Numerical study of high-lift flow with separation control by periodic excitation

A two-element high-lift configuration at stall condition is investigated by a numerical simulation based on the Reynolds-aver aged Navier-Stokes equations and eddy-viscosity turbulence models. Flow separation can be delayed by periodic vertical suction and blowing through a slot close to the leading edge of the flap. By simulating different excitation frequencies and intensities an optimum flow control can be identified and in cooperation with experimental investigations the mechanism of separation control is studied. Special attention is drawn to the turbulent time-scales to check the applicability of statiscal turbulence models for unsteady flows. Introduction During take-off and landing, wings of planes need to generate an enormous amount of lift to reduce ground speeds and runway lengths. Instead of providing complex and heavy multi-element high-lift devices, single flaps without slat are desirable. Such flaps, however, can only be applied if flow-separation on the flap at high flap angles can be avoided. Recent experimental investigations by Nitsche and Tinapp have shown that separation can be delayed by periodic excitation near the flap leading edge. There are a number of experimental and numerical studies showing the general effectiveness of flow control for single airfoils. In most investigations, leading edge suction is applied for transition delay, nonetheless, jet flaps are also employed for lift increase and manoeuvering. Surface suction/blowing can be used to rapidly change lift and drag on rotary wing aircraft. However, most control techniques considered in the past showed low or negative effectiveness. Oscillatory suction and blowing is about 10 times more efficient with respect to lift than steady blowing. The process becomes extremely efficient if the excitation frequencies correspond to the most unstable frequencies of the free shear layer, generating arrays of spanwise vortices that are convected downstream and upper tunnel-wall * Research Assistant '''Professor Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Fig. 1 Sketch of wind tunnel and two-element high-lift configuration continue to mix across the shear layer. Suction and blowing can be applied tangential to the airfoil surface, rectangular, or with cyclic vortical oscillation. In the present study, periodic excitation is applied to delay flow separation on the flap of a two-element high-lift configuration resulting in enhanced lift and reduced drag. The objective of this investigation is to better understand the functionality mode of the periodic excitation on pressure-driven separated flow over a two-element high-lift configuration. The numerical simulation of the unsteady turbulent flow is based on the two-dimensional Reynoldsaveraged Navier-Stokes equations (RANS). One goal is to verify the applicability of statistical turbulence models for this kind of flow and to prove that all important flow features can be captured. High-Lift Configuration The present numerical study is related to experimental investigations by Tinapp and Spang. The test model is a generic two element high-lift configuration, consisting of a NACA 4412 main airfoil and a NACA 4415 flap with c^/c — 0.4 relative chord length. Both profiles have bluff trailing edges. A previous study of a similar test case showed that due to strong blocking the effect of the tunnel walls is very important and needs to be considered. The main airfoil is mounted at 52% of the tunnel height (h — 7.8 c), whereas the flap is situated at a fixed position underneath the trailing edge of the main airfoil, thus forming a gap of FG = 0.0 78c with an overlap of FO = 0.027c (Fig. 1). In the numerical study, the American Institute of Aeronautics and Astronautics (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. angle of attack is fixed at a = 3° for the main airfoil and (3 = a + Sf = 40° for the flap. The freestream velocity is u^ ~ 14m/s corresponding to a Reynolds-Number of Re — 1.6 • 10 based on the main-airfoil chord. Transition is fixed at the positions of turbulator strips at 4.5% chord on the main airfoil and 2.8% chord on the flap according to the experimental setup. In the experiments periodic oscillating pressure pulses are generated externally by an electrodynamic shaker driving a small piston. It results in an oscillating jet emanating perpendicular to the chord from the narrow slot 4% chord behind the flap leading edge. This excitation is presumed to be completely twodimensional and it does not introduce extra mass-flux (zero-net-mass). To model the excitation apparatus, a suction/blowing type boundary condition is used. The perturbation to the flowfield is introduced through the inlet-velocity ue to a small chamber representing the excitation slot: Ue(t) =Ua \/2 • COs(27TtF) (1) where F is the pertubation frequency and ua is the RMS velocity of the excitation oscillation. The excitation intensity is given by the non-dimensional steady momentum blowing coefficient Cu = 2 — (-^ ] with ^ c \ °° / is the slot-width H = 0.004 ck. Computational Method The applied numerical method is based on a twodimensional incompressible Finite-Volume scheme to solve the Reynolds-averaged Navier-Stokes equations. The method is fully implicit and of second order in space and time. Based on the SIMPLE pressure correction algorithm, a co-located storage arrangement for all quantities is applied. Convective fluxes are approximated by a TVD-MUSCL-scheme. The wind tunnel walls are considered as slip walls for the simulation. The computational domain starts 4 chords upstream and ends 8 chords downstream of the configuration. The computational c-type mesh provides 202 chordwise cells around the main airfoil and 196 around the flap resulting in 37,000 cells in total. The nondimensional wall-distance of the first cell center remains below Y — 1 on the complete surface for an attached steady case. Additional simulations use a 64,000 cells mesh to evaluate the measure of mesh dependency. Turbulence modelling In previous investigations of unsteady turbulent flows, improved oneand two-equation models exhibited the best performance. Therefore three different eddy-viscosity turbulence models are applied to the present case: Spalart-Allmaras (SA) oneequation model, Wilcox k-u model and the LLR k-uj model. The latter is an improved two-equation model with special respect to the readability conditions. In simulations of unsteady turbulent flows by Reynolds-averaged approaches, the treatment of turbulent time-scales always requires special attention. An important assumption in the derivation of statistical turbulence models is that time-aver aging can be used instead of ensemble-averaging. Therefore the applicability of these models depends on the existence of a spectral gap of one or two orders between the resolved time-scales and the modelled scales. Otherwise a formal conflict can arise from an overlapping of resolved and modelled motions. The turbulence model will transfer engergy from the large-scale motion into dissipation. But a RANS approach cannot provide a counteracting mechanism (back-scatter). It is difficult to get a reliable estimation for the existence of a spectral gap in advance. To check the applicability of RANS simuations Rung suggests an approximation for the ratio between resolved timescale Tm and modelled turbulent time-scale Tt: