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Role of pseudo-turbulent stresses in shocked particle clouds and construction of surrogate models for closure

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Abstract

Macroscale models of shock–particle interactions require closure terms for unresolved solid–fluid momentum and energy transfer. These comprise the effects of mean as well as fluctuating fluid-phase velocity fields in the particle cloud. Mean drag and Reynolds stress equivalent terms (also known as pseudo-turbulent terms) appear in the macroscale equations. Closure laws for the pseudo-turbulent terms are constructed in this work from ensembles of high-fidelity mesoscale simulations. The computations are performed over a wide range of Mach numbers (M) and particle volume fractions (\(\phi )\) and are used to explicitly compute the pseudo-turbulent stresses from the Favre average of the velocity fluctuations in the flow field. The computed stresses are then used as inputs to a Modified Bayesian Kriging method to generate surrogate models. The surrogates can be used as closure models for the pseudo-turbulent terms in macroscale computations of shock–particle interactions. It is found that the kinetic energy associated with the velocity fluctuations is comparable to that of the mean flow—especially for increasing M and \(\phi \). This work is a first attempt to quantify and evaluate the effect of velocity fluctuations for problems of shock–particle interactions.

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Acknowledgements

We gratefully acknowledge the financial support by the Air Force Office of Scientific Research under Grant Number FA9550-12-1-0115. H.S. Udaykumar also acknowledges support from a Grant from AFRL, Eglin AFB (Program Manager: Martin Schmidt).

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Authors and Affiliations

  1. Mechanical and Industrial Engineering, The University of Iowa, Iowa City, IA, 52242, USA

    O. Sen, K. K. Choi & H. S. Udaykumar

  2. RAMDO Solutions, LLC, Iowa City, IA, 52240, USA

    N. J. Gaul

  3. Aerospace Engineering, San Diego State University, San Diego, CA, 92115, USA

    S. Davis & G. Jacobs

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Communicated by D. Frost and A. Higgins.

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Sen, O., Gaul, N.J., Davis, S. et al. Role of pseudo-turbulent stresses in shocked particle clouds and construction of surrogate models for closure. Shock Waves 28, 579–597 (2018). https://doi.org/10.1007/s00193-017-0801-1

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