Simulation of natural convection with the collocated clustered finite volume scheme

Journal of Computational Physics

Eymard

Herbin

2009

International audienceWe 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

Section: Discretization Of Diffusive Termsmentioning

confidence: 99%

Section: Discretization Of Diffusive Termsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Journal of Computational Physics

Eymard

Herbin

2009

“…The mass, momentum and energy conservation equations were spatially discretized by using the collocated finite volume method presented in [19,20], applied here for structured meshes. The key features of this method are:…”

Section: Numerical Methods and Validationmentioning

confidence: 99%

On the modeling of aiding mixed convection in vertical channels

Sun

et al. 2012

Heat Mass Transfer

This paper aims at showing that to prescribe a flow rate at the inlet section of a vertical channel with heated walls leads to surprising and counterintuitive physical solutions, especially when the problem is modeled as elliptical. Such an approach can give rise to the onset of recirculation cells in the entry region while the heat transfer is slightly increased under the influence of the buoyancy force. We suggest an alternative model based on more realistic boundary conditions based on a prescribed total pressure at the inlet and a fixed pressure at the outlet sections. In this case, the pressure and buoyancy forces act effectively in the same direction and, the concept of buoyancy aiding convection makes sense. The numerical results emphasize the large differences between solutions based on prescribed inlet velocity and those obtained with the present pressure-based boundary conditions. List of symbols aThermal diffusivity (m 2 s -1 )c z Stretching parameters, Eq. 13 D Plate spacing (m) D h Hydraulic diameter, D h = 2D (m) g Gravitational acceleration (m s -2 ) Gr H Grashof number based on H, Gr H = gb 0 DTH 3 /m 0 2 h Heat transfer coefficient (W m -2 K -1 ) H Channel height (m) k Thermal conductivity (W m -1 K -1 ) L Channel length in the spanwise direction (m) _ m Mass flow rate (kg s -1 ) n x , n z Numbers of grid points in x-and z-directions p Pressure (Pa) p s Pressure at the outlet section (Pa) Pr Prandtl number, Pr = m 0 /a 0 Q Heat flux (W) Q en Enthalpy heat flux (W) Q 2w Convective heat flux along the two channel walls (W) Re Reynolds number based on D h , Re = w 0 D h /m 0 Ri Richardson number, Ri = Gr/Re 2 S c Area of the channel cross section, S c = DL (m 2 ) t Time (s) T Temperature (K) u, w Velocity components (m s -1 ) x, z Coordinates (m) Greeks b Coefficient of thermal expansion, b = 1/T 0 (K -1 ) DT Temperature difference, DT = (T h -T 0 ) (K) l Dynamic viscosity (Pa s) m Kinematic viscosity (m 2 s -1 ) q Density (kg m -3 ) h Dimensionless temperature ratio, h = (T -T 0 )/DT s Dimensionless time Subscripts a, b Analytical solutions h Hot wall H Quantity based on channel height nc Natural convection 0 Inlet section Superscripts -Averaged quantity * Dimensionless quantity

“…2) and energy (Eq. 3) are discretized by a collocated finite volume scheme based on methods initially developed for incompressible fluid flows on unstructured meshes and for fully coupled velocity-pressure equations [51], and later on extended to the low Mach number approximation [52]. This latter method has been adapted to a velocity-pressure decoupling scheme and applied here for structured rectangular grids.…”

Section: Numerical Schemementioning

confidence: 99%

Effect of surface radiation on natural convective flows and onset of flow reversal in asymmetrically heated vertical channels

Bousetta

International Journal of Thermal Sciences

et al. 2013

Self Cite

To cite this version:R. Li, M. Bousetta, Eric Chénier, Guy Lauriat. Effect of surface radiation on natural convective flows and onset of flow reversal in asymmetrically heated vertical channels. International Journal of Thermal Sciences, Elsevier, 2013, 65 (-), pp.9-27. <10.1016/j.ijthermalsci.2012.10.023>. Effect of surface radiation on natural convective flows and onset of flow reversal in asymmetrically heated vertical channels AbstractNumerical solutions on the influence of surface radiation on the laminar air flow induced by natural convection in vertical, asymmetrically-heated channels are discussed. Variable property effects are accounted for in a full-elliptic mathematical formulation. The density variation is determined from the state equation for ideal gas. The experimental design and data reported in Webb and Hill [1] are taken as the base cases for carrying out the computations. The occurrence of flow reversals is first considered and revisited for pure natural convection, and the Nusselt number correlations derived from the numerical results are favorably compared with those reported in [1]. It is shown that the general effect of surface radiation is to delete the onset of pocketlike recirculations at the top part of the channel, to reduce the heated wall temperatures, and to increase the facing wall temperatures. Comparisons with usual methods used for decoupling the surface radiation effects are discussed. In the range of parameters investigated, increases in differences between inlet and maximum wall temperatures up to 200 K are shown to have small influences on the flow field and negligible effects on heat transfer performances.Keywords: Natural convection, surface radiation, vertical channels, flow reversal, variable property effects, numerical simulations order of consistency of the numerical scheme β thermal coefficient of volumetric expansion,