Surrogate Model-Based Strategy for Cryogenic Cavitation Model Validation and Sensitivity Evaluation

Cryogenic cavitation experiences phase change in an environment where the vapor pressure is temperature dependent. The cavitation dynamics have critical implications on the performance and safety of liquid rocket engines, but there is no established method to estimate the actual loads due to cavitation on the inducer blades. To help develop such a computational capability, we conduct a systematic investigation of a transport-based, homogeneous cryogenic cavitation model for code validation and model improvement exercises. We assess the role of model parameters in the cavitation model and uncertainties in material properties via global sensitivity analysis coupled with multiple surrogate models including polynomial response surface, radial basis neural network, Kriging and a weighted average composite model. The results indicate that while the predictions are more sensitive to changes in cavitation model parameters than uncertainties in material properties, the impact of uncertainty in temperature dependent vapor pressure on the performance is significant. We calibrate the cryogenic cavitation model parameters using a multiple surrogates-based optimization strategy. The optimal parameters increase the importance of condensation terms and show improved prediction performance on a number of benchmark problems. Nomenclature b Estimated coefficient vector associated with polynomial basis functions dest C , prod C Empirical parameters used in cavitation model Cp Pressure coefficient Cpm Specific heat of mixture 1 2 , C C ε ε k ε − turbulence model coefficients D Characteristic length scale E(f(x)) Expected value of f(x) with respect to x f(x) Function of variable vector x fv Mass fraction of vapor h Specific enthalpy k Turbulent kinetic energy L Latent heat of vaporization m − ɺ , m + ɺ Cavitation source terms min (a, b) Minimum of a and b max (a, b) Maximum of a and b NRBF Number of radial basis functions * PhD Candidate, Student Member AIAA † Graduate Student, Student Member AIAA ‡ Visiting Professor, AIAA Member § Distinguished Professor, Fellow AIAA ** Clarence L “Kelly” Johnson Professor, Fellow AIAA 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 9 12 July 2006, Sacramento, California AIAA 2006-5047 Copyright © 2006 by Tushar Goel, Jinhui Zhao, Siddharth Thakur, Raphael Haftka, Wei Shyy. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. American Institute of Aeronautics and Astronautics 2 Ns Number of sampled points Nsm Number of surrogate models N β Number of basis functions in polynomial response surface approximation Nvar Number of variables p Pressure Pdiff L2 norm of difference between experimental and predicted pressure Pt Production term in turbulence model