Three-dimensional Lid-driven Cavity Flow Research Articles

Numerical Simulation and Computational Fluid Dynamics Analysis of Two-Dimensional Lid-Driven Cavity Flow Within the Weapon Bay of an Autonomous Fighter Drone

The efficient deployment of weapons in military operations is critical for mission success, and the flow of air within the weapon bay of an autonomous fighter drone plays a vital role in achieving this objective. In this paper, we present a comprehensive numerical simulation and computational fluid dynamics (CFD) analysis of the three-dimensional lid-driven cavity flow within the weapon bay of an autonomous fighter drone. To address this challenging problem, we employ CFD analysis and a multigrid approach to solve the Navier-Stokes equations for the aerodynamic problem. Our simulations include high Reynolds numbers of up to 10,000, which demonstrates the potential of CFD analysis in optimizing the design of autonomous fighter drones for military operations. We evaluate the effectiveness of the linked strongly implicit multigrid technique in estimating high-Re fine-mesh flow solutions using the vorticity-stream function formulation of the two-dimensional incompressible Navier-Stokes equations. The model issue is the driven flow in a square cavity, and we consider meshes up to 1024 x 1024 points and combinations with Reynolds numbers as high as 1000. To further improve the accuracy of our simulations, we employ one-dimensional grid clustering coordinate transformations instead of uniform mesh refinement, as the flow field exhibits one or more secondary vortices. Our findings demonstrate that CFD analysis can provide valuable insights into the complex flow dynamics within the weapon bay of autonomous fighter drones, which can lead to the optimization of their design for enhanced mission capabilities. Overall, our study highlights the significance of numerical simulations and CFD analysis in the design and optimization of autonomous fighter drones for military applications. Our results can serve as a basis for future research in the field of UAV aerodynamics and contribute to the development of more efficient and effective military operations.

GPU implementation of the discrete unified gas kinetic scheme for low-speed isothermal flows

In this paper, two GPU parallel algorithms are proposed for the discrete unified gas kinetic scheme (DUGKS) for simulating low-speed isothermal flows. Algorithm-I uses a two-level fine-grain technique for the parallelization of physical spatial space, while Algorithm-II adopts this technique for both physical spatial and particle velocity spaces. To evaluate the performance of the proposed algorithms, several typical benchmark problems are simulated, including the two-dimensional (2D) and three-dimensional (3D) lid-driven cavity flows, the micro channel and cavity flows. Numerical results show that our GPU algorithms can achieve satisfactory computational efficiency. For Algorithm-I, the speedup can reach 250 and 338 on a Tesla V100 GPU card for the 2D and 3D continuum cavity flows, respectively, and a hundredfold acceleration can be obtained for the rarefied cases. While for Algorithm-II, a speedup of about 70 can be attained for rarefied cases. However, it is not applied to continuum problems that only require a small number of velocity points. Moreover, comparisons between the two GPU algorithms are also conducted for the rarefied flows with various grid meshes and velocity directions. The results show that Algorithm-I performs better when physical mesh size is large, while Algorithm-II can provide higher efficiency for a coarser mesh with medium number of discrete velocities. Special attention is also paid to comparisons between Algorithm-I and MPI parallelization with 128 CPU cores based on physical space discretization approach, and it is found that Algorithm-I has a clear advantage on V100 GPU when dealing with sparse physical grids in both continuum and rarefied cases.

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.

Discrete unified gas kinetic scheme for incompressible Navier-Stokes equations

The discrete unified gas kinetic scheme (DUGKS) combines the advantages of both the unified gas kinetic scheme (UGKS) and the lattice Boltzmann method. It can adopt the flexible meshes, meanwhile, the flux calculation is simple. However, the original DUGKS is proposed for the compressible flows. When we try to solve a problem governed by the incompressible Navier-Stokes (N-S) equations, the original DUGKS may bring some undesirable errors because of the compressible effect. To eliminate the compressible effect, the DUGKS for incompressible N-S equations is developed in this work. In addition, the Chapman-Enskog analysis ensures that the present DUGKS can solve the incompressible N-S equations exactly, meanwhile, a new non-extrapolation scheme is adopted to treat the Dirichlet boundary conditions. To test the present DUGKS for incompressible N-S equations, four problems are adopted. The first one is a periodic problem driven by an external force, which is used to test the influences of Courant–Friedrichs–Lewy condition number and the Mach number (Ma). Besides, some comparisons between the present DUGKS and some available results are also conducted. The second problem is Womersley flow, it is also used to test the influence of Ma, and the results show that the compressible effect is reduced obviously. Then, the two-dimensional lid-driven cavity flow is considered. In these simulations, the Reynolds number is varied from 400 to 1000000 to illustrate the accuracy, stability and efficiency of the present DUGKS. Finally, the numerical solutions of the three-dimensional lid-driven cavity flow suggest that the present DUGKS is suitable for the three-dimensional problems.

Global transition dynamics of flow in a lid-driven cubical cavity

The dynamics of a fully three-dimensional lid-driven cubical cavity (3D-LDC) flow at several post-critical conditions, i.e., beyond the first bifurcation, are elucidated using both linear and nonlinear analyses. When the Reynolds number is increased beyond the critical value, symmetry breaks down intermittently with subsequent gradual growth in spanwise inhomogeneity. This results in crossflow as well as pronounced secondary flow due to enhanced imbalance between centrifugal and pressure forces. Thus, while a stable solution is obtained at \(\hbox {Re}=1900\) (Reynolds number based on lid velocity and cavity side length), nonlinear analysis identifies intermittent and nearly saturated regimes at \(\hbox {Re}=2100\) and \(\hbox {Re}=3000\), respectively. These changes in the regime are examined by considering five basic states at different Reynolds numbers starting from \(\hbox {Re}=1900\). At the lowest Reynolds number, linear analysis yields only symmetric modes, characterized by Taylor–Görtler-like (TGL) vortices. However, at \(\hbox {Re}=2100\), the intermittent breakdown of symmetry results in the emergence of an antisymmetric low-frequency mode apart from primary high-frequency mode. The frequencies of both these modes are numerically close to those obtained from corresponding nonlinear simulations. When the Reynolds number is increased even further, the TGL structures drift under the influence of the crossflow to occupy the previously structureless region near the wall. The frequency of each mode decreases with increase in \(\hbox {Re}\); between 1900 and 3000, the frequency of the primary mode changes by more than 20%. Furthermore, the spatial support of each mode becomes larger within the cavity. Both primary and secondary modes are increasingly destabilized with \(\hbox {Re}\); however, the secondary antisymmetric mode is destabilized at a higher rate. The current study thus provides a comprehensive picture of the overall dynamics of 3D-LDC flows in pre- and post-bifurcation regimes in an extended \(\hbox {Re}\) range not considered hitherto.

Large-eddy simulation of wall-bounded turbulent flow with high-order discrete unified gas-kinetic scheme

In this paper, we introduce the discrete Maxwellian equilibrium distribution function for incompressible flow and force term into the two-stage third-order Discrete Unified Gas-Kinetic Scheme (DUGKS) for simulating low-speed turbulent flows. The Wall-Adapting Local Eddy-viscosity (WALE) and Vreman sub-grid models for Large-Eddy Simulations (LES) of turbulent flows are coupled within the present framework. Meanwhile, the implicit LES are also presented to verify the effect of LES models. A parallel implementation strategy for the present framework is developed, and three canonical wall-bounded turbulent flow cases are investigated, including the fully developed turbulent channel flow at a friction Reynolds number (Re) about 180, the turbulent plane Couette flow at a friction Re number about 93 and lid-driven cubical cavity flow at a Re number of 12000. The turbulence statistics, including mean velocity, the r.m.s. fluctuations velocity, Reynolds stress, etc. are computed by the present approach. Their predictions match precisely with each other, and they are both in reasonable agreement with the benchmark data of DNS. Especially, the predicted flow physics of three-dimensional lid-driven cavity flow are consistent with the description from abundant literature. The present numerical results verify that the present two-stage third-order DUGKS-based LES method is capable for simulating inhomogeneous wall-bounded turbulent flows and getting reliable results with relatively coarse grids.

Lagrangian chaos in steady three-dimensional lid-driven cavity flow.

Steady three-dimensional flows in lid-driven cavities are investigated numerically using a high-order spectral-element solver for the incompressible Navier-Stokes equations. The focus is placed on critical points in the flow field, critical limit cycles, their heteroclinic connections, and on the existence, shape, and dependence on the Reynolds number of Kolmogorov-Arnold-Moser (KAM) tori. In finite-length cuboidal cavities at small Reynolds numbers, a thin layer of chaotic streamlines covers all walls. As the Reynolds number is increased, the chaotic layer widens and the complementary KAM tori shrink, eventually undergoing resonances, until they vanish. Accurate data for the location of closed streamlines and of KAM tori are provided, both of which reach very close to the moving lid. For steady periodic Taylor-Görtler vortices in spanwise infinitely extended cavities with a square cross section, chaotic streamlines occupy a large part of the flow domain immediately after the onset of Taylor-Görtler vortices. As the Reynolds number increases, the remaining KAM tori vanish from the Taylor-Görtler vortices, while KAM tori grow in the central region further away from the solid walls.

Numerical verification of a non-residual orthogonal term-by-term stabilized finite element formulation for incompressible convective flow problems

The modeling of turbulent flows is relevant in many engineering applications and, is an active field of research on numerical methods. Convergence and stability of proposed formulations are crucial to predict transitional flows from laminar to turbulent flows. In this work, a recently developed stabilized finite element formulation is used as a powerful tool to describe such kind of problems. The essential point of the formulation is the time dependent nature of the subscales and, contrary to residual based formulations, the introduction of two velocity subscale components. The theoretical rate of convergence of the method is verified numerically using linear and quadratic equal-order finite element discretizations. To this end, a standard convergence test of L2-norm is presented where the computed solutions are compared when manufactured solutions are imposed at Gauss-point level. Moreover, the Hopf bifurcation is studied for two well-known benchmark problems: flow past a cylinder and the three-dimensional lid-driven cavity flow. For the flow past a cylinder case, the Hopf bifurcation is verified using dynamic subscales and is assessed so that they do not disturb the solution. In particular, a dominant convective problem (Re=4000) is solved using both the quasistatic and dynamic versions of the method, evaluating the performance of each one in the quality of the solution and in the CPU time needed to obtain a converged solution. For the 3D lid-driven cavity flow problem, the Hopf bifurcation is determined using two different boundary conditions, analyzing their effect on the dynamics of the problem and on the thickness and shape of the boundary layer. The final test case is the turbulent 3D lid-driven cavity problem (Re=12000), where velocity profiles are compared with experimental, LES and DNS reference solutions. Additionally, pressure and velocity spectra are shown at certain representative points of the domain, as well as phase diagrams, correlation function graphs, the Poincaré map, and the Lyapunov exponent, typical mathematical tools used in dynamical system analysis. From the results, the method is robust and accurate for all the numerical tests both in viscous dominant problems as in dominant convective ones.

Development of a three dimensional meshless numerical method for the solution of the Boltzmann equation on complex geometries

We propose a three dimensional meshless numerical scheme based on the Boltzmann equation for the simulation of fluid flows in domains of complex geometries. The velocity space discretization in our method is the same as the standard lattice Boltzmann method, i.e. the same lattices are used to discretize microscopic velocities. The velocity-discrete Boltzmann equation with the BGK collision approximation is discretized in time using the Lax–Wendroff scheme, and subsequently in space using the meshless local Petrov–Galerkin method based on local radial basis functions augmented with polynomials. The method is first validated and tuned by solving two benchmark problems: The pressure-driven flow in an elliptical tube, and the three-dimensional lid-driven cavity flow. The error analysis for the first case shows the second order accuracy of the proposed method. The flow in a packed bed is then solved in order to illustrate the efficiency of the proposed method in the simulation of geometrically complex flows. The results show that both the computational time and the memory usage of our method are lower than those of the standard lattice Boltzmann method for the geometrically complex flows.

High-Reynolds-number turbulent cavity flow using the lattice Boltzmann method

We present a boundary condition scheme for the lattice Boltzmann method that has significantly improved stability for modeling turbulent flows while maintaining excellent parallel scalability. Simulations of a three-dimensional lid-driven cavity flow are found to be stable up to the unprecedented Reynolds number $\mathrm{Re}=5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ for this setup. Excellent agreement with energy balance equations, computational and experimental results are shown. We quantify rises in the production of turbulence and turbulent drag, and determine peak locations of turbulent production.

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.

Numerical Modeling of 2-D and 3-D Flows using Artificial Compressibility Method and Collocated Mesh

In this paper, applications of a numerical model on simulation of two and three-dimensional flows are presented. This model solves Navier-Stokes equations using finite volume method and large eddy simulation (LES) in a collocated mesh. Artificial compressibility method with dual t ime stepping is used to solve the time dependent equations. Also a modified m omentum i nterpolation method (MIM) based on the unsteady flows i s deployed t o overcome t he non-physical pressure oscillation. Capability of the presented numerical code for flow s imulation, i s a ssessed by a pplication f or twodimensional square and three-dimensional lid-driven cavity flows. Numerical r esults of cavity flow presents very good agreement with the numerical and experimental data of other existent researches.

New lifting relations for estimating LBM distribution functions from corresponding macroscopic quantities, based on equilibrium and non-equilibrium moments

Due to superior accuracy and stability of multiple relaxation time (MRT) collision operator over its single relaxation time (SRT) counterpart, new lifting relations are proposed here to construct single particle distribution functions for MRT-LBM from macroscopic variables. Using these lifting relations, a new hybrid FVM-LB method is presented (called Finite type-LB hybrid method), which is consistent with MRT-LBM. In this new hybrid method, single-particle distribution functions in MRT-LBM sub-domain boundaries are computed, using equilibrium and non-equilibrium moments. These moments are computed in Navier–Stokes/FVM sub-domain boundaries, using macroscopic variables and their derivatives. The new method is validated by solving three benchmark problems, i.e., two- and three-dimensional lid driven cavity flows and two-dimensional unsteady flow around a squared section cylinder. These problems are analyzed with pure FVM, pure LBM, and Finite type-LB hybrid method (FTLBHM) and the related results are compared with each other and with benchmark data. These comparisons clearly demonstrate the accuracy of the present novel methodology for simulating steady/unsteady flow fields in two and three dimensions.

Lattice Boltzmann simulation of the three-dimensional motions of particles with various density ratios in lid-driven cavity flow

An estimation of solid particle dynamics through a fluid has been studied. Although traditional computational fluids dynamics models can predict multiphase flow and the interactions between the fluid and solid particles, a high level of accuracy of an appropriate numerical model for this type of difficulty is still in demand. Some researchers examining this problem dedicated their research to the particle motions under the influence of gravity. Therefore, in this study a modern computational fluid dynamic model, the Lattice Boltzmann Method (LBM), was proposed to predict the three-dimensional cubic lid-driven cavity flow and combined with the Lagrangian approach on the prediction of solid particles in the range of different density ratios. To solve the term, flow fluid, the mesoscale numerical scheme of the Multi Relaxation Time (MRT) lattice Boltzmann method was used to simulate the objects at higher stability. In the present study, the different densities of the particles were considered and the effects of gravity were included in the calculation. The 4th Runge-Kutta method was functioned to determine the effect of an external force on a particle because this method is accurate enough compared to other known numerical schemes. The hard sphere model was used to model particle-particle and particle-wall collisions. The solid particle subtleties determined using a numerical fluid dynamic simulation of LBM showed good agreement with the reputable benchmark results by previous researchers. Furthermore, according to the results, the dependency of the particle trajectories on the magnitude of the density of the particles can be observed. The results revealed the significant effect of collision, drag force, gravity force, and vortex structure on a particle's trajectory. Consequently, the LBM model is suitable for this type of problem, and the proposed model is expected to have a wide range of applications.

Visualisation and analysis of large-scale vortex structures in three-dimensional turbulent lid-driven cavity flow

In this paper, large eddy simulation (LES) of a three-dimensional turbulent lid-driven cavity (LDC) flow at Re = 10,000 has been performed using the multiple relaxation time lattice Boltzmann method. A Smagorinsky eddy viscosity model was used to represent the sub-grid scale stresses with appropriate wall damping. The prediction for the flow field was first validated by comparing the velocity profiles with previous experimental and LES studies, and then subsequently used to investigate the large-scale three-dimensional vortical structures in the LDC flow. The instantaneous three-dimensional coherent structures inside the cavity were visualised using the second invariant (Q), Δ criterion, λ2 criterion, swirling strength (λci) and streamwise vorticity. The vortex structures obtained using the different criteria in general agree well with each other. However, a cleaner visualisation of the large vortex structures was achieved with the λci criterion and also when the visualisation is based on the vortex identification criteria expressed in terms of the swirling strength parameters. A major objective of the study was to perform a three-dimensional proper orthogonal decomposition (POD) on the fluctuating velocity fields. The higher energy POD modes efficiently extracted the large-scale vortical structures within the flow which were then visualised with the swirling strength criterion. Reconstruction of the instantaneous fluctuating velocity field using a finite number of POD modes indicated that the large-scale vortex structures did effectively approximate the large-scale motion. However, such a reduced order reconstruction of the flow based on the large-scale vortical structures was clearly not as effective in predicting the small-scale details of the fluctuating velocity field which relate to the turbulent transport.

Lattice Boltzmann simulation of solid particles behavior in a three-dimensional lid-driven cavity flow

This paper reports the behavior of solid particles in a three-dimensional lid-driven cavity. The prediction of solid particle dynamics through a fluid has been an important research topic over the past few decades. Difficulties arise when trying to understand the interactions between the particle and surrounding fluid. Therefore, the Lattice Boltzmann Method (LBM) was proposed to analyze three-dimensional cubic lid-driven cavity flow at range of Reynolds numbers. The mesoscale numerical scheme of the Single Relaxation Time (SRT) lattice Boltzmann method was used to solve the equation of flow fluid. The 4th Runge–Kutta method was applied to determine the effects of the drag force on the particle, and the hard sphere model was functioned to calculate the collisions between the particle and walls. The dynamics of a solid particle using a numerical simulation of LBM showed good agreement with the established benchmark results from previous studies. In addition, the results showed that the particle trajectories are critically dependent on the magnitude of the density, diameter and vortex behavior in the cavity. Overall, the results highlight the applicability of the present method to a range of applications.

Parallel numerical algorithm for simulation of a three-dimensional lid-driven cavity flow problem with the use of compact schemes

The parallel algorithm for simulation of the three-dimensional lid driven cavity flow problem with Reynolds numbers up to 10000 on a grid 128x128x128 was developed and implemented in the research. The problem is solved by numerical method where momentum equation is solved by a modified fractional step method with the use of compact scheme and pressure equation is solved by Fourier method in combination with the matrix sweep. The technique of the domain decomposition for parallelization of the proposed numerical method is described. In the process of computing and comparative experiment the dependency of the resulted acceleration and the coefficient of the calculation scalability on number of processors was found. Mathematics Subject Classication: 76F65

Observability of periodic lines in three-dimensional lid-driven cylindrical cavity flows

This study employs three-dimensional particle-tracking velocimetry (3D-PTV) for experimental investigation of the existence and properties of periodic lines in 3D lid-driven time-periodic flows inside a cylindrical cavity. These periodic lines, consisting of material points that periodically return to their initial position, play a central role in the transport properties of laminar flows, yet their existence has so far been demonstrated only in numerical simulations. The formation and characteristics of periodic lines are inextricably linked with spatiotemporal symmetries of the flow. 3D-PTV measurements determined that relevant symmetries, identified with previous symmetry analyses, are satisfied within experimental error bounds. These measurements subsequently isolated periodic lines in the designated symmetry planes, thus offering first experimental evidence of their physical existence and their fundamental reliance on symmetries. Experimental periodic lines are topologically equivalent to those in simulated flows with identical symmetries and exhibit the same response to changes in forcing conditions. The laboratory experiments by these observations bridge the gap from theoretical and numerical predictions on periodic lines to real 3D flows.

1303 高レイノルズ数流れに対する格子ボルツマン法の適用に関する検討(OS13-1.流体力学の先端的な数値解法と応用(1),OS・一般セッション講演)

The most basic form of LBM is lattice Bhatnager-Groos-Krook (LBGK) model. LBGK requires relatively large number of lattices to simulate flow at even moderately high Reynolds number. Various methods for improving numerical stability of LBM have been proposed. In this work, we examined RLBM and MRT-LBM implementation for three-dimensional lid-driven cavity flow at high Reynolds number.

Enhanced Mixing at Low Reynolds Numbers Through Elastic Turbulence

A generic nonlinear Maxwell model for the stress tensor in viscoelastic materials is studied under mixing scenarios in a three-dimensional steady lid-driven cavity flow. Resulting laminar and turbulent flow profiles are investigated to study their mixing efficiencies. Massless tracer particles and passive concentrations are included to show that the irregular spatio-temporal chaos, present in turbulent flow, is useful for potential mixing applications. A Lyapunov measure for filament divergence confirms that the turbulent flow is more efficient at mixing