Method For Simulation Of Flows Research Articles

Prismatic mesh generation based on anisotropic volume harmonic field

In this paper, we present an effective prismatic mesh generation method for viscous flow simulations. To address the prismatic mesh collisions in recessed cavities or slit areas, we exploit 3D tensors controlled anisotropic volume harmonic field to generate prismatic meshes. Specially, a well-fitting tetrahedral mesh is first constructed to serve as the discrete computation domain of volume harmonic fields. Then, 3D tensors are exploited to control the volume harmonic field that better fits the shape geometry. From the topological perspective, the generation of the prismatic mesh can be treated as a topology-preserved morphing of the viscous wall. Therefore, iso-surfaces in the volume harmonic field should be homeomorphic to the viscous wall while fitting its shapes. Finally, a full prismatic mesh can be induced by estimating the forward directions and visible regions in the volume harmonic field. Moreover, to be compatible with different simulation situations, the thickness of prismatic meshes should be variable. Our approach provides local adjustable thickness of prismatic meshes, which can be achieved by controlling local 3D tensors. The proposed anisotropic volume harmonic field based prismatic meshes are efficient and robust, and a full prismatic mesh can be guaranteed without low quality collisions. Various experiments have shown that our proposed prismatic meshes have obvious advantages in terms of efficiency and effectiveness.

A non-linear finite volume method coupled with a modified higher order MUSCL-type method for the numerical simulation of two-phase flows in non-homogeneous and non-isotropic oil reservoirs

In this work, we propose a finite volume scheme to simulate two-phase flows in non-homogeneous and non-isotropic 2-D petroleum reservoirs. The governing equations are solved using the IMPES (IMplicit Pressure and Explicit Saturation) procedure, where the face fluxes from the pressure equation are approximated by a non-linear two-point flux approximation (NL-TPFA) that guarantees monotone solutions for the absolute pressure field. The scheme is based on the construction of one-sided fluxes on each adjacent cell independently and then, the unique edge flux is built as a linear combination of the one-sided fluxes. In our NL-TPFA finite volume scheme, we use auxiliary variables that are located on the vertices of the primal mesh. The nodal auxiliary unknowns are written as linear combinations of the neighboring cell-centered unknowns reducing our scheme to a fully cell-centered one. To solve the non-linear system of equations and to guarantee monotone solutions for arbitrarily anisotropic permeability tensors, we use the Picard iteration method with the Anderson acceleration technique to improve the computational efficiency. On the other hand, to solve the hyperbolic saturation equation, we propose a modified second-order finite volume method. The basic idea of our method is that the reconstructed saturation on the edge that violates the local Discrete Maximum Principle (DMP) is limited, otherwise, the reconstructed saturation is expressed as a convex combination of its unlimited and limited reconstructed values.

Modeling of Flow and Transport in Saturated and Unsaturated Porous Media

Modeling fluid flow and transport processes in porous media is a relevant topic for a wide range of applications. In water resources problems, this topic presents specific challenges related to the multiphysical processes, large time and space scales, heterogeneity and anisotropy of natural porous media, and complex mathematical models characterized by coupled nonlinear equations. This Special Issue aims at collecting papers presenting new developments in the field of flow and transport in porous media. The 25 published papers deal with different aspects of physical processes and applications such as unsaturated and saturated flow, flow in fractured porous media, landslide, reactive transport, seawater intrusion, and transport within hyporheic zones. Based on their objectives, we classified these papers into four categories: (i) improved numerical methods for flow and mass transport simulation, (ii) looking for reliable models and parameters, (iii) laboratory scale experiments and simulations, and (iv) modeling and simulations for improved process understanding. Current trends on modeling fluid flow and transport processes in porous media are discussed in the conclusion.

A locally conservative mixed finite element framework for coupled hydro-mechanical–chemical processes in heterogeneous porous media

This paper presents a mixed finite element framework for coupled hydro-mechanical–chemical processes in heterogeneous porous media. The framework combines two types of locally conservative discretization schemes: (1) an enriched Galerkin method for reactive flow, and (2) a three-field mixed finite element method for coupled fluid flow and solid deformation. This combination ensures local mass conservation, which is critical to flow and transport in heterogeneous porous media, with a relatively affordable computational cost. A particular class of the framework is constructed for calcite precipitation/dissolution reactions, incorporating their nonlinear effects on the fluid viscosity and solid deformation. Linearization schemes and algorithms for solving the nonlinear algebraic system are also presented. Through numerical examples of various complexity, we demonstrate that the proposed framework is a robust and efficient computational method for simulation of reactive flow and transport in deformable porous media, even when the material properties are strongly heterogeneous and anisotropic.

Model order reduction of flow based on a modular geometrical approximation of blood vessels

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g., straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by Proper Orthogonal Decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the Navier–Stokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the Newton–Raphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.

A well-defined grid line-based immersed boundary method for efficient and accurate simulations of incompressible flow

A well-defined grid line-based immersed boundary method is presented for efficient and accurate simulation of unsteady, incompressible flow using non-body conformal, Cartesian grids. Near the fluid–solid interface, the spatial discretization of Navier–Stokes equations is modified to enforce desired boundary conditions in a well-defined manner. Desired modifications can be stably derived using a one-dimensional reconstruction scheme along grid line directions. Eligible grid points and corresponding stencils for reconstruction are determined as grid-IB relationship is described using a grid line-based algorithm. The present method is globally second-order accurate in space and time. For the laminar flow around a circular cylinder, perfect agreement with benchmark numerical studies conducted on body conformal grids is achieved. A strictly linear relationship between the separation bubble length and the Reynolds number within the steady flow regime is reported. Capable of treating a fluid–solid interface with arbitrary geometric complexity, the present method is qualified for efficient simulation of real-world flow problems without necessarily sacrificing accuracy.

Computational methods for pore-scale simulation of rarefied gas flow

Direct simulation at the pore-scale is crucial to unravel rarefaction effect on gas transport in tight porous media. To satisfy the dual demands on modeling accuracy and computation effort, an appropriate method must be chosen. This work, therefore, evaluates four numerical methods for pore-scale rarefied gas flows in a two-dimensional (2D) model porous media over a wide range of rarefaction. These methods are the incompressible Navier-Stokes equation with the first-order velocity-slip boundary condition, and three gas-kinetic solvers i.e. a finite-difference (FD) iterative solver for the linearized Bhatnagar, Gross and Crook (BGK) model kinetic equation, a finite-volume (FV) solver for the non-linear Shakhov model, and an open-source direct simulation Monte Carlos (DSMC) solver. The benchmark cases cover the characteristic Knudsen number ranging from 0.0231 to 4.62 while the characteristic Reynolds numbers are kept to be less than 1.0. All the solvers are developed in OpenFOAM, except the FD solver, allowing us to investigate the effect of local grid refinements using the automatic Cartesian grid generator in OpenFOAM. The flow fields and the apparent permeabilities predicted by all the solvers have been compared in detail. Besides, the computational time of these solvers is measured and analyzed to demonstrate the relative cost of the three kinetic solvers. It is found that the FD solver is the most efficient one and gives accurate results over the whole range of Knudsen number. Finally, this study also evaluates the feasibility of the recently developed discrete unified gas-kinetic scheme (DUGKS), the algorithm in the aforementioned non-linear Shakhov model equation solver, for pore-scale rarefied gas flow. It is found the results predicted by this solver agree well with the other two kinetic solvers.

A divergence-free inflow turbulence generator using spectral representation method for large-eddy simulation of ABL flows

The generation of inflow turbulence is the first necessary step to conduct a successful large-eddy simulation (LES) of atmospheric boundary layer (ABL) flows. It is required that the generated inflow turbulence is divergence-free and satisfies essential target statistical properties, including the two-point statistics of the flow described by the coherency function and the spatial correlation. In this paper, a computationally efficient synthetic inflow turbulence generation technique with explicitly defined two-point flow statistics is proposed based on the spectral representation method. The divergence-free condition is imposed on the generated turbulence through a posteriori procedure embedded in the Pressure-Implicit with Splitting of Operators (PISO) solver of OpenFOAM. The efficacy of the proposed method to represent one-point and two-point statistics is demonstrated by comparing the generated turbulence with wind field measurements taken at the Boundary Layer Wind Tunnel Laboratory of Western University. The proposed method is then applied to LES of ABL flows for three exposure conditions, and the wind profiles downstream of the inlet are examined. The mean velocity, turbulence intensity, integral length scale profiles, and the velocity spectra are in good agreement with the target experimental data, thus, indicating the potential of the method for computational wind engineering applications such as wind load evaluation studies. The implementation of the proposed method is available at https://github.com/GBitsuamlak/DFSR.

Joint-velocity scalar energy probability density function method for large eddy simulations of compressible flow

The combination of large eddy simulation (LES) and probability density function (PDF) methods is a general framework to model turbulent reactive flows. The coupled approach provides direct closures for the nonlinear subgrid source terms typical of chemically reacting flows. LES-PDF methods have a wide range of applicability and they are started to be used in high-speed flows with strong compressibility effects. However, PDF formulations are more complex in compressible flows, where mechanical and thermodynamic contributions are more coupled. The paper presents a novel PDF framework that uses a full thermodynamic closure (scalar-energy-density-velocity) with the Eulerian Monte Carlo stochastic field approach. The work uses simple closures for the subgrid terms using the advantages of the Eulerian formulation and recasts the stochastic equations in a pseudoconservative form. The resultant formulation is applied to three canonical compressible flows: turbulent shock-tubes, compressible homogeneous turbulence, and a reactive free-moving premixed flame. All cases show large density and pressure fluctuations. The effects of underlying numerical schemes and PDF closures to represent compressible effects are investigated along with the statistical convergence of the method.

Research on Nozzle Flow Field and Performance of Water Ramjet at Large Depth

For coprecipitating vehicle, water ramjet is an ideal way to reduce drag. In this paper, the performance of water ramjet at large depth and the flow field structure at nozzle are simulated and analyzed. Through the numerical simulation method of underwater Jet flow, this paper studies the development process of flow field at the initial stage and the parameters variation with time of Jet flow in steady state when the working depth is 200meters. The results show that at the beginning of the jet flow, the water blocking effect seriously prevents the development of the gas bubble, and the gas bubble turns over at the nozzle outlet, and expands in length and width. The unsteady process of ‘necking expansion necking’ occurs repeatedly at the nozzle outlet, with the pressure, velocity and temperature change dramatically near the nozzle outlet. When the flow field is fully developed, the pressure, density, flow rate and thrust of the nozzle outlet fluctuate repeatedly with time, and finally tend to a stable value after many oscillations.

An off-lattice Boltzmann method for blood flow simulation through a model irregular arterial stenosis: The effects of amplitude and frequency of the irregularity

In this work, a finite-difference-based axisymmetric off-lattice Boltzmann solver is developed to simulate blood flow through pathological arteries. The proposed solver handles arterial geometries using a body-fitted curvilinear mesh. The axisymmetric nature of the flow and the non-Newtonian behavior of blood are incorporated using external source terms. The solver is verified for spatially developing pulsatile inflow through an abdominal aortic aneurysm using reference data from literature. Thereafter, the effects of amplitude and frequency of an irregular-shaped stenosed artery are systematically studied. The results are analyzed using the instantaneous vorticity contours, streamlines, cycle-averaged and phase-averaged profiles of wall shear stress (WSS), and oscillatory shear index. Further, the correlation between the luminal surface concentration (LSC) of low-density lipoproteins and the WSS is studied to predict potential disease initiation and progression locations. It is noted that an increase in the amplitude of irregularity of the stenosis increases the magnitudes of maxima and minima of WSS profiles without altering their locations. On the other hand, an increase in the frequency of irregularity increases the magnitudes of WSS extrema while bringing the peaks closer together. Further, a positive correlation is found between the degree of irregularity as well as the number of locations of elevated LSC. The presence of irregularity creates additional vortices in the upstream section of the stenosis. Both the upstream and downstream sections of the stenosis are subjected to the opposing shear-layers with higher magnitudes, which may lead to endothelial damage. Finally, the shear-thinning effect of blood is studied using the power-law model. The magnitudes of the maxima and minima in WSS have a lower value for the shear-thinning model than the Newtonian case. Also, the vortices that were produced in the upstream section because of the irregularity get suppressed by the shear-thinning effect of the blood.

Investigation on the thermal performance of spiral wound heat exchanger for the superfluid helium cryogenic system

Spiral wound heat exchanger has compact structure, good thermal performance per volume and simple manufacture process. It is the key equipment for the superfluid helium cryogenic system, which is able to recover the cold capacity and improve the refrigeration effectiveness. To investigate the influence of fins structure on the thermal performance of spiral wound heat exchanger is essential for its structure design. This study combines experiment and CFD simulation methods, which means a performance test rig of heat exchanger in superfluid helium cryogenic system is designed and constructed, and a numerical simulation method of flow and heat transfer in heat exchanger is established with working medium as helium in the temperature range of 2 K~4.2 K. In this study, the heat transfer effectiveness and pressure drop in shell domain of spiral wound heat exchanger is obtained with the number of fins in the range of 40~135, area of single fin in the range of 669 mm2~1885 mm2, area ratio in the range of 0%~36%. Furthermore, the mechanics of fins structure affect the thermal performance of spiral wound heat exchanger is explored. This study provides reliable method and experimental data for the structure design and thermal performances analysis of spiral wound heat exchanger with helium in the temperature range of 2 K~4.2 K. It is significant for the design and experimental test of superfluid helium cryogenic system.

An improved immersed boundary method for turbulent flow simulations on Cartesian grids

In this paper, we present recent improvements of an Immersed Boundary Method (IBM) for the simulation of turbulent compressible flows on Cartesian grids. The proposed approach enables to remove spurious oscillations at the wall on skin pressure and friction coefficients. Results are compared to a body-fitted approach using the same wall function, showing that the stair-step immersed boundary provides a smooth solution compared to the body-fitted one.The immersed boundary method has been modified to adapt the location of forced and forcing points involved in the immersed boundary reconstruction to the Reynolds number. This method has been validated either for subsonic and transonic flow regimes, through the simulation of the subsonic turbulent flow around a NACA0012 profile and the transonic flow around a RAE2822 profile and the three-dimensional ONERA M6 wing.

Hierarchical Adaptive Eddy-Capturing Approach for Modeling and Simulation of Turbulent Flows

A short review of wavelet-based adaptive methods for modeling and simulation of incompressible turbulent flows is presented. Wavelet-based computational modeling approaches of different fidelities are recast into an integrated hierarchical adaptive eddy-capturing turbulence modeling framework. The wavelet threshold filtering procedure and the associated wavelet-filtered Navier–Stokes equations are briefly discussed, along with the adaptive wavelet collocation method that is used for numerical computations. Depending on the level of wavelet thresholding, the simulation is possibly supplemented with a localized closure model. The latest advancements in spatiotemporally varying wavelet thresholding procedures along with the adaptive-anisotropic wavelet-collocation method make the development of a fully adaptive approach feasible with potential applications for complex turbulent flows.

Design and Experimental Study of a Wine Grape Covering Soil-Cleaning Machine with Wind Blowing

Due to the cold and dry climate during the winter season of Central Asia, in order to prevent frostbite and vines drying out for wine grapes, the common methods are burying the vines in winter under a thick layer of soil and then cleaning them out in the next spring. The design of existing vine digging machinery is not precise enough and can only remove the outer layer of the soil on both sides and the top. It cannot clean the soil from the central area of the buried vine. Sometimes, the branches and buds get damaged due to uneven driving condition. To solve the problem, an innovative non-contact blower was designed and tested to clean the vine. In this paper, the design specifications and operation parameters of the blower were determined according to the agronomic properties of the grapevines. Fluent-EDEM coupling, that is, with the help of Engineering discrete element method (EDEM) and CFD fluid simulation software Fluent, was the most common method for dynamic simulation of gas-solid two-phase flow. The Fluent-EDEM coupling simulation was used to simulate the dynamics of soil particles under the action of different wind speeds and blowing patterns, with the goal of a high soil cleaning rate. A prototype of the soil cleaning blower was manufactured and tested at the vineyards of Ningxia Yuquanying Farm in China. The results showed that the blower had an operation efficiency of 4669 m2·h−1, with an average soil removal rate of 80%. The efficiency of covering soil cleaning and rattan raising was greatly improved, and the damage rate of the vines, branches and the buds was greatly reduced.

A Review of Vortex Methods and Their Applications: From Creation to Recent Advances

This review paper presents an overview of Vortex Methods for flow simulation and their different sub-approaches, from their creation to the present. Particle methods distinguish themselves by their intuitive and natural description of the fluid flow as well as their low numerical dissipation and their stability. Vortex methods belong to Lagrangian approaches and allow us to solve the incompressible Navier-Stokes equations in their velocity-vorticity formulation. In the last three decades, the wide range of research works performed on these methods allowed us to highlight their robustness and accuracy while providing efficient computational algorithms and a solid mathematical framework. On the other hand, many efforts have been devoted to overcoming their main intrinsic difficulties, mostly relying on the treatment of the boundary conditions and the distortion of particle distribution. The present review aims to describe the Vortex methods by following their chronological evolution and provides for each step of their development the mathematical framework, the strengths and limits as well as references to applications and numerical simulations. The paper ends with a presentation of some challenging and very recent works based on Vortex methods and successfully applied to problems such as hydrodynamics, turbulent wake dynamics, sediment or porous flows.

A coupled level set/volume of fluid method for simulation of two-phase flow on unstructured grids

We present a fully coupled level set and volume of fluid method for free surface flow simulations on unstructured grids in two- and three-dimensions. The evolution of the level set function and the volume fraction are updated at each time step. The level set advection equation is solved by a least squares weighted residual method while the volume fraction advection is solved using an unsplit Eulerian-Lagrangian scheme. The reconstruction of the interface in the volume of fluid method is performed using the volume fraction information together with the normal vector obtained from the level set function. The reconstructed interface is then used to reinitialize the level set function. Thanks to the fully coupling of the two methods, the interface reconstruction is carried out efficiently and the mass conservation is preserved exactly. The proposed method is validated against several benchmarks and is coupled with the incompressible Navier-Stokes solver to solve two-phase flow problems. Numerical results show that the method is capable of resolving complex interface changes efficiently and accurately.

On the Scope of Lagrangian Vortex Methods for Two-Dimensional Flow Simulations and the POD Technique Application for Data Storing and Analyzing.

The possibilities of applying the pure Lagrangian vortex methods of computational fluid dynamics to viscous incompressible flow simulations are considered in relation to various problem formulations. The modification of vortex methods—the Viscous Vortex Domain method—is used which is implemented in the VM2D code developed by the authors. Problems of flow simulation around airfoils with different shapes at various Reynolds numbers are considered: the Blasius problem, the flow around circular cylinders at different Reynolds numbers, the flow around a wing airfoil at the Reynolds numbers and , the flow around two closely spaced circular cylinders and the flow around rectangular airfoils with a different chord to the thickness ratio. In addition, the problem of the internal flow modeling in the channel with a backward-facing step is considered. To store the results of the calculations, the POD technique is used, which, in addition, allows one to investigate the structure of the flow and obtain some additional information about the properties of flow regimes.

Weakly compressible Navier-Stokes solver based on evolving pressure projection method for two-phase flow simulations

An evolving pressure projection method for numerical computations of the weakly compressible Navier-Stokes equations is proposed. Fully explicit time integration is achieved using an independent pressure evolution equation. To damp the acoustic wave in a weakly compressible fluid flow, we iteratively compute the pressure evolution equation coupled with a projection step. Due to the simplicity and locality of this iteration procedure, it does not increase the computational amount too much. The computation is performed on a staggered Cartesian grid. By introducing the phase field model for interface capturing, this solver can be directly applied to two-phase flow simulations using a one-fluid model. Exact mass conservation is ensured by a finite-volume formulation of the conservative phase field equation. Various benchmarking problems are simulated to validate accuracy. The stability of a violent two-phase flow with large density and viscosity ratio is demonstrated in a three-dimensional dam break simulation. Numerical results show that the proposed method for weakly compressible Navier-Stokes equations can prevent oscillations of pressure and velocity.

APPLICATION OF LEXICOGRAPHIC METHODS IN FINDING NEW SOLUTIONS FOR THE CONSTRUCTION OF SWITCH FAUCETS

Methods and techniques to stimulate creativity are indispensable in the process of obtaining more reliable and competitive products. For the elaboration and efficient use of logical-deductive methods and techniques in creativity, it is necessary to know a minimum of combinatorics, which include arrangements, combinations, permutations, graphs and finite networks. From the multitude of methods of orderly enumeration of all ensembles, without omissions or repetitions, the lexicographic method is recommended, according to which, the assemblies are ordered in ascending order according to the sum of the component elements index. The main purpose of this paper is to apply the lexicographic method to obtain a more efficient flow faucet body in terms of working fluid behavior. Thus, the pressure, flow, velocity variation and degree of fluid vorticity have better values for the faucet body obtained by applying the lexicographic method. Therefore, by applying the flow simulation method, it was possible to characterize the behavior of the working fluid.