Shock Wave

Producing closed-cell foams is generally cheaper and simpler than open-cell foams. However, the acoustic and filtration efficiency of closed-cell foam materials is generally poor because it is very difficult for fluid or acoustic waves to penetrate into the material. A new method using shock waves to remove the membranes closing the cell pores (known as reticulation) and thus to improve the acoustic and filtration behavior of closed-cell foam material is presented. Various shock treatments have been carried out on polyurethane and polyimide foams and the following conclusions were drawn: (1) reticulation efficiency increased and thus the airflow resistivity and tortuosity decreased when increasing the amplitude of the shock treatment; (2) the rigidity of the foam is decreased; (3) the process is reliable and repeatable and (4) obtained acoustic performance is comparable to classical thermal reticulation.

We propose a new model and a solution method for two-phase compressible flows. The model involves six equations obtained from conservation principles applied to each phase, completed by a seventh equation for the evolution of the volume fraction. This equation is necessary to close the overall system. The model is valid for fluid mixtures, as well as for pure fluids. The system of partial differential equations is hyperbolic. Hyperbolicity is obtained because each phase is considered to be compressible. Two difficulties arise for the solution: one of the equations is written in non-conservative form; non-conservative terms exist in the momentum and energy equations. We propose robust and accurate discretisation of these terms. The method solves the same system at each mesh point with the same algorithm. It allows the simulation of interface problems between pure fluids as well as multiphase mixtures. Several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible. The method provides reliable results, is able to compute strong shock waves, and deals with complex equations of state.

Turbulence modeling remains a major source of uncertainty in the computational prediction of aerodynamic forces and heating for hypersonic vehicles. Dodson developed a methodology for assessing experiments appropriate for turbulence model validation and critically surveyed the existing hypersonic experimental database. We limit the scope of our current effort by considering only twodimensional/axisymmetric flows in the hypersonic speed regime where calorically perfect gas models are appropriate. We extend the prior database of recommended hypersonic experiments by adding three new cases. The first two cases, the flat plate/cylinder and the sharp cone, are canonical test cases which are amenable to theory-based correlations, and these correlations are discussed in detail. The third case added is the two-dimensional shock impinging on a flat plate boundary layer. The second goal is to review and assess the validation usage of various turbulence models on the existing experimental database. Here we limit the scope to one-and two-equation turbulence models where integration to the wall is used (i.e., we omit studies involving wall functions). In order to preserve a models prior validation history, we omitted corrections to the standard turbulence models in cases where the impact of such corrections on low-speed flows had not been adequately addressed (either through a re-validation of the models on a wide range of low-speed test cases or theoretical arguments). A methodology for validating turbulence models is given, and turbulence model comparisons from various authors are compiled and presented in graphical form. Conclusions are drawn for those models which have been applied to a sufficiently wide range of two-dimensional/axisymmetric hypersonic flows, and recommendations for future experimental and modeling efforts are given. ongoing research efforts in advanced turbulence models such as Reynolds stress models and large eddy simulation, the most complex models currently employed in design studies (where a large number of parametric cases must be considered) are one-and two-equation turbulence models. We therefore limit the current study to these models. We also limit this study to models where integration of the governing equations to the wall is performed, thereby eliminating the use of wall functions. This choice was primarily driven by the fact that a majority of the cases of interest for hypersonic flows include shock-boundary layer interactions, where the assumptions inherent in the use of wall functions are difficult to justify. We further limit our scope to cases where the transition from laminar to turbulent flow occurs naturally, and where this transition location is specified in the experimental description. The focus here is not on the prediction of transition, which itself is a difficult challenge for hypersonic flows. Finally, the effects of surface roughness, ablation, chemical reactions, real gases, and body rotation are all neglected as the existing experimental database does not yet adequately address these phenomena. Typically turbulence models have been developed for incompressible flows and then extended without much change to compressible flows. This approach in many cases is not adequate. For complex turbulent flows, Coakley et al. [86] have recommended corrections to apply to the twoequation and turbulent eddy viscosity models. In addition, Aupoix and Viala [87] have proposed corrections to the model for compressible flows. The authors have used flat plate flows and mixing layers to assess the compressible corrections introduced. Significant efforts to assess turbulence models for compressible flows have occurred at NASA Ames Research Center. The results of these investigations have been published by Horstman [88], Horstman [89], Coakley and Huang [84], Huang and Coakley [90], Coakley et al.[86], Bardina et al. [91], and Bardina et al. [92]. See Appendix A for additional discussion of the compressibility effects for hypersonic flows. 2. Turbulence models 2.1. One-equation models (eddy-viscosity transport models) 2.1.1. Spalart-Allmaras (SA) A transport equation for determining the eddy viscosity with near-wall effects included has been developed by Spalart and Allmaras [7], [8]. The accuracy of the predictions with the Spalart-Allmaras model is fairly insensitive to the y + spacing at the wall relative to the two-equation models, at least for high-speed flows [9]. Our experience with this model suggests that it has a good combination of accuracy and robustness for attached flows. While stable for large y + values, the maximum for accurate solutions should be roughly y + ≤ 1. 2.1.2. Goldberg (UG) Goldberg has developed a one-equation turbulence model [158], [97]. 2.1.3. Menter one-equation model (MTR) Menter has developed a one-equation turbulence model [6]. 2.2. Two-equation models 2.2.1. Jones and Launder high Reynolds number k-ε (kεJL) The basic k-ε model was developed by Jones and Launder [10] in 1972, and is valid for high Reynolds number flows only. Damping functions or wall functions must be used in order to handle wall-bounded flows.