International Journal of Numerical Methods for Heat and Fluid Flow

P. Nithiarasu

2008 International Journal of Numerical Methods for Heat and Fluid Flow

doi: 10.1108/09615530810846284

Purpose – This paper aims to present briefly a unified fractional step method for fluid dynamics, incompressible solid mechanics and heat transfer calculations. The proposed method is demonstrated by solving compressible and incompressible flows, solid mechanics and conjugate heat transfer problems. Design/methodology/approach – The finite element method is used for the spatial discretization of the equations. The fluid dynamics algorithm used is often referred to as the characteristic‐based split scheme. Findings – The proposed method can be employed as a unified approach to fluid dynamics, heat transfer and solid mechanics problems. Originality/value – The idea of using a unified approach to fluid dynamics and incompressible solid mechanics problems is proposed. The proposed approach will be valuable in complicated engineering problems such as fluid‐structure interaction and problems involving conjugate heat transfer and thermal stresses.

Ben Q. Li

2008 International Journal of Numerical Methods for Heat and Fluid Flow

doi: 10.1108/09615530810846293

Purpose – The aim of this paper is to determine a parallel computational methodology for simultaneously predicting the macro/micro scale phenomena occurring during solidification processing with external electromagnetic stirring. Design/methodology/approach – Macro and micro phenomena occurring in an electromagnetically‐stirred solidifying melt are simulated using a numerical model that integrates the finite element methodology for transport phenomena and the Monte‐Carlo cellular‐automata method for microstructure formation. Parallel algorithm is introduced to enhance the computational efficiency. Findings – Computed results show that parallel algorithm can be effective in enhancing the computational efficiency of a combined macro/micro model if it is applied appropriately. Also, electromagnetically induced stirring can have a strong effect on the nucleation and grain growth and hence the final solidification microstructure. Originality/value – This paper fulfils a need for developing an efficient numerical methodology to simulate complex electromagnetically‐assisted transport phenomena and microstructure formation during solidification processing systems.

Maher M. Abou Al‐Sood; Madjid Birouk

2008 International Journal of Numerical Methods for Heat and Fluid Flow

doi: 10.1108/09615530810846301

Purpose – The purpose of this paper is to develop a three‐dimensional (3D) numerical model capable of predicting the vaporization rate of a liquid fuel droplet exposed to a convective turbulent airflow at ambient room temperature and atmospheric pressure conditions. Design/methodology/approach – The 3D Reynolds‐Averaged Navier‐Stokes equations, together with the mass, species, and energy conservation equations were solved in Cartesian coordinates. Closure for the turbulence stress terms for turbulent flow was accomplished by testing two different turbulence closure models; the low‐Reynolds number (LRN) k ‐ ϵ and shear‐stress transport (SST). Numerical solution of the resulted set of equations was achieved by using blocked‐off technique with finite volume method. Findings – The present predictions showed good agreement with published turbulent experimental data when using the SST turbulence closure model. However, the LRN k ‐ ϵ model produced poor predictions. In addition, the simple numerical approach employed in the present code demonstrated its worth. Research limitations/implications – The present study is limited to ambient room temperature and atmospheric pressure conditions. However, in most practical spray flow applications droplets evaporate under ambient high‐pressure and a hot turbulent environment. Therefore, an extension of this study to evaluate the effects of pressure and temperature will make it more practical. Originality/value – It is believed that the numerical code developed is of great importance to scientists and engineers working in the field of spray combustion. This paper also demonstrated for the first time that the simple blocked‐off technique can be successfully used for treating a droplet in the flow calculation domain.

M.K.M. Ho; G.H. Yeoh; J.Y. Tu

2008 International Journal of Numerical Methods for Heat and Fluid Flow

doi: 10.1108/09615530810846310

Purpose – This study aims to examine both the population balance approach based on the MUltiple SIze Group (MUSIG) model and the average bubble number density transport equation (ABND) model for 3D, low pressure, gas‐liquid, subcooled boiling, vertical flows. The purpose is to assess the ability of both models to predict the radial profile of void fraction, bubble Sauter mean diameter and interfacial area concentration which characterise subcooled boiling. Design/methodology/approach – Improvement in the ABND model to simulate gas‐liquid bubbly flows with heat transfer was achieved by combining the condensation expression with the gaseous mass transport equation within the CFD commercial code CFX4.4. Findings – Overall, both the ABND model and the MUSIG model provided good results in terms of the above‐mentioned criteria when compared against experimental measurements. However, the ABND model was found to have limitations in predicting high‐subcooled boiling flows due to the lack of bubble size resolution to adequately capture the effect of condensation over a range of bubbles sizes. Originality/value – It is shown that the ABND model provides an economic alternative to the MUSIG model in terms of complexity and computational time, as long as one is aware of the limitations in simulating high‐subcooling flow regimes.

P.J. Coelho; D. Aelenei

2008 International Journal of Numerical Methods for Heat and Fluid Flow

doi: 10.1108/09615530810846329

Purpose – This paper sets out to implement bounded high‐order (HO) resolution schemes in a hybrid finite volume/finite element method for the solution of the radiative transfer equation. Design/methodology/approach – The hybrid finite volume/finite element method had formerly been developed using the step scheme, which is only first‐order accurate, for the spatial discretization. Here, several bounded HO resolution schemes, namely the MINMOD, CLAM, MUSCL and SMART schemes, formulated using the normalized variable diagram, were implemented using the deferred correction procedure. Findings – The results obtained reveal an interaction between spatial and angular discretization errors, and show that the HO resolution schemes yield improved accuracy over the step scheme if the angular discretization error is small. Research limitations/implications – Although the HO resolution schemes reduce the spatial discretization error, they do not influence the angular discretization error. Therefore, the global error is only reduced if the angular discretization error is also small. Practical implications – The use of HO resolution schemes is only effective if the angular refinement yields low‐angular discretization errors. Moreover, spatial and angular refinement should be carried out simultaneously. Originality/value – The paper extends a methodology formerly developed in computational fluid dynamics, and aimed at the improvement of the solution accuracy, to the hybrid finite volume/finite element method for the solution of the radiative transfer equation.

J.J. Pretorius; A.G. Malan; J.A. Visser

2008 International Journal of Numerical Methods for Heat and Fluid Flow

doi: 10.1108/09615530810846338

Purpose – One‐dimensional pipe network flow analysis can be used in many applications to satisfactorily solve various engineering problems. The paper aims to focus on this. Design/methodology/approach – A hybrid nodal method is detailed, which solves the pressure field prior to the elemental flows, and models both compressible gas and incompressible liquid and gas flows. Findings – The results obtained by the algorithm were verified against a number of published benchmark flow problems. The methodology was found to yield accuracy similar or improved, compared with that of others, while being applicable to both incompressible liquid and compressible gas flows. Convergence performance was found to be similar to other hybrid techniques. Originality/value – All flows are modelled via a single governing equation set. In the case of incompressible flow, the method is capable of dealing with both constant and variable cross‐sectional area ducts. The latter includes geometrically complex pipes such as sudden expansions.

H.M. Duwairi; Rebhi A. Damseh

2008 International Journal of Numerical Methods for Heat and Fluid Flow

doi: 10.1108/09615530810846347

Purpose – The aim of this paper is to formulate and analyze thermophoresis effects on mixed convection heat and mass transfer from vertical surfaces embedded in a saturated porous media with variable wall temperature and concentration. Design/methodology/approach – The governing partial differential equations (continuity, momentum, energy, and mass transfer) are written for the vertical surface with variable temperature and mass concentration. Then they are transformed using a set of non‐similarity parameters into dimensionless form and solved using Keller‐box method. Findings – Many results are obtained and a representative set is displaced graphically to illustrate the influence of the various physical parameters. It is found that the increasing of thermophoresis constant or temperature differences enhances heat transfer rates from vertical surfaces and increases wall thermophoresis velocities; this is due to favorable temperature gradients or buoyancy forces. It is also found that the effect of thermophoresis phenomena is more pronounced near pure natural convection heat transfer limit, because this phenomenon is directly temperature gradient‐ or buoyancy forces‐dependent. Research limitations/implications – The predicted results are restricted only to porous media with small pores due to the adoption of Darcy law as a force balance. Originality/value – The paper explains the different effect of thermophoresis on forced, natural and mixed convection heat, and mass transfer problems. It is one of the first works that formulates and describes this phenomenon in a porous media. The results of this research are important for scientific researches and design engineers.

H. Ahmadi‐Noubari; A. Pourshaghaghy; F. Kowsary; A. Hakkaki‐Fard

2008 International Journal of Numerical Methods for Heat and Fluid Flow

doi: 10.1108/09615530810846356

Purpose – The purpose of this paper is to reduce the destructive effects of existing unavoidable noises contaminating temperature data in inverse heat conduction problems (IHCP) utilizing the wavelets. Design/methodology/approach – For noise reduction, sensor data were treated as input to the filter bank used for signal decomposition and implementation of discrete wavelet transform. This is followed by the application of wavelet denoising algorithm that is applied on the wavelet coefficients of signal components at different resolution levels. Both noisy and de‐noised measurement temperatures are then used as input data to a numerical experiment of IHCP. The inverse problem deals with an estimation of unknown surface heat flux in a 2D slab and is solved by the variable metric method. Findings – Comparison of estimated heat fluxes obtained using denoised data with those using original sensor data indicates that noise reduction by wavelet has a potential to be a powerful tool for improvement of IHCP results. Originality/value – Noise reduction using wavelets, while it can be implemented very easily, may also significantly relegate (or even eliminate) conventional regularization schemes commonly used in IHCP.

Sanjay Kumar Khattri

2008 International Journal of Numerical Methods for Heat and Fluid Flow

doi: 10.1108/09615530810846365

Purpose – This paper seeks to develop an adaptive finite volume algorithm, and to present an extensive numerical analysis of it. Design/methodology/approach – The effectiveness of the developed algorithm is demonstrated through practical and computationally challenging problems. The algorithm is tested for a wide range of singularities. Findings – The convergence of the presented algorithm is independent of the regularity of the problems. It is shown that the our algorithm produces more accurate and well conditioned matrix systems. Research limitations/implications – Though the presented algorithm works for extreme singularities on rectangular meshes, it may not be as efficient if the underlying meshes are distorted, and it may not converge. Further research is under way for including the multi‐point approximation technique into the algorithm. Practical implications – Almost all reservoir simulators use the two‐point method, and this algorithm is based on this method. The algorithm can be easily incorporated into the reservoir simulators. The results show that such an implementation will greatly improve the computational efficiency of the simulators. The work is useful for computational scientists, and especially for the researchers in oil industries. The paper reports the numerical work with practical applications. Originality/value – The paper develops an adaptive finite volume algorithm. It is shown that adaptive meshes represent the underlying problem more accurately, and matrix systems associated with adaptive meshes are easier to solve compared with matrix systems associated with uniform meshes.

Hector Iacovides; Mehrdad Raisee

2008 International Journal of Numerical Methods for Heat and Fluid Flow

doi: 10.1108/09615530810846374

Purpose – This paper aims to compute flow and heat transfer through a straight, orthogonally rotating duct, with ribs along the leading and trailing walls, in a staggered arrangement and at an angle of 45° to the main flow direction. Design/methodology/approach – Flow computations have been produced using a 3D non‐orthogonal flow solver, with two two‐layer models of turbulence (an effective‐viscosity model and a second‐moment closure), in which across the near‐wall regions the dissipation rate of turbulence is obtained from the wall distance. Flow comparisons have been carried out for a Reynolds number of 100,000 and for rotation numbers of 0 (stationary) and 0.1. Temperature comparisons have been obtained for a Reynolds number of 36,000, a Prandtl number of 5.9 (water) and rotation numbers of 0 and 0.2 and also at a Prandtl number of 0.7 (air) and a rotation number of 0. Findings – It was found that both two‐layer models returned similar flow and thermal predictions which are also in close agreement with the flow and thermal measurements. The flow and thermal developments are found to be dominated by the rib‐induced secondary motion, which leads to strong span‐wise variations in the mean flow and the local Nusselt number and to a uniform distribution of turbulence intensities across the duct. Rotation causes the development of stronger secondary motion along the pressure side of the duct and also the transfer of the faster fluid to this side. The thermal predictions, especially those of the second‐moment closure, reproduce the levels and most of the local features of the measured Nusselt number, but over the second half of the rib interval over‐predict the local Nusselt number. Originality/value – The work contributes to the understanding of the flow and thermal development in cooling passages of gas turbine blades, and to the validation of turbulence models that can be used for their prediction, at both effective viscosity and second‐moment closure levels.