1、Designation: D6793 02 (Reapproved 2012)Standard Test Method forDetermination of Isothermal Secant and Tangent BulkModulus1This standard is issued under the fixed designation D6793; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, th
2、e year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers the determination of isothermalsecant and tangent bulk modulus of liquids which are
3、stableand compatible with stainless steel under the conditions of test.1.2 This test method is designed to be used over thetemperature range from -40 to 200C and from ambient to68.95 Mpa (10 000 psig).NOTE 1Because of the design of the test apparatus, the upper limit ofpressure which can be attained
4、 is limited by the bulk modulus of the testfluid. Pressures as high as 68.95 Mpa will not be attained for fluids ofrelatively low bulk modulus at the test temperature.1.3 This test method assumes that the user is proficient inthe assembly and use of medium pressure (m/p) threaded andconed fittings w
5、hich are intended for use at pressures up to137.9 Mpa (20 000 psig).1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the a
6、pplica-bility of regulatory limitations prior to use.NOTE 2Because hydraulic pressure in the test system is produced bypurely mechanical means, the test method is not subject to the hazardsassociated with systems which are pressurized pneumatically. Even smallleaks will result in immediate drop in p
7、ressure to ambient withoutproduction of a high pressure liquid stream or mist.2. Referenced Documents2.1 ASTM Standards:2D235 Specification for Mineral Spirits (Petroleum Spirits)(Hydrocarbon Dry Cleaning Solvent)D4057 Practice for Manual Sampling of Petroleum andPetroleum ProductsD4177 Practice for
8、 Automatic Sampling of Petroleum andPetroleum ProductsE300 Practice for Sampling Industrial Chemicals3. Terminology3.1 Definitions:3.1.1 isothermal secant bulk modulus, nthe product oforiginal fluid volume and the slope of the secant drawn fromthe origin to any specified point on the plot of pressur
9、e versusvolume change divided by volume at constant temperature.3.1.2 isothermal tangent bulk modulus, nthe product offluid volume at any specified pressure and the partial derivativeof fluid pressure with respect to volume at constant tempera-ture.4. Summary of Test Method4.1 Determination of Isoth
10、ermal Secant Bulk Modulus:4.1.1 A piston in the form of a medium pressure valve isforced into a chamber which is liquid-filled. The pressurecreated by the insertion of the piston is measured.4.2 A system constant V/DV is determined by use of astandard of known bulk modulus as follows:SVDVD5BiP5BiPn2
11、 Po!(1)where:Bi= isothermal secant bulk modulus,Po= pressure at the origin before insertion of the piston,andPn= pressure of the system at insertion of piston toPosition n.NOTE 3V/DV is thus a constant determined by system volume andpiston displacement only. It is independent of temperature and when
12、known, can be used to determine isothermal secant bulk modulus frompressure data obtained for various degrees of piston insertion.1This test method is under the jurisdiction of ASTM Committee D02 onPetroleum Products and Lubricants and is the direct responsibility of SubcommitteeD02.L0.07 on Enginee
13、ring Sciences of High Performance Fluids and Solids(Formally D02.1100).Current edition approved April 15, 2012. Published May 2012. Originallyapproved in 2002. Last previous edition approved in 2007 as D679302(2007).DOI: 10.1520/D6793-02R12.2For referenced ASTM standards, visit the ASTM website, www
14、.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.4.3 I
15、sothermal tangent bulk modulus and sample density, ifdesired, may be determined from isothermal secant bulkmodulus data determined as a function of pressure by use of thecalculations in Section 12.5. Significance and Use5.1 Isothermal secant bulk modulus (static bulk modulus) isa property that measu
16、res the compressibility of a liquid. Thegreater the value, the less the compressibility of the liquid.5.2 Isothermal secant bulk modulus is employed in thedesign of high performance hydraulic fluid and braking sys-tems. High bulk modulus is desirable in that the response timeof a system is faster wh
17、en applied pressure more directlyeffects the action of the system rather than in the compressionof the working liquid.5.3 If isothermal secant bulk modulus is known as afunction of pressure, the data may be used to calculateisothermal tangent bulk modulus and density as a function ofpressure. The da
18、ta may not, however, be used to determineisentropic (dynamic) bulk modulus. That property is usuallydetermined from velocity of sound measurements and differsfrom isothermal bulk modulus by the ratio of Cp/Cv= g (theratio of heat capacity at constant pressure to that at constantvolume for the test s
19、pecimen.6. Apparatus6.1 The apparatus for the determination of isothermal secantbulk modulus is shown schematically in Fig. 1. An ovencapable of maintaining temperature within 60.1C at thedesired test temperature is required.All fittings are of the conedand threaded m/p type for use at working press
20、ures up to 137.9Mpa (20 000 psig). Pressure is created in the system by use ofthe pressure valve (see 3 in Fig. 1) by which a piston (valvestem) is inserted into the liquid-filled system by turning1,2,3n turns as determined by a scale affixed to the valve stemto ensure repeatability of turns from th
21、e starting point. Pressuretransducers, thermocouples and system fixtures should be suchas to have minimal contribution to system volume so that thesystem volume is such as to allow a maximum pressureincrease for any given degree of insertion of the pressure valvestem.7. Reagents and Materials7.1 Cle
22、aning SolventMineral spirits conforming to Speci-fication D235, Type I.7.2 Other SolventsSome test specimens may not besoluble in mineral spirits. A suitable solvent for such materialswill be needed to clean the apparatus after their use. Thesolvent must be compatible with stainless steel and theela
23、stomeric components of the valves in the test apparatus.8. Sampling8.1 Obtain a representative sample of the test specimen inaccordance with the requirements of Practice D4057, D4177,or E300.9. Preparation of Apparatus9.1 Introduce a portion of mineral spirits into the samplecontainer (Fig. 1, Item
24、8).9.2 Open Valves 1 and 4 and slowly draw the mineral spiritsthrough the system by gentle application of vacuum.NOTE 4Always use a trap between the test apparatus and the vacuumsource to prevent introduction of the liquid solvent or the test specimeninto the vacuum system.9.3 Replace the sample con
25、tainer with an empty vessel andallow excess solvent to drain from the test system. Repeat9.1-9.3.9.4 Remove the vessel containing excess solvent and withValves 1 and 4 open allow the vacuum pump to draw airthrough the test system to evaporate the residual solvent. Startat ambient temperature and rai
26、se the oven temperature to100C while drawing air through the system.1 = Top valve2=ATee3 = Pressure valve4 = Bottom valve5 = Thermocouple6 = Pressure transducer7 = Oven8 = Sample containerNOTEAll fittings are m/p coned and threaded type for use at workingpressure up to 20 000 psig.FIG. 1 Apparatus f
27、or Determination of Secant Bulk ModulusD6793 02 (2012)29.5 When the oven temperature reaches 100C, close Valve4 and allow the vacuum pump to release the pressure in the testsystem to complete removal of solvent residues by evapora-tion.10. Calibration10.1 With the cleaned system at ambient temperatu
28、re intro-duce the calibrating fluid (usually water) into container 8.10.2 Open Valves 1 and 4 and draw sufficient fluid into thetest cell to ensure that it is liquid-filled. Close Valve 4.10.3 Adjust the oven to the preselected test temperaturewith Valve 1 still open and Pressure Valve 3 set at the
29、0 turn orfull open position.10.4 Apply vacuum to the system to remove any residual airbubbles. Close Valve 1 and record the system pressure withpressure transducer 6.10.5 Turn Pressure Valve 1 full turn and record the pressure.Repeat for turns 2 through n (usually n = 7) and record thesystem pressur
30、e after each full turn.10.6 Calculate V/DV for each pressure valve position asdescribed in 4.2, Eq 1. An example is shown in Appendix X1.10.7 Drain the calibration fluid from the test cell. If waterwas used for calibration, remove all residual traces as de-scribed in 9.4 and 9.5. If an organic stand
31、ard was used, cleanthe cell in accordance with 9.1-9.5.11. Procedure11.1 Introduce the test specimen into the test cell as de-scribed in 10.1-10.4. Record the pressure reading at turn 0 ofPressure Valve 3.11.2 Turn Pressure Valve 1 a full turn and record thepressure. Repeat for turns 2 through n (us
32、ually n = 7) andrecord the system pressure after each full turn.11.3 Calculate the isothermal secant bulk modulus of thetest specimen as described in Section 12. An example is shownin Appendix X2.12. Calculations12.1 Isothermal Secant Bulk ModulusCalculate accordingto the following equation:Bi5VDVPn
33、2 Po! (2)where:Bi= isothermal secant bulk modulus, psi,VDV= ratio of volume to volume change as determinedby Eq 1,Pn= pressure of the system at insertion of Position n,psi, andPo= pressure at origin, psi.12.2 Isothermal Tangent Bulk ModulusCalculate accord-ing to the following equation:Bi5BiBi2 P!Bi
34、o(3)where:Bi= isothermal tangent bulk modulus, psi, andBio = isothermal secant bulk modulus at 0 psig as deter-mined by linear extrapolation, psi.12.3 Density from Secant Bulk ModulusCalculate accord-ing to the following equation:d 5do1 2 P/Bi(4)where:do= density at 0 Pa (ambient), kg/m3, andd = den
35、sity at P, kg/m3.13. Report13.1 Report the isothermal secant bulk modulus at the testtemperature and whatever pressure is desired within range ofpressures observed in 11.2 and 11.3. Since isothermal secantbulk modulus is a linear function of pressure with the rangefrom ambient to 68.95 Mpa (10 000 p
36、sig) extrapolation may beemployed to obtain values at pressures above and below thosewhich can be obtained directly (depending upon the actualisothermal secant bulk modulus of the test specimen).13.2 If determination of isothermal tangent bulk modulus isrequired, convert the isothermal secant bulk m
37、odulus dataobtained as above as described in 12.2.13.3 If determination of density as a function of pressure isrequired, calculate density at non-ambient pressures providedthe density of the test specimen at ambient pressure is knownfrom the isothermal secant bulk modulus as described in 12.3.14. Pr
38、ecision and Bias14.1 Because of the complex nature of the procedure for thedetermination of isothermal secant and tangent bulk modulus,and because of the expensive equipment required in the initialset-up of the procedure, there is not a sufficient number ofvolunteers to permit a cooperative laborato
39、ry program fordetermination of the precision and bias of this test method. Ifthe necessary volunteers can be obtained, a program will beundertaken at a later date.15. Keywords15.1 density; dynamic bulk modulus; isentropic bulk modu-lus; isothermal bulk modulus; isothermal secant bulk modulus;isother
40、mal tangent bulk modulus; pressure; static bulk modulusD6793 02 (2012)3APPENDIXES(Nonmandatory Information)X1. ISOTHERMAL BULK MODULUS CALIBRATIONX1.1 Calibration FluidWater.X1.2 Calibration Temperature40C.X1.3 Data from International Critical Tables:3Pressure, psig Bulk Modulus7349 354 29914 697 38
41、2 654X1.4 CalibrationSee Table X1.1.X2. DETERMINATION OF ISOTHERMAL SECANT BULK MODULUSX2.1 Once the volume constant, (V/DV), has been deter-mined for the test system, the data may be used with dataobtained with the test specimen to determine its isothermalsecant bulk modulus as follows:Bi5 Pn2 Po!
42、V/DV! (X2.1)X2.2 Test SpecimenUnknown hydraulic fluid.X2.3 Test Temperature40C.X2.4 Calibration FluidWater at 40C.X2.5 CalibrationSee Table X2.1.3International Critical Tables, Vol 3, McGraw Hill Co. Inc., New York, NY.TABLE X1.1 Calibration for Isothermal Bulk ModulusNOTE 1Because the volume consta
43、nt is a unit-less quantity consistingof a volume divided by a volume difference, it is independent oftemperature.TurnNo.(1) (2) (3) (4)P, psi PnPoBs, psi V/DV0361 1318 1282 330 888 258.103002 2681 2654 336 147 127.087703 4084 4048 341 561 84.377724 5531 5495 347 145 63.174705 7022 6986 352 899 50.51
44、5176 8549 8513 358 791 42.146257 10 129 10 093 364 888 36.15258(1) Pressure readings at the 0 and nthturn of the valve.(2) Pressure difference between the nthturn and the 0 turn.(3) Secant bulk modulus of the calibration fluid at the observed pressure asobtained by linear interpolation and/or extrap
45、olation.(4) Volume constant of the system equal to:SVDVD5BiPn2 Po!TABLE X2.1 Calibration for Isothermal Secant Bulk ModulusTurnNo.(1) (2) (3) (4)P, psi PnPoV/DVBi, psi0361 825 789 258.10300 203 6442 1661 1625 127.08770 206 5183 2545 2509 84.37772 211 7044 3473 3437 63.17470 217 1325 4448 4412 50.515
46、17 222 8736 5470 5434 42.14625 229 0237 6539 6503 36.15258 235 101(1) Pressure readings at the 0 and nthturn of the valve.(2) Pn Po= pressure difference between the nthturn and the 0 turn.(3) Volume constant as determined by calibration with a fluid of knownisothermal secant bulk modulus.(4) Isother
47、mal secant bulk modulus as determined from Eq X2.1.D6793 02 (2012)4ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any
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