Numerical Simulations of Transition due to Isolated Roughness Elements at Mach 6

Abstract

An accurate prediction of transition onset behind an isolated roughness element has not yet been established. This is particularly important in hypersonic flow, where transition is accompanied by increased surface heating. In the present contribution, a number of direct numerical simulations have been performed of a Mach 6 boundary layer over a flat plate with isolated roughness elements. The effects of roughness shape, planform, ramps, and freestream disturbance levels on instability growth and transition onset are investigated. It is found that the frontal shape has a large effect on the transition onset, which is in agreement with previous studies, whereas the roughness element planform has a marginal influence. A new result is that the roughness shape in the streamwise direction (in particular, the aft section) is also an important characteristic, since an element with a ramped-down aft section allows the detached shear layer to spread out and weaken, leading to a lower instability growth rate. Above a critical value, the instability growth rate is found to be correlated with the amplitude of the low-speed streak formed by the roughness element, suggesting that a more physically based transition criterion should take account of the local liftup effect of the particular roughness shape.

DNS Study of Roughness-Induced Transition at Mach 6

“…Three different grids were used and compared: Fine (900x225x350), Medium (600x150x234), and Coarse (300x100x200). The Fine mesh is close to the one used in [11] which used a grid as fine as in the work of De Tullio and Sandham [28], based on an extensive grid convergence study. figure 2 shows a pseudo-Schlieren plot of the density gradients to better understand the topology of the flow.…”

“…where Table 1 Numerical parameters for each code used in this study Table 1 gathers the numerical parameters which have been used in the validation of elsA and OpenSBLI, as well as those used in the reference test case with SBLI (Legacy) [11].…”

“…The same principle as in [11] was used for the computational domain and for the grid generation. The numerical domain and setup can be seen on figure 1.…”

“…Validation of elsA and OpenSBLI with reference to the work done in [11] with the code SBLI was carried out. The comparison is made on a transitional case, which is more discriminating for the choice of the numerical schemes used for the simulations and more sensitive to boundary conditions.…”

“…Advances in numerical methods and computing capabilities now make it possible to study hypersonic transitional flows with a good accuracy. The factors affecting whether or not a roughness element will be effective in tripping a high-speed flow to turbulence, include the Reynolds number [10], the roughness size, and its shape [11], but also the wall temperature [12] and Mach number [4]. The way in which roughness induces transition is now better understood.…”