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A numerical investigation of laminar flow over a backward facing inclined step

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Abstract

The aim of the present study is to analyze the two dimensional flow over a backward-facing-inclined step in laminar flow regime. The inspiration for the present work is derived from the fact that in automobile industry, analyzing the flow over an inclined step shall help in understanding the characteristics of the rear vehicle wake. A considerable percentage of the energy needed to propel the vehicle is dissipated by the vorticity generated in the rear of the vehicle, hence it is of utmost importance to understand the properties of the wake. In the present paper, the flow over a backward step is initially analyzed and the results are compared with the existing literature to validate the code developed. The inclined step simulations were carried out by varying different aspects of the geometry i.e. different tilts, several upstream lengths and a range of different Reynolds numbers. Critical Reynolds numbers for vortex shedding in the wake of different step inclinations have been analyzed for all cases studied. A discussion on the time-averaged drag and lift coefficients as a function of Reynolds number and for all cases undertaken, are among the results presented. Among the conclusions, it is particularly interesting to point out that the inclination angle of 15° was found to be the critical angle for vortex shedding, after which critical Reynolds number remains constant.

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Abbreviations

a:

Height of the inclined step (m)

CD :

Drag coefficient

CL :

Lift coefficient

FD :

Dimensional drag force (N)

Ff :

Flux through face f of the control volume

FL :

Dimensional lift force (N)

Fp :

Dimensional normal force (N)

Fs :

Dimensional shear force (N)

h:

Height of the non-orthogonal physical domain

l:

Length of the non-orthogonal physical domain

Lr :

Non-dimensional vortex recirculation length

\({\hat{\text{n}}}\) :

Outward normal of the surface S

P:

Non-dimensional pressure

Re:

Reynolds number

S:

Surface onto the control volume

t:

Non-dimensional time

ul:

Upstream length of the physical domain

u:

Non-dimensional velocity X direction

U:

Free stream velocity in X direction at the inlet (m/s)

v:

Non-dimensional velocity Y direction

\(\forall\) :

Control volume (m3)

x:

Non-dimensional Eulerian coordinates in horizontal direction

xp :

Dimensional horizontal coordinate of the physical domain (m)

y:

Non-dimensional Eulerian coordinates in vertical direction

yp :

Dimensional vertical coordinate of the physical domain (m)

δ:

Non-dimensional boundary layer thickness on the upstream surface

η:

Non-dimensional coordinates of transformed domain in vertical direction

θ:

Angle of inclination (deg)

ξ:

Non-dimensional coordinates of transformed domain in horizontal direction

References

  1. Anderson JD (1995) Computational fluid dynamics. McGraw Hill, New York City

    Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Armaly BF, Li A, Nie JH (2003) Measurements in the three-dimensional laminar separated flow. Int J Heat Mass Transf 46:3573–3582

    Article  Google Scholar 

  4. Chen YT, Nie JH, Hsieh HT, Sun LJ (2006) Three-dimensional convection flow adjacent to inclined backward-facing step. Int J Heat Mass Transf 49:4795–4803

    Article  MATH  Google Scholar 

  5. Chowdhary H, Dhiman A (2011) Two-dimensional laminar fluid flow and heat transfer over a backward-facing step: effects of Reynolds and Prandtl numbers. Heat Transf Res J 42(4):379–402

    Article  Google Scholar 

  6. Cogotti A (1998) A parametric study on the ground effect of a simplified car model. SAE paper 980031, pp 37–63

  7. Franck G, Nigro N, Storti M, D’Elía J (2009) Numerical simulation of the flow around the Ahmed vehicle model. Lat Am Appl Res 39:295–306

    Google Scholar 

  8. Gandjalikhan Nassab SA, Moosavi R, Hosseini Sarvari SM (2009) Turbulent forced convection flow adjacent to inclined forward step in a duct. Int J Therm Sci 48:1319–1326

    Article  Google Scholar 

  9. Gartling DK (1990) A test problem for outflow boundary condition flow over a backward-facing step. Int J Numer Methods Fluids 11:953–967

    Article  Google Scholar 

  10. Guilmineau E (2008) Computational study of flow around a simplified car body. J Wind Eng 96:1207–1217

    Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  12. Kaiktsis L, Karniadakis GE, Orszag SA (1996) Unsteadiness and convective instabilities in a two-dimensional flow over a backward-facing step. J Fluid Mech 321:157–187

    Article  ADS  MATH  Google Scholar 

  13. Kaltenbach HJ, Janke G (2000) Direct numerical simulation of flow separation behind a swept rearward-facing step at ReH = 3000. Phys Fluids 129:2320–2337

    Article  ADS  MATH  Google Scholar 

  14. Kaltenbach HJ (2004) Turbulent flow over a swept backward-facing step. Eur J Mech B Fluids 23:501–518

    Article  MATH  Google Scholar 

  15. Kapadia S, Roy S, Wurtzler K (2003) Detached eddy simulation over a reference Ahmed car model. AIAA paper 0857, pp 1–10

  16. Kim J, Moin P (1985) Application of a fractional-step method to incompressible Navier–Stokes equations. J Comput Phys 59:308–323

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Kotapati RB, Shock R, Chen H (2014) Lattice–Boltzmann simulations of flows over backward-facing inclined steps. Int J Mod Phys C 25(1):1340021-1-14

    Article  ADS  MathSciNet  Google Scholar 

  18. Krajnovic S, Davidson L (2004) Large-eddy simulation of the flow around simplified car model. SAE world congress, Detroit USA. Paper 01-0227, pp 1–10

  19. Leinhart H, Stoots C, Becker S (2003) Flow and turbulence structures in the wake of a simplified car model (Ahmed model). SAE technical paper series. Paper 01-1315, pp 1–8

  20. Louda P, Príhoda J, Kozel K, Svácek P (2013) Numerical simulation of flows over 2D and 3D backward-facing inclined steps. Int J Heat Fluid Flow 43:268–276

    Article  Google Scholar 

  21. Makiola B (1992) Experimentelle Untersuchungen zur strömung über Schräge stufe. PhD Thesis, Univ. of Karlsruhe

  22. Nguyen TD, Wells JC, Nguyen CV (2012) Velocity measurement of near-wall flow over inclined and curved boundaries by extended interfacial particle image velocimetry. Flow Meas Instrum 23:33–39

    Article  Google Scholar 

  23. Roberts GO (1971) Computational meshes for boundary layer problems. In: Proceedings of the second international conference on numerical methods and fluid dynamics, vol 8. Lecture notes in physics. Springer, New York, pp 171–177

  24. Sohankar A, Davidson L, Norberg C (1995) Numerical simulation of unsteady flow around a square two dimensional cylinder. In: 12th Australian fluid mechanics conference. University of Sydney, Australia, pp 517–520

  25. Sohankar A, Norberg C, Davidson L (1998) Low Reynolds number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition. Int J Numer Methods Fluids 26:39–56

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Fluid Mechanics Department, Technical University of Catalunya, 08222, Terrassa, Barcelona, Spain

    Aditya Mushyam & Josep M. Bergada

  2. Hermann Föttinger Institute für Experimentelle Strömungsmechanik, Technical University of Berlin, 10623, Berlin, Germany

    C. Navid Nayeri

Authors
  1. Aditya Mushyam
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  2. Josep M. Bergada
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  3. C. Navid Nayeri
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Correspondence to Aditya Mushyam.

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Mushyam, A., Bergada, J.M. & Navid Nayeri, C. A numerical investigation of laminar flow over a backward facing inclined step. Meccanica 51, 1739–1762 (2016). https://doi.org/10.1007/s11012-015-0335-5

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