E-01 Admin. Bldg.

3 1969

NBS TECHNICAL NOTE

374

Incipient and Developed Cavitation

in Liquid Cryogens

D. K. EDMONDS AND J. HORD

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U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. Today, in addition to serving as the Nation's central measurement laboratory,

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UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

NBS TECHNICAL NOTE 374

ISSUED FEBRUARY 1969

INCIPIENT AND DEVELOPED

CAVITATION IN LIQUID CRYOGENS

D. K. EDMONDS AND J. HORD

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means tor making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402

Price 35 cents.

TABLE OF CONTENTS

Page

Abstract 1

1. Introduction 1

2. Description of Apparatus and Operating Procedure 3

3. Instrumentation 6

4. Discussion and Analysis of Experimental Data 7

5. Extension of the Cavitation Similarity-Equation Theory .... 13

6. Discussion of Results Given in Tables 1 and 2 20

7. Summary ZZ

8. Recommendations for Future Work 22

9. Nomenclature 23

10. References 26

List of Figures

Figure 1. Schematic of cavitation flow apparatus 4

Figure 2. Detail of plastic venturi and location of pressure and

temperature taps 5

Figure 3. Incipient-cavitation parameter for liquid hydrogen as a function of test-section inlet velocity and liquid

temperature 8

Figure 4. Incipient-cavitation parameter for liquid nitrogen as a

function of test-section inlet velocity and liquid

temperature 9

Figure 5. Typical pressure depressions within cavities in liquid

hydrogen 11

Figure 6. Typical pressure depressions within a cavity in liquid

nitrogen 12

Figure 7. Photographs showing effects of velocity and temperature

on the appearance of developed cavities in liquid

nitrogen; nominal cavity length, 3. 25 in 14

in
TABLE OF CONTENTS (CONTINUED)

List of Tables

Table 1. Evaluation of Similarity Equation Using Liquid Hydrogen

Data 17

Table 2. Evaluation of Similarity Equation Using Liquid Nitrogen

Data 18

IV
INCIPIENT AND DEVELOPED

CAVITATION IN LIQUID CRYOGENS*

D. K. Edmonds and J. Hord

Cavitation characteristics of liquid hydrogen and

liquid nitrogen flowing in a transparent plastic venturi

have been determined and conventional cavitation-inception-parameter curves are given. Representative developed- cavitation data, consisting of pressure and

temperature measurements within fully-developed cavities, are also given; measured temperatures and pressures within the cavities were generally not in thermodynamic equilibrium. Existing theory was used to

obtain equations which correlate the experimental data

for developed cavities in liquid hydrogen or liquid

nitrogen. The theory is extended to include the effect

of cavity thickness and the experimental data are used

to evaluate the results. Some recommendations for

future work are given.

Key words: Cavitation, cryogens, incipience

1. Introduction

Cavitation is usually categorized as gaseous or vaporous; in

this paper it is also necessary to distinguish between incipient (or

desinent) cavitation and fully-developed cavities. Cavitation is usually

defined as the formation, caused by a reduction in pressure, of a

vapor phase within a flowing liquid or at the interface between a liquid

and a solid surface. For incipient cavitation, this definition is somewhat ambiguous because various criterion and methods are used to

detect the vapor phase. Incipient cavitation as used herein refers to

the fluid condition where the vapor phase is barely visible to the unaided

eye. The visual inception criterion was chosen to conform with the bulk

of the literature, and also chosen because the sensitivity [ l-3]t of

* The experimental work described in this paper was performed at NBS

under the sponsorship of Lewis Research Center (NASA-LeRC) under

Contract No. C-35560-A.

t Numbers in brackets indicate references at the end of this paper.
various acoustic detectors can vary appreciably. An acoustic detector,

which would detect cavitation in what appeared to be a pure liquid phase,

was developed in the course of a recent study and is described in detail

in reference [4]. Pressure and temperature profiles within fullydeveloped cavities were measured and are referred to herein as

developed- cavitation data.

To design liquid handling equipment such as pumps and flowmeters, the designer must determine whether cavitation will occur,

and in many cases, to what extent. While the non- cavitating performance of hydraulic equipment may be predicted from established

similarity laws, cavitating performance can seldom be predicted from

fluid to fluid. The effects of fluid properties on cavitation performance

are well recognized [5-14] and require more understanding to develop

improved similarity relations [15] for equipment design. NASA has

undertaken a program [ 16] to determine the thermodynamic behavior

of different fluids in an effort to obtain improved design criteria to aid

in the prediction of cavitating pump performance. The experimental

study described herein was conducted in support of this program. Two

kinds of data are reported here: (1) cavitation inception (incipient)

and (2) developed- cavitation; both are an extension of work done at

NASA-LeRC, see references [15-22], The main purpose of our

experimental study [4] was to extend the experimental investigation

to liquid hydrogen, and determine the scale effects of using a test

section that was half the flow area of the NASA test section. Scale

effects in incipient cavitation were determined by using liquid nitrogen

and comparing the results with NASA nitrogen data. The purpose of

the present manuscript is twofold: (1) to briefly review key experimental results of reference [4], and (2) to propose and evaluate

possible improvements to existing theory regarding the effects of
fluid properties on developed- cavitation performance of equipment.

The analytical part of this work extends the similarity equation [ 1 5]

by permitting the cavity thickness, t, to vary as a function of velocity

and cavity length. The cavity thickness was taken as constant in

reference [ 15]

„

The similarity equation is useful for correlating the cavitating

performance [ 1 5, 16] of a particular piece of equipment from fluid to

fluid; this equation is also useful in extending the velocity and temperature range of data for any given fluid. Experimental data from reference [4] were used to evaluate the postulated improvements, theory,

etc. , concerning this similarity equation.

2. Description of Apparatus and Operating Procedure

Figure 1 is a schematic of the test apparatus, and figure 2

shows some details of the clear-plastic test section -- pressure and

temperature tap locations are shown. Highly compressed elastomeric

"O" rings were used to seal both faces of each of the aluminum end

flanges. The entire flow system was vacuum insulated.

The operating procedure consisted of first filling the supply

dewar with liquid and slowly cooling the flow system (using valves A

and B -- figure 1) to the normal boiling-point temperature of the

cryogen. Special attention was given to cooling the plastic test section,

as it failed from thermal shock in some of the earlier tests. When the

system was sufficiently cooled, the contents of the supply dewar were

slowly transferred to the receiver dewar and back again in order to

assure complete cooldown. The system was kept cold by maintaining

See reference [4] for greater detail.
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liquid in the test section and transfer line. Bottled gas provided the

required pressure for all liquid transfers. In order to make a test,

the liquid in the supply dewar was heated to the desired temperature,

pressures in the supply and receiver dewars were adjusted for the

desired flow conditions, and the valves (C and D) in the main flow line

were then opened. Flow conditions were changed during a test by

varying the receiver dewar pressure and throttling with valve D.

Cavity formations in the flowing cryogens were visually monitored by

focusing a closed-circuit television camera on the test section; necessary changes in flow conditions were then made to secure the desired

cavitation patterns. Also, each test was recorded on 16 mm, 20

frames/ sec film that was subsequently used for data reduction.

3. Instrumentation

Test fluid temperatures at the flowmeter and test section were

determined by platinum resistance thermometers, see figure 1, The

overall accuracy of the platinum-thermometer temperature measurement is estimated to be within ± 0.09 R. Miniature chromel-constantan thermocouples were used to determine the temperature profile

within the cavities and assure rapid response during the developedcavitation tests. The reference thermocouple was placed in the plenum

chamber beside the platinum thermometer that was used to determine

bulkstream temperature at the test- section inlet. The cavity temperature measurements are estimated to be accurate within ± 1 R for

hydrogen and ± 0. 4 R for nitrogen; the inaccuracies in these measurements are due to the low emf produced by the thermocouples at low

temperatures.
System gage and differential pressure measurements were

obtained with pressure transducers mounted in a temperature stabilized

box near the test section. The overall accuracy of the pressure measurement, including calibration and read-out errors, is estimated to

be within ± 2%. Bourdon gages were used to monitor the various tests.

Volumetric flow rates were determined by a Herschel venturi

flowmeter designed to ASME standards [23], An error analysis of

this flow device and associated pressure and temperature measurements indicates the deduced mass flow should be accurate within about

one percent.

An electronic pulsing circuit provided a common time base for

correlating data between oscillograph, digital voltmeter (with printer),

and movie film. The data were reduced by first viewing the film of

the test event. A solenoid-actuated counter, installed adjacent to the

test section, was energized by the electronic pulser and appears on

the film. Thus, the data are reduced at the desired instant of time

by simply matching the number of voltage pulses which have elapsed.

4. Discussion and Analysis of Experimental Data

Since the temperature of the cryogen changed in flowing from

the supply dewar to the test section, the experimental data varied in

temperature around the selected nominal temperatures. A detailed

method [ 4] of temperature compensation was used for the incipient

and desinent cavitation data. No attempt was made to separate incipient and desinent cavitation data, as both were found to occur at

identical flow conditions; therefore, incipience and desinence are used

synonymously in this paper. Figure 3 illustrates cavitation-parameter

curves, K. versus V , for hydrogen. Similar data are shown on

IV o figure 4 for nitrogen. Note that the K^v curves for hydrogen cross at
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about 140 ft/sec: intersection of these curves may be tenable; however,

it is also possible that instrument error amplified in the K. paraIV

meter [4] is responsible for this behavior. The nitrogen K. curves

IV

also tend to a common value at the higher velocities. Minimum local

wall pressure at incipience was calculated to be less than bulkstream

vapor pressure in all of the inception tests (as much as 328 feet of

hydrogen head and 63 feet of nitrogen head).

Inception data furnished by Ruggeri [ 18] for liquid nitrogen in a larger (1.414:1) test section were found to be coincident with the NBS

[4] liquid nitrogen inception data; thus, it was concluded that the scale

factor was negligible.

The developed- cavitation data did not require temperature

compensation because the similarity equation compensates for varia2

tions in the temperature of the test fluid. Figure 5 presents typical

cavity pressure-depression curves for liquid hydrogen; figure 6 shows

similar data for nitrogen. "Pressure-depression" refers to the

difference between saturation pressure at inlet temperature and

measured cavity pressure. Cavity temperature measurements have

been converted into equivalent saturation pressures, subtracted from

the bulkstream vapor pressure, and plotted on these figures for comparison with the measured pressures. This pressure-depression is

plotted as a function of distance along the cavity, beginning at the

minimum pressure point in the test section throat. Note that the

measured pressure in the cavity is generally lower than the vapor

pressure of the bulkstream liquid (in some cases [4] as much as 651

feet of hydrogen head and 44 feet of nitrogen head). In many of these

2

More graphical and tabulated developed-cavitation data are given in

reference [ 4] .

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Nominal cavity length ll^in. 2 in. 3!/4in.

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V (ft/sec) 197.6 198.4 201.1

Kv 1.93 1.90 1.84

AXIAL DISTANCE FROM MINIMUM

PRESSURE LOCATION, x, inches

Figure 5. Typical pressure depressions within cavities in liquid

hydrogen.

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Figure 6. Typical pressure depressions within a cavity in liquid

nitrogen.

12
developed- cavitation tests, the measured cavity pressure exceeded the

saturation pressure corresponding to the measured cavity temperature

by an amount which could not be attributed to errors in pressure and

temperature measurements. Also, examination of the data revealed

that the degree of metastability in the cavity appeared to be a function

of bulkstream liquid temperature, velocity, and axial position within

the cavity. It was therefore concluded that, in general, the pressures

and temperatures within the cavity are not in thermodynamic equilibrium.

A series of photographs of developed- cavitation in liquid

nitrogen are shown in figure 7; the porosity of the nitrogen cavities

usually decreases with increasing velocity or increasing temperature.

These photographs are representative of conditions at which data were

reduced. Similar photographs of hydrogen cavities are not shown

because the cavities are nonporous and uniform in structure, see reference [ 4] .

3

5. Extension of the Cavitation Sirrii la r it y- Equation Theory

The similarity equation for developed- cavitation is given in

reference Ll5] as follows:

a

' I , V 0.5

B=B Yf *e^ f re£\f o

ref L V a / \ I / \ V t o, ref re f

(1)

The symbols are identified in the nomenclature section of this paper;

B is the volume of vapor in the cavity divided by the volume of liquid

3 Applications of the similarity equation are described in the introduction to this paper, see references [l5, 16, 24].

13
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>-<

—3.25-—»-

V = 35.22 ft /sec, T = 140.1 R, V = 72.89 ft /sec, T = 140.7 R,

P = 15.55 psia, Kv

= 1.86 P = 16.20 psia, Kv

= 2.15

V = 45.84 ft /sec, T = 150.7 R, V =73.13 ft /sec, T = 150.5 R,

P =29.25 psia, Kv

= 1.53 P = 28.90 psia, Kv =2.04

V =38.25 ft /sec, T = 160.7 R,

P = 49.20 psia, Kv

= 0.97

V = 74.14 ft/sec, T = I60.7 R,

P = 48.95 psia, Kv =l.82

Figure 7. Photographs showing effects of velocity and temperature

on the appearance of developed cavities in liquid nitrogen;

nominal cavity length, 3„ 25 in.

14
from which heat has been extracted (due to vaporization) in forming

the cavity. B can also be obtained from a theoretical expression

relating cavity pressure-depression to "B" factor; this theoretical

value is called B . The B is derived from an energy balance

between the vapor and the cooled liquid film at the liquid-vapor interface. The main assumptions used to derive B have been attributed

to several authors (see ref. [14]) and are summarized in reference

[ 15], For purposes of calculation, the numerical value of B can be

obtained from 1) fluid properties and 2) the expression for B

given in reference [ 15] .

To account for the difference between theory and practice,

equation (1) can be written in the following form,

cc ,. m -t ,. n V PTv

B=B

ref (-^) (-pi) (^_)

P

(T

i-). („

o, ref re f

The exponents in equation (2) are evaluated from experimental data

as follows:

(1) B is obtained for each experimental data point from a

cavity pressure-depression (P - P ) versus "B" factor plot, see

v n

reference [ 15] .

(2) One data point is arbitrarily chosen as a "reference"; the

Ct, t , V , and B from the chosen experimental run are then

o t inserted into equation (2) as constants where the subscript "ref"

occurs. The t term can be considered equal to unity (as in previous

studies [4, 15]) or a function of cavity length, t, and velocity, V

(see discussion below); in the latter case, the t term is absorbed

into the t and V terms.

o

15
(3) Values of ct, I, and V from each data point are then

inserted into equation (2) as the non- subscripted terms. This produces an equation for every data point except the one chosen as a reference. Note that the unknowns in this set of simultaneous equations are

B and the exponents m, n, and p.

(4) The computer is then programmed to range through values

of the exponents — one at a time. For each new value of m, n, or

p the computer finds the value for B, on the left side of equation (2),

then computes the sum of the squares of the differences between the

calculated B and the B for each equation. The computer adjusts

the exponents until the sum of the squares of the differences are minimized; in some cases, one or more exponents were held constant at

theoretical or arbitrary values. This process ensures that the calculated B values are brought as closely as possible to their respective

theoretical B values; the exponents computed in this manner represent

the best agreement between experiment, equation (2), and the energy

balance equation for B .

In the work of Gelder, et al. [ 15], the cavity thickness ratio

in equation (2) was assumed to be unity and the exponents for the

other terms were experimentally evaluated. The exponents obtained

by Gelder, et al. for F-114, along with the theoretical exponents,

equation (1), were applied to the data obtained in recent NBS experiments [4], The "best fit" set of exponents were also obtained by

computer for these data, again assuming the t term equal to unity.

Tables of exponents, along with their standard deviations in the B

factor, are given in table 1 for hydrogen and table 2 for nitrogen.

The standard deviation is a measure of the validity of the theories

for the similarity and B expressions as both are evaluated from

16
Table 1: Evaluation of Similarity Equation Using Liquid Hydrogen Data.

Data

Identi- fication

Source of Exponents

(i.e., assumed cavity

shapes from this paper

and exponents obtained

from reference material. )

Exponents*

Standard Deviations T Using reference

cavity lengths as follows: m n P 1.25 in. 2. Do in. 3.25 in.

T 1-1 Theory [ 1 5| ; See equation (1). ref

. 5 . 5 . 5 1.64 1.36 2.22

T 1-2 Gelder, et al. [15], experimental data

with F-l 14.

. 5 -.16 .85 .83 .92 .67

T 1-3 NBS Seek-Fit . 5 .5 .314=:= 1. 33

T 1-4 . 5 -.278* .5 .58

T 1-5 . 5 -.332* .5 . 58

T 1-6 . 5 -.372* .5 .56

T 1-7 .5 -.308* .7 32=:= .56

T 1-8 .5 -.348=:= .446=:= .57

T 1-9 .5 -.39=: .61* .56

T 1-10 -3. 52* -. 348* .554* .38

T 1-11 -3. 82 -. 30 4* . 644* .36

T 1-12 -3.82* -.41 4* .496=:= .41

T 1-13 \

' 1 r -4.62* .5 .5 1. 17

T 1-14 Exponents chosen

as a compromise

between theory

and experiment

ref

. 5 -.3 .5 .59 . 58 .58

T 1-15 Semi-cubical

parabola

3 , 2

t = kx .5 -. 167 .5 .74 .63 .62

T 1-16 Concave

parabola

2

t = kx .5 .5 .98 .76 .84

T 1-17 Straight line t = kx .5 -.5 .5 .66 .63 .71

T 1-1& Semi-cubical

parabola

3 2

t = kV x

o .5 -. 167 .833 .82 .89 .65

T 1-19 Concave

parabola

t = kV x

o .5 1.0 1. 1 1 1,23 .99

T 1-20 Straight line t = kV x

o

. 5 -.5 1.5 .77 2.49 .78

-*• B = B

ref (WC¥T(^l,ref

Standard Deviation = \ [ £(B-B) 2 ]/N where N - number of data points , B is computed

from theory [15], and B is computed from equation (2).

Exponents selected by computer, from experimental data, using a "least squares" fitting

technique

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two and five.

Because the "best fit" exponents vary appreciably from the

theoretical values, one possibility for improvement is to let t be a

function of cavity length and velocity. As an example, assume that

3 2

the cavity has the shape of a semi- cubical parabola, t = ax ; if we

also assume that the coordinate proportionality factor is linearly

related to V , then a = kV where k is constant for any given

o o

y &

fluid and test item. Obtaining the expression for t requires an

integration:

I

1 .... .1/3 2/3

(kV ) x dx. (3) o o

Integration of equation (3) and substitution of the resulting t into

equation (1) produces the following:

a r 0. 5 I r -0.167 V 0.833 , 0.333

ref

\

/ ref\ / o \ / k

B = B refl-r-J [nr {-—7) hr-; - (4)

o, ref ref

0. 333 The (k/k .) term is taken as unity because the similarity

ref

equation requires geometrically similar cavity shapes from fluid to

4

fluid for a specific test item; also, correlations between fluids are

not being evaluated here and

4 Limited nitrogen data precluded correlation between nitrogen and

hydrogen fluids, and NASA-LeRC personnel are preparing computer

correlations [25] using available hydrogen and F-114 data.

19
a rx °- 5 / l r -0- I 67 , V 0.833 (5) ref \ / ref \ / o B = B

ref V a / \ I J \ V

o, ref

Other basic geometrical cavity shapes can be assumed and different

exponents for the I and V terms will result. Table 1 lists the

o standard deviation in B factor resulting from use of several assumed

cavity shapes, as applied to the liquid hydrogen cavitation data obtained

from recent experiments. The cavity thickness may also be treated as

a function of cavity length, but independent of velocity. In this case

q w

t = kx , and q and w depend only upon the assumed cavity geometry;

e.g., q = w = 1 for a straight-line variation, etc. Computer results

for some basic cavity shapes (neglecting effect of velocity on cavity

thickness) are also given in table 1.

6. Discussion of Results Given in Tables 1 and 2

Developed- cavitation data for nitrogen were obtained for one

cavity length only; therefore, the postulations concerning cavity shape

could only be applied to the hydrogen data where three cavity lengths

were available. Examination of table 1 shows that the basic theory

(data set Tl-1) gives rather poor results in terms of the standard

deviation: better results are obtained by using the exponents of Gelder,

et al. , (data set Tl-2) or by permitting the computer to select one or

more of the exponents (Tl-3 through Tl-13); of course, the "best fit"

5

exponents in sets Tl-10 through Tl-12 give the best results .

5

Standard deviation is minimized in those computations where one or

more exponents are selected by the computer; the absolute minimum

standard deviation is obtained by permitting the computer to select

all three exponents.

20
In table 1, three different cavity lengths were used as references in order to determine the effect of reference length upon

standard deviation. The exponents m = 0. 5, n = -0. 3, and p = 0. 5

(see data set Tl-14) were least affected by reference cavity length;

note that these exponents produce a low standard deviation. In general,

the 2.0 in. and 3.25 in. cavities provided the lowest standard deviations,

Note that the exponent p is theoretically 0. 5 for all cavity shapes

assumed to be independent of velocity (Tl-15, Tl-16 and T 1- 17); also

p tends to 0. 5 when all three exponents are allowed to seek a best

fit (Tl-10, Tl-11 and Tl-12 for hydrogen; T2-4 for nitrogen).

Table 1 shows that velocity-dependent cavity shapes (Tl-18,

Tl-19 and Tl-20) produce standard deviations that exceed those for

cavity shapes where velocity is neglected (Tl-15, Tl-16 and Tl-17).

However, the semi-cubical parabola with a velocity-dependent shape

(Tl-18) does give almost the same exponents that Gelder, et al. , obtained (Tl-2) with F-114. Perhaps the concept of velocity-dependent

cavity shape is pertinent for some fluids other than hydrogen. The

assumption that average cavity thickness is a function of cavity length

indicates considerable promise for hydrogen; the semi-cubical parabola (Tl-15) and the straight line (Tl-17) shapes give the best results

of the three cavity shapes examined here.

The lack of variation in Ct(<10%) may explain why the exponent

m tends to a negative number in a seek fit (Tl-10 through Tl-13 for

hydrogen and T2-4 for nitrogen); because the standard deviation is

barely affected by this small variation in 0L, m was usually held at

the theoretical value of 0.5.

21
7. Summary

1) Incipient- cavitation-parameter curves are given for liquid hydrogen

in the ranges of 36. 5 to 41 R and up to 180 ft/ sec, and for liquid

nitrogen in the ranges of 140 to 170 R and 20 to 70 ft/ sec. A comparison of this liquid nitrogen incipient- cavitation data with

nitrogen data obtained by NASA indicated negligible scale effects.

Bulkstream vapor pressure exceeded the calculated minimum

local wall pressure in all of the incipient cavitation tests.

2) Some characteristic data for developed- cavitation in both hydrogen

and nitrogen are given in the form of pressure-depression curves.

These curves show that the pressure and temperature in the cavity

are generally not in thermodynamic equilibrium.

3) Recent NBS data are used to analyze and evaluate the basic

similarity- equation theory and to compare these results with the

experimental work of others; the cavity thickness ratio is assumed

to be unity, see tables 1 and 2.

4) An analytical method, to account for variations in cavity thickness,

is proposed and evaluated using the NBS hydrogen data; the results

are again compared with the experimental work of others, see

table 1. The proposed method holds some promise for improvement of the cavitation similarity equation.

8. Recommendations for Future Work

1) More developed- cavitation data, using closely spaced pressure

and temperature taps, is needed to ascertain more precisely the

cavity pressure profile and fluid meta stability.

22
2) All existing developed- cavitation data, including Gelder, et al.

Ll5], should be computer correlated in order to determine the

pertinency of assumptions concerning cavity shape; these correlations would use the existing "static-model" theory.

3) Experiments should be designed to indicate the general shape of

the cavity, thereby putting the theory on a firmer basis.

4) An analysis should be performed to redevelop the cavity model,

accounting for dynamic effects. Existing data could be used to

evaluate the results of this analysis.

9. Nomenclature

a = coordinate proportionality factor in cavity shape

equations

B = ratio of vapor to liquid volume associated with the

formation and sustenance of a fixed cavity in a liquid

g

= gravitational acceleration, local, given in engineer2

ing units as g = 32.2 ft/ sec

h = test section inlet head corresponding to absolute inlet

pressure, ft h = head corresponding to saturation pressure at the test

section inlet temperature, ft v

k = constant used in expression for cavity thickness t

r 2 1 K. = incipient cavitation parameter L= (h - h )/(V /2g)J

IV o v o

2

K = fully-developed cavitation parameter [= (h - h )/(V /2g)] v o v o t = total cavity length measured from minimum-pressure

point on quarter- round contour along axis of plastic

venturi

23
P = (n = 2, 4, 5, 7, or 9): absolute cavity pressure measured

n

at a particular station or instrument port in wall of

plastic venturi

P = (n = 2, 6, or 8): saturation pressure corresponding to

n, T

the measured cavity temperature at a particular station

or instrument port in wall of plastic venturi

P = test section absolute inlet pressure

o P = saturation pressure at test section inlet temperature

v

t = local thickness of vapor-filled cavity at any x value

t = average thickness of vapor- filled cavity

T = bulkstream temperature, in degrees Rankine, of liquid

entering the test section

V = velocity of liquid at inlet to test section

o x = distance measured from minimum-pressure point on

quarter-round contour along axis of plastic venturi

(The minimum pressure point is located on the

quarter-round at 24 degrees of arc measured from

the point of tangency between quarter- round and venturi

throat)

Greek

a = thermal diffusivity of liquid

Subscripts

ref = reference test, or set of test conditions, to which a computation is being referenced when attempting to

correlate cavitation performance via the similarity

equation ( 1)

t = denotes theoretical origin

24
Superscripts

m = exponent of thermal-diffusivity ratio in equation (2) n = exponent of cavity-length ratio in equation (2)

p

= exponent of test- section-inlet-velocity ratio in

equation (2)

q

= exponent in expression for cavity thickness

w = exponent in expression for cavity thickness

25
10. References

1. C. P. Kittredge, "Detection and Location of Cavitation", Rept.

MATT- 142, Plasma Physics Lab. , Princeton Univ. , Princeton,

N. J. (1962). Available from the Clearinghouse for Federal

and Scientific Technical Information, Springfield, Va.

2. A. F. Lehman and J. O. Young, "Experimental Investigations

of Incipient and Desinent Cavitation", ASME Journ. of Basic

Eng., 86: 275 (1964).

3. J. W. Holl (ed.), "Discussions - Symposium on Cavitation Research

Facilities and Techniques", Presented at Fluids Eng. Div. Conf.

(Phila., Pa., May 18-20, 1964). Available from ASME, United

Eng. Center, 345 East 47th St. , New York 17, N. Y.

4. J. Hord, D. K. Edmonds, and D. R. Millhiser, "Thermodynamic

Depressions Within Cavities and Cavitation Inception in Liquid

Hydrogen and Liquid Nitrogen", NASA Rept. CR-72286, (1968).

Available from NASA, Office of Scientific and Technical Information, AFSS-A, Wash., D. C.

5. J. Hord, R. B. Jacobs, C. C. Robinson and L. L. Sparks,

"Nucleation Characteristics of Static Liquid Nitrogen and Liquid

Hydrogen", ASME Journ. of Eng. for Power, 86: 48 5 (1964).

6. R. S. Brand, "The Motion of a Plane Evaporation Front in a

Superheated Liquid", Tech. Rept. No. 2, Univ. of Conn. , Storrs,

Conn. (1963).

7. J. A. Clark, "The Thermodynamics of Bubbles", Tech. Rept. No. 7,

Mass. Inst, of Tech. , Cambridge 39, Mass. (1956).

8. J. W. Holl and G. F. Wislicenus, "Scale Effects on Cavitation",

ASME Journ. of Basic Eng., 83: 385 (1961).

26
9. M. C. Huppert, W. S. King, and L. B. Stripling, "Some Cavitation

Problems in Rocket Propellant Pumps", Rocketdyne Rept. , Rocketdyne, Canoga Park, Calif. Presented at ASME Confer,

Houston, Texas (1959).

10. V. Ya. Karelin, " Cavitation Phenomena in Centrifugal and Axial

Pumps", NASA accession no. N66-14532, (1963). Available from

Scientific and Technical Information Facility, P.O. Box 33,

College Park, Md. , (consists of 128 pages).

11. W. A. Spraker, "The Effects of Fluid Properties on Cavitation in

Centrifugal Pumps", ASME Journ. of Eng. for Power, 87: 309 (1965).

12. A. J. Stepanoff, "Cavitation Properties of Liquids", ASME Journ.

of. Eng. for Power, 86: 195 (1964).

13. W. W. Wilcox, P. R. Meng, and R. L. Davis, "Performance of

an Inducer-Impeller Combination at or Near Boiling Conditions for

Liquid Hydrogen", in: K. D. Timmerhaus (ed.), Advances in

Cryogenic Engineering, Vol. 8, Plenum Press, New York ( 1963),

p. 446.

14. A. Hollander, "Thermodynamic Aspects of Cavitation in Centrifugal

Pumps", ARS Journ., ^32: 1594(1962).

15. T. F. Gelder, R. S. Ruggeri, and R. D. Moore, "Cavitation

Similarity Considerations Based on Measured Pressure and

Temperature Depressions in Cavitated Regions of Freon 114",

NASA TN D-3509 (1966).

16. I. I. Pinkel, M. J. Hartmann* C. H. Hauser, M. J. Miller,

R. S. Ruggeri, and R. F. Soltis, "Pump Technology", NASA

accession no. N66-33672, (1966). Available from Scientific and

Technical Information Facility, P.O. Box 33, College Park, Md.

,

(consists of 20 pages).

27
17. R. S. Ruggeri and T. F. Gelder, " Cavitation and Effective Liquid

Tension of Nitrogen in a Hydrodynamic Cryogenic Tunnel", in:

K. D. Timmerhaus (ed. ), Advances in Cryogenic Engineering,

Vol. 9, Plenum Press, New York ( 1964), p. 304.

18. R. S. Ruggeri, private communication to the authors.

19. R. S. Ruggeri, R. D. Moore, and T. F. Gelder, "Incipient Cavitation of Ethylene Glycol in a Tunnel Venturi", NASA TN D-2772,

(1965).

20. R. S. Ruggeri and T. F. Gelder, "Effects of Air Content and Water

Purity on Liquid Tension at Incipient Cavitation in Venturi Flow",

NASA TN D-1459, (1963).

21. R. S. Ruggeri and T. F. Gelder, " Cavitation and Effective Liquid

Tension of Nitrogen in a Tunnel Venturi", NASA TN-2088 (1964).

22. T. F. Gelder, R. D. Moore, and R. S. Ruggeri, "Incipient Cavitation of Freon - 114 in a Tunnel Venturi", NASA TN D-2662 (1965).

23. Flow Measurement, Chap. 4, Part 5, ASME, 29 West 39th St.

,

New York 18, (1959), p. 17.

24. R. S. Ruggeri and R. D. Moore, "M*ethod for Prediction of Pump

Cavitation Performance in Various Liquids", to be published.

25. R. D. Moore and R. S. Ruggeri, "The Prediction of Thermodynamic

Effects of Developed Cavitation Based on Liquid Hydrogen and

Freon - 114 Data in Scaled Venturis", to be published.

^" GPO 848 -757
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