Direct Numerical Simulation of Supersonic Turbulent Boundary Layer over a Compression Ramp

Abstract

A direct numerical simulation of shock wave and turbulent boundary layer interaction for a 24 deg compression ramp configuration at Mach 2.9 and Re 2300 is performed. A modified weighted, essentially nonoscillatory scheme is used. The direct numerical simulation results are compared with the experiments of Bookey et al. [Bookey, P. B., Wyckham, C., Smits, A. J., and Martin, M. P., "New Experimental Data of STBLI at DNS/LES Accessible Reynolds Numbers," AIAA Paper No. 2005-309, Jan. 2005 at the same flow conditions. The upstream boundary layer, the mean wall-pressure distribution, the size of the separation bubble, and the velocity profile downstream of the interaction are predicted within the experimental uncertainty. The change of the mean and fluctuating properties throughout the interaction region is studied. The low frequency motion of the shock is inferred from the wallpressure signal and freestream mass-flux measurement. Nomenclature a = speed of sound C f = skin friction coefficient C r k = optimal weight for stencil k f = frequency f s = frequency of shock motion IS k = smoothness measurement of stencil k L sep = separation length M = freestream Mach number p = pressure q k = numerical flux of candidate stencil k Re = Reynolds number based on Re = Reynolds number based on r = number of candidate stencils in WENO S L = dimensionless frequency of shock motion T = temperature u = velocity in the streamwise direction v = velocity in the spanwise direction w = velocity in the wall-normal direction x = coordinate in the streamwise direction y = coordinate in the spanwise direction z = coordinate in the wall-normal direction = 99% thickness of the incoming boundary layer = displacement thickness of the incoming boundary layer = momentum thickness of the incoming boundary layer = density ! k = weight of candidate stencil k Subscripts w = value at the wall 1 = freestream value Superscript = nondimensional value

Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble

“…This was the main objective that motivated the choice of the digital-filter approach, where no cyclic patterns is enforced, as shown by the correlation function. In contrast, the correlation function in Wu and Martin's DNS (figure 4 in [54]) does not drop to zero and does not extend to the period of the recycling/rescaling technique used by the authors. From the point of view of the digital filter, we made sure that no structure longer than O(δ 0 ) was introduced and this is confirmed by the observed correlation function.…”

“…Secondly, the recycling nature of the method will, by construction, introduce a distinct low-frequency tone that can interfere with the study of the low-frequency content in SBLI [1] 2 . All the LES [19,32,47] and most of the DNS [54,1] results available so far on SBLI have used the recycling technique. However, for their DNS, Pirozzoli and Grasso [37] have chosen to use a long domain to simulate the transition to turbulence (note that to achieve this, they forced the flow at the wall over a short streamwise distance).…”

Recovery of a supersonic turbulent boundary layer after an expansion corner

“…Many DNS databases of wall-bounded supersonic flows are attainable, including fundamental supersonic boundary layer [15][16][17][18] , supersonic boundary layer interaction with shock waves [19,20] , and supersonic boundary layer over a 4 compression ramp [21] etc. Recently Fang et al [22] calculated a supersonic flow at Ma=2.9 over an expansion-compression corner and found that the re-laminarized expansion flow is far from recovered before the separation region in the compression corner.…”

Numerical Study on Wall Temperature Effects on Shock Wave/Turbulent Boundary-Layer Interaction

“…Both experiments [8,9] show that the higher the wall temperature, the greater the separation bubble is. Adams [10], Wu and Martín [11,12], and Li et al [13] used direct numerical simulation (DNS) to study the turbulence statistical characteristics and shock wave motion of STBLI, especially the low-frequency unsteadiness of STBLI. In general the study of wall-temperature effects on STBLI of compression corner is still not very sufficient.…”