NUMERICAL SIMULATION OF THREE-DIMENSIONAL SEPARATED FLOW AND HEAT TRANSFER AROUND STAGGERED SURFACE-MOUNTED RECTANGULAR BLOCKS IN A CHANNEL

ABSTRACT

Numerical results simulating a three-dimensional laminar separated flow and heat transfer around staggered surface-mounted rectangular blocks in a plane channel are presented. Treated in the present study is a case of staggered three-row blocks. The finite-difference method is employed to solve the Navier-Stokes and energy Equations directly, and the resulting finite-difference Equations are solved with the SMAC method for Re = 100–500 and Pr = 0.7. The present numerical results are found to simulate well the visualization results such as horseshoe vortices and recirculating flow. The heat transfer coefficient greatly varies on the different side surfaces of blocks and also with Reynolds number.     

NUMERICAL METHOD FOR HEAT TRANSFER,FLUID FLOW,AND STRESS ANALYSIS IN PHASE-CHANGE PROBLEMS

This work presents a finite-volume method for simultaneous prediction of physical phenomena occurring during a solid / liquid phase change, including buoyancy-driven flow in the liquid, deformation and stresses in the solid, and heat transfer in both the liquid and solid parts of the solution domain. The liquid is treated as a Newtonian incompressible fluid and it is assumed that the solid behaves as a thermoelastic body, although other constitutive equations for liquid and / or solid could easily be incorporated. The method solves integral equations of mass, momentum, and energy balance discretized on numerical meshes consisting of cells of arbitrary polyhedral shape. The method is validated by comparing numerical results with analytical solutions and available measurement data.     

NUMERICAL SIMULATION OF HEAT TRANSFER IN MIST FLOW

A numerical simulation of heat transfer over a row of tubes, in the presence of mist flow, is described. Computations include the solution of the flow field around the tubes, the prediction of the motion of water droplets, and the evaluation of the cooling effect of the water film on the tube surface. The entire analysis is carried out using FENSAP-ICE (Finite Element Navier-Stokes Analysis Package for In-flight icing), a simulation system developed by Newmerical Technologies for icing applications. The numerical model is described, including the Navier-Stokes solution, the water thin film computation, the droplet impingement prediction, and the conjugate heat transfer procedure. The predictions are verified against experimental data for different droplet mass flow rates, showing satisfactory agreement and allowing a useful insight in the physical characteristics of the problem.     

NUMERICAL INVESTIGATION OF FLOW AND HEAT TRANSFER IN TWISTED CIRCULAR-SECTOR DUCTS

Flow and heat transfer in a twisted circular-sector duct are analyzed numerically for steady, fully developed, and incompressible laminar flow with a uniform-wall-temperature boundary condition. A rotating coordinate system is employed to account for the duct twist. The friction factors and Nusselt numbers are predicted for duct sector angles ranging from 15° to 90°, Reynolds numbers ranging from 1 to 1,000, and Prandtl numbers ranging from 1 to 100. Results show significant influence of duct twist on both friction factors and Nusselt numbers, particularly at large values of Reynolds and Prandtl numbers. Accurate correlations are developed to predict the friction factors and Nusselt numbers for the entire range of geometric and operating conditions studied.     

NUMERICAL STUDY ON TURBULENT FLOW AND HEAT TRANSFER IN CIRCULAR COUETTE FLOWS

Abstract

A numerical study is performed to investigate heat transfer and fluid flow in the entrance and fully developed regions of an annulus, consisting of a rotating, insulated inner cylinder and a stationary, heated outer cylinder. Several different k-ε turbulence models are employed to determine the turbulent kinetic energy, its dissipation rate, and the heat transfer performance. The governing boundary layer equations are discretized by means of a control volume finite difference technique and numerically solved using the marching procedure. In the entrance region the axial rotation of the inner cylinder induces a thermal development and causes an increase in both the Nusselt number and the turbulent kinetic energy in the inner cylinder wall region. In the fully developed region, an increase in the Taylor number causes an amplification of the turbulent kinetic energy over the whole cross section, resulting in a substantial enhancement in the Nusselt number. These transport phenomena are also affected by the radius ratio and Reynolds number.     

NUMERICAL ANALYSIS OF FLUID FLOW AND HEAT TRANSFER CHARACTERISTICS IN THREE-DIMENSIONAL PLATE FIN-AND-TUBE HEAT EXCHANGERS

This numerical study provides three-dimensional (3-D) time-dependent modeling of unsteady laminar flow and heat transfer over single- and multirow plate fin-and-tube heat exchangers. The complex nature of the flow field featuring a horseshoe vortex is investigated for both configurations. The time-dependent evolution of the horseshoe vortex mechanism on the forward part of the tube and its journey to the rear of the tube are studied to provide fundamental information on the local flow structure and the corresponding heat transfer characteristics. The effects of various governing parameters, such as fin spacing, Reynolds number, tube row number, and tube arrangement, on the heat transfer and flow characteristics are also studied for the Reynolds number range investigated. It is found that the local flow structure including formation and evolution of vortex systems and singular-point interactions correlates strongly with the heat transfer characteristics. The numerical results for the integral heat transfer parameters agree well with available experimental measurements.     

HEAT TRANSFER CHARACTERISTICS OF FLOW PAST A RECTANGULAR PROTRUDING BODY

Flow over a protruding body is an attractive research field in thermal engineering. In the present study, laminar flow over a protruding body is considered. Unsteady two-dimensional Navier-Strokes and energy equations are solved numerically using a control volume approach. The heat transfer characteristics due to vortex shedding are examined in detail. The flow and heat transfer characteristics are compared with their counterparts obtained from the steady flow case. The entropy analysis is carried out and irreversibility generated because of fluid friction is computed. The relative heat transfer and irreversibility ratios are introduced to compare the heat transfer performance characteristics of unsteady and steady flow cases. It is found that the relative heat transfer ratio attains higher value, whereas relative irreversibility ratio becomes less for unsteady flow as compared with that obtained for the steady flow case.     

NUMERICAL PREDICTION OF BUOYANCY-INDUCED PERIODIC FLOW PATTERN AND HEAT TRANSFER IN A LID-DRIVEN ARC-SHAPE CAVITY

Numerical simulation has been carried out to study the unsteady phenomenon of a buoyancy-induced periodic flow and convection heat transfer in a lid-driven arc-shape cavity. The governing equations in terms of the stream function-vorticity formulation are solved by the finite-volume method coupled with a body-fitted coordinate transformation scheme. In the range of the Reynolds number (Re) from 100 to 2,000 and Grashof number (Gr) up to 5 2 10 7 , the heat transfer characteristics and flow pattern have been predicted. Attention has been focused on the combined effects of the inertial and buoyant forces exerted on the fluid. Results show that only when the inertial and buoyant forces are of approximately equal strength that can the periodic flow pattern be observed. For an inertia-dominant or buoyancy-dominant situation, the periodic flow pattern is not visible.     

NUMERICAL METHOD FOR THE PREDICTION OF INCOMPRESSIBLE FLOW AND HEAT TRANSFER IN DOMAINS WITH SPECIFIED PRESSURE BOUNDARY CONDITIONS

A variety of engineering applications involve incompressible flows in devices for which boundary pressures are known. The purpose of this article is to present a mathematical formulation and a computational method for the prediction of incompressible flow in domains with specified pressure boundaries. The computational treatment of specified pressure boundaries in complex geometries is presented within the framework of a nonstaggered technique based on curvilinear boundary-fitted grids. The construction of the discretization equations for unknown velocities on specified pressure boundaries and the solution of the discretization equations using the SIMPLE algorithm are discussed. The proposed method is applied for predicting incompressible forced flows in branched ducts and in buoyancy-driven flows. These examples illustrate the utility of the proposed method in predicting incompressible flows with specified boundary pressures encountered in practical applications.     

NUMERICAL SIMULATION OF TWO-DIMENSIONAL HEAT AND MOISTURE TRANSFER DURING DRYING OF A RECTANGULAR OBJECT

The present article deals with the numerical modeling of heat and moisture transfer during the drying process of a two-dimensional (2-D) rectangular object subjected to convective boundary conditions. As is common in solids drying, it is assumed that drying takes place as a simultaneous heat and moisture transfer whereby moisture is vaporized by means of a drying fluid (e.g., air), which passes over a moist object. The governing equations representing the drying process in a 2-D rectangular object are discretized using an explicit finite-difference approach, and a computer code is developed to predict the temperature and moisture distributions inside the object. Moreover, the results obtained from the present model are compared with the experimental data available in the literature, and considerably high agreement is found.     

太阳能热气流发电系统的传热与流动数值分析

建立了集热棚、烟囱以及多孔蓄热层的太阳能热气流发电系统传热与流动数学模型,分析了太阳辐射对蓄热介质的蓄热特性的影响.计算结果表明,在太阳辐射为200～800W/M2的范围内,随着太阳辐射的增强,蓄热介质的蓄热比例先减小后增大;烟囱底部的最小相对压力显著减小,流动速度增大;系统内空气的温升增大,蓄热介质表面的温度也显著升高.     

NUMERICAL MODEL FOR RADIATIVE HEAT TRANSFER ANALYSIS IN ARBITRARILY SHAPED AXISYMMETRIC ENCLOSURES WITH GASEOUS MEDIA

A numerical model is presented for evaluating thermal radiative transport in irregularly shaped axisymmetric enclosures containing a homogeneous, isotropically scattering medium. Based on the discrete exchange factor (DEF) method, exchange factors between arbitrarily oriented differential surface/volume ring elements are calculated using a simple approach. The present method is capable of addressing blockage effects produced by inner/outer obstructing bodies. The results obtained via the current method are found to be in excellent agreement with existing solutions to several cylindrical media benchmark problems. The solutions to several rocket-nozzle and plug-chamber geometries are presented for a host of geometric conditions and optical thicknesses.     

NUMERICAL STUDY OF TURBULENT FLOW AND HEAT TRANSFER IN A CONVEX CHANNEL OF A CALORIMETRIC ROCKET CHAMBER

A numerical study on flow and heat transfer in double-wave cross-corrugated passages with different structure parameters was conducted. The three-dimensional governing equations for mass, momentum, and heat transfer were solved using a control volume finite difference method and a validated low-Reynolds number k-? model. The effects of Reynolds number and structure parameters, including pitch ratio (P₁/P₂) and height ratio (H₁/H₂), were studied. It was found that with a decrease in height ratio, the mainstream flow changed from a pattern dominated by L-shaped flow to one dominated by Z-shaped flow, whereas pitch ratio had almost no influence on the flow pattern. The average Nusselt number Nu_av first increased and then decreased gradually with either an increase in the pitch ratio or a decrease in the height ratio. Pressure drop showed the same trend as heat transfer performance. The best performance evaluation criterion number (g) of double-wave passage was nearly 20% higher than that of the corresponding single-wave passage, whereas the worst was nearly 40% lower. On the whole, the double-wave plate with H₁/H₂ = 5 showed better overall performance. The double-wave plate with P₁/P₂ = 1 had better overall performance for Re < 5,000, whereas that with P₁/P₂ = 3 was better for Re > 7,500.     

THE METHOD OF LINES SOLUTION OF THE DISCRETE ORDINATES METHOD FOR RADIATIVE HEAT TRANSFER IN ENCLOSURES

A radiation code based on the method of lines (MOL) solution of the discrete ordinates method (DOM) for transient three-dimensional radiative heat transfer in rectangular enclosures for use in conjunction with a computational fluid dynamics (CFD) code based on the same approach was developed. Assessment of the predictive accuracy of the code by benchmarking its steady-state solutions against exact solutions on one- and three-dimensional test problems shows that the MOL solution of the DOM provides accurate and computationally efficient solutions for radiative heat fluxes and source terms and can be used with confidence in conjunction with CFD codes for transient problems.     

LAMINAR FLOW AND HEAT TRANSFER IN BLOCKED ANNULI

Laminar flow and heal transfer in annular passages with axially nonuniform inner tubes are obtained numerically. A characteristic feature of these passages is that the flow separates in the streamwise direction. An axisymmetric coordinate system with an algebraic transformation in the radial direction kas been used. Fully elliptic vorticity-slream function and energy equations in the transformed coordinates are solved using an iterative alternate direction implicit (ADI) method. In an annulus with a smooth blockage, the flow separates immediately downstream of the blockage at Reynolds numbers greater than 100. The main features of the flow are established at a Reynolds number of 1000. The pressure drop is drastic near the maximum constriction. The heat flux is also high in the constricted region. A sharp increase in the heat transfer occurs where the fluid reattaches itself to the wall. The increase in the total pressure drop is about an order of magnitude greater than that in the average Nusselt number.     

INCOMPRESSIBLE FLOW AND HEAT TRANSFER COMPUTATIONS USING A CONTINUOUS PRESSURE EQUATION AND NONSTAGGERED GRIDS

A pressure-based algorithm for incompressible flows is presented. The algorithm employs a finite-volume discretization in general curvilinear coordinates on a nonstaggered mesh. This approach is derived from a finite-element algorithm, and is here extended to the finite-volume/finite-difference context. The algorithm can be classified as a SIMPLE-like sequential method, and is validated in two classical test cases: the lid-driven cavity and the differentially heated cavity problems. Good results, with no pressure checkerboarding, are achieved up to Reynolds numbers Re = 10⁴ and Rayleigh numbers Ra = 10⁸ , respectively.     

TRANSIENT CONDUCTION AND RADIATION HEAT TRANSFER WITH HEAT GENERATION IN A PARTICIPATING MEDIUM USING THE COLLAPSED DIMENSION METHOD

In order to study the mechanisms of heat and mass transfer at the gas–liquid interface, flows inside and around a rising inert bubble are considered and calculated using the numerical algorithm developed in a companion article. Studies of heat and mass transfer are carried out while special attention is paid to the effects of wake vortices. Recoveries of the Sherwood and Nusselt numbers are observed in the wake zone behind bubbles, and a physical explanation is proposed.     

NUMERICAL SIMULATION OF THE THERMODYNAMIC,FLUID FLOW,AND HEAT TRANSFER PROCESSES IN A DIESEL ENGINE

A comprehensive model for the complete second-law analysis of a diesel engine has been developed. The model incorporates formulations for zero-dimensional estimation of the convective and radiative heat transfers in the engine cylinder. Models for the valve flow and manifold gas dynamics are also included in order to estimate the second-law losses. The results obtained help identify the engine processes where irreversible losses occur and the magnitudes of these losses relative to the work output. For example, at 2000 rpm and 0.7 overall fuel/air equivalence ratio, the indicated work for the single-cylinder engine simulated in this study is 49% of the fuel exergy. The loss due to irreversibilities is 27.6%, of which 14.8% is due to throttling loss in the exhaust valve, 9.3% is due to combustion irreversibilities, and the remainder is due to throttling toss in the intake valve.     

NUMERICAL PREDICTIONS OF HEAT TRANSFER AND FLUID FLOW CHARACTERISTICS FOR SEVEN DIFFERENT DIMPLED SURFACES IN A CHANNEL

Heat transfer and fluid flow characteristics for seven different dimpled surfaces on one surface of a channel are predicted numerically using version 6.1.18 of FLUENT. The turbulent model employed is a realizable κ–? model without a wall function. The different dimples investigated are spherical dimples, tilted cylinder dimples, cylinder dimples, in-line triangular dimples, reverse in-line triangular dimples, staggered triangular dimples, and reverse staggered triangular dimples. Results show the existence of a centrally located vortex pair and vortex pairs near the spanwise edges of each dimple for the three circular dimple types, which augment local magnitudes of eddy diffusivity for momentum and eddy diffusivity for heat. Advection of reattaching and recirculating flows from locations within the spherical-type dimple cavities, as well as strong instantaneous secondary flows and mixing within the vortex pairs, are especially apparent. For the four triangular types of dimples, only one primary flow circulation zone generally is present within individual dimples. In all cases, regions of augmented streamwise vorticity show approximate correspondence to locations where eddy diffusivities for momentum and heat are increased. Overall, the highest heat transfer augmentations, and the most significant local and overall increases to eddy diffusivity for momentum and eddy diffusivity for heat, are produced by the spherical dimples and the tilted cylinder dimples.     

MODELING SIMULTANEOUS HEAT AND MASS TRANSFER USING THE CONTROL-VOLUME METHOD

A control-volume formulation for the solution of a set of two-way coupled heat and diffusive moisture transfer equations is presented in three dimensions. The three-dimensional model in Cartesian coordinates was extended to other geometries using an equivalent surface area-to-volume ratio index. The solution procedure developed uses a fully implicit time-stepping scheme for the solution of the coupled set of equations to study the drying behavior of barley and starch food. Simulated results of the one-way and the two-way coupled equations were compared with the finite-element analysis (two-way coupled and three-way coupled equation set) and experimental results from the literature. Among the products tested, the maximum deviations between experimental and simulation results were 5.0°C in temperature for barley drying, and 0.2 % moisture for starch drying. The overall predictions agreed well with the available experimental data and show good potential for application in grain and food drying.