A LOCALLY IMPLICIT SCHEME FOR TURBULENT FLOWS ON DYNAMIC MESHES

A locally implicit scheme with an anisotropic dissipation model is developed on dynamic quadrilateral-triangular meshes. The unsteady Favre-averaged Navier-Stokes equations with moving domain effects and a low-Reynolds-number k  ? ε turbulence model are solved to study turbulent flows over vibrating blades with negative interblade phase angle. A treatment of viscous flux on quadrilateral-triangular mesh is also presented. To assess the accuracy of the locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, the turbulent flow around an NACA 0012 airfoil is investigated. Based on the comparison with the experimental data, the accuracy of the present approach is confirmed. From the distributions of magnitude of the first harmonic dynamic pressure difference coefficient which includes the present solution and the related experimental and numerical results, it is found that the present solution approach is reliable and acceptable. The unsteady flow behaviors for turbulent flows over vibrating blades with negative interblade phase angle are demonstrated.     

Coupled Turbulent Flow,Heat, and Solute Transport in Continuous Casting Processes with an Electromagnetic Brake

ABSTRACT

This study describes the numerical modeling of coupled turbulent fluid flow, heat, and solute transport in a continuous slab caster with an electromagnetic brake (EMBr). Transport equations of total mass, momentum, energy, and species for a binary iron–carbon alloy system are solved using a continuum model. The turbulent effects are taken into account using the standard k–? equations, where coefficients are appropriately modified for phase change. The electromagnetic field is described by Maxwell equations. A finite-volume method is employed to solve the conservation equations associated with appropriate boundary conditions. The process variables considered are the casting speed, magnetic flux density, and carbon segregation. The effects of these process variables on the velocity, temperature, and solute distributions are reported and discussed.     

A FULL 3-DIMENSIONAL ADAPTIVE FINITE VOLUME SCHEME FOR TRANSPORT AND PHASE-CHANGE PROCESSES,PART I: FORMULATION AND VALIDATION

A full three-dimensional (3-D) numerical formulation for accurate simulation of transport and phase-change processes is presented. These processes are characterized by a variety of flow and heat transfer mechanisms in irregular domains with or without the movement of phase-change interfaces and free surfaces. A generalized 3-D nonorthogonal curvilinear finite volume formulation is developed in conjunction with a robust mesh generation scheme known as multizone adaptive grid generation (MAGG) to tackle such problems. The coupling between the interfacial dynamics and transport phenomena in the bulk of the phases is inherent in this formulation. A 3-D k-epsilon model is also incorporated to tackle the turbulent flows in these applications. The unified numerical model is validated against classical 3-D problems such as turbulent natural convection in a differentially heated cube, solidification in a cavity, and so on. In a companion paper, Part II (see this issue), application of this formulation to 3-D simulation of hydrothermal crystal growth and low and high pressure Czochralski (Cz) crystal growth is presented.     

Thermal transport phenomena of turbulent jet diffusion flames by means of anisotropic k–ϵ–t2–ϵt model

A numerical study is performed on transport phenomena in a turbulent jet diffusion flame of hydrogen from a vertical circular nozzle. An anisotropic k–ϵ–t² –ϵ_t model and the eddy‐dissipation model are employed to simulate thermal fluid flow and combustion phenomena, respectively. The governing boundary‐layer equations are discretized by means of a control volume finite‐difference technique and are numerically solved. The model predicts the experimental data in the existing literature. It is found from the study that (i) the model employed here can be applied to combustion phenomenon, and (ii) the presence of flame enhances the anisotropy of turbulence and causes a substantial attenuation in the turbulent kinetic energy, that is, most turbulent kinetic energy in the flame in the downstream part is laden exclusively in the streamwise fluctuation. Copyright © 1999 John Wiley & Sons, Ltd.     

The effects of turbulence on molten pool transport during melting and solidification processes in continuous conduction mode laser welding of copper–nickel dissimilar couple

The melting and solidification stages of a continuous copper–nickel dissimilar metal conduction mode laser welding have been simulated numerically in this study. The heat, mass and momentum transports in molten metal pool have been analysed using both laminar and turbulent flow models separately for the same process parameters. The phase change aspects related to solidification and melting are accounted for by a modified enthalpy–porosity technique while the turbulent transport is modelled by a high Reynolds number k–ε model. It has been observed that temperature fields obtained from both laminar and turbulent transport simulations are qualitatively similar to each other. The molecular thermal diffusivity of the molten metal mixture is found to be in the same order of magnitude as eddy thermal diffusivity, as a result of which the thermal field gets marginally affected by fluid turbulence. By contrast, eddy viscosity remains much greater than molecular viscosity, which leads to greater amount of momentum diffusion in the case of a turbulent molten metal pool, in comparison to that obtained from the corresponding laminar simulation. This is reflected in the reduction in maximum velocity magnitude in the turbulent simulation in comparison to the maximum velocity obtained from laminar simulation. In the case of species transport, the turbulent mass diffusivity is found to be about 10⁷–10⁸ times greater than molecular mass diffusivity. As a result, the species field in turbulent simulation shows characteristics of better mixing between two dissimilar molten metals than the species field obtained using the laminar transport model. The species distribution obtained from turbulent transport is shown to be in better agreement with experimental data reported in literature than the corresponding mass fraction distribution obtained from laminar simulation. It is also found that species distribution in the molten pool is principally determined by advective and diffusive transport during the melting stage and species transport by advection and eddy diffusion in turbulent pool increasingly weakens with decreasing temperature during the cooling following the laser melting stage.     

Turbulence modeling of atmospheric boundary layer flow over complex terrain: a comparison of models at wind tunnel and full scale

The aim of this work is to evaluate the performance of two popular k ? ? turbulence closure schemes for atmospheric boundary layer (ABL) flow over hills and valleys and to investigate the effect of using ABL‐modified model constants. The standard k ? ? and the RNG k ? ? models are used to simulate flow over the two‐dimensional analytical shapes from the RUSHIL and RUSHVAL wind tunnel experiments. Furthermore, the mean turbulent flow over the real complex terrain of Blashaval hill is simulated and the results verified with a data set of full‐scale measurements. In general, all models yield similar results. However, use of ABL‐modified constants in both models tends to decrease the predicted velocity and increase the predicted turbulent kinetic energy. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic and thermal study of air flow control by chicanes with inclined upper parts in solar air collectors

A dynamic and thermal simulation for two-dimensional model is developed on air flow and heat transfer control by chicanes in solar air collectors. New chicane form is adopted with two parts: the first is orthogonal to the air flow direction and the second is titled (α=60°). It is apparent that the turbulence created by introducing chicanes, resulting in greater increase in heat transfer inside the dynamic air vein with a rise of 23%. The effect of the variation of the Reynolds number in the range of 100<Re<4500, on the convective heat transfer coefficient, the pressure drop and Nusselt number are analysed and have shown good agreements with the literature results. Therefore, the mass flow rates effect on the velocity magnitude, temperature and the turbulent intensity is analysed. The Reynolds number variation showed a substantial effect on the mechanism of vortex development and separation phenomenon.     

Flow Field Calculations for Afterburner

Ｆｌｏｗ　Ｆｉｅｌｄ　Ｃａｌｃｕｌａｔｉｏｎｓ　ｆｏｒ　ＡｆｔｅｒｂｕｒｎｅｒＦｌｏｗＦｉｅｌｄＣａｌｃｕｌａｔｉｏｎｓｆｏｒＡｆｔｅｒｂｕｒｎｅｒ￥ＺｈａｏＪｉａｎｘｉｎｇ；ＬｉｕＱｕａｎｚｈｏｎｇ；ＬｉｕＨｏｎｇ（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔ...     

A Study of the Effect of Duct Width on Fully Developed Turbulent Flow Characteristics in a Corrugated Duct

Abstract

In this article, the effect of duct width on fully developed turbulent air flow characteristics in a corrugated duct is investigated numerically. The k-? model is adopted for turbulent closure, and the governing equations in three dimensions are solved using a finite volume technique. The calculations were performed with the width aspect ratio (interwall spacing/channel width) ranging from 0.1 to 1.0, with the Reynolds numbers ranging from about 2000 to 15000, and corrugation angles of 30° and 45°. An experimental study was also performed for pressure drop, velocity, and flow visualization. The detailed predictions are compared with the experimental measurements, and a good agreement between the two is obtained.     

Simulation of Swirling Turbulent Heat Transfer in a Vortex Heat Exchanger

ABSTRACT

This article presents a numerical simulation of swirling turbulent flow and heat transfer in a novel vortex heat exchanger. A new algebraic Reynolds stress/heat flux model (ASM/AFM) is applied to the simulation. The computation is performed under different air flow rates for both swirling and nonswirling flows. The calculated mean heat transfer coefficients on both inner and outer walls of the annular duct are compared with the measured data. They are generally improved over the results predicted by the new ASM/k–? model. The effects of swirl on enhancing heat transfer in the annular duct are illustrated. The heat transfer performance of the vortex heat exchanger under different air flow rates is obtained.     

A numerical study of turbulent flow and conjugate heat transfer in concentric annuli with moving inner rod

A numerical study is conducted to investigate turbulent flow and conjugate heat transfer in a concentric annulus with a heated inner cylinder moving in the streamwise direction. A modified two-equation k-ε model with low Reynolds number treatment near wall is employed to model the Reynolds stress and turbulent thermal field which are based on Boussinesq’s approximation. The governing equations are numerically resolved by means of a hybrid finite analysis method. A uniform inlet flow and thermal conditions are specified to consider the effects of entrance of both solid and fluid regions. For a constant Prandtl number of 6.99 of water flow, calculating results of the time-averaged streamwise velocity, turbulent viscosity and temperature field are obtained for the Reynolds numbers from 1.0 × 10⁴ to 5.0 × 10⁵, rod velocity ratio between 0 and 1.0, and the radius ratio ranging from 0.286 to 0.750. The parametric studies show that the bigger rod speed ratio or the radius ratio is, the temperature is higher within solid rod. For a certain absolute rod speed, temperature profile diminishes at both sides of solid rod and fluid as Reynolds number grows. Numerical results also show that compared with the case of β=0 where solid rod is stationary, for large rod speed ratio the averaged axial velocity and turbulent viscosity profiles have substantial deformations, that is, the gradient of averaged axial velocity and turbulent viscosity near rod surface greatly reduced by the axial movement of solid rod.     

NUMERICAL SIMULATIONS ON THE HYDRODYNAMICS OF A TURBULENT SLOT JET IMPINGING ON A SEMICYLINDRICAL CONVEX SURFACE

This study presents the numerical simulations of flow characteristics of a turbulent slot jet impinging on a semicylindrical convex surface. The turbulent-governing equations are solved by a control-volume-based finite difference method with power-law scheme, and the well-known k  ? ε turbulence model associated with the wall function is used to describe the turbulent behavior and structure.

While the width of the slot nozzle is fixed at 9.38 mm, the diameter of the semicylinder is at 150 mm, and air is the working medium, the adopted modifying parameters here include the Reynolds number of the inlet flow (Re = 6000 ~ 20000), jet to impingement surface spacing (y / w = 7 ~ 13), and the entrainment or wall boundary is employed nearby the convex surface. The numerical simulations of flow fields indicate that the velocity distribution of the free jet region departs from the center with increasing y / w. When we increase Reynolds number Re, the variation of the velocity on the convex surface becomes rapid, and the turbulent kinetic energy increases.     

Numerical investigation on heat transfer of supercritical water in a roughened tube

ABSTRACT

The turbulent mixed convection heat transfer of supercritical water flowing in a vertical tube roughened by V-shaped grooves has been numerically investigated in this paper. The turbulent supercritical water flow characteristics within different grooves are obtained using a validated low-Reynolds number κ-ε turbulence model. The effects of groove angle, groove depth, groove pitch-to-depth ratio, and thermophysical properties on turbulent flow and heat transfer of supercritical water are discussed. The results show that a groove angle γ = 120° presents the best heat transfer performance among the three groove angles. The lower groove depth and higher groove pitch-to-depth ratio suppress the enhancement of heat transfer. Heat transfer performance is significantly decreased due to the strong buoyancy force at T_b = 650.6 K, and heat transfer deterioration occurs in the roughened tube with γ = 120°, e = 0.5 mm, and p/e = 8 in the present simulation. The results also show that the rapid variation in the supercritical water property in the region near the pseudo-critical temperature results in a significant enhancement of heat transfer performance.     

A comparative study of four low-Reynolds-number k-ε turbulence models for periodic fully developed duct flow and heat transfer

ABSTRACT

In this study, streamwise-periodic fully developed turbulent flow and heat transfer in a duct is investigated numerically. The governing equations are solved by using the finite-control-volume method together with nonuniform staggered grids. The velocity and pressure terms of the momentum equations are solved by the SIMPLE algorithm. A cyclic tri-diagonal matrix algorithm (TDMA) is applied in order to increase the convergence rate of the numerical solution. Four versions of the low-Reynolds-number k-ε model are used in the analysis: Launder-Sharma (1974), Lam-Bremhorst (1981), Chien (1982), and Abe-Kondoh-Nagano (1994). The results obtained using the models tested are analyzed comparatively against some experimental results given in the literature. It is discussed that all the models tested failed in the separated region just behind the ribs, where the turbulent stresses are underpredicted. The local Nusselt numbers are overpredicted by all the models considered. However, the Abe-Kondoh-Nagano low-Re k-ε model presents more realistic heat transfer predictions.     

Numerical modelling in wave energy conversion systems

This paper deals with a numerical modelling devoted to predict the flow characteristics in the components of an oscillating water column (OWC) system used for the wave energy capture. In the present paper, the flow behaviour is modelled by using the FLUENT code. Two numerical flow models have been elaborated and tested independently in the geometries of an air chamber and a turbine, which is chosen of a radial impulse type. The flow is assumed to be three-dimensional (3D), viscous, turbulent and unsteady. The FLUENT code is used with a solver of the coupled conservation equations of mass, momentum and energy, with an implicit time scheme and with the adoption of the dynamic mesh and the sliding mesh techniques in areas of moving surfaces. Turbulence is modelled with the k–ε model. The obtained results indicate that the developed models are well suitable to analyse the air flows both in the air chamber and in the turbine. The performances associated with the energy transfer processes have been well predicted. For the turbine, the numerical results of pressure and torque were compared to the experimental ones. Good agreements between these results have been observed.     

Aerodynamic investigation of the shock train in a scramjet with the effects of backpressure and divergent angles

Numerical simulations are carried out to study the effect of divergence angle and adverse pressure gradient on the movement of a shock wave train in a scramjet isolator. The commercial software tool ANSYS Fluent 16 was used to simplify the two-dimensional Reynolds-averaged Navier-Stokes equation with the compressible fluid flow by considering the density-based solver with the standard k-ε turbulence model. The species transport model with a single-step volumetric reaction mechanism is employed. Initially, the simulated results are validated with experimental results available in the open literature. The obtained results show that the variation of the divergence angle and backpressure on the scramjet isolator has greater significance on the flow field. Also, with an increase in the backpressure, due to the intense turbulent combustion, the shock wave train developed should expand along the length and also move towards the leading edge of the isolator leading to a rapid rise in the pressure so that the pressure at the entrance of the isolator can match the enhanced backpressures.     

UNSTRUCTURED GRID FINITE VOLUME ANALYSIS FOR ACOUSTIC AND PULSED WAVE PROPAGATION CHARACTERISTICS IN EXHAUST SILENCER SYSTEMS

Abstract

The unstructured grid finite volume method has been applied to predict the linear and nonlinear attenuation characteristics of the expansion chamber type silencer system. In order to achieve grid flexibility and a solution adaptation for geometrically complex flow regions associated with the actual silencers, the unstructured mesh algorithm in context with the node-centered finite volume method has been employed. The validation cases for the linear and nonlinear wave propagation characteristics include the acoustic field of the concentric expansion chamber and the axisymmetric blast flow field with the open end. Effects of the chamber geometry on the nonlinear wave propagation characteristics are discussed in detail.     

Turbulent fluid flow,heat transfer and onset of nucleate boiling in annular finned passages

An analytical model has been formulated for fully-developed turbulent flow and heat transfer in finned annuli using a modified mixing-length turbulence model. The model accounts for the conjugate heat transfer in the fluid and the solid, and the finite thickness of the fins. Solutions were obtained using the finite element method adopting a mesh that exactly fits the solution domain with fine elements near the solid boundaries. Predictions of the model have been compared with experimental results for smooth and finned annuli with generally good agreement between data and predictions. The model has been extended to predict the conditions at the onset of nucleate boiling using the criterion of Davis and Anderson. Again, these predictions agreed well in magnitude and trend with experimental data of finned annuli.     

Numerical prediction of performance of a low-temperature-differential gamma-type Stirling engine

Abstract

In this study, a numerical simulation model is used to analyze thermodynamic performance of a low temperature-differential gamma-type Stirling engine by adjusting some values of the operating and geometrical parameters around a designated baseline case. The influences of these operating and geometrical parameters on engine performance such as working fluid materials, the stroke of piston and displacer, charged pressure, the heating temperature, and so on, are concerned. A numerical simulation model is established based on turbulent flow assumption and the realizable k – ε model is employed to solve the flow and thermal fields in the engine. In regard to flow in regenerator, Darcy–Forchheimer model was used to depict dynamic behavior of working fluid. Besides, thermal equilibrium model was used for solving the energy equation. Finally, working fluid in the engine undergoes a wide range of pressure and temperature so the effects of temperature and pressure on the viscosity and thermal conductivity of the working fluid are required to include. Thermal conductivity of porous medium matrix is affected by wide range of temperature as well.     

The numerical computation of the evaporative cooling of falling water film in turbulent mixed convection inside a vertical tube

An analysis has been developed for studying the evaporative cooling of liquid film falling inside a vertical insulated tube in turbulent gas stream is presented. Heat and mass transfer characteristics in air–water system are mainly considered. A low Reynolds number turbulence model of Launder and Sharma is used to simulate the turbulent gas stream and a modified Van Driest model suggested by Yih and Liu is adopted to simulate the turbulent liquid film. The model predictions are first compared with available experimental data for the purpose of validating the model. Parametric computations were performed to investigate the effects of Reynolds number, inlet liquid temperature and inlet liquid mass flow rate on the liquid film cooling mechanism. Results show that significant liquid cooling results for the system with a higher gas flow Reynolds number Re, a lower liquid flow rate Γ₀ or a higher inlet liquid temperature T_L0.