Investigation of supersonic turbulent flows over a sphere by fully resolved direct numerical simulation

Abstract

In this work, a fully resolved direct numerical simulation study of the interaction between supersonic turbulent flow and inertial particle is carried out. For the compressible flow, an eighth-order bandwidth optimization weighted essentially nonoscillatory scheme is used for shock capturing, and the central finite difference scheme is used for the spatial discretization of diffusion terms. The three-dimensional ghost zone immersed boundary method is adopted for solid-fluid interface identification. These numerical schemes are integrated in a direct numerical simulation solver, and its validation is demonstrated by comparing to several benchmark cases. Such a developed method is then used to attack the problem of an upstream supersonic turbulent flow over a spherical particle. Three cases with different inflow turbulence intensities are studied. It is shown that with the turbulence intensity increasing the drag force coefficient presents a smaller relative increase compared to the incompressible situation. Analysis of the bow shock-turbulence interaction is also reported. Similar to the normal shock-turbulence interaction, both the Kolmogorov and Taylor scales decrease after being compressed by the shock. Moreover, both the streamwise and transverse Reynolds stresses have a peak at the shock position. These results indicate the significance of taking the effects of shock into consideration when modeling the modulation of a solid particle to the compressible turbulence.

Application of bandwidth-optimized WENO schemes to DNS of shock–turbulence interaction problems

“…Similar to the WENO-JS scheme, the flux reconstruction procedure of the WENO-Z [5] scheme will be as given by ( 14) to (22). The terms associated with the stencil S L 3 will not play any role in reconstruction.…”

“…The smoothness indicator, (β L 3 ), of the additional stencil S L 3 , shown in (22), is replaced with the smoothness indicator (β L 6 ), based on the six-point stencil [7] and is given by…”

“…The expression of the smoothness indicator of the participating stencils based on three points (S 0 , S 1 , and S 2 ) arranged as per Fig. 2 of Fu et al [7] ) for the TENO6 scheme is the same as those stencils (S L 1 , S L 2 , and S L 0 ), shown in (22), which are based on the same points as shown in Fig. 1.…”

“…Recently, DNS of shock-turbulence interaction has been performed using a bandwidth-optimized WENO scheme with limiter for a compression ramp [17][18][19]. DNS studies have also been performed for a supersonic jet flame [20], compressible isotropic turbulence [21], and shock-turbulence interaction over a sphere [22] using a high-order optimized WENO scheme without a limiter. Recently proposed variants of the WENO scheme such as the sixth-order central upwind scheme [6] and a family of targeted essentially non-oscillatory (TENO) schemes [7,8,23,24] are also considered to be suitable for DNS of shock-turbulence interaction.…”

High-order gas kinetic flux solver for simulation of two dimensional incompressible flows

“…Due to its high accuracy, the high-order method has been an important topic in the field of computational fluid dynamics (CFD). It has wide application in direct numerical simulation (DNS), [1][2][3][4] large eddy simulation (LES), [5][6][7][8] aeroacoustics, [9][10][11] etc. Nowadays, many high-order methods have been developed to address the challenging task of obtaining a high-order accurate, efficient, and robust solution of the Euler and Navier-Stokes equations.…”