H.N. Abramson - The dynamic behavior of liquids in moving containers. With applications to space vehicle technology (798543), страница 99
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IVe \vill add to theengineering side of the<e c.u~umentsin section11.5.Forced OscillationsAt this writing, very little is known about thepeculiarities of forced oscillations a t low g.Tong and Fung (ref. 11.41) studied the motionin an elastic tank subjected to periodic axialoscillations using a variational method. Theyfound that surface tension becomes veryimportant a t low Bond numbers, and that thestability limits and frequencies can be shiftedconsiderably by surface tension. Eide (ref.11.52) has examined the motion of a spacevehicle brought about by sloshing in a rectangular tank.
His analysis shows that thrustingimpulses can be properly phased so as t o minimize the effects of sloshing on the vehicleattitude, and to control the amplitude of sloshwithin a maneuvering vehicle.Although the published work on forced low-gsloshing is limited, the methods of analysispresented throughout this monograph may bereadily applied to treat particular cases ofinterest in design.The positioning of liquids in large rockettanks is not a straightforward task underconditions met in space vehicle operation.During prelaunch and ascent conditions, liquidlocation is determined by the direction of theacceleration-induced body forces.
If the behavior of liquids in a spacecraft. were clearlydominated by surface forces, the matter wouldbe simple. Cnlculation of the Bond numberfor a typical large space vehicle using anacceleration of lo-" go (Bo=37 for the SaturnS-IV) indicates that the liquid will be dominated by adversely directed acceleration-inducedbody forces under practically any conceivablemission (ref. 11.53). With this in mind, meansmust be found to effect control over the locationof the liquid in spite of significant extraneousforces acting on the space vehicle.
(For recentsummaries of zero-g propellant-handling problems, see refs. 11.54 and 11.55.)One method of positioning liquids in tanks isto provide strategically located surfaces for theliquid to wet (since all propellants now in usewet most practical tank materials). Underlow-g conditions, wetting liquids will tend towet more solid surfaces. An example of thissystem is the central standpipe liquid positioner tested b y the Lewis Research Center onthe Mercury MA-7 spacecraft (ref.
11.56).This device is shown schematically in figure11.36.r Tank- StandpipeOrifices ( 4 )FIGURE11.36.-MercuryMA-7 liquid positioning experiment.LIQUID PROPELLANT BEHAVIOR AT LOW AND ZERO GThe device tested consisted essentially of an8.9-centimeter ID plastic sphere with a 2.79-centimeterdiameter standpipe fixed to one end asshown.
The lower edge of the standpipe waspenetrated by four 0.79-centimeter-radius semicircular holes to provide communication between the central standpipe and the tank.Body force direction during ascent is indicatedby the arrow g and the resultant liquid level isshown by the dotted line.Using the Bond number as a modeling basis,the data from reference 11.56 indicate that themaximum transverse g loading for-which sucha system can retain control of the liquid isapproximatelywhere D is the baffle diameter.
An estimate ofthe time required for a baffle of this sort to gaincontrol of the liquid, based on the data ofreference 11.56 and equation (11-llb), is "When body forces are directed parallel to theaxis of the tank and toward the end in whichthe baffle is located, the height of capillaryrise can be estimated using the theory developedin the previous sect,ions.The use of perforated materials, such asscreening, in small model tests has been reported (ref. 11.17).
This sort of materialaffords useful weight saving, since the liquidwets i t almost as readily as if i t were solid sheetmetal.Siege1 (ref. 11.19) reports the results of ananalysis and experiments which allow time estimates to be made for the filling rate of largeye-v lcw-n~ n n r t.innclicn,nillnry t.=hPsa ----------.His method of analysis is given in sufficientdetail to be used as a guide in calculating therate a t which a capillary tube type of locatorbaffle in a propellant tank will fill when thebody forces acting on the liquid are suddenlyreduced to very low levels.1iIl1 For this particular geometry, pressure drop throughthe semicircular orifices probably plays an importantrole in determining the time to reach equilibrium.421An important use of the stability ideas is theenhancement of meniscus stability with screens.A typical application is the placement of aplane screen mesh or perforated sheet metalbaffle across the tank, as shown in figure 11.37.If the liquid in the tank is subjected to bodyforces tending to make the liquid run in thezdirection, the liquid forward of the baffle willdo so, provided meniscus A is unstable.
Theliquid behind the screen mesh can be stabilizedby the capillary surfaces in the screen mesh.If the liquid in the tank is subjected to a transverse body force, the liquid wvill be kept fromrunning out through the screen by the capillarypressure across the liquid-gas interfaces in thescreen mesh. This method is being applied tocurrent liquid rocket systems. The newestmodel of the Agena upper stage vehicle, forexample, has been redesigned incorporating acontainment sump system (fig. 11.38).
Thiscontainment sump is separated from the mainpropellant tank by a conical screen mesh ofapproximately 30 holes per centimeter and aporosity of about 50 percent. This assures theGasIFIGURE11.37.-Screen baffle for liquid control.422THE DYNAMIC BEHAVIOROF LIQUIDSIScreen mounting ringlr c o n t a i n m e n t screenFIGURE11.38.-Agenacontainment sump.presence of liquid a t the tank outlet when theengine is restarted, and thus eliminates the needfor auxiliary rocket motors. The conical screenseparating the sump from the tank will retainsufficient liquid in the sump ready for use bythe engine. After restnrt, the rnain body ofliquid is carried to and through the screen b ythe thrusting forces, refilling the sump for asubsequent engine operation.The two propellant-positioning methods justdescribed are best suited for propellants storedin a single phase (the so-called storable propellants).
The unavoidable heat transfer t ocryogenic tankh nlny cause local boiling of thepropellant within the region of the screenbaffle, thus forcing liquid out and destroyingthe baffle effectiveness.Capillary PumpingThe pressure differences across liquid-gasinterfaces of different curvature can be used topump liquids from one place t o another. Thepressure differences are extremely small, so theexpected pumping rates are very small. Thisuse of capillary forces therefore has limitedapplic4tion. Consider the tanks shown infigure 11.39.
The pressure difference acrossthe liquid-gas interface in the larger tank \\illbe less than that across the interface in thesmaller tank because the curvature of thesurface in the larger tank is smaller. Thus,PI>P2, and the liquid will move toward thesmaller tank. It is a straightforward mannerto develop a single relat,ionship to express theflow rate in terms of the geometry of the system(assuming laminar flow and no losses duo tobends or enlargements and contractions andthat the transfer line and pressure communication line have the same diameter). When-Liquid 7Direction of liquid motionFIGURE11.39.-Capillary pumping systems.typical vdues (rl=4.57 m, r2=1.52 m, r,=0.152 m) of tank, and transfer and communication line radii and lengths are int,roduced, theexpected flow rate is very small, on the order of0.5X10-' kg/hr ior liquid hydrogen.
This'rate could be increased considerably by bafflingthe smaller tank, creating more highly curvedmenisci.Petrash and Otto (ref. 11.57) have suggesteda similar scheme for orienting liquid within asbgle tank in a desired location. T h e tank istapered as shown in figure 11.39(b). Thedrain end of the tank is connected temporarilyt o the far end of the tank b y a pressure communicating line. Under zero-g conditions, thepressure equalization in the gas afforded throughthe line will cause the liquid in the tank to movetoward the smaller end of the tank.
Theprocess will continue until the liquid has filledthe pressure equalization line such that its interface spreads out on the inside of the tankopposite the drain end.Application of systems of this type will bevery limited in larger systems. First, the timerequired t o transfer the large quantities ofliquids from one tank t o another or from oneend of the tank to the other \\rill be too greatfor operational convenience.
Second, thepumping action \\-ill occur only so long as noadverse forces act on the tanks. Forces of anyLIQUID PROPELLANT BEHAVIOR AT LOW AND ZERO G,size at all would probably stop the pumpingaction.Capillary pumping on a small scale has beenproposed as a means for providing smallquantities of liquid needed to feed certaindevices. For example, McGinnes (ref. 11.58)experimented with a capillary pumping systemin which liquid is first evaporated at one temperature; the vapor then flows through somedevice requiring a very small gas flow rate (suchas a gas bearing for a gyro) and is condensed at,101%-ertemperature. The liquid is then returnedto the point of evaporation by capillary actionIn the experiments, capillary pumping pressureson the order of 0.011 kilogram (force) persquare centimeter were developed across thewick material, resulting in flow rates on theorder of 0.11 ~ 1 0 kilograms- ~per second.423inviscid irrotational treatment is reasonable,but the large changes in surface shape meanthat the nonlinear effecls must be considered;as yet, there has been no really satisfactorycomputation method for this problem.
(Seethe recent calculation scheme of Concus, Crane,and Perko (ref. 11.60), however.)We can, however, make some estimates asto the maximum draining rate for which themeniscus will retain its initial shape, using thereorientation-time correlation as a basis. Forthe draining rate to be sufficiently slow thatthe meniscus has time to adjust, the reorientation period must be shorter than the timerequired for the meniscus to travel its length.Using equation (11.105) for the response timeand setting the time for the meniscus to travelits depth asProblems and Methods of Liquid Expulsion at Low gThere is growing interest in problems ofliquid expulsion from a container at low g,both for feeding of rocket engines and transferof propellants from one vehicle to another.What limited information is presently availablesuggests that draining rates will have to beconsiderably less than at 1 go.
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