Wall-Resolved Large-Eddy Simulations of Transonic Shock-Induced Flow Separation

Abstract

This paper reports the wall-resolved large eddy simulations of shock-induced boundary layer separation over an axisymmetric bump for a flow Mach number of 0.875 and a chord-based Reynolds number of 2.763 million. The incoming boundary layer has a momentum-thickness Reynolds number of 6600 at one and a half chord lengths upstream of the leading edge. The calculations simulate the experiment by Bachalo and Johnson (AIAA Journal, Vol. 24, No. 3, 1986), except that the tunnel walls are ignored and the simulations are performed assuming free air with as many as 24 billion grid points. The effects of domain span, grid resolution and time step on the predictions are examined. The results are found to show some sensitivity to the studied parameters. Owing to the outer boundary conditions, the predicted surface pressure distribution as well as the flow separation and reattachment locations tend to agree better with the experimental results from the larger (6 × 6 ft) tunnel than those from the smaller (2 × 2 ft) tunnel. The predicted Reynolds shear stress profiles in the separated region differ by as much as 31% from the experimental results that were only obtained in the smaller tunnel. The most accurate surface pressure distribution obtained in this study lies within the scatter of the measurements taken in the two facilities.

Continuous Eddy Simulation (CES) of Transonic Shock-Induced Flow Separation

“…In contrast, the CES-KOS model provides the highest accuracy regarding the estimation of the separation length, with an error of only ≈4%. Figure 19 shows in its first row streamwise velocity profiles obtained by CES-KOS, WMLES [41], and WRLES [42]. It may be seen that the CES-KOS model predicts the streamwise velocity more accurately than WMLES and WRLES.…”

“…Figure 19. CES-KOS vs. LES-type WRLES [42] and WMLES [41] models: Profiles of the normalized streamwise velocity ⟨U⟩/U re f , Reynolds stress ⟨uv⟩/U 2 re f , pressure, and skin-friction coefficients at different locations.…”

“…Simulation cost estimates (C/T) for WRLES[42,58], WMLES[41,58], DES[21,34,59], and CES-KOS.Re Re 0 ) 0.545 ∆t = α 2 ( Re Re 0 ) −0.554 N/∆t = α 3 ( Re Re 0 ) 1.099 α 3 = (1.08 − 10.8) × 10 9 WRLES N = α 1 ( Re Re 0 ) 1.86 ∆t = α 2 ( Re Re 0 ) −0.857 N/∆t = α 3 ( Re Re 0 ) 2.72 α 3 = (1.05 − 8.39) × 10 14 WMLES N = α 1 ( Re Re 0 ) 1.0 ∆t = α 2 ( Re Re 0 ) −0.143 N/∆t = α 3 ( Re Re 0 ) 1.143 α 3 = (8.3 − 9.96) × 10 10 DES N = α 1 ( Re Re 0 ) 0.545 ∆t = α 2 ( Re Re 0 ) −0.554 N/∆t = α 3 ( Re Re 0 ) 1.099 α 3 = (4.7 − 32.0) × 10 11…”

Numerical and experimental investigations on the jet and shock wave dynamics during the cavitation bubble collapsing near spherical particles based on OpenFOAM

“…Tian et al [34] numerically investigated the jet and shock waves generated by near-wall bubble. Based on the numerical schlieren method, which is also used to show the flow as well as the turbulent structure [35] , [36] , [37] , when the jet impinges on the wall, the shear flow will tear the toroidal bubble and generate two toroidal shock waves. Zevnik and Dular [27] conducted a numerical study of a cavitation bubble near a rigid particle.…”

Numerical Investigation of Cavitation Bubble Jet Dynamics near a Spherical Particle

“…Liu et al [15] found that the jet induces a first peak at the center of the wall and a second peak at high pressure inside the bubble, based on the front tracking method. Based on numerical schlieren (which also visualize turbulent structures [16,17]), Tian et al [18] state that the shock wave causes the first pressure peak, and the jet causes the second pressure peak. Sun et al [19] reported that the rigid wall with a gas entrapping hole can reduce the pressure of the jet on the wall.…”