Interior fluid dynamics of liquidfilled projectiles
Abstract
Theoretical and numerical studies were conducted to analyze the flow in spinning and coning liquidfilled payload cylinders and to provide efficient tools for estimating and calculating the liquid moments as input data for flight simulations. Earlier analytical studies for cylinders of large aspect ratio were extended to the nonlinear problem to provide estimates for all moments. This perturbation analysis is currently used to investigate the influence of partial liquid fills, central rods, and twofluid fills on the moments. A new method was developed to obtain the moments from volume integrals rather than surface integrals and thus increase the accuracy of the results at fixed numerical approximation. An efficient spectral code was developed for routine application to solve the threedimensional NavierStokes equations. Utility of this code for efficient flight simulations was demonstrated. The code was applied to investigate liquid moments, velocity field, and pressure field in situations of pure forcing as well as resonance with inertial waves at Reynolds numbers up to 2000. For the linearized problem, a simplified set of equations was developed that permits closed form solutions for spatial eigenfunctions and highly efficient solution by spectral methods.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 December 1989
 Bibcode:
 1989STIN...9020330H
 Keywords:

 Computational Fluid Dynamics;
 Fluid Flow;
 Liquid Filled Shells;
 Liquid Surfaces;
 Moments;
 Projectiles;
 Spin Dynamics;
 Aspect Ratio;
 Ballistics;
 Conical Bodies;
 Elastic Waves;
 Flight Simulation;
 Integrals;
 NavierStokes Equation;
 Nonlinear Equations;
 Numerical Stability;
 Perturbation Theory;
 Pressure Distribution;
 Reynolds Number;
 Spectral Theory;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer