Modeling unsteadiness in steady cavity simulations. I - Parametric solutions

Abstract

The goal of this research was to develop a source term module to model the effect of cavity unsteadiness in gas-path only simulations. In this approach the unsteady effect of the cavity on the main gas-path solution is modeled by adding source terms to the right hand side of the Navier-Stokes equations instead of resolving the cavity geometry. This idea increases considerably the numerical efficiency of the scheme by avoiding the computation of small-scale fluid dynamic structures and the geometric details of the cavity. The paper is a two-part work. In the first part the source terms are developed via a lumped deterministic source term (LOST) approach using unsteady complete cavity geometry simulations. A simplified rectangular cavity has been used for the present work. A parametric study of the source term variation with Mach number is presented. Steady simulations of the passage only (i.e., sans cavity) with source terms inserted have been performed and the results obtained compared to timeaveraged solutions that resolve the cavity. The steady state solution using source terms was able to correctly incorporate all unsteady effects present in the time average of the unsteady cavity solution. The second part of the paper discusses the modeling of cavity source terms via back-propagation neural networks. Sample analyses for subsonic Mach numbers, input pressures and boundary layer * Student Member AIAA, Research Assistant f Senior Member AIAA, Associate Professor * Associate Fellow AIAA, Aerospace Engineer Copyright © 2001 by Ashutosh Gangwar, Bojan Lukovic, Paul D. Orkwis and Balu Sakar. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. thicknesses, are presented. A background neural network is trained to generate a source term for any combination of parameters. The resultant flow field is computed for a finite number of test cases. Neural networks are then utilized to model the complex data dependencies instead of computing source terms for every test case. The neural network can be trained to generate quickly a source term for any combination of input parameters. The steady state flow through the passage including the unsteady effect of the cavity was obtained using neural network generated source terms. The resultant flow fields are only slightly different from the calculated time average results and thus encourage the further development of this method.