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Title: Two-way coupled particle-turbulence interaction: Effect of numerics and resolution on fluid and particle statistics

Abstract

Euler-Lagrange point-particle simulation has emerged as a premier methodology for studying dispersed particle-laden flows. This method's popularity stems from its ability to resolve fine-scale fluid structures while also tracking individual particles at reduced cost using an appropriate particle acceleration model. However, the point-particle model has known convergence issues in that refinement of the fluid grid can lead to changes in the predicted statistics. The reasons for non-convergence are twofold: the point-particle two-way coupling force in the Navier-Stokes equations requires a numerical regularization and, without careful implementation, yields a singular force on the fluid with grid refinement. The second factor that yields grid-dependent statistics is that the point-particle force model in general depends on the undisturbed fluid velocity. When the undisturbed fluid velocity is not robustly modeled in a grid-insensitive way, the calculated force for both particles and fluid will be grid-dependent, contaminating their respective statistics. While the first issue regarding regularizing the point-particle source term has received attention in the literature, the consequences of robustly modeling the undisturbed velocity in the context of grid refinement of turbulence has received little attention. Here, we consider decaying homogeneous isotropic turbulence laden with particles at different Stokes numbers. For a given Stokes number,more » we systematically refine the grid and demonstrate that explicitly modeling the undisturbed fluid velocity yields relative grid insensitivity for the energy of the particle and fluid phases, as well as acceleration of the particles. We also demonstrate that an appropriately defined dissipation rate is also grid-insensitive when an undisturbed fluid velocity correction is used. In contrast, when the undisturbed fluid velocity is modeled using the conventional approach of interpolating the local fluid velocity to the particle location, we show this procedure yields divergent statistics with grid refinement. In particular, we show that higher-order interpolation of the fluid velocity in two-way coupled problems is worse than lower-order interpolation, in the absence of a correction procedure to estimate the undisturbed fluid velocity. We also examine velocity derivative statistics of the fluid phase and demonstrate that these statistics are not in general convergent even when the undisturbed fluid velocity is explicitly modeled. Collectively, the observations in this paper are used to present a philosophy on the types of questions which are answerable with point-particle methods.« less

Authors:
 [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Stanford Univ., CA (United States)
  2. Stanford Univ., CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
OSTI Identifier:
1673189
Report Number(s):
LLNL-JRNL-791338
Journal ID: ISSN 2469-990X; 988559
Grant/Contract Number:  
AC52-07NA27344; NA0002373; DGE-114747
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Fluids
Additional Journal Information:
Journal Volume: 5; Journal Issue: 10; Journal ID: ISSN 2469-990X
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; point-particle; Euler-Lagrange; grid convergence; two-way coupling

Citation Formats

Horwitz, J. A. K., and Mani, A. Two-way coupled particle-turbulence interaction: Effect of numerics and resolution on fluid and particle statistics. United States: N. p., 2020. Web. https://doi.org/10.1103/physrevfluids.5.104302.
Horwitz, J. A. K., & Mani, A. Two-way coupled particle-turbulence interaction: Effect of numerics and resolution on fluid and particle statistics. United States. https://doi.org/10.1103/physrevfluids.5.104302
Horwitz, J. A. K., and Mani, A. Mon . "Two-way coupled particle-turbulence interaction: Effect of numerics and resolution on fluid and particle statistics". United States. https://doi.org/10.1103/physrevfluids.5.104302.
@article{osti_1673189,
title = {Two-way coupled particle-turbulence interaction: Effect of numerics and resolution on fluid and particle statistics},
author = {Horwitz, J. A. K. and Mani, A.},
abstractNote = {Euler-Lagrange point-particle simulation has emerged as a premier methodology for studying dispersed particle-laden flows. This method's popularity stems from its ability to resolve fine-scale fluid structures while also tracking individual particles at reduced cost using an appropriate particle acceleration model. However, the point-particle model has known convergence issues in that refinement of the fluid grid can lead to changes in the predicted statistics. The reasons for non-convergence are twofold: the point-particle two-way coupling force in the Navier-Stokes equations requires a numerical regularization and, without careful implementation, yields a singular force on the fluid with grid refinement. The second factor that yields grid-dependent statistics is that the point-particle force model in general depends on the undisturbed fluid velocity. When the undisturbed fluid velocity is not robustly modeled in a grid-insensitive way, the calculated force for both particles and fluid will be grid-dependent, contaminating their respective statistics. While the first issue regarding regularizing the point-particle source term has received attention in the literature, the consequences of robustly modeling the undisturbed velocity in the context of grid refinement of turbulence has received little attention. Here, we consider decaying homogeneous isotropic turbulence laden with particles at different Stokes numbers. For a given Stokes number, we systematically refine the grid and demonstrate that explicitly modeling the undisturbed fluid velocity yields relative grid insensitivity for the energy of the particle and fluid phases, as well as acceleration of the particles. We also demonstrate that an appropriately defined dissipation rate is also grid-insensitive when an undisturbed fluid velocity correction is used. In contrast, when the undisturbed fluid velocity is modeled using the conventional approach of interpolating the local fluid velocity to the particle location, we show this procedure yields divergent statistics with grid refinement. In particular, we show that higher-order interpolation of the fluid velocity in two-way coupled problems is worse than lower-order interpolation, in the absence of a correction procedure to estimate the undisturbed fluid velocity. We also examine velocity derivative statistics of the fluid phase and demonstrate that these statistics are not in general convergent even when the undisturbed fluid velocity is explicitly modeled. Collectively, the observations in this paper are used to present a philosophy on the types of questions which are answerable with point-particle methods.},
doi = {10.1103/physrevfluids.5.104302},
journal = {Physical Review Fluids},
number = 10,
volume = 5,
place = {United States},
year = {2020},
month = {10}
}

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