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MODEL EXPERIMENTS FOR THE DESIGN ~~--~ ---~------- --- ------
8 I X T Y
OF A
WATER - - - ...... -
PART III
TUN N E> L ---_-. ....
TEST SECTION AND
CAVITATION INDEX STUDIES
by
st. Anthony Falls Hydraulic Laboratory
University of Minnesota
Project Report Noo 12
Submitted by
Lorenz G. Straub Director
Prepared by
James S. Holdhusen
September, 1948
Prepared for the David Taylor Model Basin Department of the Navy
Washington, D.C.
Bureau of Ships Contract NObs-34208 Task Order 2
" .
l'-'
PREFACE TO REPORT SERIES
Contraot NObs-34208 between the Uni versi ty of Minnesota and the
Bureau of Ships, Department of the Navy, provides for making hydrodynamic
studies in compliance with specific task orders iseued by the David Taylor
Model Basin oalling for services to be rendered by the sto Anthony Falls
Hydraulio Laboratory. Certain of these task orders related to model experi
ments for the design of a 6o-in. water tunnel.
The end result of the studies related to the 60-in. water tunnel
proposed eventually to be constructed at the David Taylor Model Basin was
orystallized as a series of six project reports, each issued under separate
cover as follows:
Part I DESCRIPTION OF APPARATUS AND TEST
PROCEDURES (Projeot Report No. 10)
Part II CONTRACTION STUDIES (Project Report
No. 11)
Part III TEST SECTION AND CAVITATION IN D EX
STUDIES (Project Report NOQ 12)
Part IV DIFFUSER ST U DIE S (Project Report
No. 13)
Part V VANED ELBOW STUDIES (projeot Report
No. 14)
Part VI PUMP STUDIES (project Report No. 15)
The investigational program _s under the general direction of
Dr. Lorenz G. Straub, Direotor of the st. AnthoflY Falls Hydraulio Laboratory,
and the work was supervised. by John F. Ripken, Associate Professor of
Hydraulics.
11
"
PREFACE TO PART III
Pa.rt III of the report series was prepared in accord wi tb'
Task Order 2 of Contract NObs-34208.
This report was "written by James s. Holdhusen, Research
Fellow. Mr. Holdhusen was project leader on the experimental work
and was assisted by Clyde o. Johnson and Harry D. purdy. Ethel
Swan assisted in preparation of the manuscript.
"'
iii
..
SYNOPSIS --------A study of the teat section for a water tunnel was made at
the St. Anthony Falls aydraulic Laboratory as part of the research
program for the design of the proposed 6o-in. water tunnel of the
David Taylor Model Basin" Bureau of Ships" Department of the NavY. ,
It was determined that the variation in velocity across the test
stream would be less than one per cent everywhere except in the
boundary layer" which would have a maximum thickness of ten per cent
of the diameter of the test section. The pressure gradient and ener-
gy loss in the test section were computed assuming the test section
boundary layer to be analogous to that of a plate in a uniform stream.
The critical cavitation area in the tunnel circuit was found to be
at the transition from the test section to the diffuser .. and the
corresponding critical cavitation indexes were calculated for sev-
eral points in the test section •
iv
•
section
I
CON TEN T S
Preface to Report Seriee.
Preface to Part III • .
Synopsis •••
· . . . . · . . . . . . · . . . . . .
Frontispiece •• · . . . . . . . . . . • • •
INTRODUCTION •• · . . . . . . . . .
Page
ii
iii
iv
vi
1
II VELOCITY DISTRIBUTION AND BOUNDARY LAYER THICKNESS • • • • • • . • • • • • • • • • 1
II! ENERGY LOSS AND PRESSURE DISTRIBUTION • • • .3
IV DIFFUSER TRANSITION AND TUNNEL CAVITATION IN])EX . • . • • • • • • • • • • • • • 6
v CONCLUSIONS • • · . . . . . . . . . • • • • 1.3
List of Illustratiol~ • • • . . . . . . 1, Figures 1 through.9 • • • . • • • • . • • • 16-24
v
n < .....
-0 I
-10
"""
~ VI; 'I ...
~ 'if: r..
I
~ ~ ,.;.~
~' ~
~
I CONTRACTION TEST SECTION DIFFUS E R 25'-0" 30'-0" 65'-0'
J b
~ + _1_- _ - r DIFFUSER 10
t J 0 1O
~
.L FLOW -0 ;
- ... ' - 0 r co 10 "'""- . - \
t 156' _ 8"
PROPOSED 60 11 WATER TUNNEL
! i
':'.'" " " -
'!'."' .... ~ r
-0 ·II'-d'+ - I
I 0 r<")
-~ f\ :I.J'; :J ,
/ ~~
V
"
TEST SECTION AND
C A V I TAT ION I N D E X S'T U DIE S
I. INTRODUCTION
The primary objective of a water tunnel is the production of a mov-
" ing flow stream of such quality that the' mechanics of flow between the stream
and a test body mounted in the test section most nearly simulates the movement ~
of the t.est body throueh still watero The experimental work on the contrac
tion cone has shown that the stream entering the test section will meet these
conditions in that the velocity variations will be less than one per cent across
the main body of the streamo As the stream passes through the test section,
however, there is a continual growth of the boundary layer with which is asso
ciated an axial pressure gradient and reduction of velocity in the boundary
layer. The axial pressure gradient is the result of two phenomena, both of
which cause the pressure to decrease in the direction of flow. The more effec
tive of the two is the pressure drop caused by the frictional resistance of
the walls on the test stream. This pressure gradient is further strengthened
by a redistribution of velocity and an increase in kinetic energy with an ac
companying drop in pressure, resulting from the growth of the boundary layer.
Thus, the test body is acted upon by an over-all pressure gradient. which is
comparable to a "horizontal buoyancy" that must be compensated for if the
test results are to be valid.
The cavitation index of the water tunnel is of importance inasmuch
as it restricts the severity of cavitation conditions which can be imposed on
tlle test installation without cavitating the water tunneL
II. VFLOCITY DISTRIBUTION AND BOUNDARY LAYER THICKNESS
Velocity traverses were taken on horizontal and vertical diameters
,~ in. upstream and .~ in. downstream of the test section of the model water
tunnel by using the adapter flange and the i-in. stainless steel pi tot cylin
der, which are described in PART I, DESCRIPTION OF APPARATUS AND TFBT PROCE
DURE. 'rhese traverses, which are plotted in Figs. 2 and 3, are rendered di
mensionless by dividing the local velocities by the velocity at the axis of
the test section. It will be noted that the velocity is very uniform over the
central area of the flow and the variation present is well within the maximum
prescribed variation of one per cento Only in the boundar,y layer does the ve
loci ty fall below 99 per cent of the velocity at the axis of the test sectiono
·0'
•
2.
An analysis of the thickness of the boundary layer in the test sec
tion of the prototype tunnel is made difficult because the Reynolds numbers
of operation will be considerably higher than those for which previous ex
perimental results are available. The problem is further complicated by the
fact that the boundary layer is in the process of formation in the curved,
converging section of the contraction cone.
Boundary layer thickness is important in that it affects the amount
of the test stream which can be used for testing purposes. The prescribed
limit for the variation of velocity in the test stream is one per cent, and
the velocity traverses in the downstream end of the test section of the model
indicate that the velocity is 99 per cent of the centerline velocity to with
in a distance of about 0.90 in. from the wall (0.15 diameters). Theory indi
cates that the boundary layer will be thinner at higher Reynolds numbers;
* according to the formula of Prandt1,
where
..sL= x ...Q;El
Re 1/5 ' x
d ~ thickness of boundary layer,
x = distance along flow direction from point where the boundary layer begins to form, and
V-x Rex = --:;r- •
Al though this formula is supposedly not valid for Re grea te r 7 x
than 2 x 10 and the maximum Re in the prototype test section will prob-8 x . ably be 2.3 x 10 , the fonnula will give at least an approximation to the
boundary layer thickness in the prototype. If ~ is the scale ratio between r
prototype and model (in this case, ..R. r
flow and equal kinematic viscosities, = 10) for equal mean velocities of
k ::: dm 1 4/5 == 104/ 5 = 6.31 • r
In this formula, cf equals boundary layer thiclcness in the prototype, and p cfm equals boundary layer thickness in the model.
* Hunter Rouse, ELEMEN'l'ARY MECHANICS OF FLUIDS, p. 188.
.' .3.
The velocity at the downstream end of the test section will be 99 per cent of the centerline velocity at a distance of about 0.90 x 6 • .31 =- .5.68
in. from the boundary (0.09.5 diameters).
It should be noted here that there will be a deceleration of the
boundary layer and, in order to satisfy continuity, a consequent increase in
the velocity of the central core as it passes throueh the test section. In
the model test section, the velocity of the central core was 1.010 V at the
upstream end of the test section and 1.0,50 V at the downstream end of the
test section where V is the mean section velocity.
In the prototype, the increase in the velocity of the central core
will be less. If it is assumed that the boundary layer is 6.31 times as thick
in the prototype as in the model, the veloci ty of the central core will be
1.004 V at the upstream end and 1.036 V at the downstream end of the proto
type test section.
III. ENERGY LOSS AND PRESSURE DISTRIBUTION
Much of the energy loss in the tunnel circuit occurs in the test
section. The energy loss cannot be computed by the regular formulas for head
loss in circular conduits since the loss occurs in a region in which the ve
locity varies along the flow direction from point to point. Since no method
was available for computation of the energy loss in the inlet length of smooth
pipes, recourse was made to laws derived for progressive skin friction changes
for flow along a flat plate held parallel to the strewn. One would expect
this method to be applicable in pipes where the boundary layer was thin in
comparison with the pipe diameter, since each incremental area of wall would
be little affected by the other portions of the wall. The validity of apply
ing this method to the test section was verified by the model study.
The Prandt1 formula * for the coefficient of skin drag on a flat
plate held parallel to the flow is
0.074 Cf = Re 1/5 '
x (1)
where Of: coefficient of drag and is supposedly valid up to Rex ~ 2 x 107,
or in the region in which the seventh-root law of velocity distribution
*Ibid.
4. 7 ~ I exists. For Reynolds numbers higher than 2 x 10, the Karman-Schoenherr·
formula, * which is based on the logarithmic law of velocity distribution, has
been found to be in Eood accord with experimental results:
1 (2 )
Both Eqa. (1) and (2) are plotted in Fig. 6.
Values of Cf in the model were determined by measuring the pres
sure drop along the test section at three different mean velocities of flow
(18.00, 30.00, and 49.62 ft per sec). The pressure drop as experime~tally
determined is divided by the velocity head of the test stream and presented
in Fig. 4. The pressure difference was measured from the downstream manifold
on the contraction cone to four different piezometer taps in the test section
and to the two piezometer taps in the diffuser transition. The location of
the pressure taps is sho1vn in Figs. 1 and 4. The reference manifold (R) was
actually l~' in. upstream from the beginning of the test section, but the diam
eter of the contraction cone at this point was 6.004 inches. Since the sur
face\ was the same (smooth-machined aluminum) as the test section, the portion
of the contraction cone downstream of the reference manifold was assumed to
have the same surface character.:i.stics as the test section. In order to deter
mine the true frictional head loss, the pressure drop as determined experi-
mentally was corrected for the change in kinetic energy of
passed throur.;h the test section. Values of ex. _ ~ 6AV3 - AV3
the stream as it
were determined
from velocity traverses taken upstream and downstream of the test section.
It was determined that ex. : 1. 0015 one-half inch downstream of the beginning
of the test section, and ex: '= 1.0160 one-half inch downstream of the end of
the test section. Values of 0( at the piezometer taps and reference mani
fold were computed by linear interpolation or extrapolation. Since the diam
eter of the test section also varied slightly (from 5.999 in. to 6.018 in.),
correction was also made for the pressure change caused by the area differ
ence. Using Bernoulli's equation, modified to account for frictional head
loss,
? -2 v2 ~
L+CX_V_+A2- __ , w 2g d 2g
Ii l' id -4fi •
where
p = pressure at a piezometer tap (lb per sq ft)
w ~ specific weight of water (lb per ft3)
V ~ mean velocity of flow at a piezometer tap (ft per sec)
A= coefficient of friction
x = distance from the reference manifold to a piezometer tap ,
d ~ diameter of test section at piezomoter tap
(subscript R refers to the reference manifold) •
The friction factor )\ was computed from
A:..2S... -d
PR - P w -_ .... , 2:0:---- + ocR - ex
VR/2g (3 )
Values of A' ~ are plotted in Fig.5 as determined from the above formula o
Since Cf , as used in Eqs. (1) and (2), is defined by
where
ofi-F:;CfA 2 ='T"oA,
F :; force on one side of a plate of area A,
f = density of fluid,
V ~ velocity of free stream, and
~ ~ average boundary shear on plate,
the relation between Cf and )\ can be computed. Since in a cylindrical
pipe,
then,
A V-x Values of Cf = -U- versus Rex = yare plotted in Figo 6 as determined
in the model. The values of Rex were computed assuming ~ to be the dis
tance from the reference manifold to a piezometer tap. This seemed a logical
assumption to make since the extrapolated values of ()( were nearly unity
\.
--..
6.
(1.0007) at this point. It is seen that the experimenta.l points plot quite
closely to the semi-empirical curve of. Prandtl* (Fig. 6), and the correlation
is in general at least as good as the. experimental points obtained by Wiese"ls-iB~
berger.
In extrapolating to determine the head loss in the prototype test
section, it was necessary to use the K~mn~n-Schoenherr equation, since the
values of Rex will be in general ten times as great as in the model and
thus will exceed the range of Rex for which the Prandtl equation ~ valid.
Values of Re were computed assuming a water temperature of 75 F 0 and x
assuming that the boundary layer will start to develop at a point 1. 25 ft up-
stream of the test section, which is a point homologous to that assumed in
the model (the reference manifold). Values of Rex' 4- and AT for the
prototype test section are tabulated in Table I for four different test sec
tion velocities at 5-ft intervals along the test section. The value of A ~ for x = 31.25 ft is the amount of the test section velocity head lost in wall
friction between a point in the contraction cone 1.25 ft upstream of the test
section and the downstream end of the test section; these values are plotted
in Fig. 7 for four different velocities of flow in the test section.
In computing the variation in pressure along the prototype test
section, values of 0( were recomputed taking into account the relatively
thinner boundary layer in the prototype. The value of ex at the upstream
end of the test section will be approximately 1.0003, and at the downstream
end ex will be approximately 1.0127. It was again assumed that the varia
tion in DC between these two points was linear, and it was assumed that ex was 1.0000 at a point 1.25 ft upstream of the beginning of the test section o
The pressure gradient along the prototype test section (from the upstream end
to its downstream end) is plotted in Fig. 8, the ordinate being the pressure
difference in feet between the upstream end of the test section and any other
point in the test section divided by the velocity head of the stream.
IV. DJ:l<'ltl]SER TRANSITION AND TUNNEL CAVITATION INDEX
One of the important uses of the water tunnel is the study of cavi
tation on test bodies, propellers, and sonic gear. In studying cavitation on
i~ Ibid.
** Ibid., po 187.
Table I
v = 18.00 fps V = 30.00 fps V = 50.00 fps V = 84.5 fps
x Rex· 10-1 A Re 010-1 ?\ /'1:2- Re 010-7 A- Re 010-7 A x Jt:2- x
Cft) U- k- 4 '"4 T A·~ d x d x d x
1 .. 25 0.225 0.00397 0 .. 0040 0 .. 375 0.00357 0.0036 0.625 0 .. 00324 0 .. 0032 1 .. 060 0.00292 0.0029
6 .. 25 1.125 0.00287 0.0143 1..875 0,,00265 0 .. 0133 3.125 0.00246 0.0123 5.281 0.00228 0.01.14
11.25 2.025 0.00262 0.0?36 3.375 0.00243 0.0219 5.625 0.00226 0.0204 9.506 0 .. 00209 0.0188
16.25 2.925 0.00249 0.0323 4.875 0.00230 0.0299 8.125 0.00214 0.0277 13.73 0.00198 0.0258
21.25 3.825 0.00239 0.0406 6.375 0.00222 0.0376 10.625 0 .. 00206 0.0350 11.96 0.00191 0.0322
26,,25 4.725 0.00232 0.0486 7.875 0.00215 0.0452 13.125 0.00200 0.OU9 22.18 0.00186 0 .. 0391
3L25 5.625 0.00226 0.0563 9.375 0.00210 0.0524 15 .. 625 0.00195 0.0487 26.41 0.00182 0.0454
Pu - Px CT"min Pu -'Px <Tmin Pu - Px CTmin Pu - Px CTmin
: 1.25 0.000 0.1327 0.000, 0.1292 0.000 0.1259 0.000 0.1228
i 6,,25 0.0124 0.1203 0.012k 0.1174 0.0112 0.1141 0.0105 0.1123
! 1L25 0.0237 0.1090 0.0237 0.1068 0.0213 001046 0.0199 0.1029
16.25 0.0)4.5 0.0982 0.034.5 0.0961 0.0307 0.09.52 0.0290 0.0938 .
21.. 2.5 0.0449 0.0878 000449 .0.0869 0.0401 0.0858 0.0375 0.0853 ,
26 .. 25 0.0550 0.0777 0.0550 0.0772 000491 0 .. 0768 0.0465 0.0763
3L25 0.0641 0 .. 068 0.0647 0,,068 0.0579 0.068 0.0548 0.068 - ----- - --
--J •
8.
a body, it is desirable to impose as severe conditions as possible on the.test
body without cavitating the water tumlel; that is, the static pressure in the
test stream should be as small as possible and the velocity on the test body
as high as possible without cavitation occurring in the tunnel circuit. This
is desirable not only for maintenance of high tunnel energy efficiency and
elimination of boundary pitting, but because the increasing use of sonic
methods of observing cavitation on the test body makes it desirable to main
tain a low ambient noise level.
The pressure drop in the test section is important in conjunction
with· operation involving cavitation as well as in ?onjunct~on with drag meas
urements. The model studies showed that the critical point in the tunnel
circuit in regard to cavitation is the transition from the cylindrical test
section to the conical diffuser. The model tunnel cavitated at this point
when the value of the cavitation index a- was 0.058 at the top of the dif-cr fuser transition,
where
0- '= cr
Pcr - Pvp
V2/2g
Pcr = absolute pressure (lb per ft2) at point of incipient cavitation, and
Pvp = vapor pressure of fluid (lb per ft2 ).
In determining the value of cr ,the pressure was lowered in the cr model tunnel to approximately -30 ft of water relative and the tunnel was
allowed to run at very low speed for about one hour, or until no more dis-
solved gases were vdthdrawn from the water. The tunnel pressure was then
raised to above atmospheric and the test section velocity was set at the de
sired speed. The pressure was again reduced until cavitation occurred quite
violently in the diffuser tranSition, as could be detennined audibly, and
then the pressure was allowed to rise slowly. The pressure, relative to atmos
pheric, was recorded at Tap E by a U-tube manometer containing mercury when
cavitation had just ceased. The cessation of cavitation was determined audi
bly by placing one end of a metal rod between the observer's teeth and the
other against the wall of the tunnel. The barometric pressure ~as obtained from an accurate, standardized recording aneroid barometer. The average of
four detenninations of <Tcr was 0.0580" the maximum value being 0.058, and the minimum 0.0571.
..
9.
The value of 0- at any other point in the test section can be deter
mined if the absolute pressure at this point is known. The preceding section
of this report has defined the pressure variation between the upstream and
downstream end of the test section. In order to determine the pressure ex
isting at an intermediate point in the test section when cavitation is incipi
ent at the transition to the diffuser, it is necessary to determine the pres
sure difference between the point of incipient cavitation and the downstream
end of the test section. The cavitation index 0- can then be determined for
any point in the test section as follows:
where
p - P Yl?
w
ifJ/2g --
0-min : minimum cavitation index at a point in the test section" .
p : absolute pressure (lb per sq ft) at a point in the test section, and
Pd : absolute pressure (lb per aq it) at the downstream end of the test section.
In order to prevent a sharp break in the boundary at the junction
of the cylindrical test section and the conical diffuser, with accompanying
high local velocities and low pressures from curvilinear flow" a parabolic
transition arbitrarily selected as one-half diameter long was provided. The
transition was designed to be tangent to both the test section and the 50 diffuser, which is discussed in PART IV, DIFFUSER STUDIES. For the condi tiona
above, .
and
yield the equation"
2 r-r :Kx" o
dr ro =)0 and -ax- = 0 when x = 0
when x ::30
2 r :t )0 + 0.000728 x I
. '
10.
for the transition in the prototype. Similar reasoning leads' to the equation,
r = 3.0 + 0.00728 x2 ,
as the equation for the transition in the model where x and I' are in
inches. A template which was made to dimensions obtained from this equation
was used in boring the aluminum casting for the first section of the diffuser.
Although the construction of the template and the boring of the casting were
done with a cumulative error of lees than 0.005 inches in radius, this error
was enough to substantially alter the constants in the equation for the tran
sition. Comparative plots of the actual and designed model transition diam
eters are given in Fig. 9 •
In Fig. 4 are presented graphs of the variation of pressure along
the test section and in the transition region of the diffuser, as determined
from the model tests. It will be noted that the lowest pressure attained is
at Tap E~ which is in the transition to the diffuser, even though the flow
has been decelerated to a velocity lower than that exj.sting in the test sec
tion. There are two reasons for this decrease in pressure where a pressure
gain would be expected by application of Bernoulli's theorem to the axial
velocity. The two causes preventing the regain of pressure are friction head
loss and the pressure drop caused by curvilinear flow along the convex wall
of the diffuser transi tione Theoretical evaluation of the pressure drop
owing to the curvilinear flow is made somewhat complex by the velocity gradi
ent in two directions caused by the growth of the boundary layer and diver
gence of the streamo
In Fig. 5 is plotted A' ~ , as defined in Eqo 3Q This plot 0 f
A'+ represents the pressure drop along the test section and in the dif
fuser transition which is in excess of that to be expected by an applicati.on
of Bernoulli's equation, considering the flow at all points to be purely
axial. Thus, where the flow is actually purely axial (in the test section),
the r,raph represents the head loss from the reference manifold 1ft ino up
stream of the test section to a point in the test section. Where the flow is
not purely axial (in the diffuser transition), the graph represents pressure
loss caused both by head loss and flow along the convex wall of the diffuser
transitiono
Figure 5 shows that the maximum pressure drop in the model diffuser I,
I -2 transition is about 0.016 ~ greater than that which would occur had the
..,
...
\ 110
loss caused by wall friction continued at the same rateo This pressure drop
may therefore be attributed to the curvature of the walls of the diffuser
transition. This pressure drop theoretically should be a function of velo
city head and radius of curvature of the wall; the drop owing to curvature
'Would be expected to decrease with increasing radius of curvatureo The radius
of curvature of the transition in the model as designed is 1/10 the radius
of curvature in the prototype (actuallY the ratio is about 1/15 owing to in
accuracies in boring the model diffuser transition). Since the functional
relation between radius of curvature and pressure drop is not obtainable I it
is therefore arbitrarily assumed that the pressure drop caused by wall curva-fj2
ture in the prototype is 0.010 ~.
From the comparative plots of the diffuser transition as designed
and machined (Fig. 9), it will be observed that the curvature of the. walls
of the transition of the model begins one inch downstream of the designed /
beginning of the transition and that the curvature li in. downstream (where
the pressure tap which recorded the critical cavitation pressure was placed)
is quite severe. In computing o-cr from the pressure measured at this tap,
it is tacitly assumed that this tap was recording the pressure at the PC?int
of cavitation. This is probably a valid assumption to make since the curva
ture is quite severe at this pointo The assumption is not too important,
however, in evaluating th~ cavitation index existing at the upstream end of
the prototype test section. If cavitation had ooc~red at another point in
the model diffuser transi ti.on l since the absolute statio pressure at this
point would have been lower than that measured at Tap E" the calculated value
of 0-01' would have been lower and the pressure drop attributed to wall our
vature would have been greatero These would in effect cancel each other, and
thus the calculated CT min at some point upstream would have been approxi
mately the same.
In the prototype water tunnel, the curvature of tl1e diffuser tran
sition will begin at the end of the test section as de8igned~ and, since the
radius of curvature is practically constant along the transition, it will be
assumed that the pressure drop caused by curvature is effective immediately -2
downstream of the end of the test section and is 0 0 01 ~ 0 Thus,
V2 Pd - Per:: 0.01 2'g ,
and
0- in = cr + 0 G 01 + m cr if. / 2g
Values of r:r i were computed for 5-ft increments of the prototype mn test section. It should be noted that these values, which are plotted in
Fig. 8, were computed for the top of the test section and thus are the mini~
mum values for any cross section of the test section. For a point in the
test stream, the cavitation index wOlud be
where
, Ad (T :: cr min + ;;2 / 2g I
D. d :! distance in feet from top of test section to
a point in the test stream.
If a test body is installed in the test section, the cavitation
index upstream of the model will be increased because of the increased pres
sure drop in the test section. In the case of a test body one-sixth the
diameter of the test section having a coefficient of drag of 1.00, or. up-. m~n
stream of the test body would be increased by approximately 0003.
The question naturally arises as to whether or not the one-half
diameter long parabolic transition is an adequate design. Logically, there
should be some best design of the transition shape so that the pressure re
gain caused by deceleration and the pressure drop caused by wall friction and
curvature would combine to give the smallest sag in the pressure curve. For
instance, a shorter transition would give a faster regain of pressure by de
celerating the stream more rapidly and allowing a smaller friction loss, but
these factors might be offset by a greater pressure drop caused by curvature
of the flow. Conversely, if the transition were longer, the various factors
might also combine to give the optimum design. The difficulty in analyzing
the problem lies in defining the pressure drop caused by the curvature of the
streamlines. Unless this ca.n be determined analytically .. the problem probably
cannot be solved except by experiments on the prototype. Model studies would
probably be of small value, since a homologous model would not have the same radius of curvature.
The problem loses some of its importance in the water tunnel facility, however, when it is remembered that the cavitation index at the upstream
..
1.3.
end of the test section is of paramount importance. Even if the pressure drop
caused by curvature could be entirely eliminated-which" of course, it can
not--the minimum value of cr at the upstream end of the test section would
be reduced from 0.125 to 0.115. It is therefore felt that the present design
is adequate.
v. CONCLUSIONS
On the basis of these experimental investigationa" the follo,?,ing
conclusions concerning the test section of the 60-in. prototype tunnel are
drawn:
1. The velocity distribution in the test section will
be entirely satisfactory over the main body of the flow.
Variations in axial velocity from point to point of any
section will not exceed one per cent, except in the bound
ary layer which will have a maximum thickness at the down
stream end of the test section of approximately ten per
cent of the diameter of the test section.
2. The head loss from a point in the contraction
cone 1.25 ft upstream of the beginning of the prototype
test section to the downstream end of the test section
will vary from 0.056 f at a test section velocity of . g 2
18 ft per sec to 0.045 * at a test section velocity of
84.5 ft per sec •
.3. The pressure drop along the test section will be
practically linear, and the total pressure drop from the
upstream end of the test section to the downstream end
will vary from 0.06, ~ for a test section velocity of
18 ft per sec to 0.0,5 for a test section velocity of 8405
ft per sec ..
4. The critical cavitation index of the water tunnel
without an installed model will be 0.0,8 at the crown of
the diffuser transition.. and will vary at the crown of the
upstream end of the test section from 0.1.3.3 at a test sec
tion velocity of 18 ft per sec to 0.12.3 at a test section velocity of 84.5 ft per sec.
..
5. The transition from the test section to the dif
fuser is an adequate, though probably not optimum, design
on the basis of cavitation characteristics of the water
tunneL
14.
1,.
o F \1 L L U S T RAT 1 0 N S ....... -_ .... -----_ ..... - .........
Figure Page
1 Seotional Elevation of Test Section Flow Circuit • • 0 16
2 Velocity Traverse on Horizontal Diameter • , . . • • • 17
1 .3 Velocity Traverse on Vertical Diameter • • • • • • • •
4 Measured Pressure Drop in Model Tunnel Test Section,. 19
, Oomputed Head Loss in Model Tunnel Test Section. • •• 20
6 Friction Factor Versus Reynolds Number • • • • • • • • 21
7 Head L088 in Prototype Test Section. • • • • • • • • • 22
8 Pressure Drop and Cavitation Index in Prototype Test
Section , • • • • • •• • • • • • • • • • • • • • 23
9 Aotual and Designed Model Diffuser Transition Boundaries. • • • • • • • • • • • • • • • • • • • 24
"
30.75" 30" ~ ~f
96° VANE : APPROACH CONDUIT I STAGGER ANGLi.! .
CONTRACTION
1.00" GAP
1 I
~1 Fr,. i <i. 5 !! ["" ~ .r,; _
' 'i;r, REFERE~~1 f/ MANIFOL
FIG. I
~.
36"
TEST SECTION
TAP I X(in) R 0 A 12 B 21 C 24 o 36 E 39 F 39.8
<t o
DIA.(in) 6.004 6.006 6.015 6.018 5.999 6.015 6.062
I -"~ ~,.-,
78"
DIFFUSER
o 10
FLOW.
SECTIONAL ELEVATION OF TEST SECTION FLOW CIRCUIT }-J :J-• •
~
"
'>
0.9
1.0 0 ::::.....
( T ......
1% V Vc
5 - ~--- --
I
0.9 CI- .--- --_. __ . -
::l-Ve 0.8 5 -
0- V = I 8.00 F. P. S. o-v = 30.00 F.P,S. L::!.- V = 49.62 F.P'S.
0.8 0
0.7 5 DOWNSTREAM END OF TEST SECTION
0
0.700 2 3 4 5 6 DISTANCE FROM WALL (IN.)
1.00 r ~
~ ~
0.95
0.90 UPSTREAM END OF TESJ SECTION
.~
0.85
FIG.2 VELOCITY TRAVERSE ON HORIZONTAL DIAMETER
','
1.00
0.95
1 0.90
v Vc 0.85
0.80
0.75
0.700
1.00
r 0.95
0.90
0.85
v T ~
, 1% ~c
0- V = 1 8.0 0 F. P. S. D-V = 30.00 F.P.S. /}. - V = 4 9. 6 2 F. P. S.
DOWNSTREAM END OF TEST SECTION
234 DISTANCE FROM WALL (IN.)
A .. 1,1
TOP OF TEST SECTION
.
UPSTREAM END OF TEST SECTION
5
18.
6
~ ~
FIG.3 VELOCITY TRAVERSE ON VERTICAL DIAMETER
" .;,.'
0.00 IX I
FIG. 4 MEASURED PRESSURE DROP IN
0.02 I I :-.... , I MODEL TUNNEL TEST SECTION
0.041 'It
CP ~
TEST SECTION
0.06 ~----J--------~--~-----i--------~-:r--~~' ~
~. 1:1 V ;0 49.62 f.p.s.
CL
I 13: ~
CL
o V: 30.00 f.p. s.
o V = I 8 .00 f. p. s. I
0.08 I I I :\
0.10 I , I I I
, I I
'TAPC REFERENCE MANIFOLD (R) ,TAP A TAP B ' I I I I
0.12 0 5 10 15 20 25 30
DISTANCE FROM REFERENCE MANIFOLD
35
( IN.)
DIFFUSER TRANSITION
:TAP F
40 45 f-I \()
•
, <'
O.OOK I I Fl G. 5 . I
0.021- X I-o ~ II
'+-IN r~ -'= I> (\J
0.04~ II
r.,. -..gl-o '---"
0.061- ~
a:: ~ --
COMPUTED HEAD LOSS IN I
MODEL TUNNEL TEST SECTION---+-----+-------I
~"'-....: ! L
I I
. I I "-....11 A ii· 49.62 f. p.'. I I I "-.! i L---..J
I 0.08 r- +
a. I I
I I I~ 1°'
C V=- 30.00f.p.s. I I t~ \~ ~ o ii = 18.00,f,p... +:: -,-
~-1_=-_-+_t-1 --1--- I I I I ~ I I I I C? 0
I
~ ~ I> '" I I I
I I I q t:: I \:=\:=-~ I I~O 1
0.10
R I,
0.12' 5 o
c. ~ .:..
000~4l I I I I I n
0.004210- \V~ PRANDTL: ! ,1--- I r-- I I I I I r'-r If I i Cf: 0.074 I 1 r FIG. 6 :' RE l' I I
0.0040: i \ I X I I -~RIC.TION FACTOR VS REYNOLDS NO. 000':10 I I 8~ I ,I I EXPERIMENTAL POINTS FROM MODEL
. =1 I' 1 I , I I 0 I 0 TEST SECTION VELOCITY :. 18.00 f.p.s.
00036. ~ I [] TEST SECTION VELOCITY - 30.00 f.p.s. I · . I I ~ I : tJ. TE ST SECTION VELOCITY = 49.62 f.p.s. I
· 1 ! I I ~I 0.0030 I I ii!~ A
II! I ,.~ II I : RAN~E COVERED I~ MODEL O~ERATIO~'" RANGE COVERED IN PROTOTYPE OPERATION)IIr I I i
Q0028 1 i I 11!! I ~ I \1 I i,l! I ! I I . I ~ I i i \' I I ;
0.002..6 1 I ; : ~ 1 I I T
I f ;:1 "'" 1.1 00024' I I,;~ "'" iii · '4~ Ii" I I I
::.. I I I ~r-...... KARMAN-SCHOENHERR I,... 10 i I I I........... V I rv· 0022 I I I ; I "" 17 F-:: 4.13 LOG (REX'Cf) ! I I ! I I I
I I : . ,,~,ef . I 000201 j I ~ '1 I I I ~ 1 I\)
O.OOISt-L- -.--.-t--.-I~ . -- I I I II ~ I I I RE X - '?' I I I I I I I I 1 .. J_ ---.l ;
106 2 3 4 5 6 7 8 9 107 2 3 4 5 6 7 8 9108 2 3 4 5 6 7 8 9 109
.~
0.0570 --.,..------,----...,..------,----,..-----r----,
I 0.0 560\-----I------I-----+-----If-----+----+--------i
0.0540-~+------f-- HEAD LOSS FROM POINT IN CONTRACTION
1.25 FT. UPSTREAM OF TEST SECTION TO
DOWNSTREAM END OF TEST SECTION
0.0520\-----+--~--+----I-----+----+-----f-----t
0.0500 -------'k
0.048°-i>l~ --~-'
.,. '+-..c
II xl"O
0.0460- ,,<
0.0440 ----j-
0.04 0 15 25
HEAD LOSS FROM
UPSTREAM END TO DOWNSTREAM
END OF TEST SEC TION
35 45 55 65
TEST SECTION VELOCITY (F.P.S.)
FIG.7
75
HEAD LOSS IN PROTOTYPE TEST SECTLON
85
'..I
I "
',~
;.>
"
23. 0.00 b----,..-------,-----r----.,.----,--.-----,0.140
l-->.;:---~~---____jl_______--------'----I------+---__+_--~ 0.130
PRESSURE DROP FROM
UPSTREAM END OF 0.120 TEST SECTION
0.030 0.110 ----6-These ymbols
~>I~ are r ve.rsed-Shou\d be
'1' e:: 0;04 .- 0.100 a.. 't:JE I ~
a?
0.0501---~----t----t-~~~-~~~~---I0.090
MINIMUM CAVITATION INDEX
0.0601-__ -t-___ ---+_T~h~e_=s ___ e_+a.::.....r-=e---O-=-K=-=--_+_---.:~..._+-~~
0.070
0.080
0.085
0- V= 18 F.P.S. C-V=30F.P.S.
.0. - V =50 F.P.S. 0- V=84.5 F.P.S.
OCr = 0.058
0 5 10 15 20 25 30
DISTANCE FROM UPSTREAM END OF TEST SECTION (FT.)
FIG.8 PRESSURE DROP AND CAVITATION
INDEX IN PROTOTYPE TEST SECTION
0.070
0.060
0.055
Q~ . .l.....t: '" ... ~.~ " -q
3.10
-z END OFTRANSITION
- 3.08 z 0 I-
en ~ 3.06 0::: I-
0::: W en ::::> 3.04 LL LL
0
LL
o 3.02 en ::::> -0 <l: 0:::
3.000 ~ 6 zc=:=::: I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
FIG.9
DISTANCE FROM END OF TEST SECTION (.1 N.)
ACTUAL AND DESIGNED MODEL DIFFUSER TRANSITION
BOUNDARIES
"" ..... "V,,-
t\)
J::-•
