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Application of a sensitivity equation method to the k–ε model of turbulence

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Abstract

In this paper, we present some examples of sensitivity analysis for flows modeled by the standard k–ε model of turbulence with wall functions. The flow and continuous sensitivity equations are solved using an adaptive finite element method. Our examples emphasize a number of applications of sensitivity analysis: identification of the most significant parameters, analysis of the flow model, assessing the influence of closure coefficients, calculation of nearby flows, and uncertainty analysis. The sensitivity parameters considered are closure coefficients of the turbulence model and constants appearing in the wall functions.

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Abbreviations

SEM:

Sensitivity Equation Method

RANS:

Reynolds-Averaged Navier–Stokes Equations

a :

Design parameter

C 1,C 2,C μ ,σ k ,σ ε :

k–ε model constants

C f :

Skin friction coefficient

d :

Imposed distance to the wall

E :

Roughness parameter

k :

Turbulent kinetic energy

\(\mathcal{K}\) :

Natural logarithm of k

L :

Reference length

p :

Pressure

P :

Production of turbulence

Re:

Reynolds number

s x :

Sensitivity of the variable x

u :

Velocity

u,v :

Velocity components

u k :

Velocity scale based on k

u ** :

Friction velocity τ w =ρ u ** u k

x,y :

Cartesian coordinates

y :

Distance to the wall

ε :

Turbulent dissipation rate

ℰ:

Natural logarithm of ε

κ :

Kármán constant

μ :

Viscosity

μ t :

Eddy viscosity

ρ :

Density

τ w :

Wall shear stress

t :

Tangent to the wall

′ :

Sensitivity (derivative)

+:

Dimensionless (wall functions)

T :

Transpose

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Authors and Affiliations

  1. Département de Génie Mécanique, École Polytechnique de Montréal, Montréal, PQ, H3C 3A7, Canada

    É. Turgeon, D. Pelletier & S. Etienne

  2. Interdisciplinary Center for Applied Mathematics, Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061-0531, USA

    J. Borggaard

Authors
  1. É. Turgeon
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  2. D. Pelletier
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  3. J. Borggaard
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  4. S. Etienne
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Correspondence to D. Pelletier.

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Turgeon, É., Pelletier, D., Borggaard, J. et al. Application of a sensitivity equation method to the k–ε model of turbulence. Optim Eng 8, 341–372 (2007). https://doi.org/10.1007/s11081-007-9003-5

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