Damped Fluid Oscillations in a Circular Cylindrical Tank Due to Bending of Tank Wall

Bauer, Helmut F.

doi:10.21236/ad0201440

Cited by 27 publications

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“…£e"(f, g mn <*)) sinh (Z£)df [4b] In the limiting case of zero ellipticity (c -*-0, |ce* -> r), the previous results agree with those of a circular cylindrical tank (4,5).…”

Section: /mentioning

confidence: 63%

“…The incompressible potential problem (3,4,5,13) is solved by separation of variables and expansions analogous to those in the problem of vibration of elliptic membrane (10).…”

Section: Force and Moment Acting On The Tankmentioning

confidence: 99%

“…Then yk* = J2 Qny n +k [5] 71=1 It is found that the following identity holds between the observed values y k and the predicted values y k * m /ra\ 2/o* = E (-l) y+1 ( • \Vi + 0'(Vi* ~ Vi)] [6] This identity may be employed as a prediction formula, and we term it "the short formula of prediction." Thus the predicted value is given as a linear function of the last m observed values and the last m predicted values.…”

Section: Finite Prediction Formulamentioning

confidence: 99%

“…For k = -1 it would appear that Equation [7] cannot be applied because y 0 is not known. However, if we assume y 0 = y 0 *, then Equation [7] does yield a value for 2/-1*. It can be shown, moreover, that y-i* = p(-l) where p(x) is the polynomial minimizing Equation [2].…”

Section: Finite Prediction Formulamentioning

confidence: 99%

“…For any arbitrary limiting value of R t with a given nose radius R bo , the range of flight Mach numbers and altitudes can be found, below which the stagnation flow can be considered < 10-2 i where relative mass fractions have been introduced for the mole fractions in the rate term. According to Hirschfelder (2) J 7 \5/2 k, = 1.2 X 10 16 ( -1 300/ (moles) 2 sec [7] and as noted, is calculated using T w . Using values given in (3 and 4), R t R bQ was computed and plotted as a function of altitude with Mach number as a parameter (Fig.…”

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confidence: 99%

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Tecnical Notes

Adamson

1960

ARS Journal

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A N IMPORTANT question which arises in the consideration of aerodynamic heating problems is that of ascertaining the flight regimes in which nonequilibrium reaction occurs. A general idea of this regime may be gained by an order of magnitude analysis where the characteristic time of reaction is compared to the characteristic residence time, with limiting values of the ratios obtained, arbitrarily assigned. Moreover, such an order of magnitude analysis is useful in those cases where the flow is very far from equilibrium; and recombination may take place, finally, along the surface, since an idea of the wetted area of reaction may be obtained. This type of study is of value in those cases where either catalytic or reaction poisoning surfaces are being considered.In this analysis, the flow field is assumed to be that around a blunt body at hypersonic speeds such that a detached shock exists. The field is divided into two separate regions, each with its own characteristic time. One is the stagnation point flow between the detached shock and the body. The other is the laminar boundary layer flow along the body surface. Each region has a characteristic residence time which is to be compared with the characteristic chemical reaction time.According to Li and Geiger (1) the detachment distance between a detached shock and the stagnation point is, as in Fig.l where k •• Pco/(pS)x=o s = conditions immediately behind the shock R 8a = radius of curvature if the shock at x -0 If, as assumed by Li, the radius of curvature of the shock is the same as that of the body, at x = 0, then b may be calculated. Also, from his calculations, the velocity in the y direction outside the boundary layer is essentially proportional to y; since the v velocity in the boundary layer is well approximated by a linear function, the average velocity in the region between the detached shock and the body along the stagnation streamline is, to good approximation Vavg = Vs/2The residence time in this region is thus[3] The characteristic chemical time consistent with Equation [3] is thenwhere X is any third body and the subscript 2 refers to oxygen atoms. (w 2 ) recombination is that part of the reaction rate which holds for the recombination of oxygen atoms, since this is the essential reaction in the decreasing temperature field. It is calculated using the concentration of 0 and 0 2 existing behind a normal shock, but at the wall temperature. This is a very conservative calculation, since an average temperature between the wave and the body would certainly be higher than the wall temperature, and the recombination rate term is sensitive to changes in temperature. Since no accurate value for the average temperature was known and since it is evident that a linear variation is unrealistic, the conservative value for the reaction rate constant was chosen. For a Shock Boundary / Layer Blunt Body V, Oo Fig. 1 Stagnation point region between a detached shock and a blunt body EDITOR'S NOTE: The Technical Notes and Technical Comments sections of ARS JOURNAL are ...

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“…£e"(f, g mn <*)) sinh (Z£)df [4b] In the limiting case of zero ellipticity (c -*-0, |ce* -> r), the previous results agree with those of a circular cylindrical tank (4,5).…”

Section: /mentioning

confidence: 63%

“…The incompressible potential problem (3,4,5,13) is solved by separation of variables and expansions analogous to those in the problem of vibration of elliptic membrane (10).…”

Section: Force and Moment Acting On The Tankmentioning

confidence: 99%

Section: Finite Prediction Formulamentioning

confidence: 99%

Section: Finite Prediction Formulamentioning

confidence: 99%

mentioning

confidence: 99%

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Tecnical Notes

Adamson

1960

ARS Journal

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Note on Linear Hydroelastic Sloshing

Bauer

Siekmann

1969

Z Angew Math Mech

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The present paper deals with the general problem of hydroelastic sloshing of a liquid in a partially filled circular cylindrical container with either rigid walls and a flexible flat bottom or a rigid bottom and elastic walls. Free coupling oscillations of the tank‐liquid system are investigated including the effect of surface tension. Forces and moments excerted on the walls by the liquid as well as the form of the free surface are determined. A procedure to investigate approximately the oscillations of the liquid under weak gravitation is outlined.

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Analysis of shear stress bending moment and deflection design of side wall for circular water tank resting on ground with varying outer wall cross section and its comparison using manual and STAAD Pro

Rabbani

Tholkapiyan²

2023

Materials Today: Proceedings

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Damped Fluid Oscillations in a Circular Cylindrical Tank Due to Bending of Tank Wall

Cited by 27 publications

References 0 publications

Tecnical Notes

Tecnical Notes

Note on Linear Hydroelastic Sloshing

Analysis of shear stress bending moment and deflection design of side wall for circular water tank resting on ground with varying outer wall cross section and its comparison using manual and STAAD Pro

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