Using stokes expansion for natural convection inside a two-dimensional cavity

1993 ◽  
Vol 12 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Natural Convection ◽  
Two Dimensional

Grid-Free Vortex Methods for Natural Convection in Two-Dimensional Domains

2012 ◽  
Author(s):  
Issam Lakkis
Keyword(s):  
Natural Convection ◽  
Nonlinear Diffusion ◽  
Reacting Flows ◽  
Ideal Gas ◽  
Two Dimensional ◽  
Vortex Methods ◽  
Free Vortex ◽  
Low Mach Number ◽  
Buoyancy Driven Flows ◽  
Vorticity Generation

Vortex methods for simulating natural convection of an ideal gas in unbounded two-dimensional domains are presented. In particular, the redistribution method for diffusion is extended to enable simulation of nonlinear diffusion of an ideal gas in isobaric conditions encountered in unbounded low-Mach number flows. We also address the problem of handling source terms in grid-free vortex methods and propose a fast, accurate, and physically motivated method for solving the associated inverse problems. Examples include generation of baroclinic vorticity in non-reacting buoyancy driven flows, and in addition, generation of internal energy and species in buoyant reacting flows. Accuracy and speed of the proposed algorithms for nonlinear diffusion and vorticity generation are investigated separately. Simulations of natural convection of a “thermal patch” for Grashof number ranging from to 1562.5 to 25000 are presented.

Numerical Investigation of Natural Convection in a Mono-Span Greenhouse

2012 ◽  
Author(s):  
Sunita Kruger ◽  
Leon Pretorius
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Natural Convection ◽  
Pitch Angle ◽  
Design Tool ◽  
Design Parameters ◽  
Two Dimensional ◽  
Cfd Model ◽  
Indoor Climate ◽  
Contour Plots

In this paper, the use of computational fluid dynamics is evaluated as a design tool to investigate the indoor climate of a confined greenhouse. The finite volume method using polyhedral cells is used to solve the governing mass, momentum and energy equations. Natural convection in a cavity corresponding to a mono-span venlo-type greenhouse is numerically investigated using Computational Fluid Dynamics. The CFD model is designed so as to simulate the climate above a plant canopy in an actual multi-span greenhouse heated by solar radiation. The aim of this paper is to investigate the influence of various design parameters such as pitch angle and roof asymmetry and on the velocity and temperature patterns inside a confined single span greenhouse heated from below. In the study reported in this paper a two-dimensional CFD model was generated for the mono-span venlo-type greenhouse, and a mesh sensitivity analysis was conducted to determine the mesh independence of the solution. Similar two-dimensional flow patterns were observed in the obtained CFD results as the experimental results reported by Lamrani et al [2]. The CFD model was then modified and used to explore the effect of roof pitch angle and roof asymmetry at floor level on the development of the flow and temperature patterns inside the cavity for various Rayleigh numbers. Results are presented in the form of vector and contour plots. It was found that considerable temperature and velocity gradients were observed in the centre of the greenhouse for each case in the first 40mm above the ground, as well as in the last 24mm close to the roof. Results also indicated that the Rayleigh number did not have a significant impact on the flow and temperature patterns inside the greenhouse, although roof angle and asymmetry did. The current results demonstrate the importance of CFD as a design tool in the case of greenhouse design.

Modeling of Mixed Convection Between Vertical Parallel Plates in Electric Equipment Immersed in High-Pr Liquids

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Thomas B. Gradinger ◽  
T. Laneryd
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Parallel Plates ◽  
One Dimensional ◽  
Electric Equipment

Natural-convection cooling with oil or other fluids of high Prandtl number plays an important role in many technical applications such as transformers or other electric equipment. For design and optimization, one-dimensional (1D) flow models are of great value. A standard configuration in such models is flow between vertical parallel plates. Accurate modeling of heat transfer, buoyancy, and pressure drop for this configuration is therefore of high importance but gets challenging as the influence of buoyancy rises. For increasing ratio of Grashof to Reynolds number, the accuracy of one-dimensional models based on the locally forced-flow assumption drops. In the present work, buoyancy corrections for use in one-dimensional models are developed and verified. Based on two-dimensional (2D) simulations of buoyant flow using finite-element solver COMSOL Multiphysics, corrections are derived for the local Nusselt number, the local friction coefficient, and a parameter relating velocity-weighted and volumetric mean temperature. The corrections are expressed in terms of the ratio of local Grashof to Reynolds number and a normalized distance from the channel inlet, both readily available in a one-dimensional model. The corrections universally apply to constant wall temperature, constant wall heat flux, and mixed boundary conditions. The developed correlations are tested against two-dimensional simulations for a case of mixed boundary conditions and are found to yield high accuracy in temperature, wall heat flux, and wall shear stress. An application example of a natural-convection loop with two finned heat exchangers shows the influence on mass-flow rate and top-to-bottom temperature difference.

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