Prediction of Unsteady Natural Convection within a Square Cavity Containing an Obstacle at High Rayleigh Number Value (original) (raw)
Related papers
2013
A numerical study is performed to analyze the steady natural convection phenomena of air in a square cavity with different locations of the heating portion. The heat sources parts in the left, right and bottom walls of the cavity are maintained at a higher temperature Th, whereas the other parts of these sidewalls are kept at a lower temperature Tc. The enclosure’s top wall is kept insulated. The coupled equations of continuity, momentum and energy are solved by a finite volume method. The SIMPLE algorithm is used to solve iteratively the pressurevelocities coupling. The numerical investigations in this analysis is made over a wide range of parameters, Rayleigh number ( ) and dimensionless heater lengths. The effect of three different heating locations on the vertical walls (bottom, Centre, and top) and the local heat source on the bottom wall was evaluated. Results are presented graphically in the form of streamlines, isotherms and also with a velocity profiles and average Nusselt ...
A Study on Natural Convection of Air in a Square Cavity with Partially Thermally Active Side Walls
Open Journal of Fluid Dynamics, 2017
In this present work, we study heat transfer in a confined environment. We have to determine the thermal and dynamics fields of the cavity while observing the effect of the Rayleigh number which depends on the characteristics of the fluid and the temperatures imposed. The behavior of boundary layers in natural convection is analyzed along this square cavity. The central halves of its vertical walls are heated at different temperatures. The left active part is at a higher temperature than the one on the right wall. The remaining inactive parts and the horizontal walls (upper and lower) are adiabatic. The thermal and dynamic modeling of two-dimensional problem was done using a calculation code Fortran 90 and a visualization software ParaView based on the finite volume method. The equations governing this phenomenon of unsteady flow have thus been solved. This allows the modeling of both air flow and heat transfer with a numerical stabilization of the solution. So, we have presented our results of numerical simulations using a visualization tool. The results show the different velocity and temperature curves, velocity vectors and isotherms in laminar flow regime.
Steady natural convection flows in a square cavity with linearly heated side wall(s)
International Journal of Heat and Mass Transfer, 2007
The present numerical study deals with natural convection flow in a closed square cavity when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Non-linear coupled PDEs governing the flow have been solved by penalty finite element method with bi-quadratic rectangular elements. Numerical results are obtained for various values of Rayleigh number (Ra) (10 3 6 Ra 6 10 5 ) and Prandtl number (Pr) (0.7 6 Pr 6 10). Results are presented in the form of streamlines, isotherm contours, local Nusselt number and the average Nusselt as a function of Rayleigh number.
Simulation of Natural Convection in a Square Cavity with Partially Heated and Cooled Vertical Walls
Proceeding of 5th Thermal and Fluids Engineering Conference (TFEC)
Natural convection driven by temperature differences between partially heated and cooled vertical walls in a square cavity is studied numerically. Steady or unsteady cellular flow structures and temperature patterns are illustrated along with the evolution of heat transfer rates in terms of Nusselt number. The cavity is filled with fluids of various Prandtl number, including .024 (liquid metal), .71 (air), 6 (water), and 450 (silicon oil). The effect of Prandtl and Rayleigh numbers on the flow regime and heat transfer is established along with two different thermal boundary conditions.
International Journal of Heat and Mass Transfer, 2007
A numerical study of natural convection in cavity filled with air has been carried out under large temperature gradient. The flows under study are generated by a heated solid body located close to the bottom wall in a rectangular cavity with cold vertical walls and insulated horizontal walls. They have been investigated by direct simulations using a two-dimensional finite volume numerical code solving the time-dependent Navier-Stokes equations under the low Mach number approximation. This model permits to take into account large temperature variations unlike the classical Boussinesq model which is valid only for small temperature differences. We were particularly interested in the first transitions which occur when the Rayleigh number is increased for flows in cavities of aspect ratio A = 1, 2, 4. Starting from a steady state, the results obtained for A = 1 and A = 4 show that the first transition occurs through a supercritical Hopf bifurcation. The induced disturbances determined for weakly supercritical regimes indicate the existence of two instability types driven by different physical mechanisms: shear and buoyancy-driven instabilities, according to whether the flow develops in a square or in a tall cavity. For A = 2, the flow undergoes a pitchfork bifurcation leading to an asymmetric steady state which in turn becomes periodic via a supercritical Hopf bifurcation point. In both cases, the flow is found to be strongly deflected towards one vertical wall and instabilities are found to be of shear layers type.
Numerical Study of Natural Convection Inside a Square Cavity with Non-uniform Heating from Top
Journal of The Institution of Engineers (India): Series C, 2020
The prime objective of the present numerical study is to analyse buoyancy-driven thermal flow behaviour inside an enclosure with the application of nonlinear heating from top surface which is commonly essential in glass industries. A fluid-filled square cavity with sinusoidal heating from top surface, adiabatic bottom wall and constant temperature side walls is considered here. The thermal flow behaviour has been numerically observed with the help of relevant parameters like stream functions, isotherms and Nusselt number. For the present investigation, Rayleigh number (Ra), Prandtl number (Pr) and heating frequency of the wall (x) are varied from 10 3 to 10 6 , 0.7 to 7 and 0.5 to 2, respectively. It has been noticed from the investigation that flow dynamics drastically alter with Ra, x and Pr. However, the effect of Ra on heat transfer rate has been found to be significantly higher while compared with the influences by x and Pr. Keywords Free convection Á Buoyancy Á Rayleigh number Á Pr number Á Sinusoidal heating Greek letters a Thermal diffusivity (m 2 s-1) b Volumetric expansion coefficient (K-1) q Kinetic viscosity (m 2 s-1) t Density of fluid (kg m-3) h Dimensionless temperature x Heating frequency of the top wall
In the present study, natural convection problem has been solved in a cavity having three flat walls and the right vertical wall consisting of one undulation and three undulations. The two vertical and bottom walls are cold walls maintained at a fixed temperature whereas the top wall is heated with spatially varying temperature distribution. Air has been taken as the working fluid with Pr =0.71. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear coordinates. A wide range of Rayleigh number (10 3 to 10 6) has been chosen for this study. For small Ra, the heat transfer was dominated by conduction across the fluid layers. With increase of Ra, the process began to be dominated by convection. In the presence of undulation the peak point of the heat rejection (negative local Nusselt number) in the right wall increases by 5.54% than left wall for Ra = 10 4. The three undulations case had maximum heat transfer to the uppermost undulation compared to that of the one undulation case.
Natural convection in rectangular cavities at high Rayleigh number
1990
Natural convection in rectangular two-dimensional cavities with differentially heated side walls is a standard problem in numerical heat transfer. Most of the existing studies has considered the low Ra laminar regime. The general thrust of the present research is to investigate higher Ra flows extending into the unsteady and turbulent regimes where the physics is not fully understood and appropriate models for turbulence are not yet established. In the present study the Boussinesq approximation is being used, but the theoretical background and some preliminary results have been obtained[1] for flows with variable properties.
Journal of Fluid Mechanics, 1981
The paper summarizes results from an experimental study of buoyancy-induced motion and heat transfer in a horizontal rectangular cavity with the two vertical ends at different temperatures and the long horizontal walls adiabatic. The cavity height/ length ratio is A = 0.0625. The high-Rayleigh-number range reported on in this paper, 2 x 108 < Ra < 2 x 109, has not been studied before. It is shown that, contrary to lower-Rayleigh-number behaviour known previously, the core flow structure is nonparallel and is dominated by horizontal intrusions flowing along each of the two insulated horizontal walls of the enclosure. The fluid embraced by the two horizontal jets is practically stagnant and thermally stratified. Flow visualization experiments suggest that adjacent to the two horizontal jets two secondary flat cells are formed by the baroclinic pressure field in an analogous way to what is observed in intrusions in a stratified fluid. Nusselt-number-Rayleigh-number results for the overall end-to-end heat transfer in the horizontal direction are reported and compared with previous experimental and theoretical results available for lower Rayleigh numbers. It is shown also that the transition from a parallel core structure to one dominated by intrusion layers is governed by the parameter RaiA, with RatA < 1 aa necessary condition for a parallel core flow.
Natural convection in a rectangular cavity with wall temperature decreasing at a uniform rate
W�rme - und Stoff�bertragung, 1982
The transient natural convection in a fluid contained in a rectangular enclosure, the wall of which is maintained at a uniform temperature which changes at a steady rate, is approached by a numerical method. Numerical solutions are obtained for Pr = 0.73, 7.3 and 73 and a range of Rayleigh numbers Ra = 102 ~ l0 s. At relatively low Rayleigh numbers the flow is characterized by the development of double cells with flow up the center and down the sidewalls. However it was found that an increase of the Rayleigh number leads to the development of strong secondary circulation on the axis of symmetry of the cavity near the top wall. Thus, as the Rayleigh number is increased the secondary cells grow in size. The effects of the secondary cells on the temperature field and heat transfer coefficients are discussed. Most results are obtained for the case of a square cavity (E ~-2) but the influence of the aspect ratio of the cavity is also studied for E = 1 and 4. Freie Konvektion in reehtwinkeligen Riiumen bei mit der Zeit linear fallenden Wandtemperaturen