High-order discretization–based self-adaptive turbulence eddy simulation for supersonic base flow with PHengLEI software

Purpose The purpose of the present study is to develop a new numerical framework that can predict the supersonic base flow more accurately, including the development of axisymmetrically separated shear layer and recompression shock. To this end, two aspects are improved and combined, i.e. a newly self-adaptive turbulence eddy simulation (SATES) turbulence modeling method and a high-order discretization numerical scheme. Furthermore, the performance of the new numerical framework within a general-purpose PHengLEI software is assessed in detail. Design/methodology/approach Satisfactory prediction of the supersonic separated shear layer with unsteady wake flow is quite challenging. By using a unified turbulence model called SATES combining high-order accurate discretization numerical schemes, the present study first assesses the performance of newly developed SATES for supersonic axisymmetric separation flows. A high-order finite differencing-based compressible computational fluid dynamics (CFD) code called PHengLEI is developed and several different numerical schemes are used to investigate the effects on shock-turbulence interactions, which include the monotonic upstream-centered scheme for conservation laws (MUSCL), weighted compact nonlinear scheme (WCNS) and hybrid cell-edge and cell-node dissipative compact scheme (HDCS). Findings Compared with the available experimental data and the numerical predictions, the results of SATES by using high-order accurate WCNS or HDCS schemes agree better with the experiments than the results by using the MUSCL scheme. The WCNS and HDCS can also significantly improve the prediction of flow physics in terms of the instability of the annular shear layer and the evolution of the turbulent wake. Research limitations/implications The small deviations in the recirculation region can be found between the present numerical results and experimental data, which could be caused by the inaccurate incoming boundary layer condition and compressible effects. Therefore, a proper incoming boundary layer condition with turbulent fluctuations and compressibility effects need to be considered to further improve the accuracy of simulations. Practical implications The present study evaluates a high-order discretization-based SATES turbulence model for supersonic separation flows, which is quite valuable for improving the calculation accuracy of aeronautics applications, especially in supersonic conditions. Originality/value For the first time, the newly developed SATES turbulence modeling method combining the high-order accurate WCNS or HDCS numerical schemes is implemented on the PHengLEI software and successfully applied for the simulations of supersonic separation flows, and satisfactory results are obtained. The unsteady evolutions of the supersonic annular shear layer are analyzed, and the hairpin vortex structures are found in the simulation.