Showing papers on "Boussinesq approximation (buoyancy) published in 2012"

Eddington-inspired Born-Infeld gravity: nuclear physics constraints and the validity of the continuous fluid approximation

Abstract: In this paper we investigate the classical non-relativistic limit of the Eddington-inspired Born-Infeld theory of gravity. We show that strong bounds on the value of the only additional parameter of the theory \kappa, with respect to general relativity, may be obtained by requiring that gravity plays a subdominant role compared to electromagnetic interactions inside atomic nuclei. We also discuss the validity of the continuous fluid approximation used in this and other astrophysical and cosmological studies. We argue that although the continuous fluid approximation is expected to be valid in the case of sufficiently smooth density distributions, its use should eventually be validated at a quantum level.

On the Müller paradox for thermal-incompressible media

Abstract: In his monograph Thermodynamics, I. Muller proves that for incompressible media the volume does not change with the temperature. This Muller paradox yields an incompatibility between experimental evidence and the entropy principle. This result has generated much debate within the mathematical and thermodynamical communities as to the basis of Boussinesq approximation in fluid dynamics. The aim of this paper is to prove that for an appropriate definition of incompressibility, as a limiting case of quasi-thermal-incompressible body, the entropy principle holds for pressures smaller than a critical pressure value. The main consequence of our result is the physically obvious one that for very large pressures, no body can be perfectly incompressible. The result is first established in the fluid case. In case of hyperelastic media subject to large deformations, the approach is similar, but with a suitable definition of the pressure associated with a convenient stress tensor decomposition.

Influence of the variable thermophysical properties on the turbulent buoyancy-driven airflow inside open square cavities

Abstract: The effects of the air variable properties (density, viscosity and thermal conductivity) on the buoyancy-driven flows established in open square cavities are investigated, as well as the influence of the stated boundary conditions at open edges and the employed differencing scheme. Two-dimensional, laminar, transitional and turbulent simulations are obtained, considering both uniform wall temperature and uniform heat flux heating conditions. In transitional and turbulent cases, the low-Reynolds k − ω turbulence model is employed. The average Nusselt number and the dimensionless mass-flow rate have been obtained for a wide and not yet covered range of the Rayleigh number varying from 103 to 1016. The results obtained taking into account variable properties effects are compared with those calculated assuming constant properties and the Boussinesq approximation. For uniform heat flux heating, a correlation for the critical heating parameter above which the burnout phenomenon can be obtained is presented, not reported in previous works. The effects of variable properties on the flow patterns are analyzed.

Numerical study of the onset of thermosolutal convection in rotating spherical shells

Abstract: The influence of an externally enforced compositional gradient on the onset of convection of a mixture of two components in a rotating fluid spherical shell is studied for Ekman numbers E = 10−3 and E = 10−6, Prandtl numbers σ = 0.1, 0.001, Lewis numbers τ = 0.01, 0.1, 0.8, and radius ratio η = 0.35. The Boussinesq approximation of the governing equations is derived by taking the denser component of the mixture for the equation of the concentration. Differential and internal heating, an external compositional gradient, and the Soret and Dufour effects are included in the model. By neglecting these two last effects, and by considering only differential heating, it is found that the critical thermal Rayleigh number Rec depends strongly on the direction of the compositional gradient. The results are compared with those obtained previously for pure fluids of the same σ. The influence of the mixture becomes significant when the compositional Rayleigh number Rc is at least of the same order of magnitude as the ...

On the M\"uller paradox for thermal-incompressible media

Abstract: In his monograph Thermodynamics, I. M\"uller proves that for incompressible media the volume does not change with the temperature. This M\"uller paradox yields an incompatibility between experimental evidence and the entropy principle. This result has generated much debate within the mathematical and thermodynamical communities as to the basis of Boussinesq approximation in fluid dynamics. The aim of this paper is to prove that for an appropriate definition of incompressibility, as a limiting case of quasi thermal-incompressible body, the entropy principle holds for pressures smaller than a critical pressure value. The main consequence of our result is the physically obvious one, that for very large pressures, no body can be perfectly incompressible. The result is first established in the fluid case. In the case of hyperelastic media subject to large deformations the approach is similar, but with a suitable definition of the pressure associated with convenient stress tensor decomposition.

Influence of Density Fluctuation on DNS of Turbulent Channel Flow in the Presence of Temperature Stratification

Abstract: To investigate the effect of density variation on turbulent heat transfer prediction, we perform a direct numerical simulation (DNS) of turbulent flow in a horizontal channel with varying wall temperature using a new method dealing with the effect of density variation. As a result, asymmetric profiles are observed in turbulence statistics. This tendency cannot be reproduced by the Boussinesq approximation, which is based on the constant-density formulation. A quadrant analysis of the turbulent shear stress finds that the density variation affects ejection events in the vicinity of the walls. It is also revealed that the variable viscosity and thermal conductivity change the dynamic and thermodynamic balances of the flow.

Boussinesq Approximation and Numerical Simulation of Natural Convection in a Closed Square Cavity

Abstract: The numerical simulation was carried out by using three different methods to express density when analyzing the natural convection in a closed square cavityThe results of flow and heat transfer were obtained for Rayleigh Numbers in the range of 103 to 106 and have been validated by comparing with the published data in literatureMoreover,the results of incompressible ideal gas,the density with the changes of temperature,and the Boussinesq approximation were analyzedThe numerical results also show that in the small wall temperature difference,Boussinesq approximation can reduce computation cost and accelerate the convergence,but it will bring large error for large wall temperature difference

Experimental investigations in an air-filled differentially-heated cavity at large Rayleigh Numbers

Abstract: A large-scale experimental differentially heated cavity was built and instrumented. Rayleigh numbers up to 1.2×1011 can be obtained with a temperature difference, ΔT = 20°C, between the hot and cold walls leaning in the range of validity of the Boussinesq approximation. Previous data obtained locally for mean velocity by 2D LDV in the range give rise to questions regarding the general air flow circulation in the cavity. Particularly, a downstream flow along the vertical boundary layer was observed. This reverse flow caused by the temperature stratification outside this layer is not present in the upstream parts and was not previously observed in smaller cavities. The question of the global circulation in this cavity is thus posed. Evolution laws providing Nusselt numbers are also given and when possible compared to the literature for a large range of Rayleigh numbers.

Transient mixed convection in a channel with an open cavity filled with porous media

Abstract: In this work transient mixed convection in a porous medium in a horizontal channel with a open cavity below is studied numerically. The cavity presents a heated wall at uniform heat flux and the other walls of the cavity and the channel are assumed adiabatic. Air flows through the horizontal channel. The heated wall of the cavity experiences a uniform heat flux in such a way that the forced flow is perpendicular to the motion due to natural convection. The study is carried out employing Brinkman-Forchheimer-extended Darcy model and two energy equations due to the local thermal non-equilibrium assumption. The flow in the channel is assumed to be two-dimensional, laminar, incompressible. Boussinesq approximation is considered. The thermophysical properties of the fluid are evaluated at the ambient temperature. The results for stream function and temperature distribution given at different times are obtained. Wall temperature value are given and also, the velocity and temperature profiles in several sections of the cavity are presented. In addition, the Nusselt number, both local and average, is presented along with the temporal variations of the average Nusselt number.

Finite difference analysis of laminar mixed convection with vertical channel in downflow

Abstract: In this paper, finite difference analysis of Laminar mixed convection in vertical channel is studied. The distance between the plates is ‘b’ and g is the gravitational force. The buoyancy effect is taken into account according to the Boussinesq approximation. The flow problem is described by means of parabolic equations and the solutions are obtained by the use of an implicit finite difference technique coupled with a marching procedure. The velocity, the temperature and the pressure profiles are shown in graphs and their behaviour is discussed for different values of buoyancy parameter Gr/Re and Prandtl number Pr.

Magnetic Helicity and Planetary Dynamos

Abstract: A model planetary dynamo based on the Boussinesq approximation along with homogeneous boundary conditions is considered. A statistical theory describing a large-scale MHD dynamo is found, in which magnetic helicity is the critical parameter

Evaluation of the Use of Solar Assisted Buoyancy Driven Natural Ventilation of Smaller Theatres in Canada

Abstract: The possibility of using stored hot water generated during the day by using solar energy to assist in the provision of adequate buoyancy driven natural ventilation flow rates through small theatres during the evening hours has been numerically investigated in a very basic manner. The hot water would be used to heat the air using a plate type heat exchanger system mounted in a roof-top chimney-like air discharge system. A simple building with a given cross-sectional design has been considered. Twodimensional steady flow has been assumed to exist and the flow has been assumed to be symmetrical about the vertical centre-line through the building. The Boussinesq approximation has been adopted, i.e., the air properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated assuming a linear relation between the density changes and the temperature change. Radiant heat transfer effects have been neglected. The standard k-epsilon turbulence model with buoyancy effects being fully accounted for has been used. The heat generation from the audience has been treated as a uniformly distributed heat flux over the floor, the smaller the audience, the lower being this heat flux. The solution has been obtained using the commercial CFD solver FLUENT © . The results, while of a very preliminary nature, indicate that the proposed system could provide an adequate natural ventilation flow rate.