H.N. Abramson - The dynamic behavior of liquids in moving containers. With applications to space vehicle technology (798543), страница 27
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3 2 for X , l d 0.00417, 0.00833 & 0.0107 I000.080.16a 240.32Baffle depth, dslR0.40a48FIGURE4.42.-Comparison of theoretical and experimentalpressures on a solid-ring baffle (ref. 4.41).0.010510152025303540dS, cmFIGURE4.41.-Comparisonof theory and experiment forforces acting on an annular-ring baffle (ref. 4.39).paragraph.) The effects of several baffle variables on the liquid resonant frequency, forceresponse, and damping factor defined by 6=lnthe figure by 90" gives the horizontal arrangement,.) The total force response and thedamping factors obtained from force responsedntn by means of the bandwidth techniqueare shown in figure 4.1s.
It is seen from thesedata that while the baffles lowered the fundamentnl frequency, they prorided considerabledamping over that of an unbaffled tank. Ittllso appears that the horizontal bnffle configurlition provides greater damping than doesthe cruciform configuration.Sumner (ref. 4.42) also considered the perfolniunce of l~luiulnr ring baffles in sphericaltanks containing water (fig. 4.47). (Note thatthis h n f l c tlrrangernent is entirely differentfrom either of those considered by Abramson(ref. 4.29) and mentioned in the precedingI)&(were in~estigat~ed.-4s also indicatedby the earlier experiments (ref.
4.29), thedynamic behavior of liquids in spherical tanksis relntively nonlinear and complex, thus imposing sonle difficulties in presentation of data.The liquid resonant frequency increases withincreasing liquid depth and incrertsing bafflewidth, as sho~vn in figure 4.48. A sharpincrease in this frequency occurs for liquidlevels a t or slightly above the baffle; furtherincrease in depth then results in a sharp decrease in the frequency.
This rapid rariatioriis believed to be cnused by the bnffle effect'ivelychanging the tank geometry. Figure 4.49compares relative data for single-ring andthree-ring configurations, for a single baffle\rid th.DAMPING OF LIQUID+SwRI-+Ref.133MOTIONS AND LATERAL SLOSHINGexper~mental4.40---0- Ref. 4. 39-(Values are RMS forcefor X, ' d = 0.00417,0.00833 & 0.0107)Solid ring - w l RWater - h l d > l- 0.157000.10.20.3 0.4 0.5 0.6Tank fullness. h 12b0.70.8O.'iFIGURE4.45.-Variationof damping with tank fullnessfor oblate spheroidal tanks with and without ringbaffles (ref. 4.12).00.080.160.24Baffle depth,0.32dSIR0.400.48FIGURE4.43.-Comparisonof theoretical and experimentalforces on a solid-ring baffle (ref.
4.41).00.020.040.060.08Amplitude ratio. 112 b0. 100. 120. 3FIGURE4.G.-Variationof damping factor with sloshamplitude ratio for oblate spheroidal tanks with ringbaffles (ref. 4.12).E012=-wI r 0 . 2CO-,0. 1L0Um.-C55n00. 20.3FIGURE4.44.-Variation0. 4Tank fullness,0. 50. hh12bof damping factor with tankfullness for ring baffles in oblate spheroidal tanks(ref. 4.12).Single - ring baffleFIGURE4.47.--4nnularThree - ring bafflering baffles in a spherical tank.134THE DYNAMIC BEHAVIOR OF LIQUIDSThe effect of excitation frequency, liquiddepth, and baffle width on damping ratio maybe seen in figures 4.53 through 4.56, the firsttwo for a single-ring arrangement and the lasttwo for a three-ring arrangement.
The maximum ralue of the damping obtained by varyingthe excitation frequency and holding constantthe other variables is denoted as the first-modedamping ratio. Maximum damping was generally obtained mhen the liquid depth wasapproximately a t the baffle. These rigid bafflesprovided high damping mhen the liquid surfacewas less than 0.1R below and 0.5R above thebaffle. The three-ring baffle configuration provided damping ratios greater than 0.1 througha range of liquid depths 0.25 <h/d 1 0 . 8 0 .1.00.10.20.3 0.40.5 0.60.7Liquid - depth ratio, h 12R0.80.9FIGURE 4.48.-Variationof fundamental frequencyparameter with liquid depth ratio for rigid single-ringbaffles in a spherical tank (ref. 4.42).The slosli forces vary with escitation frequency and reach n rnaximunl at approximatelythe liquid resonant frequency, increasing withincreasing excitation amplitude and decreasingbaffle width, as shown in figures 4.50 and 4.51 ;the variation \vit,h liquid depth may be seen infigure 4.52.
In general, it was found that, forthis series of esperiments, the optJimum bafflewidth, from considerations of slosh suppressioncharac teristics and baffle weight, correspondedto w/R=0.125. Also, for each baffle configuration, the slosh forces were most effectivelysuppressed when the liquid free surface wasa t or slightly above the baffle so that thebaffle remained completely submerged duringthe liquid oscillations. The rigid baffles wereineffective in reducing the slosh forces forliquid levels more than 0.30R to 0.40R aboveand below the baffle location.
The rigid,three-ring baffle configuration effectively suppressed the slosh forces for all liquid depthstested.Flexible BafflesAll the foregoing considerations of dampingby fixed baffles have referred to rigid solid orperforated baffles. A number of studies, however, suggested that flexible baffles may offersubstantial advantages in terms of both increased damping effectiveness and reducedbaffle weight (refs. 4.28 and 4.42). An investi-heoretical unrestrlcfundamental frequency( ref.
4.26 )Test Iiqu id, water1.00.10.20.30.40.50.6 0.7Liquid - depth ratio, h 12 R0.80.9FIGURE4.49.-Variation of average fundamental frequencyparameter with liquid depth ratio for a rigid three-ringbaffle in a spherical tank (ref. 4.42).DAMPING OF LIQUID LMOTIONS AND LATERAL SLOSHINGFIGURE4.50.-Slosh-force229-64s +87-10135parameter as a function of excitation frequency parameter for rigid single-ring baffles in aspherical tank (ref. 4.42).136THE - DYNAMIC BEHAVIOR OF LIQUIDSgation of flexible baffles u7as therefore undertaken and reported by Stephens (ref.
4.43).The various baffle configurations examined byStephens are shon-n in figure 4.57. Of these,the elastic cantilever configuration was so farsuperior in its high damping and very lowweight characteristics (quite thin and flexiblematerials ]\-ere considered, dotl-n to 0.005l-cmthick Mylar) that most effort was devoted to it.The mechanism of energy dissipation is involvedwith the formation of a strong vortex in theliquid as it flows past the baffle.Two nondimensional parameters were foundto be of importance, as shown in figure 4.58.The first involves the periodicity of the liquidand the second the baffle flexibility.
The effectof baffle flexibility is shown in figure 4.59, withliquid period as a parameter. The magnitudeof the relative damping is greater than unityover all of the range of baffle flexibility sho~vn,but decreases rapidly as flexibility increasesto the point, a t - which the baffle offers noresistance to the flow.IIIIBaffle width ratio.wlRNo baffleIIExcitation amplitude parameter, (X,ld lFIGURE4.51.-Variation of first-mode slosh-force parameter with excitation amplitude parameter for rigidsingle-ring baffles in a spherical tank (ref.
4.42).l a ) Excitation amplitude parameter, X,ld-0.00488FIGURE4.55.-Variation of first-mode slosh-force parameter with liquid depth ratio for rigid single-ring baffles in a sphericaltank (ref. 4.42).DhWING OF LIQUID MOTIONS AND LATERAL SLOSMNGIIIIIIIIBaffle width ratio.14l.61.8Excitation frequency parameter. T ) * a1.220fiIwlRNo baffle0LO137222426FIGURE4.53.-Damping ratio as a function of excitation frequency parameter for rigid single-ring baffles intank (ref.
4.42).a sphericalTHE DYNAMIC BEHAJ7IOR OF LIQUIDSFIGURE4.54.-Variation of first-mode damping ratio withliquid depth ratio for rigid single-ring baffles in a spherical tank (ref. 4.42).00.20.30.40.50.60.70.8Liquid - depth ratio, h 1 2 RFIGURE 4.55.-Dampingratio as a function of excitation frequency parameter for rigid three-ring bafne in a sphericaltank (ref. 4.42).DAMPING OF LIQUID MOTIONS AND LATERAL SLOSHINGIBaffle1397FIGURE4.56.-Variation of first-mode damping ratio withliquid depth ratio for rigid three-ring baffles in a spherical tank (ref. 4.42).0.10.2RigidbaffleS p r i i g restrainedrigid baffle0.3 0.4 0.50.60.7Liquid - depth ratio, h 12R0.8Cantileverflexit'eRigid bafflewith clearanceFIGURE4.57.-Flexibleor movable baffle configurations.140THE DYNAMIC BEHAVIORLiquid amplitude at baffleDeflection of baffleBaffle widthBaffle widthOF LIQUIDSFIGURE4.58.-Governing nondimensionalparameters for flexible baffles.V- Maximumfluid velocityp, E, tat baffle location.T - Period of the liquidoscillation.pL I- Poisson'sratio, modulus ofelasticity, and thickness ofthe baffle material.- Fluiddensity.Sf- Damping provided by flexible baffle6,- Damping provided by a rigid baffle of thesame width w and under similar flowconditions as those for flexible baffle15FIGURE4.59.-Effect of baffle flexibility onrelative damping (ref.
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