Review on thermal energy storage with phase change: materials, heat transfer analysis and applications

Variations of the SIMPLE method of Patankar and Spalding have been widely used over the past decade to obtain numerical solutions to problems involving incompressible flows. The present paper shows several modifications to the method which both simplify its implementation and reduce solution costs. The performances of SIMPLE, SIMPLER, and SIMPLEC (the present method) are compared for two recirculating flow problems. The paper is addressed to readers who already have experience with SIMPLE or its variants.

Enhancements of the simple method for predicting incompressible fluid flows

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

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Numerical solution of saddle point problems

http://www.inf.ufes.br/~luciac/comcie/JFNK-Knoll.pdf

Jacobian-free Newton-Krylov methods: a survey of approaches and applications

The accuracy of numerical simulation algorithms is one of main concerns in modern Computational Fluid Dynamics. Development of new and more accurate mathematical models requires an insight into the problem of numerical errors. In order to construct an estimate of the solution error in Finite Volume calculations, it is first necessary to examine its sources. Discretisation errors can be divided into two groups: errors caused by the discretisation of the solution domain and equation discretisation errors. The first group includes insufficient mesh resolution, mesh skewness and non-orthogonality. In the case of the second order Finite Volume method, equation discretisation errors are represented through numerical diffusion. Numerical diffusion coefficients from the discretisation of the convection term and the temporal derivative are derived. In an attempt to reduce numerical diffusion from the convection term, a new stabilised and bounded second-order differencing scheme is proposed. Three new methods of error estimation are presented. The Direct Taylor Series Error estimate is based on the Taylor series truncation error analysis. It is set up to enable single-mesh single-run error estimation. The Moment Error estimate derives the solution error from the cell imbalance in higher moments of the solution. A suitable normalisation is used to estimate the error magnitude. The Residual Error estimate is based on the local inconsistency between face interpolation and volume integration. Extensions of the method to transient flows and the Local Residual Problem error estimate are also given. Finally, an automatic error-controlled adaptive mesh refinement algorithm is set up in order to automatically produce a solution of pre-determined accuracy. It uses mesh refinement and unrefinement to control the local error magnitude. The method is tested on several characteristic flow situations, ranging from incompressible to supersonic flows, for both steady-state and transient problems.

Error analysis and estimation for the finite volume method with applications to fluid flows

An analysis has been made of laminar flow and heat transfer in channels whose walls are interrupted periodically along the streamwise direction. Such channels are frequently employed in high-performance compact heat exchangers. Numerical solutions of the mass, momentum, and energy conservation equations yielded local heat transfer and pressure drop results. These results were obtained for a range of Reynolds numbers and for several values of a dimensionless geometrical parameter characterizing the streamwise length L of the individual plate segments which make up the interrupted walls. The Prandtl number was fixed at 0.7 for all the calculations. The basic heat transfer and pressure drop results were employed to investigate whether an interrupted-wall channel experiences an augmented heat transfer rate compared with that for a parallel plate channel. For conditions of equal heat transfer surface area and equal pumping power, appreciably higher heat transfer rates prevailed in the interrupted-wall channel for a wide range of operating conditions. The augmentation was especially marked for relatively short channels and high Reynolds numbers. The results also demonstrated the existence of a new type of fully developed regime, one that is periodic. At sufficiently large downstream distances, the velocity and temperature profiles repeat their values at successive axial stations separated by a distance 2L and, in addition, the average heat transfer coefficient for a plate segment takes on a constant value.

Heat transfer and fluid flow analysis of interrupted-wall channels with application to heat exchangers

A finite volume method (FVM) is presented in this article. This procedure can be used to model transparent, absorbing, emitting, and anisotropically scattering media. A procedure to capture collimated beam is also presented. The FVM is applied to six test problems, and the results compared favorably against other published results. The test problems include two- and three-dimensional enclosures with participating media, collimated incidence, and heat generation. The efficiency of the FVM procedure is also investigated using a three-dimensional test problem.

Suhas V. Patankar

Papers

Heat transfer and fluid flow analysis of interrupted-wall channels with application to heat exchangers

Improved Treatment of Scattering Using the Discrete Ordinates Method

Analysis of Turbulent Flow and Heat Transfer in Internally Finned Tubes and Annuli

Recent Developments in Computational Heat Transfer

Effect of Subcooling on Cylindrical Melting