DNS and modeling of a turbulent boundary layer with separation and reattachment over a range of Reynolds numbers

The separation of a turbulent boundary layer, which is encountered in devices such as airfoils, diffusers and turbomachinery, is one of the most challenging research topics in fluid mechanics. Its understanding and its prediction with turbulence models are however still not satisfactory. The reason may be partly due to a shortage of reliable data from numerical simulations, which account for Reynolds number dependence systematically. Direct numerical simulation (DNS) yields accurate and detailed turbulence quantities , thus allowing the development of turbulence models based on much more complete information than experiments provide. A large number of DNS databases have been established in canonical flows (i.e., homogeneous, channel, pipe and boundary layer) so far, where significant attention is given to Reynolds number effects. For separated flows, on the other hand, there is still limited information available from DNS due perhaps to difficulties associated with inflow, boundary conditions, domain size and ultimately computing cost. In particular, unlike for separation forced by the configuration of such a backward-facing step, only a few DNS attempts have been made for pressure-induced separation in a flat-plate turbulent boundary layer. For the latter DNS, seminal studies were carried out by Spalart & Coleman (1997) and Na & Moin (1998) at Reynolds number Re θ ≡ U ∞ θ 0 /ν = 300 (U ∞ and θ 0 denote the freestream velocity and inlet momentum thickness, respectively, and ν is the kinematic viscosity) where the former (Spalart & Coleman 1997) and latter (Na & Moin 1998) dealt with incipient and massive separation , respectively. Later, Skote & Henningson (2002) achieved the DNS at Re θ = 300 but with a large recirculation region. Manhart & Friedrich (2002) performed the DNS at a higher Reynolds number of Re θ = 870. However, the Re dependence of the mean and turbulence quantities together with turbulence structure has yet to be examined. Currently, we are working on a series of DNS of a turbulent boundary layer with separation and reattachment where a relatively large magnitude of blowing and suction is imposed at the upper boundary, producing a large separation bubble. The inlet Reynolds number Re θ is equal to 300, 600 and 985, the latter value being about three times larger than that in the seminal DNS works (Spalart & Coleman 1997; Na & Moin 1998), but still only about half of that in the Simpson (1989) experiment. The objectives of the …