H.N. Abramson - The dynamic behavior of liquids in moving containers. With applications to space vehicle technology (798543), страница 36
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5.12) give similar plots167SIMSTLATION AND EXPERIMENTAL TECHNIQUESvfiRange -LOX, prototypeFIGURE5.11.-Approximatesimulation ranges: Inertialviscous-surface tension scaling (model fluid temperaturesrestricted to normal ambient).for inertial surface tension scaling for particularmodel and prototype fluids. The applicableapproximate ranges for liquid oxygen andkerosene prototypes from figure 5.11 have beendrawn in on two plots from reference 5.12 andare shown herein as figures 5.12 and 5.13. I tcan be seen from these figures that the approximate simulation ranges of fi,we 5.11 are reasonably valid within the assumption of modelfluid a t ambient temperature which mas madein the preparation of figure 5.10 for inertialsurface tension scaling alone.
I t is also interesting to note from a comparison of figures5.12, 5.13, and figure 5.11 that even quitefantastic increases in model fluid temperaturewill apparently not result in simulation pointsoutside the extreme range shown on figure 5.11.Evidently there is hope for inertial-viscoussurface tension scaling of low gravity fluid behavior in the laboratory a t 1 g ( a , > > l ) if theprototype fluid 'sviscous' Fromfigures 5.12 and 5.13, and other figures ofPrototype : Liquid Owen+Model fluid at O'CMcdel fluid at 2d--bFIGURE5.12.-Simulation229-84s 0-67-12cModelfluidat300'~plot: Prototype liquid, liquid oxygen (inertial-viscous-surfacetension scaling).THE DYNM6IC BEHAVIOR OF LIQUIDS-u-Model fluld at$chlodelfluldat2W'~IFIGURE5.13.-Simulation plot: Prototype liquid, JP-4 (inertial-vilcouraurface tenrion waling).reference 5.12, it appears that the possibility ofa corresponding simulation of liquid oxygen andliquid hydrogen (possibly all the cryogenicsalso) is rather low.If figure 5.11 is modified to reflect the cavitation scaling of figure 5.9, there results5.14 which (within the limitations on modelfluids noted) pertains to simultaneous inertial,viscous, surface tension, and cavitation scaling.It is evident that the addition of cavitationscaling, where the model fluid is a t room temperature and atmospheric pressure, wipes out hopesfor low gravity simulation in the laboratory andrestricts the simulation range for liquid oxygenfor practical purposes to roughly 'life sizeJJand "bigger than lifeJ1models.Matters become even worse if all five of thesimulation plots are superimposed (fig.
5.15).In this case, the fluid compressibility and tankelasticity criteria combine to decrease both theextreme range of possible simulations and therange for liquid oxygen 8h01\m in figure 5.14.It should be remembered that a large number of.F I G U B5.14.-Approximate~simulation rangee: Inertialvircour~rurfacetenrion.cavitation rcaling (model fluidtemperaturee reevicted to room temperature, prerrurer1 atmoephere).SIMULATION AND EXPERIMENTAL TECHNIQUES169their basic lack of coverage of the situationwhere the model is significantly smaller than theprototype, as well as the situation where theprototype acceleration field is much smallerthan 1 g.5.6 CONCLUDINGNote : Since fluid properties arenot inde~endentof one another.the above ranges are optimisticREMARKS ON SIMULATIONThe foregoing treatment has been as generalas possible in hopes of yielding some perspectiveon the extent to which fluid dynamic and fluidstructure interaction problems may be simulated.
In brief, the prognosis for small-scaledirect simulation of every problem in fuel sloshing is not very good, a t least not withoutconsiderable sophistication of equipment andtechniques. However, the general approach tosimulation as outlined herein has been of immense practical value and will continue to be,when paralleled with judgment on the part ofthe experimental designer.I t will continue to be necessary to do experiments aimed at discovering the practical effectof going out of scale with respect to one parameter or another in the problem a t hand, if theoretical considerations do not plainly indicatethe course to take.
There are many instancesin the treatment given herein, particularly withrespect to surface tension and low-gravi typhenomena, where the analysis becomes incomplete through omission of thermodynamiceffects. With respect to low gravity phenomena, this situation is corrected to a great extentin chapter 11 of this monograph.jIrnFIGURE5.15.-Approximatesimulation plot: Simultaneous inertial viecous, cavitation, compressibility, surfacetension waling for maled elastic replica tank (modelfluids mtricted to normal laboratory temperatures andpressures).restrictions were placed on the conditions ofthe model fluid in the preceding section and thatone of the bases for the possible simulationrange for tank elasticity in a replica model wasthat the model structure probably could not beas strong per unit mass as the prototype (theseassumptions tend to make the modeling easier).The results shown in figure 5.15 are notable forPart 11.
Experimental Techniques and ApparatusGeorge W . Brooks5.7INTRODUCTIONIt is generally true in technological developments that adequate understanding of complexphysical phenomena is enhanced by, and generally dependent upon, the combined use ofexperimental and theoretical techniques in support of each other. The complexity of thedynamics of sloshing liquids is well establishedthrough the analytical, laboratory, and flightexperiences reviewed in other chapters of thismonograph, and a review of the literature onthe sloshing of liquid propeIlants in the tanks oflaunch vehicles clearly shows the eminent rolewhich experimental research has played in boththe definition of the problem and in the realization of adequate solutions.The role of experimental research in propellant sloshing is wide and varied.
Its initialfunction has been, and is, a qualitative one-toshow what is happening and why and how. Inthis phase, it provides the necessary clues tosupport the selection of theoretical concepts andprinciples. But of even greater significance isthe role which experimental programs must,play in providing the quantitative data neededfor design. The fact is that current theoreticalanalyses are limited to treatment of a very fewidealized tank configurations which are seldomused in vehicle design, and the theory for eventhese cases requires restrictive assumptions offluid idealization and small motions.
Thus,experimental programs are necessary to checkthe validity of t,he theoretical assumptions andapproximations, and to extend the theory fortreating configurations representative of manyof those selected for flight vehicles on the bnsisof other design considerations nnd compromises.Many specialized problems such as dome impact, vortex motions, low gravity effects, andflow in baffled tanks are not, currently amenable170to theoretical analysis and, consequently, experimental data provide the only reliable basisfor design.
This category also includes theessential aspects of the coupled dynamics ofthe fluid with the motions of the tank and sloshsuppression baffles.The experimental techniques and apparatusdeveloped for research on the dynamics ofsloshing propellants reveal many practical, andofttimes ingenious, approaches, and i t is theprimary purpose of this section of the monograph to present a review of the literature onthe subject. This review is intended to berepresentative rather than exhaustive, andsince experimental techniques for zero-g studiesare highly specialized and adequately treatedin chapter 11, they will not be included here.5.8FUNDAMENTAL STUDIES OF LIQUID SLOSHING IN SMALL TANKSTank Construction TechniquesA brief review of launch vehicle configurationsreveals that tanks of varied geometry are therule rather than the exception.
The basiccylindrical section is usually modified by use ofconical or elliptical bottoms and tops whichmay be interior or exterior to the cylinder perse, and by the use of partitions to effectivelyreduce the free surface area. Other configurations employ variations of oblate spheroidsranging in eccentricity from that of the spheredown to a value of about one-half. Particularconfigurations, such as the toroid, are aIso ofinterest because of their pressure stability andthe convenience provided for nesting multipletanks for minimum overall volume.Among the various tJechniques available forthe construction of suitable tanks of varied geometry for basic research in propellant sloshing,SIMULATION AND EXPERIMENTAL TECHNIQUES171the technique of vacuum molding plastics suchas Plexiglas or Lucite is perhaps the moreversatile. As shown in the sketch of figure 5.16,the technique consists of constructing a femalemold of wood, placing a sheet of plastic (heatedto permit ready forming to the mold geometry)over the mold cavity, and evacuating the cavity.Two matching half sections are usually madein this manner after which they are trimmedand cemented together to achieve the finishedtank.
This technique was employed in theconstruction of the tanks used for the spheroidsand toroids of references 5.16 through 5.18 forexample.Plastic sheet heated for forming7FIGURE5.17.-Model tank constructed from Lucite blockshaving internally formed tank geometry.for vacuum sealG-/asketIn addition to their relative ease and er.onomy of construction, clear plastic tanks alsopermit visual and photographic observation ofthe fluid motions-animportant featurefor documenting unusual or unexpectedphenomena.'Female mold of woodTank Support and ExcitationManifold-TO vacuu m sourceFIGURE5.16.-Molding technique for model tankconstruction.Another method used successfully to construct tanks for small-scale fluid slosh studies(refs.
5.19 through 5.22) is shown in figure5.17. I t involves forming the mating halves ofthe desired geometrical configurations in Luciteblocks which are subsequently bolted togetherhis technique has theto form the tank.advantage of providing accessibility to thetank interior for installation of baffles, expulsiondiaphragms, and so forth, but it has a disadvantage in that the weight of the tank isrelatively high and consequently large tareforces make it more difficult to measure accurately the forces imposed on the tank by thecontained fluid.The problem of supporting and oscillatingsmall tanks to induce fluid-sloshing motionshas been treated in many ways.
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