Simulation of Shock/Boundary-Layer Interactions with Bleed Using Immersed-Boundary Methods

Abstract

This work uses an immersed-boundary method to simulate the effects of arrays of discrete bleed holes in controlling shock-wave/turbulent-boundary-layer interactions. Both Reynolds-averaged Navier-Stokes and hybrid large-eddy/Reynolds-averaged Navier-Stokes turbulence closures are used with the immersed-boundary technique. The approach is validated by conducting simulations of Mach 2.5 flow over a perforated plate containing 18 individual bleed holes. Computed values of discharge coefficient as a function of bleed plenum pressure are compared to experimental data. Simulations of an impinging-oblique-shock/boundary-layer interaction at Mach 2.45 with and without bleed control are also performed. For the studies with bleed, two different bleed rates are employed. The 68 hole bleed plate is rendered as an immersed object in the computational domain. Wall pressure predictions show that, in general, the large-eddy/Reynolds-averaged Navier-Stokes technique underestimates the upstream extent of axial separation that occurs in the absence of bleed. Good agreement with pitot pressure surveys throughout the interaction region is obtained, however. Flow control at the maximum-bleed rate completely removes the separation region and induces local disturbances in the wall pressure distributions that are associated with the expansion of the boundary-layer fluid into the bleed port and its subsequent recompression. Computed pitot pressure distributions are in good agreement with experiment for the cases with bleed. Swirl-strength probability density distributions are used to estimate the evolution of turbulent length scales throughout the interaction. These, along with Reynolds-stress predictions, indicate that an effect of strong bleed rates is to accelerate the recovery of the boundary layer toward a new equilibrium state downstream of the interaction region. Nomenclature a 1 = model constant for Menter baseline model C f = skin-friction coefficient C M = model constant for mixed-scale model C = model constant for Menter baseline model D = diameter of bleed hole d = distance from nearest-wall/immersed-surface point d ; = normalized distance F 2 = model constant for Menter baseline model f, g = scaling functions G = Heaviside step function based on signed distance function k = turbulent kinetic energy/power law L = length of bleed hole M = Mach number n = coordinate normal to immersed surface P = static pressure P t = pitot pressure Q = sonic flow coefficient or discharge coefficient q 2 = estimate of subgrid kinetic energy R = universal gas constant Re = Reynolds number R n1;l i = residual vector at cell i for time step n 1 and subiteration l r = recovery factor S = characteristic filtered rate of strain T = temperature u = velocity vector, x component of velocity u = friction velocity V = primitive variable vector v = component of velocity in y direction w = component of velocity in z direction X = streamwise distance from leading edge of bleed-plate insert x = streamwise distance from leading edge of computational domain Y = ...

Progress in shock wave/boundary layer interactions

“…In contrast to the DES approaches, which switch from RANS to LES in separated flows away from walls, hybrid methods also treat attached flows, reducing the required computational resources with tailored near-wall RANS blended with LES away from the surface. A series of publications by Edwards et al describes the evolution of the procedure for different types of flows, including SBLI [133][134][135][136]. The corresponding required extension to the upstream profile generation approach based on recycling-rescaling is presented in Ref.…”

Flow Control in a Mach 4.0 Inlet by Slotted Wedge-shaped Vortex Generators

“…This immersed-boundary method is suitable for high-speed turbulent flows and has been used previously with success to simulate flows with similar flow-control devices. 9,10,13,17 The L 2 norm of the residual and the net mass balance are monitored for checking the convergence of the solution. The solution is considered converged when the normalized residual -with respect to the starting residual -reaches a value of about 1.0E − 08.…”

Progress in Shock Wave/Boundary Layer Interactions

“…A series of publications by Edwards et al describes the evolution of the procedure for different types of flows, including SBLI. [131][132][133][134] The corresponding required extension to the upstream profile generation approach based on recycling-rescaling is presented in Ref. 135.…”