Effect of circular cylinder location on three-dimensional natural convection in a cubical enclosure

This paper presents the results of immersed boundary method-based three-dimension numerical simulations of natural convection in a cubical enclosure with an inner circular cylinder at a Prandtl number of 0.7. This simulation spans three decades of Rayleigh number, Ra, from 10³ to 10⁶. The location of the inner circular cylinder is changed vertically along the centerline of the cubical enclosure. This study primarily focuses on the effects of both buoyancy-induced convection and the location of the inner circular cylinder on heat transfer and fluid flow in the cubical enclosure. In the range of Rayleigh numbers considered in this study, the thermal and flow fields eventually reach steady state, regardless of the location of the inner cylinder. When Ra is 10³, the end wall of the cubical enclosure has a negligible effect on the thermal and flow fields in the enclosure. However, in the range of 10⁴ ≤ Ra ≤ 10⁶, the effect of the end wall on heat transfer and fluid flow in the enclosure depends on both the location of the inner cylinder and the Rayleigh number. Detailed analysis results for the distribution of streamlines, isotherms, and Nusselt numbers are presented in this paper.     

Magnetic field effect on mixed convection in a lid-driven square cavity filled with nanofluids

A numerical investigation of laminar mixed convection heat transfer in a lid-driven cavity filled with nanofluid under the influence of a magnetic field is executed. The left and right vertical walls of the cavity are insulated while the top and bottom horizontal walls are kept constant but different temperatures. The top wall is moving on its own plane at a constant speed while other walls are fixed. A uniform magnetic field is applied in the vertical direction normal to the moving wall. The governing differential equations are discretised by the control volume approach and the coupling between velocity and pressure is solved using the SIMPLE algorithm. The heat and mass transfer mechanisms and the flow characteristics inside the cavity depended strongly on the strength of the magnetic field. A comparison is also presented between the results obtained from the Maxwell and modified Maxwell models. The results show that the heat transfer is generally higher based on the modified Maxwell model.     

Analysis of mixed convection in an inclined lid-driven cavity with a wavy wall

A numerical study is performed to analyze the mixed convection flow and heat transfer in a lid-driven cavity with sinusoidal wavy bottom surface. The cavity vertical walls are insulated while the wavy bottom surface is maintained at a uniform temperature higher than the top lid. A finite volume method is used to solve numerically the non-dimensional governing equations. The tests were carried out for various inclination angles ranging to 0° from 180° and number of undulation varied from 4 to 6, while the Prandtl number was kept constant Pr = 0.71. Three geometrical configurations were used namely four, five and six. The distributions of streamlines and isotherms, and the variations of local and average Nusselt numbers with the inclination angle are presented. The results of this investigation illustrate that the average Nusselt number at the heated surface increases with an increase of the number of undulations as well as the angle of inclination.     

The forced convection flow over a flat plate with finite length with a constant convective boundary condition

The flow of a fluid past a flat plate of finite length and infinite width (two-dimensional flow) is considered. The plate is heated by convection from a fluid with constant temperature T _f with a constant heat transfer coefficient h _f . In all previous works, the problem was considered using boundary layer theory whereas, in the present work, the solution is based on the full Navier-Stokes equations. The problem is investigated numerically with a finite volume method using the commercial code ANSYS FLUENT. The governing parameters are the Reynolds number, the new heat transfer parameter, and the Prandtl number. In addition, the influence of these three parameters on the temperature field is investigated. It is found that high Reynolds and high Prandtl numbers the wall temperature increases along the plate. They reach a maximum near the trailing edge then decrease. The same occurs as the heat transfer parameter increases. When the Reynolds and Prandtl numbers are low, the plate temperature tends to become symmetric, with a maximum at the middle of the plate. The temperature profiles become thicker as the Reynolds number and the Prandtl number is reduced while the temperature profiles become thicker as the heat transfer parameter increases.     

An analytic study on laminar film condensation along the interior surface of a cave-shaped cavity of a flat plate heat pipe

An analytic approach has been employed to study condensate film thickness distribution inside cave-shaped cavity of a flat plate heat pipe. The results indicate that the condensate film thickness largely depends on mass flow rate and local velocity of condensate. The increasing rate of condensate film for circular region reveals about 50% higher value than that of vertical region. The physical properties of working fluid affect significantly the condensate film thickness, such as the condensate film thickness for the case of FC-40 are 5 times larger than that of water. In comparison with condensation on a vertical wall, the average heat transfer coefficient in the cave-shaped cavity presented 10-15% lower values due to the fact that the average film thickness formed inside the cave-shaped cavity was larger than that of the vertical wall with an equivalent flow length. A correlation formula which is based on the condensate film analysis for the cave-shaped cavity to predict average heat transfer coefficient is presented. Also, the critical minimum fill charge ratio of working fluid based on condensate film analysis has been predicted, and the minimum fill charge ratios for FC-40 and water are about Ψ_crit= 3-7%, Ψ_crit=0.5-1.3%, respectively, in the range of heat fluxq” = 5-90kW/²     

Numerical investigation of effects of buoyancy around a heated circular cylinder in parallel and contra flow

Two-dimensional, steady, incompressible Navier-Stokes and energy equations are expressed in the stream function/vorticity formulation and solved numerically by finite difference method to study effects of buoyancy on fluid flow and heat transfer from a horizontal circular cylinder. The cylinder is exposed to approaching flow stream, for parallel (parallel flow) and opposing (contra flow) directions to the buoyant force. Two different thermal boundary conditions were considered at the cylinder surface: constant temperature (CT) and constant heat flux (CHF). The results elucidating the dependence of the flow and heat transfer characteristics on the Richardson number 0≤ Ri ≤ 2, Prandtl number 0 ≤ Pr ≤ 100 and Reynolds number 0 ≤ Re ≤ 40 are presented. Overall, for parallel flow regime, an increase in the Ri led to a raise in both Nusselt number and drag coefficient. However, for contra flow regime, these trends were reversed. For both regimes, the aforementioned behaviors were more pronounced for CT boundary condition than that for the CHF boundary condition.     

Double-diffusive natural convection of Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-water nanofluid in an enclosure with partially active side walls using variable properties

Natural convection heat and mass transfer characteristics in a square enclosure using variable thermal conductivity and variable viscosity are numerically studied. The fluid in the enclosure is a water-based nanofluid containing Al₂O₃ nanoparticles. The top and bottom horizontal walls are insulated, while a source (T_h, C_h) and a sink (T_c, C_c) are located at the vertical left and right walls as active parts, respectively, with T_h>T_c and C_h>C_c. The governing equations in the two-dimensional space are discretized using the control volume method. A proper upwinding scheme is employed to obtain stabilized solutions. The study has been carried out for the Rayleigh numbers of 10⁴ to 10⁶, the buoyancy ratios of ?5～5, and different configurations of the source and sink. Results are presented in the form of the streamlines, isotherms and iso-concentraions as well as the average Nusselt and Sherwood numbers. It is observed that average Nusselt number is increased by adding the nanoparticles, while average Sherwood number is reduced. Moreover, both Nusselt and Sherwood number are increased as absolute value of the buoyancy ratio or Rayleigh number is increased.     

Effect of thermal radiation on convection heat transfer in cooling channel of photovoltaic thermal system

The effect of thermal radiation on convection heat transfer in flat-box type cooling channel of photovoltaic thermal system with tilt angle of 30 degree was studied by 3D numerical simulation under constant heat flux boundary condition. The temperature contours and velocity fields of fluid near the outlet were obtained. The variations of wall temperature and convection Nusselt number along flow direction for all the separate walls composing the cooling channel were compared and analyzed. The results show that due to thermal radiation, the deflection of the maximum velocity region to heated top wall, together with the asymmetry of temperature field is weakened. For natural convection, radiation promotes the formation of multi-vortices. For mixed convection, heat transfer on all the cooling channel walls is enhanced under the condition of lower heat flux while heat transfer on heated top wall is deteriorated when the heat flux is relative high. Also, pressure re-rising is promoted by thermal radiation.     

Combined Streamline Upwind Petrov Galerkin method and segregated finite element algorithm for conjugate heat transfer problems

A combined Streamline Upwind Petrov-Galerkin method (SUPG) and segregated finite element algorithm for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow is presented. The Streamline Upwind Petrov-Galerkin method is used for the analysis of viscous thermal flow in the fluid region, while the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the presented method is to consistently couple heat transfer along the fluid-solid interface. Four test cases, which are the conjugate Couette flow problem in parallel plate channel, the counter-flow in heat exchanger, the conjugate natural convection in a square cavity with a conducting wall, and the conjugate natural convection and conduction from heated cylinder in square cavity, are selected to evaluate efficiency of the presented method.     

Numerical simulation of the electro-convective onset and complex flows of dielectric liquid in an annulus

We conducted a numerical study on the onset of electro-convection as well as the complex flow phenomena of dielectric liquid subjected to unipolar autonomous charge injection in the annular gap between two concentric circular cylindrical electrodes. The Nernst-Planck equations governing the charge density transport, the Poisson equation for the electric potential and the Navier-Stokes equations for the fluid flow are solved numerically using the finite volume method. The developed code is validated by comparing the critical stability parameter values for the onset of electro-convection with those obtained from the linear stability analysis. We identify in a parameter space the stable hydrostatic state and the electro-convection state. The electro-convection is again divided into three regimes: stationary, oscillatory and chaotic. For inner cylinder radius r _i ≥ 1.0, we observed an increase in the number of charged plumes and vortex pairs with stability parameter T before the electro-convection becomes chaotic. For outer injection, although the onset of electroconvection starts at T higher than the inner injection, the onset of chaotic motion occurs at lower T.     

A second-order time-accurate finite element method for analysis of conjugate heat transfer between solid and unsteady viscous flow

A fractional four-step finite element method for analyzing conjugate heat transfer between solid and unsteady viscous flow is presented. The second-order semi-implicit Crank-Nicolson scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy. The streamline upwind Petrov-Galerkin method (SUPG) is applied for the weighted formulation of the Navier-Stokes equations. The method uses a three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the method presented is to consistently couple heat transfer along the fluid-solid interface. Five test cases, which are the lid-driven cavity flow, natural convection in a square cavity, transient flow over a heated circular cylinder, forced convection cooling across rectangular blocks, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the method presented. This paper was recommended for publication in revised form by Associate Editor Kyung-Soo Yang Atipong Malatip received his B.S. degree in Mechanical Engineering from King Mongkut’s University of Technology North Bangkok, Thailand, in 2002. He then received his M.S. degree in Mechanical Engineering Chulalongkorn University, Thailand, in 2005. He is currently pursuing a Ph.D. degree in Mechanical Engineering at Chulalongkorn University. His research interests include computational fluid dynamics and fluid-thermal-structural interaction. Niphon Wansophark received his B.S., M.S., and Ph.D. degrees in Mechanical Engineering from Chulalongkorn University, Thailand in 1996, 2000, and 2007, respectively. He is an Assistant Professor of Mechanical Engineering at Chulalongkorn University, Bangkok, Thailand. His research interests are numerical methods and finite element method. Pramote Dechaumphai received his B.S. degree in Industrial Engineering from Khon-Kaen University, Thailand, in 1974, M.S. degree in Mechanical Engineering from Youngstown State University, USA in 1977, and Ph.D. in Mechanical Engineering from Old Dominion University, USA in 1982. He is currently a Professor of Mechanical Engineering at Chula-longkorn University, Bangkok, Thailand. His research interests are numerical methods, finite element method for thermal stress and computational fluid dynamics analysis.     

Suppression of flow-induced vibration of a circular cylinder by means of a flexible sheet

In this study, the suppression of flow-induced vibration of an elastically supported circular cylinder by attachment of a flexible sheet was investigated experimentally. In particular, the dependence of flow-induced vibration characteristics of the circular cylinder upon the flow velocity was investigated in detail by axially attaching the flexible poly-ethylene sheet to the cylinder surface. The characteristics of the flow-induced vibration of the cylinder were investigated by changing the attachment angle ?? and the length l of the flexible sheet (rectangular type) as experimental parameters in various combinations. The angle ?? was set at five different angles, 90°, 45°, 0°, ?45° and ?90°. The angle??s base point was the back side stagnation point of the cylinder. The length l of the flexible sheet varied from 0.5 to 3.0 times of the cylinder??s diameter at the interval of 0.5 times. The width T of the flexible sheet along the span of the cylinder also varied in 7 cases from 1.0L to 0.4L (L is the length of the cylinder) in order to discover the minimum width of the sheet necessary to effectively suppress the flow-induced vibration of the cylinder. Furthermore, the flexible sheet of the minimum width was split into 2 to 5 pieces and attached to the cylinder, and changes in the flow-induced vibration characteristics were investigated. Also, vibration characteristics were investigated for a flexible sheet in the shape of an isosceles triangle. As a result, the optimal length l and minimum width T of the flexible rectangular sheet were found to be 2??2.5D and 0.7L, respectively, to suppress the flow-induced vibration of the cylinder. Most importantly, it was found that the sheet located at the back side stagnation point can suppress the flow-induced vibration generated by any directional flow to strike the front surface of the cylinder.     

Numerical investigation on the melting of circular finned PCM system using CFD & full factorial design

Heat energy storage equipment has the advantages of highly efficient energy storage performance and constant temperature owing to its adoption of Phase change material (PCM); however, its shortcoming is that it takes longer to complete thermal energy storage due to its low thermal conductivity. New technologies are being developed to overcome such shortcomings, including technology that would improve the heat transfer. This study is aimed at analyzing the impact on the energy storage time of the PCM via the Design of experiments (DOE) method and with changes to the following variables: The number of installed fins; the employed material (thermal conductivity); and the temperature of the supplied warm water, all by relying on Computational fluid dynamics (CFD). The PCM system is in the shape of a long vertical cylinder, with circular fins. The number of installed circular fins was one or five, the material used in the pipe and circular fins was changed from iron to copper, and the temperature of the warm water was 309.15 or 313.15 K. The thermal conductivity of each material employed for the CFD was 80.2 or 401.0 W/m-K. The DOE analysis was also performed to check for any curvature effect by adding a center point. The PCM used in this study is n-Octadecane 99% (CH₃(CH₂)16CH₃) with its melting temperature being roughly 300.85 K. To sum up the conclusions of this study, the change in the number of installed circular fins and the temperature of supplied warm water have a substantial influence on the melting of the PCM. The change in the thermal conductivity of the pipe and circular fins has only a meager influence on the melting of the PCM. To reduce the melting time of the PCM most effectively, it is recommended to install as many circular fins as possible and to raise the temperature of the supplied warm water. This may be related to the fact that the melting of the PCM is influenced more by convection inside the PCM system rather than conduction.

     

Experimental and numerical study of heat transfer downstream of an axisymmetric abrupt expansion and in a cavity of a circular tube

This research is an experimental and numerical investigation of heat transfer and fluid flow characteristics in separated, recirculated and reattached regions created by an axisymmetric abrupt expansion and by an abrupt expansion followed by an abrupt contraction (called a “cavity”) in a circular tube at a uniform wall temperature. The flow just upstream of the expansion was unheated and proved to be fully-developed at the entrance to the heated cavity region. Local heat transfer coefficients were measured using a balance-type isothermal heat flux gage. Measurements were made at a small-to-large tube diameter ratio of d/D = 0.4 and downstream Reynolds numbers ranging from Re_D = 4,300 to 44,500. Generally, the maximum Nusselt numbers downstream of an axisymmetric abrupt expansion at a uniform wall temperature occur between 9 and 12 step heights from the expansion step. Numerical simulation has been carried out by a two-equation turbulence model and its results such as mean velocity profiles and local Nusselt numbers are in good agreement with experimental results.     

Isothermal characteristics of a rectangular parallelepiped sodium heat pipe

The isothermal characteristics of a rectangular parallelepiped sodium heat pipe were investigated for high-temperature applications. The heat pipes was made of stainless steel of which the dimension was 140 m(L) ×95m(W) ×46m(H) and the thickness of the container was 5 mm. Both inner surfaces of evaporator and condenser were covered with screen meshes to help spread the liquid state working fluid. To provide additional path for the working fluid, a lattice structure covered with screen mesh wick was inserted in the heat pipe. The bottom surface of the heat pipe was heated by an electric heater and the top surface was cooled by circulating coolant. The concern in this study was to enhance the temperature uniformity at the bottom surface of the heat pipe while an uneven heat source up to 900 W was in contact. The temperature distribution over the bottom surface was monitored at more than twenty six locations. It was found that the operating performance of the sodium heat pipe was critically affected by the inner wall temperature of the condenser region where the working fluid may be changed to a solid phase unless the temperature was higher than its melting point. The maximum temperature difference across the bottom surface was observed to be 114^°C for 850 W thermal load and 100^°C coolant inlet temperature. The effects of fill charge ratio, coolant inlet temperature and operating temperature on thermal performance of heat pipe were analyzed and discussed.     

Characteristics of flow past a circular cylinder with a rectangular groove

In the present study, features of the flow past a circular cylinder with single longitudinal groove pattern placed on its surface were investigated. Six different rectangular groove sizes were tested for angular position of the groove from the forward stagnation point of the circular cylinder within 0°≤θ≤150°. The particle image velocimetry (PIV) technique were employed to measure flow field downstream of the cylinder immersed in a uniform flow field with the Reynolds number, Re=5000. Time-averaged flow data such as vorticity, 〈ω〉 streamline, 〈Ψ〉, streamwise, 〈u′u′〉 and transverse, 〈v′v′〉 Reynolds normal stresses, turbulent kinetic energy, TKE and RMS of streamwise, u_rms and transverse, v_rms velocity components were obtained from PIV data to demonstrate flow features. Moreover, frequency of Karman vortex shedding was explored using single point spectral analysis. It is concluded that presence of the groove on a cylinder surface significantly affects the near wake flow structure and turbulence statistics. Karman vortex shedding frequency, f_k strongly depends on the groove size. Moreover, the shear layer instability is induced on the grooved side with additional frequencies.     

Effect of the Reynolds number on the conjugate heat transfer around a circular cylinder with heat source

Conjugate heat transfer around a circular cylinder with heat source was numerically investigated. Both the forced convection of water and conduction of carbon-steel were involved in the present simulation. A finite element formulation based on SIMPLE type algorithm was adopted for solving the incompressible Navier-Stokes equations coupled with energy equation. A conduction heat transfer problem inside the cylinder was trivially coupled with forced convection around the cylinder by using the Galerkin formulation of energy equation. The proposed algorithm was verified by solving the benchmark problem of conjugate heat transfer inside a cavity having a centered body. The effect of the Reynolds number on the temperature distribution on the cylinder surface and the maximum temperature inside the cylinder was examined. It was shown that the maximum temperature decreased as Reynolds number increased and that the position of the maximum temperature moved from the center to the rear part of the cylinder till Re = 20 and then moved back toward the center beyond Re = 20 since the reverse flow around the rear part of the cylinder became stronger as the Reynolds number further increased. Lastly, the maximum temperature of the cylinder with rotation was higher than that of the fixed one and the position of the maximum temperature inside the cylinder depended on the position and the strength of the dead zone.     

Turbulence modeling of natural convection in enclosures: A review

In this paper a review of recent developments of turbulence models for natural convection in enclosures is presented. The emphasis is placed on the effect of the treatments of Reynolds stress and turbulent heat flux on the stability and accuracy of the solution for natural convection in enclosures. The turbulence models considered in the preset study are the two-layer k − ɛ model, the shear stress transport (SST) model, the elliptic-relaxation (V2-f) model and the elliptic-blending second-moment closure (EBM). Three different treatments of the turbulent heat flux are the generalized gradient diffusion hypothesis (GGDH), the algebraic flux model (AFM) and the differential flux model (DFM). The mathematical formulation of the above turbulence models and their solution method are presented. Evaluation of turbulence models are performed for turbulent natural convection in a 1:5 rectangular cavity ( Ra= 4.3×10¹⁰) and in a square cavity with conducting top and bottom walls ( Ra= 9 1.58×10⁹) and the Rayleigh-Benard convection ( Ra = 2 × 10⁶ ∼ Ra = 10⁹). The relative performances of turbulence models are examined and their successes and shortcomings are addressed.     

Combined convection and radiation in a tube with circumferential fins and circular disks

Combined convection and radiation heat transfer in a circular tube with circumferential fins and circular disks is investigated for various operating conditions. Using a finite volume technique for steady laminar flow, the governing equations are solved in order to study the flow and temperature fields. TheP- 1 approximation and the weighted sum of gray gases model (WSGGM) are used for solving the radiation transport equation. The results show that the total Nusselt number of combined convection and radiation is higher than that of pure convection. If the temperatures of the combustion gas and the wall in a tube are high, radiation becomes dominant. Therefore, it is necessary to evaluate the effect of radiation on the total heat transfer. Key Words: Convection, Radiation, Nongray Radiation,P- 1 Approximation, Weighted Sum of Gray Gases Model     

Effects of flexible plate attached to the rear of the cylinder on flow structure

In this experimental study, the flow structure in the wake flow region was investigated with the Particle image velocimetry technique (PIV) by attaching elastic plates at different lengths behind the cylinder. The flow structure occurred at the wake flow region altered depending on the length of the flexible matter. In this experiment, the strips with the lengths of 75, 90, 120, 135 and 180 mm were used to control instabilities. Diameter of the cylinder (D) is 60 mm and the water height (h _w ) is 600 mm. Reynolds number was kept constant as 5000 based on cylinder diameter. The images were captured at mid-height of the cylinder (h _m ) which is 250 mm. As a result of experimental studies, attached flexible strip suppressed vortex shedding occurred in the behind of the cylinder and it is observed that effect of the length flexible of the strip is pretty much. Maximum level of flow characteristics such as Reynolds stress, fluctuation velocities and turbulent kinetic energy were decreased with flexible splitter plate and shifted through the downstream region.