Xavier Nicolas

Revue bibliographique sur les écoulements de Poiseuille–Rayleigh–Bénard : écoulements de convection mixte en conduites rectangulaires horizontales chauffées par le bas

An exhaustive bibliographical review on the Poiseuille-Rayleigh-Benard (PRB) flows, the mixed convection flows in horizontal rectangular ducts uniformly heated from below, is presented. This review covers the period 1920-2001 and counts 154 references. The concerned parameter range is 0 < Pr ≤ 1000, 0 ≤ Re ≤ 1000 and 0 ≤ Ra ≤ 106. The interest of these flows in the industrial world is presented for the chemical vapor deposition studies (CVD) and for the cooling of the electronic equipments. After having done a synthesis of the temporal or spatial linear stability studies in the thermal entrance zone and in the fully-developed thermoconvective zone, we consider the linear or weakly non-linear spatio-temporal stability analyses, which take into account the concepts of convective and absolute instabilities and which are more appropriate to represent the dynamics of the PRB flows. All the stability results are systematically compared with the experimental and numerical results. The theoretical or experimental correlation formulae giving the variations of the Nusselt number, of the wave length, of the frequency and of the velocity of the transversal (R⊥) and/or longitudinal rolls (R//), as a function of Re, Ra, Pr and B = l/h, are collected. The influence of the inlet and of the outlet boundary conditions on the space and time development of the R⊥ in the experiments and in the numerical simulations is also analysed. A synthesis of the very recently discovered complex thermoconvective patterns (superposition of R⊥ and R//, periodic and aperiodic patterns, wavy or oblique rolls) is presented. To end, the badly known or badly understood aspects of the PRB flows are summed up and subjects for future investigations are proposed.

Benchmark solution for a three-dimensional mixed convection flow - Part 1: reference solutions

A solution to a benchmark problem for a three-dimensional mixed-convection flow in a horizontal rectangular channel heated from below and cooled from above (Poiseuille-Rayleigh-Bénard flow) is proposed. This flow is a steady thermoconvective longitudinal roll flow in a large-aspect-ratio channel at moderate Reynolds and Rayleigh numbers (Re = 50, Ra = 5,000) and Prandtl number Pr = 0.7. The model is based on the Navier-Stokes equations with Boussinesq approximation. We propose reference solutions resulting from computations on large grids, Richardson extrapolation (RE), and cubic spline interpolations. The solutions obtained with one finite-difference, one finite-volume, and two finite-element codes are in good agreement, and reference values for the flow and thermal fields and for the heat and momentum fluxes are given with four to five significant digits.

Efficient vectorized finite-difference method to solve the incompressible navier-stokes equations for 3-D mixed-convection flows in high-aspect-ratio channels

A very efficient vectorized code is tailored to solve 3-D incompressible Navier–Stokes equations for mixed-convection flows in high streamwise aspect ratio channels. It is based on Godas algorithm, second-order finite differences, an incremental factorization method of alternating direction implicit (ADI) type, spectral decomposition of the 1-D Laplace operators, and the tridiagonal matrix algorithm (TDMA). It is shown to be of second order in both space and time by a general method of determining code convergence orders and to have good performance on a NEC-SX5 supercomputer. It is validated through experiments of various Poiseuille-Rayleigh-Bénard flows with steady longitudinal, unsteady transverse, and convectively unstable wavy rolls.

Influence of a white noise at channel inlet on the parallel and wavy convective instabilities of Poiseuille-Rayleigh-Bénard flows

The present paper concerns Poiseuille-Rayleigh-Benard mixed convection flows in horizontal rectangular air-filled channels of large spanwise aspect ratio (W/H ≥ 10) and it focuses on the primary and secondary thermoconvective instabilities made of steady longitudinal and unsteady wavy rolls for 100 ≤ Re ≤ 200, 3000 < Ra < 15 000, Pr = 0.7, and W/H = 10. Time linear stability analysis of longitudinal rolls and 3D nonlinear numerical simulations using a specially tailored finite difference code is performed for this purpose. A bibliographical review, linear stability analysis and 3D numerical simulations allow establishing the full stability diagram for Re ≤ 300 and Ra ≤ 20 000. The linear stability analysis indicates that the critical Rayleigh number Ra≈*(Re) of the neutral curve between longitudinal and wavy rolls for W/H = 10 is increased at least by a factor of 1.5 in comparison with infinite W/H. The numerical study shows that the usual definitions of growth lengths for longitudinal rolls are inappropr...

Benchmark Solution for a Three-Dimensional Mixed-Convection Flow, Part 2: Analysis of Richardson Extrapolation in the Presence of a Singularity

A reference solution to a benchmark problem for a three-dimensional mixed-convection flow in a horizontal rectangular channel differentially heated (Poiseuille-Rayleigh-Bénard flow) has been proposed in Part 1 of the present article (Numer. Heat Transfer B, vol. 60, pp. 325–345, 2011). Since mixed Dirichlet and Neumann thermal boundary conditions are used on the horizontal walls of the channel, a temperature gradient discontinuity is generated. The aim of this article is to analyze the consequences of this singularity on Richardson extrapolation (RE) of the numerical solutions. The convergence orders of the numerical methods used (finite difference, finite volume, finite element), observed from RE of local and integral quantities are discussed with an emphasis on singularity influence. With the grids used, it is shown that RE can increase the accuracy of the discrete solutions preferentially with the discretization methods of low space accuracy order, but only in some part of the channel and for a restricted range of the extrapolation coefficient. A correction to the Taylor expansion involved in the RE formalism is proposed to take into account the singularity and to explain the majority of the RE behaviors observed.

Simplified Modelling of the Infrared Heating Involving the Air Convection Effect before the Injection Stretch Blowing Moulding of PET Preform

Initial heating conditions and temperature effects (heat transfer with air and mould, self-heating, conduction) have important influence during the ISBM process of PET preforms. The numerical simulation of infrared (IR) heating taking into account the air convection around a PET preform is very time-consuming even for 2D modelling. This work proposes a simplified approach of the coupled heat transfers (conduction, convection and radiation) in the ISBM process based on the results of a complete IR heating simulation of PET sheet using ANSYS/Fluent. First, the simplified approach is validated by comparing the experimental temperature distribution of a PET sheet obtained from an IR camera with the numerical results of the simplified simulation. Second, we focus on the more complex problem of the rotating PET preform heated by IR lamps. This problem cannot be modeled in 2D and the complete 3D approach is out of calculation possibilities actually. In our approach, the IR heating flux coming from IR lamps is calculated using radiative laws adapted to the test geometry. Finally, the simplified approach used on the 2D plane sheet case to model the air convection is applied to the heat transfer between the cylindrical preform and ambient air using a simple model in Comsol where only the preform is meshed. In this case, the effect of the rotation of the preform is taken into account in the radiation flux by a periodic time function. The convection effect is modeled through the thermal boundary conditions at the preform surface using the heat transfer coefficients exported from the simulations of the IR heating of a PET sheet with ANSYS/Fluent. The temperature distribution on the outer surface of the preform is compared to the thermal imaging for validation.

A Finite Volume Scheme for the Transport of Radionucleides in Porous Media

The COUPLEX1 Test case (Bourgeat et al., 2003) is devoted to the comparison of numerical schemes on a convection–diffusion–reaction problem. We first show that the results of the simulation can be mainly predicted by a simple analysis of the data. A finite volume scheme, with three different treatments of the convective term, is then shown to deliver accurate and stable results under a low computational cost.

Simplified modeling of the convection and radiation heat transfers during the infrared heating of PET sheets and preforms Nomenclature

Abstract Initial heating conditions and temperature effects have an important influence during the injection stretch blow molding process of PET preforms. The paper provides a simplified modeling of the infrared (IR) flux provided by the IR lamps and the convection heat transfer with air, for the finite element simulation of the heating of PET samples. This modeling enables fast thermal simulations in industrial context. First, a complete 2D simulation of the air convection around a PET sheet sample is conducted using ANSYS/FLUENT to compute the local convection heat transfer coefficient. The distribution of this coefficient along the PET wall is then interpolated by a best linear fit function of the wall position to provide the boundary condition of the convection heat transfer thereafter. This boundary condition, coupled with the calculation of the infrared flux absorbed by the PET sheet sample, allows a 3D calculation of the time evolution of the sample temperature. This calculation is validated by comparing the experimental temperature distribution of the PET sheet obtained from an IR camera with the numerical results of the simulation. Second, we focus on the modeling of the heating of a cylindrical PET preforms by IR lamps. In our approach, the IR heating flux is calculated using the spectral and surfaceto-surface radiation laws adapted to the sample geometry. The air convection effect around the preform is modeled using the heat transfer coefficient identified from the 2D plane sheet case. It is applied on the boundaries of a simpler model in Comsol where only the preform is meshed. The temperature distribution on the outer surface of the preform is compared to experimental measurements by thermal imaging. A good agreement is observed which validates the whole approach used.

Characterisation of a Wavy Convective Instability in Poiseuille-Rayleigh-Bénard Flows: Linear Stability Analysis and Non Linear Numerical Simulations Under Random Excitations

The aim of the present paper is to characterize a secondary convective instability of Poiseuille-Rayleigh-Benard (PRB) mixed convection flows in air that takes the shape of wavy thermoconvective rolls, for 70≤Re≤300 and 3000 3Ra*. Comparisons with the experiments by Pabiou et al. [JFM, 2005] are proposed.Copyright

Transient Evaporation of Liquid Water Films and Condensation of Humid Air at the Isothermal Walls of a Square Cavity

The aim of this paper is to present modelling and numerical simulations of heat and mass transfer by double-diffusive convection and surface condensation or evaporation in a two-dimensional square cavity subjected to a uniform, but time-dependent wall temperature. At initial state, the cavity is filled with quiescent humid air at uniform temperature and density. By decreasing the wall temperature, condensation occurs at the four wall surfaces. The walls are then heated and evaporation of the liquid water is considered. Since the mass of humid air and average pressure experience noticeable changes during the periodic process, a weakly compressible formulation has been used for the modelling of the thermosolutal flow. Local thermodynamic assumption at the liquid-vapor interface and thin liquid film approximation are introduced.Copyright