High-speed turbulent flows with shock waves are characterized by high localized surface heat transfer rates. Computational predictions are often inaccurate due to the limitations in modelling of the unclosed turbulent energy flux in the highly non-equilibrium regions of shock interaction. In this paper, we investigate the turbulent energy flux generated when homogeneous isotropic turbulence passes through a nominally normal shock wave. We use linear interaction analysis where the incoming turbulence is idealized as being composed of a collection of two-dimensional planar vorticity waves, and the shock wave is taken to be a discontinuity. The nature of the postshock turbulent energy flux is predicted to be strongly dependent on the angle of incidence of the incoming waves. The energy flux correlation is also decomposed into its vortical, entropy and acoustic contributions to understand its rapid non-monotonic variation behind the shock. Three-dimensional statistics, calculated by integrating two-dimensional results over a prescribed upstream energy spectrum, are compared with available data from direct numerical simulations. A detailed budget of the governing equation is also considered in order to gain insight into the underlying physics.
We perform direct numerical simulations of shock-wave/boundary-layer interactions (SBLI) at Mach number M ∞ = 1.7 to investigate the influence of the state of the incoming boundary layer on the interaction properties. We reproduce and extend the flow conditions of the experiments performed by Giepman et al. [1], in which a spatially evolving laminar boundary layer over a flat plate is initially tripped by an array of distributed roughness elements and impinged further downstream by an oblique shock wave. Four SBLI cases are considered, based on two different shock impingement locations along the streamwise direction, corresponding to transitional and turbulent interactions, and two different shock strengths, corresponding to flow deflection angles φ = 3 o and φ = 6 o . We find that, for all flow cases, shock induced separation is not observed, the boundary layer remains attached at φ = 3 • and close to incipient separation at φ = 6 • , independent of the state of the incoming boundary layer.We characterize the regions of instantaneous separation by computing the statistical probability (γ) of the wall points with local flow reversal. The analysis shows that the turbulent interactions are characterized by a higher peak of γ, although the region of separation is slightly wider in the transitional interaction cases. The extent of the arXiv:1709.05096v1 [physics.flu-dyn] 15 Sep 2017 interaction zone is mainly determined by the strength of the shock wave, and the state of the incoming boundary layer has little influence on the interaction length scale L.The scaling analysis for L and the separation criterion developed by Souverein et al.[2] for turbulent interactions are found to be equally applicable for the transitional interactions. The findings of this work suggest that a transitional interaction might be the optimal solution for practical SBLI applications, as it removes the large separation bubble typical of laminar interactions and reduces the extent of the high-friction region associated with an incoming turbulent boundary layer.
SUMMARYContributions to the aerodynamics development have to be involved to achieve an increase in quality, reducing time and computer costs. Therefore, this work develops an optimization method based on the ÿnite volume explicit Runge-Kutta multi-stage scheme with central spatial discretization in combination with multigrid and preconditioning. The multigrid approach includes local time-stepping and residual smoothing. Such a method allows getting the goal of compressible and almost incompressible solution of uid ows, having a rate of convergence almost independent from the Mach number. Numerical tests are carried out for the NACA 0012 and 0009 airfoils and three-dimensional wings based on NACA proÿles for Mach-numbers ranging from 0.8 to 0.002 using the Euler equations. These calculations are found to compare favorably with experimental and numerical data available in the literature. Besides, it is worth pointing out that these results build on earlier ones when ÿnding appropriate new three-dimensional aerodynamical geometries.
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