Combined finite volume and finite element method for convection-diffusion-reaction equation

A combined finite volume and finite element method is presented for solving the unsteady scalar convection-diffusion-reaction equation in two dimensions. The finite volume method is used to discretize the convection-diffusion-reaction equation. The higher-order reconstruction of unknown quantities at the cell faces is determined by Taylor’s series expansion. To arrive at an explicit scheme, the temporal derivative term is estimated by employing the idea of local expansion of unknown along the characteristics. The concept of the finite element technique is applied to determine the gradient quantities at the cell faces. Robustness and accuracy of the method are evaluated by using available analytical and numerical solutions of the two-dimensional pure-convection, convection-diffusion and convection-diffusion-reaction problems. Numerical test cases have shown that the method does not require any artificial diffusion to improve the solution stability. This paper was recommended for publication in revised form by Associate Editor Dongshin Shin Pramote Dechaumphai received his B.S. degree in Industrial Engineering from Khon-Kaen University, Thailand, in 1974, M.S. degree in Mechanical Engineering from Youngstown State University, USA in 1977, and Ph.D. in Mechanical Engineering from Old Dominion University, USA in 1982. He is currently a Professor of Mechanical Engineering at Chulalongkorn University, Bangkok, Thailand. His research interests are numerical methods, finite element method for thermal stress and computational fluid dynamics analysis. Sutthisak Phongthanapanich received his B.S. degree in Mechanical Engineering from Chiangmai University, Thailand in 1990. He then received his M.S., and Ph.D. degrees in Mechanical Engineering from Chulalongkorn University, Thailand in 2002, and 2006, respectively. He is a Lecturer of Mechanical Engineering Technology at King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand. His research interests are finite element method, finite volume method, mesh generation and adaptation, and shock wave dynamics.     

Nodeless variables finite element method and adaptive meshing teghnique for viscous flow analysis

A nodeless variables finite element method for analysis of two-dimensional, steady-state viscous incompressible flow is presented. The finite element equations are derived from the governing Navier-Stokes differential equations and a corresponding computer program is developed. The proposed method is evaluated by solving the examples of the lubricant flow in journal bearing and the flow in the lid-driven cavity. An adaptive meshing technique is incorporated to improve the solution accuracy and, at the same time, to reduce the analysis computational time. The efficiency of the combined adaptive meshing technique and the nodeless variables finite element method is illustrated by using the example of the flow past two fences in a channel.     

Nodeless variable finite element method for stress analysis using flux-based formulation

A nodeless variable element is combined with an adaptive meshing technique to improve solution accuracy of the finite element method for analyzing two-dimensional elasticity problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without requiring additional actual nodes. The fluxbased formulation is developed for the nodeless variable finite element to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The superconvergent patch recovery procedure is implemented to compute accurate stresses from the nodeless variable finite element solutions. The effectiveness of the combined procedure for providing higher solution convergence rate from the proposed formulation is evaluated by two well-known examples.     

Interaction of high-speed compressible viscous flow and structure by adaptive finite element method

Interaction behaviors of high-speed compressible viscous flow and thermal-structural response of structure are presented. The compressible viscous laminar flow behavior based on the Navier-Stokes equations is predicted by using an adaptive cell-centered finite-element method. The energy equation and the quasi-static structural equations for aerodynamically heated structures are solved by applying the Galerkin finite-element method. The finite-element formulation and computational procedure are described. The performance of the combined method is evaluated by solving Mach 4 flow past a flat plate and comparing with the solution from the finite different method. To demonstrate their interaction, the highspeed flow, structural heat transfer, and deformation phenomena are studied by applying the present method to Mach 10 flow past a flat plate.     

Thermal conductivity of ge and ge-si core-shell nanowires in the phonon confinement regime

Heterostructure core-shell semiconductor nanowires (NWs) have attracted tremendous interest recently due to their remarkable properties and potential applications as building blocks for nanodevices. Among their unique traits, thermal properties would play a significant role in thermal management of future heterostructure NW-based nanoelectronics, nanophotonics, and energy conversion devices, yet have been explored much less than others. Similar to their electronic counterparts, phonon spectrum and thermal transport properties could be modified by confinement effects and the acoustic mismatch at the core-shell interface in small diameter NWs (<20 nm). However, fundamental thermal measurement on thin core shell NWs has been challenging due to their small size and their expected low thermal conductivity (κ). Herein, we have developed an experimental technique with drastically improved sensitivity capable of measuring thermal conductance values down to ～10 pW/K. Thermal conductivities of Ge and Ge-Si core-shell NWs with diameters less than 20 nm have been measured. Comparing the experimental data with Boltzmann transport models reveals that thermal conductivities of the sub-20 nm diameter NWs are further suppressed by the phonon confinement effect beyond the diffusive boundary scattering limit. Interestingly, core-shell NWs exhibit different temperature dependence in κ and show a lower κ from 300 to 388 K compared to Ge NWs, indicating the important effect of the core-shell interface on phonon transport, consistent with recent molecular dynamics studies. Our results could open up applications of Ge-Si core shell NWs for nanostructured thermoelectrics, as well as a new realm of tuning thermal conductivity by "phononic engineering".     

Flux‐difference splitting scheme with modified multidimensional dissipation on unstructured meshes

Abstract

A flux‐difference splitting scheme with a modified multidimensional dissipation for high‐speed compressible flow analysis on unstructured meshes is presented. The scheme eliminates unphysical flow behaviors such as a spurious bump of the carbuncle phenomenon that occurs on the bow shock from flow over a blunt body, and the expansion shock generated from flow over a forward facing step. The switching function suggested by Quirk is implemented as a choice to detect the vicinity of strong shock. The proposed scheme is further extended to obtain higher‐order spatial and temporal solution accuracy. The scheme is, in addition, combined with an adaptive meshing technique that generates unstructured triangular meshes to resemble the flow phenomena for reducing computational effort. The entire procedure is evaluated by solving several benchmarks as well as steady‐state and transient high‐speed compressible flow problems.     

A second-order time-accurate finite element method for analysis of conjugate heat transfer between solid and unsteady viscous flow

A fractional four-step finite element method for analyzing conjugate heat transfer between solid and unsteady viscous flow is presented. The second-order semi-implicit Crank-Nicolson scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy. The streamline upwind Petrov-Galerkin method (SUPG) is applied for the weighted formulation of the Navier-Stokes equations. The method uses a three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the method presented is to consistently couple heat transfer along the fluid-solid interface. Five test cases, which are the lid-driven cavity flow, natural convection in a square cavity, transient flow over a heated circular cylinder, forced convection cooling across rectangular blocks, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the method presented. This paper was recommended for publication in revised form by Associate Editor Kyung-Soo Yang Atipong Malatip received his B.S. degree in Mechanical Engineering from King Mongkut’s University of Technology North Bangkok, Thailand, in 2002. He then received his M.S. degree in Mechanical Engineering Chulalongkorn University, Thailand, in 2005. He is currently pursuing a Ph.D. degree in Mechanical Engineering at Chulalongkorn University. His research interests include computational fluid dynamics and fluid-thermal-structural interaction. Niphon Wansophark received his B.S., M.S., and Ph.D. degrees in Mechanical Engineering from Chulalongkorn University, Thailand in 1996, 2000, and 2007, respectively. He is an Assistant Professor of Mechanical Engineering at Chulalongkorn University, Bangkok, Thailand. His research interests are numerical methods and finite element method. Pramote Dechaumphai received his B.S. degree in Industrial Engineering from Khon-Kaen University, Thailand, in 1974, M.S. degree in Mechanical Engineering from Youngstown State University, USA in 1977, and Ph.D. in Mechanical Engineering from Old Dominion University, USA in 1982. He is currently a Professor of Mechanical Engineering at Chula-longkorn University, Bangkok, Thailand. His research interests are numerical methods, finite element method for thermal stress and computational fluid dynamics analysis.     

Effects of ferric chloride on thermal degradation of γ‐oryzanol and oxidation of rice bran oil

The kinetics of γ‐oryzanol degradation in antioxidant‐stripped rice bran oil were investigated at 180°C for 50 h. Ferric chloride was added to the oil at different concentrations (0, 2.5, 5.0, and 7.5 mg/kg‐oil) to determine the degradation reaction rate of γ‐oryzanol and the extent of lipid oxidation (peroxide value and p‐anisidine value). It was found that the losses of γ‐oryzanol and its four components (cycloartenyl ferulate, 24‐methylene cycloartanyl ferulate, campesteryl ferulate, and β‐sitosteryl ferulate) could be described by a first‐order kinetics model. The degradation rate constant, k, linearly increased (p < 0.05) with the ferric chloride concentration, and increased about 1.5 times when 7.5 mg/kg‐oil ferric chloride was added. Ferric chloride addition also accelerated the lipid oxidation of rice bran oil significantly (p < 0.05). Practical applications: This paper describes the kinetic analysis of the degradation of γ‐oryzanol, a major phytochemical in rice bran oil, at its frying temperature. The results indicated that iron in the form of ferric chloride accelerated both the degradation of γ‐oryzanol and lipid oxidation.     

Decomposition Kinetics of Glucose and Fructose in Subcritical Water Containing Sodium Chloride

The kinetics of the decomposition and isomerization of glucose and fructose in pure water and water containing sodium chloride (1–20 % w/w) under subcritical conditions at 180–220 °C was investigated. The addition of sodium chloride in subcritical water accelerated the decrease of glucose, and the rate was expressed by the Weibull equation. Although the isomerization of glucose to fructose was observed in parallel with decomposition, the yield of fructose was lower at higher sodium chloride concentrations. Mannose was also formed from glucose with very low yield. It was seen that fructose decomposed much faster than glucose, in pure and salty subcritical water. The decomposition of fructose obeyed first-order kinetics in the initial stages of the reaction and could be expressed by the autocatalytic model in the later stages. The formation of glucose and mannose from fructose was not observed under any of the conditions investigated.