Direct Numerical Simulation of Compressible and Incompressible Wall Bounded Turbulent Flows with Pressure Gradients

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Wei, Liang
Direct numerical simulation , Discontinuous Galerkin method , Wall bounded Turbulent flow , Adverse pressure gradient , Favourable pressure gradient , Compressible channel flow , Pressure gradient vorticity flux correlation
This thesis is focused on direct numerical simulation (DNS) of compressible and incompressible fully developed and developing turbulent flows between isothermal walls using a discontinuous Galerkin method (DGM). Three cases (Ma = 0.2, 0.7 and 1.5) of DNS of turbulent channel flows between isothermal walls with Re ~ 2800, based on bulk velocity and half channel width, have been carried out. It is found that a power law seems to scale mean streamwise velocity with Ma slightly better than the more usual log-law. Inner and outer scaling of second-order and higher-order statistics have been analyzed. The linkage between the pressure gradient and vorticity flux on the wall has been theoretically derived and confirmed and they are highly correlated very close to the wall. The correlation coefficients are influenced by Ma, and viscosity when Ma is high. The near-wall spanwise streak spacing increases with Ma. Isosurfaces of the second invariant of the velocity gradient tensor are more sparsely distributed and elongated as Ma increases. DNS of turbulent isothermal-wall bounded flow subjected to favourable and adverse pressure gradient (FPG, APG) at Ma ~ 0.2 and Reref ~ 428000, based on the inlet bulk velocity and the streamwise length of the bottom wall, is also investigated. The FPG/APG is obtained by imposing a concave/convex curvature on the top wall of a plane channel. The flows on the bottom and top walls are tripped turbulent and laminar boundary layers, respectively. It is observed that the first and second order statistics are strongly influenced by the pressure gradients. The cross-correlation coefficients of the pressure gradients and vorticity flux remain constant across the FPG/APG regions of the flat wall. High correlations between the streamwise/wallnormal pressure gradient and the spanwise vorticity are found near the separation region close to the curved top wall. The angle of inclined hairpin structure to streamwise direction of the bottom wall is smaller (flatter) in the FPG region than the APG region.
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