r AD-7eO 776

IhL COMHUIATIOtl OF THE BULK HÜDULl OF A

SYfiMTIC HYDROCARBON HYDRAULIC FLUID

AIR FORCE KATLRIALS LABORATORY

APRIL 1^75

Distributed By:

Natioiial Tickiicai liftnHtiM Sirvici U. S. DEPARTMENT OF COMMERCE

i

AFMl-TR-73-81

THE COMPUTATION OF THE BULK MODULI OF A SYNTHETIC HYDROCARBON HYDRAULIC FLUID

CO

o <

h C BROOKS 1 :; , . 7 1375

JUUv-

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APRIL 1973

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Air Fore* Materials Laboratory Wright-Patterson Air Fore* Baa«, Ohio 45433

|l* «C»0"' »t Co« '• C t.**>IF<C*'IO*

UMCUSSIFIED Ik ••Ou»

I mtPomi TiTLt

The Computation of ehe Bulk Moduli of a Synthetic Hydrocarbon Hydraulic Fluid

( OltCOI^Tlvt MO*CI (Trprn al mm"

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AIR FORCE MATERIALS LABORATORY (MIT) AIR FORCE SYSTEMS COHMAKD JWRIGHT-FATTERSOH AIR FORCE BASE, OHIO

II «atTMACI

The bulk noduli of a aynthetic hydrocarbon are calculated and appropriate equations are preaented. Methods of datemlnlnt and predicting bulk aodull are reviewed. A conservative low value of isothermal secant bulk modulus of the aynthetic hydrocarbon candidate was selected from determinations produced with the .aaua apparatus. This selected value served aa the primary datum point for calculating Isothermal aecant and tangent bulk moduli and adiabatlc eecant and tangent bulk moduli.

The results of thsee calculations are preaented in tabular and graphical form for temperatures of 100, 200. 275, 300, 400 nd 500 F and pressures between 0 and 5000 pslg.

DD '^ 1473 UNCLASSIFIFD Security Classifirabon

UNCUS SIFTED Secur:t Classtfication

•• l<I:Y WOI'OS

SYNTHETIC HYDROCARBON

BULK MODULUS

ADIABATIC

ISOTHERMAL

TANGENT

SECANT

INSTilUCTIONS

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UIICLA!»SIFIED Security Cluaific:atlon

THE COMPUTATION OF THE BULK MODULI OF A SYNTHETIC HYDROCARBON HYDRAULIC FLUID

F C BROOKS

Approved (or public release; distribution unlimited.

Ih

*m

FOREWORD

This report was prepared by the Lubricants and iribology Branch of

the Nonmetallic Materials Division, Air "^orce Materials Laboratory. Air

Force Systems Coraraard. Wright-Patterson Air Foice Base, Ohio. This -»ffort

was conducted under Project No. 7340, "Nonmetallic and Composite Materials."

Task No. 7 54008, "Energy Transfer Fluids," with F. C. Brooks acting as

Project Engineer.

This report presents the purpose and results of an effort expended

between November 1972 and January 1973.

This technical report has been reviewed and is approved.

a*«*' (&CKeJ' KENNETH A. DAVIS, MAJOR, USAF Chief Lubricants and Tribology Branch Air Force Materials Laboratory

ii

iMMiAHMMM

ABSTRACT

The bulk moduli of a synthetic hydroca-'^on are calculated and appro-

priate equations are presented. Methods of determinirg and predicting

bulk moduli are reviewed. A conservative low value of isothermal secant

bulk modulus of the synthetic hydrocarbon candidate was selected from

determinations produced with the Klaus apparatus. This selected value

served as the primary datum point for calcolating isothermal secant and

tangent bulk moduli and adiabatic secant and tangent bulk moduli.

The results of these calculations are presented in tabular and graph-

ical form for temperatures of 100, 200, 275, !00, 400 and 500 F and pres-

sures between Ü and 5000 psig.

in

I^M*

I

CONTENTS

ction Page

I Introduction 1

II Isothermal Secant Bulk Modulus of Mil-H-83282

5

III Isothermal Tangent etc 9

IV Adiabatic Tangent etc. 12

V Adiabatic Secant etc. 15

VI Reference 20

IV

ILLUSTRATIONS

FIGURE PAGE

1 A COMPARISON OF BULK MODULUS RESULTS FROM THREE INVESTIGATORS 4

2 THE ISOTHERMAL SECANT BULK MODULUS OF MIL-H-83282 8

3 THE ISOTHERMAL TANGENT BULK MODULUS OF MIL-H-83282 II

4 THE ADIABATIC TANGENT BULK MODULUS OF MIL-H-83282 14

5 THt ADIABATIC SECANT BULK MODULUS OF MIL-H-83282 17

6 BETA AS A FUNCTION OF PRESSURE 18

7 GAMMA AS A FUNCTION OF TEMPERATURE FOR MIL-H-5606A 19

HYDRAULIC FLUID

TABLES

TABLF

I

II

III

IV

V

THE BULK MODULUS OF MIL-H-5606A HYDRAULIC FLUID

ISOTHERMAL SECANT BULK MODULUS OF MIL-H-83282

ISOTHERMAL TANGENT BULK MODULUS OF MIL-H-83282

ADIABATIC TANGENT BULK MODULUS OF MIL-H-83282

ADIABATIC SBCANI BULK MODULUS OF MIL-H-83282

Page

3

7

10

13

16

VI

mm

Wljmmmm—m^^m

SECTION I

INTRODUCTION

Bulk modulus is one of the important engineering properties of a hydra-

ulic fluid. Therefore it is advantageous that accurate, reliable bulk

modulus values be distributed. It is the purpose of this effort to provide

reliable values, of isothermal and adiabatic secant and isotherma. and

adiabatic tangent bulk moduli of MIL-H-83282 hydraulic fluid for engineering

ant research applications.

Bulk modulus is the volumetric modulus of elasticity of a liquid, or

simply, a measure of a liquid s spring rate. It is, therefore, the recip-

rocal of liquid compressibility.

Hydraulic fluid bulk moduli are used in hydraulic system and component

design calculations to determine such factors as static and dynamic stiffness,

resonant frequencies and pump characteristics. The kind of bulk modulus

values which are used depends upon the factors which are being studied.

There are two common methods of determining bulk modulus. One is the

pressure-volume-temperature (P-V-T) method which measures the isothermal

secant bulk modulus of the test liquid. Klaus and associates (references

1, 2) have reported on the development of a direct reading apparatus which

utilizes calibrated pycnometers housed in a high pressure glass windowed

cell. Liquid densities aay be determined to ^ 0.2 percent of a pressure

range of 0 to 10,000 psig. These measurements result in a precision of

+0.5 percent when translated to bulk modulus.

The second common method of determining bulk modulus is the sonic method,

which measures the velocity of sound in the liquid and determines the adia-

batic tangent bulk modulus. Peeler and Green (Reference 3) , and Noonan

(Reference 4) have studied several hydraulic fluids using the sonic method

of bulk modulus dgtermination.

1

Wright (Reference 5) made a comprehensive study of bulk modulus deter-

minations and proposed a method of predicting the bulk modulus of petroleum

oils from their density. Wright notes that the bulk modulus determinations

made by Klaus are in agreement with his findings.

The results of bulk modulus determinations of MIL-H-5606A hydraulic

fluid, conducted by three investigators, are shown in Table I. The iso-

the.-mal secant data, reported by investigator B, cannot be directly com-

pared to the adiabatic tangent data reported by investigators A and C. By

calculating ^iabatic tangent bulk modulus from the isothermal secant

values, the results of the three investigators, as shown in Figure 1, became

comparahTe. The results of investigators A and B are in excellent agree-

ment over the pressure range of 2000 to 5000 p -g. The results reported by

investigator C are approximately 21,000 psi less than investigator B's

results, over the entire pressure range.

Klaus, Fteference 6, presented a method for predicting the isothermal

secant and isothermal tangent bulk moduli of several hydraulic fluid species.

Over the 0 to 10,000 psig pressure range, the predicted values agree with

experimental bulk modulus determinations within + 2.'0 percent. Predicted

values of isothermal secant bulk modulus were related to ASME "Pressure-

Viscosity Report" density results with an accuracy of +_ 4.0 percent over a

temperature range of 32 to 425 F and a pressure range of 0 to 150,000 psig.

The bulk moduli values computed during this program were obtained by

reviewing the isothermal secant bulk modulus of four different samples of

MIL-H-83282, which were measured with the Klaus apparatus, and selecting a

conservative value as a starting point. From this starting point, isother-

mal secant and isothermal tangent bulk moduli values were calculated using

the Klaus equations. These values wert then used to calculate adiabatic

tangent and secant bulk moduli values.

TABLE I

THE BULK MODULUS OF MIL-H-5606A HYDRAULIC FLUID

Temperature: 100 F

Investigator A Investigator B | Investigator C j Pressure Adiabatic Tangent Isothermal Secant Adiabatic Tangent

psiq psi psi psi

1,000 235,000 191,000 220,300

2,000 254,000 196,600 233,800

1 3,000 268,000 202,000 245,400

4,000 279,000 207,500 258,400

5,000 291,000 i 213,000 270,200

10,000 240,500 i

A COMPARISON OF BULK MODULUS

DETERMINATIONS BY THREE INVESTIGATORS

FLUID: MIL-H-5606A TEMPERATURE: 100 F

300

i o

Q Ö

§

250

200

PRESS^P, PS IG x 10 -3

FIGURE 1

SECTION II

ISOTHERMAL SECANT BULK MODULUS OF MIL-H-83282

The isothermal secant bulk modulus of qualification samples of MIL-H-

83282, as determined in the Klaus apparatus, were compared and a conserva-

tive low value was selected for the starting point of this effort. The

value selected was 202.500 psi at 100 F and 2000 psig.

Using this datura point and equation (1), the isothermal secant bulk

modulus at 100 F and 0 psig was calculated.

|^B = Bo + 5.30 PJ i (1)

where:

B = isothermal secant bulk modulus at pressure P

and temperature T, expressed in pounds/square inch.

B0 B isothermal secant bulk modulus at 0 psig and

temperature T, expressed in pounds/square inch.

F = pressure, in psig.

Using this calculated value B0 ad BT, at 0 psig and equation (2),

values B0 were calculated for temperatures of 200, 275, 300, 400 and 500 F.

1r. log

3 (T2 - T1) (2)

—j p

where:

B_ = isothermal secant bulk modulus at pressuie P and 1

temperature T^, ''F, and

BT = isothermal secant bulk modulus at pressure P and 2

temperature T0, F.

Values of (3 , a generalized relationship of the slope as a function of

pressure, are presented in Figure 6.

Using the calculated values of B0, at temperatures of 100, 200, 275,

I

300, 400 and 500 F, and equation (1), a complete set of values of B were

calculated for pressures of 1000, 2000, 3000, 4000, 5000, 6000, 8000, and

10,000 psig. The results of these calculations are shown in Table II, and,

for easy access of intermediate pressure values, is presented graphically

to 5000 psig in Figure 2.

*—mt

00 (M

00

X I

OQ

o o o o o o o o o lr. o o o o o o 0 o c

a (N m oo r-< ■t N CO o ! O

o M 00 en 00 t a ^r in in 1 in m in vO o N N 00 a o

r-l |

o o o o o o o o o 1 i ^ o s o o o o o O o !

o vO a 0» in 00 t '0 1 o n oo m oo t <?> Tt in ■c

1 ^ i^ r- ao oo a> a o rH

I-I

r-l

o o o o o o o O c i

o o o

o s s o o s O rH

O 1

o o r-l m H t^ (N CO w o o rH r-l CM CJ CO 'd1 in l-l rH H r-l r-l i-i r-l iH 1-1 !

o o O O O O o O o 1 lb o o O O o o 2 o o

00 iH t t^ o ri CNJ oo

N m oo CO o» 3 a o 9 VI o i-( rH (M (N co m <o

iH H r-l r-l r-l i-i r-l i-i iH !

o O o o o o o o lb o o o Q o o Ü o 2 0 o

o ro o o w m oo ■<t

a •<* o> ■« 8 m o r-l N 1 M C1 Tf ■* m «o N 00 0»

H r-l r-l r-t r-l H 1-1 1-1 H

U. o o o o O O o o o o o s o o O o o 2 o N oo rH ■<* t^ CO a 1 1-1 N CM h< M co CO •* "* Ov a o 8 H rH <M CO ' H r-l CM (N rg (M M N

1 31 M 0> o 8 o o o 8 O o o 3'H o o o 8 o o vi in o o o Ü o o o o (X •> * • •> •• " 1

1 01 iH M CO ■>* in <o ao o ^ I-I 1

Bu

•H in

I/I tfl (U

VI 01 J

rH «

in 3 i-l 3 •o 0 B

3

ISOTHERMAL SECANT BULK MODULUS OF MIL-H-83282

300

i o

IT D-

tf)

Q

i

250

200

150

100

50

P%ASSURE, PSIG x 10"

FIGURE 2 8

mm

SECTION III

THE ISOTHERMAL TANGENT BULK MODULUS OF MIL-H-83282

The isothermal tangent bulk modulus of MIL-H-83282 was calculated for

temperatures of 100, 200, 275, 300, 400 and 500 F at pressures of 1000,

2000, 3000, 4000 and 5000 psig using the previously calculated values of

B and equation (3).

(BR)p = 8^ (3)

where:

(BR)p = isothermal tangent bulk modulus at tempera-

ture T and pressure P, and

Bp- = isothermal secant bulk modulus at temperature

T and twice pressure P.

The results of these calculations are shown in Table III and are pre-

sented graphically in Figure 3.

00

CO oo

X I

tu

O o o o o o u. O o o o Ü o

O in r-l r- n ON

o o (N ro t t m m m in X> N oo a O

o o o o o o (b o 0 o o o o

o v.0 M 00 t o o o

m,

-o ro ■t TT in NO

I1 I-- oo ON o r-l r-l r-l

o O o o O o u. o s o o O o

N a m iH N o o o t-l rH w cn m en o H N ro T» m

i-H H r-l rH i-j iH

o O O o O u. o o Q O o o

oo ■t Q o M oo IT) » »V m r- *■ f»

f-. t^ 00 ON O o o N o 1-1 O) n m NO

H iH 1-1 r-l iH r-l

o o o O o O (I. o o o O o o

o o

o ■c f\) oo ■<* o

a a o o iH CN)

N m -«t >o ^ OO ON H H iH iH i-H 1-1

o o o o o o fb o o o o o O

ON m iH N en ON

o o H N m n 3 ■«*

H Ov o rH (N T*

H (M (N N CV) CNJ

a M 0 3 -H O O o Q o o (A 1/1 O o Q O o (fl 0

N

O o o o o i-( CV) ro ^t m

0.

•rl ID a

'S w m 41 u

e- (H

v. 01 3 H n > in 3 r-l 3 •0 0 e

3

10

ISOTHERfliU. TANGENT BULK MODULUS OF MIL-H-83282

JOO

n i o

a.

i

250

200

150

100

1 2 3

PRESSURE, PSIG x 10"3

FIGURE 3 11

SECTION IV

THE ADIAB.ATIC TANGENT BULK MODULUS OF MIL-H-83282

The relationship between adiabatic and isothermal tangent bulk modulus

may be expressed by equation (4).

fs= Y =fp BR Cy

(4)

where:

and pressure P,

and pressure P,

Bg = adiabatic tangent bulk modulus at temperature T

BR = isothermal tangent bulk modulus at temperature T

Cp = specific heat at constant pressure,

Cv = specific heat at constant volume,

Y = ratio of specific heats or bulk moduli.

The adiabatic tangent bulk modulus of MIL-H-83282 was calculated by

using the previously calculated values of isothermal tangent bulk modulus

and equation (4). Values of Y, which are presented in Figure 4, were deter-

mined for hydraulic fluid MIL-H-5606A. However, these data are considered

applicable to calculations for typical mineral oil base fluids (references

3 and 6).

The results of these calculations are shown in Table IV and are pre-

sented graphically in Figure 4.

12

MMa rfk

CQ

o c o o o o u. o o o c c o

i Q

>0 0> n >o o 1^ 1

■o s o- c <M r^ 1 m m 'O r- a c rH 1

rH j

o o o o o u. o o c o o o o 00 ^0 fl f-H a o * ► i

•^ f-l rg t ■a » a> Tt oo a- c —I O) n

f-H f-* ^H rH 1

;

o o o o o o U. o c o o Ü o

o CO o n t «o ao in 00 o (M t vO

fO r-t rj <* in >o t^ i—i FH f-i i-i r-( rH 1

o O o o o 0 u. o s o o o Q o o a M in in ^ fc » * I t^ in t~- a rH ^t vC (M

PH r-4 r-( rH CO rH 1

o o o O o o 1 ^ o o 2 O o o

^r o m a m o *■ » • • '' 1 o m GO c m m 00 1

1 M «0 r^ a O rH N 1 »-» r-* r-l N <N (N

u. o 8 8 o o O

o s s r- 1-1 <N C) (N 1

o •> » • » 1

o <c a (N m ao ^H 1 r-t c^ •<» 'O h- ou Q 1

<N (\ (M CJ (N en 1

Oi v^CJ o c g C c 3-H rt o c o 1 m i/i O o Q o 1 '/i a ■> - • * 1 « r-t rj m f if\ [ u a.

in

in in 0)

IT i> 3

rH I« >

3 rH 3

3

i

13

vwpi

ADIABATIC TANGENT BULK MODULUS OF MIL-H-83282

300

n i o

in

I

250

200

150

100

1 2 T

PRESSURE, PSIG x 10"3

FIGURE 4

14

SECTION V

ADIABATIC SECANT BLLK MODULUS OF MIL-H-83282

The adiabatic secant bulk modulus of MIL-H-83282 was calculated by

using the previously calculated adiabatic tangent bulk modulus values and

equation (5).

BB - BR + BR (5)

where:

and pressure P,

B = adiabatic secant bulk modulus at temperature T

Bp = adiabatic tangent bulk modulus at temperature T o

anH 0 psig, and

B = adiabatic tangent bulk modulus at temperature T

and pressure P.

The results of these calculations are shown in Table V and are pre-

sented graphically in Figure 5.

15

tM jtm

>

<

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16

ADIABATIC SECANT BULK MODULUS OF MIL-H-83282

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19

SECTION VI

REFERENCES

2.

3.

1. Klaus, E.E., Fenske, M,R., and Tewksbury, E.J., "Fluids, Lubricants,

Fuels, and Related Materials," WADD TR 60-898, Parts TI and III,

1962 and 1963.

O'Brien, J.A., M.S. Thesis, "Precision Measurement of Liquid Bulk

Modulus," The Pennsylvania State University, 1962.

Peeler, R.L., and Green, J., "Measurement of Bulk Modulus of Hydraulic

Fluids," American Society of Testing Materials, Bulletin 235, p. 51,

January 1959.

4. Noonan, J. , "The Ultrasonic Determination of the Bulk Modulus of Hydrau-

lic Fluids at Elevated Temperatures and Pressures," National Research

Council of Canada, Report NX: No. 8455, March 1, 1965.

5. Wright, W.A., "Prediction of Bulk Moduli and Pressure-Volume-Temperature

Data for Petroleum Oils," Transactions, American Society of Lubri-

cation Engineers, Vol 10, p. 349, 1967.

6. Klaus, E. E. , and O'Brien, J.A. , "Precise Measurement and Prediction of

Bulk Modulus Values of Fluids and Lubricants," presented at the

American Society of Mechanical Engineers Lubrication Symposium,

Boston, Mass., June, 1963.

20