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High Reynolds number flow over a backward-facing step: structure of the mean separation bubble

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Abstract

In the present paper, the structure of the mean separation bubble downstream of the backward-facing step is studied at large Reynolds numbers. The flow over the step at these Reynolds numbers is turbulent with the presence of unsteady large-scale structures. There is however a well-defined time-averaged mean separation bubble. We study the effect of Reynolds number and expansion ratio on the structure of this mean separation bubble, the expansion ratio being the primary geometrical parameter in this case. Using PIV measurements within the separation bubble, parameters such as the reattachment length, mean velocity field, and the turbulent stresses are systematically mapped out. These measurements show that there exists a high Reynolds number separation bubble structure that is nearly independent of both Reynolds number and expansion ratio, as long as the Reynolds numbers are large (Re > 36,000 based on step height). Within this large Reynolds number separation bubble, the normalized mean velocity field and the normalized turbulent stresses are found to be similar for all expansion ratio cases studied. Using these measurements, the streamwise force balance of the mean separation bubble is studied. The analysis of the data shows that in this case, the contribution to the streamwise force from both the Reynolds normal and shear stress is significant, although the Reynolds shear stress contribution is larger. Differences in the force contributions from other geometries are highlighted.

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References

  • Adams EW, Johnston JP (1988) Effects of the separating shear layer on the reattachment flow structure part 2: reattachment length and wall shear stress. Exp Fluid 6:493–499

    Google Scholar 

  • Arie M, Rouse H (1956) Experiments on two-dimensional flow over a normal wall. J Fluid Mech 1:129–141. doi:10.1017/S0022112056000093

    Article  Google Scholar 

  • Armaly BF, Durst F, Pereira JCF, Schonung B (1983) Experimental and theoretical investigation of backward-facing step flow. J Fluid Mech 127:473–496

    Article  Google Scholar 

  • Baker S (1975) Regions of recirculating flow associated with two-dimensional steps. PhD Thesis, Dept of Civil Eng, University of Surrey

  • Balchandar S, Mittal R, Najjar FM (1997) Properties of the mean recirculation region in the wakes of two-dimensional bluff bodies. J Fluid Mech 351:167–199

    Article  Google Scholar 

  • Barkley D, Gomes MGM, Henderson RD (2002) Three-dimensional instability in flow over a backward-facing step. J Fluid Mech 473:167–190

    Article  MATH  MathSciNet  Google Scholar 

  • Barri M, El Khoury GK, Andersson HI, Pettersen B (2010) Dns of backward-facing step flow with fully turbulent inflow. Int J Numer Methods Fluids 64(7):777–792. doi:10.1002/fld.2176

    MATH  MathSciNet  Google Scholar 

  • Beaudoin JF, Cadot O, Aider JL, Wesfreid JE (2004) Three-dimensional stationary flow over a backward-facing step. Eur J Mech B Fluids 23(1):147–155

    Article  MATH  Google Scholar 

  • Biswas G, Breuer M, Durst F (2004) Backward-facing step flows for various expansion ratios at low and moderate reynolds numbers. Trans ASME J Fluids Eng 126:362–374

    Article  Google Scholar 

  • Cantwell B, Coles D (1983) An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder. J Fluid Mech 136:321–374. doi:10.1017/S0022112083002189

    Article  Google Scholar 

  • Chandrsuda C (1975) A reattaching turbulent shear layer in incompressible flow. PhD Thesis, Departmentt of Aeronautics, Imperial College of Science and Technology

  • Chun KB, Sung HJ (1996) Control of turbulent separated flow over a backward-facing step by local forcing. Exp Fluid 21(6):417–426

    Article  Google Scholar 

  • De Brederode V, Bradshaw P (1972) Three-dimensional flow in nominally two-dimensional separation bubbles. I. Flow behind a rearward-facing step. IC Aero Rep 72-19 Imperial College, London

  • Driver DM, Seegmiller HL (1985) Features of a reattaching turbulent shear-layer in divergent channel flow. AIAA J 23(2):163–171. doi:10.2514/3.8890

    Article  Google Scholar 

  • Durst F, Tropea C (1981) Turbulent backward-facing step flows in two-dimensional ducts and channels. In: Proceedings of turbulent shear flow 3 symposium Davis September 1981

  • Durst F, Tropea C (1982) Flows over two-dimensional backward-facing steps. Structure of complex turbulent shear flow: IUTAM-symposium, Marseille, France, August 31–September 3, 1982

  • Eaton JK, Johnston JP (1980) Turbulent flow reattachment: an experimental study of the flow and structure behind a backward-facing setp. Rept MD-39, Dept of Mech Eng, Stanford University, Stanford, CA

  • Eaton JK, Johnston JP (1981) Review of research on subsonic turbulent flow reattachment. AIAA J 19(9):1093–1100

    Article  Google Scholar 

  • Etheridge DW, Kemp PH (1978) Measurements of turbulent flow downstream of a rearward-facing step. J Fluid Mech 86:545–566. doi:10.1017/S0022112078001275

    Article  Google Scholar 

  • Feng K, Ying-zheng L, Wei-zhe W, Han-ping C (2006) Wall pressure fluctuations of turbulent flow over backward-facing step with and without entrainment: microphone array measurement. J Hydrodyn 18(4):393–396. doi:10.1016/S1001-6058(06)60110-8

    Article  Google Scholar 

  • Furuichi N, Hachiga T, Kumada M (2004) An experimental investigation of a large-scale structure of a two-dimensional backward-facing step by using advanced multi-point ldv. Exp Fluids 36(2):274–281. doi:10.1007/s00348-003-0718-6

    Article  Google Scholar 

  • Hudy LM, Naguib A, William MH (2007) Stochastic estimation of a separated-flow field using wall-pressure-array measurements. Phys Fluids 19(2):024103. doi:10.1063/1.2472507

    Article  Google Scholar 

  • Jovic S, Driver D (1995) Reynolds number effect on the skin friction in separated flows behind a backward-facing step. Exp Fluids 18(6):464–467. doi:10.1007/BF00208471

    Article  Google Scholar 

  • Kaiktsis L, Karniadakis GE, Orszag SA (1991) Onset of 3-dimensionality, equilibrium and early transition in flow over a backward-facing step. J Fluid Mech 231:501–528

    Article  MATH  Google Scholar 

  • Kang SW, Choi H (2002) Suboptimal feedback control of turbulent flow over a backward-facing step. J Fluid Mech 463:201–227

    Article  MATH  Google Scholar 

  • Kasagi N, Matsunaga A (1995) Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow. Int J Heat Fluid Flow 16(6):477–485. doi:10.1016/0142-727X(95)00041-N

    Article  Google Scholar 

  • Kim J, Kline SJ, Johnston JP (1978) Investigation of separation and reattachment of a turbulent shear layer: flow over a backward-facing step. Rept MD-37, Dept of Mech Eng, Stanford University, Stanford, CA

  • Kostas J, Soria J, Chong MS (2002) Particle image velocimetry measurements of a backward-facing step flow. Exp Fluid 33(6):838–853

    Article  Google Scholar 

  • Kuehn DM (1980) Effects of adverse pressure-gradient on the incompressible re-attaching flow over a rearward-facing step. AIAA J 18(3):343–344

    Article  MathSciNet  Google Scholar 

  • Le H, Moin P, Kim J (1997) Direct numerical simulation of turbulent flow over a backward-facing step. J Fluid Mech 330:349–374

    Article  MATH  Google Scholar 

  • Leder A (1991) Dynamics of fluid mixing in separated flows. Phys Fluids A 3(7):1741–1748. doi:10.1063/1.857953

    Article  Google Scholar 

  • Lee I, Ahn SK, Sung HJ (2004) Three-dimensional coherent structure in a separated and reattaching flow over a backward-facing step. Exp Fluid 36(3):373–383. doi:10.1007/s00348-003-0367-6

    Article  Google Scholar 

  • Narayanan MA, Khadgi YN, Viswanath PR (1974) Similarities in pressure distribution in separated flow behind backward-facing steps. Aeronaut Q 25:305–312

    Google Scholar 

  • Nie JH, Armaly BF (2004) Reverse flow regions in three-dimensional backward-facing step flow. Intl J Heat Mass Transf 47:4713–4720

    Article  Google Scholar 

  • Otugen MV (1991) Expansion-ratio effects on the separated shear-layer and reattachment downstream of a backward-facing step. Exp Fluid 10(5):273–280

    Article  Google Scholar 

  • Raffel M, Willert C, Kompenhans J (1998) Particle image velocimetry: a practical guide. Spinger, Berlin

    Book  Google Scholar 

  • Roshko A (1993) Free shear layers base pressure and bluff-body drag In: Proceedings of symposium on developement in fluid dynamics and aerospace engineering. Bangalore, India, December 9–10, 1993

  • Scarano F, Benocci C, Riethmuller ML (1999) Pattern recognition analysis of the turbulent flow past a backward facing step. Phys Fluids 11(12):3808–3818

    Article  MATH  Google Scholar 

  • Schram C, Rambaud P, Riethmuller M (2004) Wavelet based eddy structure eduction from a backward facing step flow investigated using particle image velocimetry. Exp Fluid 36:233–245. doi:10.1007/s00348-003-0695-9

    Article  Google Scholar 

  • Spazzini PG, Iuso G, Onorato M, Zurlo N, Di Cicca GM (2001) Unsteady behavior of back-facing step flow. Exp Fluids 30:551–561

    Google Scholar 

  • Sychev V (1982) Asymptotic theory of separation flows. Fluid Dyn 17(2):179–188

    Article  Google Scholar 

  • Tani I, Iuchi M, Komoda H (1961) Experimental investigation of flow separation associated with a step or groove. Report No 364, Aero Research Institute, University of Tokyo

  • Tylli N, Kaiktsis L, Ineichen B (2002) Sidewall effects in flow over a backward-facing step: experiments and numerical simulations. Phys Fluids 14:3835–3845

    Article  Google Scholar 

  • Westphal RV, Johnston JP, Eaton JK (1984) Experimental study of flow reattachment in a single-sided sudden expansion. NASA CR-3765

  • Williams PT, Baker AJ (1997) Numerical-solutions of laminar flow over a 3D backward-facing step. Int J Numer Methods Fluids 24:1159–1183

    Article  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Science, Bangalore, 560 012, India

    Pankaj M. Nadge & R. N. Govardhan

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  1. Pankaj M. Nadge
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  2. R. N. Govardhan
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Correspondence to R. N. Govardhan.

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Nadge, P.M., Govardhan, R.N. High Reynolds number flow over a backward-facing step: structure of the mean separation bubble. Exp Fluids 55, 1657 (2014). https://doi.org/10.1007/s00348-013-1657-5

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