Natural convection in an enclosed vertical air layer with large horizontal temperature differences

Chenoweth, D. R.; Paolucci, Samuel

doi:10.1017/s0022112086000587

Cited by 257 publications

(165 citation statements)

References 31 publications

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“…Fig. 5 compares the Nusselt number at the left side wall with the result of Chenoweth and Paolucci [51] and Choi and Merkle [23], they are in excellent agreement. Figs.…”

Section: Cavity Natural Convection Flowsupporting

confidence: 62%

Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

Shen

Zha

2012

Computers & Fluids

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a b s t r a c tA low diffusion E-CUSP (LDE) scheme for preconditioned Navier-Stokes equations is developed. The LDE scheme with high-order WENO reconstruction and high order difference scheme for viscous terms is used to simulate several flows at various speed from low speed natural convection to supersonic flows. The unfactored implicit Gauss-Seidel relaxation scheme, in which the preconditioned Roe's matrices are used, is used for time integration. Numerical results are presented to show efficiency, accuracy and robustness of the new preconditioning scheme.

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“…Fig. 5 compares the Nusselt number at the left side wall with the result of Chenoweth and Paolucci [51] and Choi and Merkle [23], they are in excellent agreement. Figs.…”

Section: Cavity Natural Convection Flowsupporting

confidence: 62%

Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

Shen

Zha

2012

Computers & Fluids

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“…The local entropy generation can be putted in a dimensionless form by using the dimensionless variables listed in Equation (10) in the following way:…”

Section: Formulationmentioning

confidence: 99%

“…Chenoweth and Paolucci. [10], Vierendeels et al [11], Sivasankaran and Ho [12] and Nishimura et al [13] studied this topic. Chamkha, Al-Naser and Sathiyamoorthy [14][15][16][17] numerically studied the hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Magnetic Field Effect on Entropy Generation at Thermosolutal Convection in a Square Cavity

Bouabid

Hidouri

Magherbi

et al. 2011

Entropy

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Thermosolutal convection in a square cavity filled with air and submitted to an inclined magnetic field is investigated numerically. The cavity is heated and cooled along the active walls with a mass gradient whereas the two other walls of the cavity are adiabatic and insulated. Entropy generation due to heat and mass transfer, fluid friction and magnetic effect has been determined in transient state for laminar flow by solving numerically the continuity, momentum energy and mass balance equations, using a Control Volume Finite-Element Method. The structure of the studied flows depends on four dimensionless parameters which are the Grashof number, the buoyancy ratio, the Hartman number and the inclination angle. The results show that the magnetic field parameter has a retarding effect on the flow in the cavity and this lead to a decrease of entropy generation, Temperature and concentration decrease with increasing value of the magnetic field parameter.

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“…Also, there are many forms of compressible equations. It is common to see variable density simulations modeled with all, or partly, primitive variable equation sets [9,15,5]. In this context, the use of "compressible" to describe an equation seems to be arbitrary.…”

Section: The Conservative Navier-stokes Equationsmentioning

confidence: 99%

Comparative Analysis of Natural Convection Flows Simulated by both the Conservation and Incompressible Forms of the Navier-Stokes Equations in a Differentially-Heated Square Cavity

Martineau¹,

Berry²,

Esteve³

et al. 2009

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This report illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially-heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated body force, velocity, and divergence of velocity distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present. The results show that the use of the incompressible flow assumption with the Boussinesq gravitational body force approximation should be restricted to flows where the density change of a fluid particle along a pathline is negligible.4

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Natural convection in an enclosed vertical air layer with large horizontal temperature differences

Cited by 257 publications

References 31 publications

Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

Low diffusion E-CUSP scheme with implicit high order WENO scheme for preconditioned Navier–Stokes equations

Analysis of the Magnetic Field Effect on Entropy Generation at Thermosolutal Convection in a Square Cavity

Comparative Analysis of Natural Convection Flows Simulated by both the Conservation and Incompressible Forms of the Navier-Stokes Equations in a Differentially-Heated Square Cavity

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