Simulation of droplet spreading,splashing and solidification using smoothed particle hydrodynamics method

Spreading, splashing and solidification of yttria stabilized zirconia (YSZ) droplet after inclined impact are simulated by smoothed particle hydrodynamics. The artificial heat model has been improved and a simple solidification model is included. It is found that the droplet splashes when the impact angle is less than 44° with the Reynolds number of 3535. Otherwise the droplet will deposit. The result is in good agreement with the theoretical prediction. The temperature distribution and solidification interface movement during the droplet impacting on an inclined surface are presented. The flattening ratio is found to increase with the impact angle.     

Steady state conduction through 2D irregular bodies by smoothed particle hydrodynamics

This paper uses a Lagrangian formulation namely smoothed particle hydrodynamics (SPH) technique for the prediction of conduction heat transfer in irregular geometries. Suitable schemes for the placement of particles inside irregular computational domain have been described. Organization and locations for virtual particles are also discussed for both Dirichlet and Neumann boundary conditions. Three different problems having typical geometries that pose numerical complications in grid based technique, are tackled by SPH efficiently. Conduction shape factor (CSF) for all the problems calculated through SPH shows a good agreement with published results or analytical solutions. Further, the temperature profiles computed by SPH depict close matches with those obtained through numerical software Fluent. The present exercise opens up the possibility of using SPH in varied geometries using different schemes of particle positioning and their judicial combinations.     

An efficient BEM formulation for three-dimensional steady-state heat conduction analysis of composites

In this work, an efficient boundary element formulation has been presented for three-dimensional steady-state heat conduction analysis of fiber reinforced composites. The cylindrical shaped fibers in the three-dimensional composite matrix are represented by a system of curvilinear line elements with a prescribed diameter which facilitates efficient analysis and modeling together with the reduction in dimensionality of the problem. The variations in the temperature and flux fields in the circumferential direction of the fiber are represented in terms of a trigonometric shape function together with a linear or quadratic variation in the longitudinal direction. The resulting integrals are then treated semi-analytically which reduces the computational task significantly. The computational effort is further minimized by analytically substituting the fiber equations into the boundary integral equation of the material matrix with hole, resulting in a modified boundary integral equation of the composite matrix. An efficient assembly process of the resulting system equations is demonstrated together with several numerical examples to validate the proposed formulation. An example of application is also included.     

Research on melting and solidification processes for enhanced double tubes with constant wall temperature/wall heat flux

Latent heat thermal energy storage (LHTES) improves the energy utilization efficiency between energy supply and energy demand of heating storage in buildings and liquid desiccant air conditioning systems. The present work is focused on validated numerical investigation of the thermal performances of LHTES inside enhanced double tubes. The effects of the number of fins ranging from 2 to 10 and boundary conditions of the inner tube wall on the melting and solidification processes are examined. The results indicate that number of fins and wall boundary conditions play an important role in the thermal performances of LHTES. It is noted that recirculation flow in the liquid phase change material region is formed remarkably. The enhancement ratio for constant wall temperature is more significant than that of constant wall heat flux during the melting process. However, the discrepancy of the enhancement ratio for different inner wall temperatures is limited during the solidification process.     

Finite element method formulation in polar coordinates for transient heat conduction problems

The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.     

General formulation and analysis of hyperbolic heat conduction in composite media

Some recent experimental results show the existence of reflections of thermal waves at the interface of dissimilar materials in superfluid helium. In light of these results, a theoretical investigation of thermal waves in composite is provided to give a theoretical foundation to the observed phenomenon. A general one-dimensional temperature and heat flux formulation for hyperbolic heat conduction in a composite medium is presented. Also, the general solution, based on the flux formulation, is developed for the standard three orthogonal coordinate systems. Unlike classical parabolic heat conduction, heat conduction based on the modified Fourier's law produces non-separable field equations for both the temperature and flux and therefore standard analytical techniques cannot be applied in these situations. In order to alleviate this difficulty, a generalized finite integral transform technique is proposed in the flux domain and a general solution is developed for the standard three orthogonal coordinate systems. The general solution is applied to the case of a two-region slab with a pulsed volumetric source and insulated exterior surfaces which displays the unusual and controversial nature associated with heat conduction based on the modified Fourier's law in composite regions.     

A new stochastic approach to transient heat conduction modeling with uncertainty

We present a generalized polynomial chaos algorithm for the solution of transient heat conduction subject to uncertain inputs, i.e. random heat conductivity and capacity. The stochastic input and solution are represented spectrally by the orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener [Am. J. Math. 60 (1938) 897]. A Galerkin projection in random space is applied to derive the equations in the weak form. The resulting set of deterministic equations is subsequently discretized by the spectral/hp element method in physical space and integrated in time. Numerical examples are given and the convergence of the chaos expansion is demonstrated for a model problem.     

A node-based smoothed point interpolation method (NS-PIM) for three-dimensional heat transfer problems

A node-based smoothed point interpolation method (NS-PIM) is formulated for three-dimensional (3D) heat transfer problems with complex geometries and complicated boundary conditions. Shape functions constructed here through PIM possess the delta function property and hence allow the straightforward enforcement of essential boundary conditions. The smoothed Galerkin weak form is employed to create discretized system equations, and the node-based smoothing domains are used to perform the smoothing operation and the numerical integration. The accuracy and efficiency of the NS-PIM solutions are studied through detailed analyses of actual 3D heat transfer problems. It is found that the NS-PIM can provide higher accuracy in temperature and its gradient than the reference approach does, in which very fine meshes are used in standard FEM code available with homogeneous essential boundary conditions. More importantly, the upper bound property of the NS-PIM is obtained using the same tetrahedral mesh. Together with the FEM, we now have a simple means to obtain both upper and lower bounds of the exact solution to heat transfer using the same type of mesh.     

Study and modeling of heat transfer during the solidification of semi-crystalline polymers

Semi-crystalline polymers are materials whose behavior during their cooling is difficult to model because of the strong coupling between the crystallization, heat transfer, pressure and shear. Thanks to two original apparatus we study solidification of such a polymer without shear. Firstly the comparison between experimental results and a numerical model will permit to validate crystallization kinetic for cooling rate reachable by DSC. The second experiment makes it possible to analyze solidification for high cooling rate, corresponding to some manufacturing processes. It appears that crystallization has an influence on the thermal contact resistance.     

Analysis and modeling of char particle combustion with heat and multicomponent mass transfer

A char combustion model suitable for a large-scale boiler/gasifier simulation, which considers the variation of physical quantities in the radial direction of char particles, is developed and examined. The structural evolution within particles is formulated using the basic concept of the random pore model while simultaneously considering particle shrinkage. To reduce the computational cost, a new approximate analytical boundary condition is applied to the particle surface, which is approximately derived from the Stefan–Maxwell equations. The boundary condition showed reasonably good agreement with direct numerical integration with a fine grid resolution by the finite difference method under arbitrary conditions. The model was applied to combustion in a drop tube furnace and showed qualitatively good agreement with experiments, including for the burnout behavior in the late stages. It is revealed that the profiles of the oxygen mole fraction, conversion, and combustion rate have considerably different characteristics in small and large particles. This means that a model that considers one total conversion for each particle is insufficient to describe the state of particles. Since our char combustion model requires only one fitting parameter, which is determined from information on the internal geometry of char particles, it is useful for performing numerical simulations.     

蓄能互联热泵系统相变装置熔化与凝固过程特性分析

介绍了一种新型的蓄能互联热泵系统。利用数值模拟的方法对填充石蜡C17的球型蓄热单元的熔化与凝固过程进行研究,分析了球壁温度、相变单元尺寸和相变材料初始温度三种影响因素对熔化过程和球壁温度对凝固过程的影响。通过对两个过程对比发现相变单元尺寸对相变过程影响最大,在相同温差条件下完全熔化时间少于完全凝固时间,熔化过程中始终存在的石蜡-壁面与液相石蜡-固相石蜡之间的对流换热过程增加了熔化速率。     

A two-dimensional adaptive remeshing method for solving melting and solidification problems with convection

Melting and solidification problems in presence of natural convection are known to require high computational resources. Very fine meshes are essential to accurately determine the flow structure and interface position between the different phases. In this work, a time-dependent adaptive remeshing method based on an efficient error estimator is presented. The proposed method greatly reduces the number of mesh elements while maintaining and even enhancing the efficiency of the simulations. A variant of the enthalpy-porosity formulation is used where the different thermo-physical properties between the solid–liquid phases are easily taken into account. A second order mixed finite element formulation for both space and time is employed for solving the momentum and energy equations. The efficiency of the proposed methodology is established by comparing solutions on very fine meshes with those obtained on adapted meshes and with existing experimental and numerical results found in the literature.     

Numerical techniques for solving solidification and melting phase change problems

This article reviews several mathematical formulations including the corresponding boundary conditions for numerical predictions of solidification and melting. Emphasis is on techniques that are used in solving solid–liquid interface phenomena. The fixed grid enthalpy method is reviewed based on the solution techniques of conduction and convection related phase change problems. Variable grid methods are categorized and then analyzed based on their accuracy, computational efforts and convergence characteristics. The article concludes with some guidance for selecting the accurate solution techniques for solving solidification and melting problems.     

An edge-based smoothed point interpolation method (ES-PIM) for heat transfer analysis of rapid manufacturing system

This paper formulates an edge-based smoothed point interpolation method (ES-PIM) for analyzing 2D and 3D transient heat transfer problems with mixed boundary conditions and complicated geometries. In the ES-PIM, shape functions are constructed using the polynomial PIM with the Delta function property for easy treatment of essential boundary conditions. A generalized smoothing technique is used to reconstruct the temperature gradient field within the edge-based smoothing domains. The generalized smoothed Galerkin weak form is then used to establish the discretized system equations. Our results show that the ES-PIM can provide more close-to-exact stiffness compared with the “overly-stiff” finite element method (FEM) and the “overly-soft” node-based smoothed point interpolation method (NS-PIM). Owing to this important property, the present ES-PIM provides more accurate solutions than standard FEM using the same mesh. As an example, a practical cooling system of the rapid direct plasma deposition dieless manufacturing is studied in detail using the present ES-PIM, and a set of “optional” processing parameters of fluid velocity and temperature are found.     

A Novel Variational Formulation of Inverse Problem of Heat Conduction with Free Boundary on an Image

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Sensitivity analysis and shape optimization for transient heat conduction with radiation

Transient heat conduction problem is stated by the differential heat conduction equation, thermal boundary conditions on the external and internal boundary portions and the initial condition within the domain. Next an arbitrary behavioral functional is defined and its first-order sensitivities are determined using the material derivative concept as well as both the direct and adjoint approaches. The most used shape domain modifications are discussed in order to investigate the effect of design parameters on the integral radiation condition. The shape optimization problem is next formulated applying the obtained sensitivities. The illustration is the simple example of the shape optimization.     

Solving heat transfer problems with phase change via smoothed effective heat capacity and element-free Galerkin methods

This paper presents a smoothed effective heat capacity model that is combined with element-free Galerkin (EFG) method, to solve heat transfer problems with phase change. The Sigmoid function is employed to build a continuous and smooth effective heat capacity function, so as to avoid possible error caused by the step-jump. The proposed numerical model is verified via numerical examples, and the effects of arrangement of EFG nodes and parameters relevant with Sigmoid function on the solutions are investigated. Satisfactory results are achieved in comparison with analytical solutions.