A new multi-phase model for low speed gas/liquid mixtures is presented; it does not require ad-hoc closure models for the variation of mixture density with pressure and yields thermodynamically correct acoustic propagation for multi-phase mixtures. The solution procedure has an interface-capturing scheme that incorporates an additional scalar transport equation for the gas void fraction. Cavitation is modeled via a finite rate source term that initiates phase change when liquid pressure drops below its saturation value. The numerical procedure has been implemented within a multi-element unstructured framework CRUNCH that permits the grid to be locally refined in the interface region. The solution technique incorporates a parallel, domain decomposition strategy for efficient 3D computations. Detailed results are presented for sheet cavitation over a cylindrical head form and a NACA 66 hydrofoil.

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Reynolds-Averaged Navier-Stokes (RANS) models are not very accurate for high Reynolds number, compressible jet-in-crossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form error in the RANS model. In this work we pursue the hypothesis that RANS predictions could be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow. We formulate a Bayesian inverse problem to estimate 3 RANS parameters (C µ , C ǫ2 , C ǫ1) and use a Markov chain Monte Carlo (MCMC) method to develop a probability density function for them. The cost of MCMC is addressed by developing statistical surrogates for the RANS models. We find that only a subset of the (C µ , C ǫ2 , C ǫ1) space, R, supports realistic flow simulations. We use R as our prior belief when formulating the inverse problem. It is enforced with a classifier in our MCMC solution. We find that the calibrated parameters improve predictions of the entire flowfield substantially, compared to the nominal/literature values of (C µ , C ǫ2 , C ǫ1); further, this improvement is seen to hold for interactions at other Mach numbers and jet strengths for which we have experimental data to provide a comparison. We also quantify the residual error, which is an approximation of the model-form error; it is most easily measured in terms of turbulent stresses.

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Results from an investigation of the predictive capabilities of various two-equation RANS models for the jet-in-crossflow problem are presented. The flow regime consists of a supersonic jet issuing into a transonic cross flow. The parameters varied are the jet momentum ratio, jet inclination angle, and cross flow Mach number. The goal of the investigation is to characterize the behavior of the turbulence models in this flow regimethis has implications for accurate predictions of vortex-fin interactions. The results of this study show that none of the RANS model examined are capable of capturing the vortex location and strength accurately. A detailed analysis of available experimental data shows that the Boussinessq approximation, fundamental to these models, is itself deficient for this category of flows. The analysis shows that vastly different length scales are associated with each component of the Reynolds stress and a single length scale model deficient in capturing this.