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This study aims to modify the standard probabilistic lattice Boltzmann methodology (LBM) cellular automata (CA) algorithm to enable a more realistic and accurate computation of the ensemble rather than individual particle trajectories that need to be updated from one time step to the next (allowing, as such, a fraction of the collection of particles in any lattice grid cell to be updated in a time step, rather than the entire collection of particles as in the standard LBM-CA algorithm leading to a better representation of the dynamic interaction between the particles and the background flow). Exploitation of the inherent parallelism of the modified LBM-CA algorithm to provide a computationally efficient scheme for computation of particle-laden flows on readily available commodity general-purpose graphics processing units (GPGPUs).

This paper presents a framework for the implementation of a LBM for the simulation of particle transport and deposition in complex flows on a GPGPU. Towards this objective, the authors have shown how to map the data structure of the LBM with a multiple-relaxation-time (MRT) collision operator and the Smagorinsky subgrid-scale turbulence model (for turbulent fluid flow simulations) coupled with a CA probabilistic method (for particle transport and deposition simulations) to a GPGPU to give a high-performance computing tool for the calculation of particle-laden flows.

A fluid-particle simulation using our LBM-MRT-CA algorithm run on a single GPGPU was 160 times as computationally efficient as the same algorithm run on a single CPU.

The method is limited by the available computational resources (e.g. GPU memory size).

A new 3D LBM-MRT-CA model was developed to simulate the particle transport and deposition in complex laminar and turbulent flows with different hydrodynamic characteristics (e.g. vortex shedding, impingement, free shear layer, turbulent boundary layer). The solid particle information is encapsulated locally at the lattice grid nodes, allowing for straightforward mapping of the datastructure onto a GPGPU enabling a massive parallel execution of the LBM-MRT-CA algorithm. The new particle transport algorithm was based on the local (bulk) particle density and velocity and provides more realistic results for the particle transport and deposition than the standard LBM-CA algorithm.

Performance of various k‐ε models on turbulent forced convection in a channel with periodic ribs is assessed.

The influence of the Yap correction and the non‐linear stress‐strain relation on the predictions of mean‐flow, turbulence quantities and local heat transfer rate is examined. The effect of thermal boundary conditions on the heat transfer predictions is investigated by employing both the prescribed heat flux approach and the conjugate heat transfer approach.

It was found that the inclusion of the Yap correction in the ε‐equation significantly improves the predictions of mean velocity and wall heat transfer for both high‐Reynolds number and low‐Reynolds number k‐ε models in the present ribbed channel flow with massive flow separation. The employment of the non‐linear stress‐strain relation only marginally improves the predictions of turbulence quantities: the turbulence anisotropy is reproduced although the level of turbulence intensity is still too low. In general, the conjugate heat transfer approach predicts better average Nusselt number than the prescribed heat flux approach. However, both approaches under‐predict the experimental value by about 28‐33 percent when the low‐Reynolds number k‐ε model of Lien and Leschziner (1999) with the Yap term is adopted.

Thorough numerical treatments of the thermal boundary conditions at the solid‐liquid interface, and detailed periodic condition in the periodic regime, were given in the paper to benefit researchers interested in solving similar problems.

Industrial simulations of turbulent flows often rely on Reynolds-averaged Navier-Stokes (RANS) turbulence models, which contain numerous closure coefficients that need to be calibrated. This paper aims to address this issue by proposing a semi-automated calibration of these coefficients using a new framework (referred to as turbo-RANS) based on Bayesian optimization.

The authors introduce the generalized error and default coefficient preference (GEDCP) objective function, which can be used with integral, sparse or dense reference data for the purpose of calibrating RANS turbulence closure model coefficients. Then, the authors describe a Bayesian optimization-based algorithm for conducting the calibration of these model coefficients. An in-depth hyperparameter tuning study is conducted to recommend efficient settings for the turbo-RANS optimization procedure.

The authors demonstrate that the performance of the k-ω shear stress transport (SST) and generalized k-ω (GEKO) turbulence models can be efficiently improved via turbo-RANS, for three example cases: predicting the lift coefficient of an airfoil; predicting the velocity and turbulent kinetic energy fields for a separated flow; and, predicting the wall pressure coefficient distribution for flow through a converging-diverging channel.

To the best of the authors’ knowledge, this work is the first to propose and provide an open-source black-box calibration procedure for turbulence model coefficients based on Bayesian optimization. The authors propose a data-flexible objective function for the calibration target. The open-source implementation of the turbo-RANS framework includes OpenFOAM, Ansys Fluent, STAR-CCM+ and solver-agnostic templates for user application.

To present the detailed implementation processes of the IDEAL algorithm for two-dimensional compressible flows based on Delaunay triangular mesh, and compare the performance of the SIMPLE and IDEAL algorithms for solving compressible problems. What’s more, the implementation processes of Delaunay mesh generation and derivation of the pressure correction equation are also introduced.

Programming completely in C++.

Five compressible examples are used to test the SIMPLE and IDEAL algorithms, and the comparison with measurement data shows good agreement. The IDEAL algorithm has much better performance in both convergence rate and stability over the SIMPLE algorithm.

The detail solution procedure of implementing the IDEAL algorithm for compressible flows based on Delaunay triangular mesh is presented in this work, seemingly first in the literature.

The purpose of this study is to propose a novel relaxation modified factor to accelerate the numerical solution of the radiative transfer equation (RTE) with several high-resolution total variation diminishing schemes. The methodology proposed is denoted as the X-factor method.

The X-factor method was compared with the technique deferred-correction (DC) for the calculations of a two-dimensional cavity with absorting-emiting-scatteting gray media using the discrete ordinates method. Four parameters were considered to evaluate: the absorption coefficient, the emissivity of boundary surface, the scattering albedo and under-relaxation factor.

The results showed the central processing unit (CPU) time of X-factor method was lower than DC. The reductions of CPU time with the X-factor method were observed from 0.6 to 75.4%.

The superiority of the X-factor method over DC was showed with the reduction of CPU time of the numerical solution of RTE for evaluated cases.

This paper aims to present an evolutionary algorithm (EA) to accelerate the convergence for the radiative transfer equation (RTE) numerical solution using high-order and high-resolution schemes by the relaxation coefficients optimization.

The objective function minimizes the residual value difference between iterations in each control volume until its difference is lower than the convergence criterion. The EA approach is evaluated in two configurations, a two-dimensional cavity with scattering media and absorbing media.

Experimental results show the capacity to obtain the numerical solution for both cases on all interpolation schemes tested by the EA approach. The EA approach reduces CPU time for the RTE numerical solution using SUPERBEE, SWEBY and MUSCL schemes until 97% and 135% in scattering and absorbing media cases, respectively. The relaxation coefficients optimized every two numerical solution iterations achieve a significant reduction of the CPU time compared to the deferred correction procedure with fixed relaxation coefficients.

The proposed EA approach for the RTE numerical solution effectively reduces the CPU time compared to the DC procedure with fixed relaxation coefficients.

This paper seeks to explore the fiber orientation distribution and rheological properties of turbulent fiber suspensions flowing through a contraction.

The Reynolds averaged Navier‐Stokes equation was solved with the Reynolds stress model to get the mean fluid velocity and the turbulent kinetic energy in the turbulent flow of a contraction with rectangular cross‐section. The turbulent velocity fluctuations were represented as a Fourier series with random coefficients. Then the slender‐body theory was used to predict the fiber orientation distribution, orientation tensor, additional shear stress and first normal stress difference of suspensions in the flow.

It is found that the longer fibers tend to align the streamline easily. Increased contraction ratio results in higher fiber alignment in the direction of flow. The fibers are weakly and strongly aligned in the direction of flow in the region near the inlet and the exit, respectively. Fibers are significantly more aligned in the plane of the contraction than in the x‐z plane. Contraction ratio and fiber length were shown to strongly and weakly affect the distributions of additional shear stress and first normal stress difference.

It is the first time that the fiber orientation distribution and rheological properties of turbulent fiber suspensions flowing through a contraction have been computed numerically. The computational approach and results are valuable to the design and operation of contraction used in the industrial processes.

Numerical results are reported for a dilute turbulent liquid‐solid flow in an axisymmetric sudden‐expansion pipe with an expansion ratio 2:1. The two‐phase flow has a mass‐loading ratio low enough for particle collision to be negligible. The numerical predictions for the dilute two‐phase flow are based on a hybrid Eulerian‐Lagrangian model. A nonlinear k‐ε model is used for the fluid flow to account for the turbulence anisotropy and an improved eddy‐interaction model is used for the particulate flow to account for the effects of turbulence anisotropy, turbulence inhomogeneity, particle drift, and particle inertia on particle dispersion. The effects of the coupling sources, the added mass, the lift force and the shear stress on two‐phase flow predictions are separately studied. The numerical predictions obtained with the improved and conventional particle dispersion models are compared with experimental measurements for the mean and fluctuating velocities at the different measured planes.

The averaged Navier‐Stokes and the k‐e turbulence model equations are used to simulate turbulent flows in some internal flow cases. The discrete equations are solved by different variations of Multigrid methods. These include both steady state as well as time dependent solvers. Locally refined grids can be added dynamically in all cases. The Multigrid schemes result in fast convergence rates, whereas local grid refinements allow improved accuracy with rational increase in problem size. The applications of the solver to a 3‐D (cold) furnace model and to the simulation of the flow in a wind tunnel past an object prove the efficiency of the Multigrid scheme with local grid refinement.

The purpose of this paper is to consider the conjugate heat transfer from a flat plate involving a turbulent plane wall jet. The bottom wall of the solid block is heated by a constant heat flux.

High Reynolds number two‐equation model (κ‐ϵ) has been used for turbulence modeling. The parameters considered are the conductivity ratio of solid and fluid, the solid slab thickness and the Prandtl number. The Reynolds number considered is 15,000 because the flow becomes fully turbulent and then is independent of the Reynolds number. The range of parameters considered are: conductivity ratio = 1‐1,000, solid slab thickness = 1‐10 and Prandtl number = 0.01‐100.

The non‐dimensional bottom surface temperature is high for high‐Prandtl number fluid and vice versa. As conductivity ratio increases, it decreases whereas it increases with the increase in slab thickness. Similar trend is observed for the distribution of the interface temperature. The Nusselt number computed based on the interface temperature increases with Prandtl number. It is observed that for the range of parameters considered, local Nusselt number distribution superimposes with each other. The average heat flux at the interface has been computed and found to be equal with average heat flux at the bottom which ensures the overall heat balance.

The study of conjugate heat transfer with a turbulent wall jet will be useful for cooling of heated body.