Moment of inertia and damping of liquids in baffled cylindrical tanks.
Mechanical model for representing moment of inertia and fuel sloshing in baffled cylindrical missile tanks
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Mechanical model for representing moment of inertia and fuel sloshing in baffled cylindrical missile tanks
Cylindrical propellant tanks dynamic stability and parametric resonance, analyzing axial preload, liquid depth, top impedance and ullage pressure by Donnell theory
Cylindrical propellant tanks dynamic stability and parametric resonance, analyzing axial preload, liquid depth top impedance and ullage pressure by Donnell theory
An experimental investigation was conducted to determine the effects of several basic variables upon the damping of the fundamental antisymmetric mode of liquids in right-circular cylindrical tanks without baffles. The variables examined include liquid depth, efflux rate, liquid amplitude, kinematic viscosity, and tank size. The data are presented in dimensionless form and compared with available theory. For the range of variables examined, variations of efflux rate and liquid amplitude were found to have no significant effects on the liquid damping. The following theoretical relationship was found to be adequate for the prediction of the variation of damping with liquid depth, kinematic viscosity, and tank size: [for equation see full text] where v is the kinematic viscosity, R is the cylinder radius, g is the acceleration due to gravity, and h is the liquid depth. However, the constant K was experimentally found in this investigation to have the value 5.23, which is 50 percent higher than the theoretically predicted value.
Head to base transfer function characteristics of partially filled cylindrical propellant tank
Behavior of propellant liquid-vapor interface outflow from cylindrical space vehicle tanks in weightlessness
Symmetric and antisymmetric tank modes of free fluid surface motion under random excitation
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Experimental data are presented for verifying the computer program for computing propellant oscillation modes and frequencies for tanks of any shape, fill level, or orientation. The experimental apparatus including the tank, support and excitation system, and instrumentation is described along with the procedures. Results showing slosh forces and moments are tabulated for different fill heights. It was found that for the vertical tank excited along the long axis, the frequencies of the higher modes are significantly higher than with the tank tilted. Little difference was noted for excitation along the short axis.
An approximate analytical technique is presented for estimating the liquid residual in a tank of arbitrary geometry due to vapor ingestion at any drain rate and acceleration level. The bulk liquid depth at incipient pull-through is defined in terms of the Weber and Bond numbers and two functions that describe the fluid velocity field and free surface shape appropriate to the tank geometry. Numerical results are obtained for the Centaur LH2 tank using limiting approximations to these functions.
A correlation is presented of experimental measurement and analytical prediction of free, planar oscillations of a tank of mercury hung on a pendulum. Measured frequencies are presented for the slosh mode and the pendulum-tank mode, and time-history wave forms are included for qualitative comparisons. The sloshing is represented analytically by a single pendulum or a spring-bob, and the size and location of their inertias are determined by matching forces and moments on the tank surface with linearized hydrodynamic theory for inviscid fluids. It is concluded that such analytical models are identical for small displacements in the present application (as they are in simpler applications) and that they provide excellent simulation of the stiffness and in ertia terms for fuel sloshing.
Skin-stringer Tank Analysis Spreadsheet System (STASS) computer program developed for use as preliminary design software tool that enables quick-turnaround design and analysis of structural domes and cylindrical barrel sections in propellant tanks or other cylindrical shells. Determines minimum required skin thicknesses for domes and cylindrical shells to withstand material failure due to applied pressures (ullage and/or hydrostatic) and runs buckling analyses on cylindrical shells and skin-stringers. Implemented as workbook program, using Microsoft Excel v4.0 on Macintosh II. Also implemented using Microsoft Excel v4.0 for Microsoft Windows v3.1 IBM PC.
Liquid propellant sloshing in a cylindrical quarter tank and its effect on spacecraft stability
Natural frequencies and mode shapes for longitudinal oscillations of liquid filled elastic circular cylindrical tank with flexible inverted conical bulkhead
Several analytical mechanical slosh models for a cylindrical tank with flat bottom are reviewed. Even though spacecrafts use cylinder shaped tanks, most of those tanks usually have elliptical domes. To extend the application of the analytical models for a cylindrical tank with elliptical domes, the modified slosh parameter models are proposed in this report by mapping an elliptical dome cylindrical tank to a flat top/bottom cylindrical tank while maintaining the equivalent liquid volume. For the low Bond number case, the low-g slosh models were also studied. Those low-g models can be used for Bond number > 10. The current low-g slosh models were also modified to extend their applications for the case that liquid height is smaller than the tank radius. All modified slosh models are implemented in MATLAB m-functions and are collected in the developed MST (Mechanical Slosh Toolbox).
Grid stiffened tank structures such as Ortho-Grid and Iso-Grid are widely used in cryogenic tanks for providing stiffening to the tank while reducing mass, compared to tank walls of constant cross-section. If the structure is internal to the tank, it will positively affect the fluid dynamic behavior of the liquid propellant, in regard to fluid slosh damping. As NASA and commercial companies endeavor to explore the solar system, vehicles will by necessity become more mass efficient, and design margin will be reduced where possible. Therefore, if the damping characteristics of the Ortho-Grid and Iso-Grid structure is understood, their positive damping effect can be taken into account in the systems design process. Historically, damping by internal structures has been characterized by rules of thumb and for Ortho-Grid, empirical design tools intended for slosh baffles of much larger cross-section have been used. There is little or no information available to characterize the slosh behavior of Iso-Grid internal structure. Therefore, to take advantage of these structures for their positive damping effects, there is much need for obtaining additional data and tools to characterize them. Recently, the NASA Marshall Space Flight Center conducted both sub-scale testing and computational fluid dynamics (CFD) simulations of slosh damping for Ortho-Grid and Iso-Grid tanks for cylindrical tanks containing water. Enhanced grid meshing techniques were applied to the geometrically detailed and complex Ortho-Grid and Iso-Grid structures. The Loci-STREAM CFD program with the Volume of Fluid Method module for tracking and locating the water-air fluid interface was used to conduct the simulations. The CFD simulations were validated with the test data and new empirical models for predicting damping and frequency of Ortho-Grid and Iso-Grid structures were generated.
An existing empirical analysis relating to the reorientation of liquids in cylindrical tanks due to propulsive settling in a low gravity environment was extended to include the effects of geyser formation in the Weber number range from 4 to 10. Estimates of the minimum velocity increment required to be imposed on the propellant tank to achieve liquid reorientation were made. The resulting Bond numbers, based on tank radius, were found to be in the range from 3 to 5, depending upon the initial liquid fill level, with higher Bond number required for high initial fill levels. The resulting Weber numbers, based on tank radius and the velocity of the liquid leading edge, were calculated to be in the range from 6.5 to 8.5 for cylindrical tanks having a fineness ratio of 2.0, with Weber numbers of somewhat greater values for longer cylindrical tanks. It, therefore, appeared to be advantageous to allow small geysers to form and then dissipate into the surface of the collected liquid in order to achieve the minimum velocity increment. The Bond numbers which defined the separation between regions in which geyser formation did and did not occur due to propulsive settling in a spherical tank configuration ranged from 2 to 9 depending upon the liquid fill level.
Dynamic stability and parametric resonance in cylindrical shell system, part 2