Validation, Uncertainty Quantification and Uncertainty Reduction for a Shock Tube Simulation

Abstract

While we rely on simulations to predict the response of complex systems, we recognize that the models that underlie these simulations are never perfect. Comparison of simulations with experiments is an important tool for exposing limitations of models, and providing insights into which models need improvement. However, errors in numerical model and uncertainties in experiments can obscure the true discrepancies between predictions and physical reality, and therefore need to be reduced. In order to expose model deficiencies it is important to assess the magnitude of these uncertainties and reduce them until modeling errors become apparent. In this paper we describe an effort to reduce numerical model errors and expose physics model errors for shock tube simulations of a shock wave hitting a curtain of particles. The experiment was designed to explore models of particle interactions with the flow, and was performed initially with a flux calculation model known as AUSM+. Uncertainties in experimental conditions were propagated into simulations output with the aid of the method of converging lines, which generates simulations along multiple lines converging to a single point in input space. This approach exposed noisy behavior of the simulations that appeared to be numerical in nature. However, discrepancies between lines and negative pressures and temperatures at some points indicated modeling deficiencies. When the flux calculation model was corrected to a better numerical model known as AUSM+up, the numerical noise was greatly reduced and the discrepancy between lines eliminated, thus showing that modeling errors can produce noise that wrongly appears as numerical in nature. Another curiosity of the present study was that when the numerical model was improved, the discrepancy between simulations and experiments increased, pointing to cancelling modeling errors in the original simulations.