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The study of differential schemes with high accuracy and low dispersion is of great significance for the numerical simulation of aeroacoustics over complex geometries. The midpoint-and-node-to-node explicit finite difference is employed to solve the flux derivatives of the linear Euler equations for improving the robustness. To obtain the numerical flux at the center of the grid element, we adopted a hybrid interpolation method of center and upwind interpolations, combined with a symmetrical conservative metric method, to achieve high-resolution discretization of the acoustic field variables and geometric variables of the structural grid. To suppress spurious oscillations and improve the resolution of discontinuous regions, a family of mapping functions is developed to establish different smoothness indicators and applied to the sixth-order weighted compact nonlinear hybrid scheme (WCNHS), forming a new WCNHS scheme based on piecewise exponential mapping functions (WCNHS-Pe). The approximate dispersion relation shows that the dispersion error and numerical dissipation of WCNHS-Pe are smaller than those of WCNHS with a simple mapping function to the original weights in Jiang and Shu and other mapping function-weighted WCNHS schemes. We have applied various WCNHS schemes to the numerical simulation of the Shu–Osher problem, propagation of Gaussian impulses on two-dimensional wavy grids, sound transmission at discontinuous interfaces, propagation of Gaussian impulses on three-dimensional wavy grids, etc. Numerical results indicate that the WCNHS-Pe scheme has better discontinuity capture capability, higher resolution, and lower dispersion under the same differential stencil, and is suitable for computational aeroacoustics of complex geometries.

The streaky boundary layers have very important roles in laminar-turbulent transition. Streaks of appropriate size can influence stabilities in boundary layers. In this paper, the effect of steady streamwise elongated, spanwise periodic wall heating elements on the first mode instability in supersonic flat plate boundary layers was investigated. For the balance of the efficient and accuracy, the linearized Navier–Stokes equations are used to obtain the base flow and compared with compressible Navier–Stokes equations. A bi-global analysis tool is used for the instability analysis because the heating source has a much larger length-scale in the streamwise direction than that in the spanwise direction, and the streamwise velocity is much larger than the normal velocity and the spanwise one. Results indicated that the distortion caused by the three-dimensional surface heating elements could modify the first mode, resulting in a lower frequency but with an uncertain effect on the higher frequency modes. Additionally, the streaks make the lower spanwise wave number components of the even first mode disturbance in a three-dimensional supersonic boundary layer in the freestream. As a result, the spontaneous radiation of an acoustic wave to the far field was found for the even mode. These findings suggest that laminar-turbulence transition can be suppressed or enhanced by the three-dimensional wall heating.

It is known that boundary layer transition and turbulent separation flow after transition can be influenced significantly by surface roughness. Because the traditional hybrid Reynolds-averaged-Navier–Stokes (RANS)/large eddy simulation method cannot predict the boundary layer transition, and the RANS-based transition model cannot accurately simulate the massively separated flow, the present study sought to build an effective modeling strategy for the laminar, roughness-induced-transition and attached turbulence/massively separated flows that couple the very-large-eddy-simulation model and a transition model considering roughness effects. This new hybrid model was examined in the cases of the separated flat plate and the rough cylinder. Our analysis shows that the new hybrid model operates in these transitional separated flows over smooth and rough walls. Compared with the results of other classical methods, the present results are more consistent with the measured data. Furthermore, the “drag crisis” phenomenon of the cylinder is accurately simulated by the present model.

In hypersonic boundary layers, Mack modes play a crucial role in flow instability, whose secondary instability is a hot research topic. Since hypersonic flight vehicles will probably work under high-stagnation temperature conditions, which significantly affect the aerodynamic heating calculation and aero-thermal protection design of hypersonic vehicles, it is necessary to compare the primary and secondary instabilities in high-stagnation temperature boundary layers and that in the Boeing/AFOSR Mach 6 quiet tunnel (BAM6QT). Herein, wall-cooling is adopted in order not to consider chemical reactions. With the same freestream temperature of 100 K, two Mach 6 boundary layers with the wall temperature of 20 and 600 K, corresponding to the cooled wall condition and the quiet wind tunnel condition, respectively, are chosen to conduct the linear/non-linear stability and the secondary instability analysis. Our results show that the most dangerous Mack mode originates from a fast discrete mode in the present cooled-wall flow and the most dangerous Mack mode is born from the slow discrete modes in BAM6QT boundary layers. Furthermore, when the primary amplitude of Mack mode disturbances is large, the fundamental resonance always dominates the secondary instability, resulting in steady streaky structures that have the largest amplitude in the spectrum. In addition, the present results point out that the distribution of the eigenfunctions of the fundamental modes and subharmonic modes are significantly different under various wall-temperatures. What is more, different ratios of wall temperature to incoming flow temperature have changed the spanwise wave-angle of the secondary disturbances.

In a previous study, we developed a one-equation transition model for the bypass and laminar separation bubble (LSB)-induced transition based on local variables. In this paper, distributed surface roughness effects are taken into account by constructing a new transport equation for the roughness amplification factor Ar. Modified criteria taking account of Ar are proposed to describe the roughness effects on the bypass and LSB-induced transitions. Moreover, to predict the flow properties in the laminar–turbulent region more accurately, a modified boundary condition for rough surfaces is employed. The calculations show that, overall, the rough wall promotes the bypass transition and reduces the size, or even causes the disappearance, of the LSBs. Good agreement of the numerical results from the proposed model with the experimental data indicates that the present roughness correction formula is reasonable and accurate.

A one-equation Reynolds-averaged Navier–Stokes closure model is established for bypass transition in this paper. A new local indicator is proposed to describe the variation of turbulence intensities and pressure gradients. Based on this new indicator, a novel and efficient transition criterion is formulated. For laminar separation bubble induced transition, a reasonable modified intermittency factor is developed to complete the reattachment process and control the size of separation bubbles. Incorporated with Menter's k−ω shear stress transport turbulence model, the new transition-turbulence model is built for a high turbulence intensity environment. Several classical flow cases, including the ERCOFTAC (European Research Community on Flow, Turbulence and Combustion) series flat plates with various pressure gradients, the Pratt and Whitney low pressure turbine cascade, and a highly loaded linear compressor cascade, are all employed for the model verifications. Decent agreement with the experimental data and direct numerical simulation data can be obtained in a wide range of incoming flow conditions.