Meshless approach to the large-eddy simulation of the continuous casting process

This paper explores the application of the mesh-free Local Radial Basis Function Collocation Method (LRBFCM) [1] in solution of coupled heat transfer and fluid flow problems associated with solidification of a binary alloy. The involved temperature, velocity, species and pressure fields are represented on overlapping sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBF’s. The energy and momentum equations are solved through explicit time stepping. The pressure-velocity coupling is calculated iteratively, with pressure correction, predicted from the local continuity equation violation [2,3]. The solution procedure is demonstrated in simulation of solidification of 8 wt % Pb-Sn alloy and 5 wt % Sn-Pb alloy in rectangular cavity at conditions, defined in [4]. The numerical examples include studies with different uniform discretization and its influence on final macrosegregation map. The solution is assessed by comparison with the reference results of the finite volume and finite element method. The advantages of the method are simplicity, accuracy and straightforward applicability in non-uniform node arrangements. The methodology will be use in complementing our heat transfer model [5] of the continuous casting of steel.

Simulation of laminar backward facing step flow under magnetic field with explicit local radial basis function collocation method

A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory

Using a local radial basis function collocation method to approximate radiation boundary conditions

In many references, both the ill-posed and inverse boundary value problems are solved iteratively. The iterative procedures are based on firstly converting the problem into a well-posed one by assuming the missing boundary values. Then, the problem is solved by using either a developed numerical algorithm or a conventional optimization scheme. The convergence of the technique is achieved when the approximated solution is well compared to the unused data. In the present paper, we present a different way to solve an ill-posed problem by applying the localized and space-time localized radial basis function collocation method depending on the problem considered and avoiding the iterative procedure. We demonstrate that the solution of certain ill-posed and inverse problems can be accomplished without iterations. Three different problems have been investigated: problems with missing boundary condition and internal data, problems with overspecified boundary condition, and backward heat conduction problem (BHCP). It has been demonstrated that the presented method is efficient and accurate and overcomes the stability analysis that is required in iterative techniques.

The local radial basis function (RBF) method is a promising solver for variable‐order time fractional diffusion equation (TFDE), as it overcomes the computational burden of the traditional global method. Application of the local RBF method is limited to Fickian diffusion, while real‐world diffusion is usually non‐Fickian in multiple dimensions. This article is the first to extend the application of the local RBF method to two‐dimensional, variable‐order, time fractional diffusion equation in complex shaped domains. One of the main advantages of the local RBF method is that only the nodes located in the subdomain, surrounding the local point, need to be considered when calculating the numerical solution at this point. This approach can perform well with large scale problems and can also mitigate otherwise ill‐conditioned problems. The proposed numerical approach is checked against two examples with curved boundaries and known analytical solutions. Shape parameter and subdomain node number are investigated for their influence on the accuracy of the local RBF solution. Furthermore, quantitative analysis, based on root‐mean‐square error, maximum absolute error, and maximum error of the partial derivative indicates that the local RBF method is accurate and effective in approximating the variable‐order TFDE in two‐dimensional irregular domains.

This article presents a local knot method (LKM) to solve inverse Cauchy problems of Helmholtz equations in arbitrary 2D and 3D domains. The Moore–Penrose pseudoinverse using the truncated singular value decomposition is employed in the local approximation of supporting domain instead of the moving least squares method. The developed approach is a semi‐analytical and local radial basis function collocation method using the non‐singular general solution as the basis function. Like the traditional boundary knot method, the LKM is simple, accurate and easy‐to‐program in solving inverse Cauchy problems associated with Helmholtz equations. Unlike the boundary knot method, the new scheme can directly reconstruct the unknowns both inside the physical domain and along its boundary by solving a sparse linear system, and can achieve a satisfactory solution. Numerical experiments, involving the complicated geometry and the high noise level, confirm the accuracy and reliability of the proposed method for solving inverse Cauchy problems of Helmholtz equations.

The paper analyses the effect of the nozzle arrangement on the continuous steel casting, depending on its shape and dimensions. At the same time, the work analyses the effect of cooling water pressure on the contact with the cast in order to improve the heat transfer coefficient at boiling. The present research in that, more specifically, disposed cooling water injection nozzle during the continuous casting method for arranging the nozzle for spraying cooling water to the cast surface to cool the play cast steel during the continuous casting of a continuous cooling water jetting nozzle alignment during casting It relates. An injection nozzle arrangement method during continuous casting is provided to evenly inject cooling water onto the surface of a continuous cast steel slab in a secondary cooling zone during the continuous casting.

This article outlines the advantages of the steel continuous casting, along with its developments and challenges for improvement. It describes the process of the steel continuous casting. The article provides a description of the design and layout of a steelmaking facility for continuous casting of steel. It reviews the trends in the steel industry, such as near-net shape casting, the use of tundish metallurgy, and pouring stream protection. The article discusses the use and capabilities of different molds for steel continuous casting. These include thin-wall tube-type molds, solid molds, and plate molds. The article explains the operations for productivity improvements and quality improvements in steel continuous casting. It reviews the applications of horizontal continuous casting in casting steel. An emphasis on the development of continuous casting depending on control systems and automation, with the objective of maintaining high quality and high productivity, is also provided.

Simulation of electromagnetic wave propagations in negative index materials by the localized RBF-collocation method

Production of round billets by steel continuous casting, widely used for manufacturing seamless pipes, railway wheels and tyres, quality long rolled products etc., is widely spread in the world steel industry. Constant search for improved design of CCM takes place, separate parts of existing machines are being perfected. An analysis of collected in the world practice experience of solving problems, related to production of round continuously casted billets, enables to choose proper technical solutions for each particular situation, to determine rational parameters of technology. History of development of round continuously casted billets production technology considered. Data on their modern producers presented. Peculiarities of steel continuous casting technology, as well as reasons of defects of round continuously casted billets have been discussed. Classification of basic kinds of cracks of round continuously casted billet presented. Basic problems during production of round continuously casted billets relate to ovality formation, mainly because of unevenness of heat-away in the mold. The increased ovality can lead to formation of internal and external cracks. Ways of solving problems of defects formation and ways of round continuously casted billet technology perfection summarized. Application of methods of mathematical simulation for a technology, which enables to produce defectless billets considered. It was shown, that basic measures to decrease number of billet defects, relate to setting rational parameters of temperature-speed mode, transfer to internal mold profile, corresponding to the billet shrinkage. Another measure is elimination of uneven impact of the liquid metal stream on the solidifying shell in the area of small and big radius. A perspective direction of round continuously casted billets production technology perfection is application of soft reduction methods and electromagnetic stirring of the liquid metal.

Steelmakers focus on producing high quality steel to minimize defects, as this strategy maximizes their productivity and profit. The paper describes how to create a macro model of solidification of continuously cast steel. The described model is fully 3D, non-stationary and is implemented in a form suitable for GPU (Graphics Processing Unit). The formation of blank cracks follows the continuous casting of steel from the beginning and is a problem for the production of some steel grades. The various criteria that can predict the occurrence of defects in continuous steel casting can serve to optimize the casting process, control the blank cooling, and then predict the quality of the resulting blank.

In this study, the thermal performance of a jacketed heat exchanger with a stirrer was experimentally and numerically investigated under different jacket side water inlet temperature and flow rate conditions. In the numerical study, a three-dimensional computational fluid dynamics (CFD)model of the heat exchanger was generated and the analyzes were performed with the ANSYS-Fluent software package. In addition, a stirrer was added to both the experimental and the numerical study to obtain the effects of the stirrer on the temperature and velocity values of the water in the tank. It was seen that the results of the analyzes performed under similar conditions to the experimental study were in good agreement with the experimental study. It was concluded that the effect of the flow rate decreases with increasing inlet temperature. When the stirrer was activated and the flow rate was increased from 0.5 to 2.5 l/min in 30, 40, and 50°C inlet temperature conditions, the time to reach the target temperature inside the tank decreased from approximately 1600 to 900, from 2500 to 1350, and from 4900 to 1400, respectively. In general, it was observed that the effect of the stirrer increased with increasing inlet temperature in all flow rate conditions.

Multi-scale and multi-physics simulation of central segregation in an equiaxed dendritic mushy zone during continuous casting of steel

A reduced-order model of mould heat transfer in the continuous casting of steel