of
with
the
the
A further
reached
before
conditions,
four
tunnel
any
as
discussion
of
the
optimum
measurements
shown
desireable
choking
I V,
in
Table
conditions
problem
optimum
operating
were
3,
taken.
were
listed
mentioned
in
conditions
a
above,
Chapter
is
given
41
in
{ I },
where
a
theoretical
approach
to
a
laminar
FSL
is
pre s e n te d .
TABLE 3 .
OPTIMUM OPERATING CO ND ITI O NS .
Configuration
p Ol
P 02
T 01
( mm Hg )
(mm H g ) 0
■ T02
The
<
R>
three
required
to
compares
the
tra ilin g
edge
momentum
thicknesses
second
the
FSL
of
theory
B .L .
section
the
tran sitio n
laminar
the
flow
above
an
The
on
in
the
stream
the
region
As n o t e d
im portant
last
section
of
{1}.
data.
in
of
mean
in
in
this
provided
First,
the
B.L.
edge
quality.
properties
of
Determination
the
Chapter
experimental
curves
the
flow.
role
section
tra ilin g
flow
of
param eters
fourth
the
discussion
free
theoretical
presented
a
the
the
provides
addresses
comparison
corresponding
codes
and
adjacent
play
and
experimental
section
exists.
o u tlin e
theory
to
focuses
development.
graphical
the
IV
460
130
580
se ctio n s
verify
and
Configuration
425
170
605
next
The
III
2,
the
FSL
all
by
which
three
of
th e o r e tic a l
chapter
data
in
gives
points
the
a
and
computer
42
T railin g
Ed^e
Boundary; L a ^ e r
A laminar
,important
flow>
T.E.
in
in
the
{1},
for
23,
The
and
from
limit
TABLE 4 .
can
is
that
where
B.L .
Fast-side
S I ow-side
boundary
and
B .L .
As
th e
tran sitio n
to
intensity
in Figures
lim its
tabulated
at
discussed
wide-band
IV a p p e a r
of
the
in Table
22
flow
4.
The
begins.
III
Configuration
P Q 2 ( m m Hg )
Pg^fmm
Hg )
boundary
layer
layer
P q 2 ( mm
the
wall
from
free
stream
comparisons
the
(0)
thickness
from
Hg )
is
where
profiles,
actual
and
velocity.
of
80-200
mean, f l o w
of
momentum
distance
IV
300-500
upstream
the
and
the
100-200
identify
24)
in
detect
300-600
just
the
laminar
BOUNDARY LAYER LAMINAR REGION.
PQ^Cmm Hg )
point
To a s s u r e
to
separation
Configuration
T .E .
v ita lly
varied.
Pq versus
are
was
was
p ressu re
survey
T.E.
placed
used
III
lam inar
the
FSL.
was
be
resulting
the
from
pressure
Configurations
resulting
lower
anemometer
h o t —f i l m
turbulence.
shed
a laminar
stagnation
the
signal
being
attaining
a hot-film
and
and
B.L .
B.L .
T.E.,
(8)
B .L.
experimental
differs
and
a
to
The
as
profiles
B .L.
at
used
defined
velocity
The
were
thicknesses.
hereafter
the
taken
that
by
I %
(Figure
momentum
43
'
r I
I
CONFIGURATION III
FAST-SI DE
UPPER B.L. AT TE.
SLOW SIDE
UPPER ftL. AT TJ
NOISE
ZERO SIGNAL
LOWER R U AT TE.
LOWER 8.L. AT T E.
R.M.S SIGNAL
INTENSITY
200 300 4 0 0 SOO 600
(MM HG)
Figure
22.
2 00
300
Pqz (MM HG)
400
P q v . RMS B . L . t r a n s i t i o n
Configuration I I I .
CONFIGURATION IV
FAST-SPE
LOWER R L . / AT
TE.
900
trace
for
SLOW-SIDE
UPPER B.L. AT
TE
NOISE
ZERO SIGNAL —v
UPPER R L .
AT
TE.
LOWER B L
AT T E .
RMS. SIGNAL
INTENSITY
200
(MM HG)
Figure
23
(MM
P q v . RMS B . L . t r a n s i t i o n
C o n f i g u r a t i o n I V.
250
300
HG)
trace
for
44
"i
I
SLOW-SIDE
M=I.6 7
% =130 mm Hg
TE'
.24
I
SLOW-SIDE
M=2.I5
P0=ITO mm Hg
rTTTTnrrrm^ V
r~
~1
T
TE.
;
y (CM)
.16
.08
0
FAST-SIDE
M= 2.80
P =425 mm Hg
FAST-SI DE
M= 2.65
P =4 6 0 mm Hg
T? j j j j ,
h
.24
y (CM)
.16
•
•
.08 —
•
•
•
•
•
.
0
0
. •
'
200
,
400
I
600
•
D
VELOCITY
Figure
24.
—
Experimental
B.L.
I
200
( M/ S)
profiles.
I
400
I
600
45
thicknesses
to
are
presented
26.
Low's
theory
Low's
in
Table
theory
developed
TABLE 5 .
is
by
8/0
2.80
2.65
2.15
1.67
an
also
extension
BI a s i n s ,
as
of
Blasius'
pressure
of
consistency
agreement
8/6
error.
in
with
values
This
the
{25}
8/0
T his
each
thicknesses
were
theoretical
answer
to
parameters
B .L .
unexpected
curve
this
B.L.
almost
0
27),
came
for
5)
when
from.
the
(Figure
but
the
B.L.
s a me
Figure
= 2.8
p / p e TJ/ Ue ( l - U / U e )
at
not
the
On
27)
shows
only
fair
it
28
are
B.L.
dy
since
worst
question
did
to
zero
unexpected,
the
with
incidence,
showed
raised
identical
d istrib u tio n
CO
G = /
0
% ERROR
8.1
4.1
10.8
12.1
was
p r o f ile s
contradiction.
defining
{25}.
findings,
(Table
and
THEORY
zero
result
result
(Figure
curve
in
theory
experimental
non-dim ensional
theoretical
plate,
25
incompressible
( t h e ory)
B .L . v e l o c i t y
theory
Figures
MEASURED V.
flat
theory.
for
the
presented
incompressible
the
in
plate
14.42
13.83
12.09
10.76
of
gradient,
flat
appear
15.59
14.42
13.55
12.24
that
the
5 and
(measured)
A comparision
the
compressible,
BOUNDARY LAYER 5 / 0 ,
MACH NO.
the
{24}
12 %
of
why
match
the
and momentum
theory
that
provides
plotted
an
the
TE MOMENTUM
THICKNESS VS.
STAGNATION PRESSURE
TE. BOUNDARY LAYER
THICKNESS VS
STAGNATION PRESSURE
LOW'S
THEORY
LOW'S
THEORY*
M=2.80
M-265
• M.2 80
• M-2 65
I M-2.15
A M -1 .67
(MM HG)
P0 (MM HG)
Figure
25.
Experimental
theory.
B. L . 6 v.
Figure
26.
Experimental
theory.
B. L . 6 v.
47
a *A A *
• M = 2 .8 0
\
E X P O N E N T IA L
A M = I.6 7
UZUe = l- E X P ( - y /6 )
B L A S IU S -F L A T
PLATE
THEORY
d p /d x = O
Figure
27.
Experimental
B.L .
comparison
to
Blasius
profile.
A iPZpe E X P E R IM E N T A L
A U ZU e (I-U Z U e) E X P E R IM E N T A L
• ^ Z p e UZUe (I-UZUe)
P Z p e (C RO CC O
R E L A T IO N )
U Z U e (I-U Z U e ) [ B L A S I U S ]
/
Figure
28.
p Z p e U ZU e (I-U Z U e)
G r a p h i c a l c o m p a r i s o n of t h e o r e t i c a l
e n t e r i n g t he i n t e g r a n d of 0.
v.
experimental
properties
49
Only
one
shown
B.L . was
in
Figure
compared
27.
(p/P@U/Ug(l-U/Ug)
the
range
that
from
to
6
does
along
not
the
8)
Fre^e^ S h ^ a r
Number,
both
(Figures
the
also
/
in
0.004(probe
according
to
and
or
0 to
and
This
the
in
result
of
(0.18
c m. )
(seen
theory
to
= 18}.
thick
Probe
since
and
(0.01
This
exist
nozzle.
disparity,
in.
the
being
investigation.
cause
4,
suggests
a diverging
0.004
d i a .)
from
curve.
each
theoretical
curve
gradients
this
was
y/6
of
The L o w / B l a s i u s
30)
in.
the
the
occured
29 a n d
available
of
the
pressure
0.07
under
outside
a possible
stream
properties
velocity
and
cm. )
is
the
O. D.
a region
{15}.
the
29
in
Figures
f a s t —s i d e
and
30),
underexpans ion
experimental
data.
(edge
Reynolds
c o n fig u ra tio n s
in
range
consistency
Lj iy e i r . a n d Myzin FjLow M e y y u r e m y n y y
graphically
flow
the
under
present
typically
uncertainty
Free
are
probe
{0.07(B.L.
area
has
for
Figures
was
was
smallest
of
account
conditions
B. L.
effect
the
the
are
are
to
= ©(theoretical).
FSL i n
interference
the
they
a cancellation
also
In
values
12
©(experimental)
Both
Notice
curve.
experimental
due
the
is
in
31,
properties)
Number
Table
32
6
and
are
and
33.
such
as
summarized
also
Even
though
was
not
fully
results
show
good
consistency
believed
to
for
d e ta ile d
channel
not
Ma c h
the
expanded
compromise
and
the
"Q-XXW \ \ \ ^ \ \ \ \ \ \ \ \ \ N K \ \ > x :
EXPANSION
%
ASURFACE
- I MEASURED
along
fsl
O ON THIS SURFACE
A \ \X x L ALONG f I
FSL
A
•
O T H lS
MEASURED
ESTIMATED
SHOCK
THEORETICAL
M-1.6 NOZZLE
/ ASYMPTOTE
SURFACE
ON THIS SURFACE
I
FROM M«3 NOZZLE
AREA RATIO
z I
I
THEORETICAL
M -3 NOZZLE
ASYMPTOTE.
THEORETICAL
M - Z Z S NOZZLE
ASYMPTOTE \
THEORETICAL
M -3 NOZZLE ASYMPTOTE
DISTANCE FROM M=3 THROAT (INCH)
Figure
29
Configuration
gradients.
III
pressure
iO
DISTANCE FROM
Figure
30
M -3
20
THROAT
Configuration
gradient s .
30
IV p r e s s u r e
51
Table
6.
BOUNDARY LAYER AND EDGE P R O P E R T I E S .
Configuration
O^
©2
(cm.)
( cm.)
III
Configuration
.0123
.0152
.0120
.0125
U^ h i g h
U j I ow
Uj a v g
( cm/s )
( cm/s )
(cm/s)
65700
65050
65300
63400
62000
62700
U2 h i g h
U 2 I ow
U2 a v g
( cm/s )
(cm/s)
(cm/s)
58800
57650
58300
52100
50000
51400
Rej '
Re j '
Re j '
high
low
avg
( c m ^)
(cm I )
( c m- 1 )
40000
37400
38900
53200
50800
51800
Rej'
Rej'
Re j '
high
low
avg
( c m- ?-)
( c m - *)
(cm 1 )
21700
20600
21100
20800
20300
20500
high
low
avg
2.93
2.87
2.90
2.81
2.70
2.76
Mj h i g h
M2 I OW
Mj a v g
2.34
2.25
2.29
1.93
1.76
1.87
Mj
Mj
Mj
IV
r
C O N F IG U R A T IO N
»
F A S T -S ID E
O
S L O W -S ID E
I
III
3-
620
-
A
* U,
OU2
a
O
3-
540
O
-
-
•
I-
500
I
(m .)
.
4
D O W N S TR E AM
Figure
31.
Ma c h No .
distance
(cml
DISTAN C E
v.
in
•
•
-
I
(m.)
2
3
-J-----------------------------1-------------------------1---------------- 1_____
___________
2
(x )
4
DO W NSTREAM
Figure
•
I
6
downstream
FSL.
•
I
C
J ----------------------- 1____ ,_________ I
2
O
S L O W -S ID E
O
•
IV
O
F A S T -S ID E
IV
• U2
-
O
*
u,
-
M ACH
NO.
C O N F IG U R A T IO N
»
*
CONFIGURATION III; CONFIGURATION
(M/S)
580
A
a
A
V E L O C IT Y
I-
*
&
A
■— I----------
32.
Velocity
distance
(cm.)
6
D IS T A N C E
v.
in
(« )
downstream
FSL.
53
CONFIGURATION IV
• SLOW-SIDE
a
CONFIGURATION
III
FAST-SIDE
• SLOW-SIDE
* FAST-SIDE
O ESTIMATES
4
(cm.)
6
DOWNSTREAM DISTANCE (*)
Figure
33.
Reynolds
No .
v .
downstream
distance
in
FSL.
54
Figures
static
34
pressure
the
FSL.
The
the
consistency
trough
in
in
latter
the
95 % o f
tank.
a
pitot
in
the
total
due
Reference
detail
to
results
the
of
seen
x
total
temperature
•* ■ 0 2 ^ 0 1
^
This
taking
through
the
stagnation
FSL
velocity
is
the
profiles
defined
point
as
as
on
was
the
in
the
the
the
free
on
s l o w —s i d e .
in
were
being
stagnation
regarding
tunnel
facility .
accounted
in
The
for
depth
two
free
so
that
the
heat
equal
air
by
stream
connecting
flowing
the
P
q^
nozzle.
the
FSL,
stream
the
evidence
not
measurements
shown
x in Figure
fast-side
and
T. E.
the
are
existed
decrease
(h )
distance,
plots
the
expected.
pipe
through
trough
at
wind
secondary
slow-side
h versus
% from
the
the
th ick n ess
and p l o t t e d
in
be
n o n -in su la te d
to
this
values
phenomena
place
tank
measured
experimental
would
stream
transfer
The
to, s y s t e m a t i c a l l y
as
taken
measurements
temperature
95 % f o r
temperature,
s h o w n on t h e s e
profile.
wall
shows
total
profiles
pressure
temperature
increasing
I -
pressure
static
{17}
was
typical
pressure
factor
trough
with
and
total
recovery
The
35
noteworthy
the
the
and
in
were
taken
Figures
36
38.
measured
from
and
37,
The FSL t h i c k n e s s
in
the
where
the
velocity
velocity,
and
a
FSL,
between
differs
corresponding
by
I
point
55
O TOTAL TEMPERATURE
A STATIC PRESSURE
• PITOT PRESSURE
Ps (MM HG)
P0 (MMHG)
- 180
-140
-IOO
y - POSITION (CM)
Figure
34.
Configuration
FSL .
III
typical
properties
I
I '
I
CONFIGURATION IV
P5IMM HG)
yPglMM HG)
tO10r) /
/
590
r220
21 ------
- 180 -
•
•
e
•
*
O
A
580
A
I
O TOTAL TEMPERATURE
a STATIC PRESSURE
• PITOT PRESSURE
o
o o o
A
A
through
A
A
A
A
*
*
*
O O O O
57
- 140
560
550
•
- IOO
540
•
it
Figure
36.
-.3
Configuration
FSL.
e
•
-.2
M
O
y- POSITION (CM)
IV t y p i c a l
•
.1
properties
through
56
700
600
• Q
#
* S
,
500
VELOCITY
Y
(M /S)
»
A
•
Of ? *
^
&$ Y
A Q Y
A *
SHEAR LAYER PROFILES "
VELOCITY VS. y POSITION
M=2.I5
400
M=ZBO
TE.
—
300-
I »-
SYMBOL
200
-
ICO
%-POSITION (IN)
•
30
A
O
2.0
1.0
+
0.5
T
0.0
I
I
-.3
I ______
36.
I
>• °
-I
O
.1
y-POSITION (CM)
I
-H0 A 3 %
■
O
I
I
I
I
.2
V e l o c i t y v . y - p o s i t ion
Configuration III.
?
<n o
Figure
-.2
I
plot
in
FSL
I
A
»
O • V1
o «
V E L O C IT Y
- . O
O - O - O i s i s
■
(m /s)
• O • O • O
A •
A
“
•
A
400
•
«
CONFIGURATION
■ e
*
A
*
h
6 •
_
SYMBOL
#
A
f
o
i
-.3
i
-.2
i
T
. .I
i
O
y - P O S IT IO N
Figure
37.
"
A
M =2.65'
200
IV
M=I 67
i
-I
.2
,-P O SITIO N (in.
0°5
1.0
2 .0
3 .0
I
.3
(c m )
V e l o c i t y v . y - p o s i t i on
C o n f i g u r a t i o n I V.
plot
in
F SL
57
xT
V
(
.
i
O
•
o
o
O
O
O
O
i,
.4-.
O
r ------------------------ 1------------------------
-
•
h(cm)
4)
•
e
\ XT
#
I
CONFIGURATION IV
• -EXPERIMENTAL FSL
!-EXPERIMENTAL
B.L.
h
7
TE. % ---------------------- --- rI - I
CONFIGURATION III
O -EXPERIMENTAL
FSL
A-EXPERIMENTAL
B.L.
i
I
i
0
I
2
in.
3
--------------------1--------------------- 1-------------------- 1--------------4
cm.
6
DISTANCE
Figure
38.
h v .
x along
FS L
DOWNSTREAM
for
(x)
Configurations
III
and
I V.
58
Tr a n o n
Determination
The
determination
necessity
in, t h i s
v e r if ie d
is
A ctually,
of
only
itself
tran sitio n
versus
said
laminar
might
38,
that
a
III
tran sitio n
is
for
Configuration
the
T.E.
for
downstream
The
was
FSL
of
the
second
the
would
and
a
result.
a
ways
be
in
were
a
being
region.
point,
but
region
be
to
used
for
locating
the
used
much
in
this
in
Using
(4.6
III
and
1.5
will
used
decrease
Schlieren
in
in.
in
of
the
Arrows,
is
than
plot
seen
thickness
in
for
method,
it
appears
downstream
of
the
(3.8
The
denoted
for
rapidly
slope
FSL
this
cm. )
I V.
be
the
thickness
Turbulence
more
behavior;
change
I V.
profiles,
plotted.
change
photography.
FSL,
will
which
layer
in.
method
a
laminar
point
velocity
1.8
T.E,
at
was
theory
lam inar
a totally
can
Configuration
Schlieren
spread
flow
shear
slope
FSL
the
of
point
below.
tran sitio n al
show
Configurations
mean
the
occur
these
therefore
indicate
Figure
of
distance
the
growth,
not
from
detailed
the
spread
in
a variety
five
downstream
to
are
are
from
since
Transition
point,
First,
does
gradually
There
investigation,
tran sitio n
a p p lic ab le
turbulence.
sim plicity.
the
investigation,
t r a n s i t i o n
manifests
one
of
cm. )
downstream
tran sitio n
by
of
distance
xj,.
transition
determination
Since
tran sitio n
density
gradients
photographs
T. E.
of
tends
to
across
the
continuous
and
59
spark
exposures
contrast
can
be
due
seen
Schlieren
1.5
Yf oul d
to
in
the
decrease
Schlieren
photography
in.
(3.8
exhibit
cm.)
a
of
loss
density
photographs.
locates
fo r
of
black-white
gradients.
Figures
x-j, a s
2.3
in.
C o n f i g u r a t io n s
18
This
and
39.
(5.8
c m. )
and
I I I
and
IV
respectively.
The
la s t
tran sitio n
traverses
various
of
point
was
through
gave
hot-film
the
in s ta b ilitie s
As
to
an
has
been
early
from
as
Konrad
pairing
the
following
layers
the
T. E.
and
a brief
taken
at
proceeding
Before
in
A low
{26})
ways.
she d
manifests
presenting
discussion
in order
from
of
to give
low
speed
can
be
speed
a
flows,
good
these
by
in
to
this
of
a
is
vortex
vorticies
wave.
Sato
Figure
picture
related
p artitio n
into
sinusoidal
photograph
a
of
a
in stab ility )
itself
(pairing)
creates
provides
and
are
(Kelvin-Helmho.lz
direction
phenomena
at
the
anemometer
signal,
w i t h a FSL i s
amalgamation
observed,
1956.
hot-film
hot-film
indications,
instability
downstream
determ ining
results.
boundary
The
of
information.
associated
the
This
The
beginning
in sta b ility
structure.
a
FSL.
transition
two
created.
in
the
ways
qualitative
transition
the
credibility
three
by
x-positions,
downstream
(T.E.),
the
This
{19}
40
this
as
(taken
vortex
experiment
in
k
*
Figure
39.
Schlieren
Sp a r k and
photograph
continuous
*
.
&
t
„ %JL*
of C o n f i g u r a t i o n I I I t r a n s i t i o n d e t e r m i n a t i o n .
e x p o s u r e above and b e l ow r e s p e c t f u l l y .
Figure
40.
Edge a nd p l a n v i e w s of a l ow s p e e d
s h o w i n g wa ve s t r u c t u r e ( t a k e n f r o m
d i m e n s i o n o f p i c t u r e i s 15 c m.
( i n c o m p r e s s i b l e ) mixing l a y e r
{22}).
Scale:
streamwise
62
1.
Schlieren
39,
photographs,
show
t r a c e s
p articu la rly
2.
Hot-film
studies
and
42)
for
as
transition
Making
use
structure
of
the
F irst,
attached
to
a
above
the
at
component
of
region
o u t p u t ) of
at
that
shows
the
point
this
at
the
gave
set
region.
these
waves.
be
131
the
(Figures
FSL
free
KHz a n d 9 3
with
This
KHz
peak
increasing
x
in.
concerning
ways
to
this
wave
judge
where
was
3 4 0 0 A RMS
and
taken,
The
as
RMS
to
signal
shown
signal
therefore,
stream)
a
a RMS
voltm eter
intensity
in Figures
measures
traversing
one
of
q u a lita tiv e
was
43
the
from
a
t r a n s it io n a l
in d ic a tio n
of
activity.
peak p o s i t i o n
RMS p l o t
(frequency
the
s t r u c t u r e
respectively.
different
signal
flow,
(free
laminar/transitional
to
frequency
to
x values.
the
(FSL),
Second,
in
of
and
was.
trace
succeeding
a c ti v it y
III
18
frequency
of
information
three
hot-film
and
lam inar
in
versus
Hewlett-Packard
y-position
a .c.
and
thought
point
versus
44
was
cause
a frequency
IV
Figures
tran sitio n al
(thought
decreased
resulted
transition
peak
at
Configurations
systematically
the
intensity
a
boundary)
in
in
w a v e —l i k e
a possible
of
reveal
seen
t h i s
not!cable
B addresses
stream
the
of
Appendix
41
as
was
vs.
( ma xi mum
noted
a
spectrum
intensity).
Figures
corresponding
and
intensity
x-values.
wideband
was
41
taken
and
42
63
Third,
succeeding
and
of
x-positions
three
plotted
at
the
175
KH z
downstream
versus
c a n be
y —p o s i t i o n
seen
which
Us e
in
at
Figures
45
is
ju stifie d
the
in
applied.
(3.3
cm. )
not
for
respectively.
mean
Table
portion
was
mid-point
of
As
begins
This
was
flow,
transition
Transition
flow
intensity.
increasing
determining
laminar
dispersion
magnitudes
stated
from
the
graphs
therefore
{27},
noting
with
denotes
in
a
the
in
are
the
decrease
onset
which
chosen
for
of
the
the
point.
of
summarized
peak
tran sitio n
spectral
is
relative
and 48.
The
transitional
above
47
o scillatio n
intensity
theory
the
x in F ig u res
for
turbulence.
of
of
versus
criterio n
point
in
signal
46.
All
a
a
Schlieren
gave
and
transition
hot-film
points
methods
that
are
since
the
where
the
7.
determination
was
of
the
the
The
observed
FSL w a s
above
important
only
results
beyond
Configuration
2.0
III
region
suggest
in.
and
(5.1
that
cm. )
and
laminar
1.3
Configuration
in.
I V,
INTENSITY
NOISE
CONFIGURATION
f (KHZ)
Figure
41.
Configuration
III
spectra
v. X.
INTENSITY
NOISE
f (K HZ)
Figure
42.
Configuration
IV spectra v. x.
CONFIGURATION III
NOISE
O
0.5
1.0
15
2.0 25
2.75 3.0 3.25 3.5 3.75 4.0
DOWNSTREAM
Figure 43.
Configuration
III RMS v . x .
DISTANCE (IN.)
I
I
I
i
I
I
I
I
CONFIGURATION
IV
rms
NOISE
_____ I_____ I_____ i_____ i
O
Figure
44.
0.5
i
i
i
i
1.0 1.5 2.0 2.5 3.0
DOWNSTREAM DISTANCE
Configuration
IV RMS v . x .
.
(IN .)
CONFIGURATION
175 KHZ
III
NOISE
O 0.5
Figure
45.
1.0
1.5 2.0 2.5 2.75 3 0 3.25 3.5 3.75 4.0
DOWNSTREAM DISTANCE (IN.)
Configuration
III 175 KHz.
signal v . x .
CONFIGURATION
NOISE
O 0.5
1.0
DOWNSTREAM DISTANCE
Figure
46.
Configuration
IV 175 KHz.
(IN )
signal v. x .
IV
CONFIGURATION IV
HOT-FILM INTENSITY
VS. DOWNSTREAM
DISTANCE
* RMS SIGNAL
* 175 KHZ SIGNAL
O 130 KHZ SIGNAL
INTENSITY
SLOW
SlOE
(orbilrory
units)
14
INTENSITY
(ARBITRARY 12
UNITS) IO
O
• 175 KHZ SIGNAL .
A RMS SIGNAL
O 93 KHZ SIGNAL '
IO
(CM)
4 (IN)
X-DISTANCE DOWNSTREAM
DOWNSTREAM
Figure
47.
G r a p h i c a l r e s u l t s showing
Configuration III hot-film
transition points.
Figure
48.
DISTANCE
U)
G r a p h i c a l r e s u l t s showing
C o n f i g u r a t i o n IV h o t - f i l m
transition points.
71
TABLE 7 .
SUMMARY OF TR A N S IT I O N P O I N T S .
Configuration
Me t h o d
xT i n .
h v . x
S c h l i e r e n Pho t o s
RMS v . x
RMS P e a k S p e c t r u m v . x
175 KBz. s i g n a l v . x
Average
Comparison
The
needed
The
Configuration
(cm.)
in .
X rji
I . 8 (4.6)
1.8 (4:6)
2.0 (5.1)
1.8 (4.4)
2.3 (5.7)
2.0 (5.1)
IV
(cm.)
1 . 5 (3.8)
1.5 (3.8)
.7 ( 1 . 8 )
1.0 (2.5)
I . 8 (4.6)
1.3 (3.3)
w.i.th T h e o r y
previous
as
inputs
graphical
development
curves
III
experimental
into
the
present
computer
that
increasing
downstream
generated
results
by
of
the
a ll theparam eters
code
comparisons
with
were
sections
provided
follow detail
distance.
computer
Configuration
{ I }.
the
FSL
The
code
III
in
and
solid
and
the
IV
are
s u p e r i m p o se d .
Configuration
Figure
x-position
found
in
pronounced
prediction
49
IJI
shows
the
proceeding
the
cusp
deviation
at
x'
=
minimum
velocity
downstream.
of
the
from
0 .1 1 2
The
trough
the
(x
minimum
(y'
theoretical
=
1 .0
growth
in.).
= 0).
each
velocity
Notice
laminar
This
at
is
is
the
growth
1.0
in.
72
before
the
suggests
x
= 1.0
transition
that
laminar
in.
50
the
and
at
in.
0.112).
=
experimental
the
at
the
T.E.
a point
use
T.E.
the
of
points
in
Table
exsists
51
show
progressing
at
obtained
of
d if f e r e n t
the
the
at
the
development
to
x'
just
firs t
x = 1. 0
= 0
of
the
upstream
of
FSL t r a v e r s e
Chapter
probes
result
x = 0 and
downstream
T.E.
p ito t
This
FSL
a point
in
7.
between
consistency
taken
downstream
two
only
the
points
just
given
and
Note
B .L .
and
flow
Figures
beginning
(x '
point
5 discusses
for
these
two
measurements .
C o n f J - J j u r a.I:. i o n
Figure
IV
52
shows
configuration.
already
7,
two
At
reached
tran sitio n
Figure
53
shows
corresponding
x'
to
=
minimum
0. 3
the
sets
x —p o s i t i o n s
the
(x
the
the
velocity
minimum
asymptote.
in
rapidly,
= 0
and
As
in.)
FSL d e v e l o p m e n t
x ' = 0 and
velocity
therefore,
x = .5
at
x ' = 0.059.
growth
noted
only
will
these
be
of
this
ratio
has
in
Table
the
firs t
compared.
x-positions
73
C O N F IG U R A T IO N
U g /U ,
III
ASYMPTOTE
r = .893
D E M E T R IA D E S '
L A M IN A R F S L
M1= 2.9
THEORY
Figure 49.
Theoretical v. experimental minimum velocity
growth in FSL of Configuration III.
CONFIGURATION III
DEMETRIADES
FSL THEORY
• F S L - EXPERIMENTAL
a
BLASIUS
T.E. B. L.
EXPERIMENTAL
SLOW-SIDE
FAST-SIDE
Figure
50.
Theoretical v. experimental FSL development at
x ' = 0 of Configuration III.
75
x' " 0 . 0 5 6
*'■ 0.112
Figure
51.
Theoretical
x ' = 0.056
v . e x p e r i m e n t a l FSL d e v e l o p m e n t a t
and x ' = 0.112 of C o n f i g u r a t i o n
76
C O N FIG U R A TIO N
IV
U m in./U
U g /U l
ASYMPTOTE
P= .96
D EM ETR IA D E S
L A M IN A R
THEORY
— = .983
Figure 52.
Theoretical v . experimental minimum velocity
growth in FSL of Configuration IV.
77
DEMETRIADES
FSL THEORY
CONFIGURATION IV _
• F S L -EXPERIMENTAL
A T E. B.L.
EXPERIMENTAL
-
BLASIUS
Figure
53.
Theoretical v . experimental
x ' = 0 and x ' = 0 . 0 5 9 .
FSL d e v e l o p m e n t
at
CHAPTER 7
CONCLUSIONS
The
the
conclusions
FSL
region
Configuration
< I
in.
shows
for
good
III
1.
uses
theory
Figures
show
at
that
the
2.
profile
was
The
range
the
T .E .
is
re s tric tio n
FSL r e g i o n
I V.
The
in
1.5
the
theory
of
in.
for
range
0 < x
Demetriades
following
statments.
shown
in
the
exponential
52.
and
initial
FSL
The
profiles
be
the
arbitrarily
in
the
to
in
profiles
(x'
= 0)
considerably
difference
show
choice
the
to
in
that
define
exponential
theory.
exponential
chosen
is
figures
than
seen
x = 0
The
a better
profile
B. L.
at
profile
proceeding
would
used
profile
Experimental
exponential.
that
Demetriades
in itia l
simplify
the
velocity
algebra
equations.
places
not
<
be
velocity
governing
x
in
agreement
3 5 %.
{1}
<
obtained
poor
Profile
theory
0
results
but
and
currently
in
the
an
the
qualitatively,
the
in itia l
states
of
in
on
measured v e lo c i ty
than
Blasius
profile
and
50
the
thickness
the
the
will
27,
thicker
the
in
agreement
as
taken
based
Configuration
quantitatively
The
are
met
restric tio n s
in
this
on
the
experiment
flow.
was
that
One
the
79
pressure
Figures
3,
was
29
and
theory
shows
FSL
in
initial
its
also
51
53),
and
The
the
The
experimental
this
5.
The
this
h
theory
width
(Figures
50,
51
in
at
its
laminar
of
the
range
of
in
and
of
in
the
53).
The
(Figure
Figures
50,
considerably,
x (far
velocity
x
(h)
portion
comparisons
large
investigation
shows
parallel
An e r r o r
for
from
the
profile
laminar
not
and
thickness
T. E. )
is
flow
was
not
in
sufficient
velocity
the
experimental
between
results
20-50 % e x is ts
to
this
verify
results^
required
experimental
to
match
theoretical
curve
experimental
the
shown
point
in
growth
The
Figure
horizontally
in the
factor
that
points
to
the
moving
the
49,
to
rates
qualitatively.
quantitatively
experimental/theoretical
by
the
right,
is
is
2.
expression:
* . 9 —
= x / p nRe’
x'
where
K = 2 is
error
of
point
were
the
shown
statement.
that
The
was
the
differs
that
shape
important.
This
in
experimental
states
in itia l
growth
stages
although
theory
the
little
confirms
38 a n d
constant.
30.
The
experiment
4.
everywhere
required.
between
20-30
matched
experimental
to
point
An e r r o r
% exists
the
of
if.
theoretical
vertically
50 % i s
the
seen.
An
experimental
curve
downward.
by
moving
80
6.
Waves
in
the
FSL
Chapter
6 and
address
the
were
also
seen
to
exist
in Appendix
presence
of
C.
waves
as
The
or
discussed
theory
their
does
effect
in
not
on
the
flow.
7.
The
theory
of
downstream
Demetriades
distance
x '
where
Re'
average
is
average
unit
Number
Reynolds
is
the
non-dimensioning
the
downstream
lim iting
= 0,
near-wake
closely
+
looked
(r
at.
In
Re ' ( s I o w - s i d e ) } / 2
Re ' ( f a s t - s i d e )
will
{Re'(fast-side)
this
case
fraction
it
of
flow.
In
found
that
U2 ) / 2 , b u t
study
.53
+
is
the
a
in
not
unit
U1 .
wave
the
the
=
wake,
Number.
obvious
distance
and
Re '
r = 1>
In
since
the
Reynolds
speed
was
obvious
incompressible,
Brown
not
in
until
the
wake)
are
near-wake,
and
= 0.
Roshko
flows
=
In
this
govern
necessarily
turbulent
Re'
that
Number wo uld
argument
choice
Obviously,
Re'(slow-side)
in tu itiv e ly
The
= {Re'(fast-side)
R e '(fa s t-s id e ).
govern.
0}/2
sim ilar
the
non-dimensional
as:
Reynolds
cases
the
= x * / PRe'
the
unit
defines
the
{28}
( U^
+
under
81
APPEND ICES
82
APPENDIX A
T R A N S IT I O N THEORY COMPARISON
The
of
la tte r
transition
and
portion
as
2.0
in.
IV r e s p e c t f u l l y .
these
two
known
about
appear
a
{29}.
in
The
FSL
equilibrium
agreement
be
region.
to
this
C o n fig u ratio n
III
not
in
equilibrium
FSL
theoretical
wake
p o s itio n
speculative
of
curve
Configuration
This
IV
experimental
suggested
2.0
in.,
The
curve
X
this
in
and
Brower
{1}
point
from
was
in
point
that
it
Figure
the
above
shear
the
layer
seen
fall
on
was
0.06
either.
on
transition
in
36
the
so
The
the
for
Figure
predictive
is
showed
Figure
expected.
As
FSL
from
54,
to
the
in
measured
f a llin g
approach
aI .
present
point,
was
could
the
not
applicable
successful.
falls
clearly
should
not
theoretical
proved
and
the
is
mini mum
et.
occuring
Since
III
l it tl e
transition
{(U^-Uj) / ( U ^ + l ^ ) }
experim ental
drawn
a
onset
compare
on
Demetriades
54);
region,
curve.
the
Continuing
the
was
tran sitio n
with
based
before
by
to
since
A theory
transition
(Figure
distance
a
advantageous
satisfied
theory
the
Configurations
a theory,
FSLs .
with
identifies
for
Demetriades
transition
the
to
proposed
dealt
6
in.
w o u l d be
in
to
was
theory
1. 3
points
transition
needing
Chapter
and
It
tran sitio n
conditions
of
55,
curves.
already
in
a
83
transitional
combined
allowed
state
B.L.'s
for
distance
in.
this
flow.
past
case.
th eo retical
curves
(increase
before
h)
the
(8^ + 82) at
lam inar
finite
in
before
the
An
T. E.
the
Of
T. E.
This
T.E.
point
suggest
transition
would
that
set
the
larger
h
itself,
falling
the
in.
FSL
of
than
tra n sitio n
manifest
experimental
would
was
course
to
meant
the
the
h
needs
a
about
1.3
below
the
must
grow
84
FSL A S Y M P T O T IC
FOR A
I
WAKE A S Y M P T O T IC
FO R A - O
SPECULATIVE
CONFIG URATIO N
DATUM
Figure
54.
III
Experimental transition point for
Configuration III.
85
FSL A SYM PTO TIC
FOR A
I
WAKE A S Y M P T O T IC
FOR A - O
CONFIGURATION IV
DATUM
SPE C U LA T IV E
I l l i
Figure 55.
Experimental transition point for
Configuration IV.
86
AP P ENDI X B
TUNNEL VI BR AT I ON
The wave
attributed
tend
1.
2.
to
structures
to
tunnel
invalidate
vibration.
this
observations
any movement
of
An
as
the
accelerometer
0 < f
the
wind
intensity
The
in
to
plate
was
be
a bar
T.E.
MB 3 0 3 ,
placed
(Figure
with
about
of
the
did
c o u l d he
observations
not
indicate
56)
frequency
above
operating.
natural
is
following
flow
p late.
No.
was
activity
fundamental
s p litte r
plate
< 5 0 KHz)
spectrum
a decrease
of
splitter
(Model
tunnel
The
in the
statem ent.
M icroscopic
range
3.
seen to e x is t
The
that
42 KHz,
constant
of
section
frequency
versus
indicated
frequency.
the
assuming
cross
test
resulted
increasing
frequency
the
response
cantilevered
the
section.
s p litte r
87
INTENSITY
NOISE
NOT
APPLICABLE
FREQUENCY
Figure
56.
Frequency v . in te n s ity
accelerometer attached
section.
(KHZ)
s p e c t r a from
above the t e s t
APPENDIX C
WAVE STRUCTURES
During
the
reasonable
lifetim e
that
it
of
travels
a wave
at
structure
some
constant
average
( U^
+ U2 ) / 2 .
Then
passing
any
station
x would
be
invariant
frequency
is
observed
constant,
but
the
increasing
x past
Therefore,
to
speed,
The
keep
As
Figure
h
57
to
lam inar
the
= frequency)
mechanism
width.
in
f
the
frequency
region
governing
valid,
increase
increases
the
the
the
wave
wave
would
speed
seem
near
the
(f )
of
the
if
X
rem ained
to
Xf
length
length
wave
decrease
(Figures
equation
X increases
it
41
for
and
42).
= u (u = wave
must
is
h,
proportionately
increase.
the
as
FSL
show n
giving:
X
= 1 .4 h
"1X u s e d h e r e i s t h e w a v e l e n g t h o f t h e w a v e ,
confused w ith the n o n -d im e n sio n a l speed r a t i o
U0 ) .
<U 1 " U 2 ) / ( U 1
Not
to
be
89
T
T
A
1 .0 -
CONFIGURATION III
# CONFIGURATION
IV
A-jM
.8
-
.6
-
.4 -
2 -
.2
.3
.4
.5
%
Figure
57.
N o n - d i m e n s i o n a l g r a p h s h o w i n g t h e wave
s t r u c t u r e w a v e l e n g t h t o be p r o p o r t i o n a l
t o t h e F SL t h i c k n e s s .
90
APPENDIX D
DATA REDUCTION PROGRAM FOR BOUNDARY LAYER P R O F IL E S
LIST
10 REM LAST UPDATED: 1-30-83
20 REM
*»*86*6»466*#*BOUNDARY-LAYER PROGRAM*****&*******8*
30 REM
40 REM
PROGRAM TO CALCULATE MEAN FLOW PROPERTIES OF A BOUNDARY LAYER
50 REM
WITH ASSUMED STATIC PRESSURE AND TOTAL TEMPERATURE
51 REM
52 REM
A CORRECTION IS USED FOR POINTS THAT HAVE A REYNOLDS
53 REM
NUMBER BASED ON PROBE DIA. LESS THAN 200.
54 REM
60 DIM Y l ( 4 4 0 ) , YY( 4 4 0 ) ,MACH(440) ,PO( 4 4 0 ) , P02( 4 ^ 0 ) ,U(4 4 0 ), P l (4 4 0 ), P (440)
70 DIM TS( 4 4 0 ) ,D( 4 4 0 ) ,YTILL(440)
80 REM
90 PRINT "WHAT IS FILE FOR PITOT DATA"
100 INPUT FlO
HO PRINT "WHAT IS STATIC PRESSURE"
120 INPUT Pl
130 PRINT "WHAT IS TOTAL TEMP"
140 INPUT TO
150 PRINT "FOR LOW RE PITOT CORRECTION: WHAT ARE CALIBRATION POINTS"
160 PRINT "Y=A+BX+CX''2+DX''-3+EX''4+F)(A5"
170 PRINT " i . e . I . 0 . 0 . 0 . 0 , O WOULD BE INPUT FOR NO CORRECTION"
180 INPUT Z 1,Z2,Z 3,Z4,Z5,Z6
190 K=O
200 K=I
210 PRINT "OUTPUT FILE NAME FOR VELOCITY V. DIST"
220 INPUT V*
230 PRINT "OUTPUT FILE NAME FOR DIMENSIONLESS GROUP"
240 INPUT WS
250 OPEN ,0",#2,V S
260 OPEN "0".#3,WS
270 OPEN " ! " , D l l FlS
280 REM
290 REM
300 REM
************* NOMENCLATURE ***********************
310 REM
H=HEADER NO.
320 REM
x=distance from t r a il in g edge
330 REM
PO=STAGNATION PRESSURE
340 REM
TOI =STAGNAt I ON TEMP
350 REM
. Al=CAL CONSTANT (SLOPE) OF PITOT PRESSURE
360 REM
A2= "
"
(INTERCEPT) OF PITOT PRESSURE
370 REM
Cl= "
"
(SLOPE) OF Y-POSITION
380 REM
C2= “
"
(INTERCEPT) OF Y-POSITION
390 REM
N=NO. OF POINTS IN PROFILE
400 REM
Yl=Y-POSITION IN COUNTS
410 REM
YY=Y-POSITION IN CM
420 REM
P02=STAGNATI0N PRESSURE IN MM HG
430 REM
U=VELOCITY IN CM/S
440 REM
Pl=STATIC PRESSURE IN MM HG
450 REM
TS=STATIc TEMPERATURE IN DEG R
460 REM
D=DENSIty IN GM/CM''3 '
470 REM
YTI LL=NON-DIMENSI ONAL
480 REM
RENUM=UNIT REYNOLDS NUMBER
490 INPUTDl, H ,X, PO,TOl, A l, A2,C l , C2.N
500 REM
510 REM
520 PRINT
530 PRINT
540 PRINT "********************************"
550 PRINT "********************************"
91
560 PRINT "
B . L . DATA FOR RUN NO.";H
570 PRINT "*#***$***$$C**#****#$*#*{[A##o$$(["
580 PRINT
590 PRINT
600 FOR I=I TO N
610 INPUT#1,Y1( I ) 1PO(I)
620 YY(I)=ABS<.00254*(C l#Y1( I >+02))
630 NEXT I
640 PRINT
650 PRINT
660 PRINT "***********#$##****#''
670 PRINT
680 PRINT "ASSUME STATIC PRESSURE
= CONSTANT =";P1
690 PRINT "ASSUME TOTAL TEMPERATURE = CONSTANT = " ; TO
700 PRINT
*
710 PRINT »#
8
6
$
8
8
8
8
8
6"
720 PRINT
"Y (CM) " , "PO (MM HG)" , "PS (MM HG) ", "TSTATI C (R) "
730 PRINT "POINT
740 PRINT
" . "VEL <CM/SEC> " ," MACH #"
750 REM
NEWTON-RAPHSON METHOD TO SOLVE RAYLEIGH'S FORMULA
760 REM
FOR MACH NO. GIVEN P1/P02 RATIO
770 REM
780 FOR I=I TO N
790 J=O
800 P 0 2 ( I ) =Al#P0( I ) +A2
810 REM IF Pl
P02 SOMETHING IS WRONG WITH THE CALIBRATION
820 IF (P 1 /P 0 2 (I> ) > .9999 GOTO 1150
830 IF (P 1 /P 0 2 ( I )) > .5283 GOTO 950
840 M=I.3
850 F=( ( ( I; 16667*M-'2-. 1 6 6 6 6 7 ) '2 .5 ) / ( 1. 2#M"'2) ^ (+3.5) ) - ( P l / P 0 2 ( I ) )
860 DF1=3.08164*M"2* ( I . 16667*M''2 - . 166667)"'1.5
870 DF2=3.69 797*(I . 16667*M '2-.166667)"2.5
BBO DF=(DFl-DF2>/M'-8
890 DELTA=F/DF
900 M=ABS(M-DELTA)
910 IF ABS (DELTA)<=.0001 GOTO 930
920 GOTO 850
930 MACH(I)=M
940 GOTO 980
950 MACH ( I >= ( ( (P02 ( I ) / P l ) ' v. 2857-1) *5) 5
960 REM
970 REM
980 REM CALCULATION OF LOCAL TEMP USING MACH NO. AND TOl
990 TS( I ) =TO/( I + . 2*MACH( I ) A2)
1000 REM
1010 REM
1020 REM
CALCULATION OF VELOCITY USING SP OF SOUND AND MACH NO. (CM/SEC)
1030 U ( I ) =1494*SQR(TS(I)) AMACH(I)
1040 REM
1050 REM
1060 REM CALCULATION OF DENSITY <GM/CM/;3>
1070 D ( I ) = . 000836AP1/TS <I >
1080 IF (J) =1 GOTO 1150
1090 VIS=( . 7*TS <I >/311) * 1 . 7498E-07
1100 RE=U(I)*D(I ) * . 0 1 / (VIS6981)
. .
1110 IF (RE) > 200 GOTO 1150
1120 P02 ( I ) =P02 (J ) / (Z1+Z2BRE+Z3ARE 2+Z4*RE''3+Z50RE/'4+Z6*RE/'5)
92
1130
1140
1150
1160
1170
1180
1190
1200
1210
J =I
GOTO 820
PRINT I . YY( I ) , P02<I >. P l f TS(I)
PRINT ,
. U ( I ) f MACH(I)
PRINT # 2 . Y Y (I),U (I)
NEXT I
PRINT
PRINT
REM
TE IS THE FREE STREAM TEMPERATURE
1220 REM
1230
1240
1250
1260
1270
1280
1290
1300
1310
1320
1330
1340
1350
1360
1370
1380
1390
1400
1410
1420
1430
1440
1450
1460
1470
1480
1490
1500
1510
1520
1530
1540
1550
1560
Ok
DE IS THE FREE STREAM DENSITY
REM UE IS THE FREE STREAM VELOCITY
REM
THETA IS THE MOMENTUM THICKNESS
REM
THETA WILL BE AN INPUT INTO SHEAR PROGRAM
REM
TE=O
DE=O
UE=O
THETA=O'
YTILL(O)=O
YY(O)=O
FOR I=I TO 10
TE=(.1*TS(N+1-I)+TE)
UE=( . I $U <N+1- 1) +UE >
DE=( . I 8D(N+I - I ) +DE)
NEXT I
FOR I=I TO N
THETA=THETA+D ( I ) »U ( I >* <I-U ( I >/UE) * (YY(I) -YY ( I - D )
YTILL ( I ) =YTfLL ( I - I ) + (D <I ) /DB) * (YY ( I ) -YY ( I - D )
NEXT I
THETA=THETA/(DE*UE)
FOR I=I TO N
YT=YTILL(I)/THETA
UT=Ud ) /UE
PRINT #3,UT.YT
NEXT I
REM CALCULATION OF VISCOSITY (GM*SEC/CM-'2> USING SWT-TR-Bl-Ol
VIS=( . 7STE/31I ) * 1 .7498E—07
REM
UNIT REYNOLDS NO. /C M
RNUMl=<UE*DE>/ (VIS*9BD
PRINT
PRINT
PRINT “MOMENTUM THICKNESS (THETA)=";THETA:" (CM)"
PRINT "UNIT REYNOLDS NO. =
RNUMl; " (/CM)"
END
93
APPENDIX E
DATA REDUCTION PROGRAM FOR FREE SHEAR LAYER P R O F IL E S
LIST
10 REM UPDATED LAST 1-23-83
11 REM *******SHEAR2*$**#**
12 REM THIS PROGRAM HAS INPUTS OF PITOT PRESSURE, STATIC PRESSURE AND
13 REM TOTAL TEMPERATURE. THESE INPUTS ARE IN THE FORM OF PROFILES.
14 REM THE PROGRAM THEN USES THESE PROFILES TO CALCULATE MEAN FLOW
15 REM PROPERTIES ACROSS THE SHEAR LAYER. OUTPUTS ARE IN THE FORM
16 REM OF HARD COPY AND INTERNALLY SAVED NON-DIMENSIONAL FILES
17 REM USED AT A LATER TIME.
18 REM
19 REM
20 DIM YK 300) , YY(300) , MACH (300) , PO (300) , P02 (300). U <300 >. P K 300) .P t 300)
30 DIM TS( 3 0 0 ).D ( 3 0 0 ),T 0 4 <300), T (300).T 0 3 (300), UT<300) ,YTILL(300)
40 REM
50 REM
60 PRINT “WHAT ARE FILES PDATAXXXX,SDATAXXXX, TDATAXXXX,TOl"
70 INPUT FlS
I
BO INPUT F2S
90 INPUT F3S
1 0 0 INPUT TOl
HO DUMPl=TOl
120 OPEN “ I " ,# 1 ,F 1 $
130 OPEN " I “ ,#2,F 2$
140 OPEN " I “ ,#3.F3S
150 REM
H HEADER NO.
160 REM
X=DISTANCE FROM TRAILING EDGE
170 REM
PO=STAGNATI ON PRESSURE
180 REM
TOI =STAGNAt I ON TEMP; ASSUMED
190 REM
Al=CAL CONSTANT (SLOPE) OF PITOT PRESSURE
200 REM
A2=
(INTERCEPT) OF PITOT PRESSURE
210 REM
BI =
(SLOPE) OF STATIC PRESSURE
220 REM
(INTERCEPT) OF STATIC PRESSURE
82=
230 REM
Cl =
(SLOPE) OF Y-POSITION
240 REM
C2(INTERCEPT) OF Y-POSITI ON
250 REM
REMEMBER THAT TO ACCOUNT FOR ANGLE OFF T.E. THIS INTERCEPT
260 REM
MUST BE CHANGED PROCEEDING DOWNSTREAM AS:
270 REM
NEW "b" = OLD "b" * NEW "COUNTS" / OLD "COUNTS"
280 REM
Dl=CAL CONSTANT (SLOPE) OF TOTAL TEMPERATURE
290 REM
D2= “
"
(INTERCEPT) OF TOTAL TEMPERATURE
300 REM
N=NO. OF POINTS IN PROFILE
310 REM
THETAl=MOMENTUM THICKNESS OF FAST-SIDE AT T.E.
320 REM
THETA2=M0MENTUM THICKNESS OF SLOW-SIDE AT T.E.
330 INPUT#I . H ,X, PO,TOl, A l, A2,C l , C 2,N,THETAl, THETA2
340 I NPUT#2, HH, XX, PPO. TTOI , BI , B2
350 INPUT#3,HHH,XXX, PPPO,TTTOl, D l, D2
360 REM
370 REM
380 PRINT
390 PRINT
400 PRINT "#****$*#*#*#******#*****$*$**8*#"
410 PRINT "*&8*#*8*****&&8*&8&8&****$a*8*@8"
420 PRINT "
DATA FOR RUN NO."jH
430 PRINT "&#8&**&8*&**&88***8&&888p8888888"
440 PRINT
450 PRINT
460 FOR I=I TO N
470 INPUT#1, Y l ( I ) , P O ( I )
480 INPUT#2, Y2, P d )
490 INPUT03,Y3.T (I)
94
500 YY <I ) =. 002546 (Cl SYl ( I >■«-C2>
310 NEXT I
520 PRINT
530 PRINT
540 PRINT
550 PRINT
560 PRINT
570 PRINT "0
S
$
6
8
8
8
8
8
8
$M
580 PRINT
590 PRINT "POINT 0 " , "Y <CM>" , "PO (MM H G )"."PS (MM H G ) “TSTATI C (R)“
600 PRINT "
","TTOTAL (R)","VEL (CM/S)" , "MACH #"
610 REM
NEWTON-RAPHSON METHOD TO SOLVE RAYLEIGH'S FORMULA
620 REM
FOR MACH NO. GIVEN P1/P02 RATIO
630 REM
640 FOR I=I TO N
650 P02(I)=A1*P0(I)+A2
660 P l (I)=B1*P(I)+B2
670 IF ( P I ( I ) /PQ2( I )) > .5283 GOTO 790
680 M=I . 3
690 F=< ( ( I . 16667*M '2-.1 6 6 6 6 7 ) '2 .5 ) / < 1. 28MA2 ) ^ ( + 3 .5 ) ) - ( P l ( I >/PQ2( I )>
700 DFl=3.08164*M-'-28(l. 16667*M''2-. 166667)^1.5
710 DF2=3.69797* ( I . 166678M''2-. 166667) A2 . 5
720 DF=(DF1-DF2)/MA8 •
730 DELTA=F/DF
740 M=ABS(M-DELTA)
750 IF ABS (DELTA)< = .OOOl GOTO 770
760 GOTO 690
770 MACH(I)=M
780 GOTO 820
790 MACH <I ) = < ( (P02( I >/ P l ( I ) ) ^ . 2857-1> 8 3 ) 5
800 REM
810 REM
CALCULATION OF TOTAL TEMP
820 REM
CALCULATION OF LOCAL TEMP USING MACH NO. AND TOl
830. REM CALCULATION OF VELOCITY USING SP OF SOUND AND MACH NO.
840 REM CALCULATION OF DENSITY (GMZCMaS)
850 REM
CALCULATION OF VISCOSITY (GM8SEC/CMA2)
860 REM
CALCULATION OF REYNOLDS NO. BASED ON .013 CM-DIA THERMOCOUPLE
870 TOl=DUMPl
880 T03( I ) =DI *T( I >+D2+460
890 TSS=TOl/ ( I + . 28MACH( I ) A2>
900 UU=I 494*SQR(TSS)SMACH(I)
910 DD=.000836&P1( I ) /TSS
920 VIS=( . 7#TSS/311 ) 8 1 .7498E-07
930 RED=UU*DD*.013/(VIS8981)
940 DUMP=.9151+.0004799*REDA. 5 - 2 . 302E-058RED
950 T02= (T03<I ; -TSS)/DUMP+TSS
960 IF ABS (T02-T01) <= .0 5 GOTO 990
970 T01=T02
980 GOTO 890
990 T0 4 ( I ) =T02
1000 U(I)=UU
1010 TS(I)=TSS
1020 D(I)=DD
1030 PRINT I . Y Y (I),P 0 2 ( I ) . P l ( I ) ,T S(I)
1040 PRINT ,TOA(I),U(I),MACH(I)
1050 NEXT I
1060 REM
1070 REM
1080 REM
TEl IS THE FAST-SIDE FREE STREAM TEMPERATURE
1090 REM
TE2 IS THE SLOW-SIDE FREE STREAM TEMPERATURE
1100 REM
DEl IS THE FAST-SIDE FREE STREAM DENSITY
1110 REM
DE2 IS THE SLOW-SIDE FREE STREAM DENSITY
1120 REM
UEl IS THE FAST-SIDE FREE STREAM VELOCITY
1130 REM
UE2 IS THE SLOW-SIDE FREE STREAM VELOCITY
1140 TEl=OsTE2=0
1150 DEl=OsDE2=0
95
1160
1170
I 130
1190
1200
1210
1220
1230
UEl=0sUE2=0
YT=O
.CLOSE #1
FOR I=I TO 10
TE!=< .I #TS<N*1—I ) *TE1)
TE2=( . I 8TS( I ) +TE2)
DE1=(.1*D<N+1-I)+DE1)
DE2= <. I 6D ( I >•*-DE2)
1240 LIE I = ( . I #U <N+1 —I ) -e-ljEl)
1250
1260
1270
.1280
1290
1300
1310
1320
1330
1340
1350
1360
1370
1380
1390
1400
1410
1420
1430
1440
1450
1460
1470
1480
1490
1500
1510
1520
1530
1540
1550
1560
1570
1580
1590
1600
1610
1620
1630
I 640
1650
1660
1670
1680
1690
1700
1710
Ok
UE2=(.1*U(I)+UE2)
NEXT I
REM
REM
CALCULATION OF VISCOSITY (GM*SEC/CM^2) USING SWT-TR-Bl-Ol
V IS l= <.7*TE1/ 3 1 1 ) #1.7498E-07
VIS2=(.7*TE2/311)*1.7498E-07
REM
CALCULATION OF UNIT REYNOLDS NO./CM ON FAST-SIDE
RNUMl= <UE1*DE1> / (VIS I »981)
REM
CALCULATION OF UNIT REYNOLDS NO../CM ON SLOW SIDE
RNUM2=<UE24DE2>/ <VIS2#981>
PRINT
PRINT "REV = "RNUM1;" /CM"
PRINT "RE2'= ";RNUM2s" /CM"
XP=(X #2.54>/(<(RNUM1+RNUM2)/2 )& (THETA1+THETA2)^2)
PRINT "X'= ";XP
REM FIND WHERE U(MIN) IS
FOR J=I TO N-I
IF (YY(J)) < ABS(YY(J + l >) GOTO 1440
NEXT J
M=J
REM
REM CALCULATION OF. DIMENSIONLESS PARAMETER GROUP
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT "OUTPUT FILENAME FOR DIMENSIONLESS GROUP"
INPUT W$
OPEN "0".#1.W$
DUMPS=YY(M+l)
YY(M+l)=O
FOR I = I TO M
YT=YT+(D(M +l-I) /DE2)6 ( ABStYY(M + l-I>>-ABS(YY(M+2-I>>)
YTILL(I)=YT/(THETAI +THETA2)
UT( I >=UlM + l-I) /UEl
PRINT #1,U T (I ) . YTILL(I)
NEXT I
YY(M+l)=DUMPS
YT=O: YY(M-I)=O
FOR I=M TO N
YT=YT+(D(I)/ DEl ) > (YY( I ) -YY( I —I ))
YTILL(I)=YT/(THETA1+THETA2)
UT(I)=U(I)ZUEl
PRINT # 1 , UT(I), YTILL(I)
NEXT I
.
END
96
REFERENCES
CI TED
97
RE FERENCES
CITED
1.
D e m e t r i a d e s , A. a n d B r o w e r , T. L . , " E x p e r i m e n t a l S t u d y
of a C om pressible Free Shear Layer",
MSU/ SWT R e p o r t
TR 8 2 - 0 5 ,
Montana
State
U niversity,
Bozeman,
MT
December 1982.
2.
R ayleigh,
Lord,
"On
the
I n s t a b il it y
of
Jets",
P r o c e e d i n g s .of. t h e L o n d o n Ma t h e m a t i c a l S o c i e t y , X,
1 87 9 , p p . 4 - 1 3 .
3.
Goldstein,
S.,
Boundary Layer
C a mb r i d g e P h i l .
4.
T o l l m i e n , W. , " G r e n z s c h i c h t e n " , H a.n d. bu_c h, d. e. r. E x p e r .
Z k y. s. i k , Vo I . 4 , H y d r o - u n d A e r o - D y n a m i k ,
Part I ,
A k a d e m i c - V e r l a g , L e i p a i g , 1 9 3 3 , p. 2 6 7 .
5.
Chapman,
D. R . ,
"Laminar
F l u i d " , NACA TR 9 5 8 , 1 9 5 0 .
6.
D e n i s o n , M. R. a n d B a u m , E . , " C o m p r e s s i b l e F r e e S h e a r
L a y e r W i t h F i n i t e I n i t i a l T h i c k n e s s " , Al . AA J o u r n a l ,
V o l . I , No. 2 , F e b . 1 9 6 3 , p. 3 4 2 .
7.
Kubota,
T. and Dewey,
C. F . ,
"Momentum I n t e g r a l
Methods
for
the
Laminar
Free
Shear
Layer",
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MONTANA STATE UNIVERSITY LIBRARIES
stks N378, B81 !©Theses
RL
Experiments on the free shear layer betw
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