Method For Computation Of Flows Research Articles

Space–Time method for flow computations with slip interfaces and topology changes (ST-SI-TC)

Abstract The Space–Time Variational Multiscale (ST-VMS) method was introduced to function as a moving-mesh method. It is the VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method. It has reasonably good turbulence modeling features and serves as a core computational method. The ST Slip Interface (ST-SI) method was introduced to addresses the challenge involved in high-resolution representation of the boundary layers near spinning solid surfaces. The mesh covering a spinning solid surface spins with it and thus maintains the high-resolution representation near it. The ST-TC method was introduced for moving-mesh computation of flow problems with topology changes, such as contact between solid surfaces. It deals with the TC while maintaining high-resolution boundary layer representation near solid surfaces. The “ST-SI-TC” method we introduce here integrates the ST-SI and ST-TC methods in the ST-VMS framework. It enables accurate flow analysis when we have a spinning solid surface that is in contact with a solid surface. We present two test computations with the ST-SI-TC method, and they are both with models of flow around a rotating tire with road contact and prescribed deformation, one with a 2D model, and one with a 3D model.

The numerical simulation of draft tube cavitation in Francis turbine at off-design conditions

Purpose – The vortex ropes in draft tube of Francis turbine always cause fluctuation and vibration, which consequently threaten the safety and stability of hydro turbines. The purpose of this paper is to use a cavitation flow computational method to simulate spiral vortex ropes under part load conditions and columnar vortex ropes under high-load conditions in draft tube. The unsteady cavitating flow characteristics in draft tube and its interaction with runner cavitation were analyzed. Design/methodology/approach – The calculation method was verified by cavitation simulation around a 3D hydrofoil. The results show that the Large Eddy Simulation (LES) turbulence model with the Zwart-Gerber-Blemari cavitation model have comparative advantage in cavitation simulations whether from capture of cavity shape or prediction of pressure changes. So it was chosen to simulate the two-phase cavitation flow in Francis turbine. The boundary conditions for inlet and outlet were set to inlet total pressure and outlet static pressure. The finite volume method with the central difference was adopted to discretize the equations. Findings – The calculated Thoma number agreed well with the experimental data. The vortex rope diameter and length increased with the cavitation development for both of the two types of vortex ropes conditions. The maximum peak-to-peak values of pressure pulsations located in the draft tube elbow part under all of the Thoma numbers conditions. Under spiral vortex rope conditions, the pressure pulsation in the same section of draft tube cone show obviously phase shift. The vortex rope affects the development of runner cavitation, which induces the symmetric and axisymmetric cavitation region in the suction side of blades for spiral and columnar vortex rope condition, respectively. Research limitations/implications – The mesh independence had been checked only in non-cavitation flow; in addition, the mesh density did not well satisfy the requirements of LES due to the limitations of computing power. The higher mesh density on a simplified model with one blade flow path and the entire draft tube may be helpful for obtaining more precise results. Originality/value – The spiral and columnar vortex ropes in a Francis turbine were compared and analyzed. The annular hydraulic jump appeared in the columnar vortex rope conditions has little effects on the pressure pulsations. The uneven flow field caused by spiral vortex led to the asymmetric cavitation development.

Discrete unified gas kinetic scheme on unstructured meshes

The recently proposed discrete unified gas kinetic scheme (DUGKS) is a finite volume method for multiscale flow computations with asymptotic preserving property. The solution of the Boltzmann model equation is directly used for the construction of numerical flux and makes the scheme applicable in all flow regimes. In previous applications of the DUGKS, structured meshes have been mostly employed, which may have difficulties for problems with complex geometries. In this paper we will extend the DUGKS to unstructured meshes, with the implementation of computational fluid dynamics techniques to the DUGKS. Several test cases, i.e., the cavity flow ranging from continuum to free molecular regimes, a multiscale flow problem between two connected cavities with large pressure and density variations, high speed flows past multiple cylinders in slip and transitional regimes, and an impulsive start problem are performed. The results are compared with the well-defined Direct Simulation Monte Carlo (DSMC) or Navier–Stokes (NS) solutions in their applicable regimes. The numerical results demonstrate the effectiveness of the proposed DUGKS for the study of multiscale flow problems.

Three-dimensional building-cube method for inviscid compressible flow computations

In this study, the Building-Cube method (BCM) devised for calculating large-scale flows and getting rid of the grid dependencies of computational results is extended to perform 3D inviscid compressible fluid flow simulations. The proposed scheme divides a computational domain into a large number of cubes with different sizes, and each individual cube is a sub-flow field simulated with a Cartesian grid of uniform spacing and an equal number of cells and nodes. Through the proposed scheme, we determine the geometric size of individual cube by Adapting the flow characteristics and geometrical shapes using an adaptively refining Cartesian grid approaches. The uniform spacing and equal number of cells and nodes in the Cartesian grid of individual cubes ensure a good performance for parallel computations; large result data can be handled efficiently. Further, an algorithm to solve the inviscid flow equations on the Building-Cube mesh for three-dimensional (3D) geometries is presented. The validation and performance of the proposed 3D BCM are demonstrated through comparisons of the computed results with the experimental data for the ONERA M6 wing and ONERA M5 wing-fuselage configurations.

Weakly swirling flow in a model of blood vessel with stenosis: Numerical and experimental study

Investigation of weakly swirling flow in a model of a blood vessel with asymmetrical stenosis has been performed using both experimental flow measurement techniques (ultrasound Doppler) and computational fluid dynamics methods. A special attention is paid to getting data for the length of the reverse-flow zone occurring past the stenosis. It has been established that the laminar steady-state flow model is acceptable for numerical analysis of flow past the given-geometry stenosis at Reynolds number values less than 300. At higher values of this parameter, application of the semi-empirical k-ω SST turbulence model is preferable. It has been shown that flow swirl can lead to an increase of the reverse-flow zone.

Space–time VMS method for flow computations with slip interfaces (ST-SI)

We present the space–time variational multiscale (ST-VMS) method for flow computations with slip interfaces (ST-SI). The method is intended for fluid–structure interaction (FSI) analysis where one or more of the subdomains contain spinning structures, such as the rotor of a wind turbine, and the subdomains are covered by meshes that do not match at the interface and have slip between them. The mesh covering a subdomain with the spinning structure spins with it, thus maintaining the high-resolution representation of the boundary layers near the structure. The starting point in the development of the method is the version of the arbitrary Lagrangian–Eulerian VMS (ALE-VMS) method designed for computations with "sliding interfaces". Interface terms similar to those in the ALE-VMS version are added to the ST-VMS formulation to account for the compatibility conditions for the velocity and stress. In addition to having a high-resolution representation of the boundary layers, because the ST framework allows NURBS functions in temporal representation of the structure motion, we have exact representation of the circular paths associated with the spinning. The ST-SI method includes versions for cases where the SI is between fluid and solid domains with weakly-imposed Dirichlet conditions for the fluid and for cases where the SI is between a thin porous structure and the fluid on its two sides. Test computations with 2D and 3D models of a vertical-axis wind turbine show the effectiveness of the ST-SI method.

High-Order Discontinuous Galerkin Method for Computation of Turbulent Flows

This paper presents a high-order discontinuous Galerkin method for computation of compressible turbulent flows in three space dimensions. A modified Spalart-and-Allmaras turbulence model is implemented and discretized to the same order of accuracy as that for the Reynolds-averaged Navier–Stokes equations. The creation of curvilinear meshes for arbitrary three-dimensional configurations is achieved through the aid of a computational analysis programming interface, which enables direct communications with the computer-aided design module to determine the true positions of surface quadrature points for high-order geometric representations. A modified linear elasticity approach is used sequentially and is of crucial importance for reshaping the interior mesh to allow high-aspect-ratio curved elements in turbulent boundary layers. Requirements of the mesh parameters, including the wall spacing and viscous stretching factor, are studied; and it is concluded that, for attached turbulent flows, the conventional settings often used in low-order methods should be less stringent when a higher-order method is considered. Several other numerical examples, including a direct numerical simulation of the Taylor–Green vortex and turbulent flow over an ONERA M6 wing, are considered to assess the solution accuracy and to demonstrate the performance of high-order discontinuous Galerkin methods in capturing transitional and turbulent flow phenomena.

A new adaptive Cartesian-grid CIP method for computation of violent free-surface flows

A new adaptive Cartesian-grid for the CIP (constrained interpolation profile) method is proposed and applied to two-dimensional numerical simulations of violent free-surface flows. The CCUP (CIP combined and unified procedure) method is employed and combined with this adaptive Cartesian-grid for robust and efficient computation. This adaptive grid is capable of tracking regions where flows vary violently, and a much finer grid is then concentrated automatically on these regions to adapt to the violent changing of the flow. Unlike the abacus-like Soroban grid which is an adaptive meshless grid with complicated algorithms and inefficiency of evaluation of frequently computed spatial derivatives, the present approach not only simplifies computational algorithm but also enhances efficiency of frequently-computed spatial derivatives. It is also different from most of the remeshing schemes that no additional CPU-time for the value-mapping from the old grid to the new grid is taken in this adaptive grid system provided that the advection velocity is interpolated, since the value-mapping process is accomplished simultaneously within the advection process. To validate the accuracy and efficiency of this newly-proposed CFD model, several two-dimensional benchmark problems are performed, and the results are compared with experimental measurements and other published numerical results. Numerical simulations show that the proposed numerical model is robust, accurate, and efficient for strongly nonlinear free-surface flows.

Space–time VMS computation of wind-turbine rotor and tower aerodynamics

We present the space---time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called "DSD/SST-VMST" method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of flows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this "ST/NURBS Mesh Update Method (STNMUM)." The STNMUM increases computational efficiency in terms of computer time and storage, and computational flexibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion.

Model of Flow in the Side Chambers of an Industrial Centrifugal Pump for Delivering Viscous Oil

A series of experiments has been conducted to identify the effects of both fluid viscosity and wear-rings gap on the performance of a low specific speed industrial centrifugal pump of type 65Y60 for transporting viscous oils by the author group. Unfortunately, the experimental results remained unexplained on a fluid dynamics base. To remedy this problem, a highly viscous oil flow model and computational method in the side chambers in that pump were proposed based on the existing theoretical and experimental results. The flow coupling between the chambers and the gaps of the wear-rings and/or the balance holes was realized. The model was validated by making use of the existing experiment data in the chamber between a rotating disk and the walls of a stationary cylindrical container. Then the flow model was applied into the two side chambers in that pump when the wear-rings clearances and liquid viscosity were changed. The results demonstrated that the flow model is sensitive to wear-rings gap, liquid viscosity, the roughness of the wet walls of the chambers, and leakage flow rate. For this pump, an enlarged clearance can improve the mechanical efficiency, but the increment in the efficiency is unable to compensate for the considerable drop in the volumetric efficiency, causing the gross efficiency not be improved, especially at a high viscosity.

Linking local and global optical flow computation by subspace regularization

Optical flow computation methods are traditionally classified to two categories: local and global. Several previous works have investigated the combination of them by exploiting their complementary effects. Unlike previous works, this paper is motivated by the common weakness of the two schemes and proposes linking local and global computation by subspace regularization. We will show that the subspace regularization can effectively reduce the error caused by ill-conditioned local computation systems, while inhibiting error diffusion suffered by the global regularization. Experimental results on benchmark sequences validate the enhanced performance of the proposed combination scheme.

Determination of Design Floods by Aspects of Peak Flow and Flood Hydrograph in Watershed of Larbaâ River, Taza (Morocco)

Determination of Design Floods by Aspects of Peak Flow and Flood Hydrograph in Watershed of Larbaâ River, Taza (Morocco) The major task of a hydrology study is to compute the design flow. There are conceptual and empirical methods for computation of design flow. The following paper shows the Gradex method estimating the design flood and the volumes corresponding of flows. This approach allowed us to know the design floods by aspects of peak flow and flood hydrograph. The study is based on long series of observations (49 years) of the annual maximum daily rainfall, and the Intensity-Duration-Frequency curves of the raingauge station of Taza located in the Larbaâ catchment. The Gradex method aims to find the maximum flow of floods for the rare frequency of occurrence (return time over 100 years). Hence, we attempted to explains why and how the combined use of rainfall and floods of different sub-catchments of Larbaâ River.

Action Recognition by Joint Spatial-Temporal Motion Feature

This paper introduces a method for human action recognition based on optical flow motion features extraction. Automatic spatial and temporal alignments are combined together in order to encourage the temporal consistence on each action by an enhanced dynamic time warping (DTW) algorithm. At the same time, a fast method based on coarse-to-fine DTW constraint to improve computational performance without reducing accuracy is induced. The main contributions of this study include (1) a joint spatial-temporal multiresolution optical flow computation method which can keep encoding more informative motion information than recent proposed methods, (2) an enhanced DTW method to improve temporal consistence of motion in action recognition, and (3) coarse-to-fine DTW constraint on motion features pyramids to speed up recognition performance. Using this method, high recognition accuracy is achieved on different action databases like Weizmann database and KTH database.

De-Interlacing Using Nonlocal Costs and Markov-Chain-Based Estimation of Interpolation Methods

A new method of de-interlacing is proposed. De-interlacing is revisited as the problem of assigning a sequence of interpolation methods (interpolators) to a sequence of missing pixels of an interlaced frame (field). With this assumption, our de-interlacing algorithm (de-interlacer), undergoes transitions from one interpolation method to another, as it moves from one missing pixel position to the horizontally adjacent missing pixel position in a missing row of a field. We assume a discrete countable-state Markov-chain model on the sequence of interpolators (Markov-chain states) which are selected from a user-defined set of candidate interpolators. An estimation of the optimum sequence of interpolators with the aforementioned Markov-chain model requires the definition of an efficient cost function as well as a global optimization technique. Our algorithm introduces for the first time using a nonlocal cost (NLC) scheme. The proposed algorithm uses the NLC to not only measure the fitness of an interpolator at a missing pixel position, but also to derive an approximation for transition matrix (TM) of the Markov-chain of interpolators. The TM in our algorithm is a frame-variate matrix, i.e., the algorithm updates the TM for each frame automatically. The algorithm finally uses a Viterbi algorithm to find the global optimum sequence of interpolators given the cost function defined and neighboring original pixels in hand. Next, we introduce a new MAP-based formulation for the estimation of the sequence of interpolators this time not by estimating the best sequence of interpolators but by successive estimations of the best interpolator at each missing pixel using Forward-Backward algorithm. Simulation results prove that, while competitive with each other on different test sequences, the proposed methods (one using Viterbi and the other Forward-Backward algorithm) are superior to state-of-the-art de-interlacing algorithms proposed recently. Finally, we propose motion compensated versions of our algorithm based on optical flow computation methods and discuss how it can improve the proposed algorithm.

Arbitrary Lagrangian–Eulerian finite-element method for computation of two-phase flows with soluble surfactants

A finite-element scheme based on a coupled arbitrary Lagrangian–Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier–Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Second-order isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant.

Dynamic multiphase modeling and optimization of fluid jet polishing process

Fluid jet polishing is a machining process used increasingly in the ultra-precision manufacture of optical components and replication molds. While the process bears some similarities with abrasive water jet machining, it operates at much lower pressure and grit size. This paper presents a computational fluid dynamics model based on latest multiphase turbulent flow computational methods, simulating dynamically the interface between fluid and air. The model is then used to optimize surface texture performance down to 1nm Ra on electroless nickel plated optical dies, while removing diamond turning marks. Some conclusions are drawn regarding the nature of the removal mechanism.

Rapid Optical Flow Computation Based on Multigrid

In order to make optical flow methods suitable for real-time applications, this paper presents a rapid optical flow computation method based on multigrid. Multigrid computation method is well known for being the fastest numerical method when solving elliptic boundary-value problems, so we integrate multigrid into Horn-Schunck algorithm in order to obtain rapid computation. Firstly, we analyze the convergence process of traditional methods for optical flow computation; secondly, we combine the multigrid method with Horn-Schunck method, and in this way optical flow can be calculated efficiently; finally, the experiments show that our rapid optical flow computation method is efficient for target detection and video tracking systems.

An Improved Volume of Fluid Method for Two-Phase Flow Computations on Collocated Grid System

An improved volume of fluid method called the accurate density and viscosity volume of fluid (ADV-VOF) method is proposed to solve two-phase flow problems. The method has the following features: (1) All operations are performed on a collocated grid system. (2) The piecewise linear interface calculation is used to capture interfaces and perform accurate estimations of cell-edged density and viscosity. (3) The conservative Navier–Stokes equations are solved with the convective term discretized by a second and third order interpolation for convection scheme. (4) A fractional-step method is applied to solve the conservative Navier–Stokes equations, and the BiCGSTAB algorithm is used to solve the algebraic equations by discretizing the pressure-correction equation. The above features guarantee a simple, stable, efficient, and accurate simulation of two-phase flow problems. The effectiveness of the ADV-VOF method is verified by comparing it with the conventional volume of fluid method with rough treatment of cell-edged density and viscosity. It is found that the ADV-VOF method could successfully model the two-phase problems with large density ratio and viscosity ratio between two phases and is better than the conventional volume of fluid method in this respect.

An Integrated RBFN-Based Macro-Micro Multi-Scale Method for Computation of Visco-Elastic Fluid Flows

An Integrated RBFN-Based Macro-Micro Multi-Scale Method for Computation of Visco-Elastic Fluid Flows

Space–time discontinuous Galerkin finite element method for two-fluid flows

A novel numerical method for two-fluid flow computations is presented, which combines the space–time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space–time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local hp-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative. The numerical method is applied to one and two dimensional two-fluid test problems using the Euler equations.