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Particle‐resolved turbulent flow in a packed bed: RANS, LES, and DNS simulations

Aiche Journal

February 2022
69(1)

DOI:10.1002/aic.17615

Authors:

Ulrich Rüde

Friedrich-Alexander-University Erlangen-Nürnberg

Packed bed reactors are widely used to perform solid‐catalyzed gas‐phase reactions and local turbulence is known to influence heat and mass transfer characteristics. We have investigated turbulence characteristics in a packed bed of 113 spherical particles by performing particle‐resolved Reynolds‐averaged Navier–Stokes (RANS) simulations, Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS). The predictions of the RANS and LES simulations are validated with the lattice Boltzmann method (LBM)–based DNS at particle Reynolds number (Rep) of 600. The RANS and LES simulations can predict the velocity, strain rate, and vorticity with a reasonable accuracy. Due to the dominance of enhanced wall‐function treatment, the turbulence characteristics predicted by the ε‐based models are found to be in a good agreement with the DNS. The ω‐based models under‐predicted the turbulence quantities by several orders of magnitude due to their inadequacy in handling strongly wall‐dominated flows at low Rep. Using the DNS performed at different Rep, we also show that the onset of turbulence occurs between 200≤Rep≤250.

Schematic of the fluid domain with (A) boundary conditions and (B) planes used for analysis

…

Effect of grid resolution on the velocity predictions on the (A) XZ plane at Y = 8 mm, and (B) line 1 (located on the XZ plane as shown in the inset) for RANS simulations performed using the RNG‐κε turbulence model (Rep = 600). RANS, Reynolds‐averaged Navier‐Stokes; Rep, particle Reynolds number; RNG, Renormalization Group

…

Effect of grid resolution on the TKE predictions on the (A) XZ plane at Y = 8 mm, and (B) line 1 (located on the XZ plane [Y = 8 mm] as shown in the inset) for RANS simulations performed using RNG‐κε turbulence model (Rep = 600). RANS, Reynolds‐averaged Navier‐Stokes; Rep, particle Reynolds number; RNG, Renormalization Group; TKE, turbulence kinetic energy

…

Effect of different numerical approaches on the predictions of the velocity distribution on the (A) XZ plane (Y = 8 mm; the LHS color bar is for DNS and RHS color bar is for all other simulations), and (B) line 1 (located on the XZ plane as shown in the inset) at a Rep of 600. DNS, Direct Numerical Simulation; LES, Large Eddy Simulation; LHS, left‐hand side; Rep, particle Reynolds number; RHS, right‐hand side; RNG, Renormalization Group; RSM, Reynolds stress model; SST, Shear‐Stress Transport; WALE, Wall‐Adapted Local Eddy‐viscosity

…

Effect of different numerical approaches on the predictions of TKE distribution on the (A) XZ plane (Y = 8 mm; the LHS color bar is for DNS and RHS color bar is for all other simulations), (B) line 1 (located on the XZ plane as shown in the inset), and the (C) XY plane at Z = 32.75 mm (Rep = 600; note the logarithmic scales used for TKE). DNS, Direct Numerical Simulation; LES, Large Eddy Simulation; LHS, left‐hand side; Rep, particle Reynolds number; RHS, right‐hand side; TKE, turbulence kinetic energy; RNG, Renormalization Group; RSM, Reynolds stress model; SST, Shear‐Stress Transport; WALE, Wall‐Adapted Local Eddy‐viscosity

…

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RESEARCH ARTICLE

Transport Phenomena and Fluid Mechanics

Particle-resolved turbulent flow in a packed bed: RANS, LES,

and DNS simulations

Aniket S. Ambekar

| Christoph Schwarzmeier

| Ulrich Rüde

2,3

| Vivek V. Buwa

Department of Chemical Engineering, Indian

Institute of Technology Delhi, New Delhi, India

Department of Computer Science, Chair for

System Simulation, Universität Erlangen-

Nürnberg, Erlangen, Germany

Parallel Algorithms Team, CERFACS,

Toulouse, France

Correspondence

Vivek V. Buwa, Department of Chemical

Engineering, Indian Institute of Technology

Delhi, New Delhi 110016. India.

Email: vvbuwa@iitd.ac.in

Funding information

Deutscher Akademischer Austauschdienst;

University Grants Commission; Deutsche

Forschungsgemeinschaft

Abstract

Packed bed reactors are widely used to perform solid-catalyzed gas-phase reactions

and local turbulence is known to influence heat and mass transfer characteristics. We

have investigated turbulence characteristics in a packed bed of 113 spherical parti-

cles by performing particle-resolved Reynolds-averaged Navier–Stokes (RANS) simu-

lations, Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS). The

predictions of the RANS and LES simulations are validated with the lattice Boltzmann

method (LBM)–based DNS at particle Reynolds number (Re

) of 600. The RANS and

LES simulations can predict the velocity, strain rate, and vorticity with a reasonable

accuracy. Due to the dominance of enhanced wall-function treatment, the turbulence

characteristics predicted by the ε-based models are found to be in a good agreement

with the DNS. The ω-based models under-predicted the turbulence quantities by

several orders of magnitude due to their inadequacy in handling strongly wall-

dominated flows at low Re

. Using the DNS performed at different Re

, we also show

that the onset of turbulence occurs between 200 ≤Rep≤250.

KEYWORDS

Direct Numerical Simulations, Large Eddy Simulations, Packed bed, Particle-resolved

simulations, Turbulence models

1|INTRODUCTION

Packed bed reactors (PBRs) have widespread applications in the

chemical process industry. One of the important applications of

these reactors is to perform solid-catalyzed reactions such as

methane-steam reforming, methanol or dimethyl ether synthesis,

water–gas shift reactions, etc. These solid-catalyzed reactions are

either exothermic or endothermic. Randomly packed porous parti-

cles, either with internal or external shaping with varying size, are

used to perform these reactions. The overall (bed-scale) performance

of the PBRs, that is, reactant conversion, product selectivity, yield,

pressure drop, and other quantities, is significantly influenced by the

particle-scale heat and mass transfer characteristics which in turn

are determined by the particle-scale flow. The particle-scale flow is

governed by the shape and size of catalyst particles. Therefore,

particle-resolved simulations of a small section of PBR (i.e., with a

few hundreds of particles) are extensively used to evaluate the

effects of particle shape, to innovate new particle shapes. and also

to analyze particle-scale heat and mass transfer (see 1–7and the ref-

erences cited therein). However, despite the extensive use of

particle-resolved computational fluid dynamics (CFD) simulations,

the rigorous validation of the predictions of particle-resolved simula-

tions lacks to a great extent.

One of the approaches, traditionally used to validate the particle-

resolved simulations, is to compare their predictions of bed-scale per-

formance with the predictions of semi-empirical correlations available

in the literature, for example, the pressure drop characteristics are

compared with the predictions of correlations proposed by Ergun,

1,2,7

Reichelt,

3,8

Zhavoronkov et al.,

3,4,8

and so forth. The predicted pres-

sure drops, and other bed-scale characteristics are in a reasonable

agreement with the correlations. While particle-scale CFD simulations

can predict the overall/macroscopic characteristics like pressure drop,

their ability to predict particle-scale velocity and turbulence character-

istics needs to be investigated.

Received: 22 July 2021 Revised: 16 December 2021 Accepted: 15 January 2022

DOI: 10.1002/aic.17615

https://doi.org/10.1002/aic.17615

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Particle‐resolved turbulent flow in a packed bed: RANS, LES, and DNS simulations

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