Control of shock-wave/boundary-layer interactions with passive blowing and bleeding

Computations were performed to investigate the utility of three passive devices for controlling obliqueshock-wave/boundary-layer interactions on a flat plate. All three devices involve a cavity with two slots one upstream of the incident shock where blowing takes place and another downstream of it where bleeding takes place. The blowing and bleeding rates were determined passively by the pressure difference across the shock. Results are presented which show the nature of the flow field induced by passive blowing and bleeding. This study is based on the ensemble-averaged conservation equations of mass, momentum (compressible Navier-Stokes), and energy closed by a low Reynolds number k-oo model of turbulence. Solutions were obtained by using a cell-centered finite-volume method based on flux-difference splitting of Roe with slope limiter of Chakravarthy and Osher and a diagonalized alternating-direction implicit scheme with multigrid on a patched/ overlapped grid system. * Graduate student. ** Graduate student. Now, research staff at Sterling Software/NASA Ames Research Center. Professor. Senior Member AIAA. Research Engineer. Member AIAA. Copyright © 1997 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royaltyfree license to exercise all rights under the copyright claimed herein for government purposes. All other rights are reserved by the copyright owner. INTRODUCTION Effective control of shock-wave/boundary-layer interactions to prevent flow separation and minimize flow distortions is important in a number of applications. These include airframes of supersonic aircraft, external and mixed-compression inlets, and wind tunnels. For some of these applications, shock-wave induced boundary-layer separations are not just annoyances because of reductions in efficiency but rather a very serious operational hazard. As an example, shock-wave induced separations in mixed-compression inlets can lead to the unstart condition requiring the entire propulsion system to undergo a restart sequence during flight. A number of techniques have been developed to control the detrimental effects of incident shock waves on boundary layers. Of these, bleeding and blowing have been found to be highly effective in eliminating both flow separation and improving boundary-layer profile." In terms of implementation, blowing and bleeding have been operated mostly in an active mode. By active, it is meant that a source of high or low pressure must be maintained in order to ensure blowing or bleeding. Since maintaining such a source requires additional energy which also reduces efficiency, a passive mode of operation is desirable. In 1979, Bushnell and Whitcomb (see Ref. 11) proposed a passive control device made up of a porous surface over a cavity or plenum. It was suggested that placing this device over a shock-wave/boundary-layer interaction region will produce a flow through the cavity from downstream to upstream of the shock because of the static pressure rise across the shock. Since that Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc. time, a number of investigators have studied passive devices for controlling shock-wave/boundary-layer interactions. They found success in reducing shock drag over transonic airfoils (see review in Ref. 11). Recently, passive control was also found to be successful in controlling normal shock/boundary-layer interactions about an external compression inlet. So far, passive blowing and bleeding have been applied only to flows with low supersonic speeds (Mach numbers less than 1.4) so that the resulting shocks have been relatively weak. Also, no studies computational or experimental have been reported that show the nature of the multidimensional flow field about passive control devices. The objective of this study is to investigate computationally the utility of three passive devices for controlling oblique-shock-wave / boundary-layer interactions on a flat plate in which the freestream Mach number is much higher than 1.4 and the incident shock wave can induce boundary-layer separation in the absence of control. The focus is on understanding the nature of the flow and the usefulness of passive bleed in controlling strong shocks. In the next section, the problem studied along with the three passive control devices investigated are described. Afterwards, the formulation, numerical method of solution, and results obtained are presented. DESCRIPTION OF PROBLEM Figure 1 shows a schematic diagram of the passively controlled oblique-shock-wave/boundary-layer interaction problem being studied. It involves a supersonic turbulent boundary layer flowing past a flat plate with an incident oblique shock wave and blowing/bleeding from a passive device. Figures 2 to 4 show details of the three passive devices analyzed. The reasons for selecting these three configurations are given in the results section. The physical dimensions in Figs. 1 to 4 are as follows: LI = 57.34 cm, H = 25.4 cm, L = 7.65 cm, al = 1.14 cm, a2 = 0.76cm, a3 =0.38 cm, bl = 1.62 cm, b2 = 1.08 cm, b3 = 0.54 cm, cl = 8.6 cm, c2 = 7.65 cm, cl = 6.06 cm, c2' = 5.11 cm, h = 0.0381 cm, and s = 0.635 cm. Othei dimensions are given later in this section. Fig. 1. Schematic of problem studied. Fig. 2. Passive device 1: flap. Fig. 3. Passive device 2: big ellipse. ff{\_ JL-' — i " l IBlcalin Fig. 4. Passive device 3: small ellipse. For the problem shown in Fig. 1, the computational domain is the region bounded by the dashed lines. The fluid that enters the domain above the flat plate is air Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc. with a specific-heats ratio (y) of 1.4. The freestream Mach number (Moo), static pressure (Poo), and static temperature (T») are 2.46, 10.736 KPa, and 131.93 K, respectively. This supersonic flow has a turbulent, boundary layer next to the flat plate. At the inflow boundary, the thickness of that boundary layer (5) is 3.244 cm. The displacement thickness (8*) is 0.196 cm. A shock-wave generator characterized by L2 and a causes an oblique shock wave to strike the turbulent, boundary layer on the flat plate, a was set at 8° which produced a shock wave that was strong enough to induce flow separation on the flat plate in the absence of bleed or blowing. L2 was chosen so that the shock would incident on the flat plate at a distance of 34.4 cm measured from the inflow boundary under inviscid flow conditions (i.e., zero boundary-layer thickness). Aside from studying the three passive control devices shown in Figs. 2 to 4, the following were investigated: two locations of the incident shock wave relative to the passive control device (one just upstream of the bleed slot as shown in Figs. 2 to 4 and another just downstream of the blowing slot as shown in Figs. 5 and 6) and two boundary-layer heights at the inflow boundary (one finite as shown in Figs. 2 to 5 and the other zero as shown in Fig. 6). Note that when the shock impingement location change, the passive control device moved not the flat plate (i.e., L2 remains constant). Also, note when the boundary-layer height is zero at the inflow, the wall was kept inviscid until reaching the passive device. All cases studied are summarized in Table 1. Table 1 Summary of Cases Studied*