Improved Rhie-Chow interpolation for unsteady flow computations

Shen, Wen Zhong; Michelsen, Jess; Sørensen, Jens Nørkær

doi:10.2514/3.15042

Cited by 31 publications

(51 citation statements)

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“…As all variables are defined at cell centers, no special treatment is needed for the singularity problem at the center axis. In the corrector step, the new Rhie-Chow interpolation developed by Shen et al 28 and the new SIMPLE-C scheme on collocated grids 29 …”

Section: Formulation Of the Problem And Numerical Methodsmentioning

confidence: 99%

Numerical study of swirling flow in a cylinder with rotating top and bottom

2006

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A numerical investigation of oscillatory instability is presented for axisymmetric swirling flow in a closed cylinder with rotating top and bottom. The critical Reynolds number and frequency of the oscillations are evaluated as function of the ratio of angular velocities of the bottom and the top ͑ = ⍀ bottom / ⍀ top ͒. Earlier linear stability analysis ͑LSA͒ using the Galerkin spectral method by Gelfgat et al. ͓Phys. Fluids, 8, 2614 ͑1996͔͒ revealed that the curve of the critical Reynolds number behaves like an "S" around = 0.54 in the co-rotation branch and around = −0.63 in the counter-rotation branch. Additional finite volume computations, however, did not show a clear S behavior. In order to check the existence of the S shape, computations are performed using an axisymmetric finite volume Navier-Stokes code at aspect ratios ͑ = H / R͒ 1.5 and 2.0. Comparisons with LSA at = 1.5 show that the S shape does exist. The S shape of the stability diagram predicted by LSA is thus confirmed by a finite-volume based Navier-Stokes solver. The additional computations at aspect ratio = 2 show that the curve of critical Reynolds number has a wider S shape in the co-rotating branch for about 0.7 whereas a sharp "beak" appears in the counter-rotating branch for approximately −0.5.

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Section: Formulation Of the Problem And Numerical Methodsmentioning

confidence: 99%

Numerical study of swirling flow in a cylinder with rotating top and bottom

2006

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“…The often mentioned problems of momentum interpolation methods when a small time-step is used for unsteady calculations (see e.g. [12]) are avoided thanks to the transporting velocity proposed in [11].…”

Section: Introductionmentioning

confidence: 99%

Non-reflective inlet conditions for the calculation of unsteady turbulent compressible flows at low Mach number

Moguen

Bruel

Perrier

et al. 2014

Mechanics & Industry

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-For the unsteady simulation of compressible subsonic flows (Large Eddy Simulation or Direct Numerical Simulation), the proper handling of the inlet boundary is a challenging task. Indeed, inflow generation through imposition of the velocity may lead to a non-physical reflection of the upstream acoustic waves. In the present contribution, a method that allows both filtering of these waves and proper imposition of the required variables is proposed. This method is based on identification of the roles of the temporal rate of change of wave amplitudes at the inlet in the low Mach number regime. The formulation obtained is tested numerically on unsteady one-dimensional flows at low Mach number for which the unsteady inlet velocity signal is purely harmonic or harmonic with the superimposition of synthetic turbulence.Key words: Non-reflective boundary conditions / inlet conditions / low Mach number / turbulence / acoustics Résumé-Conditions d'entrée non réfléchissantes pour le calcul d'écoulements turbulents compressiblesà bas nombre de Mach. Pour le calcul instationnaire d'écoulements turbulents compressibles subsoniques (simulations des grandeséchelles ou simulation numérique directe), la prescription de conditions d'entrée satisfaisantes pose problème. En effet, générer l'écoulement en entrée via l'imposition du champ de vitesse peut conduireà une réflexion non physique des ondes acoustiques qui remontent l'écoulement. Dans la présente contribution, une méthode permettantàl af o i sd efi l t r e rc e so n d e se t d'imposer les variables requises en entrée est proposée. Cette méthode repose sur l'identification des rôles respectifs des variations d'amplitude des ondes acoustiques et convectives en entrée,à bas nombre de Mach. Elle est testée numériquement pour la simulation d'unécoulement instationnaireà bas nombre de Mach avec un signal d'entrée de type harmonique seul ou combinéa v e cu ns i g n a ls y n t h etique de turbulence.

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“…It is well known that the original Rhie-Chow interpolation could fail to prevent a checkerboard pressure field if a very small time step is used [29,[31][32][33]. Explanation for such behaviour can be provided by analysing limiting values of expressions (20) when time step size tends to zero:…”

Section: Discretisation Of the Mathematical Modelmentioning

confidence: 99%

“…Here we came across a limitation of the original Rhie and Chow interpolation connected with the application of very small time steps (due to semi-implicit treatment of surface tension forces). It is known that the original Rhie and Chow interpolation is time step size dependent and that it could fail to prevent the appearance of a checkerboard pressure field if a very small time step size is used [29][30][31][32][33]. Yu et al [33] proposed a remedy for this problem on a fixed mesh and we have extended their solution, obtaining time step size independent Rhie and Chow interpolation on a moving mesh.…”

Section: Introductionmentioning

confidence: 99%

A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow

2012

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a b s t r a c tThis paper describes a moving mesh interface tracking method implemented in OpenFOAM for simulating three-dimensional (3-D) incompressible and immiscible two-phase interfacial fluid flows with dominant surface tension forces. Collocated finite volume (FV) method is used for spatial discretisation of Navier-Stokes equations on moving polyhedral mesh. The mesh consists of two parts separated on interface. Fluid flow is solved on each mesh separately and coupling is accomplished in an iterative manner by enforcing the kinematic and dynamic condition at the interface. Surface tension force is calculated on arbitrary polygonal surface mesh with second order accuracy using a ''force-conservative'' approach. Arbitrary polyhedral mesh adapts to the time-varying shape of the interface using vertex-based automatic mesh motion solver which calculates the motion of internal points based on the prescribed motion of interface points by solving the variable diffusivity Laplace equation discretised using the finite element method. The overall solution procedure based on iterative PISO algorithm with modified Rhie-Chow interpolation is second-order accurate in space and time, as is confirmed by numerical experiments on small amplitude sloshing in a two-dimensional (2-D) tank, 3-D droplet oscillation and buoyant rise of a 3-D air bubble in water. Numerical results are found to be in excellent agreement with available theoretical and experimental results.

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Improved Rhie-Chow interpolation for unsteady flow computations

Cited by 31 publications

References 0 publications

Numerical study of swirling flow in a cylinder with rotating top and bottom

Numerical study of swirling flow in a cylinder with rotating top and bottom

Non-reflective inlet conditions for the calculation of unsteady turbulent compressible flows at low Mach number

A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow

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