1 ISABE-2005-1041 Control of Laminar Separation Bubbles Using Instability Waves Ulrich Rist, Kai Augustin Institut für Aerodynamik und Gasdynamik Universität Stuttgart, Pfaffenwaldring 21 70550 Stuttgart, Germany rist@iag.uni-stuttgart.de ABSTRACT This paper presents detailed investigations related to active transition control in laminar separation bubbles. The investigations rely on direct numeri- cal simulations based on the complete Navier- Stokes equations for a flat-plate boundary layer, such that the wall boundary layer is fully resolved. A laminar separation bubble is created by imposing a streamwise adverse pressure gradient at the free- stream boundary of the integration domain. Differ- ent steady and unsteady boundary layer distur- bances are then introduced at a disturbance strip upstream of separation and their effects on the sepa- ration bubble are studied. It is shown that the size of the separated region can be controlled most effi- ciently by very small periodic oscillations, which lead to travelling instability waves that grow to large levels by the hydrodynamic instability of the flow. Indications for the preferred frequency of these waves can be obtained from linear stability theory, but since the problem is non-linear, only direct numerical simulations can really qualify or disqualify the predictions. Over all, it turns out that unsteady two- or three-dimensional disturbances have a stronger impact on the size of the bubble than steady disturbances, because they directly provide initial amplitudes for the laminar-turbulent transition mechanism. NOMENCLATURE Symbols δ* [m] displacement thickness Θ [m] momentum thickness H = δ*/Θ [–] shape parameter f [Hz] disturbance frequency L [m] reference length U ∞ [m/s] free-stream velocity v’ [m/s] wall-normal disturbance amplitude at the wall x [m] streamwise coordinate y [m] wall-normal coordinate z [m] spanwise coordinate Re* = U ∞ ⋅δ*/υ [–] displacement-thickness Reynolds number Re Θ = U ∞ ⋅Θ/υ [–] momentum-thickness Reynolds number α [–] streamwise wave number α T [ o ] spreading angle of turbu- lence (conceptual) β = 2πfL/ U ∞ [–] disturbance frequency ϖ z [–] time-averaged vorticity Abbreviations DNS direct numerical simulation (h/k) mode of the frequency (index h) spanwise wavenumber spectrum (index k) LSB laminar separation bubble LST linear stability theory R re-attachment point S separation point T laminar-turbulent transition 2-d two-dimensional 3-d three-dimensional INTRODUCTION The occurrence of laminar separation and turbulent reattachment in a so-called laminar or transitional separation bubble is a typical problem for low to medium Reynolds-number aerodynamics, e.g. on aircraft wings or blades of turbo machines, where they lead to unwanted performance penalties. Laminar separation bubbles should hence be avoided using some means of control. So far, this has been achieved primarily by a ‘cautious’ design or by placing some kind of turbulence trips or vor- tex generators upstream of separation. However, these approaches cannot adapt themselves to chang- ing operation conditions such that performance penalties may occur under off-design conditions. On the other hand, avoiding laminar separation bubbles by design sacrifices the maximal possible efficiency or adds extra weight and costs to a tur- bine because of extra blades which are needed to make the passage narrower in order to keep the flow attached. Therefore, some active separation control methods have been proposed recently. Mostly, they consist of using vortex generator jets (e.g. [1]) which enforce an earlier transition of the flow to turbulence and hence an earlier re-attachment or no laminar separation at all using brute force. More recently periodically pulsed jets have been found to