Insights in Turbulence Modeling for Crossing-Shock-Wave/Boundary-Layer Interactions

Abstract

The impact of turbulence modeling on the numerical simulation of the crossing-shock-wave/boundary-layer interactions occuring in a Mach 4 ow on 7 £ £ 7 deg, 7 £ £ 11 deg, and 15 £ £ 15 deg double-sharp n plates is analyzed.The full Reynolds-averaged Navier-Stokes equations are solved with linear and weakly nonlinear formulations of the k-! turbulence model, on grids up to 4 £ £ 10 6 cells. The overpredicted heat transfer on the bottom plate is shown to be closely related to the main three-dimensional features developing in these ows. The stronger the interaction, the more the numerical solutions violate the realizability principles. By introducing a dependence of cµ on the velocity gradients, realizable solutions are obtained and analyzed. The heat-transfer coef cients are effectively lowered but not suf ciently to meet the experimental data. The expected impact of other corrections, based on a limitation of the turbulent length scale or some compressibility effects, is evaluated and shown to be insuf cient to ll the gap between computed and measured heat-transfer coef cients. The streamlines arriving near the wall in the regions of overpredicted heat transfer are shown to originate from the very narrow regions close to the n leading edges, in the upper part of the incoming boundary layer, and to be associated with an increase of turbulent kinetic energy when approaching the bottom wall, rather than when crossing the shock waves. Nomenclature C h= heat-transfer coef cient or Stanton number; Eq. (1) c l = coef cient in the constitutive equation for l t , 0.09 D t (q } ) = substantial derivative, @q } / @t @q U õ } / @X i k = turbulent kinetic energy (TKE), 1 2 ] u õ u õ P k = TKE production rate, q ] u õ u Ò S õ Ò S = strain invariant, (2S õ Ò S õ Ò ) S õ Ò = strain rate, 1 2 (@U õ / @x Ò @U Ò / @x õ ) S õ Ò = traceless strain rate, S õ Ò 1 3 S kk d õ Ò s = dimensionless strain invariant, S/ x U õ = mass-averaged velocity components U , V , W u õ = uctuating velocity components u, v, w (mass averaging) ] u õ u Ò = mass-averaged velocity correlations x Ò = Cartesian coordinates x, y, z a m = realizability factor; Eq. (8) d õ Ò = Kronecker symbol d 0 = incoming boundary-layerthickness, 3.5 mm ² = dissipation of TKE l , m = dynamic and kinematic molecular viscosities, l q m l t , m t = Dynamic and kinematic turbulent viscosities, l t q m t $ = dimensionless vorticity invariant, X / x q = mass density X = vorticity invariant, (2X õ Ò X õ Ò )

Numerical Study on the Aerodynamic Heating Characteristics of the Cantilevered Injection System for Oblique Detonation Engine Inlets

“…As for the investigation of three-dimensional protrusions on bodies, several canonical configurations are simplified to provide a fundamental understanding [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], such as the semi-conical model, compression ramp, unswept/swept sharp/blunt fin [12][13][14][15][16][17][18][19][20], and double sharp fin [21][22][23][24][25][26][27][28][29][30][31]. Hypersonic flows over these configurations lead to complex flow phenomena including shock wave/shock wave and shock wave/boundary layer interactions, horseshoe vortices, separations, and reattachments.…”

“…The flow structures and aerodynamic load features associated with blunt swept fins and sharp fins have been studied in the past decades [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In the classical flowfield upstream of a blunt fin, the lambda-shaped shock wave structure consists of a separation shock wave and a trailing shock wave, both of which intersect with the inviscid bow shock at the triple point.…”

Uncertainty Analysis of Parameters in SST Turbulence Model for Shock Wave-Boundary Layer Interaction

“…Therefore, enhancing the performance of the RANS method remains a research focus. It is well known that due to introduced assumptions and the lack of cognition of turbulence model parameters, the RANS method fails to acquire satisfactory results for the prediction of SWBLIs, particularly for wall heat flux after the reattachment of the separated boundary layer [10]. For deficiencies caused by introduced assumptions, many efforts have been undertaken.…”

Numerical Simulation of Crossing Shock Waveturbulent Boundary Layer Interaction

“…In his summarize Zheltovodov [1] introduced numbers of researches on 3-D crossing shock wave/turbulent boundary layer interaction using double-fin-plate model. Garrison [2], Kussoy [3] and Zheltovodov [4] have carried out series of high Mach number (3)(4)(5)(6)(7)(8) double-fin-plate experiments during which numbers of basic values had been measured such as the wall pressure, wall temperature exchange, wall friction coefficients as well as oil-flow visualization of flow stream on wall and these would help analyzing flow structures and validating numerical calculation. Narayanswa [5], Gaitonde [6], Schmisseur [7] and Thivet [8] have numerically simulated double-fin-plate models of different fin angles under symmetric conditions.…”

“…Garrison [2], Kussoy [3] and Zheltovodov [4] have carried out series of high Mach number (3)(4)(5)(6)(7)(8) double-fin-plate experiments during which numbers of basic values had been measured such as the wall pressure, wall temperature exchange, wall friction coefficients as well as oil-flow visualization of flow stream on wall and these would help analyzing flow structures and validating numerical calculation. Narayanswa [5], Gaitonde [6], Schmisseur [7] and Thivet [8] have numerically simulated double-fin-plate models of different fin angles under symmetric conditions. These simulations analyze effects on flow structures induced by shock-wave of different strength; revealed the change of crossing shock wave type along flow orientation; compared the precision of computational results calculated from different turbulent models such as B-L and its modified models, k-ε, k-ω and their compressibility corrected models.…”