Simulation Of Cavity Flow Research Articles

Unified Gas Kinetic Simulations of Lid-Driven Cavity Flows: Effect of Compressibility and Rarefaction on Vortex Structures

Unified Gas Kinetic Simulations of Lid-Driven Cavity Flows: Effect of Compressibility and Rarefaction on Vortex Structures

Physics-informed neural network simulation of thermal cavity flow

Physics-informed neural networks (PINNs) are an emerging technology that can be used both in place of and in conjunction with conventional simulation methods. In this paper, we used PINNs to perform a forward simulation without leveraging known data. Our simulation was of a 2D natural convection-driven cavity using the vorticity-stream function formulation of the Navier-Stokes equations. We used both 2D simulations across the x and z domains at constant Rayleigh (Ra) numbers and 3D simulations across the x, z and Ra domains. The 3D simulation was tested for a PINN’s ability to learn solutions in a higher-dimensional space than standard simulations. The results were validated against published solutions at Ra values of 103\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{3}$$\\end{document}, 104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{4}$$\\end{document}, 105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{5}$$\\end{document}, and 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{6}$$\\end{document}. Both the 2D simulations and 3D simulations successfully matched the expected results. For the 2D cases, more training iterations were needed for the model to converge at higher Ra values (105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^5$$\\end{document} and 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^6$$\\end{document}) than at lower Ra (103\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document} and 104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^4$$\\end{document}) indicating increased nonlinear fluid-thermal coupling. The 3D case was also able to converge but, but it required more training than any of the 2D cases due to the curse of dimensionality. These results showed the validity of standard simulations via PINNs and the feasibility of higher-order parameter space solutions that are not possible using conventional methods. They also showcased the additional computational demand associated with increasing the dimensionality of the learned parameter space.

Lattice Boltzmann simulation of cavity flows driven by shear and internal heat generation for both Newtonian and viscoplastic fluids

Following our recent investigation [G. Kefayati, “Internally heated convection of viscoplastic fluids in enclosures using a lattice Boltzmann method,” Phys. Fluids 35, 013108 (2023)], this paper centers on exploring the influence of shear on internally heated convection and its flow within a square cavity. The study delves into the behavior of both Newtonian and viscoplastic fluids within this setup. The cavity features two vertical side walls that consistently maintain low temperatures, serving as isotherms. Meanwhile, the horizontal walls are adiabatic and provide thermal insulation. In this work, we present dimensional macroscopic equations and introduce innovative non-dimensional macroscopic equations. To generate shear, the top lid is continuously translated, and we quantify its intensity using the corresponding Richardson number. For investigating the viscoplastic behavior and defining the yielded (fluid) and unyielded (solid) zones, we employ an exact Bingham model, which relies on a unique tensor. To tackle the problem effectively, we develop a dimensionless lattice Boltzmann method to derive the specified macroscopic non-dimensional equations and subsequently solve the fluid motion scenario. Throughout the study, we introduce modified non-dimensional parameters, including the introduced yield number (Y), Reynolds number (R) ranging from 0 to 400, Prandtl number (Pr) ranging from 0 to 100, and the modified Grashof number (G) within the range of 104–106. By varying these parameters, we analyze their influence on streamlines, isotherms, and the regions of yield and unyielded zones. The obtained results revealed that shear plays a significant role in influencing fluid flow, heat transfer, and the behavior of the unyielded section within the enclosure.

GPU based lattice Boltzmann simulation and analysis of two-dimensional trapezoidal cavity flow

In this study, we utilize the lattice Boltzmann method to investigate the flow behavior in a two-dimensional trapezoidal cavity, which is driven by both sides on the upper wall and lower wall. Our calculations are accelerated through GPU-CUDA software. We conduct an analysis of the flow field mode by using proper orthogonal decomposition. The effects of various parameters, such as Reynolds number (<i>Re</i>) and driving direction, on the flow characteristics are examined through numerical simulations. The results are shown below. 1) For the upper wall drive (T1a), the flow field remains stable, when the <i>Re</i> value varies from 1000 to 8000. However, when <i>Re</i> = 8500, the flow field becomes periodic but unstable. The velocity phase diagram at the monitoring point is a smooth circle, and the energy values of the first two modes dominate the energy of the whole field. Once <i>Re</i> exceeds 10000, the velocity phase diagram turns irregular and the flow field becomes aperiodic and unsteady. 2) For the lower wall drive (T1b), the flow is stable when <i>Re</i> value is in a range of 1000－8000, and it becomes periodic and unsteady when <i>Re</i> = 11500. The energy values of the first three modes appear relatively large. When <i>Re</i> is greater than 12500, the flow field becomes aperiodic and unsteady. At this time, the phase diagram exhibits a smooth circle, with the energy values of the first two modes almost entirely dominating the entire energy. 3) For the case of upper wall and lower wall moving in the same direction at the same speed (T2a), the flow field remains stable when <i>Re</i> changes from 1000 to 10000. When <i>Re</i> varies from 12500 to 15000, the flow becomes periodic and unstable. The velocity phase diagram is still a smooth circle, with the first two modes still occupying a large portion of the energy. Once <i>Re</i> exceeds 20000, the energy proportions of the first three modes significantly decrease, and the flow becomes aperiodic and unsteady. 4) For the case in which the upper wall and lower wall are driven in opposite directions at the same velocity (T2b), the flow field remains stable when <i>Re</i> changes from 1000 to 5000. When <i>Re</i> = 6000, the energy of the first mode accounts for 86%, and the flow field becomes periodic but unstable. When <i>Re</i> exceeds 8000, the energy proportions of the first three modes decrease significantly, and the flow field becomes aperiodic and unsteady.

A simple one-step index algorithm for implementation of lattice Boltzmann method on GPU

We proposed a simple one-step index (OSI) algorithm for solving the lattice Boltzmann equation, particularly the streaming of particle distribution functions (PDFs) on a single grid system. The OSI algorithm is derived from the conventional A-B pattern. The memory addresses of the PDFs are fixed in this algorithm and consistent with collision principles. The streaming process is implicitly computed by reassigning their indexes corresponding to the time steps, spatial coordinates, and directions of the PDFs. The algorithm is simple to program because it reads and writes the PDFs only once per time step and does not require the synchronization of odd and even time steps. In this implementation, the data layout of the PDFs is the structure of arrays (SoA), suitable for the memory access pattern of graphics processing units (GPUs). The accuracy and single-precision performance of the proposed algorithm for the three-dimensional lid-driven cavity flow simulation with the D3Q19 model were validated and tested on an NVIDIA A100 having a 40 GB PCIe using CUDA and OpenACC. Performances of 8.4 and 8.1 giga lattice updates per second were obtained for CUDA and OpenACC, respectively. OpenACC can outperform CUDA by up to 95% with significantly less programming work. The bandwidth usage rates on a single GPU were 96% and 94% for CUDA and OpenACC, respectively, close to the theoretical values. Lattice Boltzmann method parallelism is implemented using CUDA and MPI for multi-GPU usage. Finally, computation and communication overlaps were implemented to optimize the parallel efficiency, where the weak scaling parallel efficiency exceeded 0.98 on up to 512 GPUs.

An uncertainty-quantification framework for assessing accuracy, sensitivity, and robustness in computational fluid dynamics

Combining different existing uncertainty quantification (UQ) techniques, a framework is obtained to assess a set of metrics in computational physics problems, in general, and computational fluid dynamics (CFD), in particular. The metrics include accuracy, sensitivity and robustness of the simulator’s outputs with respect to uncertain inputs and parameters. These inputs and parameters are divided into two groups: based on the variation of the first group (e.g. numerical/computational parameters such as grid resolution), a computer experiment is designed, the data of which may become uncertain due to the parameters of the second group (e.g. finite time-averaging). To construct a surrogate model based on uncertain data, Gaussian process regression (GPR) with observation-dependent (heteroscedastic) noise is used. To estimate the propagated uncertainties in the simulator’s outputs from the first group of parameters, a probabilistic version of the polynomial chaos expansion (PCE) is employed Global sensitivity analysis is performed using probabilistic Sobol indices. To illustrate its capabilities, the framework is applied to the scale-resolving simulations of turbulent channel and lid-driven cavity flows using the open-source CFD solver Nek5000. It is shown that at wall distances where the time-averaging uncertainty is high, the quantities of interest are also more sensitive to numerical/computational parameters. In particular for high-fidelity codes such as Nek5000, a thorough assessment of the results’ accuracy and reliability is crucial. The detailed analyses and the resulting conclusions can enhance our insight into the influence of different factors on physics simulations, in particular the simulations of high-Reynolds-number turbulent flows including wall turbulence.

A wall-resolved large-eddy simulation of deep cavity flow in acoustic resonance

Abstract

Optimal Simulation of Wind Field under Disaster Conditions based on PSO and Entropic Lattice Boltzmann Method

The entropic lattice Boltzmann method (ELBM) is an excellent method of numerical stability among of different versions of the lattice Boltzmann method for the simulation of hydrodynamics, especially for wind field simulation application of power grid disaster conditions. In this paper, an efficient improved particle swarm optimization (PSO) algorithm is studied for optimizing calculation parameters to achieve load balancing of ELBM on nonuniform grids in a heterogeneous computing platform. We also introduce a new concept of multi-block ELBM on composite grids for realization of the ELBM simulations of incompressible driven cavity flow. These new approaches rely on a two-dimensional space-time interpolation and solving the relaxation time parameter by direct approximation optimization strategy to guarantee conservation. Our CPU–GPU implementation of multi-block ELBM based on the improved PSO algorithm not only exploits adequately multi-core CPU computing resources for load balancing, but also follows carefully optimized storage to increase coalesced access on a GPU platform. The three-dimensional-driven cavity flow simulations validate the proposed multi-block ELBM even with severely under-resolved grids. In addition, some performance metrics are investigated based on the implementations of different refined grids and threading blocks. These results exhibit the improved PSO algorithm of the ELBM method which can optimize computing resource parameters in heterogeneous platforms, and the present multi-block ELBM can substantially improve the accuracy and computational efficiency for viscous flow computations.

Direct Numerical Simulation of Gas-Liquid Drag-Reducing Cavity Flow by the VOSET Method.

Drag reduction by polymer is an important energy-saving technology, which can reduce pumping pressure or promote the flow rate of the pipelines transporting fluid. It has been widely applied to single-phase pipelines, such as oil pipelining, district heating systems, and firefighting. However, the engineering application of the drag reduction technology in two-phase flow systems has not been reported. The reason is an unrevealed complex mechanism of two-phase drag reduction and lack of numerical tools for mechanism study. Therefore, we aim to propose governing equations and numerical methods of direct numerical simulation (DNS) for two-phase gas-liquid drag-reducing flow and try to explain the reason for the two-phase drag reduction. Efficient interface tracking method—coupled volume-of-fluid and level set (VOSET) and typical polymer constitutive model Giesekus are combined in the momentum equation of the two-phase turbulent flow. Interface smoothing for conformation tensor induced by polymer is used to ensure numerical stability of the DNS. Special features and corresponding explanations of the two-phase gas-liquid drag-reducing flow are found based on DNS results. High shear in a high Reynolds number flow depresses the efficiency of the gas-liquid drag reduction, while a high concentration of polymer promotes the efficiency. To guarantee efficient drag reduction, it is better to use a high concentration of polymer drag-reducing agents (DRAs) for high shear flow.

Uncertainty Quantification for Direct Aeroacoustic Simulations of Cavity Flows

We investigate the influence of uncertain input parameters on the aeroacoustic feedback of cavity flows. The so-called Rossiter feedback requires a direct numerical computation of the acoustic noise, which solves hydrodynamics and acoustics simultaneously, in order to capture the interaction of acoustic waves and the hydrodynamics of the flow. Due to the large bandwidth of spatial and temporal scales, a high-order numerical scheme with low dissipation and dispersion error is necessary to preserve important small scale information. Therefore, the open-source CFD solver FLEXI, which is based on a high-order discontinuous Galerkin spectral element method, is used to perform the aforementioned direct simulations of an open cavity configuration with a laminar upstream boundary layer. To analyze the precision of the deterministic cavity simulation with respect to random input parameters, we establish a framework for uncertainty quantification (UQ). In particular, a nonintrusive spectral projection method with Legendre and Hermite polynomial basis functions is employed in order to treat uniform and normal probability distributions of the random input. The results indicate a strong, nonlinear dependency of the acoustic feedback mechanism on the investigated uncertain input parameters. An analysis of the stochastic results offers new insights into the noise generation process of open cavity flows and reveals the strength of the implemented UQ framework.

Non-equilibrium thermal transport and entropy analyses in rarefied cavity flows

Thermal transport in rarefied flows far removed from thermodynamic equilibrium is investigated using kinetic-theory-based numerical simulations. Two numerical schemes – unified gas kinetic scheme (UGKS) and direct simulation Monte Carlo (DSMC) – are employed to simulate transport at different degrees of rarefaction. Lid-driven cavity flow simulations of argon gas are performed over a range of Knudsen numbers, Mach numbers and cavity shapes. Thermal transport is then characterized as a function of lid Mach number and Knudsen number for different cavity shapes. Vast deviations from the Fourier law – including thermal transport aligned along the direction of temperature gradient – are observed. Entropy implications are examined using Sackur–Tetrode and Boltzmann$H$-theorem formulations. At low Knudsen and Mach numbers, thermal transport is shown to be amenable to both entropy formulations. However, beyond moderate Knudsen and Mach numbers, thermal transport complies only with the Boltzmann$H$-theorem entropy statement. Two extended thermodynamic models are compared against simulation data and found to account for some of the observed non-equilibrium behaviour.

A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller (HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257–311 (2004)). By analyzing the distribution of the finite-time Lyapunov exponent (FTLE) along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.

Numerical investigation of the accuracy, stability, and efficiency of lattice Boltzmann methods in simulating non-Newtonian flow

The Lattice Boltzmann Method (LBM) is a numerical method based on computational statistical mechanics that is well-suited for approximating complex flow behaviors such as non-Newtonian, free surface, and multiphase multicomponent flow. LBM is typically applied to simulate flow through a series of time steps, each consisting of streaming particle distributions to neighboring nodes and collisions of particle distributions at each node through a collision operator. The collision operator is of interest because it, along with the equilibrium distribution function, determines the physics that are simulated (e.g. constitutive laws, interfacial dynamics, etc.) and it has implications on numerical stability and computational efficiency. This work examines various collision operators and methods for stability enhancement for their suitability for simulating non-Newtonian fluid flows in terms of their accuracy, numerical stability and computational efficiency. The investigation was carried out as a numerical study looking for qualitative, yet practical, results, including testing the BGK and MRT collision operators, with and without entropic filtering, as applied to Bingham plastics and power-law fluids. Two different benchmark problems were chosen for the flows: Poiseuille flow, and lid-driven square cavity flow. The results of the numerical study showed that the MRT collision operator can have an advantage in terms of stability and accuracy for a variety of non-Newtonian flow behaviors, but at an increased computing cost that was, in some cases, as much as five times greater than the BGK collision operator. It was also shown that, although it introduces error in the constitutive response of the fluid (and therefore, may not accurately capture the physics of the flow), artificial dissipation can be an effective technique for stabilizing the numerics of non-Newtonian, lid-driven cavity flow simulations, and is particularly effective for stabilizing shear-thinning fluids.

Numerical Simulation of Cube Cavity Flow by Viscoelastic Fluid

Numerical Simulation of Cube Cavity Flow by Viscoelastic Fluid

Lattice Boltzmann Simulations of Cavity Flows on Graphic Processing Unit with Memory Management

AbstractLattice Boltzmann method (LBM) is adopted to compute two and three-dimensional lid driven cavity flows to examine the influence of memory management on the computational performance using Graphics Processing Unit (GPU). Both single and multi-relaxation time LBM are adopted. The computations are conducted on nVIDIA GeForce Titan, Tesla C2050 and GeForce GTX 560Ti. The performance using global memory deteriorates greatly when multi relaxation time (MRT) LBM is used, which is due to the scheme requesting more information from the global memory than its single relaxation time (SRT) LBM counterpart. On the other hand, adopting on chip memory the difference using MRT and SRT is not significant. Also, performance of LBM streaming procedure using offset reading surpasses offset writing ranging from 50% to 100% and this applies to both SRT and MRT LBM. Finally, comparisons using different GPU platforms indicate that Titan as expected outperforms other devices, and attains 227 and 193 speedup over its Intel Core i7-990 CPU counterpart and four times faster than GTX 560Ti and Tesla C2050 for three dimensional cavity flow simulations respectively with single and double precisions.

유동함수-와도 관계를 이용한 격자볼츠만 방법에서의 격자 세밀화 모델

In this study, we present a grid refinement model in the lattice Boltzmann method (LBM) for two-dimensional incompressible fluid flow. That is, the model combines the desirable features of the lattice Boltzmann method and stream function-vorticity formulations. In order to obtain an accurate result, very fine grid (or lattice) is required near the solid boundary. Therefore, the grid refinement model is used in the lattice Boltzmann method for stream function-vorticity formulation. This approach is more efficient in that it can obtain the same accurate solution as that in single-block approach even if few lattices are used for computation. In order to validate the grid refinement approach for the stream function-vorticity formulation, the numerical simulations of lid-driven cavity flows were performed and good results were obtained.

Regularized lattice BGK versus highly accurate spectral methods for cavity flow simulations

The regularized lattice BGK (RLBGK) is validated against high-accuracy spectral Chebyshev methods for lid-driven cavity flows. RLBGK is shown to provide a viable alternative to standard lattice BGK schemes, with significant enhancement of numerical stability at a very moderate computational extra-cost.

Cavity Flow Control Experiments and Simulations

In this work we describe a summary of flow control research studies on active, passive and adaptive methodologies designed to attenuate large scale flow unsteadiness and the resulting pressure fluctuations in cavity flows. Spectral analysis of high frequency dynamic pressure measurements is used to determine the control effectiveness. Various control techniques, depending on their geometry and or distribution, can be advantageous in attenuating both the peaks and the broad spectral bands generated by flow unsteadiness. Increased effectiveness is associated with redistribution of the shear-layer vorticity. Combination of experimental and numerical results assists in understanding the underlying flow physics and interaction processes involved.

2D lid-driven cavity flow simulation using GPU-CUDA with a high-order finite difference scheme

The high parallelism and low cost of the graphic processing units (GPUs) have attracted the interest of scientists and engineers requiring high computational power with a modest investment. This work explores the use of a GPU in the solution of the 2D lid-driven cavity flow problem using the pressure–velocity formulation for Reynolds numbers up to $$10{,}000$$ and turning to a 4th order finite difference scheme for spatial discretization. Results showed good agreement with those reported in the literature. The solver was implemented in both the CPU and the GPU in order to compare their performance, whereupon the latter was seventy times faster.

Regularized lattice Bhatnagar-Gross-Krook model for two- and three-dimensional cavity flow simulations.

We investigate the accuracy and performance of the regularized version of the single-relaxation-time lattice Boltzmann equation for the case of two- and three-dimensional lid-driven cavities. The regularized version is shown to provide a significant gain in stability over the standard single-relaxation time, at a moderate computational overhead.