NUMERICAL SIMULATION OF NONISOTHERMAL FLOW OF POLYMER MELT IN A SINGLE-SCREW EXTRUDER: A VALIDATION STUDY

A recently developed approach to simulate the nonisothermal polymer melt flow in a single-screw extruder is validated against experimental data taken from the literature. Comparisons are made with eight sets of experimental results, and for each case several numerical runs are performed to provide some insight into the sensitivity of simulation outcomes to input material parameters (i.e., viscosity, density, thermal conductivity, and specific heat). In general, predictions for the pressure distribution along the extruder and for the mean melt temperature at the exit of the extruder compare favorably with pertinent experimental results. On the other hand, calculated estimates for the power consumption of an extruder are systematically lower than corresponding measured values.     

A NUMERICAL STUDY OF THE HEAT TRANSFER TO FLUID FLOW THROUGH CIRCULAR POROUS PASSAGES

A detailed numerical study of heat transfer to a fluid passing through a saturated porous medium is the subject of this study. The Green's function solution method is selected in order to accomplish this task. The interesting features of this methodology are the focus of this article. As a test case, primary consideration is given to the computation of heat transfer to a fluid flowing through a circular passage with impermeable walls filled with porous materials. The analysis includes the heating/cooling effects due to a temperature change at the wall of the passage. In addition, the contributions of frictional heating are examined.     

HYDROMAGNETIC FLOW AND HEAT TRANSFER OF A HEAT-GENERATING FLUID OVER A SURFACE EMBEDDED IN A POROUS MEDIUM

Similarity solutions for the laminar boundary-layer equations describing steady hydromagnetic two-dimensional flow and heat transfer in a stationary electrically-conducting and heat-generating fluid driven by a continuously moving porous surface immersed in a fluid-saturated porous medium are obtained. The flow is exposed to a transverse magnetic field and the surface is moving with a constant velocity. Fluid suction or injection is imposed at the wall. The dimensionless similar equations are solved numerically by an implicit finite-difference method. The numerical flow and heat transfer results are illustrated graphically for various parametric conditions to show special features of the solutions. Favorable comparisons with previously published work confirm the correctness of the numerical results. © 1997 Elsevier Science Ltd     

NUMERICAL STUDY OF COMPRESSIBLE TURBULENT FLOW IN MICROTUBES

Micro- and conventional compressible, turbulent tube flows were solved numerically in this study. The numerical procedure solves the compressible, turbulent boundary-layer equations using an implicit finite-difference scheme. The parabolic character of the boundary-layer equations renders the numerical procedure a very efficient, accurate, and robust tool for studying compressible microtube flows. The Baldwin–Lomax two-layer turbulence model is adopted in the numerical procedure. The numerically calculated friction factors are compared with the Blasius correlation, the Fanno line flow prediction, and the experimental data. The comparison shows that the numerically calculated friction factors for conventional tube flows agree quite well with the Blasius correlation. The numerical friction factors for microtube flows are larger than the Blasius correlation due to the compressibility effects. They also are greater than the Fanno line flow prediction and the experimental data. This is because the Fanno line flow and the experimental data assume that the flow is adiabatic, but in reality, compressible, turbulent microtube flows are neither adiabatic nor isothermal, as demonstrated by the numerical results in this study.     

NUMERICAL STUDY OF CONVECTION HEAT TRANSFER DURING THE MELTING OF ICE IN A POROUS LAYER

A numerical study is made of the melting of ice in a rectangular porous cavity heated from above. The Landau transformation is used to immobilize the ice-water interface, and the Darcy-Boussinesq equations are solved by a finite-difference technique. Results are analyzed in terms of the heating temperature and the aspect ratio of the cavity. A comparison is made with the case of melting from below. It was found that melting from above is more effective than melting from below when the heating temperature is between 0 and 8°C: convection arises earlier, the melting process is faster, and the total melt at steady state is thicker. The critical time for onset of convection is minimum when the upper boundary is heated at 6°C. At this heating temperature, one also obtains a maximum heat transfer rate (Nusselt number).     

A NUMERICAL STUDY OF SOLIDIFICATION IN THE PRESENCE OF A FREE SURFACE UNDER MICROGRAVITY CONDITIONS

A numerical study of the relative importance of Marangoni effects under microgravity conditions is presented. The mathematical formulation adopted is based on the enthalpy porosity method. One of the advantages of the fixed grid method is that a unique set of equations and boundary conditions is used for the whole domain, including both solid and liquid phases. The governing equations written in a vorticity-velocity formulation are discretized using a finite volume technique on a staggered grid. A fully implicit method has been adopted for the mass and momentum equations, while the temperature field is solved separately in order to evaluate the variation in the local liquid mass fraction. The resulting algebraic system of equations is solved using a preconditioned BI-CGStab method. Numerical results modelling the free surface, including the effects on it of Marangoni convection, are presented. The influence of the presence of argon in the gap above the free surface is investigated. During the numerical simulations presented in this paper 161 2 41 and 641 2 161 uniform meshes on the whole computational domain for values of Marangoni number ( Ma ) up to 16,120 and Rayleigh number ( Ra ) of 5 have been used.     

NUMERICAL STUDY OF MULTILAYERED FLOW REGIME IN DOUBLE-DIFFUSIVE CONVECTION IN A ROTATING ANNULUS WITH LATERAL HEATING

Combined radiation and natural convection in a participating medium between two horizontal confocal elliptical cylinders is investigated numerically. The equations of steady, laminar two-dimensional natural convection are written by using an elliptic-cylinder coordinates system, the stream function, and the vorticity. The finite volume radiation solution method and the control volume technique are used to discretize the coupled equations of momentum, energy, and radiative transfer. Numerical solutions are obtained for Rayleigh numbers in the range 104 to 2x105 and the radiation-conduction parameter ranging from 0 to infinity. The special case corresponding to the convective flow within the annulus formed by an elliptical cylinder surrounding a flat plate is also considered.     

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.     

A NUMERICAL STUDY OF TWO-PHASE FLOW USING A TWO-DIMENSIONAL TWO-FLUID MODEL

Two-phase flow is studied numerically in two dimensions using a two-fluid equation system. The development is based on the surface-tension force terms incorporated in the momentum equations. The governing equations become hyperbolic type for which an upwind method such as flux vector splitting (FVS) avails. As a benchmark problem, a two-phase shock tube is first used to study the wave propagation characteristics and interaction between the gas and liquid phases. Fluid sedimentation due to the density difference and cavity growth in a duct with a bend are showed next. Advantages and capabilities of the present formulation are discussed in some detail.     

EFFECT OF THE CONVECTIVE INERTIA TERM ON BENARD CONVECTION IN A POROUS MEDIUM

The thermal impact of the convective inertia term, which resembles the term used in the Navier-Stokes equation for pure fluids, is investigated numerically considering Bénard convection in a fluid-saturated porous medium. There has been some theoretical discussion in the archival literature about the correctness of including an inertia term in the form of a velocity divergent. The present study shows numerically that this convective term (inertia) is negligible for most cases and has a negligible effect on the overall heat transfer. The relative importance of the inertia and Forchheimer terms bated on scale analysis is found to agree with the numerical results. This evidence adds strength to the theoretical assessment found in the literature.     

EFFECTS OF TRANSVERSE MAGNETIC FIELD,PRANDTL NUMBER AND REYNOLDS NUMBER ON NON-DARCY MIXED CONVECTIVE FLOW OF AN INCOMPRESSIBLE VISCOUS FLUID PAST A POROUS VERTICAL FLAT PLATE IN A SATURATED POROUS MEDIUM

The effect of transverse magnetic field parameter (Hartmann number, Ha), Reynolds number (Re) and Prandtl number (Pr) on the mixed convection flow past a semi-infinite vertical porous plate in a non-Darcian porous medium with variable viscosity and porosity, viscous dissipation and fluid–solid thermal conductivity ratio in the presence of plate transpiration (lateral mass flux) is investigated theoretically and numerically using Keller's implicit finite difference scheme. It is shown that the Hartmann number acts as a retarding force and increases the momentum boundary layer thickness, analogous to the flow against a positive pressure gradient, simultaneously decreasing local skin friction (shear stress). The heat transfer rate is however enhanced by the magnetic field (for positive values of the Eckert number) since the fluid is heated and temperature gradients become reduced between the fluid and the plate, with important potential applications in MHD power generators, materials processing and geothermal systems containing electrically-conducting fluids. The effects of high velocity flow (larger Re) and different Prandtl numbers corresponding to different industrial and geophysical fluids on heat transfer are also discussed. © 1997 by John Wiley & Sons, Ltd.     

EFFECTS OF HETEROGENEITY IN FORCED CONVECTION IN A POROUS MEDIUM: TRIPLE LAYER OR CONJUGATE PROBLEM

The effects of variation (in the transverse direction) of permeability and thermal conductivity, on fully developed forced convection in a parallel plate channel or circular duct filled with a saturated porous medium, is investigated analytically on the basis of a Darcy model, for the cases of isoflux and isothermal boundaries. Previous work is extended to the case of a medium composed of three layers, or two layers with an adjacent solid layer. For the parallel plate channel with isoflux boundaries, some general multilayer results are given.     

A NUMERICAL STUDY OF JETS IN A REACTING CROSSFLOW

This article is concerned with computational modeling of the mixing of circumferentially placed round jets with a crossflow in a circular duct. This flow is relevant to many engineering applications including gas turbines and steel melting furnaces. Both nonreacting and reacting flows are considered. The fundamental characteristics that govern the mixing of the air and fuel streams are investigated. Further, the applicability of a laminar flamelet model for prediction of the combustion process is assessed through comparison of code predictions to experimental 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.     

除湿条件下波纹通道内对流传热传质的数值研究

通过数值计算对紧凑换热器一种波纹翅片通道内除湿条件下周期性充分发展的对流传热传质情况进行数值研究。计算采用曲线坐标系下压力与速度耦合的SIMPLER算法,湿空气流动Re数的范围为100～1100,Pr数为0.71,Sc数为0.61。讨论了不同波纹高度、波纹间距对阻力与换热的影响,给出了不同Re数下的浓度场,并对动量、传热及传质进行了定量比较分析。计算结果表明,整体Nu数及fRe数随着波纹高度的增加或波纹间距的减小而增加;浓度随着Re数的增加沿着流动方向迅速降低;计算能较好的满足Chilton-Colburn相似,表明传热特性均可类推到传质特性中去。     

CONJUGATE FREE CONVECTION FROM VERTICAL FINS EMBEDDED IN A POROUS MEDIUM

The problem of conjugate free convection in a porous medium from a vertical plate and a vertical cylindrical fin is considered. The governing equations for the convective flow in the porous medium are coupled to the governing equation for the heat flow in the fin by the conditions of continuity of the temperature and the heat flux at the interface. The heat flow in the fin is taken to be either two-dimensional or one-dimensional, in order to compare the results provided by both approaches. The nondimensional parameters that appear are the convection-conduction parameter, N cc , and the aspect ratio of the fin, u p for the plate fin and u c for the cylindrical fin. The surface curvature parameter u C appears as a parameter which is directly dependent on u c in the case of the cylindrical fin. Considering two-dimensional conduction in the solid fin is a more realistic approach from a practical standpoint, but the shortcoming of specifying zero heat flux at the tip of the fin is discussed.     

MAGNETOHYDRODYNAMIC MIXED CONVECTION FROM A VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM

Magnetohydrodynamic mixed convection flaw about a vertical flat plate embedded in a porous medium is considered. The effect of the magnetic field strength on the local Nusselt number and local wait shear stress is presented. The non-Darcian model including both the inertia and boundary effects is used. A particular transformation for the governing equations is adopted to cover the whole mixed convection regime within two finite limits. Appreciable effects of the magnetic field strength on the local Nusselt number as well as on the local wall shear stress in the mixed convection regime are found.     

BUOYANT CONVECTION IN A SQUARE CAVITY PARTIALLY FILLED WITH A HEAT-GENERATING POROUS MEDIUM

Steady-state buoyant convection in a rectangular cavity, partially filled with a fluid-saturated porous medium with spatially uniform internal heat generation, is considered. The Brinkman-extended Darcy model in the porous region is adopted. The overall Rayleigh number is large to render a boundary-layer-type global flow pattern. Scale analysis is performed to obtain a rudimentary understanding of the flow characteristics. In parallel with the theoretical endeavors, numerical solutions are secured over broad ranges of nondimensional parameters. The results indicate that there exists an asymptotic convection regime where the flow is nearly independent of the permeability and conductivity of the porous medium. The effect of the thermal conductivity of porous material is appreciable in the intermediate regime. In the conduction-dominant regime, the porous region acts like a heat-generating solid block. The numerical study gives credence to the reliability of the theoretical arguments.