Detached eddy simulation

Aerodynamic heating greatly affects the overall design of aerospace vehicles.  Most research has focused on the forebody flow that is characterized by high levels of radiative and convective heating. However, the flow on the afterbody of the vehicle also results in significant aerothermal loads. In contrast to a laminar boundary layer on the forebody, the flow in the large wake region enclosing the afterbody can be transitional or turbulent. Turbulent mixing often alters the structure of the wake and enhances the heat transfer to the vehicle considerably.

Until recently, engineering prediction of turbulent flows relied exclusively on Reynolds-averaged Navier Stokes (RANS) simulations that compute the time-averaged flow field. However, RANS turbulence models yield large errors in regions of large-scale separation. The inaccuracies in predicting turbulent heating rates are generally compensated by a large safety factor in the design of afterbody heat shields. Detached eddy simulation (DES) significantly improves predictions in massively separated flows by simulating the unsteady dynamics of the dominant length scales. DES has mostly been used in low-speed flows, with limited application at supersonic speed.

We use detached eddy simulation to study the flow field at the base of the Fire II re-entry vehicle. Project Fire flights were conducted to investigate the heating environment on a blunt-nosed, Apollo-shaped vehicle entering the earth's atmosphere at a velocity in excess of the escape velocity. We simulate the conditions at a point in the later part of the trajectory where the freestream Mach number is 16 and the Reynolds number based on the body diameter is 1.76E6. The figures below show a schematic of the vehicle and the computed temperature field around it.

The figures above show a schematic of the vehicle and a snapshot of the computed temperature field around it. The freestream flow is from left to right, and is slowed down by the bow shock ahead of the body. The flow expands around the corners and separates to form a large recirculation region behind the vehicle. The flow in this region is highly unsteady and three - dimensional with a large range of length and time scales. The shear layers enclosing the recirculation region come together at the neck region. A recompression shock is formed at this point that turns the outer flow to make it parallel to the vehicle axis.

The figure below presents the temperature distribution in an axial plane as well as several cross-sections through the wake. The temperature in the recirculation region varies between a cooled wall temperature of 553 K and a maximum of about 9000 K in the neck region. There is a low temperature region next to the wall that corresponds to a laminar boundary layer. Some of the cold fluid from this region is swept away from the wall. The temperature increases as the size of the recirculation region reduces up to the neck region. The highest temperature is found in the neck region due to the recompression shock. Downstream of the neck, the wake expands and the temperature drops considerably.