H.N. Abramson - The dynamic behavior of liquids in moving containers. With applications to space vehicle technology (798543), страница 2
Текст из файла (страница 2)
A fine example of the application of such techniques to problems of engineering significance is that of the critical designof the Mulberry harbors for the Normandyinvasion of World War I1 (ref. 1.8). Seismologists have been particularly interested not onlyin the liquid motion but in the forces producedby them on containing structures (refs. 1.9through 1.14). The recent catastrophe ofLongarone, Italy (October 9, 1963), in whichlandslides into the contained lake induced suchviolent sloshing motions of the water that, eventhough the dam structure itself did not fail,the overspilling water resulted in almost totaldestruction of the village and loss of life,represents yet another stark example of thereal significance of these problems.Oceangoing vessels are, of course, subject torather violent sea conditions at times, resultingin fairly large amplitudes of pitching, heaving,rolling, and other motions.
The response ofliquids contained in cargo, ballast, or fueltanks has therefore often been of concern, although the problem is usually alleviated to alarge extent by the ship's master operating withtanks as nearly completely empty or completelyfull as he can arrange. On the other hand, theTHE DYNAMIC BEHAVIOR OF LIQUIDSstabilization of ships in roll by means of passively acting partially full tank systems hasproved quite effective in many instances, eventhough the optimum design of such tanks isas yet an uncertain art (refs. 1.15 and 1.16).In similar fashion, the motions of liquids inautomotive, or rail vehicle, cargo or fuel tankshave at times been of concern. Usually, however, in these cases the volume and weight ofthe contained liquid has been suEciently smallcompared with vehicle weight that the forcesproduced are of little consequence, such thateven very crude and simple baffles have servedto suppress the liquid motion suiliciently. Aninteresting case in point, however, is that thefuel tanks of all racing cars in the Indianapolis500 of 1965 contained hollow plastic ball-likedevices ("wiWe" balls) intended to prevent fuelsloshing.sircraft certainly constitute a class of vehiclesin which one would anticipate that liquid response in fuel tanks might be a significantproblem.
Indeed, such is the case, althoughthe earliest occurrence of such problemsarose not just of itself, but through couplingwith other well-known aircraft dynamic problems. The first was probably that of sloshingin wing fuel tanks coupling with the wingvibration modes so as to modify seriouslythe flutter characteristics (ref. 1.17) ;the secondwas probably that of the overall effect of fuelsloshing on aircraft dynamic stability (ref. 1.18).For aircraft such as the supersonic transport,in which a large portion of the takeoff grossweight may be in fuel, this problem could be ofgoverning importance to many aspects of thedesign.Perhaps just two more examples, this timefrom particularly military applications, mayserve to round out this brief survey of liquidresponse problems which precedes our primaryarea of application to space technology.
Oneof these concerns the flight characteristics of aspin-stabilized projectile having a liquid core(refs. 1.19 and 1.20). In fact, it has been foundthat the motions of the contained liquid maycouple with the natural nutational mode ofmotion of the projectile so as to cause actualflight instabilities. The entire question of liquidbehavior in spinning tanks (refs. 1.21 and 1.22)is a very interesting one which, unfortunately,we shall not be able to discuss in any detailin this monograph.
The other problem relatesto explosion effects on liquid-filled tanks (ref.1.23). In the case of nuclear detonations, ofcourse, the loading on the tank may result fromeither the airblast or the ground shock, thelatter case being somewhat related to theproblem of earthquake excitation mentionedpreviously.1.2 PROPELLANT SLOSHING IN LAUNCH M-HICLESTurning our attantion now to those aspectsof the general problem that are of most directimportance to space technology, consider thelarge liquid-filled boost or launch vehicle.
Suchdevices have an enormous percentage of theirinitial weight as fuel and consequently thedynamic forces resulting from the motions ofthese large liquid masses could be very substantial, even beyond the capabilities of thecontrol system to counteract them or the structure to resist them. The important thing torealize, however, is that we are dealing with afairly complex dynamical system and musttherefore be especially aware of the possibilityof coupling between various of its components.Thus, the control system natural frequencies,the elastic body frequencies, and the fuel-sloshfrequencies must all be fairly widely separated;unfortunately, this is not always the case.Table 1.1 gives data for several representativevehicles, from which one can see that thevarious frequencies are indeed not alwayswidely separated.If the dominant fuel-slosh frequencies areclose to any of the control system frequencies,an instability in the flight characteristics canresult; while if the fuel-slosh frequencies areclose to the elastic body bending frequencies, alarge amplitude dynamic response problem mayarise.
In any case, the governing design problem is that of stability and control, so that onemust also carefully consider the location andconfiguration of the propellant tanks and thecharacteristics of the control sensing elements(ref. 1.24).Saturn I provides us with a clear example ofan actual in-flight stability problem arising as a\3INTRODUCTIONTABLE1.1.-CharacterisdcsLength, Diammeter, mVehicle_ _--Redstone,, ReddoneMercuryJupiter-- - - - --- -VehicIesFundaFund*Control mentalmentalfreslosh fre- bendingRange,n. rm. quency, quency a t f uency~ t o f f cps,axtoff,cpecps21251.781.7832000320002002000.5.50.8.810-1210202.65680001500.4692.656.51068000685 0003.4X 108Juno I1-------2560Saturn t------130Saturn V -----,-bThrust,kpof some Representdue Lmmdt--------...4.3.16----,-----------8.6.45b 0.3-0.421Important missionsExploration.Suborbital mannedflights.Reentry, recovery ofmonkeys Able andBaker.Moon try, Sun orbit.Manned space flight.Manned space flight.Large slosh masses in unfavorable locations.Exceptionally large slosh masses because of the large tank diameter.consequence of fuel slosh (ref.
1.25). Thisvehicle, it may be recalled, is unusual by virtueof its clustered-tank configuration: A singlelarge cylindrical tank, surrounded by a clusterof eight smaller cylindrical tanks (this is butone of several types of segmented or comparemented tank designs, as shown in fig. 1.1). Figure1.2 shows a representation of two of the manytelemetry records, taken during an early flight(1961), the upper one being the liquid-9loshamplitude in one of the outer LOX tanks andthe lower one being the vehicle angular velocityin roll. The early parts of these records, sayup to some time just under 100 seconds, aremore or less random and of relatively s m damplitude.
At a flight time of about 100seconds, however, the amplitudes of both theslosh motion and the roll velocity build uprapidly, with a fairly discrete frequency, for10 seconds or so, and then begin to decay.The cause of these observed oscillations wasattributed to a phase lag in the filter networkoi ;the roii contoi ioop that exhibited itsellnear the frequency of the first rotationalsloshing mode of this vehicle.
At this particular time in the flight, the liquid level in thetank had dropped to the extent that the bafflesprovided for the purpose of suppressing sloshingmotions were no longer effective and hence thedamping of the propellant motions was verylow. As the flight continued, the propellantCircular tankJupiter( Redstone,-Clustered tanks(Saturn I )Sector compartmented tank(Saturn V lFIGURE1.1.-TypicalAnnular tankScalloped tank-Tri tanks(Titan 111 1launch vehicle tank configurations.level lowered even farther, to the extent thatthe slosh masses became quite small and achange in phasing of the liquid motions in thevarious outer tanks occurred, so that theoscillatory motions then began to damp out.Fortunahiy, t'&o e c w u d 'lab h thethrust portion of the flight so that the oscillations could not achieve dangerous levels beforethe propellant tanks became virtually exhausted; even so, there was a premature engineshutdown on this flight, which could have beencaused by this oscillatory condition.
Certainly,had this situation arisen early in the flight, theconsequences might have been severe.THE DYNAMIC BEHAVIOR OF LIQUIDSslosh amplitude, yaw2--i-I0-4I1I7882863II9094Range ti me ( sec 1IIII981021061101148090100110120Angular velocity in roll2h:1.-,." ,-,&.n1040506070Range time ( sec 1F~cms1 2.-Saturn I fusl sloeh htability during ftight (ref. 125).Of course, as is evident from this discussion,because of the consumption of propellantsduring e h t , sqpificant changes in the variousfrequencies take place rather rapidly. An ideaof these changes may be gained from figure1.3, which compares behavior in circular andscalloped tanks (ref.
1.26). There are, in fact,many interesting features to these curves, andhence we shall return to them very shortly forsome additional discussion.Generally speaking, we have seen that sloshing of the liquid propellants may interact withboth the control system dynamics and theelastic vehicle structural dynamics, each ofwhich may also couple with the other. Theliquid-sloshing frequencies are often closer tothe rigid body control frequencies than to theelastic body frequencies (see table 1.1) andtherefore might ordinarily be the more important problem area; however, the liquid system is subject to some degree of control and,hence, the interaction between the elasticstructure and the control system may becomemore important.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
