On the simulation of industrial gas dynamic applications with the discontinuous Galerkin spectral element method

In the present investigation,we demonstrate the capabilities of the discontinuous Galerkin spectral element method for high order accuracy computation of gas dynamics.The internal flow field of a natural gas injector for bivalent combustion engines is investigated under its operating conditions.The simulations of the flow field and the aeroacoustic noise emissions were in a good agreement with the experimental data.We tested several shockcapturing techniques for the discontinuous Galerkin scheme.Based on the validated framework,we analyzed the development of the supersonic jets during different opening procedures of a compressed natural gas injector.The results suggest that a more gradual injector opening decreases the noise emission.     

Discontinuous Galerkin finite element method for radiative heat transfer in two-dimensional media with inner obstacles

A discontinuous Galerkin finite element method (DGFEM) with unstructured meshes is presented to solve the radiative transfer equation (RTE) in two-dimensional media with inner obstacles. The computation domain is discretized into a tessellation of unstructured elements and the elements are assumed to be discontinuous on the inner-element boundaries. The shape functions are constructed on each element and the continuity of the computation domain is maintained by modeling an up-winding numerical flux across the inner boundaries, which makes the DGFEM suitable and numerical stable for radiative transfer problems involved with strong non-uniformity and discontinuity induced by ray effects. The DGFEM discretization for RTE is presented and the accuracy of DGFEM is verified. Radiative transfer problems in square and irregular media with inner obstacles are investigated, the influence of medium parameters and the obstacle shielding effects are discussed.     

Meshless element free Galerkin method for unsteady nonlinear heat transfer problems

In this paper, meshless element free Galerkin (EFG) method has been extended to obtain the numerical solution of nonlinear, unsteady heat transfer problems with temperature dependent material properties. The thermal conductivity, specific heat and density of the material are assumed to vary linearly with the temperature. Quasi-linearization scheme has been used to obtain the nonlinear solution whereas backward difference method is used for the time integration. The essential boundary conditions have been enforced by Lagrange multiplier technique. The meshless formulation has been presented for a nonlinear 3-D heat transfer problem. In 1-D, the results obtained by EFG method are compared with those obtained by finite element and analytical methods whereas in 2-D and 3-D, the results are compared with those obtained by finite element method.     

Numerical simulation using boundary element method of the mechanism to enhance heat transport by solitary wave on falling thin liquid films

A boundary element method has been developed for analysing heat transport phenomena in solitary wave on falling thin liquid films at high Reynolds numbers.The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function.Consequently,velocity and temperature gradients are dliminated.and the complete formulation is written in terms of velocity and temperature,This provides considerable reduction is storage and computational requirements while improving accuracy.The non-linear equation systems of boundary element discretization are solved by the quasi-Nweton iterative scheme with Broyden‘s update.The streamline maps and the temperature distributions in solitary wave and wavy film flow have been obtained,and the variations of Nusselt numbers along the wall-liquid interface are also given.There are large cross-flow velocities and S-shape temperature distributions in the recirculating region of solitary wave.This special flow and thermal process can be a mechanism to enhance heat transport.     

Compressible heat transfer computations by an adaptive finite element method

This paper presents adaptive finite element computations of laminar jet impingement heat transfer. Variable fluid properties and compressibility effects are considered. A unified formulation of the equations is used to treat the simultaneous presence of three flow regimes: incompressible (ρ=constant), compressible (ρ=ρ(p,T)), and anelastic (ρ=ρ(T)). The error estimator uses a local least squares projection method and accounts for errors in velocity, pressure and temperature. The performance of the methodology is verified by solving a problem possessing a closed form solution. Several applications are then considered. We study two different gases (air and CO₂), different conditions (heated, cooled or constant properties), compressibility and inlet velocity profile effects. Heat transfer is a key element of the study. Results indicate that the methodology can produce grid independent solutions even for derived quantities and in thin boundary layers.     

Study on heat transfer of ground heat exchanger based on wedgelet finite element method

In order to maximize the economic benefit of ground source heat pump system, it is necessary to grasp the heat transfer rules of ground heat exchanger, the wedgelet finite element method is applied in analyzing heat transfer process of ground heat exchanger. First, existing researches on heat transfer analysis of ground heat exchanger and wavelet finite element method have been summarized. Second, the basic characteristics of wedgelet function are studied. Third, the wedgelet finite element model of analyzing heat transfer rules of ground heat exchanger is constructed using wedgelet function as interpolation function. Finally, the heat transfer simulation analysis of vertical U-type ground heat exchanger is carried out, and results show that the wedgelet finite element has higher precision and efficiency, and the effect of main affecting factors on heat transfer rules of ground heat exchanger is obtained.     

Application of a new finite integral transform method to the wave model of conduction

A new finite integral transform method [Int. J. Heat Mass Transfer 44 (2001) 3307] is applied to the wave model of conduction. It is compared with a standard method of solution of the hyperbolic conduction equation. The temperature fields coincide. The chosen test problem and its results bring to the foreground some of the difficulties of standard technique applications. These difficulties are by-passed when using the new method.The Cattaneo Vernotte model is then tested through a comparison of its results with transient molecular dynamics simulations taken from Volz [Transferts de chaleur aux temps ultra-courts par la technique de la dynamique moléculaire, Thèse, Univ. de Poitiers, 1996]. When the used parameters of the continuous model are near their equilibrium values, the agreement remains weakly qualitative. An adaptation of these parameter values, notably the diffusion time scale, can give a quantitative coincidence; but never is the agreement obtained for both studied variables (internal energy and flux density). These observations are discussed. Various causes liable to justify the realized adaptations of parameters are considered. None of them gives a right explanation. Concerning the impossibility of making both variables coincide, the source of conflicts is as much in the constitutive law as in the energy conservation law. The key seems to be in thermodynamics.     

Analysis of indirect temperature-rise tests of induction machinesusing time stepping finite element method

To be able to test the temperature-rise of induction motors with indirect loading is very useful for the motor industry. In this paper different indirect loading schemes including two-frequency methods, phantom loading methods and inverter driven methods, are surveyed. Their merits and demerits are highlighted. A universal method for analyzing all these indirect temperature-rise methods is presented. The analysis is based on the time stepping finite element model of skewed rotor bar induction machines and the solution can include the effects of saturation, eddy-current and the high order harmonic fields directly. The computed losses can also include the stray losses due to the high-order harmonic fields. An 11 kW induction motor, when operating with normal full-load and on phantom loading, has been used to verify the computed results     

Numerical simulation of laser-induced transient temperature field in film-substrate system by finite element method

The transient temperature fields generated by a pulsed laser in film-substrate system are obtained by using the finite element method. Time integrations of the semi-discrete finite element equations are achieved by using approximate one order derivative of temperature. The temperature dependences of material properties are taken into account, which has a great influence on the temperature fields indicated by the numerical results. The pulsed laser-induced transient temperature fields in aluminum/methyl-methacrylate system and aluminum/copper system are obtained, which will be useful in the research on thermoelastic excitation of laser ultrasonic waves in film-substrate system.     

Application of Numerical Simulation Method to Predict the Performance of Wave Energy Device with Impulse Turbine

This paper presents the work carried out to predict the behavior of a 0.6 m Impulse turbine with fixed guide vanes with 0.6 hub-to-tip (H/T) ratio under real sea conditions. In order to predict the true performance of the actual Oscillating Water Column (OWC), the numerical technique has been fine tuned by incorporating the compressibility effect. Water surface elevation verses time history based on Pierson Moskowitz Spectra was used as the input data. Standard numerical techniques were employed to solve the non-linear behavior of the sea waves. The effect due to compressibility inside the air chamber and turbine performance under unsteady and irregular flow condition has been analyzed numerically. Considering the quasi-steady assumptions, unidirectional steady flow experimental data was used to simulate the turbine characteristics under irregular unsteady flow conditions. The results show that the performance of this type of turbine is quite stable and efficiency of air chamber and the mean conversion     

基于有限元方法的横掠错排光滑管束传热与流动特性研究

使用有限元方法对横掠不同型式措排光滑管束进行了计算分析，绘制了速度场和温度场的色差梯度图，比较了它们的传热与流动性能。有限元分析方法作为热分析和流动分析研究的有力工具，可以与实验研究相结合作为研究管束传热与流动性能的一种新方法。研究结果对于横掠光滑管束的优化设计具有一定的指导意义。     

Thermo-mechanical simulation for nozzle header of once-through steam generator by experiment and finite element method

The thermo-mechanical behaviour of the nozzle header of a steam generator developed for an integral reactor was investigated using experimental and finite element methods. The nozzle feedwater header suffers from severe thermal transient loadings during the operation of the nuclear reactor. The nozzle header is exposed to the low temperature inlet feedwater and the high temperature outlet superheated steam and the other side of the nozzle header contacts with the high temperature primary coolant. The temperature gradients result in high thermal stresses in the nozzle header. The thermal transient loading has been simulated in a test loop. The input and thermo-hydraulic parameters of the primary and the secondary system were. Strain gauges and thermocouples attached to the highly stressed region monitored the thermo-mechanical behaviour of the nozzle header. In parallel with the experimental study, the transient behaviour of the nozzle header was simulated by utilizing a commercial finite element code. The fluid temperature and pressure obtained from the test loop were used as inputs to the finite element analysis. As a result of this investigation, the thermo-mechanical load carrying capacity of the developed steam generator nozzle header was proved numerically and experimentally.     

Coupled radiation and solidification heat transfer inside a graded index medium by finite element method

Effects of thermal radiation on solidification heat transfer must be considered inside semitransparent media. This paper investigates coupled heat transfer of solidification and radiation within a two-dimensional rectangular semitransparent medium having gradient index. Solidification process is supposed to happen at some temperature range, and accordingly three zones including liquid-, solid- and mushy-zones exist in phase-change media. In different phase field, parameters of thermophysical property are assumed different and those of radiative property are assumed same. Governing equation includes conduction, radiation and phase-change terms, and radiation and phase-change are treated as source terms in the equation, respectively. A Galerkin finite element method is used to solve energy equation of coupled radiation and phase-change heat transfer. This paper analyzes effect of thermal radiation on phase-change heat transfer and those of refractive index distributions on temperature fields and liquid fraction distributions during radiation–solidification coupled heat transfer. From the results, we can find that refractive index gradient has a major influence on phase-change process and compared with the case of smaller index gradient, bigger gradient can speed up phase-change heat transfer in semitransparent media.     

A penalty finite element method for natural convection heat transfer in a partially divided enclosure

Theoretical study of natural convection has been performed in a square enclosure partitioned by a single adiabatic baffle protruding from the ceiling. A penalty finite element method with 9-node quadrilateral element and Newton-Raphson scheme are adopted in this study to solve the heat transfer coefficients of three different baffle locations and two different baffle heights. During the calculating process, an out-of-core skyline method is utilized to reduce computer memory. The fluid in the enclosure is air; Rayleigh number of 10⁴ and 10⁵ are calculated. The results show that heat transfer coefficients are influenced by the baffle height and baffle location.     

He's homotopy perturbation method for two‐dimensional heat conduction equation: Comparison with finite element method

Heat conduction appears in almost all natural and industrial processes. In the current study, a two‐dimensional heat conduction equation with different complex Dirichlet boundary conditions has been studied. An analytical solution for the temperature distribution and gradient is derived using the homotopy perturbation method (HPM). Unlike most of previous studies in the field of analytical solution with homotopy‐based methods which investigate the ODEs, we focus on the partial differential equation (PDE). Employing the Taylor series, the gained series has been converted to an exact expression describing the temperature distribution in the computational domain. Problems were also solved numerically employing the finite element method (FEM). Analytical and numerical results were compared with each other and excellent agreement was obtained. The present investigation shows the effectiveness of the HPM for the solution of PDEs and represents an exact solution for a practical problem. The mathematical procedure proves that the present mathematical method is much simpler than other analytical techniques due to using a combination of homotopy analysis and classic perturbation method. The current mathematical solution can be used in further analytical and numerical surveys as well as related natural and industrial applications even with complex boundary conditions as a simple accurate technique. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20292     

A finite element analysis for inverse heat conduction problems

This paper presents an efficient inverse analysis technique based on a sensitivity coefficient algorithm to estimate the unknown boundary conditions of multidimensional steady and transient heat conduction problems. Sensitivity coefficients were used to represent the temperature response of a system under unit loading conditions. The proposed method, coupled with the sensitivity analysis in the finite element formulation, is capable of estimating both the unknown temperature and heat flux on the surface provided that temperature data are given at discrete points in the interior of a solid body. Inverse heat conduction problems are referred to as ill-posed because minor inaccuracy or error in temperature measurements cause a drastic effect on the predicted surface temperature and heat flux. To verify the accuracy and validity of the new method, two-dimensional steady and transient problems are considered. Their surface temperature and heat flux are evaluated. From a comparison with the exact solution, the effects of measurement accuracy, number and location of measuring points, a time step, and regularization terms are discussed. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(6): 345–359, 1997     

Application of CESE method to simulate non-Fourier heat conduction in finite medium with pulse surface heating

This study employs the space–time conservation element and solution element (CESE) method to simulate the temperature and heat flux distributions in a finite medium subject to various non-Fourier heat conduction models. The simulations consider three specific cases, namely a single phase lag (SPL) thermal wave model with a pulsed temperature condition, a SPL model with a surface heat flux input, and a dual phase lag (DPL) thermal wave model with an initial deposition of thermal energy. In every case, the thermal waves are simulated with respect to time as the thermal wave propagates through the medium with a constant velocity. In general, the simulation results are found to be in good agreement with the exact analytical solutions. Furthermore, it is shown that the CESE method yields low numerical dissipation and dispersion errors and accurately models the propagation of the wave form even in its discontinuous portions. Significantly, compared to traditional numerical schemes, the CESE method provides the ability to model the behavior of the SPL thermal wave following its reflection from the boundary surface. Further, a numerical analysis is performed to establish the CESE time step and mesh size parameters required to ensure stable solutions of the SPL and DPL thermal wave models, respectively.     

Fundamental approach to anisotropic heat conduction using the element-based finite volume method

This work describes the fundamentals of the element-based finite volume method for anisotropic heat conduction within the framework of the finite element space. Patch tests indicate no element inconsistencies or deficiencies when facing mesh distortion and poor aspect ratio. Convergence and accuracy assessments show that the method presents asymptomatic rate of convergence with discretization errors approaching a second-order scheme. Anisotropic heat conduction in a periodical solid lattice illustrates the application of the method. Application of an optimization technique demonstrates that the choice of a proper material orientation when manufacturing the solid lattice can increase the global heat transfer coefficient.     

The boundary element method applied to forced convection heat problems

An integral equation formulation for steady flow of a viscous fluid is presented based on the boundary element method. The continuity, Navier–Stokes and energy equations are used for calculation of the flow and temperature fields. The governing differential equations, in terms of primitive variables, are derived using velocity–pressure–temperature parameters. The calculation of fundamental solutions and solutions tensor is shown. Applications to simple flow cases, such as driven cavity, forward facing step, deep cavity and channel are presented. Convergence difficulties are indicated, which have limited the applications to flows of low Reynolds numbers.