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Purpose - This paper aims to point out the critical problems in numerical verification of solidification simulation codes and the complexity of the verification and to propose and apply a procedure of generalized verification for macrosegregation simulation. Design/methodology/approach - A partial verification of a finite-volume computational model of macrosegregation in direct chill (DC) casting of binary aluminum alloys, including the coupled transport phenomena of heat transfer, fluid flow and species transport, is performed. The verification procedure is conducted on numerical test problems, defined as subproblems with respect to the complexity of the physical model, geometry, and boundary conditions. The studied cases are thermal convection with solidification in DC casting, thermal natural convection of a low-Prandtl-number liquid metal in a rectangular cavity and 1D directional solidification of a binary Al-Cu alloy. Grid-convergence studies, code comparison with an alternative Chebyshev-collocation method, and comparison with a reference similarity solution are used for verification. Findings - An excellent ability of the model to accurately resolve the thermal convection in the pertinent range of Prandtl and Rayleigh numbers is shown. Concerns regarding the solution of species transport in the mushy zone remain. Research limitations/implications - The proposed verification procedure is not completed in its entirety. Further verification of the solutal and thermosolutal convection problems is required. Originality/value - This paper proposes verification techniques for complex coupled solidification problems involving significant convection in the melt. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to upgrade our previous developments of Local Radial Basis Function Collocation Method (LRBFCM) for heat transfer, fluid flow and electromagnetic problems to thermoelastic problems and to study its numerical performance with the aim to build a multiphysics meshless computing environment based on LRBFCM. Design/methodology/approach – Linear thermoelastic problems for homogenous isotropic body in two dimensions are considered. The stationary stress equilibrium equation is written in terms of deformation field. The domain and boundary can be discretized with arbitrary positioned nodes where the solution is sought. Each of the nodes has its influence domain, encompassing at least six neighboring nodes. The unknown displacement field is collocated on local influence domain nodes with shape functions that consist of a linear combination of multiquadric radial basis functions and monomials. The boundary conditions are analytically satisfied on the influence domains which contain boundary points. The action of the stationary stress equilibrium equation on the constructed interpolation results in a sparse system of linear equations for solution of the displacement field. Findings – The performance of the method is demonstrated on three numerical examples: bending of a square, thermal expansion of a square and thermal expansion of a thick cylinder. Error is observed to be composed of two contributions, one proportional to a power of internodal spacing and the other to a power of the shape parameter. The latter term is the reason for the observed accuracy saturation, while the former term describes the order of convergence. The explanation of the observed error is given for the smallest number of collocation points (six) used in local domain of influence. The observed error behavior is explained by considering the Taylor series expansion of the interpolant. The method can achieve high accuracy and performs well for the examples considered. Research limitations/implications – The method can at the present cope with linear thermoelasticity. Other, more complicated material behavior (visco-plasticity for example), will be tackled in one of our future publications. Originality/value – LRBFCM has been developed for thermoelasticity and its error behavior studied. A robust way of controlling the error was devised from consideration of the condition number. The performance of the method has been demonstrated for a large number of the nodes and on uniform and non-uniform node arrangements. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present a new computational fluid dynamics model for large electrical machines to simulate the heat transfer at specific components to the appropriate ventilation method. The most damageable parts for overheating in generators are the end winding bars, pole windings and stator ducts. Design/methodology/approach – The reduced model introduced is basically derived from the state-of-the-art pole section model (PSM) and enables faster computations for heat transfer and cooling simulations of electrical machines. The fundamentals of the two methods and the grid generation are described. Two PSMs and four different reduced models are presented and compared among each other to tune the reduced model. Findings – As a topic of outstanding interest in large hydro generators, the heat transfer at the end winding bars is solved with the aid of the reduced model. This slot sector model (SSM) has been validated and the computation time has been reduced enormously in comparison to the state-of-the-art PSM. Research limitations/implications – The heat transfer has been carried out only for the end winding region of large hydro generators. The effect of the reduced model on the pole sections and stator ducts has not been investigated. Nevertheless, the reduced model is also valid for large motors. Practical implications – This reduced model can finally be used for parametric studies with different cooling schemes and boundary conditions in the design process. Originality/value – The comparison of various SSMs to PSMs shows an acceptable accuracy of the reduced model in combination with a rather low computation time. Due to modeling one slot only, the MFR-MP approach is an adequate and fast analyzing method for this kind of model structure. [ABSTRACT FROM AUTHOR]