Three-dimensional Incompressible Viscous Flow Research Articles

프로펠러 후류의 총와도 수식모델 연구

This study numerically carried out the propeller open water test(POW) by solving Navier-Stokes equations governing the three-dimensional unsteady incompressible viscous flow with the turbulence closure model of the <TEX>${\kappa}-{\omega}$</TEX> SST model. Numerical simulations are performed at various range of advance ratios. Corresponding to Reynolds numbers of <TEX>$5.89{\times}105{\sim}6.47{\times}105$</TEX> based on free stream velocity and the chord length at 0.7 propeller radius. The present results give a good agreement with those of the experiment. The propeller induced vortical structures have been analyzed by visualizing the resultant vorticity. As the advance ratio increases, the magnitude and length of the resultant vorticity decrease significantly. As the main focus of present study, the numerical model to present the (<TEX>$r-{\theta}$</TEX>) plane-averaged resultant vorticity along the streamwise direction for various advance ratios has been suggested.

Numerical Simulation of the Transient Flow in a Centrifugal Pump During Starting Period

Computational fluid dynamics were used to study the three-dimensional unsteady incompressible viscous flows in a centrifugal pump during rapid starting period (≈0.12 s). The rotational speed variation of the field around the impeller was realized by a dynamic slip region method, which combines the dynamic mesh method with nonconformal grid boundaries. In order to avoid introducing errors brought by the externally specified unsteady inlet and outlet boundary conditions, a physical model composed of a pipe system and pump was developed for numerical self-coupling computation. The proposed method makes the computation processes more close to the real conditions. Relations between the instantaneous flow evolutions and the corresponding transient flow-rate, head, efficiency and power were analyzed. Relative velocity comparisons between the transient and the corresponding quasisteady results were discussed. Observations of the formations and evolutions of the primary vortices filled between the startup blades illustrate the features of the transient internal flow. The computational transient performances qualitatively agree with published data, indicating that the present method is capable of solving unsteady flow in a centrifugal pump under transient operations.

An improved immersed boundary-lattice Boltzmann method for simulating three-dimensional incompressible flows

The recently proposed boundary condition-enforced immersed boundary-lattice Boltzmann method (IB-LBM) [14] is improved in this work to simulate three-dimensional incompressible viscous flows. In the conventional IB-LBM, the restoring force is pre-calculated, and the non-slip boundary condition is not enforced as compared to body-fitted solvers. As a result, there is a flow penetration to the solid boundary. This drawback was removed by the new version of IB-LBM [14], in which the restoring force is considered as unknown and is determined in such a way that the non-slip boundary condition is enforced. Since Eulerian points are also defined inside the solid boundary, the computational domain is usually regular and the Cartesian mesh is used. On the other hand, to well capture the boundary layer and in the meantime, to save the computational effort, we often use non-uniform mesh in IB-LBM applications. In our previous two-dimensional simulations [14], the Taylor series expansion and least squares-based lattice Boltzmann method (TLLBM) was used on the non-uniform Cartesian mesh to get the flow field. The final expression of TLLBM is an algebraic formulation with some weighting coefficients. These coefficients could be computed in advance and stored for the following computations. However, this way may become impractical for 3D cases as the memory requirement often exceeds the machine capacity. The other way is to calculate the coefficients at every time step. As a result, extra time is consumed significantly. To overcome this drawback, in this study, we propose a more efficient approach to solve lattice Boltzmann equation on the non-uniform Cartesian mesh. As compared to TLLBM, the proposed approach needs much less computational time and virtual storage. Its good accuracy and efficiency are well demonstrated by its application to simulate the 3D lid-driven cubic cavity flow. To valid the combination of proposed approach with the new version of IBM [14] for 3D flows with curved boundaries, the flows over a sphere and torus are simulated. The obtained numerical results compare very well with available data in the literature.

Numerical investigation of fluid flow and heat transfer characteristics by common-flow-up

Effects of the common-flow-up pair produced by vortex generators in a rectangular channel flow on fluid flow and heat transfer are numerically investigated. In order to analyze the common-flow-up pair, the pseudo-compressibility method is introduced into the Reynolds-averaged Navier–Strokes equations for a three-dimensional incompressible viscous flow. A two-layer k– ε turbulence model is applied to a three-dimensional turbulence boundary over a flat plate to predict the flow structure and heat transfer characteristics of the common-flow-up pair and to resolve the near-wall flow. Results reasonably predict the flow structure of the common-flow-up pair, such as secondary velocity vectors and turbulent kinetic energy contours. Also, in the prediction of thermal boundary layers, skin friction characteristics and heat transfer characteristics, the present results are reasonably close to the experimental results of other researchers even though some discrepancies are observed near the center of the vortex core.

A numerical investigation of flow and heat transfer in rotating U-shaped square ducts

Three-dimensional incompressible viscous flow and heat transfer in a rotating U-shaped duct with a square cross-section are studied numerically. The governing equations including full Navier–Stokes and energy equations are solved using a finite volume method based on the SIMPLER algorithm in an orthogonal uniform grid. The effects of wall curvature and rotation on the flow field and heat transfer considering different directions of rotation are presented in detail. The results show that in the bend region, the centrifugal forces due to curvature are significant, performing an intensive outward secondary flows resulting in an increase of heat transfer on the outer wall. But in the straight parts of the duct, secondary flows due to Coriolis forces are dominant. The comparison of numerical results at different rotation angles indicates that the maximum heat transfer rate occurs when the duct rotates about an axis parallel to the axis of duct curvature, at which both the Coriolis and the centrifugal forces intensify each other, while the minimum heat transfer rate takes place in the negative diagonal axis of rotation with angles of α = 180 and β = 135 .

A SVD-GFD scheme for computing 3D incompressible viscous fluid flows

A generalized finite difference (GFD) scheme for the simulation of three-dimensional (3D) incompressible viscous fluid flows in primitive variables is described in this paper. Numerical discretization is carried out on a hybrid Cartesian cum meshfree grid, with derivative approximation on non-Cartesian grids being carried out by a singular value decomposition (SVD) based GFD procedure. The Navier–Stokes equations are integrated by a time-splitting pressure correction scheme with second-order Crank–Nicolson and second-order discretization of time and spatial derivatives respectively. Axisymmetric and asymmetric 3D flows past a sphere with Reynolds numbers of up to 300 are simulated and compared with the results of Johnson and Patel [Johnson TA, Patel VC. Flow past a sphere up to a Reynolds number of 300. J Fluid Mech 1999;378:19–70] and others. Flows past toroidal rings are also simulated to illustrate the ability of the scheme to deal with more complex body geometry. The current method can also deal with flow past 3D bodies with sharp edges and corners, which is shown by a simple 3D case.

The simulation of 3D unsteady incompressible flows with moving boundaries on unstructured meshes

The development of a computational model for the simulation of three-dimensional unsteady incompressible viscous fluid flows with moving boundaries is presented. The numerical model is based upon the solution of the Navier–Stokes equations on unstructured meshes using the artificial compressibility approach. An ALE formulation is adopted and the equations are discretized using a cell vertex finite volume method. The formulation ensures the satisfaction of the geometric conservation law when the mesh is allowed to move. An implicit time discretization is adopted and a dual time approach is employed. Explicit relaxation is used for the sub-iterations, with multigrid acceleration. For moving geometries, the mesh is deformed by adopting a spring analogy, combined with a wall distance function approach. The numerical procedure is validated on a standard problem and is then used for the simulation of flow over a flexible fish-like body.

Numerical simulation of 3D fluid–structure interaction flow using an immersed object method with overlapping grids

The newly developed immersed object method (IOM) [Tai CH, Zhao Y, Liew KM. Parallel computation of unsteady incompressible viscous flows around moving rigid bodies using an immersed object method with overlapping grids. J Comput Phys 2005; 207(1): 151–72] is extended for 3D unsteady flow simulation with fluid–structure interaction (FSI), which is made possible by combining it with a parallel unstructured multigrid Navier–Stokes solver using a matrix-free implicit dual time stepping and finite volume method [Tai CH, Zhao Y, Liew KM. Parallel computation of unsteady three-dimensional incompressible viscous flow using an unstructured multigrid method. In: The second M.I.T. conference on computational fluid and solid mechanics, June 17–20, MIT, Cambridge, MA 02139, USA, 2003; Tai CH, Zhao Y, Liew KM. Parallel computation of unsteady three-dimensional incompressible viscous flow using an unstructured multigrid method, Special issue on “Preconditioning methods: algorithms, applications and software environments. Comput Struct 2004; 82(28): 2425–36]. This uniquely combined method is then employed to perform detailed study of 3D unsteady flows with complex FSI. In the IOM, a body force term F is introduced into the momentum equations during the artificial compressibility (AC) sub-iterations so that a desired velocity distribution V 0 can be obtained on and within the object boundary, which needs not coincide with the grid, by adopting the direct forcing method. An object mesh is immersed into the flow domain to define the boundary of the object. The advantage of this is that bodies of almost arbitrary shapes can be added without grid restructuring, a procedure which is often time-consuming and computationally expensive. It has enabled us to perform complex and detailed 3D unsteady blood flow and blood–leaflets interaction in a mechanical heart valve (MHV) under physiological conditions.

シェル屋根面周辺の流れの三次元非圧縮性粘性流体解析へのマルチグリッド法の適用

An efficient linear solver using a multigrid method is developed for solving the pressure Poisson equation. The three-dimensional incompressible viscous fluid flow analysis is performed for investigating dynamic behaviors of a shell roof under strong wind. The improved balancing tensor diffusivity method and fractional step method (IBTD+FS method) combined with the finite element method is used for discretizing the Navier-Stokes equation. In this scheme, the pressure Poisson equation is solved implicitly. Solution process of the equation, which is a large-scale system of linear equations, is the most computationally expensive part. In order to improve the computation speed, a preconditioning technique based on a multigrid method for the conjugate gradient method (CG method) is employed. A simple formulation that combines the diagonal-scaling preconditioner and coarse grid correction is proposed. In addition, a finite element mesh for a two-dimensional analysis is used as a coarse grid for the three-dimensional analysis. The proposed method is implemented in the fluid flow analysis code. Performance study of the proposed method is conducted by solving a number of illustrative examples. Computation speed of the proposed method is much faster than the CG method with a simple diagonal-scaling preconditioner.

Numerical investigation of air free convection in a room with heat source

Mathematical modelling of three-dimensional steady free convective incompressible viscous gas flows in the rooms with a heat source is carried out within the framework of the Navier — Stokes equations with the effective viscosity determined on the basis of the κ-ɛ turbulence model. The investigation is carried out for the case of model rooms and heat sources having the form of rectangular parallelepipeds with square bases. The influence of the heat source power and the sizes of the room base on local and averaged values of the air velocity and temperature in the rooms is analysed. The flow pattern in the room is shown to have a torus-like shape. It is found that the variation of sizes of the room base rather than the capacity variation of the heat source is of determining importance for the gas motion character in a closed volume.

Algebraic Multigrid Preconditioned Krylov Subspace Methods for Fluid Flow and Heat Transfer on Unstructured Meshes

ABSTRACT A numerical tool, Thermoflow, is developed for simulating the three-dimensional incompressible viscous flow and heat transfer on unstructured meshes. It is based on a cell-centered, collocated finite-volume method. The velocity–pressure coupling is treated using the SIMPLE/C algorithm. An agglomerated multigrid method (AgMG) and the AgMG preconditioned Krylov subspace methods are implemented to solve the linearized partial differential equations. Their performances are evaluated against the public code, AMG1R5. It has been found that all hybrid solvers are superior to the standalone AgMG when a stringent convergence criterion is imposed, but the superiority is weakened with the convergence criterion coarsening. Due to its expensive setup cost, AMG1R5 is not appropriate for the segregated solver.

Finite element simulation of 3D flow around a circular cylinder

The application of a finite element scheme to full three-dimensional (3D) incompressible viscous flow around a circular cylinder is presented in this paper. The scheme is based on the Petrov-Galerkin weak formulation using exponential weighting functions and on the second-order accurate Adams-Bashforth strategy as a time integration. As a typical example of the problems, flow around a circular cylinder involving an interesting phenomenon of the drag crisis is performed numerically. Numerical results demonstrate the workability and the validity of the present approach.

Systematic Derivation of Jump Conditions for the Immersed Interface Method in Three-Dimensional Flow Simulation

In this paper, we systematically derive jump conditions for the immersed interface method [SIAM J. Numer. Anal., 31 (1994), pp. 1019-1044; SIAM J. Sci. Comput., 18 (1997), pp. 709-735] to simulate three-dimensional incompressible viscous flows subject to moving surfaces. The surfaces are represented as singular forces in the Navier--Stokes equations, which give rise to discontinuities of flow quantities. The principal jump conditions across a closed surface of the velocity, the pressure, and their normal derivatives have been derived by Lai and Li [Appl. Math. Lett., 14 (2001), pp. 149-154]. In this paper, we first extend their derivation to generalized surface parametrization. Starting from the principal jump conditions, we then derive the jump conditions of all first-, second-, and third-order spatial derivatives of the velocity and the pressure. We also derive the jump conditions of first- and second-order temporal derivatives of the velocity. Using these jump conditions, the immersed interface method is applicable to the simulation of three-dimensional incompressible viscous flows subject to moving surfaces, where near the surfaces the first- and second-order spatial derivatives of the velocity and the pressure can be discretized with, respectively, third- and second-order accuracy, and the first-order temporal derivatives of the velocity can be discretized with second-order accuracy.

Numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method

In this paper, the local multiquadric differential quadrature (LMQDQ) method is applied on three-dimensional incompressible flow problems. The LMQDQ method is among the newly proposed mesh-free methods. Unlike the traditional differential quadrature (DQ) method, the weighting coefficients of LMQDQ method are determined by using the radial basis functions (RBFs) as the trial functions instead of high-order polynomials. The main concern of this paper is to discuss the effectiveness of using LMQDQ method to solve 3-D incompressible Navier–Stokes (N–S) equations in the primitive-variable form. Three-dimensional lid-driven cavity flow problem with Reynolds numbers of 100, 400 and 1000 was chosen as a test case to validate the LMQDQ method. The computed velocity profiles along the vertical and horizontal centerlines are given and compared with available data in the literature.

Parallel computation of unsteady three-dimensional incompressible viscous flow using an unstructured multigrid method

The development and validation of a parallel unstructured tetrahedral non-nested multigrid (MG) method for simulation of unsteady 3D incompressible viscous flow is presented. The Navier–Stokes solver is based on the artificial compressibility method (ACM) and a higher-order characteristics-based finite-volume scheme on unstructured MG. Unsteady flow is calculated with an implicit dual time stepping scheme. The parallelization of the solver is achieved by a MG domain decomposition approach (MG-DD), using the Single Program Multiple Data (SPMD) programming paradigm. The Message-Passing Interface (MPI) Library is used for communication of data and loop arrays are decomposed using the OpenMP standard. The parallel codes using single grid and MG are used to simulate steady and unsteady incompressible viscous flows for a 3D lid-driven cavity flow for validation and performance evaluation purposes. The speedups and efficiencies obtained by both the parallel single grid and MG solvers are reasonably good for all test cases, using up to 32 processors on the SGI Origin 3400. The parallel results obtained agree well with those of serial solvers and with numerical solutions obtained by other researchers, as well as experimental measurements.

Solution of three-dimensional unsteady external flow using a coupled arbitrary Lagrangian FEM–BEM model

A computational model has been developed in this paper to solve three-dimensional unsteady incompressible viscous flow problems in external flow fields. The model is based on primitive variables in Navier–Stokes equations under transient conditions. The model can be used to solve infinite boundary value problems by extracting the boundary effects on a specified finite computational domain using projection method of the Navier–Stokes equations. The momentum equation of fluid motion is solved using the three-step finite element method. The external flow field is simulated using the boundary element method by solving a pressure Poisson equation by considering the pressure to be zero at the infinite boundary. Arbitrary Lagrangian–Eulerian method is incorporated in the present model to solve the moving boundary problems. The model has been applied initially to simulate a cubic cavity flow problem for verification purpose and further used to simulate the flow past a square cylinder in two dimensions. Finally, the external flow problem of flow induced by the movement of a sphere inside a viscous flow field in three dimensions has also been considered. The simulation results are found to be reasonable and satisfactory.

A new stable space–time formulation for two‐dimensional and three‐dimensional incompressible viscous flow

AbstractA space–time finite element method for the incompressible Navier–Stokes equations in a bounded domain in ℝd (with d=2 or 3) is presented. The method is based on the time‐discontinuous Galerkin method with the use of simplex‐type meshes together with the requirement that the space–time finite element discretization for the velocity and the pressure satisfy the inf–sup stability condition of Brezzi and Babuška. The finite element discretization for the pressure consists of piecewise linear functions, while piecewise linear functions enriched with a bubble function are used for the velocity. The stability proof and numerical results for some two‐dimensional problems are presented. Copyright © 2001 John Wiley &amp; Sons, Ltd.

Enhanced error estimator for adaptive finite element analysis of 3D incompressible flow

This paper describes an enhanced error estimator for adaptive finite element analysis of three-dimensional incompressible viscous flow. The estimator uses a modified form of the recovery functional employed in the well-known L 2 local patch recovery technique (LPR) originally proposed by Zienkiewicz and Zhu. The modified recovery functional is obtained by penalizing the conventional recovery functional using the residual of the continuity equation for the constraint. The enhanced estimator, which we denote as LPRC, is tested on unstructured second-order tetrahedral meshes using an analytical solution to the three-dimensional incompressible Navier–Stokes equations. We report significant improvements in the effectiveness of the resulting error estimate, both for interior and boundary nodes, at virtually no additional computational cost. The LPRC estimator is particularly useful for flows in which stresses at the boundary of the computational domain play an important role, such as in blood flow modeling. Although in this paper the LPRC error estimator is tested exclusively on the 10-noded tetrahedral Taylor–Hood element, we expect that when applied to incompressible flows, the LPRC estimator will perform more effectively than the LPR estimator when used with other types of elements as well.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

Modified Galerkin Analysis for the Unsteady Three-Dimensional Viscous Fluid Flow (Approach by the Error Analysis Technique).

In our previous research, the modified Galerkin method was proposed as one of the most efficient methods for the convection-diffusion problems and the two-dimensional viscous fluid flows. In the modified Galerkin method, since the inertia term is considered explicitly, only the symmetrical matrixes appear. Then an artificial viscosity is introduced through an error analysis approach to improve its accuracy and stability. In this paper, this modified Galerkin method is applied to the three-dimensional incompressible viscous fluid flow analysis coupled with the Semi-Implicit Method for Pressure-Linked Equations formulation. The cubic cavity flow problem sare investigated for the Reynolds number of 400, 1000, 2000 and 3200. Finally, we confirmed the effectiveness of our proposed method.