Numerical investigation of the three-dimensional development in boundary layer transition

Spatial direct numerical simulation of transitional boundary layer over compliant surfaces

“…The linear wave computation of Fasel et al [12] and non-linear growth data from Saric et al [24]Õs experiments, as presented by Liu and Liu [15], are used in this comparison. Several cases of 3D linear wave evolution over compliant membranes are studied thereafter.…”

“…14 together with corresponding results for a rigid surface. Here, we have followed the mode designation scheme of Fasel et al [12] where (n, k) denotes a mode whose frequency is nx 2D and spanwise wavenumber kb 0 . Unlike the smooth and monotonic increase in amplitude of the 2D primary wave on a rigid surface, the amplitude of the 2D primary mode (1, 0) for the compliant membrane displays an oscillatory behavior.…”

“…The model is needed for investigating 3D secondary instabilities and other nonlinear transition processes in boundary layers over such surfaces. The present 3D model employs the flow variables in their primitive form, whereas Fasel et al [12] and Rist and Fasel [13] had applied a vorticity-velocity formulation for the governing flow equations. A variant of the vorticity-velocity method was developed by Davies and Carpenter [14] for simulating disturbance evolution in 3D boundary layer over compliant surfaces, and applied to boundary-layer flows over rigid and compliant rotating disks.…”

“…The specific case of a 3D wave driven by a source with b 0 = 0.10994 and x 0 = 0.054971 (or F = 100) placed at x 0 = 185.644 (Re = 549.71) is examined by Fasel et al[12] in some detail. This case is simulated here by a computational domain that spans x = [124.430, 600.6828], y = [0, 52.76] and z = [À28.575, 28.575].…”

Resolution Requirements for Numerical Simulations of Transition

“…This is a particularly important question for true spatial simulations because the limitations of current computers mandate that resolution in the spanwise direction be sacrificed to furnish the much greater resolution needed in the streamwise direction for the spatially-growing boundary layer. To date spatial simulations have employed drastic spanwise truncations, retaining only between 4 and 32 points in z (see Fasel, Rist, and Konzelmann (1987)). With so few points in the spanwise direction, truly small-scale spanwise oscillations will not occur -they will be on the scale of the spanwise grid, which in these cases is quite coarse.…”