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

A finite-element method for predicting flow through ducts of arbitrary and varying cross sections is presented. The governing differential equations are discretized using a control-volume approach. For this purpose, specially constructed three-dimensional control volumes are employed. The method is of the marching type and is based an a fully implicit formulation. Here, in part I of the paper, only the basic methodology is described; in the accompanying pan II, results of application of the method to some test problems are presented.

A control-volume finite-element method for predicting flow and heat transfer in ducts of arbitrary cross sections—part i: description of the method

This paper describes a robust and efficient subdomain solution procedure for two-dimensional recirculating flows. The solution domain is divided into a number of overlapping subdomains, and a direct fully coupled solution is obtained for each subdomain using a sparse matrix form of LU decomposition. An effective parabolic block correction procedure, which calculates global corrections to the tentative solution by a marching technique similar to that used for boundary layer flows, is used to accelerate the convergence of the basic procedure. The use of effective block correction is found to be essential for the success of the subdomain approach on strongly recirculating flows. In a number of laminar two-dimensional flows, the new block-corrected method performed extremely well, rivaling the best direct methods in execution time, while requiring substantially less computer storage. The new method proved to be from two to ten times faster than conventional iterative methods, while requiring only a moderate increase in storage.

A block-corrected subdomain solution procedure for recirculating flow calculations

Laminar flow and the associated heat transfer are computed for the situation in which a cylinder with external longitudinal fins rotates within a stationary shroud. The situation is commonly encountered in electrical motors and generators. The cylinder rotation creates a recirculating flow in the cavity between two adjacent fins and a throughflow in the clearance space between the fin tips and the shroud. Results for shear force on the shroud and heat transfer rate are presented for a range of values of the Reynolds number and geometric parameters such as the fin spacing and the fin height. Streamline and isotherm patterns are shown to provide details of the convection process.

Numerical study of heat transfer from a rotating cylinder with external longitudinal fins

Heat transfer—a review of 1980 literature

Numerical techniques have been used to solve the thermally developed regime for a laminar pipe flow that exchanges heat with a fluid environment in the presence of a circumferentiatly varying external heat transfer coefficient. By making use of the fact that the temperature distributions have similar shapes at successive streamwise locations, the three-dimensional temperature field was scaled to two dimensions. The resulting Two-dimensional eigenvalue problem was solved by a rapidly converging automated scheme that successively refines an initial guess. Solutions were obtained for two circumferential distributions of the external heat transfer coefficient respectively intended to model forced and natural convection cross flows. The circumferential average heat transfer coefficient was found to be quite insensitive to the imposed circumferential variations. The local wall heat flux is nearly circumferentially uniform when the mean value of the external coefficient is high. On the other hand, at low mean va...

Suhas V. Patankar

Papers

A control-volume finite-element method for predicting flow and heat transfer in ducts of arbitrary cross sections—part i: description of the method

A block-corrected subdomain solution procedure for recirculating flow calculations

Numerical study of heat transfer from a rotating cylinder with external longitudinal fins

Heat transfer—a review of 1980 literature

Laminar heat transfer in a pipe subjected to a circumferentially varying external heat transfer coefficient