H.N. Abramson - The dynamic behavior of liquids in moving containers. With applications to space vehicle technology (798543), страница 23
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4.20). Esperiments were conducted in circular cylindrical tanks having conical bottoms; rigid lids or covers were constructed of solid plates with diameters of 99,DAMPING OF LIQUID MOTIONS AND LATERAL SLOSHING115material to obtain necessary buoyancy. Whilethis technique was rather effective in suppressing liquid motions, difficulties were encounteredin practical applications by virtue of the mat"hanging-up" and not remaining on the liquidsurface.Floating CansFIGURE4.12.-Floatingcan slosh suppression device.Floating devices, aptly described as "floatingcans" (see fig.
4.12), were also proposed byEulitz (ref. 4.18)) and later investigated indetail by Abramson and Ransleben (refs. 4.19and 4.21). These devices were fabricated ofthin perforated material, employing a hollomsphere for buoyancy. The damping of liquidslosh forces mas fairIy effective only when thecans were packed closely, but even so was lessthan could be obtained from fixed baffles(ref. 4.19).Expulsion Bags and Diaphragms85, and 67 percent of the tank diameter. Othervariables investigated were liquid density andviscosity (three liquids were used), excitationamplitude, and excitation frequency. I t wasconcluded that: (1) the floating-lid-type devicehaving a diameter of 85 percent or more of thetank diameter provides very high force damping,5 (2) the peak force response increases withincreasing values of the ratio p/v, and (3) theforces acting directly on the lids appeared tobe rather large so tbat significant weight penalties may be involved with the use of such devices.
Of course, in actual practice, the innertank wall of a propellant tank is generally acomplex arrangement of stringers, stiffeners,other structural elements, plumbing, and soforth, so that a lid diameter of the order of85 percent to 90 percent may be difficult toachieve unless the tank is a very large one.Euiitz (ref. 4. i8j a'w studieci the possibiliiy ofemploying a porous layer of material (commercially available coco-fiber mat) on the liquidsurface, similar to the rigid lid discussed above.Aluminum spheres mere embedded in thisThe damping factor was not explicitly calculated,this conclusion being reached by observation andcomparison of the force response curves.6 Forces were actually measured by means of specialdynamometer linkages.Positive expulsion bags and diaphragmsof elastomeric materials have been consideredfor the purpose of liquid transfer in a low gravityenvironment (ch.
11). The slosh force dampingproduced by these devices has been investigatedby Stofan (refs. 4.16 and 4.17). The variablesconsidered mere tank size, diaphragm and bagthickness, and excitation amplitude. Since aslosh force parameter mas used which is independent of liquid density and since maximumslosh forces in a spherical tank occur for thehalf-full tank, the liquid density and depth offluid in the tank were considered only briefly.Slosh forces in (I $full spherical tank wereinvestigated employing two liquids : mercury(ref. 4.16) and acetylene tetrabromide (ref.4.17).In general, it was found that significantdamping ~f the tcrce respnr?se W R S obtained.but was strongly dependent upon the diaphragmthickness.
The second-mode force peak andliquid swirl were completely suppressed. Theforce parameter also increased with increasingexcitation amplitude and appeared to increasewith decreasing tank size. I t should also benoted that as the diaphragm thickness increased, the peak slosh forces occurred a t succeedingly higher values of excitation frequency.116THE DYNAMIC BEHAVIOR OF LIQUIDSThe force damping data (the damping ratioCruciform Baffles)Damping produced by cruciform baffles (fig.4.15) has been investigated in references 4.12,4.28, and 4.29. These baffles are locatedphysically in the same manner as a stringer,so that for the circular cylinder there is theadvantage of damping being independent ofliquid depth; for the spheroid and the sphere,of course, damping is not independent of depth.The disadvantage of this configuration is thatit provides only a relatively small amount ofdamping.was defined as 6=ln Fnexhibited considerableFPrflscatter (fig.
4.13). In general, the dampingratio increased with increasing diaphragmthickness and excitation amplit,ude (fig. 4.14)and decreasing tank diameter. Some effectof excitation frequency on the damping wasobserved in the 81.4-centimeter-diameter tank.Expulsion bags appeared to perform similarlyto the diaphra,pns (fig.
4.14).4.4DAMPING BY FIXED BAFFLES: NONRINGTYPEAn almost be~vilderingarray of baffle typesand arrangements, all with the common featureof being fixed in location within the container,have been proposed. Basically, all these maybe categorized as being generally of the formof annular rings or not,. The present section isconfined t o the latter.ITankConfiguratimContainedliquiddiameter.cma 24.1Diaphragm Mercury (ref. 4 16)0 24.1DiaphragmAcetylene tetrabromid0 52.1Diaphragm52.1Bag0 81.4Diaphragm----Unrestrictedsloshing ( unpublished NASA dataThickness of bag and diaphragm = 0.0254 cmI1D~aphragmthickness, cm00.025400.050800.0762A0. 1016First modeSecond modeunrestricted sloshingunrestricted sloshing0I a I Tank diameter, 52.1 crn , ;X.-0a0.0080.0160.024Excitation amplitude parameter, ( X o l d )0.0321.016 cmFIGURE4.14.vEffect of excitation amplitude parameteron maximum force parameter (ref. 4.17).00.61.01.41.82.
2Oscillatory trequency parameter, a( b ) Tank diameter. 81.4 cm , X o 8 1.016 cmTest liquid, acetylene tetrabromideFIGURE4.13.-Effectfi2.6of diaphragm thickness on dampingratio for constant excitation amplitude (ref. 4.17).Table 4.3 sho\~-sdamping factors in a circularcylinder tank x l t h cruciform baffles oriented 45"and 90" to the direction of excitation (ref.
4.28).Figure 4.16 shows the variation of dampingwith liquid depth for an oblate spheroid; thedamping increnses with decreasing depth.Damping provided by cruciform (verticalconfiguration) baffles in a sphere (fig. 4.17)has been investigated in reference 4.29. ByDAMPING OF LIQUID MOTIONS AND LATERAL SLOSHINGTABLE4.3.-Damping Ratios for Cruciform BaBesin a Cylindrical Tank[Ref. 4.281IIOrientation, deg(fig. 4.15)I1dfo/ 6 = ; l n erotating figure 4.17 by 90°, the symmetry ofthe sphere yields a completely different bafflearrangement (horizontal configuration).
Forceresponse curves for both baffle arrangementsare shown in figure 4.18, compared with similardata for the unbaffled tank.' Note that thehorizontal configuration of the baffles givesvastly more reduction in slosh force than doesthe cruciform arrangement,.-V ~ ~ W A - A-+117Sector Compartmented TanksAs discussed in detail (ch. 2), a very muchused tank configuration is the circular cylindercompartmented into sectors by means of radialwalls.8 Of course, the principal reason for employing partitions is to shift the liquid resonantfrequencies into a more desirable range, whileperforations are introduced for weight reductionand only secondarily to reduce the amplitude ofthe liquid oscillrtti~ns.~I t is thus seen thatperforation must add damping without loweringthe resonant frequencies, or else the underlyingreason for employing the partitions is defeated.The effects of sector wall perforation on theresonant frequencies and damping ratio as functions of excitation amplitude and frequency,percent and size of hole perforations, and liquiddensity and viscosity have been investigatedexperirnentally(refs.4.30through4.32).
Dnmping factors were obtained from the force responsecurves by employing the bandwidth technique.The direction of translation with respect to thesector walls is as indicated in figure 2.10 ofchapter 2, and size and liquid depth were generally held constant at d=36.6 centimeters andh/2R=1.0 (water).View B - BExcitationExc~tationTOPC---CExcitationOblate spheroid/ExcitationCircular cylinderExcitationCJTop ( Half sphere )view C - cSohereFIGURE4.15.-Cmciformbaffle configurations.Liquid Resonant FrequenciesThe variation of liquid resonant frequencywith perforation size, excitation amplitude, andliquid density and viscosity has been describedfor a given percentage opening and tank size interms of an "equivalent Reynolds number"parameter, as shown in figure 4.19.
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