Simulation of a temperature adaptive control strategy for an IWSE economizer in a data center

Data center optimization using PID regulation in CFD simulations

A two-dimensional double Multiple-Relaxation-Time thermal lattice Boltzmann method is used to simulate natural convection flows in differentially heated cavities. The buoyancy effects are considered under the Boussinesq assumption. Flow and temperature fields are respectively solved with nine and five discrete velocities' models. Boundary conditions are implemented with the classical bounce-back or an ''on-node'' approach. The latter uses the popular Zou and He and Counter-Slip formulations. This paper evaluates the differences between the two implementations for steady and time-dependent flows as well as the space and time convergence orders.

https://hal-upec-upem.archives-ouvertes.fr/hal-00857985/document

Lattice Boltzmann simulations of a time-dependent natural convection problem

Here a comprehensive survey of the literature in the area of numerical heat transfer (NHT) published in 2010 and 2011 has been conducted. Due to the immenseness of the literature volume, journals s...

Literature Survey of Numerical Heat Transfer (2010-2011)

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-Benard 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=5000) 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 the heat and momentum fluxes are given with 4 to 5 significant digits.

/pdf/benchmark-solution-for-a-three-dimensional-mixed-convection-38wgghkdjo.pdf

Benchmark Solution for a Three-Dimensional Mixed-Convection Flow, Part 1: Reference Solutions

A reference solution to a benchmark problem for a 3D mixed convection flow in a horizontal rectangular channel differentially heated (Poiseuille-Rayleigh-Benard flow) has been proposed in "Part 1: reference solution" of the present paper [Num. Heat Trans. A, vol.?, pp.?-? (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 paper is to analyze the consequences of this singularity on Richardson extrapolation (RE) of the numerical solutions. The convergence orders of the used numerical methods (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.

/pdf/benchmark-solution-for-a-three-dimensional-mixed-convection-3wny1wqbe9.pdf

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

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-Benard 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=5000) and Prandtl number Pr=0.7. The model is based on the Navier-Stokes equations with Boussinesq approximation. We propose a reference solution resulting from computations on large grids, Richardson extrapolation (RE) and cubic spline interpolations. The solutions obtained with finite difference, finite volume and finite element codes are in good agreement and reference values for the flow fields and the heat and momentum fluxes are given up to 4 to 5 significant digits. Some difficulties in the use of RE are highlighted due to the use of mixed Dirichlet and Neumann thermal boundary conditions on the same wall. The observed convergence orders of the numerical methods with RE are then discussed from the viewpoint of this singularity. 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. The results of the present study are published in two papers in Numerical Heat Transfer, Part B [1, 2].

https://hal-upec-upem.archives-ouvertes.fr/hal-00695433/document

Benchmark solution for a three-dimensional mixed convection flow - Detailed technical report

Nous presentons dans cette communication la demarche que nous avons adoptee pour conduire un exercice de comparaison de codes de calculs (benchmark) sur une configuration d'ecoulement 3D de convection mixte, ainsi que la synthese des resultats que nous avons obtenus. L'objectif de cette action vise a proposer une premiere solution numerique tridimensionnelle de reference sur ce type de configuration afin de permettre, une fois celle-ci admise et reconnue par la communaute, de valider des codes de calculs.

Vers une solution numérique de référence pour un écoulement 3D de convection mixte : démarche et résultats

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Benchmark Solution for a Three-Dimensional Mixed-Convection Flow, Part 1: Reference Solutions

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

Benchmark solution for a three-dimensional mixed convection flow - Detailed technical report

Vers une solution numérique de référence pour un écoulement 3D de convection mixte : démarche et résultats