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Assessing and improving the accuracy of synthetic turbulence generation

Published online by Cambridge University Press:  13 November 2020

J. W. Patterson ,
R. Balin  and
K. E. Jansen Open the ORCID record for K. E. Jansen [Opens in a new window]
J. W. Patterson
Affiliation:
Department of Aerospace Engineering, University of Colorado, Boulder, CO80309, USA
R. Balin
Affiliation:
Department of Aerospace Engineering, University of Colorado, Boulder, CO80309, USA
K. E. Jansen*
Affiliation:
Department of Aerospace Engineering, University of Colorado, Boulder, CO80309, USA
*
†Email address for correspondence: kenneth.jansen@colorado.edu
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Abstract

With the growing interest in scale-resolving simulations of spatially evolving boundary layers, synthetic turbulence generation (STG) has become a valuable tool for providing unsteady turbulent boundary conditions through a sum over a finite number of spatio-temporal Fourier modes with amplitude, direction and phase determined by a random number set. Recent developments of STG methods are designed to match target profiles for anisotropic and inhomogeneous Reynolds stresses. In this paper, it is shown that, for practical values of the number of modes, a given set of random numbers may produce Reynolds stress profiles that are 30 % off their target. To remedy this situation, the error in the STG stress prediction is decomposed into a steady-state bias and a purely unsteady part affecting the time convergence. Direct relationships between the random number vectors and both types of error are developed, allowing large collections of random number sets to be rapidly scanned and the best performers selected for a much improved agreement with the target. The process is verified for the inflow to a direct numerical simulation of a flat plate at $Re_\theta = 1000$. This paper demonstrates sufficient time convergence over a few flow-through times as well as a correction of the method's biases.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 906 , 10 January 2021 , R1
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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