Block-structured Mesh Research Articles

Direct numerical simulation study on convective heat transfer of two tandem permeable square cylinders

This study focuses on two-dimensional heat transfer and unsteady flow past two tandem heated porous square cylinders using lattice Boltzmann method combined with block-structured topology-confined mesh refinement. The effects of the Reynolds number (30≤Re≤150), the Darcy number (10−5≤Da≤10−2), and spacing ratio (1.5≤L/D≤5, where L and D are distance of two adjacent cylinder centers and square cylinder length, respectively) are investigated. The intended analysis links hydrodynamic and heat transfer coefficients and wake structures in parameter space of Re−Da−L/D to fluid mechanics. For upstream cylinder, drag coefficients decrease with a reduction of Da and range of Re≥100, while wake length increases with an increment of L/D ratio at the same range of Re. Time-averaged normalized velocity increases at higher permeability levels. A significant augmentation in a time-averaged Nusselt number is reported for an increase in Da and full L/D range. For downstream cylinder, the interaction of fluid vortices in the gap between the cylinders affects the flow pattern, causing irregularities in the drag coefficient variation. The impacts of L/D on the wake length is more obvious than that of Da. Both the wake length and time-averaged Nusselt number values are proportional to an increase in L/D. Consequently, all the investigated results of the upstream cylinder are significantly altered from those of the downstream cylinder due to the shadowing effect of the upstream cylinder.

Dynamic modelling of subgrid scalar dissipation rate in premixed and partially premixed flames with differential filter

Large eddy simulation (LES) paradigms are used in the present work to predict premixed and partially premixed turbulent flames with flamelets based thermochemistry and presumed filtered density function approach for turbulence-chemistry interaction modelling. The combustion model requires a closure for the scalar dissipation rate of a progress variable, in which a modelling constant must be chosen. The present work focuses on the computation of the model constant through dynamic procedures based on the scale-similarity assumption, which requires the application of test-filters. In particular, two test-filtering approaches for LES, based respectively on an algebraic formulation and a newly proposed differential equation, are tested for flame configurations at different levels of turbulence, and using block-structured and unstructured meshes. The analysis shows that the differential filter, unlike the algebraic one, is handled well in situations of weak turbulence at comparable computational costs. At higher turbulence conditions the outcome looks less dependent on the test-filter and mesh topology used, although quantitative differences in the behaviour of the dynamically-computed model constant are still observable and discussed. Further analyses to understand the behaviour of the two filters are presented in the paper.

Aircraft Simulations Using the New CFD Software from ONERA, DLR, and Airbus

This paper presents a thorough comparison between RANS simulations performed with the computational fluid dynamics by ONERA, DLR, and Airbus (CODA) new-generation flow solver and reference legacy codes TAU (DLR) and elsA (ONERA) for high-speed cruising NASA Common Research Model (CRM) configurations that were considered in the context of the 5th, 6th, and 7th Drag Prediction Workshops. The solver’s accuracy is assessed with several meshing strategies, including block-structured, hybrid-structured/unstructured, and fully unstructured tetrahedral meshes. This solver features both a cell-centered finite-volume (FV) scheme suited to arbitrary meshes as well as a modern high-order discontinuous Galerkin (DG) scheme. We show that for all cases considered, the FV component recovers an equivalent accuracy compared to elsA (cell-centered FV) on block-structured meshes and TAU (node-centered FV) on hybrid and unstructured meshes. The high-order DG scheme (third-order accurate) is found to significantly enhance the drag prediction on coarse meshes compared to legacy FV methods, both for structured and unstructured meshes.

Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing

We present a set of operators to perform modifications, in particular collapses and splits, in volumetric cell complexes which are discretely embedded in a background mesh. Topological integrity and geometric embedding validity are carefully maintained. We apply these operators strategically to volumetric block decompositions, so-called T-meshes or base complexes, in the context of hexahedral mesh generation. This allows circumventing the expensive and unreliable global volumetric remapping step in the versatile meshing pipeline based on 3D integer-grid maps. In essence, we reduce this step to simpler local cube mapping problems, for which reliable solutions are available. As a consequence, the robustness of the mesh generation process is increased, especially when targeting coarse or block-structured hexahedral meshes. We furthermore extend this pipeline to support feature alignment constraints, and systematically respect these throughout, enabling the generation of meshes that align to points, curves, and surfaces of special interest, whether on the boundary or in the interior of the domain.

Fluid–structure interaction with a Finite Element–Immersed Boundary approach for compressible flows

This paper presents the mathematical modeling and numerical simulations of fluid–structure interaction (FSI) problems. The fluid domain is discretized using a Cartesian block-structured mesh and solved using the Finite Volume Method (FVM), using the LES methodology with Smagorinsky turbulent closure model. The fluid flow in the system is considered compressible, with properties that vary. The Immersed Boundary Method (IBM) is used to model the solid–fluid interface, and the structure deformation was solved using the Finite Element Method (FEM). The Multi-direct Forcing Scheme is used to calculate the fluid-dynamics forces through the IBM. After calculating the fluid forces exerted on the solid, the forces are interpolated and transferred to the FEM model, providing the deformation of the structure at each time step. The structural domain was discretized with Hexahedral eight-noded element with extra shape functions. The simulations were carried out using MFSIm (in-house code), a multiphysics simulation framework developed by the Fluid Mechanics Laboratory of the Federal University of Uberlândia with financial support from Petrobras. This paper demonstrates the practical application of FSI analysis in an industrial context, specifically focusing on a pipeline system within a Fluid Catalytic Cracking Unit (FCCU) used in the oil and gas industry. The analysis involves the use of butterfly valves positioned at different angles of opening. The results are treated statistically, and a surface response is generated. Machine learning is employed to predict the surface response, showing the valve configurations that yield the maximum and minimum displacement magnitudes of the evaluated structural probes.

Hermes-3: Multi-component plasma simulations with BOUT++

A new open source tool for fluid simulation of multi-component plasmas is presented, based on a flexible software design that is applicable to scientific simulations in a wide range of fields. Hermes-3 is built on plasma simulation framework BOUT++, consolidating earlier SD1D and Hermes models into a single code that can be configured at run-time to solve plasma models in 1D, 2D or 3D, either for transport (steady-state) or turbulent (time-evolving) problems, with an arbitrary number of ion and neutral species. We describe the improved numerical algorithms and software design that have been implemented in Hermes-3.To demonstrate the capabilities of this tool, applications relevant to the boundary of tokamak plasmas are presented: 1D simulations of diveror plasmas evolving equations for all charge states of neon and deuterium; 2D transport simulations of tokamak equilibria in single-null X-point geometry with plasma ion and neutral atom species; and simulations of the time-dependent propagation of plasma filaments (blobs).Hermes-3 is publicly available on Github under the GPL-3 open source license. The repository includes documentation and a suite of unit, integrated and convergence tests. Program summaryProgram Title: Hermes-3CPC Library link to program files:https://doi.org/10.17632/rtkvc3r743.1Developer's repository link:https://github.com/bendudson/hermes-3Licensing provisions: GPLv3Programming language: C++14Nature of problem: Simulation of dynamics and steady-state solutions of multiple ion and neutral species in magnetised plasmas using drift-reduced fluid plasma models in 1 to 3 spatial dimensions. Focused on but not restricted to the simulation of turbulence in the boundary of tokamaks.Solution method: Hermes-3 implements a system of flexible software components, that are configured at run-time and coupled by passing a state object between them (the Encapsulate State and Command patterns). Hermes-3 builds on BOUT++ [1], employing the Method of Lines with implicit and explicit time-integration methods in curvilinear coordinates on block-structured meshes, making use of libraries including SUNDIALS, PETSc and Hypre. Hermes-3 implements drift-reduced plasma fluid equations using conservative finite difference methods, and atomic processes that couple plasma and neutral fluids.

Development of a full-scale MATCH model in heat transfer performance simulation of RPV insulation structure with experimental validation

In a core meltdown accident, the reactor pressure vessel (RPV) insulation plays a significant role in the flooding process of the reactor cavity. The research on the function role of RPV insulation has attracted lots of attention whereas there are relatively few studies on heat transfer characteristics. Besides, the majority of previous studies on RPV insulation adopted a down-scaling or partial model instead of the entire model to decrease computational complexity. In this paper, a mesh assembly method is proposed to generate block-structured meshes and the heat transfer characteristics of the RPV insulation is carried out. Then a partial validation model has been verified against the experiments results. In addition, the effects of the air supply temperature, flow rate, and insulation installation gap on the overall model heat transfer performance of RPV insulation are investigated. The results demonstrate that the mean temperature of the insulation's outer wall (42.92 °C), the local temperature of the concrete (73.85 °C), and the heat flux of the insulation's outer wall (93.48 W⋅m‐2) are less than their limit values of 60 °C, 95 °C, and 235 W⋅m‐2, respectively. And the heat leakage from the supports accounts for over 90% of the total heat dissipation.

Scale-Resolving Hybrid RANS-LES Simulation of a Model Kaplan Turbine on a 400-Million-Element Mesh

Double-regulated Kaplan turbines with adjustable guide vanes and runner blades offer a high degree of flexibility and good efficiency for a wide range of operating points. However, this also leads to a complex geometry and flow guidance with, for example, vortices of different sizes and strengths. The flow in a draft tube is especially challenging to simulate mainly due to flow phenomena, like swirl, separation and strong adverse pressure gradients, and a strong dependency on the upstream flow conditions. Standard simulation approaches with RANS turbulence models, a coarse mesh and large time step size often fail to correctly predict performance and can even lead to wrong tendencies in the overall behavior. To reveal occurring flow phenomena and physical effects, a scale-resolving hybrid RANS-LES simulation on a block structured mesh of about 400 million hexahedral elements of a double-regulated five-blade model Kaplan turbine is carried out. In this paper, first, the results of the ongoing simulation are presented. The major part of the simulation domain is running in LES mode and seems to be properly resolved. The validation of the simulation results with the experimental data shows mean deviations of less than 0.8% in the global results, i.e., total head and power, and a good visual agreement with the three-dimensional PIV measurements of the velocity in the cone and both diffuser channels of the draft tube. In particular, the trend of total head and the results for the draft tube differ significantly between the scale-resolving simulation and a standard RANS simulation. The standard RANS simulation exhibits a highly unsteady behavior of flow, which is not observed in the experiments or scale-resolving simulation.

Quadrilateral Mesh Generation Method Based on Convolutional Neural Network

The frame field distributed inside the model region characterizes the singular structure features inside the model. These singular structures can be used to decompose the model region into multiple quadrilateral structures, thereby generating a block-structured quadrilateral mesh. For the generation of block-structured quadrilateral mesh for two-dimensional geometric models, a convolutional neural network model is proposed to identify the singular structure inside the model contained in the frame field. By training the network model with a large number of model region decomposition data obtained in advance, the model can identify the vectors of the frame field in the region located in the segmentation field. Then, the segmentation streamline is constructed from the annotation. Based on this, the geometric region is decomposed into several small regions, regions which are then discretized with quadrilateral mesh elements. Finally, through two geometric models, it is verified that the convolutional neural network model proposed in this study can effectively identify the singular structure inside the model to realize the model region decomposition and block-structured mesh generation.

Two-Fluid Large-Eddy Simulation of Two-Phase Flow in Air-Sparged Hydrocyclone

The two-fluid (Euler–Euler) model and large-eddy simulation are used to compute the turbulent two-phase flow of air and water in a cyclonic flotation device known as an Air-Sparged Hydrocyclone (ASH). In the operation of ASH, air is injected through a porous cylindrical wall. The study considers a 48 mm diameter hydrocyclone and uses a block-structured fine mesh of 10.5 million hexagonal elements. The air-to-water injection ratio is 4, and a uniform air bubble diameter of 0.5 mm is specified. The flow field in ASH was investigated for the inlet flow rate of water of 30.6 L/min at different values of underflow exit pressure. The current simulations quantify the effects of the underflow exit pressure on the split ratio and the overall flow physics in ASH, including the distribution of the air volume fraction, water axial velocity, tangential velocity, and swirling-layer thickness. The loci of zero-axial velocity surfaces were determined for different exit pressures. The water split ratio through the overflow opening varies with underflow exit pressure as 6%, 8%, 16%, and 26% for 3, 4, 5, and 6 kPa, respectively. These results indicate that regulating the pressure at the underflow exit can be used to optimize the ASH’s performance. Turbulent energy spectra in different regions of the hydrocyclone were analyzed. Small-scale turbulence spectra at near-wall points exhibit f−4 law, where f is frequency. Whereas for points at the air-column interface, the energy spectra show an inertial subrange f−5/3 followed by a dissipative range of f−7 law.

Local mesh refinement sensor for the lattice Boltzmann method

A novel mesh refinement sensor is proposed for lattice Boltzmann methods (LBMs) applicable to either static or dynamic mesh refinement algorithms. The sensor exploits the kinetic nature of LBMs by evaluating the departure of distribution functions from their local equilibrium state. This sensor is first compared, in a qualitative manner, to three state-of-the-art sensors: (1) the vorticity norm, (2) the Q-criterion, and (3) spatial derivatives of the vorticity. This comparison shows that our kinetic sensor is the most adequate candidate to propose tailored mesh structures across a wide range of physical phenomena: incompressible, compressible subsonic/supersonic single phase, and weakly compressible multiphase flows. As a more quantitative validation, the sensor is then used to produce the computational mesh for two existing open-source LB solvers based on inhomogeneous, block-structured meshes with static and dynamic refinement algorithms, implemented in the Palabos and AMROC-LBM software, respectively. The sensor is first used to generate a static mesh to simulate the turbulent 3D lid-driven cavity flow using Palabos. AMROC-LBM is then adopted to confirm the ability of our sensor to dynamically adapt the mesh to reach the steady state of the 2D lid-driven cavity flow. Both configurations show that our sensor successfully produces meshes of high quality and allows to save computational time.

Wake modeling and simulation of an experimental wind turbine using large eddy simulation coupled with immersed boundary method alongside a dynamic adaptive mesh refinement

Accurate numerical models of the flow around wind turbines is highly relevant for optimizing the energy efficiency of wind farms. The main goal of this work is to apply large eddy simulation (LES) along with an immersed boundary (IB) method to generate spatial and temporal information of the velocity field and forces acting on a fully-resolved NREL S809 airfoil and NREL Phase VI wind turbine. The numerical framework used in the simulations performs LES under a Cartesian block-structured mesh that is dynamically refined via adaptive mesh refinement (AMR) to increase accuracy and reduce computational costs. The mesh refinement criteria is based on Lagrangian points and vorticity. Solid surfaces of the wind turbine are captured using the Lagrangian formulation of the IB method. The simulations are based on the NREL Phase VI wind turbine, where blade analysis of lift and drag coefficients were performed, followed by time-averaged streamwise velocity and vorticity evaluations. For different angles of attack, the wake centerline velocity analysis demonstrates high energy extraction in the near wake of the wind turbine blade. In terms of validation, the drag coefficient of the NREL S809 airfoil achieves better agreement with the experimental data than the lift coefficient. Validation from the NREL Phase VI shows that the power performance difference between the simulation and experiment is lower than 6%. Wake analysis of the wind turbine scenario are based on downstream profiles of the time-averaged streamwise velocity. The numerical simulation shows a higher loss of kinetic energy in the near wake region, mainly in the centerline, compared to benchmark data, but achieves very similar results to literature in the far-wake region.

A hierarchical wavefront method for LU-SGS

The lower–upper Symmetric-Gauss–Seidel (LU-SGS) method is one of typical implicit methods, especially for an application that requires high convergence and accuracy. However, the data-dependencies among grid points in the LU-SGS method prevent parallelization and vectorization, both of which are important for modern computing systems. As modern computing systems consist of multiple nodes, each of which is equipped with multi-core processors with a vector processing capability, to take advantages of these computing systems, both parallel computing and vector computing are mandatory. This paper proposes a hierarchical wavefront method that combines the wavefront and the hyperplane methods in order to achieve both parallelization and vectorization of the LU-SGS method with block-structured meshes. The evaluation results show that the hierarchical wavefront method is 4.9 times faster than the conventional wavefront method and 24.2 times faster than the hyperplane method.

Tree cutting approach for domain partitioning on forest-of-octrees-based block-structured static adaptive mesh refinement with lattice Boltzmann method

The aerodynamics simulation code based on the lattice Boltzmann method (LBM) using forest-of-octrees-based block-structured adaptive mesh refinement (AMR) with temporary-fixed refinement was implemented, and its performance was evaluated on GPU-based supercomputers. Although the Space-Filling-Curve-based (SFC) domain partitioning algorithm for the octree-based AMR has been widely used on conventional CPU-based supercomputers, accelerated computation on GPU-based supercomputers revealed a bottleneck due to costly halo data communication. Our new tree cutting approach adopts a hybrid domain partitioning with the coarse structured block decomposition and the SFC partitioning in each block. This hybrid approach improved the locality and the topology of the partitioned sub-domains and reduced the amount of the halo communication to one-third of the original SFC approach. In the strong scaling test, the code achieved maximum ×1.82 speedup at the performance of 2207 MLUPS (mega-lattice update per second) on 128 GPUs (NVIDIA® Tesla® V100). In the weak scaling test, the code achieved 9620 MLUPS at 128 GPUs with 4.473 billion grid points, while keeping the parallel efficiency of 93.4% from 8 to 128 GPUs.

Multiparameter Optimization of Thrust Vector Control with Transverse Injection of a Supersonic Underexpanded Gas Jet into a Convergent Divergent Nozzle

The optimal design of the thrust vector control system of solid rocket motors (SRMs) is discussed. The injection of a supersonic underexpanded gas jet into the diverging part of the rocket engine nozzle is considered, and multiparameter optimization of the geometric shape of the injection nozzle and the parameters of jet injection into a supersonic flow is developed. The turbulent flow of viscous compressible gas in the main nozzle and injection system is simulated with the Reynolds-averaged Navier–Stokes (RANS) equations and shear stress transport (SST) turbulence model. An optimization procedure with the automatic generation of a block-structured mesh and conjugate gradient method is applied to find the optimal parameters of the problem of interest. Optimization parameters include the pressure ratio of the injected jet, the angle of inclination of the injection nozzle to the axis of the main nozzle, the distance of the injection nozzle from the throat of the main nozzle and the shape of the outlet section of the injection nozzle. The location of injection nozzle varies from 0.1 to 0.9 with respect to the length of the supersonic part of the nozzle; the angle of injection varies from 30 to 160 degrees; and the shape of the outlet section of the injection nozzle is an ellipse with an aspect ratio that varies from 0.1 to 1. The computed fluid flow in the combustion chamber is compared with experimental and computational results. The dependence of the thrust as a function of the injection parameters is obtained, and conclusions are made about the effects of the input parameters of the problem on the thrust coefficient.

Implementation of a hybrid Lagrangian filtered density function–large eddy simulation methodology in a dynamic adaptive mesh refinement environment

Multispecies mixing processes play an important role in many engineering, biological, and environmental applications. Since simulating mixing flows can be useful to understand its physics and to study industrial issues, this work aims to develop the basis of a methodology able to simulate the physics of multiple-species mixing flows, using a hybrid large eddy simulation/Lagrangian filtered density function (FDF) method on an adaptive, block-structured mesh. A computational model of notional particles transport on a distributed processing environment is built using a parallel Lagrangian map. This map connects the Lagrangian information with the Eulerian framework of the in-house code MFSim, in which transport equations are solved. The Lagrangian composition FDF method, through the Monte Carlo technique, performs algebraic calculations over an ensemble of notional particles and provides composition fields statistically equivalent to those obtained by finite volume numerical solution of partial differential equations. Finally, to maintain high accuracy in the system of stochastic differential equations solver when an adaptive mesh refinement environment is used, a methodology for ensuring mass conservation is developed to preserve at least the statistical moments up to order two, even in the case of annihilation or cloning of a large number of notional particles in one time step, ensuring the applicability of Lagrangian FDF methods in dynamically adaptive grid refinement.

GPU acceleration of a 2D compressible Euler solver on CUDA-based block-structured Cartesian meshes

A novel block-structured Cartesian mesh method is developed that is well designed for the graphics processing unit (GPU) acceleration of flow simulations. The size of the mesh block is set based on the thread hierarchy in Compute Unified Device Architecture which is an easy-to-use GPU programming model. The mesh method is implemented in a finite-volume compressible flow solver, where the two-dimension steady Euler equations are solved by using the AUSM + scheme in spatial discretization and third-order total-variation-diminishing Runge–Kutta method in time discretization. For the GPU implementation, the redundant computation, data structure reorganization and Structure-of-Arrays (SoA) mesh layout are utilized to reduce the frequency and data size for information transfer between host and device. Two test cases, the supersonic flow over a circular cylinder and a NACA0012 airfoil, are presented to validate numerical approaches and valuate computational performance. Additionally, numerical experiments are carried out on a test case at different mesh sizes and execution configurations to investigate properties of the proposed method.

Quadrature-free discontinuous Galerkin method with code generation features for shallow water equations on automatically generated block-structured meshes

Although discretizations of the shallow water equations (SWE) based on the discontinuous Galerkin (DG) method are well established, their computational performance still generally lags behind that of the finite volume discretizations. In explicit and semi-implicit time stepping schemes commonly used in connection with the SWE models, the most computationally expensive parts of a DG algorithm are the element and edge integrals computed via loops over quadrature points. We propose a quadrature-free DG formulation for the SWE that replaces quadrature integrations by analytical evaluations. The method is implemented within the code generation framework of the ExaStencils project using the SymPy Python library. The new formulation uses block-structured triangular meshes automatically generated for a given number of blocks.

A wall-aligned grid generator for non-linear simulations of MHD instabilities in tokamak plasmas

Block-structured mesh generation techniques have been well addressed in the CFD community for automobile and aerospace studies, and their applicability to magnetic fusion is highly relevant, due to the complexity of the plasma-facing wall structures inside a tokamak device. Typically applied to non-linear simulations of MHD instabilities relevant to magnetically confined fusion, the JOREK code was originally developed with a 2D grid composed of isoparametric bi-cubic Bézier finite elements, that are aligned to the magnetic equilibrium of tokamak plasmas (the third dimension being represented by Fourier harmonics). To improve the applicability of these simulations, the grid-generator has been generalised to provide a robust extension method, using a block-structured mesh approach, which allows the simulations of arbitrary domains of tokamak vacuum vessels. Such boundary-aligned grids require the adaptation of boundary conditions along the edge of the new domain. Demonstrative non-linear simulations of plasma edge instabilities are presented to validate the robustness of the new grid, and future potential physics applications for tokamak plasmas are discussed. The methods presented here may be of interest to the wider community, beyond tokamak physics, wherever imposing arbitrary boundaries to quadrilateral finite elements is required.

A new numerical framework for large-eddy simulation of waves generated by objects piercing water surface

A novel numerical framework is developed for large-eddy simulation (LES) of interactions among air, water, and solid bodies. The motions of air and water are solved on a fixed block-structured mesh, with the air–water interface captured using the volume-of-fluid method. A new sub-grid scale stress model based on the vortex identifier is used to improve the robustness and efficiency of the simulation flows with air–water interface. The new framework is tested in the context of bow waves and Kelvin waves generated by a water-surface vehicle. Wave breaking at the bow of the vehicle is captured in LES. The LES results of wave geometry approaches the measurements progressively as the grid resolution is refined. The simulation results indicate that LES is a useful tool for studying wave dynamics of water-surface vehicles.