Cd. Pruett et Cl. Chang, SPATIAL DIRECT NUMERICAL-SIMULATION OF HIGH-SPEED BOUNDARY-LAYER FLOWS .2. TRANSITION ON A CONE IN MACH-8 FLOW, Theoretical and computational fluid dynamics, 7(5), 1995, pp. 397-424
The laminar breakdown of the boundary-layer flow of an axisymmetric sh
arp cone in a Mach 8 flow is simulated by a synergistic approach that
combines the parabolized stability equation (PSE) method and spatial d
irect numerical simulation (DNS). The transitional state is triggered
by a symmetric pair of oblique second-mode disturbances whose nonlinea
r interactions generate strong streamwise vorticity,which leads in tur
n to severe spanwise variations in the flow and eventual laminar break
down. The PSE method is used to compute the weakly and moderately nonl
inear initial stages of the transition process and, thereby, to derive
a harmonically rich inflow condition for the DNS. The strongly nonlin
ear and laminar-breakdown stages of transition are then computed by we
ll-resolved DNS, with a highly accurate algorithm that exploits spectr
al collocation and high-order compact-difference methods. Evolution of
the flow is presented in terms of modal energies, mean quantities (e.
g., skin friction), Reynolds stresses, turbulent kinetic energy, and f
low visualization. The numerical test case is an approximate computati
onal analog of one of the few stability experiments performed for hype
rsonic boundary-layer flows. Comparisons and contrasts are drawn betwe
en the experimental and the computational results. ''Rope-like'' waves
similar to those observed in schlieren images of high-speed transitio
nal flows are also observed in the numerical experiment and are shown
to be visual manifestations of second-mode instability waves.