A collocated finite volume scheme to solve free convection for general non-conforming grids

We present a new collocated numerical scheme for the approximation of the Navier-Stokes and energy equations under the Boussinesq assumption for general grids, using the velocity-pressure unknowns. This scheme is based on a recent scheme for the diffusion terms. Stability properties are drawn from particular choices for the pressure gradient and the non-linear terms. Numerical results show the accuracy of the scheme on irregular grids

Simulation of natural convection with the Collocated Clustered Finite Volume scheme

International audienceThis paper presents numerical results obtained in the case of natural convection within non constant fluid density, using the Collocated Clustered Finite Volume (CCFV) scheme. The continuous equations are first given in a dimensionless form. Then we present the finite volume scheme with the principles and the spatial discretization used. Analytical tests illustrate the numerical behavior of this scheme according to the type of grid, of the pressure stabilization method and check the robustness of this scheme. Next, the results obtained on the square thermally driven cavity under large temperature differences show that the CCFV scheme accurately fits the reference results

Stability of free convection in air-filled horizontal annuli: influence of the radius ratio

International audienceLinear stability of two-dimensional natural convection in air-filled horizontal annuli is numerically investigated for radius ratios in the range 1.2 less than or equal to R less than or equal to 3 and for Rayleigh numbers less than 10(4). Bifurcation diagrams are obtained for various radius ratios and the main thresholds are tracked as a function of R. A new instability mode has been highlighted which breaks the symmetry of the basic flow. This result demonstrates the need of modeling the annular gap without assuming flow symmetry. In addition to bifurcation maps drawn in the Rayleigh number-radius ratio plane, a map of possible flow patterns is also established. This map allows to foresee the number of solutions and the corresponding flow structures. (C) 2004 Elsevier Ltd. All rights reserved

Numerical results using a colocated finite-volume scheme on unstructured grids for incompressible fluid flows

International audienceThis article presents numerical results using a new finite-volume scheme on unstructured grids for the incompressible Navier-Stokes equations. The discrete unknowns are the components of the velocity, the pressure, and the temperature, colocated at the centers Of the control volumes. The scheme is stabilized using an original method leading to local redistributions of the fluid mass, which simultaneously yields the control of the kinetic energy and the convergence of the scheme. Different comparisons with the literature (2-D and 3-D lid-driven cavity, backward-facing step, differentially heated cavity) allow us to assess the numerical properties of the scheme

Stability analysis of natural convective flows in horizontal annuli: effects of axial and radial aspect ratios

International audienceLinear stability analyses for two-dimensional natural convection in horizontal air-filled annuli are performed for three-dimensional perturbations and radius ratios in the range 1.2 ≤ R ≤ 3. Flow transitions from moderate to large gap annuli, which have not been reported before, are thoroughlyinvestigated. As a result, stability diagrams are obtained for finite and for infinite length annuli. The leading disturbances and threshold values are found to agree well with experimental data and three-dimensional numerical solutions. Three-dimensional simulations were also carried out toexamine the influence on the flow stability of no-slip boundary conditions at the end walls

An extension of the MAC scheme to locally refined meshes : convergence analysis for the full tensor time-dependent Navier-Stokes equations

International audienceA variational formulation of the standard MAC scheme for the approximation of the Navier-Stokes problem yields an extension of the scheme to general 2D and 3D domains and more general meshes. An original discretization of the trilinear form of the nonlinear convection term is proposed; it is designed so as to vanish for discrete divergence free functions. This property allows us to give a mathematical proof of the convergence of the resulting approximate solutions, for the nonlinear Navier-Stokes equations in both steady-state and time-dependent regimes, without any small data condition. Numerical examples (analytical steady and time-dependent ones, inclined driven cavity) confirm the robustness and the accuracy of this method

GAS FLOWS WITH HEAT TRANSFER IN MICRO CHANNELS: CLARIFICATIONS ABOUT THE NUSSELT NUMBER

International audienceThis paper deals with the modelling of weakly rarefied and dilute gas flows in heated micro channels by the continuum approach, valid for Knudsen numbers smaller than about 0.1. The first order slip and thermal jump model usually used for the forced convection of gas flows in long micro channels between two infinite plates is discussed. Indeed, in the huge literature related to this subject, it appears that simplified models are often used without justifying them and recurrent errors propagate from one paper to the other. The erroneous models particularly concern the heat transfer analysis and the energy equation. The compatibility of the pressure work and viscous dissipation in the energy equation with the power of the viscous forces at the walls and the choice of an appropriate Nusselt number are particularly discussed. Our aim is to provide a consistent model for gaseous micro-flows and the linked heat transfer. Then, a dimensional and asymptotic analysis is performed in the context of long micro channels. An analytical solution for the temperature field and the Nusselt number is proposed in the case of a compressible gas flow in a long micro-channel maintained at a constant wall temperature. This solution is compared with the numerical solution of the full model taking into account the first order slip and thermal jump conditions at the walls, the power of the viscous forces in the wall heat flux, the thermal creep term, the pressure work and the viscous dissipation in the bulk. The vanishing values of the Nusselt number measured in the experiments by Demsis et al. (2009, 2010) are explained for the first time

Sensitivity of the liquid bridge hydrodynamics to local capillary contributions

International audienceIn the usual models of thermocapillary flows, a vorticity singularity occurs at the contact free surface-solid boundaries. The steady axisymmetric hydrodynamics of the side-heated liquid bridge of molten metal is addressed here for its sensitivity to the size delta of a length scale explicitly introduced to regularize the problem. By linear stability analysis of the flows, various stable steady states are predicted: The already known steady states which are reflection-symmetric about the mid-plane, but also others which do not possess this property. The thresholds in Ma of the associated bifurcations are strongly dependent on delta, and converge with delta-->0 towards low values. Published data give these results some physical relevance. (C) 2002 American Institute of Physics

Finite volume approximation of a diffusion-dissolution model and application to nuclear waste storage

International audienceThe study of two phase flow in porous media under high capillary pressures, in the case where one phase is incompressible and the other phase is gaseous, shows complex phenomena. We present in this paper a numerical approximation method, based on a two pressures formulation in the case where both phases are miscible, which is shown to also handle the limit case of immiscible phases. The space discretization is performed using a finite volume method, which can handle general grids. The efficiency of the formulation is shown on three numerical examples related tounderground waste disposal situations

Optimal plate spacing for mixed convection from an array of vertical isothermal plates

International audienceNumerical simulations of mixed convection of air between vertical isothermal surfaces were conducted in order to determine the optimum spacing corresponding to the peak heat flux transferred from an array of isothermal, parallel plates cooled by mixed convection. Comparisons between approximate analytical solutions for natural and forced convection are first discussed. It is shown that the agreement is fairly good. From the computations carried out for aiding mixed convection by assuming a pressure drop at the outlet section rather than a constant flow rate, it is numerically predicted that the optimum spacing is smaller than those for pure natural or pure forced convection. This spacing is determined according to the pressure drop. As a sample, we considered an array of 10 cm -height, isothermal surfaces at temperature T-h = 340 K with air as the working fluid entering into the channels at T-0 = 300 K. The increases in heat flux corresponding to the optimal spacing are discussed for outlet pressure drops ranging from -0.1 Pa to -1 Pa. Such a range covers the entire laminar mixed convection regime for this specific application