A Study of Unsteady Mixed Convection in a Lid Driven Flow Inside a Rectangular Cavity

2010 ◽  
Author(s):  
K. M. Akyuzlu ◽  
K. Hallenbeck
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Second Order ◽  
Rectangular Cavity ◽  
Constant Speed ◽  
Working Fluid ◽  
Two Dimensional ◽  
Driven Cavity ◽  
Circulation Patterns ◽  
Vertical Walls

A numerical study is conducted to identify the unsteady characteristics of momentum and heat transfer in lid-driven cavity flows. The cavity under study is filled with a compressible fluid and is of rectangular shape. The bottom of the cavity is insulated and stationary where as the top of the cavity (the lid) is pulled at constant speed. The vertical walls of the cavity are kept at constant but unequal temperatures. A two-dimensional, mathematical model is adopted to investigate the shear and buoyancy driven circulation patterns inside this rectangular cavity. This physics based mathematical model consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for compressible flows) and energy equations for the enclosed fluid subjected to appropriate boundary and initial conditions. The compressibility of the working fluid is represented by an ideal gas relation and its thermodynamic and transport properties are assumed to be function of temperature. The governing equations are discretized using second order accurate central differencing for spatial derivatives and second order finite differencing (based on Taylor expansion) for the time derivatives. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Grid independence and time convergence studies were carried out to determine the accuracy of the square mesh adopted for the present study. Two benchmark cases (driven cavity and rectangular channel flows) were studied to verify the accuracy of the CMSIP. Numerical experiments were then carried out to simulate the unsteady development of the shear and buoyancy driven circulation patterns for different Richardson numbers in the range of 0.036<Ri<100 where the Re number is kept less than 2000 to assure laminar flow conditions inside the cavity. Simulations start with a stagnant fluid subjected to a sudden increase in one of the walls temperature. At the same time the upper lid of the cavity is accelerated, instantaneously, to a constant speed. The circulation patterns, temperature contours, vertical and horizontal velocity profiles were generated at different times of the simulation, and wall heat fluxes and Nusselt numbers were calculated for the steady state conditions. Only the results for a square cavity are presented in this paper. These results indicate that the heat transfer rates at the vertical walls of the cavity are enhanced with the decrease in Richardson number.

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: Transition From Laminar to Turbulent Flow

2010 ◽  
Author(s):  
K. M. Akyuzlu ◽  
M. Chidurala
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Turbulent Flow ◽  
Numerical Study ◽  
Second Order ◽  
Working Fluid ◽  
Two Dimensional ◽  
Rectangular Enclosure ◽  
Circulation Patterns ◽  
Vertical Walls

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature stratification inside a rectangular enclosure. One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for turbulent compressible flows), and energy equations for the enclosed fluid subjected to appropriate boundary conditions. A standard two equation turbulence model is used to model the turbulent flow in the enclosure. The compressibility of the working fluid is represented by an ideal gas relation. The conservation equations are discretized using an implicit finite difference technique which employs second order accurate central differencing for spatial derivatives and second order (based on Taylor expansion) finite differencing for time derivatives. The linearized finite difference equations are solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Numerical experiments were then carried out to simulate the development of the buoyancy driven circulation patterns inside rectangular enclosures (with aspects ratios 0.5, 1 and 1.5) filled with a compressible fluid (Pr = 0.72). Experiments were repeated for various wall temperature differences which corresponded to Rayleigh numbers between 104 and 106. Changes in unsteady circulation patterns, temperature contours, and vertical and horizontal velocity profiles were predicted while the flow inside the enclosure transferred from laminar to turbulent flow due to the sudden temperature change imposed on the vertical walls of the enclosure. Only the results of the enclosure with aspect ratio one is presented in this paper. These results indicate that this transition is characterized by unicellular circulation patterns breaking up in to multicellular formations and increase in the values of the predicted wall heat fluxes and Nusselt number as flow becomes turbulent.

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

A Numerical Study of Thermoacoustic Oscillations in a Rectangular Channel Using CMSIP Method

2009 ◽  
Author(s):  
K. M. Akyuzlu ◽  
K. Albayrak ◽  
C. Karaeren
Keyword(s):  
Mathematical Model ◽  
Velocity Field ◽  
Finite Difference ◽  
Second Order ◽  
Component Model ◽  
Working Fluid ◽  
Two Dimensional ◽  
Throttle Valve ◽  
Heated Channel ◽  
Thermoacoustic Oscillations

This paper presents a mathematical model that was developed to study instabilities (primarily thermoacoustic oscillations) experienced inside a channel (with a rectangular cross section) heated symmetrically (from its top and bottom.) The heated channel is configured to simulate a combustion chamber of a rocket hybrid rocket motor and is connected to a converging–diverging nozzle in the downstream and to a plenum with a flow straightener in the upstream side. The working fluid is supplied from a pressurized storage tank to the upstream plenum through a throttle valve. A multi-component approach is used to model this test apparatus. In this integrated component model, the unsteady flow through the throttle valve and the nozzle is assumed to be one-dimensional and isentropic where as the flow in the forward plenum and the heated channel is assumed to be a two-dimensional, unsteady, compressible, turbulent, and subsonic. The physics based mathematical model of the flow in the channel consists of conservation of mass, momentum (two-dimensional Navier-Stokes) and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The working fluid is assumed to be compressible where the density of the fluid is related to the pressure and temperature of the fluid through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and second order accurate (based on Taylor expansion) finite difference approximations for temporal derivatives. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables, i.e., pressure, temperature, and the velocity field) of the problem. The turbulence model equations and the unsteady flow equation for the throttle valve are solved using a second order accurate explicit finite difference technique. Convergence and grid independence studies were done to determine the optimum mesh size and computational time increment. Furthermore, two benchmark cases (unsteady driven cavity and laminar channel flows) were simulated using the developed numerical model to verify the accuracy of the proposed solution procedure. Numerical experiments were then carried out to simulate the thermoacoustic oscillations inside rectangular channels with various aspect ratios ranging from 5 to 20 for various operating conditions (i.e., for Re numbers between 102 and 106) and to determine the flow regions where these oscillations are sustained. The numerical simulation results indicate that the mathematical model for the gas flow in the heated channel predicts the expected unsteady temperature and pressure distributions, and the velocity field, successfully. Furthermore, it is concluded that the proposed integrated component model is successful in generating the characteristics of the instabilities associated with thermal, hydrodynamic, and thermoacoustic oscillations in heated channels.

scholarly journals A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Variable Thermodynamic and Transport Properties

2009 ◽  
Author(s):  
K. M. Akyuzlu ◽  
M. Chidurala
Keyword(s):  
Mathematical Model ◽  
Transport Properties ◽  
Temperature Difference ◽  
Wall Temperature ◽  
Numerical Experiments ◽  
Working Fluid ◽  
Two Dimensional ◽  
Constant Property ◽  
Variable Property ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure (with aspect ratio of one) filled with a compressible fluid (Pr = 0.72). One of the vertical walls of the enclosure is kept at a higher temperature than the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for compressible flows) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The compressibility of the working fluid is represented by an ideal gas relation. Thermodynamic and transport properties of the fluid are assumed to be function of temperature. The governing equations are discretized using second order accurate central differencing for spatial derivatives and second order finite differencing based on Taylor expansion for time derivatives. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Grid independence and time convergence studies were carried out on different mesh sizes and also on a stretched orthogonal mesh to determine the accuracy of the square mesh adopted for the present study. Numerical experiments were carried out for a benchmark case (driven cavity flows) to verify the accuracy of the CMSIP, the proposed solution procedure. Numerical experiments were then carried out to simulate the development of the buoyancy driven circulation patterns for Rayleigh (Ra) numbers between 103 and 106. Also a parametric study was carried out (where Ra number was kept constant) to determine the effect of variations in wall temperature difference and reference length on the velocity and temperature fields. The effects of variable fluid properties on circulation patterns, temperature distributions, vertical and horizontal velocity profiles, and heat transfer from the walls of the enclosure were determined in a separate set of numerical experiments. Finally, unsteady thermal and hydrodynamic behavior of the working fluid was studied by imposing a sudden wall temperature change in the square enclosure. It is concluded that there is notable difference between the results of the variable property and the constant property models. Also, the variable property model predicts lower values for wall heat fluxes and Nu number than the constant property one. This seems to be more true when the temperature difference between the hot and cold walls of the enclosure is larger.

Heat Convection from a Horizontal Cylinder Rotating in a Quiescent Fluid

1986 ◽  
Vol 10 (3) ◽  
pp. 141-152
Author(s):  
H.M. Badr ◽  
S.M. Ahmed
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Horizontal Cylinder ◽  
Heat Transfer Process ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Boussinesq Fluid ◽  
The Mathematical Model ◽  
Quiescent Fluid

The aim of this work is a theoretical investigation to the problem of heat transfer from an isothermal horizontal cylinder rotating in a quiescent fluid. The study is based on the solution of the conservation equations of mass, momentum and energy for two-dimensional flow of a Boussinesq fluid. The effects of the parameters which influence the heat transfer process namely the Reynolds number and Grashof number are considered while the Prandtl number is held constant. Streamline and isotherm patterns are obtained from the mathematical model and the results are compared with previous experimental data. A satisfactory agreement was found.

scholarly journals Numerical study on the thermohydraulic performance of a reciprocating room temperature active magnetic regenerator

2019 ◽  
Vol 128 ◽  
pp. 07001
Author(s):  
Georges El Achkar ◽  
Bin Liu ◽  
Rachid Bennacer
Keyword(s):  
Heat Transfer ◽  
Room Temperature ◽  
Transient Flow ◽  
Numerical Study ◽  
Working Fluid ◽  
Comsol Multiphysics ◽  
Transfer Model ◽  
Two Dimensional ◽  
Active Magnetic Regenerator ◽  
Magnetic Regenerator

In this paper, the thermohydraulic performance of a reciprocating room temperature active magnetic regenerator (AMR), with gadolinium (Gd) particles used as a magnetocaloric material (MCM) and water used as a working fluid, was numerically investigated. A two-dimensional transient flow model was developed using COMSOL Multiphysics, in order to determine the water flow distribution in two AMRs of cross and parallel Gd particles distributions for different water inlet velocities of 0.06 m.s-1, 0.08 m.s-1 , 0.1 m.s-1 and 0.12 m.s-1. The Gd particles have a radius of 1.5 mm and a distance from one another of 0.9 mm. Based on the simulations results of the first model, a two-dimensional transient coupled flow and heat transfer model was then developed using COMSOL Multiphysics, in order to characterise the convective heat transfer in the AMR of cross Gd particles distribution for the same water inlet velocities.

A Study of Formation of Circulation Patterns in Laminar Unsteady Lid-Driven Cavity Flows Using PIV Measurement Techniques

2012 ◽  
Author(s):  
K. M. Akyuzlu ◽  
J. Farkas
Keyword(s):  
Steady State ◽  
Measurement Techniques ◽  
Reynolds Numbers ◽  
Working Fluid ◽  
Computational Fluid Mechanics ◽  
Square Cavity ◽  
Driven Cavity ◽  
Circulation Patterns ◽  
Piv Measurement ◽  
Steady State Predictions

An experimental study was conducted to observe/visualize, the formation of circulation patterns inside a square cavity due to the movement of a lid at constant velocity. Lid driven cavity flow is one of the benchmark studies used in the verification/improvement of CFD codes for internal flow applications/predictions. Previous work on this topic is primarily focused on improving the steady state predictions of the CFD codes using different numerical schemes and algorithms. Furthermore, almost all of the studies reported in computational fluid mechanics literature relates to steady state predictions of lid or shear driven flows. Experimental work that is reported in these studies is limited in scope and number. This paper reports on the measurements we made using Particle Image Velocimeter (PIV) technique to determine the flow field as it develops from stagnation to steady state inside a square cavity driven by a lid. For this purpose, we employed a 2-D PIV system, which uses a double-cavity, Nd:Yag laser to illuminate the test cavity. Experiments were conducted using water as the working fluid inside a square cavity that is one inch (25.4 mm) high and one inch wide. The depth of the cavity is five inches (127 mm) to ensure two-dimensional circulations patterns. Hollow glass sphere particles with 10 microns in diameter were used as seeding of the working fluid, water. Experiments were repeated for different lid velocities corresponding to lid Reynolds numbers (laminar to beginning of transition of turbulence.) Velocity fields were captured during the development of the circulations patters each being unique for the time of the measurement and value of the lid velocity. The center of the circulation pattern and its path inside the cavity is constructed from the captured images as steady state is attained. Also, the strength of the circulation (as manifested by the increase in the diameter of the circulation) is determined at different times for different Reynolds numbers.

scholarly journals Two-Dimensional Model of a Space Station Freedom Thermal Energy Storage Canister

1994 ◽  
Vol 116 (2) ◽  
pp. 114-121 ◽  
Author(s):  
T. W. Kerslake ◽  
M. B. Ibrahim
Keyword(s):  
Heat Transfer ◽  
Energy Storage ◽  
Free Convection ◽  
Phase Change ◽  
Thermal Energy ◽  
Heat Engine ◽  
Space Station ◽  
Working Fluid ◽  
Two Dimensional ◽  
Liquid Salt

The Solar Dynamic Power Module being developed for Space Station Freedom uses a eutectic mixture of LiF-CaF2 phase-change salt contained in toroidal canisters for thermal energy storage. This paper presents results from heat transfer analyses of the phase-change salt containment canister. A two-dimensional, axisymmetric finite difference computer program which models the canister walls, salt, void, and heat engine working fluid coolant was developed. Analyses included effects of conduction in canister walls and solid salt, conduction and free convection in liquid salt, conduction and radiation across salt vapor-filled void regions, and forced convection in the heat engine working fluid. Void shape and location were prescribed based on engineering judgment. The salt phase-change process was modeled using the enthalpy method. Discussion of results focuses on the role of free convection in the liquid salt on canister heat transfer performance. This role is shown to be important for interpreting the relationship between ground-based canister performance (in 1-g) and expected on-orbit performance (in micro-g). Attention is also focused on the influence of void heat transfer on canister wall temperature distributions. The large thermal resistance of void regions is shown to accentuate canister hot spots and temperature gradients.

scholarly journals Asymmetrical Flow Driving in Two-Sided Lid-Driven Square Cavity with Antiparallel Wall Motion

2020 ◽  
Vol 330 ◽  
pp. 01009
Author(s):  
El Amin Azzouz ◽  
Samir Houat
Keyword(s):  
Wall Motion ◽  
Velocity Ratio ◽  
Two Dimensional ◽  
Square Cavity ◽  
Driven Cavity ◽  
Dimensional Flow ◽  
Fluid Properties ◽  
Two Dimensional Flow ◽  
Vertical Walls ◽  
Volume Method

The two-dimensional flow in a two-sided lid-driven cavity is often handled numerically for the same imposed wall velocities (symmetrical driving) either for parallel or antiparallel wall motion. However, in this study, we present a finite volume method (FVM) based on the second scheme of accuracy to numerically explore the steady two-dimensional flow in a two-sided lid-driven square cavity for antiparallel wall motion with different imposed wall velocities (asymmetrical driving). The top and the bottom walls of the cavity slide in opposite directions simultaneously at different velocities related to various imposed velocity ratios, λ = -2, -6, and -10, while the two remaining vertical walls are stationary. The results show that varying the velocity ratio and consequently the Reynolds ratios have a significant effect on the flow structures and fluid properties inside the cavity.

Sign in / Sign up

Export Citation Format

Share Document