Transitional supersonic base flows at M = 2.46 are investigated using direct numerical simulations. Results are presented for Reynolds numbers based on the cylinder diameter Re D = 3 × × 10 4 -1 × × 10 5 . As a consequence of flow instabilities, coherent structures develop that have a profound impact on the global flow behavior. Simulations with various circumferential domain sizes are conducted to investigate the effect of coherent structures associated with different azimuthal modes on the mean flow, in particular on the base pressure, which determines the base drag. Temporal spectra reveal that frequencies found in the axisymmetric mode can be related to dominant higher modes present in the flow. It is shown that azimuthal modes with low wave numbers cause a flat base pressure distribution and that the mean base pressure value increases when the most dominant modes are deliberately eliminated. Visualizations of instantaneous flow quantities and turbulence statistics at Re D = 1 × × 10 5 show good agreement with experiments at a significantly higher Reynolds number. For these investigations, a high-orderaccurate compressible Navier-Stokes solver in cylindrical coordinates developed specifically for this research was used.
Nomenclatureturbulent kinetic energy k = azimuthal Fourier mode number L K = Kolmogorov length scale M = Mach number n = temporal mode number nr = number of radial gridpoints nz = number of streamwise gridpoints Pr = Prandtl number p = pressure q k = heat-flux vector Re = Reynolds number Sr = Strouhal number T = temperature t = time u, v, w = velocity components in the streamwise, radial, and azimuthal direction u i = velocity vector u i u k = turbulent stress tensor W ik = vorticity tensor x k = coordinate z, r, θ = streamwise, radial, and azimuthal coordinates γ = ratio of specific heats = computational grid size δ ik = Kronecker operator ε = turbulent dissipation rate . Member AIAA. μ = dynamic viscosity τ ik = stress tensor Subscripts D = quantity based on diameter of cylinder i, j, k = indices for Cartesian tensor notation in, out = inflow, outflow max = maximum of referring quantity Superscripts k = kth mode of quantity = fluctuating quantity