Numerical investigation of non-isothermal phase change phenomena in vertical Bridgman crystal growth

The non-isothermal phase change phenomena during the vertical Bridgman growth process for HgCdTe are numerically investigated using an interface capturing finite element scheme. The influence of the growth parameters such as Bi, Ste, U and the flow parameters including Gr_T and Gr_S on the non-isothermal phase change phenomena are obtained. Some new features about the melt/crystal interface shape, the temperature field near the interface and the flow field are revealed by comparing the non-isothermal phase change with the isothermal phase change. Furthermore, the comparison of the non-isothermal interfacial characteristics between the pure diffusion, the natural convection and the double-diffusive convection is made and the obvious differences are presented.     

Local heat transfer distribution on a smooth flat plate impinged by a slot jet

Experimental investigation of local heat transfer distribution on a smooth flat plate impinged by a normal slot jet is conducted. Present study concentrates on the influence of jet-to-plate spacing (z/b) and Reynolds number on the fluid flow and heat transfer distribution. A single slot jet with an aspect ratio (l/b) of about 50 is chosen to get the fully developed flow at the nozzle exit. Reynolds number based on slot width is varied from 4200 to 12,000 and jet-to-plate spacing (z/b) is varied from 0.5 to 12. The local heat transfer coefficients are estimated from the thermal images obtained from infrared thermal imaging camera. Measurement for the static wall pressure is carried out for various jet-to-plate spacings at a Reynolds number of 12,000. Normalized value of turbulence and velocity are measured using hot wire anemometer along the streamwise direction (x/b) for jet-to-plate spacings (z/b) of 1, 2, 4, 6, 8, 10 and 12. The entire flow field is divided into three regimes namely stagnation region (laminar boundary layer associated with favorable pressure gradient), transition region (associated with increase in turbulence intensities and heat transfer) and turbulent wall jet region. Semi-empirical correlation for the Nusselt number in the stagnation region is proposed. Heat transfer characteristics in the transition region are explained based on the fluid dynamic behavior from the hot wire measurements. Semi-empirical correlation for the Nusselt number in the wall jet region is presented using the velocity profile obtained from the hot wire measurements.     

Mist film cooling simulation at gas turbine operating conditions

Air film cooling has been successfully used to cool gas turbine hot sections for the last half century. A promising technology is proposed to enhance air film cooling with water mist injection. Numerical simulations have shown that injecting a small amount of water droplets into the cooling air improves film-cooling performance significantly. However, previous studies were conducted at conditions of low Reynolds number, temperature, and pressure to allow comparisons with experimental data. As a continuous effort to develop a realistic mist film cooling scheme, this paper focuses on simulating mist film cooling under typical gas turbine operating conditions of high temperature and pressure. The mainstream flow is at 15 atm with a temperature of 1561 K. Both 2D and 3D cases are considered with different hole geometries on a flat surface, including a 2D slot, a simple round hole, a compound-angle hole, and fan-shaped holes. The results show that 10–20% mist (based on the coolant mass flow rate) achieves 5–10% cooling enhancement and provides an additional 30–68 K adiabatic wall temperature reduction. Uniform droplets of 5–20 μm are used. The droplet trajectories indicate the droplets tend to move away from the wall, which results in a lower cooling enhancement than under low pressure and temperature conditions. The commercial software Fluent is adopted in this study, and the standard k–ε model with enhanced wall treatment is adopted as the turbulence model.     

Modeling of heat transfer and fluid flow characteristics of helicoidal double-pipe heat exchangers using Adaptive Neuro-Fuzzy Inference System (ANFIS)

In this paper an Adaptive Neuro-Fuzzy Inference System (ANFIS) is used for modeling the effect of important parameters on heat transfer and fluid flow characteristics of helicoidal double-pipe heat exchangers using some numerically investigated and compared with those to experimental results for training and test data. In this way, overall heat transfer coefficient (U_o) and inner and annular pressure drop (ΔP_in, ΔP_an) are modeled with respect to the variation of inner and annular dean number (De_in, De_an), inner and annular Prandtl number (Pr_in, Pr_an) and pitch of coil (B) which are defined as input (design) variables. Then, we divided these data into train and test sections in order to accomplish modeling. We instructed ANFIS network by 75% of numerical-validated data. Twenty-five percent of primary data which had been considered for testing the appropriateness of the models was entered into ANFIS network models and results were compared by two statistical criterions (R², RMSE). Considering the results, it is obvious that our proposed modeling by ANFIS is efficient and valid and it can be expanded for more general states.     

Simulations of post-filling process considering the cooling effect of the mold cooling systems

Simulation of the post-filling process has been developed and performed to study the compressible polymer melt flow during the packing phase and the pressure development inside the mold cavity for the entire post-filling process. A mixed finite-element/finite-difference numerical scheme is implemented to solve the non-isothermal, compressible viscous flow equations. The transient, non-isothermal mold cavity surface temperatures which depend on the mold cooling channel arrangement and coolant flow conditions are also incorporated during simulation using hybrid finite-element/shape-factor method. It has been found that the difference in the pressure profile variation during the post-filling stage is quite distinguished for cases assuming constant mold wall temperature and cases with the consideration of the cooling effect of the cooling system configuration.     

Thermal transport phenomena over a slot-perforated flat surface in pulsating free stream

A theoretical study is performed to investigate unsteady, two-dimensional, incompressible thermal-fluid flow over both sides of a slot-perforated flat surface, which is placed in a pulsating free stream. The effects of the pulsating Strouhal number, the Reynolds number Re, and the ratio of the slot width, d, to the plate thickness, δ, on the heat transfer performance and the velocity and thermal fields are disclosed. It is found from the study that: (i) when the free stream is pulsated, the alternating change in the fluid flow disturbs the thermal boundary layer formed along the plate and induces mixing of the upper and lower streams of the plate downstream from the slot, resulting in an amplification of heat-transfer performance; (ii) heat-transfer performance at the rear plate is induced with an increase in d/δ and Re; and (iii) heat transfer performance is intensified with an increase in fSr.     

A complete two-phase model of a porous cathode of a PEM fuel cell

This paper has developed a complete two-phase model of a proton exchange membrane (PEM) fuel cell by considering fluid flow, heat transfer and current simultaneously. In fluid flow, two momentum equations governing separately the gaseous-mixture velocity (u_g) and the liquid-water velocity (u_w) illustrate the behaviors of the two-phase flow in a porous electrode. Correlations for the capillary pressure and the saturation level connect the above two-fluid transports. In heat transfer, a local thermal non-equilibrium (LTNE) model accounting for intrinsic heat transfer between the reactant fluids and the solid matrices depicts the interactions between the reactant-fluid temperature (T_f) and the solid-matrix temperature (T_s). The irreversibility heating due to electrochemical reactions, Joule heating arising from Ohmic resistance, and latent heat of water condensation/evaporation are considered in the present non-isothermal model. In current, Ohm's law is applied to yield the conservations in ionic current (i_m) and electronic current (i_s) in the catalyst layer. The Butler–Volmer correlation describes the relation of the potential difference (overpotential) and the transfer current between the electrolyte (such as Nafion™) and the catalyst (such as Pt/C).     

Isothermal and non-isothermal oil–water flow and viscous fingering in a porous medium

Immiscible flow of heavy oil in a porous formation by high temperature pressurized water has been numerically studied. The physical region is a square domain in the horizontal plane with low and high pressure points at the opposite corners along one of the diagonals. Water, the invading fluid, when introduced at high pressure displaces the in situ oil towards the low pressure production zone. The extent of displacement of oil by water through the porous medium in a given amount of time and the appearance of preferential flow paths ( fingers) is the subject of the present investigation. The resistance to water–oil movement arises from the viscous forces in the fluid phases and the capillary force at their interface. Based on their relative magnitudes, various forms of displacement mechanisms can be realized. As the viscosity ratio of heavy oil to water is large, viscous forces in the oil phase become dominant and constitute the major factor for controlling the flow distortions in the porous formation. A mathematical model that can treat the individual fluid pressures, capillary effects and heat transfer has been employed in the present work. A fully implicit, two-dimensional numerical model has been used to compute the pressure and temperature fields. The domain decomposition technique has been adopted in the numerical solution since the problem is computationally intensive. Naturally occurring oil-rich reservoirs to which the present study is applicable are inhomogeneous and layered. A qualitative study has been carried out to explore the effect of permeability variations on the flow patterns. Numerical calculations show that non-isothermal effects as well as layering promote the formation of viscous fingers and consequently the sweep efficiency of the high pressure water front.     

Numerical analysis of heat transfer due to slot jets impingement onto two cylinders with different diameters

A numerical investigation has been performed two-dimensional slot impingement onto two heated cylinders with different diameters turbulent flow conditions. Height of slot jet is taken as constant for all cases. The study is performed to see the effects of effective parameters on heat and fluid flow as jet Reynolds number (11,000 ≤ Re ≤ 20,000), diameter ratio of cylinders (0.5 ≤ D₁/D₂ ≤ 1.5) and ratio of distance between cylinders to slot jet high (L/S). Streamlines, isotherms, local and mean Nusselt numbers and Cd coefficient were obtained. These results were compared with earlier experimental and numerical works and good agreement was obtained. It is found that diameter ratios of cylinders can be a control element for heat and fluid flow.     

The study on polymer melt front,gas front and solid layer in filling stage of gas-assisted injection molding

The algorithms are developed to predict the polymer melt front, gas front and solid layer in gas-assisted injection molding. The simulation of two-dimensional, transient, non-isothermal and high viscous flow between two parallel plates with the generalized Newtonian fluid is presented in detail. During solidification while an injection mold fills, a solid-liquid interface moves and a two-phase zone exists; an enthalpy model is used to predict this interface in the two-phase flow problem. The model takes into account the three-phase flow including the effects of the gas front, solid layer and polymer melt front.     

A comparative study of pure and zeotropic mixtures in low-temperature solar Rankine cycle

The paper presents an on site experimental study of a low-temperature solar Rankine cycle system for power generation. The cycle performances of pure fluid M₁ (R245fa) and zeotropic mixtures M₂ (R245fa/R152a, 0.9/0.1) and M₃ (R245fa/R152a, 0.7/0.3) are compared, respectively, based on the experimental prototype. The experiments have been conducted under constant volume flow rate of different fluids. The results show that, with the component of R152a increasing, the system pressure level increases and the power output varies accordingly, which provides an additional means of capacity adjustment. The collector efficiency and thermal efficiency of zeotropic mixtures are comparatively higher than pure fluid of R245fa in the experimental condition, which indicates that zeotropic mixtures have the potential for overall efficiency improvement. Due to the non-isothermal condensation of zeotropic mixture, the condensing heat could be partially recovered by adding an external heat exchanger. Thus, compared with pure fluid R245fa the system overall efficiency of zeotropic mixtures could be improved.     

Non-isothermal flow of a polymeric fluid past a submerged circular cylinder

In this paper, non-isothermal flow of a polymeric liquid past a circular cylinder in an infinite domain is investigated numerically. A non-Newtonian fluid, known as a differential-type White-Metzner model, is used in the flow simulation. The computer code developed is based on the elastic-viscous split-stress finite element method incorporating the streamline-upwind Petrov-Galerkin scheme. Numerical solutions for several cases are obtained. Global flow characteristics, such as drag coefficient and heat transfer coefficient, are derived. The effects of fluid elasticity, inertia, and shear-thinning on drag and heat transfer are also investigated.     

Multiple slot suction/injection into an exponentially decreasing free stream flow

An analysis is performed to obtain the non-similar solution of a steady incompressible laminar boundary layer flow for an exponentially decreasing free stream velocity with non-uniform multiple slot injection (suction). The difficulties in obtaining the non-similar solutions at the starting point of the stream-wise coordinate, at the edges of the slot and at the point of separation are overcome by applying an implicit finite difference scheme in combination with the quasi-linearization technique and an appropriate selection of the finer step sizes along the stream-wise direction. Results are presented for ? = 0.001 and for different values of mass transfer parameter, − 0.075 ≤ A ≤ 1.0. It is observed that the separation can be delayed by non-uniform multiple slot suction and also by moving the slots downstream but the effect of non-uniform multiple slot injection is just reverse.     

The creeping flow of a polymeric fluid through bent square ducts with heat dissipation

The 3D non-isothermal creeping flow of nylon-6 in a bent square duct with uniform temperature is studied numerically. The non-Newtonian characteristics of this fluid polymer are represented by a differential-type non-isothermal White-Metzner model. Computational results are obtained by the elastic-viscous split-stress (EVSS) finite element method, incorporating the streamline-upwind Petrov-Galerkin (SUPG) scheme. The generated thermal field is entirely due to viscous heating. Essential flow characteristics, including temperature distribution in the flow field, are predicted. The resulting average Nusselt numbers along the walls are obtained. Subsequently, the effects of flow-rate and geometry are investigated.     

Numerical investigation of developing convective heat transfer in a rotating helical pipe

Numerical simulation is carried out for heat transfer characteristics of flow in rotating helical pipes. A good agreement has been achieved compared with experimental data from literature. The impacts of both co-rotation and counter rotation on local heat transfer enhancement are discussed in detail. Different developing modes of heat transfer enhancement in laminar and transitional regions are observed. Streamwise variation of circumferential distribution of heat transfer enhancement by rotation exhibits sensitivity to rotation speed, rotation direction and curvature ratio. Within the range of De and Ro under discussion, the impact of streamwise inertial force is the major factor of heat transfer enhancement for co-rotational cases while the effect of reversed flow and accompanied Dean vortex for counter rotational cases cannot be neglected.     

A numerical study of unidirectional solidification of a binary metal alloy under influence of a rotating magnetic field

In this paper we present a numerical study of the fluid flow during directional solidification of a binary alloy (Pb85wt%Sn) in presence of a forced convection. The latter is driven by a rotating magnetic field (RMF) the strength of which, expressed by the magnetic Taylor number, varies between 10⁴ < Ta < 2 × 10⁶. The focus of this paper is the problem when cooling starts simultaneously with the acceleration of the melt from a state of rest. Thus, we study the interference of the so-called spin-up problem with the solidification of the melt. The numerical simulations are based on a mixture model formulation. We show that three distinct fluid flow phases exist. During the first two phases (initial adjustment and inertial phase) the acceleration of the liquid takes place which occurs in close similarity to the isothermal spin-up [P.A. Nikrityuk, M. Ungarish, K. Eckert, R. Grundmann, Spin-up of a liquid metal flow driven by a rotating magnetic field in a finite cylinder. A numerical and analytical study, Phys. Fluids 17 (2005) 067101]. The third phase is characterized by a braking of the fluid flow due to the progressive solidification increasing the aspect ratio of the liquid (2R₀/H_l) and decreasing the forcing. We show that as soon as the velocity of the secondary flow exceeds the velocity of the solidification front, a convex shape of the mushy zone can be observed. In parallel, Taylor–Görtler vortices advected by the secondary flow towards the mushy zone might impose a wavy substructure on the latter. At the end, predictions with respect to heat flux and macrosegregations are given.     

A simple model for evaluation of contribution factors to skin melt formation in gas-assisted injection molding

A simple formulation based on a non-isothermal power-law fluid model was derived in order to evaluate the effect of various processing parameters as well as melt rheological behavior on the skin melt formation during gas-assisted injection molding. From this model, effect of molding conditions including melt temperature, mold temperature, delay time and gas injection pressure as well as shear-thinning behavior of polymer melt on the formation of skin melt thickness was numerically evaluated in a quasi-quantitative manner. Calculated results from this model predict similar dependence of skin thickness variation on contributing parameters as those observed from experiments. The analysis also indicates that the transient nature of melt flow caused by gas penetration may exist in actual molding process.     

Conjugate heat transfer analysis of a heat generating vertical plate

This paper mainly deals with conjugate heat transfer problem pertinent to rectangular fuel element of a nuclear reactor dissipating heat into an upward moving stream of liquid sodium. Introducing boundary layer approximations, the equations governing the flow and thermal fields in the fluid domain are solved simultaneously along with two-dimensional energy equation in the solid domain by satisfying the continuity of temperature and heat flux at the solid–fluid interface. The boundary layer equations are discretized using fully implicit finite difference scheme so as to adopt marching technique solution procedure, while second-order central difference scheme is employed to discretize the energy equation in the solid domain and the resulting system of finite difference equations are solved using Line-by-Line Gauss–Seidel iterative solution procedure. Numerical results are presented for a wide range of parameters such as aspect ratio, A_r, conduction–convection parameter, N_cc, heat generation parameter, Q, and flow Reynolds number, Re. It is concluded that there exist an upper or a lower limiting value of these parameters above or below which the temperature in the fuel element crosses its allowable limit. It is also found that an increase in Re results in considerable increase in overall heat dissipation rate from the fuel element.     

Numerical study of stratified oil-water two-phase turbulent flow in a horizontal tube

Stratified oil-water two-phase turbulent flow in a horizontal tube is numerically simulated using a volume of fluid model. A single momentum equation is solved throughout the domain. The RNG k-ε model combined with a near-wall low-Re turbulence model is applied to each phase, and a continuum surface force approximation is adopted for the calculation of surface tension. The simulation is performed in a time-dependent way and the final solution which corresponds to steady-state flow is analyzed. Results of pressure loss, slip ratio, local phase fraction profile and the axial velocity profile are verified by experimental data in literature. Based on the numerical results of extensive calculations, the flow field characteristics are explored and correlations for pressure loss and hold-up are presented.     

Formulation of fully implicit method for simulation of flows with interfaces using primitive variables

This paper is concerned with simulation of flows with interface between two incompressible and immiscible fluids on a fixed grid using what is called the single fluid formalism. This formalism views flow of two fluids as that of a single fluid whose density and viscosity change abruptly at the interface. The location of the interface is apriori not known but is to be discovered as part of the solution. Problems of this type are typically solved using an equation for (a) Volume Fraction or, for (b) Level Set function. In the present paper, the governing Navier–Stokes equations in primitive variables are solved on collocated grids using SIMPLE algorithm with a specially derived smoothing pressure correction that satisfies volume conservation. A superficial density is defined and determined from mass conservation equation. It is shown that this equation can be cast in the form of a well-known volume fraction equation. The interface location is determined without interface reconstruction. The convective terms are represented by a TVD scheme to predict less-smeared interface. The surface tension force is evaluated by two methods via geometric and fluid dynamic evaluation of the interface curvature.