Computation Of Unsteady Viscous Flows Research Articles

New high-resolution-preserving sliding mesh techniques for higher-order finite volume schemes

This paper presents a new sliding mesh technique for the computation of unsteady viscous flows in the presence of rotating bodies. The compressible Euler and incompressible Navier–Stokes equations are solved using a higher-order (>2) finite volume method on unstructured grids. A sliding mesh approach is employed at the interface between computational grids in relative motion. In order to prevent loss of accuracy, two distinct families of higher-order sliding mesh interfaces are developed. These approaches fit naturally in a high-order finite volume framework. To this end, Moving Least Squares (MLS) approximants are used for the transmission of the information from one grid to another. A particular attention is paid for the study of the accuracy and conservation properties of the numerical scheme for static and rotating grids. The capabilities of the present solver to compute complex unsteady vortical flow motions created by rotating geometries are illustrated on a cross-flow configuration.

An immersed interface solver for the 2-D unbounded Poisson equation and its application to potential flow

This paper presents a novel algorithm to solve the 2-D potential flow past complex geometries with circulation in unbounded domain and in the presence of a given vorticity field. It is based on a Poisson solver that combines two components: the immersed interface method to enforce the boundary condition on each inner boundary and the James–Lackner algorithm to compute the outer boundary condition consistent with the unbounded domain solution. The algorithm is here based on second order finite differences and it requires solely 1-D stencil corrections; this makes the immersed interface part of the present method easily extendable to higher dimensional problems. The treatment of the outer boundaries requires an iterative boundary potential method. The algorithm is validated, by means of grid convergence studies, on the flow past multiple bodies. The results confirm the second order accuracy everywhere. The algorithm is also self consistent as “all is done on the grid” (thus without using a vortex panel boundary element method in addition to the grid). For cusped airfoils, a consistent way to enforce the Kutta–Joukowsky condition is also presented. The present algorithm constitutes a crucial building block towards an immersed interface-enabled vortex particle-mesh method for the computation of unsteady viscous flows, with boundary layers, detached shear layers and wakes. A possible extension to 3-D problems is also briefly discussed.

Computation of unsteady viscous flow around a locally flexible airfoil at low Reynolds number

A numerical method for fluid–structure interaction is presented for the analysis of unsteady viscous flow over a locally flexible airfoil. The Navier–Stokes equations are solved by ALE–CBS algorithm, coupling with a structural solver with large deformation. Following the validation of the method, a numerical example for the flight of micro-air vehicles at low Reynolds number is chosen for the computation. The coupling effect of flexible structure with different elastic stiffness on aerodynamic performance is demonstrated. A noticeable camber effect is induced by the deflection of the structure as the elastic stiffness of the structure goes smaller. Moreover, when the vibrating frequencies of the structure with smaller elastic stiffness have a close correlation with the shedding frequencies, the positive impact of the vibration of local flexible surface on the lift of the airfoil is highlighted, which results from the formation of the coherent vortices.

A finite volume unstructured multigrid method for efficient computation of unsteady incompressible viscous flows

AbstractAn unstructured non‐nested multigrid method is presented for efficient simulation of unsteady incompressible Navier–Stokes flows. The Navier–Stokes solver is based on the artificial compressibility approach and a higher‐order characteristics‐based finite‐volume scheme on unstructured grids. Unsteady flow is calculated with an implicit dual time stepping scheme. For efficient computation of unsteady viscous flows over complex geometries, an unstructured multigrid method is developed to speed up the convergence rate of the dual time stepping calculation. The multigrid method is used to simulate the steady and unsteady incompressible viscous flows over a circular cylinder for validation and performance evaluation purposes. It is found that the multigrid method with three levels of grids results in a 75% reduction in CPU time for the steady flow calculation and 55% reduction for the unsteady flow calculation, compared with its single grid counterparts. The results obtained are compared with numerical solutions obtained by other researchers as well as experimental measurements wherever available and good agreements are obtained. Copyright © 2004 John Wiley & Sons, Ltd.

Computation of unsteady viscous flow and aeroacoustic noise of cross flow fans

Time-accurate viscous flow solutions are sought for the prediction of unsteady flow characteristics and associated aeroacoustic blade tonal noise of a cross flow fan. The two-dimensional incompressible Navier–Stokes equations in a moving coordinate are time-accurately solved by an unstructured finite-volume method on triangular meshes, and a sliding mesh technique is utilized at the interface between the domain rotating with blades and the stationary one for allowing the unsteady interactions. An accuracy assessment of the present method is made by comparing the fan performances with experimental data for a rotational speed at 1000 rpm and the Reynolds number 5300 based on blade tip speed and chord length. With the computed unsteady viscous flow solutions, sound pressure is predicted using Curle’s equation and narrow-band noise characteristics of three impellers with a uniform and two random pitch (type-A and -B) blades are compared by their sound pressure level spectra. Also, the frequency modulations of the blade passing frequency noise by random pitch fans are discussed.

Computation of unsteady viscous flows around moving bodies using the k– ε turbulence model on unstructured dynamic grids

We consider the numerical solution on unstructured dynamic meshes of the averaged Navier–Stokes equations equipped with the k– ε turbulence model and a wall function. We discuss discretization issues pertaining to conservation laws, moving grids, and numerical dissipation. We also present a robust spring analogy method for constructing dynamic meshes. We validate our implementation of this two-equation turbulence model and justify its usage for a class of vortex shedding problems by correlating our computational results with experimental data obtained for a flow past a square cylinder. We also apply our solution methodology to the two-dimensional aerodynamic stability analysis of the Tacoma Narrows Bridge, and report numerical results that are in good agreement with observed data.

Efficient Computation of Unsteady Viscous Flows by an Implicit Preconditioned Multigrid Method

An implicit preconditioned multlgrid algorithm is developed for the efficient solution of two-dimensional, low-frequency unsteady turbulent Navier-Stokes calculations on highly stretched meshes. The efficiency of the approach derives from three key attributes: 1) an implicit time discretization that allows the time step to be determined solely by the resolution requirements of the unsteady phenomena, 2) an inner preconditioned multigrid iteration that is explicit in pseudotime and rapidly convergent even in the presence of boundary-layer anisotropy, and 3) a compact stencil that is ideally suited for parallelization on distributed memory architectures. For fully resolved turbulent Navier-Stokes calculations of low-frequency pitching airfoils, the implicit discretization allows the use of time steps that are O(10 6 ) larger than are permissible with an explicit scheme. Convergence within the inner iteration is accelerated by a combination of block-Jacobi preconditioning and J-coarsened multigrid to yield computational savings of roughly an order of magnitude over existing methods that rely on the standard combination of scalar time stepping and full-coarsened multigrid

Efficient computation of unsteady viscous flows by an implicit preconditioned multigrid method

Efficient computation of unsteady viscous flows by an implicit preconditioned multigrid method

CALCULATION OF STEADY AND OSCILLATING FLOWS IN TUBES USING A VORTICITY TRANSPORT ALGORITHM

SUMMARY Steady and oscillating axisymmetric tube flows are modelled using a vorticity transport algorithm. The axisymmetric convectivediffisive Navier-Stokes equations are solved using a splitting technique. Axisymmetric ring vortex filaments are introduced on the walls and subsequently convected and diffused throughout the flow field. An axisymmetric equation similar to the Oseen diffusion equation is used to diffuse the ring vortex filaments. Vorticity is reflected from the tube walls using two techniques. Results are presented for the developing Poiseuille flow and for the developed flow in the form of the entrance length and the axial velocity and vorticity profiles. Good agreement is achieved with a finite difference method in the developing region of Poiseuille flow. The developed flow results are compared with the analytical solutions. The developed profiles of velocity and vorticity have errors of less than 0.3 per cent for both methods of dealing with reflection of difkion at the bounding surfaces and similar accuracy is obtained for the velocity profiles in oscillating flow except at the wall. Oscillating flow is produced with a discretized sinusoidal piston motion. Velocity profiles, boundary layer thickness and entrance length are presented for oscillating flow. Good agreement is achieved for lowWomersley-number non-dimensional frequency. At higher values of this parameter, flows are inaccurately simulated, because the number of piston positions used to discretize the piston motion is inversely proportional to the non-dimensional frequency. 1. NTRODUCTION The extension of Lagrangian vortex element methods to the computation of unsteady viscous flows from two to three dimensions has evolved in recent years.’.’ A description of a two-dimensional computational model which was applied to the flow past a circular cylinder has been published by Benson et and is the basis of the present work. For axisymmetric flows the non-dimensional convective-diffusive NavierStokes equations are solved by the introduction of ring vortex filaments to represent a shear layer on the solid surfaces and by the subsequent convection and difision of these vortex filaments. The convection routine involves a cloud- in-cell type of calculation as given by Christiansen4 and the diffusion routine involves the redistribution of circulation on a mesh. The diffusion is computed from the axisymmetric solution which is derived in the Appendix. To ensure the conservation of vorticity near the solid surfaces, vorticity must be ‘treated’ in these regions. Two approximate methods of wall treatment are compared: vorticity is either specularly reflected from the solid surfaces or is allowed to diffuse beyond the solid surfaces, reallocated to mesh points and rediffised into the flow field. Results are presented using both methods. The flows are produced by the motion of a piston. Wagner’ discusses the difficulties associated with specification of the inlet

Computation of unsteady viscous flow using a pressure-based algorithm

The objective of this research is the development of an efficient and accurate numerical analysis for the prediction of unstready turbulent flows using a Navier-Stokes solver. The technique developed is to be used for incompressible flow and is an extension of the pressure-based method. The finite volume approach and a nonstagger grid formulation are used. A predictor-corrector type algorithm is applied to the governing equations to ensure time accuracy. The convergence is improved using a multigrid scheme