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This paper presents a simple computational procedure for the laminar, fully established velocity and temperature in straight ducts with irregular, singly connected cross‐sections by virtue of a control volume discretization of the momentum and energy equations in boundary‐fitted co‐ordinate systems. The combined procedure has been applied to a large group of ducts whose cross‐sections possess different levels of difficulty. The numerical predictions for the pressure drop (friction factor) and the convective heat transfer coefficient (Nusselt number) have been reported for a sub‐class of ducts with curved sides and sharp corners utilizing various grid sizes.

Presents four examples which were researched in a large eddy simulation (LES) of turbulence for engineering applications. Explains that, in the former two cases, developments of the advanced LES are indicated in a Smagorinsky model and in the treatments of the wall and the external boundary, and, in the later cases, the LES on the boundary fitted grids are applied using the finite different method (FDM) and the finite element method (FEM), where new numerical treatments, a composite grid technique and a modified scheme, are adopted for efficient calculations. Evaluates the results, and discusses the possible application of the LES for engineering problems.

A finite difference simulation for the bulk single crystal growth of indium phosphide by the liquid encapsulated vertical gradient freezing (LE‐VGF) method with a flat bottom crucible is presented. In order to treat a curvature interface, the boundary fixing method is applied. The transient behavior of the flow and temperature fields, the melt/crystal interface shape and the growth rate during growth are studied numerically. The crystal growth rate is not constant although the temperature lowering rate is constant. The effect of crucible thickness, thermal conductivity of the crucible and temperature of the growth furnace wall on the crystal growth behavior are discussed.

The purpose of the present study is to investigate the flow and turbulence characteristics of a turbulent wall jet flowing over a surface inclined with the horizontal and to investigate the effect of variation of the angle of inclination of the wall on the flow structure of the wall jet.

The high Reynolds number two-equation κ− model with standard wall function is used as the turbulence model. The Reynolds number considered for the present study is 10,000. The Reynolds averaged Navier-Stokes (RANS) equations are used for predicting the turbulent flow. A staggered differencing technique employing both contravariant and Cartesian components of velocity has been applied. Results for distribution of wall static pressure and skin friction, decay of maximum streamwise velocity, streamwise variation of integral momentum and energy flux have been compared for the cases of α=0°, 5°, and 10°.

Flow field has been represented in terms of streamwise and lateral velocity contours, static pressure contour, vorticity contour and streamwise velocity and static pressure profiles at different locations along the oblique offset plate. Distribution of Reynolds stresses in terms of spanwise, lateral and turbulent shear stresses, and turbulent kinetic energy and its dissipation rate have been presented to describe the turbulent characteristics. Similarity of streamwise velocity and the velocity parallel to the oblique wall has been observed in the developed region of the wall jet flow. A decaying trend is observed in the variation of total integral momentum flux in the developed region of the wall jet which becomes more evident with increase in oblique angle. Developed flow region has indicated trend of similarity in profiles of streamwise velocity as well as velocity component parallel to the oblique wall. A depression in wall static pressure has been observed near the nozzle exit when the wall is inclined and the depression increases with increase in inclination. Effect of variation of oblique angles on skin friction coefficient has indicated that it decreases with increase in oblique angle. Growth of the outer and inner shear layers and spread of the jet shows linear variation with distance along the oblique wall. Decay of maximum streamwise velocity is found to be unaffected by variation in oblique angle except in the far downstream region. The streamwise variation of spanwise integral energy shows increase in oblique angle and decreases the magnitude of energy flux through the domain. In the developed flow region, streamwise variation of centreline turbulent intensities shows increased values with increase in oblique angle, while turbulence intensities along the jet centreline in the region X<12 remain unaffected by change in oblique angles. Normalized turbulent kinetic energy distribution highlights the difference in turbulence characteristics between the wall jet and reattached offset jet flow. Near wall velocity distribution shows that the inner region of boundary layer of the developed oblique wall jet follows a logarithmic profile, but it shows some difference from the standard logarithmic curve of turbulent boundary layers which can be attributed to an increase in skin friction coefficient and a decrease in thickness of the wall attached layer.

The study presents an in-depth investigation of the interaction between the jet and the inclined wall. It is shown that due to the Coanda effect, the jet follows the nearby wall. The findings will be useful in the study of combined flow of wall jet and offset jet and dual offset jet on oblique surfaces leading to a better design of some mechanical jet flow devices.

In this paper new cubic v‐splines monotonic one‐dimensional profiles are presented, for the finite volume solution of convection‐diffusion problems. By studying the profile in normalized variables, some weight functions have been determined for the profile. Being free of the requirement that the volumes be equal, the volume size can be reduced where needed. Numerical properties of the proposed method were formally analysed and are confirmed by numerical examples included here.

The present investigation is an extension of the authors’ previous work on ducts with different cross sections. It concerns application of turbulence models for forced convective heat transfer in three‐dimensional corrugated or wavy ducts. Different wavy ducts with fully developed flow and temperature fields are considered. The numerical approach is based on the finite volume technique with a non‐staggered grid arrangement. For handling the pressure‐velocity coupling the SIMPLEC‐algorithm is used. Cyclic boundary conditions are imposed in the main flow direction to achieve fully developed conditions. The non‐linear k‐ε model of Speziale with wall functions is used to calculate the turbulent stresses. The simple eddy diffusivity concept is applied to calculate the heat fluxes, but the GGDH and the WET methods are also used in some cases. The influence of the geometry parameters and comparison between different ducts are presented in terms of the friction factor and average Nusselt number. In particular the secondary velocity field and the cross sectional temperature distributions are investigated.

This paper describes how non‐orthogonal geometric models may be transformed into orthogonal polyhedral models. The main purpose of the transformation is to obtain a geometric model that is easy to describe and further modify without loss of topological information from the original model.

The transformation method presented in this paper is based on fuzzy logic (FL). The idea of using FL for this type of transformation was first described by Takahashi and Shimizu. This paper describes both philosophy and techniques behind the transformation method as well as its application to some example 2D and 3D models. The problem in this paper is to define a transformation technique that will change a non‐orthogonal model into a similar orthogonal model. The orthogonal model is unknown at the start of the transformation and will only be specified once the transformation is complete. The model has to satisfy certain conditions, i.e. it should be orthogonal.

The group of non‐orthogonal models that contain triangular faces such as tetrahedra or pyramids cannot be successfully recognized using this method. This algorithm fails to transform these types of problem because to do so requires modification of the structure of the model. It appears that only when the edges are divided into pieces and the sharp angles are smoothed then the method can be successfully applied. Even though the method cannot be applied to all geometric models many successful examples for 2D and 3D transformation are presented. Orthogonal models with the same topology, which make them easier to describe, are obtained.

This transformation makes it possible to apply simple algorithms to orthogonal models enabling the solution of complex problems usually requiring non‐orthogonal models and more complex algorithms.

To improve flow solutions on meshes with cells/elements which are distorted/ non‐orthogonal.

The cell‐centred finite volume (FV) discretisation method is well established in computational fluid dynamics analysis for modelling physical processes and is typically employed in most commercial tools. This method is computationally efficient, but its accuracy and convergence behaviour may be compromised on meshes which feature cells with non‐orthogonal shapes, as can occur when modelling very complex geometries. A co‐located vertex‐based (VB) discretisation and partially staggered, VB/cell‐centred (CC), discretisation of the hydrodynamic variables are investigated and compared with purely CC solutions on a number of increasingly distorted meshes.

The co‐located CC method fails to produce solutions on all the distorted meshes investigated. Although more expensive computationally, the co‐located VB simulation results always converge whilst its accuracy appears to grace‐fully degrade on all meshes, no matter how extreme the element distortion. Although the hybrid, partially staggered, formulations also allow solutions on all the meshes, the results have larger errors than the co‐located vertex based method and are as expensive computationally; thus, offering no obvious advantage.

Employing the ability of the VB technique to resolve the flow field on a distorted mesh may well enable solutions to be obtained on complex meshes where established CC approaches fail

This paper investigates a range of cell centred, vertex based and hybrid approaches to FV discretisation of the NS hydrodynamic variables, in an effort characterize their capability at generating solutions on meshes with distorted or non‐orthogonal cells/elements.

This paper aims to investigate the thermal performance involving larger heating rate, targeted heating, heating with least non-uniformity of the spatial distribution of temperature and larger penetration of heating within samples vs shapes of samples (circle, square and triangular).

Galerkin finite element method (GFEM) with adaptive meshing in a composite domain (free space and sample) is used in an in-house computer code. The finite element meshing is done in a composite domain involving triangle embedded within a semicircular hypothetical domain. The comparison of heating pattern is done for various shapes of samples involving identical cross-sectional area. Test cases reveal that triangular samples can induce larger penetration of heat and multiple heating fronts. A representative material (beef) with high dielectric loss corresponding to larger microwave power or heat absorption in contrast to low lossy samples is considered for the current study. The average power absorption within lossy samples has been computed using the spatial distribution and finite element basis sets. Four regimes have been selected based on various local maxima of the average power for detailed investigation. These regimes are selected based on thin, thick and intermediate limits of the sample size corresponding to the constant area of cross section, Ac involving circle or square or triangle.

The thin sample limit (Regime 1) corresponds to samples with spatially invariant power absorption, whereas power absorption attenuates from exposed to unexposed faces for thick samples (Regime 4). In Regimes 2 and 3, the average power absorption non-monotonically varies with sample size or area of cross section (A_c) and a few maxima of average power occur for fixed values of A_c involving various shapes. The spatial characteristics of power and temperature have been critically analyzed for all cross sections at each regime for lossy samples. Triangular samples are found to exhibit occurrence of multiple heating fronts for large samples (Regimes 3 and 4).

Length scales of samples of various shapes (circle, square and triangle) can be represented via Regimes 1-4. Regime 1 exhibits the identical heating rate for lateral and radial irradiations for any shapes of lossy samples. Regime 2 depicts that a larger heating rate with larger temperature non-uniformity can occur for square and triangular-Type 1 lossy sample during lateral irradiation. Regime 3 depicts that the penetration of heat at the core is larger for triangular samples compared to circle or square samples for lateral or radial irradiation. Regime 4 depicts that the penetration of heat is still larger for triangular samples compared to circular or square samples. Regimes 3 and 4 depict the occurrence of multiple heating fronts in triangular samples. In general, current analysis recommends the triangular samples which is also associated with larger values of temperature variation within samples.

GFEM with generalized mesh generation for all geometries has been implemented. The dielectric samples of any shape are surrounded by the circular shaped air medium. The unified mesh generation within the sample connected with circular air medium has been demonstrated. The algorithm also demonstrates the implementation of various complex boundary conditions in residuals. The numerical results compare the heating patterns for all geometries involving identical areas. The thermal characteristics are shown with a few generalized trends on enhanced heating or targeted heating. The circle or square or triangle (Type 1 or Type 2) can be selected based on specific heating objectives for length scales within various regimes.