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Figure 3 — History of the mean separation point abscissa in the spanwise direction along the flat. plate. flat is plotted. A strong intermittency of the shedding responsible for low-frequency reattachment shock os- cillations have also been evidenced. Nevertheless, in this configuration, the separation point of the recirculation bubble has a fixed location along the flat plate as shown in figure 3, where the history of the mean value in the spanwise direction of the separation point abscissa along the flat is plotted.

Figure 3 — History of the mean separation point abscissa in the spanwise direction along the flat. plate. flat is plotted. A strong intermittency of the shedding responsible for low-frequency reattachment shock os- cillations have also been evidenced. Nevertheless, in this configuration, the separation point of the recirculation bubble has a fixed location along the flat plate as shown in figure 3, where the history of the mean value in the spanwise direction of the separation point abscissa along the flat is plotted.

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First results have shown that the location of the reattachment point of the recirculation bubble have an oscillatory motion. It is clearly visible in the figure 2 where the history of the mean value in the spanwise direction of the reattachment point abscissa along the flate is plotted versus time. The domain is discretized using a cartesian mesh with non uniform spacing in the direction normal to the wall (y). The mesh size employs 400 x 102 x 200 grid points in (x x y x z). In the normal to the wall direction, the mesh is tightened close to the wall using a hyperbolic tangent law.
First results have shown that the location of the reattachment point of the recirculation bubble have an oscillatory motion. It is clearly visible in the figure 2 where the history of the mean value in the spanwise direction of the reattachment point abscissa along the flate is plotted versus time. The domain is discretized using a cartesian mesh with non uniform spacing in the direction normal to the wall (y). The mesh size employs 400 x 102 x 200 grid points in (x x y x z). In the normal to the wall direction, the mesh is tightened close to the wall using a hyperbolic tangent law.
Figure 2 — History of the mean reattachment point abscissa in the spanwise direction along the flat plate.
Figure 2 — History of the mean reattachment point abscissa in the spanwise direction along the flat plate.
Figure 4 — Turbulent boundary layer : Q criterion colored by the longitudinal velocity.
Figure 4 — Turbulent boundary layer : Q criterion colored by the longitudinal velocity.
Figure 5 — Skin friction coefficient averaged in the spanwise direction along the flat plate. In blue, the DNS using synthetic eddy method. In red, result from [11] (coarse mesh). In yellow, result from [11] (fine mesh).
Figure 5 — Skin friction coefficient averaged in the spanwise direction along the flat plate. In blue, the DNS using synthetic eddy method. In red, result from [11] (coarse mesh). In yellow, result from [11] (fine mesh).
Figure 6 — Components of the Reynolds stress tensor (normalized using the friction velocity (u,) and the density at the wall (p,,)) with respect to the wall normal direction in wall units (yt) : In blue, Ry obtained by DNS using synthetic eddy method for x/6 = 30. In yellow, R33 obtained by DNS using synthetic eddy method for x/d = 30. In red, R22 obtained by DNS using synthetic eddy method for x/d5 = 30. In purple, Ri profile from [11] (fine mesh) for 7/d = 62.5. In cyan, R33 profile from [11] (fine mesh) for x/é = 62.5. In green, Rg2 profile from [11] (fine mesh) for x/é = 62.5.
Figure 6 — Components of the Reynolds stress tensor (normalized using the friction velocity (u,) and the density at the wall (p,,)) with respect to the wall normal direction in wall units (yt) : In blue, Ry obtained by DNS using synthetic eddy method for x/6 = 30. In yellow, R33 obtained by DNS using synthetic eddy method for x/d = 30. In red, R22 obtained by DNS using synthetic eddy method for x/d5 = 30. In purple, Ri profile from [11] (fine mesh) for 7/d = 62.5. In cyan, R33 profile from [11] (fine mesh) for x/é = 62.5. In green, Rg2 profile from [11] (fine mesh) for x/é = 62.5.
Figure 7— Van Driest transform of the time averaged streamwise velocity versus yt for x/d = 30, logarithmic law (—4-In(y+) +5) with respect to y+ and the linear evolution in the inner layer. 8 0-41
Figure 7— Van Driest transform of the time averaged streamwise velocity versus yt for x/d = 30, logarithmic law (—4-In(y+) +5) with respect to y+ and the linear evolution in the inner layer. 8 0-41
In order to perform the simulation of the SWTBLI, an incident shock wave have been created on the top boundary layer using the Rankine-Hugoniot relashionships in the simulation of the compressible turbulent boundary layer presented in 4.1. This shock wave has an angle of 33.2° with respect to the longitudinal direction, as in [12] where a LES of a SWTBLI have been per- formed with the same flow conditions. The abscissa where the Rankine Hugoniot relationships are imposed on the top boundary layer is chosen so that the shock would impinges the flat plate at x = 39.5.6 in non-viscous flow, where 6 is the boundary layer thickness prescribed at the inlet. As shown in 4.1, the turbulent boundary layer is well developed for this abscissa along the flat plate. the flat plate. Figure 8 — Numerical schlieren visualization (2D slice located at the middle of the domain) obtained by plotting the norm of the density gradient (||Vol|).
In order to perform the simulation of the SWTBLI, an incident shock wave have been created on the top boundary layer using the Rankine-Hugoniot relashionships in the simulation of the compressible turbulent boundary layer presented in 4.1. This shock wave has an angle of 33.2° with respect to the longitudinal direction, as in [12] where a LES of a SWTBLI have been per- formed with the same flow conditions. The abscissa where the Rankine Hugoniot relationships are imposed on the top boundary layer is chosen so that the shock would impinges the flat plate at x = 39.5.6 in non-viscous flow, where 6 is the boundary layer thickness prescribed at the inlet. As shown in 4.1, the turbulent boundary layer is well developed for this abscissa along the flat plate. the flat plate. Figure 8 — Numerical schlieren visualization (2D slice located at the middle of the domain) obtained by plotting the norm of the density gradient (||Vol|).
A 2D slice located at the middle of the domain, of the numerical Shlieren have been plotted in figure 8. The characteristic properties of a SWTBLI have been recovered by our DNS. Indeed, we clearly see that the boundary layer thickness increases drastically due to the pressure rise imposed by the incident shock wave, leading to the creation of the reflected shock wave. The thickening of the boundary layer is also visible in figure 9 where the Q criterion isosurfaces have been plotted, colored by the magnitude of the spanwise velocity. The system of shocks have been evidenced by plotting isosurfaces of V - u. Figure 9 — Q criterion colored by the magnitude of the streamwise velocity. Shock waves are highlighted by isosurfaces of div(u).
A 2D slice located at the middle of the domain, of the numerical Shlieren have been plotted in figure 8. The characteristic properties of a SWTBLI have been recovered by our DNS. Indeed, we clearly see that the boundary layer thickness increases drastically due to the pressure rise imposed by the incident shock wave, leading to the creation of the reflected shock wave. The thickening of the boundary layer is also visible in figure 9 where the Q criterion isosurfaces have been plotted, colored by the magnitude of the spanwise velocity. The system of shocks have been evidenced by plotting isosurfaces of V - u. Figure 9 — Q criterion colored by the magnitude of the streamwise velocity. Shock waves are highlighted by isosurfaces of div(u).
Figure 10 — Skin friction coefficient averaged in the spanwise direction along the flat plate. The red line indicates the zero value.
Figure 10 — Skin friction coefficient averaged in the spanwise direction along the flat plate. The red line indicates the zero value.
Figure 11 — History of the mean separation point abscissa in the spanwise direction along the flat plate.
Figure 11 — History of the mean separation point abscissa in the spanwise direction along the flat plate.
Figure 12 — History of the mean separation point abscissa in the spanwise direction along the flat. plate.
Figure 12 — History of the mean separation point abscissa in the spanwise direction along the flat. plate.
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Computer ScienceMechanicsShock Wave
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