Receptivity to free-stream disturbance waves for hypersonic flow over a blunt cone

A high-order shock-fitting finite difference scheme is studied and used to do direc-tion numerical simulation (DNS) of hypersonic unsteady flow over a blunt cone with fast acoustic waves in the free stream, and the receptivity problem in the blunt cone hypersonic boundary layers is studied. The results show that the acoustic waves are the strongest disturbance in the blunt cone hypersonic boundary layers. The wave modes of disturbance in the blunt cone boundary layers are first, second, and third modes which are generated and propagated downstream along the wall. The results also show that as the frequency decreases, the amplitudes of wave modes of disturbance increase, but there is a critical value. When frequency is over the critial value, the amplitudes decrease. Because of the discontinuity of curvature along the blunt cone body, the maximum amplitudes as a function of frequencies are not monotone.

A 5th order monotonicity-preserving upwind compact difference scheme

Based on an upwind compact difference scheme and the idea of monotonicity-preserving, a 5th order monotonicity-preserving upwind compact difference scheme (m-UCD5) is proposed. The new difference scheme not only retains the advantage of good resolution of high wave number but also avoids the Gibbs phenomenon of the original upwind compact difference scheme. Compared with the classical 5th order WENO difference scheme, the new difference scheme is simpler and small in diffusion and computation load. By employing the component-wise and characteristic-wise methods, two forms of the new difference scheme are proposed to solve the N-S/Euler equation. Through the Sod problem, the Shu-Osher problem and the two-dimensional Double Mach Reflection problem, numerical solutions have demonstrated this new scheme does have a good resolution of high wave number and a robust ability of capturing shock waves, leading to a conclusion that the new difference scheme may be used to simulate complex flows containing shock waves.

DNS of compressible turbulent boundary layer around a sharp cone

Direct numerical simulation of the turbulent boundary layer over a sharp cone with 20° cone angle (or 10° half-cone angle) is performed by using the mixed seventh- order up-wind biased finite difference scheme and sixth-order central difference scheme. The free stream Mach number is 0.7 and free stream unit Reynolds number is 250000/inch. The characteristics of transition and turbulence of the sharp cone boundary layer are compared with those of the flat plate boundary layer. Statistics of fully developed turbulent flow agree well with the experimental and theoretical data for the turbulent flat-plate boundary layer flow. The near wall streak-like structure is shown and the average space between streaks (normalized by the local wall unit) keeps approximately invariable at different streamwise locations. The turbulent energy equation in the cylindrical coordinate is given and turbulent en-ergy budget is studied. The computed results show that the effect of circumferen-tial curvature on turbulence characteristics is not obvious.

Optimization of the MUSCL scheme by dispersion and dissipation

A second-order optimized monotonicity-preserving MUSCL scheme(OMUSCL2) is developed based on the dispersion and dissipation optimization and monotonicity-preserving technique.The new scheme(OMUSCL2) is simple in expression and is easy for use in CFD codes.Compared with the original second-order or third-order MUSCL scheme,the new scheme shows nearly the same CPU cost and higher resolution to shockwaves and small-scale waves.This new scheme has been tested through a set of one-dimensional and two-dimensional tests,including the Shu-Osher problem,the Sod problem,the Lax problem,the two-dimensional double Mach reflection and the RAE2822 transonic airfoil test.All numerical tests show that,compared with the original MUSCL schemes,the new scheme causes fewer dispersion and dissipation errors and produces higher resolution.