H.N. Abramson - The dynamic behavior of liquids in moving containers. With applications to space vehicle technology (798543), страница 88
Текст из файла (страница 88)
Typical results of these investigationshave been presented by Binnie and his coworkers (refs. 10.17 and 10.18). Kame1 hasverified part of these results in his experiments(ref. 10.19). Figure 10.18 shows his results forthe discharge coefficient, K, of a number ofdifferent orifices located a t the bottom ofa 27-centime ter-long, 10-centimeter-diametertank, as a function of the initial swirl, X.LOOI n terms of the draining flow rate, Q, the totalliquid head, H, and the orifice diameter,Q, K and X are defined asandwhere Q is the product of the swirling (tangential) velocity near the inner surface of thetank and the tank radius.
For X=1.0, thetheoretical discharge coefficient should fall tozero; this implies that the available liquid headbas been completely converted i n t o swirlingmotion. Experimentally, tt nonzero value ofK was reported for all values of .Y; however,K does fall off significantly from its no-swirlvalue asincreases from zero. Moreover,an air core was observed in the large orifices.Reversal of the axial velocity close to the aircore was also observed, but this is a consequence of the flow through the boundarylayer on the bottom plate exceeding thedischarge cUnp:lc.ilyo f rhe o~ttlet.I n a dmining file1 tank, rotary sloshing is areadily available mechanism for producingswirling motion.
(See ch. 3.) Thus, it ispossible for effects such as those illustratedin figure 10.18 to occur naturally when sloshingand draining occur simultaneously. I n orderto compute the magnitude of the swirlingmotion due to sloshing, Hutton (ref. 10.20)has computed the transport velocity of thefluid particles during rotary sloshing. It wasnecessary to include nonlinear terms in theanalysis, which is based on the inviscid flowassumption of irrotationality, because theaverage particle displacement in a linear wavetheory is zero.
H e found that the maximumangular momentum of the fluid was about1.- '2 '2-e thG zDgAhr~A~ if the~~U.t3A{I//U'lJfluid moved as a rigid body a t the same rateas the free surface waves (7 is the peak waveheight, and dr is the tank diameter). Thus, theangular momentum of r o t a q sloshing, whilesmall, is probably sufficient t o initiate thevortex formation, according t~ Dergarabedian'stheory.OnFIGURE10.18.-Nozzle discharge coe5cients (ref. 10.17).375W l~t376THE DYNAMIC BEHAVIOR OF LIQUIDSAnother consequence of this angular momentum is that a roll torque b v i l l be exerted on thetank walls by the suirling motion. (See alsothe discussion of ch. 1 with regard to flighttests of the Saturn vehicle.) In a series of fullscale and model tests designed to test this conclusion (ref.
10. lo), i t was found that negligiblysmall torques (less than 0.15 kilogram-meter)were produced by rotary sloshing in an unbafledtank. These findings appear to disagree withthe data from the Transit 2-A flight testmentioned previously; however, the tank motion during flight ~ v a sconsiderably more severethan in the full-scale ground tests.
Also,during flight the druiti rate of the fuel \\-asapproximately 14 kilograms per second, while,in the ground tests, it was zero; thus anytorque produced by the simultaneous sloshingand draining would be absent in the groundtests. According to t,he previous paragraphs,draining tends to increase any rotational mot,ions present, so the above conclusions areprobably retxsonable.As an in tere~t~ingsidelight, the roIl torqueproduced in the bafletl tank was as large as3 kilogram-meters in some cases. This, ofcourse, is in disagreement with the commonassumption that an increase in dampingdecreases the sloshing forces and torques.A series of qualitative experiments of drainingand sloshing are reported in reference 10.11.The model tank employed in these experimentswas 28 centimeters in diameter, with a 2.9centimeter-diameter drain hole a t the bottom.The tank was drained both by gravity and bypumping, with and ~vithout initial liquidrotation.
Some of the observations \\-ere madewith a cross-type baffle over the drain, as shownin figure 10.19. The results of numerous testscan be summarized as follo~vs:(1) Tank filled and draining initiated immediately. No baffle. Vortex appeared whenthe fluid level dropped to approximately 2centimeters from bottom.
Drain time, 34.0seconds.(2) Tank filled and draining initiated aftersubstantial time delay. No baffle. Small vortex appeared when fluid level dropped toFIGURE10.19.-Cruciform vortex haWe.approximately 2 centimeters from bottom.Drain time, 23.0 seconds.(3) Tank filled and drt~ininginitiated immediately. Cross-type baffle above drain. Novortex. Drain time, 32.5 seconds.(4) Tank filled and strong initial liquidrotation introcillcerl artificially.
No baffle.Vortex ~ t p p ~ a r ewhendfluid level dropped toapprosirnutely 9 centimeters from bottom.Drain time, 40 seconds.(5) Tank filled and strong initial liquidrotation introduced artificially. Cross-typebaffle. So vortex. Drain time, 23.0 seconds.(6) Draining while undergoing normal sloshing. Similar to (1) above.(7) Draining while undergoing rotary sloshing. S i m i l ~ rto (4) above. Draining time wasvery long.(8) Draining while undergoing normal sloshing.
Cross-type baffle. Similar to (3) above,except drain time for last 2 centimeters of fluidwas considerably longer.Frorn these results it may be concluded that ttsmall amount of liquid rotation appears to haven negligible effect on vortex formation. Moreover, sloshing tends to break up a vortex assoon as it is formed, except that rotary sloshingproduces a strong vortex. This is in agreementwith the other results mentioned previously.The flow of liquid from tanks in n Low-govityfield can lead to considerable surface distortionand gas ingestion in the outlet line, even whenROTATION AND VORTEXING DURING DRAININGSuccessive stlgesInterfacedistortionLiquidI*FIGURE10.20.-Gas ingation during low-gavity draining(ref.
10.21).377the vorticity is negligible. (See fig. 10.20.)This is caused primarily by the reduced bodyforces acting in combination with the nonuniform flow velocity across the tank crosssection (ref. 10.21).As a conclusion to this brief section, i tappears that no existing theory completelyexplains vortex formation and liquid rotationduring draining.
In some cases, such as whenrotary sloshing and draining occur simultaneously, large roll torques can be exerted onthe tank, arid the draining flow rate may besubstantially decreased. Fortunately, it appears that ndeqnnte baffling can be provided onan empirical basis to ameliorate this situation.Such .;ilppressors are almost invariably provided to corltrol normal sloshing, so vortexingand rotntional motions should be adequatelycontrolled in ~iorrnalcases.
Thus, these typesof liqi~itlnlotion, while of considerable interestfro111 a fluid mechanic viewpoint, are ~ r o b a b l ~of less importance in practice.Part 111. Longitudinal Oscillations of Flight VehiclesDaniel D. Kana10.7 POGO PHENOMENALongitudinal structural oscillations a t lowfrequencies ( 5 to 25 cps), superimposed on theusual steady accelerating motion, have beenobserved on a number of rockets nnd launchvehicles during flight. The hrisic stnicturnloscillation nccltrs in the f~lndamentctl longitlidinal free-free mode, so that the vehicleexperiences an accordion-like motion, with theends of the vehicle moving out of phase 11-it11respect to each other; hence, the behavior hasbeen nicknamed "pogo" oscillation.A genernl description of this type of behavioris shown in figure 10.21, which is tnken fromthe report of Rubin (ref.
10.22). S t sonletime during the steady rising trajectory of thevehicle, an unstable coupling between somevehicle subsystem and the structure occurs, sothat an oscillation a t the structural frequencybuilds up, levels off, and then subsequentlydecays after enough change has occurred for thecoupling to become stable again. The timeof flight at the onset of the oscillations, as wellas the frequency, severity, and duration of thephenomena, depends on the particular vehiclein which this type of behavior has occurred.However, in all cases, it appears that the frequency of the oscillations tracks the changingIwith timeTimeFIGUREIO.Z~.-PO~Oowillation supimposed on risingtrajectory acceleration (ref. 10.22).378structural resonnnt frequency during the en t i r ~period of the behavior.Thor-Agena and Titan I1 have experiencedparticularly severe oscillations (typically 0.:to 3 g a t the payload) toward the end of firststage burnout.
The frequenc? vtwii~tion- t i rt.about 16.5 to 21 cps for Thor-Acenu t ~ n d10to 13.5 cps for Titan 11, wit11 the no st severeoscillations occurring nt 20 ctps and 11 cps,respectively, for the two vehicles. Characteristically, they have been referred to :is the20-cps problem and the 11-cps problem. ;Issociated with the behiivior of these vehicles arestrong pressure fluctuntions in \ritriouh parts ofthe propellant feed syqtenl. .ii;(l c ~ rrile c~t)m'n~i+tion chamber.
A~ii~lyseshave rcvellled thlitthis behavior of these ve11icle.i results from t iclosed-loop instability re3111t irlg from propulsionfeedback with the fundamental longitudinalstructural mode.A somewhat different type of instability hasoccurred on most Atlas flights.
although theresults are essentitilly the snnle. Here theoscillations occur near 5 cps, with a d ~ ~ r u t i o nof about 20 to 30 seconds immediately following liftoff. A dynamic analysis of this vehiclehas revealed that the instability resrllts fromthe coupling of the pneumatic regulationsystem for the ullage pressure and the longitudinal structural mode. The engine system isapparently not involved to tiny extent.Several other vehicles have experiencedsimilar oscillations a t various times, but notwith the severity of the cases mentioned above.I t is obvious thtit such oscillations ctt low levelsare a t best undesirable, and a t severe levelsapproach destruction of the vehicle. Elimination of pogo oscillations is particularly important i n - t h e case of launch vehicles used formanned flights because of possible adverseeffects on astronarlt's vision and manual reac-379LONGITUDINAL OSCILLATIONS OF FLIGHT VEHICLEStions.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
