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 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.

An Experimental Study of Natural Convection in a Rectangular Enclosure Using PIV Measurement Techniques

2011 ◽  
Author(s):  
K. M. Akyuzlu ◽  
J. Farkas
Keyword(s):  
Experimental Study ◽  
Natural Convection ◽  
Measurement Techniques ◽  
Flow Patterns ◽  
Working Fluid ◽  
Two Dimensional ◽  
Rectangular Enclosure ◽  
Aspect Ratios ◽  
Circulation Patterns ◽  
Piv Measurement

An experimental study is conducted to determine the circulation patterns inside a rectangular enclosure due to natural convection using a Particle Image Velocimeter (PIV). Experiments were conducted using two different fluids (air and water) and for rectangular enclosures with aspect ratios 0.5 and 1.0. Natural convection in enclosures has been experimentally studied in the past. Many of these studies cited in the literature use some kind of an optical method like interferograms, shadowgraphs, streak photographs, or multi-exposure photographs to visualize the flow patterns in the enclosure. The present study employs a commercial two-dimensional PIV to capture, instantaneously, the circulation patterns inside the test section. The test cavity in the present setup is of rectangular shape, which is 5 inches (127 mm) wide, where the height of the enclosure can be changed to obtain aspect ratios of 0.5 and 1.0. The depth of the rectangular enclosure measures 12 inches (305 mm) to minimize the effect of walls normal to the two dimensional flow patterns that are expected in this type of arrangement. The walls of the cavity are made of Aluminum plates. These plates are kept at constant but different temperatures during the experiments. In the present study, hollow glass sphere particles with 10 microns in diameter were used as seeding for water experiments and fine particles/flakes of ash generated from burned incense were used as seeding in the air experiments. For each working fluid, the experiments were repeated for different aspect ratios and for different wall temperature differences which corresponded to Rayleigh numbers in the range of 106 and 107. Velocity fields were captured at steady state for each experiment using the two-dimensional PIV system. Numerical studies were also carried out using a commercial CFD software. Comparisons of the numerical and experimental results indicate a good match in terms of circulation patterns and velocity magnitudes in the core of the buoyancy driven flow. Discrepancies in measured and predicted values of velocities are more pronounced near to the boundaries of the enclosure. Separate measurements with finer interrogation areas and different PIV setting were required to improve the accuracy of the measurements near the corners (top and bottom) of the enclosure. The results of these measurements are also presented.

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.

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.

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.

scholarly journals Numerical study of the effect of droplet coagulation intensity on polydisperse aerosol fraction distribution

2021 ◽  
Vol 1 (1) ◽  
pp. 73-80
Author(s):  
D.A. Tukmakov ◽  
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Volume Content ◽  
Fine Particles ◽  
Stokes Equations ◽  
Numerical Study ◽  
Dispersed Phase ◽  
Mass Force ◽  
Carrier Medium ◽  
The Mathematical Model

The paper is devoted to the study of the effect of the intensity of aerosol fluctuations on the dis-tribution of fractions of the dispersed component of the coagulating aerosol. Oscillations of aerosol in closed channel are numerically modeled in operation. To describe the dynamics of the carrier medium, a two-dimensional non-stationary system of Navier-Stokes equations for compressed gas is used. They are written taking into account interfacial power interaction and interfacial heat ex-change. To describe the dynamics of the dispersed phase, a system of equations is solved for each of its fractions. It includes an equation of continuity for the “average density” of the fraction, equa-tions of preservation of spatial components of the pulse and an equation of preservation of thermal energy of the fraction of the dispersed phase of the gas suspension. Phase-to-phase power interac-tion included Archimedes force, attached mass force, and aerodynamic drag force. Heat exchange between the carrier medium-gas and each of the fractions of the dispersed phase was also taken into account. The mathematical model of dynamics of polydisperse aerosol was supplemented by the mathematical model of collision coagulation of aerosol. For the velocity components of the mixture, uniform Dirichlet boundary conditions were set. For the remaining functions of the dynamics of the multiphase mixture, uniform Neumann boundary conditions were set. The equations were solved by the explicit McCormack method with a nonlinear correction scheme that allows to obtain a mono-tone solution. As a result of numerical calculations, it was determined that in the vicinity of the os-cillating piston, an area with an increased content of coarse particles is formed. The coagulation process results in a monotonous increase in volume content of the coarse particle fraction and a mo-notonous decrease in volume content of fine particles. Increasing the intensity of gas fluctuations leads to intensification of the process of coagulation of aerosol droplets.

Power Generation Using Kites in a GroundGen Airborne Wind Energy System: A Numerical Study

2019 ◽  
Vol 142 (6) ◽  
Author(s):  
Alireza Mahdavi Nejad ◽  
Gretar Tryggvason
Keyword(s):  
Wind Energy ◽  
High Speed ◽  
Stokes Equations ◽  
Numerical Study ◽  
Energy System ◽  
Staggered Grid ◽  
Immersed Boundary ◽  
Uniform Mesh ◽  
Two Dimensional ◽  
Time Step

Abstract A computational model of a massless kite that produces power in an airborne wind energy (AWE) system is presented. AWE systems use tethered kites at high altitudes to extract energy from the wind and are being considered as an alternative to wind turbines since the kites can move in high-speed cross-wind motions over large swept areas to increase power production. In our model, the kite completes successive power-retraction cycles where the kite angle of attack is altered as required to vary the resultant aerodynamic forces on the kite. The flow field is found in a two-dimensional domain near the flexible kite by solving the full Navier–Stokes equations using an Eulerian grid together with a Lagrangian representation of the kite. The flow solver is a finite volume projection method using a non-uniform mesh on a staggered grid and corrector–predictor technique to ensure a second-order accuracy in time. The two-dimensional kite shape is modeled as a slightly cambered immersed boundary that moves with the flow. The flexible kite is modeled with a set of linear springs following Hooke’s law. The unstretched length of each elastic tether at a given time step is controlled using periodic triangular wave shapes to achieve the required power-retraction phases. A study was conducted in which the wave shape amplitude, frequency, and phase (between two tethers) were adjusted to achieve a suitably high net power output. The results are in good agreement with predictions for Loyd’s simple kite in two-dimensional motion. Aerodynamic coefficients for the kite, tether tensions, tether reel-out and reel-in speeds, and the vorticity fields in the kite wake are also determined.

A Numerical Study of Turbulent Flow in Helical Static Mixers

2006 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Anahita Ayasoufi ◽  
Theo G. Keith
Keyword(s):  
Turbulent Flow ◽  
Molecular Diffusion ◽  
Stokes Equations ◽  
Numerical Study ◽  
Critical Role ◽  
Three Dimensional ◽  
Turbulent Dispersion ◽  
Working Fluid ◽  
Static Mixer ◽  
Static Mixers

Many processing applications call for the addition of small quantities of chemicals to working fluid. Hence, fluid mixing plays a critical role in the success or failure of these processes. An optimal combination of turbulent dispersion down to eddies of the Kolmogoroff scale and molecular diffusion would yield fast mixing on a molecular scale which in turn favors the desired reactions. Helical static mixers can be used for those applications. The range of practical flow Reynolds numbers for these mixers in industry is usually from very small (Re ∼ 0) to moderate values (Re ∼ 5000). In this study, a helical static mixer is investigated numerically using Lagrangian methods to characterize mixer performance under turbulent flow regime conditions. A numerical simulation of turbulent flows in helical static mixers is employed. The model solves the three-dimensional, Reynolds-averaged Navier-Stokes equations, closed with the Spalart-Allmaras turbulence model, using a second-order-accurate finite-volume numerical method. Numerical simulations are carried out for a six-element mixer, and the computed results are analyzed to elucidate the complex, three-dimensional features of the flow. Using a variety of predictive tools, mixing results are obtained and the performance of static mixer under turbulent flow condition is studied.

Numerical Study of Combined Radiation and Turbulent Mixed Convection Heat Transfer in a Compartment Containing Participating Media

2015 ◽  
Vol 31 (4) ◽  
pp. 467-480 ◽  
Author(s):  
A. Asghari ◽  
S. A. Gandjalikhan Nassab ◽  
A. B. Ansari
Keyword(s):  
Mixed Convection ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Dynamic ◽  
Convection Heat Transfer ◽  
Simple Algorithm ◽  
Convection Flow ◽  
Algebraic Equations ◽  
Mixed Convection Flow ◽  
Participating Media

AbstractThe effect of radiation on turbulent mixed convection flow, generated by two plane wall jets with different temperatures inside a cavity was studied numerically. The medium is treated as a gray, absorbing, emitting and scattering. The two-dimensional Reynolds-average Navier-Stokes equations, coupled with the energy equation are solved by using the computational fluid dynamic (CFD) techniques, while the AKN low-Reynolds-number model is employed for computation of turbulence fluctuations. The Boussinesq approximation is used to calculate the buoyancy term, and the radiation part of the problem is solved by numerical solution of the radiative transfer equation (RTE) with the well known discrete ordinate method (DOM). The governing equations are discretized by the finite volume technique into algebraic equations and solved with the SIMPLE algorithm. The effects of radiation conduction parameter, scattering albedo, optical thickness and Richardson number on the thermal behavior of the system are carried out. Results show that the gas radiation has a significant effect on the temperature distribution inside the turbulent mixed convection flow.

Sign in / Sign up

Export Citation Format

Share Document