H.N. Abramson - The dynamic behavior of liquids in moving containers. With applications to space vehicle technology (798543), страница 28
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4.43).01II10-lo-'Flexibility. FI(10- '1- p c ) P wE T''-I1DAMPING OF LIQUID MOTIONS AND LATERAL SLOSHING141REFERENCES4.1. MILES, J. W.: Note on the Damping of FreeSurface Oscillations Due to Drainage. Rept.No. TDR-930 (2270-20) TN-1, AerospaceCorp., El Segundo, Calif., Sept. 1961.4.2. MILES, J. W.: Ring Damping of Free SurfaceOscillations in a Circular Tank. J. Appl.Mech., vol. 25, no.
2, June 1958, pp. 274-276.4.3. MILES, J. W.: On the Sloshing of Liquid in aCylindrical Tank. Rept. No. AM6-5, GalTR-18, The Ramo-Wooldridge Corp., GuidedMissile Research Div., Apr. 1956.W. C.: Damping4.4. CASE,K. M.;AND P.~RxINSON,of Surface Waves in an Incompressible Liquid.J. Fluid Mech., vol.
2, part 2, Mar. 1957,pp. 172-184.4.5. NELSON,ROBERTH., JR.: The Sloshing of aFluid Draining From a Flexible Tank. Ph. D.thesis, MIT, 1960.4.6. O'NEILL,J. P.: Final Report on an ExperimentalInvestigation of Sloshing. STL/TR-59-000009960, Space Tech. Labs., Inc. Available fromDDC, AD-238107, Mar. 1960.4.7.
SCANLAN,ROBERTH.; AND ROSENBAUM,ROBERT:Introduction to the Study of Aircraft Vibrationand Flutter. Macmillan Co., 1960, pp. 72-88.4.8. GACZY,H.: Measurement of Inertia and Structural Damping. Ch. 3 in Manual on Aeroelasticity, vol. IV. North Atlantic TreatyOrganization, Advisory Group for AeronauticalResearch and Develapment .4.9. BISHOP, R. E. D.; AND GLADWELL,G. M. L.:An Investigation Into the Theory of ResonanceTesting. Phil. Trans.
Roy. Soc. London,Ser. A, vol. 255, no. 1055, Jan. 17, 1963, pp.241-280.4.10. GLADWELL,G. M. L.: A Refined Estimate of theDamping Coefficient. J. Roy. Aeron. Soc.,vol. 66, Feb. 1962, p. 125.A N D GARZA,LUIS R.:4.11. ABRAMSON,H. NORMAN;Some Measurements of the Effects of RingBaffles in Cylindrical Tanks. J. SpacecraftRockets, vol. 1, no. 5, Sept.-Oct. 1964, pp.560-562.4.12. STEPHENS,DAVIDG.; LEONARD,H. WAYNE;A N DS ~ c u r ~ n *MILTON,A.: An Experimental Investigation of the Damping of Liquid Oscillations in an Oblate Spheroidal Tank With andWithout Baffles.
NASA T N D-808, 1961.4.13. STEPHENS,DAVIDG.; LEONARD,H. W ~ Y N EAND;PERRY,TOMW.: Investigation of the Dampingof Liquids in Right-Circular Cylindrical Tanks,Including the Effects of a Time-Variant LiquidDepth. NASA T N D-1367, 1962.4.14. SUMNER,IRVINGE.; AND STOFAN,ANDREWJ.:An Experimental Investigation of ViscousDamping of Liquid Sloshing in SphericalTanks. NASA T N D-1991, 1963.4.15. MIKISHEV,G. N.; A N D DOROZHKIN,N.
YA.: AnExperimental Investigation of Free Oscillationsof a Liquid in Containers (in Russian). Izv.Akad, Nauk SSSR, Otd. Tekh. Nauk, Mekh. iMashinostr, no. 4, July/Aug. 1961, pp. 48-83.Transl. into English by D. Kana, SouthwestResearch Institute, June 30, 1963.4.16.
STOFAN,ANDREWJ.; A N D PAVLI, ALBERTJ.:Experimental Damping of Liquid Oscillationsin a Spherical Tank by Positive-ExpulsionBags and Diaphragms. NASA T N D-1311,1962.4.17. STOFAN,ANDREWJ.; A N D SUMNER,IRVINGE.:Experimental Investigation of the SloshDamping Effectiveness of Positive-ExpulsionBags and Diaphragms in Spherical Tanks.NASA T N D-1712, 1963.4.18. EULITZ,WERNER:A Can-Type Device DerivedFrom Basic Slosh Studies. Rept.
No. DSDTR-4-58, Dev. Operations Div., ABhlA, Redstone Arsenal, Ala., Aug. 1958. Availablefrom DDC, AD-203348.4.19. ABRAYSON,H. NORMAN;A N D RANSLEBEN,GUIDOE., JR.: Simulation of Fuel SloshingCharacteristics in Missile Tanks by Use ofSmall Models. ARS J., vol. 30, no. 7, July1960, pp. 603-612.4.20. ABRAMSON,H. NORMAN;A N D RANSLEBEN,GUIDOE., JR.:Some Studies of a Floating LidType Device for Suppression of Liauid Sloshingin Rigid Cylindrical Tanks. T R No. 10,Contract DA-23-072-ORD-1251,SouthwestResearch Institute, May 1961.4.21. ABRAMSON,H.
NORMAN;A N D RANSLEBEN,GUIDOE., JR.: Liquid Sloshing in Rigid Cylindrical Tanks Undergoing Pitching ?*lotion.T R No. 11, Contract DA-23-072-ORD-1251,Southwest Research Institute, May 1961.4.22. BAUER,HELMVTF.: Fluid Oscillations in theContainers of a Space Vehicle and Their Influence Upon stability. NASA T R R-187,1964.4.23. COLE, HENRYA.; A N D GAMBUCCI,BRUNOJ.:Measured Two-Dimensional Uamplng EEectiveness of Fuel Sloshing Baffles Applied toRing Baffles in Cylindrical Tanks. NASAT N D-694, 1961.4.24. HOWELL,E.; A N D EHLER,F. G.: Experimental Investigation of the Influence of MechanicalBaffles on the Fundamental Sloshing Mode ofWater in a Cylindrical Tank. Rept.
No.142THE DYNAMIC BEHAVIOR OF LIQUIDSGhI-TR-69, Space Tech. Labs., Inc., July 6,1956.LINDHOLM,ULRICS.; KANA,DANIELD.; CHU,WEN-HWA; .4ND ABRAMSOH,H. NORMAN:Research in Liquid Dynamics in Missile FuelTanks. Quarterly Prog. Rept. No. 7, ContractNo. NASw-2, Southnrest Research Institute,Jan.
1, 1962.STOFAN,ANDREWJ.; A N D ARMSTEAD,ALFREDL.:Analytical and Experimental Investigation ofForces and Frequencies Resulting From LiquidSloshing in a Spherical Tank. NASA T N D1281, 1962.SUMNER,IRVINGE.: Preliminary ExperimentalInvestigation of Frequencies and Forces Resulting From Liquid Sloshing in ToroidalTanks. NASA T N D-1709, 1963.~ ~ I L T O A.;X STEPHENS,DAVIDG.; A N DSILVEIRA,LEONARD,H. WAYNE:Damping of LiquidOscillations in Cylindrical Tanks With I'ariousBaffles. NASA TN D-715, 1961.ABRAMSON,H.
NORMAN;CHU, WEN-HWA;A N D GARZA,LUIS R.: Liquid Sloshing inSphcrical Tanks. AIAA J., vol. 1, no. 2, Fcb.1963, pp. 364-389.ABRAMSON,H. NORMAN;C;ARZA, LUIS It.;A N D KANA,DANIELD.: Liquid Sloshing inCompartmented Cylindrical Tanks. ARS J.,vol. 32, no. 6, June 1962, pp. 978-980.ABRAMSON,H. NORMAN;CHU, WEN-HWA;ANIJ GARZA,LUIS R.: Liquid Sloshing in 45"Sector Compartrncnted Cylindrical Tanks.T R No.
3, Contract NAS8-1555, SouthwestRcsearch Institute, Nov. 1, 1962.ABRAMSON,11. N.; .4ND GARZA,L. R.: Some,\lcasurements of Liquid Frequencies andDamping in Compartmented Cylindrical Tanks.-41AA J. Spacecraft Rockets, vol. 2, no. 3,May-June 1965, pp. 453-455.GARZA,LUIS R.: hleasuremcnts of Liquid Naturn1 Frcquencies and Damping in Compartmented Cylindrical Tanks.
T R No. 8, Con-tract NAS8-1555, Southwest Research Institute,Feb. 1964.COLE, HENRYA.; AND GAMBUCCI,BRUNOJ.:Tests of an Asymmetrical Baffle for FuelSloshing Suppression. NASA T N D-1036,1961.GARZA,LUIS R.: A Brief Comparison of Ringand Asymmetrical Baffle Characteristics.NASA CR-51373, 1963.KEULEGAN,G. H.; A N D CARPENTER,L. H.:Forces on Cylinders and Plates in an Oscillating Fluid.
National Bureau of StandardsReport 4821, Washington, D.C., Sept. 5, 1956.BAUER, HELMUT F.: The Damping FactorProvided by Flat Annular Ring Baffles for FreeFluid Surface Oscillations. MTP-AERO-6281, NASA-MSFC, 1962.ABRAMSON,H. NORMAN;A N D GARZA,LUIS R.:Some Measurements of the Effects of RingBaffles in Cylindrical Tanks.
AIAA J. Spacecraft Rockets, vol. 1, no. 5, Sept.-Oct. 1964,pp. 560-562.ARMSTRONG,G. L.; A N D KACHIGAN,K.: Stability and Control. Ch. 14, in Handbook ofAstronautical Engineering (H. H. Koellc,editor-in-chief), McGraw-Hill, 1961, pp. 1425-14-27.LIU, F. C.: Pressure on Baffle Rings Due to FuelSloshing in a Cylindrical Tank. R-AER0-464, NASA-PIISFC, Jnn. 17, 1964.G ARZA, L. R.
: Theoretical and Experimc~ltalPressures and Forces on a Ring Bnfflc UndcrSloshing Conditions. AIAA J., SpacecraftRockets, vol. 3, no. 2, Feb. 1966, pp. 276-278.SUMNER,IRVISGE.: Expcrimcntnl Investigationof Slosh-Suppressioll Effectiveness of AnnularRing Baffles in Spherical Tanks. NASA T N1)-2519, 1964.STEPHENS,DAVIDG.: Flexible Baffles for SloshDamping. AIAA J., Spacecraft Rockets, vol.3, no. 5, Xlay 1966, pp. 765-7636.DAMPING OF LIQUID MOTIONS AND LATERAL SLOSHING143PRINCIPAL NOTATIONSa, b=tank dimensions for an oblate spheroidao=inside radius of the baffled =tank diameterdh= diameter of perforations of perforatedbaffletl,= baffle depth below the free surfaceE=energy of motion, modulus of elasticityin tension and compressionF= forceg=gravitational accelerationh=liquid depthln=natural logarithmM= momentny =axial acceleration of the tankp=pressure on the baffleR= tank radiusro=radius of the free surfacer, 8, z=cylindrical coordinatesu;= baffle widthx,= excitation amplitudez=amplitude of liquid displacement fromundisturbed surface measured a t thewalla= cone semivertex angley=ratio of actual to critical dampingd=logarithmic decrementv =liquid kinematic viscosityp=liquid mass densityQ= excitation frequencyw=circular frequency of liquid oscillationsChapter 5Simulation and Experimental TechniquesPart I.
Simulation of Liquid SloshingJohn F. Daltell5.1INTRODUCTIONThere is considerable justification, both technical and economic, for modeling sloshingphenomena in the laboratory. The model isalmost always small relative to the prototypeand thus costs little to build, compared to theprototype, and usually proportionately less tomodify. At times models add certainty to ananalytical approach, and in other cases providethe physical insight required to formulateanalytical approaches. Small-scale modelinghas become an essential complement to theoretical stiidies and full-scale observations of thebehavior of fuel in the tanks of booster rocketsand spacecraft.The initial design of simulation experimentshas much in common with the design of thefinal product in that it is usually impossible orimpractical to satisfy simultaneously everyaspect of the ideal goals of the design.
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