Instrumentation requirements and design of a facility for turbulent natural convection studies
by David Allyn Pracht
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Mechanical Engineering
Montana State University
© Copyright by David Allyn Pracht (1983)
Abstract:
A facility was designed and constructed which is to be used for turbulent natural convection boundary
layer studies in air adjacent to a heated vertical thin wire. The apparatus was shown experimentally, by
the use of anemometer bridge voltage output fluctuations, to be of a suitable size to achieve fully
developed turbulent flow. From these fluctuations transition to turbulence has occurred by Rax. =
1.2x10^10 and by Rax = 7.8x10^11 the flow has become fully turbulent. Measurements of the mean
velocity and temperature profiles were made and the qualitative results obtained compare very
favorably with experimental data of other research efforts. As the distance along the wire is increased
the mean velocity profiles indicate a decrease in maximum velocity and a widening of the velocity
boundary layer. The temperature profiles tend to retain the same basic shape over the entire length of
the wire. A slight increase in the thermal boundary layer thickness was observed as measurements were
made further up the heated vertical wire.
INSTRUMENTATION REQUIREMENTS AND DESIGN OF A FACILITY
FOR TURBULENT NATURAL CONVECTION STUDIES
By
David A l Iyn Pracht
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
" in
Mechanical Engineering
MONTANA STATE UNIVERSITY
Bozeman, Montana
March 1983
main
UB
Pg'gs
ii
dop. £
APPROVAL
of a thesis submitted by
David A l Iyn Pracht
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committee and has been found to be satisfactory regarding
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style, and consistency, and is ready for submission to the
College of Graduate Studies.
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Date
Approved for the Major Department
Date
H e a d , Major Department
Approved for the College
Date
of Graduate
Graduate Dean
Studies
iii
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opinion
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Date
V
ACKNOWLEDGEMENTS
The pr es en t
appreciation
this
au th or w i s h e s
to the
following
to express his
for
their
thanks
contribution
and
to
investigation.
His
support
advisor.
throughout
Bill
this
Bob Warrington,
Martindale
for
his
gu id an ce
and
investigation.
Ron Mussulman and Anthony Demetriades,
for serving as committee members and reviewing this thesis.
Gordon Williamson,
their
helpful
maintenance
And
State
this
the
Pat V o w e l l
assistance
in
of the experimental
Mechanical
University,
investigation.
for
the
construction
for
an d
apparatus.
Engineering
financial
and L u t h e r Hartz
Department
assistance
and
of
Montana
funding
of
vi
TABLE OF CONTENTS
CHAPTER
PAGE
LIST OF T A B L E S . . . .......... ..... .................. .....
vii
LIST OF F I G U R E S ....... .............. ..... ..............
viii
N O M E N CL AT UR E ... ..........
ABSTRACT..................
1.
2.
4.
I
STATEMENT OF THE PR O B L E M ..........................
2
LITERATURE
R E V I E W ... ...........................
3
4
5
10
EXPERIMENTAL APPARATUS AND P R O C E D U R E ..............
16
HEATED VERTICAL WIRE AND S H R O U D ..................
HOT-WIRE AN EM OM ET R Y. .......... ............... .....
CALIBRATION FA C I L I T Y ..............
EXPERIMENTAL PRO CE D UR E ....... .....................
16
20
21
25
EXPERIMENTAL RESULTS AND DISCUSSION............ ..
29
MEAN TEMPERATURE RE S U L T S ............ ........... . .
MEAN VELOCITY RESU LTS .. .-----------------------ANEMOMETER OUTPUT FL U CT UA TI ON S.... ..............
5.
xii
INTRODUCTION AND ST ATE ME NT OF THE P R O B L E M ......
NATURAL CONVECTION - TR A N S I T I O N ..................
NATURAL CONVECTION - T U R B U L E N C E ..................
VELOCITY MEASUREMENT T E C HN IQ UE S............... . . .
3.
ix
CONCLUSION AND RECOMMENDATIONS FOR FURTHER W O R K . .
29
32
38 '
42
RECOMMENDATIONS FOR FURTHER WORK. ................
43
REFERENCES CI TE D. ................
46
APP EN DI X .. .. . .......... . ................................
49
MEAN VELOCITY AND TEMPERATURE D A T A ...............
50
vii
LIST OF TABLES
Table
Description
I.
Velocity Boundary Layer Thicknesses for
Distances Along the Heated Vertical W i r e .....
35
Dimensionless Numbers Used in the Experiment..
40
2.
Page
viii
LIST OF FIGURES
Pa^e
Figure
1.
Tower with Supporting S t ru ct ur e.... .
17
2.
Schematic of the Test Facility with Supporting
Instrumentation. .........
18
3.
Pexiglass with Aluminum Connecting Straps.....
23
4.
Calibration Equipment and Instrumentation....
23
5.
Experimental Equipment and Hot-wire Anemometer
Ins trumentation......................
27
Orientation of the Hot-wire Probe to the
Heated Vertical W i r e ...............
27
Mean Temperature Profiles for the Air Adjacent
to the Heated Vertical W i r e . . . . . ...............
30
Mean Temperature Profiles for the Air Adjacent
to the Heated Vertical W i r e . . . . .... .
31
Mean Velocity Profiles for the Air Adjacent
to the Heated Vertical Wi r e . . . . . . . ............
33
Mean Velocity Profiles for the Air Adjacent
to the Heated Vertical Wi re .. .. .. .. .. .. ......
34
Maximum Anemometer Output Fluctuations for the
Air Adjacent to the Heated Vertical Wire......
39
6.
7.
8.
9.
10.
11.
ix
NOMENCLATURE
Symbol
Descript ion
C
S p e ci fi c heat at co nstant pressure,
( JZ k g 0C ).
CF
Correction factor used to correct bridge voltage
output for variations in fluid temperature.
e
Local kinetic energy flux,
e = G '(v^Z g,x^ )^
Eb
Anemom eter bridge
fluid temperature,
output
EC
Anemometer bridge
voltage output
overheat resistance, volts.
g
Gravitational acceleration,
(9.81 mZsec ).
G*
5(Grx *Z5)1 / 5 .
Gr x
Grashof number,
•*,*
Modified Gra^shof number for
surface, Grx = gflxq'Zkv •
h
Heat t r a n s f e r
( WZ m2oC ).
k
Thermal
Nux
Nusselt number Nux = hxZk.
Pr
Prandtl
q'
Uniform heat flux, BTUZhr ft2 ( WZm^
r
d i st a nc e
( cm ) .
R
Change in overheat resistance to simulate fluid
temperature variations, ohms.
Rh
Overheat probe
voltage
volts.
fr om
with
.
variable
with variable
32.17 ftZsec
2
3
2
Grx = gpx ATw Zv
c o ef fi ci en t,
conductivity,
number,
B T U Z l b 0F
uniform
heat
flux
B T U Z h r f t P t 2 P t 0F
BTUZhr ft°F ( W Z m 0C ).
Pr = pcZk.
the h e a t e d v e r t i c a l
resistance,
ohms.
).
wire,
in.
X
Symbol
Description
Rax
Rayleigh number,
a*:*
Modified Rayleigh number for uniform heat flux
surface, Rax = Grx Pr.
T
Mean temperature
Tc
Calibration temperature
0F (0C).
T
o
Reference
Rax = GrxP r .
of the fluid,
0F (0C).
of the hot-wire
sensor,
temperature, 0F (0C).
Ts
Hot-wire
sensor temperature, 0F (0C).
TW
Temperature
Tro
Ambient
AT
Local
(0C) .
AT W
Surface
(0O .
U
M e a n v e l o c i t y i n t h e x d i r e c t i o n , ft / sec
(m/sec).
X
Distance from the leading edge of the plate/
w i r e , ft (m).
y
Horizontal
(cm).
a
Thermal
P
Coefficient
8V
Velocity boundary layer thickness,
n
Inner length scale for constant temperature
surface, n = [a ZgP(Tw -T00)] ' .
X
Resistance coefficient of temperature
wire sensor, I /0F (IZ0C ) .
p-
viscosity,
V
K i n e m a t i c v i s c a s i t y e v a l u a t e d at the m e a n
temperature, ft Zsec (m /sec).
of the heated surface,
temperature,
temperature
temperature
di st a n c e
0F (0C).
0F (0C).
di fference,
AT = T- T00, 0F
difference AT
from
= T -Tco, 0F
the flat plate,
in.
diffusivity a = k/pc.
of thermal
IbZsec ft
expansion,
I/ 0F (I /.0 C ) .
in.
(cm).
for hot­
(kg/sec m).
Symbol
Descr it)t ion
vw
Kinematic visco|ity evaluated at the surface
temperature, ft /sec (m /sec).
V 00
Kinematic viscosity evaluated at the ambient
temperature, ft^/sec (mi /sec).
P
Density,
IbZft^
(kg/m^).
xii
ABSTRACT
A facility was designed and constructed which is to be
used for t u r b u l e n t natural
c o n v e c t i o n b o u n d a r y layer
studies in air a d j ac en t to a h e a t e d v e r t i c a l thin wire.
The a p p a r a t u s wa s s h o w n e x p e r i m e n t a l l y , by the use of
anemometer bridge voltage output fluctuations, to be of a
sui tab le size to ac hi eve fully d e v e l o p e d t u r b u l e n t flow.
From
these f l u c t u a t i o n s t r a n s i t i o n to t u r b u l e n c e has
o c c u r r e d by R a 5. = 1.2x10
and by R a 3, = 7.8x10
the flow
has b e c o m e full y turbulent.
M e a s u r e m e n t s of the m e a n
v e l o c i t y and t e m p e r a t u r e p r o f i l e s were m a d e
and the
q u a l i t a t i v e resu lts o b t a i n e d c o m p a r e very f a v o r a b l y wi t h
e x p e r i m e n t a l data of other r e s e a r c h efforts.
As the
dis ta nc e along the wi re is i n c r e a s e d the m e a n v e l o c i t y
p r o f i l e s ind ic at e a dec r e a s e in m a x i m u m v e l o c i t y and a
widening of the velocity boundary layer.
The temperature
p r o f i l e s tend to re t a i n the same basic shape over the
entire le ngt h of the wire.
A slight increase in the
thermal
boundary
layer
thickness
was
observed
as
measurements were made further up the heated vertical wire.
I
CHAPTER I .
INTRODUCTION AND STATEMENT OF THE PROBLEM
A
thorough
transition
understanding
and t u r b u l e n c e
development
and
relationships
profiles
in
the
and
of
free
general
t u r bu l e n t
in na tur e
initial
free
to
convective
fo r c e d
stages
turbulence
accurate
co n v e c t i v e
mathematical
mechanics
of
the
is
transition
both
elusive
stage
within
Generally
turbulence.
ho we v e r ,
an
velocity
considered
the
similar
Beyond
the
the m e c h a n i c s
fairly unclear,
models
and
layer,
a t m o s ph er e.
turbulence
still
reactor,
m a n y studies of
temperature
boundary
of transit io n,
are
continued
nuclear
To date,
of
turbulence have provided Nusselt
e n c l o s u r e s and in an inf inite
onset
mechanics
to the
of aerospace,
and t u r b o m a c h i n e r y technology.
number
the
is e s s e n t i a l
advancement
forced and free convective
of
with
simple
goal.
are
The
even
less
of
and
actual
well
defined.
In
th i s
ve l o c i t i e s ,
fluctuations
further
process.
st ud y,
mean
the
distributions
temperatures,
have be e n
definition
Measurements
and
investigated
of
the
were
of
the
turbulent
in order
turbulent
free
mean
velocity
to provide
convection
taken at four locations
in the
2
IA
range
of
field
I9
10
around
< R a x < 10
a 24.0 ft.
in the
buoyancy
driven
(7.32 m) long heated vertical
flow
wire.
Air was used as the fluid m e d i u m .
STATEMENT OF THE PROBLEM
The
objectives
of the
investigation may be
summarized
as :
(1) To
give
show
that
turbulent
(2) To
the
facility.is
of
suitable
size
to
flow.
show that the
instrumentation used is adequate to
make temperature and velocity measurements.
(3)
To
experimentally
velocity and mean
range
of values
(4)
To
determine
temperature
profiles
in the boundary
of
mean
layer over a
of the Rayleigh number.
estimate
the
boundary
layer
size
at
v a r io us
locati ons .
It
was
en co un t er ed ,
realized,
after
that a t t a i n m e n t
several
problems
of the second o b j e c t i v e was
not p o s s i b l e w i t h the time and r e s o u r c e s available.
will be discussed further
were
in Chapters 4. and 5.
Th i s
3
CHAPTER 2.
LITERATURE REVIEW
The
problem
of turbulent
natural
layer flow, next to a h e a t e d v e r t i c a l
subject
of numerous
efforts
to
date
dynamics
of
the
studies have
temperature
depended
surface has be e n the
Almost
on
all
profiles
flow boundary
and
theoretical
analogies
layer.
fluctuations,
and
with
the
Experimental
included heat transfer relations,
typic al
cu rve d
have
forced
of the mechanisms
with
investigations.
convection boundary
velocity and
investigations
involved in the transition to turbulence,
geometries
be in g
the
flat plate
as well
as
surfaces.
The b u o y a n c y induc ed fl o w of a fluid al on g a surface
can be d i v i d e d into three regions:
tu rb ul enc e,
and
analyzed by many
discussed
turbulent.
The
investigators
further.
The
laminar,
laminar
region
in the past
remainder
of
t r a n s i t i o n to
has
be e n
and will not be
th i s
chapter
is
intended to provide a useful background for this particular
investigation
and
convection research.
is
not
The
a
complete
following
surve y
of
discussion will
natural
include
the t r a n s i t i o n to tur bu l e n t and turbu le nt studies done in
the past.
A discussion of velocity
measurement
techniques
4
used
by
previous
transfer
investigators
is also
of
natural
convection
heat
included.
NATURAL CONVECTION - TRANSITION
The
mos t
ex t e n s i v e
work
in
the
field
of
natural
c o n v e c t i o n t r a n s i t i o n has b e e n c a r ri ed out by B. Gebhart
and his c o l l e a g u e s
Gebhart
[13]
correlated
have
[4], [13], [14], and [15].
postulated
that
J a l ur ia and
transition
events
by the ratio of the modified Grashof
the characteristic length,
can be
number to
x, raised to an empirical power,
n: G / x 11: wh e r e x is the d i s t a n c e from the l o w e r edge of a
vertical
flat
plate
and
n is
of
the
order
1/2.
At
the
first t r a n s i t i o n e v e n t , from l a m i n a r to t r a n s i t i o n flow,
the
ratio
is p r o p o r t i o n a l
to a p a r a m e t e r
local k i n e t i c en e r g y flux,
with
water
separately
wh er e
the
va lue s
the
at
velocity
e =
Prand tl
and
and
number
15.2,
is
the
. In studies
transitions
r e s p e ct iv el y.
on
the
order
of
coincide.
A
value
of
In
0.7,
e
occur
air,
these
the
development of fully turbulent flow was not identified.
In
of the
nearly
thermal
)
as
for
te rm s
should
13.6
e = G (v/gx
defined
R a y l e i g h n u m b e r m o d i f i e d for
*
con st an t heat flux on the wa l l surface, Ra^ , Q u r es hi and
Gebhart
of
1.2
[4]
x
conventional
have
I O 13
identified
transition points
< Rax* < 4 x
transition
and 5 x 10 ^ 3 < R a x
turbulence.
These values
agree
I O 13
as
the
in the range
beginning
of
< 1 0 ^ ^ for fu ll y d e v e l o p e d
fairly well
with the
ranges
5
o b t a i n e d by Vlie t
and Li u
point
[6]
define
wh er e
decrease.
and Li n
the
the
as
measured
fluctuations
the
in earl ie r
initial
Cheesewright
turbulence
[6]
transition
surface
[10]
point
has
where
studies.
event
temperature
defined
Vliet
the
as
the
begins
to
beginning
of
significant
temperature
in the b o u n d a r y layer be g i n to occur.
Both
studies d e f i n e d the end of t r a n s i t i o n as that point wh e r e
the respective
temperature
fluctuations
decreased.
NATURAL CONVICTION - TURBULENCE
The earliest
attempt
convection boundary
Eckert
on
the
and Jackson
assumed
convection.
This
to analyze the turbulent natural
layer
[7]
on vertical
whose
empirical
similarity
analysis
provided
for the rate of heat transfer,
co n s i s t e n t
profile
[10].
with
and - J a c k s o n
was
due
to
approach
was
based
forced
and
free
reasonable
predictions
but has not been found to be
experimental
obtained by Warner
Ec ke rt
between
surfaces
data for the m e a n v e l o c i t y
and
Arpaci
[1]
or
Cheesewright
[7]
found
the
heat
transfer-
Rayleigh number relation to be:
N u x = ( .021)Rax2 / 5 .
More
s u c c es s fu l
(2.1)
r e c e n t l y there have b e e n a n u m b e r
attempts
to
ap p l y
turbulence
of p a r t i a l l y
computational
models to the calculation of buoyant flows next
surfaces.
assuming
Kato e t a I [12]
an
eddy
a p p l i e d the
diffusivity
in tegral
to vertical
m e t h o d by
relationship
and
a
6
distribution of the heat
so derived
flux across
the profiles
than assuming
the boundary layer and
of velocity and
temperature
rather
t h e m . They then found a local Nusselt number
relation to be:
Nu x = .149[(V/a)^175--SS](Grx ) *3 6 .
The
Eckert
re su lts
and
are
Jackson
integrated the
not
[7].
continuity,
numerically.
In
very
their
different
Cebeci
and
momentum,
study
(2.2)
from
Khattab
and energy
they
consider
those
[8]
of
have
equations
the
eddy
viscosity formulation developed for forced convection flows
and
ap pl y
it
to
free
convection
transfer rates, velocity profiles,
on v e r t i c a l
number
flat plates.
ve rs us
experimental
of
the
coefficients.
empirical
constants
they were
able
with
number
Eckert
av a i l a b l e
heat
curves
the ir Nuss el t
agree
[1]
with
the
but disagree
and Jackson.
[9] used a modification of a program
Patankar-Spalding
transfer
predict
and temperature profiles
data of W a r n e r and A rp ac i
and Seban
to
Th e y re port that
Rayleigh
with the predictions of
Mason
flows
type
After
adjusted
to
a
numerically
substantial
to fit
the
predict
heat
exploration
experimental
of
data,
to ob ta in r e s u l t s that a g r e e d f a i r l y well
measured
data.
Their
report
also
used
'
turbulence parameters
which successfully predicted
forced
c o n v e c t i o n fl o w s m o d i f i e d for free c o n v e c t i o n flows from
vertical
surfaces.
7
A more
Capp [2]
recent
ana ly s i s
has been done by George
and
in which classical scaling arguments were used to
pr e d i c t
the
ex i s t e n c e
of
a two
layer
turbulent
natural
c o n v e c t i o n b o u n d a r y layer for f l o w s ad ja ce nt to ve rt i c a l
heated
surfaces. The
two layers
include:
an outer region
c o n s i s t i n g of mo st of the b o u n d a r y layer in w h i c h v i s co us
and conduction terms
which
the
layer
is
mean
are negligible,
convection
identified
as
of several
negligible.
heat
compared well
The
flux
with
layer.
inner
The
experimental
authors.
Many different
temperature
are
a co ns t a n t
results of their analysis
data
terms
and an inner region in
and
measurements
velocity
of the heat
profiles
have
transfer and
been
tu r b u l e n t na tu ral c o n v e c t i o n past a vert i c a l
made
for
surface. The
mo s t c o m m o n g e o m e t r y used has b e e n the flat plate. One of
the
e a r li es t
conducted
mos t
recognized
Cheesewfight
wo rk s
was
p r o f i l e s next to a con sta nt t e m p e r a t u r e wall
in air. Both
distance
were
the plate
experiments
numbers
layer
we r e
and wall
reported
temperature
as
For Grx > 2x10"*"® the boundary
being
e n c o u n t e r e d was due to the
side
turbulent.
screens
causing a lack of two-dimensionality,
that
the
plate
was
varied.
ca r ri ed out over a range of Grashof
from IO^ to 1.5 xlO^^.
is
who
these
temperature
along
[10],
of
measured
The
by
and
sufficiently
wide
On e
problem
of the ap pa r a t u s
but Cheesewright felt
so that
measurements
8
down
the
c e n t e r — line
were
not
significantly
affected.
Temperature profiles are plotted as ATZATw versus
so that
Capp
the b u o y a n t
[2],
collapsed
appea rs
to
subrange,
as p r e d i c t e d by George
as a straight
a single
curve,
line.
but
appear,
as
wel l
as
the
The
also
defined inverse cube root region where
would
—
(y/n)
data
not
exhibited
the buoyant
linear
r eg io n
1/3
'
and
only
a well
sublayer
next
to
the
wall. The data are shown to be in reasonable agreement with
the
empirical
results
of Eckert
and Jackson
[71 also.
More recently Cheesewright and Doan [21] have measured
spacial
correlations normal
and l o n g i t u d i n a l
fluctuations
to a heated vertical flat plate
space-time
in
the
t u r b u l e n t regions.
correlations
transition
and
turbulence
structure
was
noted
the
dissipation
length
by
and
Another
undertaken
slow
Warner
and
su bl a y e r was
the
temperature
flat plate
Arpaci
in air, most
[1],
dimensional
dis ta nc e
from
the
of
geometry
usi ng
a
was
single
constant
of the t e m p e r a t u r e profile
data could be c o l l a p s e d w h e n p l o t t e d as
the
of
scales
aluminum flat plate. They showed that for a single
wall
sublayer
variation
length
Also
to the wall.
investigation of the
by
outside
correlation
turbulence with distance normal
developed
from that outside.
a fairly uniform
as
fully
The flow in the viscous
shown to be relatively independent
found,
of t e m p e r a t u r e
the wall.
A T /A T w v er su s y,
An e x p e r i m e n t a l
9
study
done
by
Fu ji i
ethyleneglycol
relationships
boundary
[11]
provides
ba s e d
with
the
following
on t e m p e r a t u r e
Comparison
[1]
ag re em en t .
used
4.34,
of
at
This
are useful
in his
because
Nusselt
in
number
distributions
in the
Rax < 8.5 xlOy
.49(Ra )1/4
(2.3)
Nux = .87(Rax ) 1/4
Fujii
cylinder
layer:
Nu,
Ar pa ci
a vertical
these
results
similar
seem s
to
in dicate
It
curvature
of Warner
that
sh ow s
the
number
a
length
apparatus
range,
effect.
There
poor
have
were
of
(Pr=SS),
/ diameter
may
and
re l a t i o n s
sh ould be no t e d h o w e v e r
dimensions,
cylindrical
those
numbers
only in the Prandtl
of physical
significant
with
Rayleigh
e x p e ri me n t.
Fujii's
8 . SxlO9 < Rax <8xl010
that
ratio
=
produced
a
no
velocity
profiles measured for this geometry.
Fu j ii
e t a I [3]
experiments
usi ng
temperature.
entirely
conducted
vertical
Since
g o v e r n e d by
the
the
an
extensive
cylinders
at
heat
transfer
wall
layer,
co ns ta nt
at
greater
as long as the
than the wall
layer
radius
measured
onto
over a wi de
a single
curve
range
is
expected
same as that
They found
is much
that
for
the temperature profiles
of w a l l
over most
of
wall
wall
of curvature
thickness.
a narrow range of Prandtl numbers,
the
it can be
that the heat tr a n s f e r r e l a t i o n will be the
for flat plates
series
conditions
of the b o u n d a r y
collapsed
layer. The
10
profiles
for
different
oil,
substantially
as expected.
and Mobil therm
different
The ir
Prandtl
resu lt s
numbers
for w a te r,
were
spindle
oil could be shown to correlate as:
(Mux )(VwZv00)-21= .13 (Rax ) 1/3
(2.4)
1010< Rax
These
results
are
in excellent
agreement
with George
and Capp [2], It wa s also d e t e r m i n e d by m i r a g e
method based on the principle
the
fluid
rise,
that
in the boundary layer
that
turbulence
oil. Again,
method,
the refractive
decreases with
be g a n at R a x = 2 x I 0
there were no velocity profiles
II
a
index of
temperature
for
spindle
given.
VELOCITY MEASUREMENT TECHNIQUES
Although
the
main
turbulent
flo w
make
measurements
some
region,
calibration purposes.
measuring
tu r b u l e n t
latter,
of
flows.
it was
none
the
be
flow,
in the
in te n d e d
particularly
as
both
For me a n v e l o c i t y
w as
desirable
such
velocities
work
the less
therefore
should
mean
of
in laminar
It was
technique
measurement
in te re st
to
in
to
for
that the
permit
the
laminar
an d
m e a s u r e m e n t s in the
the output of any suitable measuring
instrument had
to be capab le of be i n g a v e r a g e d over a p e r i o d of one m in ut e
or longer, be c a u s e of the e x p e c t e d low f r e q u e n c i e s of the
turbulence.velocities
below,
Many
techniques
have been
along
with
developed
a
for the measurement
and
discussion
several
of
are
three
of fluid
described
calibration
11
procedures
[16],
that
have
Cheesewright
been
used
by
Hollasch
and Gebh ar t
[10] and Aydin and Leutheusser
[22].
One of the most commonly used techniques for measuring
flow v e l o c i t i e s
difference
is that i n v o l v i n g the m e a s u r e m e n t
between
the local
static pressure
stagnation pressure at a point
in the fluid,
static tube and some form of manometer.
ob vi ous
that
this
present
problem
tec hn i q u e
because
cou ld
the
much
accuracy,
period
too
small
and the
local
using a pitot-
It was immediately
not
maximum
be
us e d
pressure
involved would be of the order of 9x10 * in.
water,
of the
in
the
difference
(2x10 ^ cm) of
to be m e a s u r e d w i t h any degree
of
p a r t i c u l a r l y in v i e w of the need for long time
averaging.
A straight
forward
tracer p ar ti cle s,
mo s t
optical
technique
often h e l i u m
of photographing
filled
bubbles,
and
measuring track lengths has been used with limited success.
This method would require a large
the
an a l y s i s
would
not
of
be
fluctuation
accuracy
ba s e d
to
measurements
near
due
to
the
make
of
the
in
turbulent
velocity
the
random
he a t e d
of work
type
flow.
and
needed
movement
vertical
involving
of
wire
It
velocity
in
the
where
this
air
good
is essential.
Another
is
p'h o t o g r a p h s
s u f fi c ie nt
in ve s t i g a t i o n ,
especially
the
amount
on
commonly used technique,
the
relationship
hot-wire
between
the
anemometry,
rate
of
heat
12
tr a n s f e r fro m a h e a t e d w i r e and the v e l o c i t y of the fluid
flowing
past
it.
eventually used
Since
to make
this
w as
velocity
the
method
measurements,
that
was
its use
in
p r e v i o u s natu ral c o n v e c t i o n heat tr an sf er i n v e s t i g a t i o n s
an d
the
respective
calibration
procedures,
discussed in the remainder of this
Although
gr e a t e r
simple
hot-wire
than
task
determine
10.0
using
(3.0
is far more
can
accurately
comparable
determine
which an anemometer output
problem
signal
ma k e s
is
relatively
a
calibration at
One
reason is due
to the pitot-static
low
velocities
can be matched.
convection
flow s
calibration
facility
experimental
apparatus.
that
sensor combined with the
are
to be
me a s u r e d .
is
the
same
as
that
in
the
Since the anemometer output bridge voltage
be in g
wi t h
Another
it n e c e s s a r y that the d i r e c t i o n of the fl o w
by the
to
encountered is due to the importance of the natural
convection cooling of the hot-wire
fo rc ed
velocites,
and thermocouple
complicated.
to the lack of an instrument
that
tube
high
a known velocity and temperature,
low velocities
tube
at
m/sec),
a pitot-static
be
chapter. ,
calibration
ft/sec
will
temperature
me as ur ed ,
temperature
correction
as well
as
calibration
encountered
in
the v e l o c i t y
must
the
be
flow
factor becomes necessary.
made
or
a
This
in the
actual
is governed
of
the
fluid
at
the
exact
temperature
13
Hollasch
calibrating
variations
and
a
Ge bh ar t
presented
constant-temperatnre
in fluid temperature.
varying
the
fluid
temperature
wire
analytically
ove rh ea t
[16]
overheat
rel at in g
re s i s t a n c e
calibration
relation
anemometer
was
(E^).
order c o r r e c t i o n term
to account
probe
of
for
consisted of
at
a constant
then
output w i t h
(Ef,) to a n e m o m e t e r
temperature variations
method
hot-wire
Their method
during
A
a
derived
a va ri ab le
output w i t h fluid
Their relation,
with a first-
for p r o p e r t y v a r i a t i o n s
is :
(2.5)
An
experimental
and G eb ha rt
error
study
to v e r i f y
in velocity
was
the
then
presented
analysis.
measurements
by
Hollasch
The m a x i m u m
without
using
percent
the
property correction term was approximately 9.0%.
variable
The error
is not significantly improved using the correction term,
fact,
the
natural
error
is greater
convection
in the
caused
low velocity range where
by
the
temperature
is equally as important
the
of the wire.
cooling
correction term
Three
were
longitudinal
use
hot-wire
by
and
sensors,
Bill
and
no r m a l
sensor
as forced convection in
of the variable
is not recommended by the authors
hot-wire
used
The
in
calibrated
Gebhart
components
in
[14]
of
property
[16],
this
manner,
to
measure
velocity
in
the
14
transition
layer
flo w
re g i m e
adjacent
surface.
to
These
a
of
the b u o y a n c y
con s t a n t
measurements
characteristics
and
beat
were
pr o f i l e s
flux
used
of
induced boundary
vertical
to determine
velocity
flat
growth
fluctuation
levels.
Cheesewright
distributions
layer,
as
a
used
of m e a n
the
calibration
laminar
boundary
Grashof
number
ambient
wa s
given
at
different
In
each
calculated
were
layer,
distribution
and
by
test
fr o m
selected
of
theoretical
the
theoretical
as
to
layer
velocity
Three
positions
in the
local
local
the
(plate)
plate
cold
and the power
at a n u m b e r
so
the
the
the
boundary
theory.
R e a d i n g s -of
then made
determine
boundary
that
that
made
layer.
convection
the hot. wire resistance,
the hot wi re
r e ad in gs
was
to
a turbulent
assuming
temperatures.
resistance,
boundary
were
in
natural
medium,
therein
tests
attempting
velocity
laminar
calibration
distribution
[17],
a
velocities.
velocities,
wire
input to
of point s
gi v e
and
in the
reasonable
From
values
these
of
the
N u s s e l t and R e y n o l d s n u m b e r s for the h o t - w i r e probe were
calculated and these
results were
then graphed.
It was c o n c l u d e d by the a u t ho rs that the c a l i b r a t i o n
curves o b t a i n e d in this m a n n e r m a y have be e n in error by up
to 15% for the h i g h e s t R e y n o l d s
divided into two parts.
One due
numbers.
This error was
to the assumption that the
15
velocity was
that
given by theory and the
errors
in measurements.
may be
made
anemometry
velocities
by
An estimate
considering
measurements
with
of the first
a comparison
of
other was due to
laminar
of these
of other hot-wire
natu ra l
convection
the th eo ry and wa s r e p o r t e d to be of the
order of 10%.
Aydin
and
Leutheusser
consisting of a square
its b o t t o m surface.
inside
base distance.
10.0
used
to
switches
wi t h
at the
(3.0 m/sec),
experimentally
which was
slot
in
two end points
carried out
and
in excellent
timed over
a digi ta l
the
calibrated
determine
agreement
tim er
of the
in the range of
d i s t r i b u t i o n in l a m i n a r plane Coue tt e flow.
obtained were
facility
tube with a narrow
distance
Calibration was
ft/sec
a towing
The probe to be c a l i b r a t e d was m o v e d
m e a s u r e d base
actuated by magnetic
were
aluminum
used
the tube by a towing carriage,
a precisely
0 to
[22]
the
probes
velocity
The results
with the analyticalIy
predicted linear velocity distribution.
16
CHAPTER 3.
EXPERIMENTAL EQUIPMENT AND PROCEDURE
HEATED VERTICAL WIRE AND SHROUD
A 0.035
was
in. (0.89 cm) d i a m e t e r
supported
cylindrical
lb.
(2.04
fr o m
a
beam
a cr os s
cylindrical
weight,
surface
for the exp eri m en t .
te n s i o n
on
copper
the
ce nter
the
wi r e
and
provided
of
a
to
keep
the
To each of the two ends
lead
wire
was
v o l t a g e to the wir e
attached
The
later
to be
of
wire' st raight
and
these
leads
were
W i t h this v a r i a c the
the t e m p e r a t u r e
of the
l e n g t h of the h e a t e d wi r e
after applying voltage was 24.0 ft.
demonstrated
he ated
of this h e a t e d wire a
a nd
and t h e r e f o r e
could be controlled.
the
The w e i g h t was used to keep
c o n n e c t e d to a va r i a c p o w e r supply.
wire
top
which
shroud and w e i g h t e d at the b o t t o m w i t h a 4.5
kg)
vertical.
tin alloy wire,
(7.32 m), which will
sufficient
length
be
to obtai n
fu ll y t u r b u l e n t flow.
The
he a t e d
investigation,
illustrated
by
a 5.0
in Figures
was to minimize
to not
ve r t i c a l
interfere
ft.
was
(1.52
I. and 2.
ambient
with
wire
m ) diameter
The purpose
influences
the natural
surrounded
and yet be
in
this
shroud
of the shroud
large enough
convective flow
from the
17
Figure I.
Tower with Supporting
Structure
18
Figure
2.
Schematic of the Test Facility with
Supporting Instrumentation
19
heated vertical
4.0
ft.
(1.22
(0.32 cm)
a
wire.
m)
It w as c o n s t r u c t e d by p l a c i n g two
by
8.0
ft.
plexiglass
end
to end
cylinderical
section
(2.44
by
m)
sheets
of
0.125
and then forming
placing
the
two
them
fr e e
in.
into
ends
together. P l e x i g l a s s was used b e c a u s e / v i s i b i l i t y through
the
shroud was
and for
essential
determining
for flow visualization
an initial
radial
techniques
distance
from
the
wire. An a l u m i n u m pla te 2.5 in. (6.35 cm) wide by 0.375.in.
(0.95
cm)
entire
th ic k
4.0 ft.
with
a groove
(1.22 m ) l e n g t h was
the ends of these plexiglass
of this
0.375
plate
along
a slot
in. (0.95 cm)
was
wide w h i c h
in t e r i o r of the shroud.
46.0
edge
used to h o l d
sheets*
cut
either
of
its
to ge t h e r
Along the center-line
in.
(116.8
cm)
long
s e rv ed as an access
by
to the
T h r o u g h these slots the hot wire
probe and support was placed and the measurements were made
radially outward from the heated vertical wire.
Five
stacked
on
of
top
these
of
c o n s t r u c t e d of 0.125
d e s c r i b e d above was
masonite
through
was
the
used
cylindrical
one
and
a
pl ac ed on the b o t t o m
reduce
section
was
costs
not
were
sixth
in. (0.32 cm) m a s o n i t e
to help
bottom
an o t h e r
sections
then
section
in the m a n n e r
as a base.
The
since v i s i b i l i t y
required
for
the
expe rim ent .
The
plexiglass
and
together with an aluminum
masonite
connecting
sections
strap,
we r e
0.375
f it te d
in. (0.95
20
cm)
th ic k by 0.75
and b o t t o m
in.
(1.91
of a d j ac en t
cm)
wide,
se ct io ns
by p l a c i n g
the
top
into a 0.25 in. (0.64 cm)
deep groove that had be e n cut along either edge. A detail
of the c o n n e c t i n g
ea r l i e r
is
section s
straps
shown
gave
a
in
Fi gu re
total
b o t t o m of the to w e r
and the
3.
height
g r o ov ed plate
described
on
These
of
page
24.7
23.
ft.
(7.53
six
m).
The
rest ed on a p a r t i c l e b o a r d pl at fo rm ,
while a masonite top was used for complete
enclosure.
HOT-WIRE ANEMOMETRY
Constant temperature hot-wire anemometry equipment was
utilized
for
all
investigation,
equipment
only
and since
measurements
the
description
further
details
to
— [20].
Basically,
concerning
hot-wire
in
the
theory of hot-wire
operation has become
a br ie f
[18]
velocity
well
will
the
be
known
anemometry
anemometry
in recent years,
presented
following
present
here.
For
discussion
refer
is concerned with
the
determination of the convective heat transfer from a heated
wire
as
fluid
composition
depends
only
moves
remains
past
constant,
the
the
wire.
If
the
convective heat
on the fluid velocity,
temperature
fluid
transfer
difference,
b e t w e e n the wir e and the fluid, and the fluid t e m p e r a t u r e
and t h e r m o d y n a m i c propert ie s.
hot-wire anemometer,
con st an t
temperature,
In a co nstant t e m p e r a t u r e
the h e a t e d sensoris m a i n t a i n e d at a
so that
in an i s o t h e r m a l
flow the
21
heat
transfer
Maintenance
depends
of
the
wi re
obtained by connecting
br id ge
circuit.
changes,
required
As
a change
circuitry
The
a
the wire
the
means
td the current
mean
converted
before
past
the
wire
t h r o u g h the wi r e
loop.
output
and this
The
bridge
is
is
anemometer
voltage
is
through the hot-wire.
to the m e a n flow dir ection,
However,
is
leg of a Wheatstone
temperature,
the
velocity.
temperature
velocity
a feedback
velocity
conveniently measured by placing
be
as one
fluid
so that
fluid
co ns t a n t
constant
of
longitudinal
voltage.
the
in current p a s s i n g
is arranged
proportional
upon
at
the
to maintain
accomplished by
only
the hot-wire
can
be
probe normal
and read in g the output bridge
the
to velocities,
component
output bridge
it was
voltages
necessary
to
could
determine
the relationship between the two by means of a calibration.
CALIBRATION FACILITY
The calibration of the hot-wire probe was accomplished
using a blower and duct work to determine
once
flow
the flo w
rate
Meter.
To
necessary
rate
was
to
a
have
c o n s i s t e d of a bell
duct work.
the
The
e nt ra n ce
th ro ug h the duct w o r k w as found.
found
find
a known velocity
by
using
velocity
a
a TSI
from
con st an t
model
this
area
test
se c ti on w as
and at a point w h e r e
flow
test
shaped n o z z l e at the
4100
The
Airflow
rate
it
section
was
which
en tr a n c e to the
18.0 in, (45.7
cm)
from
the d i a m e t e r b e c a m e a
22
con st an t
used,
4.86
the
support
in.
(12.34 cm).
electronic
with
eq u i p m e n t ,
and
4. shows
the
the nozzle
hot-wire
probe
the traverse.
Br id ge v o l t a g e s
this test
F i gu re
were
r e c o r d e d at the c e n t e r - l i n e of
section, and assuming a constant velocity profile
with the mean velocity equal to the center-line velocity,
a
velocity was matched to each bridge voltage.
Traverses
of
across the test
one
half
the
diameter
se ct ion to d e t e r m i n e
the v e l o c i t y p r o f i l e at each fl o w
p r o f i l e s an ite ra t iv e
were
then made
the actual
rate used.
shape of
F r o m these
p r o c e d u r e was used to correct
the
con sta nt v e l o c i t y p r o f i l e a s s u m p t i o n to d e t e r m i n e actual
velocities
at the center-line
Once
each
constant
the
in
the
same
Because
it
could
experimental
as
of the heated vertical
temperature.
bridge
varied
It was
voltages
test
calibrated
temperature
temperatures
the
was
temperature,
velocities
at
probe
of the
be
in this
used
apparatus
the
wire
greatly
section.
manner
to
determine
if the
fluid was
calibration
facility.
in the experiment,
from
the
the
calibration
therefore
necessary to correct
for
temperature
this
at a
each of
difference.
The
mos t a c cu ra te a p p r o a c h is to c a l i b r a t e the probe over the
range
of
temperatures
experiment.
voltages
Measurement
that
of
in the e x p e r i m e n t
will
be
encountered
in
the
temperature along with bridge
would
then be m a d e
and
these
23
Figure 4.
Calibration Equipment and Instrumentation
24
bridge voltages
recorded would be matched to a velocity for
the temperature measured.
H o w e v e r b e ca u se
facility,
one that w o u l d al lo w t e m p e r a t u r e s
encountered
used.
of a lack of a suitable
in the
Therefore
ex p e r i m e n t ,
the
this
method
readings
were
calibration
in the range
could not be
corrected
by
multiplying by the factor:
CF =
(3.1)
as suggested in [20].
reported
[2 Q ]
temperature
to
The use of this correction factor is
be
satisfactory
of
a high
speed
flow,
those encountered in the present
the
magnitude
of
the
flow
over
fo rc ed
h ig he r
investigation.
The
should be
g o ve r ns
that natural
convection
the
amount
an
in
the
of
heat
temperature
difference
in. (0.13 cm) fr o m
temperature
temperature
was
the wire
between values
and
approximately
difference,
the
than
reason
important
convection
cooling
of
the
and the a m b i e n t
transferred
natural convection from a constant temperature
The
a
is justified using an
sensor wi r e at near zero v e l o c i t y flows,
temperature
with
considerably
velocity
c o n s i d e r a t i o n is due to the fact
dominates
flows
d i f f e r e n c e up to I O O 0F (56° C ) , a l t h o u g h this
upper limit of temperature difference
example
in
by
sensor wire.
measured
at 0.05
calibration facility
I O O 0F (56°
C).
This high
along with the low velocity flows.
25
ra ise d c o n s i d e r a b l e
questions
as to the v a l i d i t y of this
temperature correction multiplying factor.
correction
factor
also
neglects
the
The temperature
effects
that
variable
thermodynamic properties have on the fluid.
A l t h o u g h there were
the
use
several p r o b l e m s e n c o u n t e r e d in
of
this
correction
correction
ma de
for
reduce
the errors
factor,
temperature
involved in using
it
remains
variat io ns .
the
To
only
help
this correction,
to
a high
sensor temperature was used and the calibration temperature
was
increased
to the
highest
the available equipment.
obtainable
By increasing these
Equation 3.1 was made as near
A
Thermal
anemometer,
we r e
utilized
with
10% r h o d i u m
(1.27 mm).
able
to
(270 C) with
temperatures.
to one as possible.
Inc.
DC voltmeter,
throughout
t h e m s e l v e s we r e
remounted
Systems,
digital
(Si0F)
the
constant
probe
temperature
and probe
i nv es ti ga ti on .
The probes
a T S I m o d e l 1210 st an d a r d st ra ig ht probe
a 0.0003
in.
(0.007 6 mm)
diameter platinum-
sensor wi r e w i t h an active l e n g t h of 0.05 in.
A probe
locate
the
support
probe
traversing mechanism
to w i t h i n
0.005
in.
which was
(0.127
a l l o w e d pr e c i s e p o s i t i o n i n g of the h o t - w i r e probe
boundary
support
mm)
in the
layer.
EXPERIMENTAL PROCEDURE
The p o w e r
applied to heat
su pp ly was ac ti vated,
and 45.0 volts were
the vertical wire. This resulted in a power
26
consumption
of
of 700
watts,
approximately
sufficient
720°F
warm-up
temperatures
and produced
over
period,
the
normally
and v e l o c i t i e s
a wire
temperature
entire
length.
A
allowed
the
48 hours,
to stabilize
in the b o u n d a r y
layer. Data was then co l l e c t e d at 5.0, 10.0, 15.0, and 20.0
ft.
(1.52,
the
wir e
3.05,
4.57,
in the
and 6.10 m)
from
f o l l o w i n g manner.
connected
to
the
probe
traversing
unit. Figure
supp or t
the b o t t o m
end of
A h o t - w i r e probe
which
5. illustrates
w as
the
held
in
the probe
i n w a r d until
the h e a t e d wi r e wa s
obtained,
from
the
linear
u s u a l l y 0.05 in. (0.13 cm),
to
the
probe
heated
support
sensor
wa s
was
was
A strip
voltage
was
turned
t im e constants
to
on
the
and
on
the
traverse.
and support
shown
in F i g u r e
to make
heated
the
with
wire.
respect
6.
certain
The
that the
Next
correct
The
the
operating
set.
of
r e co r d e r
the
300
of the bridge
the
changes
from one level to another.
The DC
con st an t was
or
graph was made
anemometer
in velocity fluctuations
v o l t m e t e r time
is
then r o t a t e d
chart
output
probe
wire
perpendicular
anemometer
resistance
vertical
from the heated wire was
scale
orientation of the hot-wire
By
a c e r t a i n d i s t a n c e from
the location of the zero distance
recorded
the
traversing unit,
the h o t - w i r e a n e m o m e t e r and other r e l at ed eq ui pment.
extending
was
to determine
set at 100 seconds
seconds
was
allowed
and three
to elapse
27
28
be for e
the
br i d g e
v o lt a g e
ou tput
was
di gi tal reado ut of the DC v o l t m e t e r .
moved
the
recorded
from
The probe
was
the
then
to a ne w l o c a t i o n f u r th er from the h e a t e d wire and
above
procedure
was
repeated,
until
re a c h e d 24.0 in. (61.0 cm) from the wire.
at each
probe
of the
sta tio ns
was
the
probe
had
The t e m p e r a t u r e
found by using
the h o t - w i r e
as a r e s i s t a n c e t h e r m o m e t e r and r e c o r d i n g the cold
resistance.
Using these r e s i s t a n c e s
the t e m p e r a t u r e was
determined, f r o m a graph of r e s i s t a n c e versus t e m p e r a t u r e
which had previously been made using known temperatures and
recording
resistances.
Th e
c o r r e c t e d for v a r i a t i o n s
calibration
correction
factor,
a velocity
curve
nine
facility,
was
Eqn.
using
3.1.
versus
velocity data points
po int s
points.
we r e
tak en
The
data
bottom
can be
at
1.0
and
end
of
the
wir e
to
From
bridge
turbulence
the
the probe
2.0
to
was
then
that of the
mentioned
corrected
and twenty-five
found
from
previously
voltage
at each level
made
transition
the
using
Strip chart re c o r d i n g s
were
voltage
in t e m p e r a t u r e
determined
of velocity
bridge
values
calibration
output.
Twenty-
temperature
for a total
of
216
data
data
in the Appendix.
of the v e l o c i t y f l u c t u a t i o n s
ft.
(0.30
determine
occurred
and
0.61m)
wh e r e
and to make
the flow was laminar in the lower regions.
the
from
onset
the
of
certain that
CHAPTER 4.
EXPERIMENTAL RESULTS AND DISCUSSION
This chapter will present and discuss the experimental
resul ts
that
were
will be divided
temperature
into
(3)
fluctuations.
temperatures
anemometer
form
with
three
sections:
measurements,
measurements,
boundary
ob t a i n e d d ur in g the i nv es ti ga ti on .
layer
be
of
of
mean
and
thicknesses
output
anemometer
the
shown,
a
will
fluctuations
Results
of mean
R e s u l t s of m e a n v e l o c i t y
Results
Profiles
will
(2)
(I)
It
will
output
velocities
discussion
be
be
and
of
presented.
given
in
the
The
graphical
a d i s c u s s i o n th e re of and a c o m p a r i s o n to other
investigators
results will be
included.
MEAN TEMPERATURE RESULTS
The distributions
in Fi g u r e s
local
the
that
vertical
the
con sta nt basi c
wire.
The
resu lt s
fluid temperature versus
heated
graphs
7. and 8.
of the mean temperatures are plotted
wire.
It
temperature
shape
with
The p r i m a r y effect
extension of the thermal
r,
are
in t e r m s
the radial
can
be
seen
profiles
seem
increasing
of T,
distance
from
to
distance
the
from
these
r e ta in
along
a
the
of i n c r e a s e d d i s t a n c e x is the
layer deeper into the ambient.
200
Symbo I
10.0
15.0
20.0
+*
100
Radial distance
Figure 7.
from the w i r e ,
r
(in.)
Mean Temperature Profiles for the Air Adj a cent to the
Heated Vertical Wire
1.22
9.73
32.8
77.8
200
SymboI
O
§
X
5.0
10.0
15.0
20.0
C
a
O
•
3 150
0
«
43
-W
O
W
W
0
*» 100
SI
M
4>
P.
B
e
*»
(ft)
Rax xlO -10
1.22
9.73
32.8
77 .8
I
8
8
§
O
8
I
I
i
1.0
1.5
2.0
(3
03
0)
ae
0.5
Radial
Figure 8
distance
from the w i r e ,
(in.)
Mean Temperature Profiles for the Air Adjacent to the
Heated Vertical Wire
2.5
32
Warner
and
Arpa c i
similar
resu lts
7.9x10*
<
RaT
r e s p e c ti ve l y.
increased
velocity
for
<
7.9x10 10
wil l
and
Cheesewright
a vertical
This
x
[I ]
of
shown
layer b e h a v i o r
plate
7 .2x10*
and
widening
be
flat
to
the
in the
< Ra'
air
with
<
6.O x l O 10
layer
co n s i s t e n t
following
investigations reported temperature
give
in
thermal
he
[10]
with
with
section.
the
Both
results by plotting the
d i m e n s i o n l e s s t e m p e r a t u r e A T /A T ^ , v e r s u s y , the di st an ce
fr om the v e r t i c a l flat plate.
temperatures
obtainable
for the entire
in the p r es e nt
were
comparisons
not
will
length
and
provided
be
of the w i r e
i n v e s t i g a t i o n due
sufficient instrumentation,
temperatures
Exa ct h e a t e d v e r t i c a l wire
made
since
by
of
temperatures measured with those
not
to a lack of
dimensional
these
the
were
fluid
investigators,
magnitude
of
no
the
of [1] and [10].
M EAN VELOCITY RESULTS
Figures
pr o f i l e s
9.
that
and
we r e
10.
show
obtained
the
from
dimensional
the
velocity
experimental
data
using the p r o c e d u r e and e q u i p m e n t d i s c u s s e d in Chapter 3.
They
are
plotted
direction,
vertical
versus
wire.
four levels
as
U,
shows
adj ace nt
outer edge of the plexiglass
a detailed
mean
velocity
r, the radial di st an ce
Figure 9.
from
the
the
from
the
x
the h ea te d
entire profiles
to the h e a t e d w i r e
shroud,
in
of
the
to near the
while figure 10. shows
graph of the profiles near the wire.
2.0
Mean velocity of the fl u i d , U
(ft/sec)
Symbol
O
D
O
•
O
O
I .5
X
(ft)
Rax xlO -10
5.0
10.0
15.0
20.0
1.22
9.73
32.8
77.8
fa
I .0 S
r*
• g o
O
•8
o
o
o
0.5 I
6
6
°
O
O
0
O
O
o
_6_
8
0.0
J_____________________________________________
5
10
Radial distance
Figure 9 .
15
from the wire,
r
(in.)
Mean Velocity Profiles for the Air Adjacent to the
Heated Vertical Wire
8
n
8
2.0
I
I
i
I
*o O *
I .5
_
O
5.0
10.0
15.0
20.0
Rax xlO~1C
1.22
9.73
32.8
77.8
O
O
O
O
O
•o
•O
eo
•
OO
I
1.0
QO
n O O
°o*
°
#0
e
fluid,
O
8
O
•
8
•
C
«
O
-
Mean
0.5
C
C
•
of
the
(ft)
O
O
a
O
O
O
velocity
%
O
a
O
•
U
(ft/sec)
SymboI
8
I
0.5
Radial
Figure 10.
i
I
1.5
O i
0.0
distance
from
the
wire,
I
2.0
r
(in.)
Mean Velocity Profiles for the Air Adjacent to the
Heated Vertical Wire
2.
u>
35
M e a s u r e d local v e l o c i t y b o u n d a r y layer thicknesses,
Sy ,
were
estimated
from
Figure
9.
However,
the
c o n v e n t i o n a l d e f i n i t i o n of the edge of the b o u n d a r y layer
as the l o c a t i o n wh e r e the v e l o c i t y has d r o p p e d to 1% of its
pea k val ue
was
portion
the b o u n d a r y
of
velocities
too
not
practical.
small.
region
The
profile
is too
Therefore,
flat
in the
and
outer
the
peak
the edge of the boundary
layer was tak en as the p o s i t i o n at w h i c h the v e l o c i t y had
dropped to 10% of its m a x i m u m va l u e .
Sy was
Using this definition
evaluated and these values are given in Table I.
Table I.
distance
Velocity Boundary Layer Thicknesses for
Distances Along The Heated Vertical Wire
from the beginning
of the wire,
feet
x
velocity
boundary
layer thickness,
meters
in
cm
5.0
1.52
13.7
34.9
10.0
3.05
13.4
33.9
15.0
4.57
15.5
39.4
20.0
6.10
15.9
40.4
&y
36
The b o u n d a r y layer thickness,
5.0 ft (1.52 m) level
is c o n s i s t e n t
with
S v i n c r e a s e d from
to the 20.0 ft (6.10 m) level.
the resu lt s
the
This
of G o d a u x and G e b h a r t
[5]
who have found that the velocity and thermal boundary layer
thicknesses
vertical
increase with length from the leading edge of a
flat
plate
in water
until
the
flow becomes
fully
t u rb ul en t at w h i c h point bo t h b o u n d a r y layer t h i c k n e s s e s
st op ped
growing.
It can be no te d that there is a s i g n i f i c a n t
increase
in Sy f r o m 10.0 ft (3.05 m) to 15.0 ft (4.57 m ) w i t h only a
slight
inc rease
shown
later
th i c k n e s s
th a t
inc rease
m ) is in the
the 20.0
at the 20.0 ft (6.10 m) level.
region
of
large
boundary
layer
(10.0 f t < x <15.0 ft) (3.05 m< x < 4.57
t r a n s i t i o n to t u r b u l e n t
(6.10 m ) level
flow
at
increase
in boundary
F i g u r e s 9. and 10. also seem to indicate
a small but
therefore
layer thickness
significant
small
would be expected.
d e c re as e
along the wire,
a very
was
The
to be fully
and
however
region.
found
turbulent
ft
the
It will be
x.
in m a x i m u m
velocity
with
This could possibly be explained if the
recirculation of the air within the shroud were
Since the t o w e r was
closed at b o t h ends
for the u p w a r d f l o w i n g
it wa s
considered.
necessary
air to reverse d i r e c t i o n near the
top of the t o w e r and r e c i r c u l a t e
botto m.
distance
itself b a c k d o w n to the
W i t h the air rising along the c e n t e r - l i n e of the
37
wire
the
recirculated
air
outsi de of the shroud.
the
shroud
mor e
w as
required
to
go
down
the
As the fl o w a p p r o a c h e d the top of
air was
evidently
reversing
direction.
The re fo r e, as the dis tan ce along the wire increased, m o r e
flow
may
have
decreasing
satisfy
A
its
diverted
maximum
from
velocity
the
fr o m
boundary-layer,
that
required
to
continuity.
dec re as e
consistent
[12],
be e n
with
[15],
in m a x i m u m
v e l o c i t y along the wire is
experimental
results
of
other
researchers
however water was used as the working fluid in
both cases and recirculation effects were present.
Results
of an experiment
in air with no recirculation were provided
[10]
no
and
show
measurements
plate,
In
decrease
in m a x i m u m v e l o c i t y as
x
p r o g r e s s e d u p w a r d along the v e r t i c a l flat
rather a slight
the
absence
theoretical
of
r e su l ts
composition
as
comparisons
of
profiles
measurements.
similar
used
in
experimental
geometry
th i s
data
In addition,
obtained
questionable
value.
fluid
investigation,
than actual
magnitudes
of the
the validity of the use
of the
factor
discussed
in Chapter
is u n c e r t a i n in this p a r t i c u l a r i n v e s t i g a t i o n ,
the
and
or
of the general trends o b s e r v e d in
rather
correction
reported.
comparable
a
those
we r e ma de
the velocity
temperature
increase was
for
the
velocity
3.,
CF,
t h er ef or e
profiles
is
of
38
ANEMOMETER OUTPUT FLUCTUATIONS
As
reported
beginning
of
temperature
occur.
earlier
Cheesewright
turbulence
as
fluctuations
the
[10] has
point
where
in the b o u n d a r y
significant
layer be g i n to
Since the a n e m o m e t e r b ri dg e volt ag e
constant
temperature
sensor
defined the
output
for a
is governed by fluctuations
the t e m p e r a t u r e as well as the v e l o c i t y of the fluid,
variations
experiment
the
in
fr om
to
it
is present.
wa s
voltage
felt
and
method
that
of
used
G eb ha rt and other r e s e a r c h e r s
in
the
this
flow begins
fu ll y
developed
is slightly different
determining
sufficient
i n f o r m a t i o n on the d e v e l o p m e n t
output
when
Although this
o b t a i n e d f r o m these fl uc t ua ti on s.
the a n e m o m e t e r
were
the point at which the
tu r b u l e n c e
C h e e s e wri ght's
events,
br id ge
to determine
transition
turbulence
output
in
transition
resu lt s
could
be
To o bt ai n q u a l i t a t i v e
of the t r a n s i t i o n region,
[5] and [13]-[153
to d e t e r m i n e v e l o c i t y
also used
disturbance
levels.
Figure
11. demonstrates
the present investigation,
the bridge
the
variations
showing the max im um
determined
in
amplitude of
output voltages for each of the four levels used
to ob t a i n v e l o c i t y and t e m p e r a t u r e data as w e l l as values
o b t a i n e d at the I ft, (0.30 m ) and 2 ft. (0.61 m ) levels.
It can c l ea r ly be
lo we st
levels
are
seen fr o m
in the
this Figure
laminar
that the two
r eg io n b e c a u s e
of
the
15
I
I
Symbo I
I
(ft)
Rax x I 0 10
-M
P
Qi
-M
A
P
O
a
O
•
O
Q>
CO
OS
M
vM
#
O
.00973
.0778
I .22
9 .73
32.8
77.8
_
O
>
O
oo
fO
•H
to
N
4>
M
0)
E
O
a
e>
fl
1.0
2.0
5.0
10.0
15.0
20.0
A
O
•
O
O
O
LU
VO
e
•
O
O
A
A
O
O
J___
i __
0.1
Radial
Figure
11.
•
O
•
O
8
o
O
8
O
O
O
O
O
□
O
•
O
o
O
I
0.2
distance
I
0.3
from the wire,
I
0.4
T
(in. )
Maximum Anemometer Output Fluctuations for the
Air Adjacent to the Heated Vertical Wire
•
f
O
0.5
40
small
amplitude
of
the
fl uc t u a t i o n s .
it
can
observing
increased
amplitude
seen
that
transition
turbulence
as defined by Cheesewright
[10],
has
the 5.0 ft. (1.52 m ) level.
to
the
Gr a s h o f
properties
are
T m = (Tw +Tco)/ 2.
the b e g i n n i n g
numbers
ev a l u a t e d
listed
in
at
mean
by
the
[10]
transition
This value w o u l d rei nf o rc e
occurring
the
5.0
ft.
has
Table
2.,
fluid
taken
according
where
(ft)
all
temperature,
R a x = I.4x10^
to his
as
criterion.
the o b s e r v a t i o n of t r a n s i t i o n
(1.52
m ) level
Dimensionless Numbers Used
Cl
M
M
X
to
started by
in
the
present
investigation.
Table 2.
the
These points w o u l d c o r r e s p o n d
Cheesewright
of
be
By
in the Experiment
Rax
I .0
I .1 6 x l 0 8
7 .91x10?
2.0
9.29x10*
6.33x10*
5.0
1 .4 5 x l 0 10
9.88xl09
10.0
I . I b x l O 11
7 . 9 1 x l 0 10
15.0
3 . 9 2 X 1 0 11
2 . 6 7 X 1 0 11
20.0
9 . 2 9 X 1 0 11
6 .S S x l O 11
P
41
Figure
11.
also
show s that
the fluctuation amplitudes
con ti nu e to inc rea se th ro ug h the 15 ft. (4.57 m) level and
then the a m p l i t u d e s dec re as e at the 20 ft. (6.10 m ) level.
This can be d e s c r i b e d as the poi nt
b e c o m e full y turbulent.
the w o r k s
reported
temperature
end
of
R a x = I .4x10
[10] and Vliet
transition
fluctuations
Cheesewright's
[1 0]
in
the
as
to
point
wh e r e
boundary
layer
decreased.
turbulence
reported fully developed turbulent
in all tests
showed that
with
the
reported
values
heat
the
had
that
resul ts
of
parameter
transition
Jularia
occurred
decreased,
at
an
with
Th e y
the
Vliet
found
are
that
G
being
the
and Liu [6]
Gebhart
number,
the
[13]
simply
number.
dependent
They
upon
the
and the
surface
transition
events
when
the
derived
from
w a t e r along a v e r t i c a l flat plate.
data to air along a vertical
and
Rayleigh
events
increasing
results
and
en d e d
is not correlated
*
q '.
at
investigation.
of G , the modified Grashof
flux,
that
c o n d u c t e d w h i c h agrees f a v o r a b l y
the end of transition
single
noted
the
flow was present by Rax
with the results obtained for this
H o w e v'e r ,
[6] w ho
that
flow was reported to be fully turbulent.
= 1.3x10 H
and L i u
investigation
transition
the flow has
These resu lt s are c o m p a r e d w i t h
of C h e e s e w r i g h t
the
at w h i c h
heat
flux
experiments
was
in
C o r r e l a t i o n s of their
thin wire were not
suggested.
42
CHAPTER 5.
CONCLUSION AND RECOMMENDATIONS FOR FURTHER WORK
The
design,
I
main
objective
con struct,
of
this
investigation
and e x p e r i m e n t a l l y v e r i f y
was
to
a fa ci l i t y
that can be used for t u r bu l e n t b o u n d a r y layer an al ys is in
n at ur al
convection
heat
transfer
studies.
sh o w n by a n e m o m e t e r bridg e v o l t a g e
that
the
facility
necessary turbulent
is
of
flow.
a
It
output
suitable
has
be e n
fl uc t u a t i o n s ,
size
to
o bt ai n
the
The approximate locations of the
beginning
and end of the transition to turbulence have been
found
be
to
< 7.8x10*^
7 .8x 1 0 8 < R a x < 1 . 2 x l 0 10
respectively.
These
over
temperature
a range
of
3 .3 x I 0 11 < R a x
values have been shown to be
consistent with results of other
Mean
and
investigators.
and
velocity
profiles
Rayleigh
numbers
in
the
were
measured
boundary
layer
(
s u r r o u n d i n g the h e a t e d ve r t i c a l wire.
trends
observed
investigators
in
the
findings,
of the m a g n i t u d e s
there
the h o t - w i r e
could
achieve
the
i n ve st ig a ti on .
the
probe s
desired
A
agreed
is some doubt
of the profiles.
ca l i b r a t e
not
profiles
While
the general
with
other
in the validity
The f a c i l i t y used to
for v e l o c i t y m e a s u r e m e n t s
temperatures
temperature
encountered
correction
factor
in
of
43
l i m i t e d a p p l i c a b i l i t y was used to adjust
br id ge
flui d
voltage
output
surrounding
the
adequate
calibration
at
temperatures
high
adjusted with
the
for
chan ge s
to
with
the
wire.
compare
same
correction factor,
using this method of correction
The
in t e m p e r a t u r e
he a t e d v e r t i c a l
facility
the a n e m o m e t e r
Without
known
an
velocities
temperature
the error
of the
flows
involved
in
is unknown.
temperatures
recorded for
the boundary
also be s u b s t a n t i a l l y
in error due
to the m e t h o d used to
determine
them.
the temperature
of
the
the
increased
probe
and
fluctuations
of
exact cold resistance
support
was
difficult
to
and again the magnitude of the error involved was
obtainable.
problems
of
adjacent to the wire,
hot-wire
determine
not
Because
layer may
wi ll
Possible
be
solutions
discussed
in
to the
the
above
mentioned
following
section.
V e l o c i t y b o u n d a r y layer size was e s t i m a t e d from
v e l o c i t y p r o f i l e s m e a s u r e d in the i n v e s t i g a t i o n
and the
thickness of the boundary layer was noticed to increase
the distance along the heated vertical wire was
the
as
increased.
R E COMMENDATIONS FOR FURTHER WORK
A calibration
facility
for
the h o t - w i r e
anemometer
probes that could be op e r a t e d at t e m p e r a t u r e s up to 2 0 0 0 F
(93*0
with
velocities
in
the
range
of
O
to
2.0
ft/sec
(0.61 m/sec) w o u l d al lo w v e l o c i t y prof i l e s to be o b t a i n e d
with
a minimal
amount
of error
from the actual velocities.
44
This
would
exact
allow
calibration
temperatures
correction
A
factor
mo re
obtained.
method
al s o
could
thermocouple
(0.0127
mm)
of
fl o w
and
achieved
[21].
probes,
in digi tal
fluid
at the
make
a
temperature
improve
by
the
using
Temperatures
form.
results
the
method
were measured
chromel-alumel,
d i a m e t e r butt jointed,
was r e c o r d e d
the
mean
greatly
be
utilized by Che es e wr ight
with
in
probe
unnecessary.
would
This
the hot-wire
encountered
s u i ta bl e
measurement
of
0.0005
and the ou tput
A sampling
in.
signal
rate of 100 Hz
Vfas used t h r o u g h o u t , w i t h a s t a n d a r d l e ng th of record of
six minutes.
A
method
of
observing
p h o t o g r a p h i n g tracer p a r t i c l e s
and very small size,
resu lts
mo r e
while
flow
visually
by
of a s u b s t a n t i a l q u a n t i t y
would improve the dependability of the
describing
meaningful
the
the
manner.
direction
Particles
to
of the
be
flow
in a
investigated
include h e l i u m fi ll ed bu b b l e s w i t h a b u o y a n c y s i m il ar to
air.
This
bubble
re q u i r e s
the
purchase
or
construction
of
a
generator.
Improved
results
could also be
a La s e r D o p p l e r A n e m o m e t e r
velocity
independent
layer flow.
to be m a d e
The
the use
of
(LDA) to make m e a s u r e m e n t s of
of temperature.
velocity measurements
boundary
obtained by
This would
without
disadvantage
allow
the
disturbing
the
of the use
of an LDA
45
sy st em
not
is that
an
easy
encountered
it req ui re s
task
in
in natural
Investigation
conditions
mesh
reduce
infinite
the
such
as
those
alternative
convection
experimental
in
ac hi e v i n g
results.
The
opened at both the top and the bottom
sc ree n p l a c e d
over
the
openings
from disturbing the flow.
a wi re
effects
of larg er
cylinder
s u p p l i e d to the wir e
area.
natural
recirculation
vertical
the heat
flows
and
These
better
to keep
openings
simulate
an
atmosphere.
Also
heated
several
turbulent
external currents
would
speed
w h i c h is
convection.
of
shroud used could be
a fine
low
m a y also prove to be b e n e f i c i a l
significant
and
s e e di ng of the flow,
flux held
could
velocities
or
con stant
cylinder
which
velocities found
are
be
or a sm a l l
investigated.
diameter
The
power
or c y l i n d e r could be i n c r e a s e d w i t h
This would increase
wire
diameter
due to the
increased
surface
the amount of heat transfer from
and
theoretically
easier
in the present
to
measure
give
than
investigation.
higher
the
low
REFERENCES CITED
47
REFERENCES CITED
1.
2.
Warn er, C . Y. and Arpaci, V., An E x p e r i m e n t a l I n v e s t i ­
ga ti on of T u r b u l e n t N a t u r a l C o n v e c t i o n in Air at
Low Pressure Along a Vertical Heated Flat Plate,
I a M r n a t i o n a l Journal of Eeat and Ma..s.s Tr an_s f_e r ,
Vo 1 . 11, pp 397-406, 1968.
e
George, W . K. and Capp, S. P.,
A T h e o r y For
Natu ra l
C o n v e c t i o n T u r b u l e n t B o u n d a r y L ay er s Next To H e a t e d
V e r t i c a l Surfaces, I n t e r n a l i o n a l J o u r n a l of Heat and
Mm
T r a n s.li r , V o l . 22, pp 8^13-826 , 197 9 .
3.
Fuj ii, T.,
Takeuchi, M.,
Fujii,. M.,
Uehara, H., E x p e r i m e n t s On N a t ur al
Transfer
From
The O u t e r
Surface
C y l i n d e r to
Liq uids, I n t e r n a t i o n a l
and Mjisjs Transfer,
Vol. 13,
pp 753-7
4.
Qureshi,
Z. H., an d G e b h a r t ,
B., T r a n s i t i o n a nd
T r a n s p o r t in a B u o y a n c y D r i v e n F l o w in W a t e r Ad ja c e n t
to a V e r t i c a l U n i f o r m Flux Surface,
Jslernallena.!
J o u r n a l o f I e s l and M a n J r a n e f e r ,
Vol. 21,
pp 1467-1479,
1978.
5.
Godaux, F . and Gebhart, B., An E x p e r i m e n t a l Study of
the Transition of Natural Convection Flow Adjacent to a
V e r t i c a l Surface, J s l e i n a!J o n al J o u r n a l of Heal and
M m
J i e s s J n * Vol. 1 7 , pp 93-107, 1974.
6.
Vliet, G . C. and Liu, C. K.,
An E x p e r i m e n t a l Study of
Turbulent Natural Convection Boundary Layers,
Journal
of HeeJ J i e s s J n > Vol. 9 i , pp 5 1 7 - 5 3 1 , 1969.
7.
Eckert, E. R. G. and Jackson, T. W.,
A n a l y s i s of
T u r b u l e n t Free C o n v e c t i o n B o u n d a r y L a y e r on a Flat
Plate,
NACA TN 1015, 1950.
8.
Cebeci, T. and Khatab, A., Prediction of Turbulent Free
C o n v e c t i o n Heat T r a n s f e r F r o m a V e r t i c a l Flat Plate,
JourseJ of HeeJ Jiess J n * Vol. 97, pp 46 9— 4 7 1, 1975.
9;
Mason, H. and Seban, R.,
Numerical
P r e d i c t i o n s For
T u r b u l e n t Free C o n v e c t i o n F r o m V e r t i c a l Surfaces,
J s J e r n e J J o s e I J o u r n e J of I e e J e s A M a e s J i e s s J n ,
Vol. 17,
P P 1329-1336, 1974.
10.
Suzaki, K., and
C o n v e c t i o n Heat
of a V e r t i c a l
J o u r n a l of Heal
87,
1970.
Cheesewright, R., Turbulent Natural Convection From a
V e r t i c a l Plane Surface, J o u r n e J e J S s s J Jl'eSSJn*
Vol. 90, pp 1-8, 1968.
48
11.
Fujii, T., E x p e r i m e n t a l Stud ie s of Free C o n v e c t i o n
H e a t T r a n s f e r , B u Jl I.e.Jfcj,n .of. J S M E , Vo I. 2, No. 8,
PP
555-558,
1959.
12.
Kato, H., Nishiwaki, N., Hirata, M.,
On The Turbulent
Heat T r a n s f e r by Free C o n v e c t i o n F r o m a V e r t i c a l
Plane,
International
Journal
of Heat
and
Mass.
Tra n sf er . Vo I. 11,
pp 1117-1125,
1968.
13.
Jaluria, Y., and Gebh art, B., On Transition Mechanisms
in V e r t i c a l N a tu r al C o n v e c t i o n Flow,
J o u r n a l of
E-IsjLd. Mjec: h.anl_c_s , Vo I. 66, p t . 2, pp 3 0 9-337 , 1974.
14.
Bill, R. G., Jr., and. G e b h a r t , B., The D e v e l o p m e n t of
Turbulent Transport in a Vertical Convection Boundary
Layer,
I n t e r n a t i o n a l J o u r n a l of H e a t an d M a s s
. T rans fer . Vol. 22, pp 267-277, 1979.
15.
Gebhart, B., Ins tab i l i t y , T r a n s i t i o n , and T u r b u l e n c e
in Buoyancy Induced Flows, Annuzil Re.vi.ew of Fluid
Me ch anic s . Vol. 5, pp 213-246,. 1973.
16.
Ho l l a s ch, K., Gebhart, B., C a l i b r a t i o n of C o n s t a n t T e m p e r a t u r e H o t - W i r e A n e m o m e t e r s at L o w V e l o c i t i e s
in Water with Variable Fluid Temperature, Journal of
Heat T ra.ns^e._r, Vol. 94, pp 17-22, 1972.
17.
Che e s e w r i g h t , R., Na t ur al C o n v e c t i o n F r o m a V e r t i c a l
Plane Surface, PhD thesis in Mechanical Engineering,
University of London, Oct. 1966.
18.
Hot Wire and Hot Film Measurements and Applications,
Thermal Systems Inc., Technical Bulletin No. 4.
19.
Fingerson, L., Freymuth, P., Thermal Anemometers,
Thermal Systems Incorporated,
1979.
20.
Heat Flux System Model 1010A Instruction M a n u a l ,
Thermal Systems Inc or porated.
21.
22
C h e e s e w r ight, R., Doan, K., S p a c e - T i m e C o r r e l a t i o n
M e a s u r e m e n t s in a T u r b u l e n t N a t u r a l C o n v e c t i o n
B o u n d a r y Layer, I n t e r n a t i o n a l J o u r n a l of Heal and
M as s Transfer, Vol. 21, pp 911-921, 1978.
A y din, M .> and L e u t h e u s ser, B., Very L o w V e l o c i t y
Calibration and Application of Hot-Wire Probes, DISA
Information Report, No. 25, F e b . 1980.
49
APPENDIX
APPENDIX
VELOCITY AND TEMPERATURE DATA
51
The
following
temperature
conditions
profile
is
a list in g
data
taken
in
of
all
this
the
velocity
and
investigation.
The
for the measurements are as follows:
T s = SOO0F
T c = 810F
Rh = 10.98 ohms
Mean Velocity Data
Distance from the beginning of
the heated vertical wire, feet
5.0
, inches
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
1.00
I .50
2.00
2.50
3.00
3.50
4.00
5.00
6.00
7.00
8.00
10.0
12.0
14.0
16.0
18.0
20.0
22.0
24.0
10.0
15.0
Mean velocity , U ,
I .16
I .51
I .63
1.62
1.61
1.64
I .57
1.51
I .54
1.35
I .23
1.14
1.06
0.92
0.85
0.67
0.45
0.31
0.24
0.17
0.18
0.19
0.16
0.16
0.16
0.14
0.10
0.11
0.54
0.90
1.06
I .13
1.14
I .24
1.23
1.26
1.24
1.25
1.20
I .08
1.02
0.91
0.84
0.78
0.75
0.63
0.49
0.46
0.35
0.25
0.16
0.11
0.06
0.04
0.00
0.01
0.01
20.0
ft/sec
0.11
0.92
0.97
1.01
1.08
I .09
1.03
0.99
0.98
0.95
0.87
0.84
0.81
0.79
0.72
0.71
0.67
0.61
0.52
0.47
0.47
0.33
0.21
0.17
0.09
0.03
0.06
0.07
0.10
0.10
0.71
0.96
0.96
1.02
0.91
0.88
0.93
0.92
0.92
0.83
0.79
0.79
0.75
0.71
0.65
0.66
0.57
0.50
0.44
0.39
0.23
0.17
0.14
0.10
0.08
0.14
0.14
0.15
52
Me^an ^ em£e.ra t.ur^ d a_t
Distance from the beginning of
the heated vertical wire, feet
5.0
Mean temperature,
, inches
0.05
0.10
0.20
0.30
0.40
0.50
1 .00
I .50
2.00
2.50
3.00
3 .50
4.00
5.00
6.00
7.00
8.00
10.0
12.0
14.0
16.0
18.0
20.0
22.0
10.0
181
147
119
116
106
101
95
93
91
91
91
89
89
89
88
88
88
86
86
86
85
85
84
84
195
150
125
116
109
106
100
96
95
93
93
93
92
92
91
91
89
89
89
89
89
88
88
88
15.0
T,
184
148
120
116
107
104
98
96
95
93
93
92
92
91
91
91
91
91
91
89
89
89
89
89
20.0
0F
184
154
126
119
113
108
100
98
98
96
95
93
93
93
93
93
92
92
92
92
91
91
91
91
MONT A N A STATE UNIVERSITY ITRRARTFt
762 10056640 3
VAIN LIB.
N378
P882
Pracht, D. A.
cop.2
Instrumentation
requirements and design
of a facility for
turbulent natural ...
I S SUED T O
DATE
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