Direct numerical simulation of the interaction of isotropic turbulence with a shock wave using shock-fitting (original) (raw)
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Direct numerical simulation of a Mach 2 shock interacting with isotropic turbulence
Applied scientific research, 1995
Direct Numerical Simulation (DNS) and linear analysis of a shock interacting with incompressible and compressible isotropic turbulence is conducted. A dependence of amplification ratios on the degree of compressibility of the incoming flow is found. It can be shown that the enhancement of rms values of turbulent quantifies across the shock varies according to the ratio of compressible to incompressible kinetic energy X (exact definition see eq. 8). Inflow conditions with high values of X display reduced amplification ratios of TKE and thermodynamic quantities while vorticity fluctuations are enhanced more strongly. The different behaviour of the turbulent kinetic energy (TKE) is due to the reduced pressure diffusion term in the TKE-equation. Experiments show qualitatively a similar behaviour as the simulation with incompressible inflow conditions, but they could so far not confirm our findings of reduced amplification rates in the compressible case, one of the reasons being the lack of knowledge of all flow parameters upstream of the shock front and the inability to generate isotropic turbulence in real life experiments. For the DNS we use a third order in space shock-capturing scheme based on the ENO algorithm of Harten [10] together with an approximate Riemann solver. This non-TVD scheme turned out to have many advantages over other common Godunov-type high resolution schemes for the specific problem of a shock interacting with turbulent fields.
Numerical Simulation of Shock-Turbulence Interactions Using High-Order Shock-Fitting Algorithms
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2010
High-order methods are critical for reliable numerical simulation of strong-shock and turbulence interaction problems. Such problems are not well understood due to limitations of numerical methods. Most widely used shock capturing methods for the numerical simulation of compressible flows are inherently dissipative, only first order accurate and may incur numerical oscillations near the shock waves. In our previous work [1, 2] we have shown that algorithms based on shock-fitting methodology can solve the flow with highorder accuracy near as well as away from the shocks without any numerical oscillations. In the current study, we extend the fifth order shock-fitting algorithm to carry out Direct Numerical Simulations (DNS) of interactions of shock waves with realistic isotropic turbulence. Incoming isotropic turbulence is developed in a temporal simulation of solenoidal fluctuations in a periodic box. Using Taylor's hypothesis these fluctuations are prescribed upstream of the shock wave and the flow behind the shock wave is computed using the shock fitting algorithm. In this paper we investigate interactions of isotropic turbulence with normal shock waves of Mach numbers 1 2.0 10.0 M and compare the results against numerical and Linear Interaction Analysis (LIA) results available in the literature. The results follow the trends observed in the previous studies which were only for the weak shocks. It is observed that velocity fluctuations are amplified across the shock wave and almost same amplification in turbulent kinetic energy observed for stronger than Mach 4 shocks. Transverse vorticity fluctuations are significantly increased across the shock and amplifications increase with increasing Mach number. Taylor microscales decrease as flow passes through a shock wave and amplification factor for transverse microscale agree well with the LIA results. Overall, the results generally confirm the findings by earlier numerical simulations and provide results for stronger shocks than those considered by numerical studies in the past. In future, higher Reynolds number flows will be considered with larger computer resources to avoid excessive viscous decay observed in the current study.
Journal of Computational Physics, 2010
Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.
Shock/turbulence interaction: turbulence modeling and scramjet application
2009
Shock/turbulent boundary layer interaction is a focus of active research because of its relevance to practical applications like scramjet inlets. Flow separation due to shock waves in the inlet duct can significantly deteriorate the performance. Computational fluid dynamic prediction of shock/turbulent boundary layer interactions are often limited by the accuracy of the turbulence models. Traditional models like k ǫ, k ω and Spalart-Allmaras cannot predict the correct level of turbulent kinetic energy k downstream of a shock wave. In-depth study of the equations governing k-amplification at a shock reveals new physical mechanisms caused by the coupling of shock motion with the turbulent velocity fluctuations. Incorporating this additional term in the turbulence models results in significant improvement in their predictions. The new models are validated against experimental data available for canonical shock/turbulent boundary layer interactions. In-house CFD codes with advanced turb...
Interaction of a thin shock with turbulence. I. Effect on shock structure: Analytic model
Physics of Fluids, 2008
BOUTþþ is a software package designed for solving plasma fluid models. It has been used to simulate a wide range of plasma phenomena ranging from linear stability analysis to 3D plasma turbulence and is capable of simulating a wide range of drift-reduced plasma fluid and gyro-fluid models. A verification exercise has been performed as part of a EUROfusion Enabling Research project, to rigorously test the correctness of the algorithms implemented in BOUTþþ, by testing order-of-accuracy convergence rates using the Method of Manufactured Solutions (MMS). We present tests of individual components including time-integration and advection schemes, nonorthogonal toroidal field-aligned coordinate systems and the shifted metric procedure which is used to handle highly sheared grids. The flux coordinate independent approach to differencing along magnetic field-lines has been implemented in BOUTþþ and is here verified using the MMS in a sheared slab configuration. Finally, we show tests of three complete models: 2-field Hasegawa-Wakatani in 2D slab, 3-field reduced magnetohydrodynamics (MHD) in 3D field-aligned toroidal coordinates, and 5-field reduced MHD in slab geometry. [