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1 Yao, Y., Fang, J., Zheltovodov, A. A. and Lu, L. (2014) Direct numerical simulation of supersonic flows passing a backward step. In: UK Turbulence Consortium Workshop, Imperial College, London, September Available from: We recommend you cite the published version. The publisher s URL is: Refereed: Yes (no note) Disclaimer UWE has obtained warranties from all depositors as to their title in the material deposited and as to their right to deposit such material. UWE makes no representation or warranties of commercial utility, title, or fitness for a particular purpose or any other warranty, express or implied in respect of any material deposited. UWE makes no representation that the use of the materials will not infringe any patent, copyright, trademark or other property or proprietary rights. UWE accepts no liability for any infringement of intellectual property rights in any material deposited but will remove such material from public view pending investigation in the event of an allegation of any such infringement. PLEASE SCROLL DOWN FOR TEXT.

2 UK Turbulence Consortium Workshop Sept, 2014 Direct Numerical Simulation of Supersonic Flows Passing a Backward Step Jian Fang, Yufeng Yao, Alexander A. Zheltovodov, Lipeng Lu

3 Problem Background Supersonic flow passing a Backward step is one of key flow phenomena in high-speed vehicle and its propulsion systems Fully developed turbulent flow Expansion fan Shock-wave

4 E(k) CFD code: Low-Dissipation Monotonicity-Preserving Scheme Bandwidth dissipation optimization method (BDOM) is used to optimize the linear part of the MP scheme 1. Fang, J., Li, Z. and Lu, L., Journal of Scientific Computing, 56:67-95, Fang, J., Yao, Y.F., Li, Z. and Lu, L., Computers and Fluids, 104: 55-72, =1/280 =0.9/ =0.8/280 1E-3 =0.7/280 k -5/3 k st order upwind scheme 3rd order upwind scheme 5th order upwind scheme 7th order upwind scheme Eq. (3.11) with different k =0.6/280 =0.5/280 =0.4/280 =0.3/280 =0.2/280 =0.1/280 =0/280 1E-4 1E-5 1E-6 Reference COMP6 MP7-LD MP7 WENO7-Z MP5-LD MP5 WENO5-Z 1 10 k Bandwidth property of MP7-LD scheme DNS of isotropic turbulence

5 Supersonic flow passing a backward step 25 Mach=2.9 Case 1: Re d =20000 Case 2: Re d =40000 Case 3: Re d =80000 Density Schlieren Pressure Field Ref: Zheltovodov, A., et al. (1990). An Experimental Documentation of Supersonic Turbulent Flows in the Vicinity of Forward and Backward-Facing Ramps.

6 Separation bubble reduces with Reynolds number Mean Streamlines Re=20000 Re=40000 Re=80000

7 Surface pressure and skin friction Cf PW/P EC CC x Wall Pressure Case 1 Case 2 Case 3 Experiment at Re d = Experiment at Re d =80000 Experiment at Re d =67600 Experiment at Re d =40700 LES of El-Askary 2011 LES of Knight et al EC: expansion corner; CC: compression corner EC CC x Skin friction Case 1 Case 2 Case 3 LES of El-Askary 2011 LES of Knight et al Experiment at Re d = Experiment at Re d =80000 Ref : Zheltovodov, A., et al. (1990). An Experimental Documentation of Supersonic Turbulent Flows in the Vicinity of Forward and Backward-Facing Ramps.

8 dpw/dx Pressure gradient and numerical Schlieren Peak 2 (r) Peak 1 (s) Separation point (s) Case 1 Case EC CC x Wall Pressure Gradient Schematic draw of separation length Re=20000 Re=40000 Re=80000

9 d Turbulent flow properties and its variation =2 =5 =6 =7 =8 =9 =11 =12 =15 =20 =23 Turbulence Kinetic Energy Reynolds Shear Stress < u v > =x EC =x CC K Peak location change lifted during separation

10 K Variation along two streamlines <u''v''> S1: near wall S2: mid-bl at inflow S1 S2 8 6 EC CC S1 S EC CC S1 S long plateau x short plateau Different evolution process of TKE and Reynolds shear stress along two streamlines x

11 Variation of cross correlation d R(us'',un'') Correlation of streamwise and normal velocity fluctuation

12 Locations for comparison Location of correlation peaks

13 Instantaneous streamwise u Streamwise velocity fluctuation along the streamlines S1 and S2

14 Finer flow structures Classic horseshoe wall turbulence Suppression of Turbulence DNS of Zhou et al Large-scale Görtler Vortex Iso-surface of l ci colored with w x Turbulent Coherent Structure Iso-surface of w colored with u x

15 Close view of flow structures Horseshoe vortex Turbulent coherent structures in the ramp region

16 Flow topology compared to Oil-flow test Time mean wall streamline and skin friction Oil-flow visualization (Zheltovodov et al., 1983)

17 Surface flow topology d d Re=20000 Re=40000 d Distance between neighbour nodes = BL thickness δ Re=80000

18 Concluding Remarks Supersonic Expansion/Compression Corner is investigated by using DNS Turbulence is suppressed during expansion but enhanced in compression; Two different characteristics of turbulent structures was found in the ramp region as In the outer layer, turbulence is consistently suppressed; In the inner layer, (1) turbulence is largely suppressed only in the corner region, then gradually redevelops; (2) coherence structure of fluctuations is preserved and it increases during the compression Large-scale Görtler vortices are clearly captured, indicating its connection to upstream wall turbulence; Reynolds number effect is observed Separation bubble shrinks with the increase of Re, but Scale of Görtler vortices is independent of Re (distance between nodes)

19 Thank You!

We recommend you cite the published version. The publisher s URL is:

We recommend you cite the published version. The publisher s URL is: Fang, J., Yao, Y., Li, Z. and Lu, L. (2014) Investigation of lowdissipation monotonicity-preserving scheme for direct numerical simulation of compressible turbulent flows. Computers & Fluids, 104. pp.

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