Numerical investigations on interactions between 2D/3D conical shock wave and axisymmetric boundary layer at Ma=2.2

Numerical simulation and analysis are carried out on interactions between a 2D/3D conical shock wave and an axisymmetric boundary layer with reference to the experiment by Kussoy et al., in which the shock was generated by a 15-deg half-angle cone in a tube at 15-deg angle of attack (AOA). Based on the RANS equations and Menter's SST turbulence model, the present study uses the newly developed WENO3-PRM211 scheme and the PHengLEI CFD platform for the computations. First, computations are performed for the 3D interaction corresponding to the conditions of the experiment by Kussoy et al., and these are then extended to cases with AOA = 10-deg and 5-deg. For comparison, 2D axisymmetric counterparts of the 3D interactions are investigated for cones coaxial with the tube and having half-cone angles of 27.35-deg, 24.81-deg, and 20.96-deg. The shock wave structure, vortex structure, variable distributions, and wall separation topology of the interaction are computed. The results show that in 2D/3D interactions, a new Mach reflection-like event occurs and a Mach stem-like structure is generated above the front of the separation bubble, which differs from the model of Babinsky for 2D planar shock wave/boundary layer interaction. A new interaction model is established to describe this behavior. The relationship between the length of the circumferentially unseparated region in the tube and the AOA of the cone indicates the existence of a critical AOA at which the length is zero, and a prediction of this angle is obtained using an empirical fit, which is verified by computation. The occurrence of side overflow in the windward meridional plane is analyzed, and a quantitative knowledge is obtained. To elucidate the characteristics of the 3D interaction, the scale and structure of the vortex and the pressure and friction force distributions are presented and compared with those of the 2D interaction

Improvements to enhance robustness of third-order scale-independent WENO-Z schemes

Although there are many improvements to WENO3-Z that target the achievement of optimal order in the occurrence of the first-order critical point (CP1), they mainly address resolution performance, while the robustness of schemes is of less concern and lacks understanding accordingly. In light of our analysis considering the occurrence of critical points within grid intervals, we theoretically prove that it is impossible for a scale-independent scheme that has the stencil of WENO3-Z to fulfill the above order achievement, and current scale-dependent improvements barely fulfill the job when CP1 occurs at the middle of the grid cell. In order to achieve scale-independent improvements, we devise new smoothness indicators that increase the error order from 2 to 4 when CP1 occurs and perform more stably. Meanwhile, we construct a new global smoothness indicator that increases the error order from 4 to 5 similarly, through which new nonlinear weights with regard to WENO3-Z are derived and new scale-independents improvements, namely WENO-ZES2 and -ZES3, are acquired. Through 1D scalar and Euler tests, as well as 2D computations, in comparison with typical scale-dependent improvement, the following performances of the proposed schemes are demonstrated: The schemes can achieve third-order accuracy at CP1 no matter its location in the stencil, indicate high resolution in resolving flow subtleties, and manifest strong robustness in hypersonic simulations (e.g., the accomplishment of computations on hypersonic half-cylinder flow with Mach numbers reaching 16 and 19, respectively, as well as essentially non-oscillatory solutions of inviscid sharp double cone flow at M=9.59), which contrasts the comparative WENO3-Z improvement

Laminar to Turbulent Transition in Hypersonic Flows: Extension of a RANS transition model for high speed flows (TN5200)

TN520

Detached Eddy Simulation of Base Flows under Subsonic Free Stream Conditions

The present work focuses on the numerical simulation of a base flow around a generic rocket model for subsonic flow conditions. In a preliminary study the flow for two reduced geometries are investigated to obtain an optimized discretization of the flow field for a detached eddy simulation (DES). First, an inflow plane with prescribed values from a Reynolds averaged Navier-Stokes (RANS) solution is used which avoids the unsteady simulation of the model support and most of the model body. Second, the problem size is halved by exploiting the symmetry of the geometry. In both calculations an indicator is tested, which quantifies the local grid quality with respect to the turbulent kinetic energy resolved by the DES. According to this indicator the grid resolution in the first case is very good and in the second case sufficient in the regions of interest. Although the physical interpretation is limited due to the approximations made, the results indicate a strong connection between the base flow and the wake of the support

Evaluation of Turbulence Models in Predicting Hypersonic and Subsonic Base Flows Using Grid Adaptation Techniques

The flows behind the base of a generic rocket, at both hypersonic and subsonic flow conditions, are numerically studied. The main concerns are addressed to the evaluation of turbulence models and the using of grid adaptation techniques. The investigation focuses on two configurations, related to hypersonic and subsonic experiments. The applicability tests of different turbulence models are conducted on the level of two-equation models calculating the steady state solution of the Reynolds-averaged Navier-Stokes(RANS) equations. All used models, the original Wilcox k-omega, the Menter shear-stress transport (SST) and the explicit algebraic Reynolds stress model(EARSM) formulation, predict an asymmetric base flow in both cases caused by the support of the models. A comparison with preliminary experimental results indicates a preference for the SST and EARSM results over the results from the older k-omega model. Sensitivity studies show no significant influence of the grid topology or the location of the laminar to turbulent transition on the base flow field, but a strong influence of even small angles of attack is reported from the related experiments.German Research Foundation (Deutsche Forschungsgemeinschaft-DFG) [Sonderforschungsbereich Transregio 40

Modeling of the interaction between a space vehicle’s external flow and it’s plume

This paper is concerned with the numerical modeling of the flow behind the base of a generic rocket. The DLR TAU code is first applied in a design study about the support of the model in the hypersonic environment. At the given circumstances a slanted support shows no advantage over an orthogonal design. The investigation then focuses on two configurations, related to hypersonic and to subsonic experiments conducted in Cologne and Aachen respectively. The applicability tests of different turbulence models are started on the level of two equation models calculating the steady state solution of the Reynolds averaged Navier Stokes equations. It will be continued with the calculation of unsteady flow fields around these simplified configurations as well as configurations with increasing complexity. All used models - the original Wilcox k-ω, the Menter SST and the EARSM formulation - predict an asymmetric base flow in both cases caused by the support of the models. A first comparison with preliminary experimental results indicates a preference for the SST and EARSM results over the results from the older k-ω model

Numerical Simulation of a Generic Rocket Base Flow with Plume in a Supersonic Environment

The numerical investigation is based on three detached eddy simulations. Similar to the experiments one simulation is performed for the configuration with a closed nozzle exit. The second one includes the nozzle flow and the interaction of the plume with the base flow. A third simulation with a refined resolution of the region where the nozzle shear layer expanded has been started to address the deviation of the numerically nearly steady expansion of the plume to the experimentally observed unsteadiness of the plume. Due to the ongoing calculations the focus of the discussion is on the mean values in comparison to respective experimental results. Good agreement is achieved for the position of the recompression shock in the base flow without plume and for Pitot pressure profiles taken at the edge of the base and in the plume. The influence of the support on the boundary layer of the model is well captured. The nozzle flow and the expansion of the plume are reproduced within the accuracy of the measurements