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Approximate coordinate transformations for simulation of turbulent flows with wall deformation

  • Thermal Engineering · Fluid Engineering · Energy and Power Engineering
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Abstract

In the present paper, approximate coordinate transformations for simulation of turbulent flows with wall deformation, significantly reducing computational cost with little degradation in numerical accuracy, are presented. The Navier-Stokes equations are coordinate-transformed with an approximation of Taylor-series truncation. The performance is evaluated by performing numerical simulations of a channel flow atRe τ =140 with active wall motions of |η + m |≤5. The approximate transformations provide flow structures as well as turbulence statistics in good agreement with those from a complete transformation [Phys. Fluids 12, 3301 (2000)] and allow 25–30% savings in the CPU time as compared to the complete one.

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Abbreviations

C, W k :

Control parameters

i :

Imaginary-number unit

P, p :

Pressure

t,x i :

Time/space

u o ,U τ :

Laminar-centerline/friction velocity

δ:

Increment

η u ,η d ,η,η o :

Displacement parameters

τ,ξ i :

Transformed time/space

h :

Channel half-width

k i ,i:

Wave numbers

S, S i :

Source terms

u i :

Velocity

v i :

Transformed velocity

δ ij :

Kronecker delta function

ϕ i , φ i :

Metric coefficients

ν:

Kinematic viscosity

Λ:

Fourier component

+:

Wall coordinates

\(Re\left( { = \frac{{u_o h}}{\nu }} \right), Re_\tau \left( { = \frac{{u_\tau h}}{\nu }} \right)\) :

Reynolds numbers

References

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Authors and Affiliations

  1. School of Automotive, Industrial and Mechanical Engineering, Daegu University, 712-714, Gyeongsan, Gyeongbuk, Korea

    Sangmo Kang

Authors
  1. Sangmo Kang
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Correspondence to Sangmo Kang.

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Kang, S. Approximate coordinate transformations for simulation of turbulent flows with wall deformation. KSME International Journal 16, 703–709 (2002). https://doi.org/10.1007/BF03184820

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  • DOI: https://doi.org/10.1007/BF03184820

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