A finite volume method to solve the Navier–Stokes equations for incompressible flows on unstructured meshes

A method to solve the Navier–Stokes equations for incompressible viscous flows and the convection and diffusion of a scalar is proposed in the present paper. This method is based upon a fractional time step scheme and the finite volume method on unstructured meshes. A recently proposed diffusion scheme with interesting theoretical and numerical properties is tested and integrated into the Navier–Stokes solver. Predictions of Poiseuille flows, backward-facing step flows and lid-driven cavity flows are then performed to validate the method. We finally demonstrate the versatility of the method by predicting buoyancy force driven flows of a Boussinesq fluid (natural convection of air in a square cavity with Rayleigh numbers of 10 ³ and 10 ⁶ ).     

FTIR–PCFC coupling: A new method for studying the combustion of polymers

Gases released from pyrolysis and partial combustion of various polymers (low-density polyethylene, polystyrene, poly(parabromostyrene), pure and flame-retarded polypolyamide 6, cellulose, and chloroprene) were studied using a new coupling between Fourier transform infrared spectrometry (FTIR) and pyrolysis combustion flow calorimetry (PCFC). Combustion in PCFC was monitored by modifying the combustion temperature between 600 and 900 °C. Decreasing the combustion temperature in PCFC leads to partial combustion and the evolution of CO, but also of methane, acetylene, or ethylene when temperature is very low. The evolution of these gases depends also on the polymer and on the presence of a flame inhibitor, demonstrating that flame inhibition can be studied using this method. A correlation between FTIR–PCFC and FTIR–cone calorimetry coupling was attempted via the CO/CO₂ ratio. The first results show that an “isoconversion temperature” in the cone calorimeter test may be estimated. Polar gases such as chlorinated or brominated gases are not fully observed using this method due to possible adsorption in the transfer line before they reach the FTIR gas cell.     

A high-order finite volume scheme for unsteady convection-dominated convection–diffusion equations

Abstract

A finite volume scheme with high-order accuracy is proposed for solving the unsteady convection-dominated transport problems. In this scheme, some weighting parameters are introduced in discretizing both the convection term and time integral. These parameters are determined analytically by making the truncation error of the proposed scheme as small as possible. Since the discretization equations of the proposed scheme share the same band structure as that of the traditional finite volume method based on the central differencing scheme, the proposed scheme does not increase computing cost. Numerical results show that the proposed scheme not only can achieve sixth-order accuracy but also avoids any unphysical oscillations in the steep gradient region of the solutions of the linear and nonlinear convection-dominated convection–diffusion problems.     

Two-level stabilized nonconforming finite element algorithms for the conduction–convection equations

In this article, we consider the two-level stabilized nonconforming finite element methods for the stationary conduction–convection equations based on local Gauss integration. The proposed methods are applied to solve conduction–convection equations with a special relationship of coarse mesh and fine mesh h?=?H/3 to avoid the coarse-to-fine intergrid operator. The methods involves three different corrections: Stokes correction, Oseen correction, and Newton correction. Moreover, the stability and convergence of the proposed methods are deduced. Finally, numerical results are shown to validate the theory analysis and demonstrate the effectiveness of the given methods.     

A lattice Boltzmann method for simulation of liquid–vapor phase-change heat transfer

A lattice Boltzmann model for the liquid–vapor phase change heat transfer is proposed in this paper. Two particle distribution functions, namely the density distribution function and the temperature distribution function, are used in this model. A new form of the source term in the energy equation is derived and the modified pseudo-potential model is used in the proposed model to improve its numerical stability. The commonly used Peng–Robinson equation of state is incorporated into the proposed model. The problem of bubble growth and departure from a horizontal surface is solved numerically based on the proposed model.     

A simplex search method for a conductive–convective fin with variable conductivity

An inverse problem is solved for simultaneously estimating the convection–conduction parameter and the variable thermal conductivity parameter in a conductive–convective fin with temperature dependent thermal conductivity. Initially, the temperature field is obtained from a direct method using an analytical approach based on decomposition scheme and then using a simplex search minimization algorithm an inverse problem is solved for estimating the unknowns. The objective function to be minimized is represented by the sum of square of the error between the measured temperature field and an initially guessed value which is updated in an iterative manner. The estimation accuracy is studied for the effect of measurement errors, initial guess and number of measurement points. It is observed that although very good estimation accuracy is possible with more number of measurement points, reasonably well estimation is obtained even with fewer number of measurement points without measurement error. Subject to selection of a proper initial guess, it is seen that the number of iterations could be significantly reduced. The relative sensitiveness of the estimated parameters is studied and is observed from the present work that the estimated convection–conduction parameter contributes more to the temperature distribution than the variable conductivity parameter.     

Mixed finite volume method for linear thermoelasticity at all Poisson’s ratios

A mixed (displacement/pressure) method for modeling both compressible and incompressible linear thermoelastic body problems is described. The method uses a form of Hooke’s law that introduces the pressure as an additional dependent variable and removes the numerical problems associated with incompressibility. A cell-centerd finite volume discretization by arbitrary polyhedral cells, an implicit temporal discretization scheme, both second-order accurate and segregated solution procedure make the method computationally e?cient.

The results of calculations are compared with analytical or finite element solutions showing a very good agreement. The present method is also compared with the displacement finite volume method and shown that it is accurate and stable for all Poisson’s ratios, while the performance of the displacement method rapidly deteriorates as the Poisson’s ratio approaches the incompressibility limit.     

A numerical method to estimate temperature intervals for transient convection–diffusion heat transfer problems

This paper presents a numerical method to estimate intervals of temperature for transient convection–diffusion heat transfer problems when uncertainty of thermal parameters is characterized by the interval. A deterministic relationship of interval variables between temperature and thermal parameters is setup by Taylor series expansion and the interval analysis, and the lower and upper bounds of temperature can be estimated by a temporally piecewise adaptive algorithm and FEM. A prescribed computing accuracy at each discretized time interval can be achieved via an adaptive process for different size of time step, thus the computing accuracy over the whole time domain can be maintained. A 2D numerical example is provided to verify the proposed approach, and a good accordance can be observed in the comparison of results given by the combinatorial, probability and proposed approaches. The impact of the order of Taylor expansion and the size of time step on the result is discussed.     

A method for the techno-economic evaluation of chemical processes—improvements to the “OPTIMO” code

This paper describes the improvement of a chemical engineering code [1] developed specifically for the evaluation and analysis of multi-step processes. The capabilities of the original code have been retained in that the mass and energy balances are the basis of a heat exchange network synthesis. However, rather than complete the evaluation with the process thermal efficiency as before, the program has been extended in order to accommodate a more detailed nuclear reactor-chemical plant coupling and new routines were written so that the hydrogen production cost can be estimated.The code was applied to two sulphur-based cycles and the results are presented later.     

On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – part I: Description of the method

ABSTRACT

The purpose of this paper is to introduce a new physical-based computational approach for the solution of convection heat transfer problems on co-located non-orthogonal grids in the context of an element-based finite volume method. The approach has already been presented in the context of two-dimensional incompressible flow problems without heat transfer. It has been shown that the pressure–velocity coupling on co-located grids can be correctly modeled via the so-called method of proper closure equations (MPCE). Here, MPCE is extended to the numerical simulation of natural, forced, and mixed convection heat transfer problems. It is shown that the couplings between pressure, velocity, and temperature can be conveniently handled on co-located grids by resorting again to the modified forms of the governing equations, i.e., the proper closure equations. The set of discrete equations is solved in a fully coupled manner in this study. Here, in part I of the paper, only the basic methodology is described; in part II, the results of application of the method to some test problems are presented.     

Modeling of Navier–Stokes equations for high Knudsen number gas flows

The possibility of modeling the Navier–Stokes equations and together with the conventional second order slip boundary condition at high Knudsen numbers is explored in this paper by incorporating the Knudsen diffusion phenomenon in rarefied gases. An effective mean free path (MFP) model is augmented to the governing equation and the slip boundary condition, as gas transport properties can be related to the MFP. This simple modification is shown to implicitly take care of the complexities associated in the transitional flow regime, without necessitating dependency of the slip coefficients on the Knudsen number. Unique analytical model with fixed values of slip coefficients is proposed and rigorous comparisons with the experimental and simulation data for pressure driven and thermally driven rarefied gas flows support this conjecture. First and second order slip coefficients have been proposed as 1.1466 and 0.9756 for rectangular channels and 1.1466 and 0.14 for the capillaries, from the continuum to the transition flow regime. The current work is significant from the numerical simulation point of view because simulation tools are better developed for Navier–Stokes equations.     

Solid-state synthesis method for the preparation of cobalt doped Ni–Al2O3 mesoporous catalysts for CO2 methanation

In this study, a simple solid-state synthesis method was employed for the preparation of the Ni–Co–Al₂O₃ catalysts with various Co loadings, and the prepared catalysts were used in CO₂ methanation reaction. The results demonstrated that the incorporation of cobalt in nickel-based catalysts enhanced the activity of the catalyst. The results showed that the 15 wt%Ni-12.5 wt%Co–Al₂O₃ sample with a specific surface area of 129.96 m²/g possessed the highest catalytic performance in CO₂ methanation (76.2% CO₂ conversion and 96.39% CH₄ selectivity at 400 °C) and this catalyst presented high stability over 10 h time-on-stream. Also, CO methanation was investigated and the results showed a complete CO conversion at 300 °C.     

Numerical solution for the hyperbolic heat conduction problems in the radial–spherical coordinate system using a hybrid Green's function method

The hyperbolic heat conduction problems in the radial–spherical coordinate system are investigated by the hybrid Green's function method. The present method combines the Laplace transform for the time domain, Green's function for the space domain and ?-algorithm acceleration method for fast convergence of the series solution. Three different examples problems have been analyzed by the present method. It is found that the present method does not exhibit numerical oscillations at the wave front and the numerical solutions are stable.     

A new method of energy degradation on-line analysis for coal-fired unit—expansion line approximating method

An energy degradation analysis process of unit and thermal system for coal-fired power plant under condition at discretion is discussed when load has been changed greatly in this paper. A new method of expansion line approximating method, which can rationally calculate the quantity of every component of energy degradation and identify the places where energy degradations arise, is put forward. In addition, the quality of every component of energy degradation is also discussed.     

Optimization of catalyst preparation conditions for hydrogen generation in the presence of Co–B using taguchi method

Efficient hydrogen generation is a significant prerequisite of future hydrogen economy. Therefore, the development of efficient non-noble metal catalysts for hydrolysis reaction of sodium borohydride (NaBH₄) under mild conditions has received extensive interest. Since the transition metal boride based materials are inexpensive and easy to prepare, it is feasible to use these catalysts in the construction of practical hydrogen generators. In this work, temperature, pH, reducing agent concentration, and reduction rate were selected as independent process parameters and their effects on dependent parameter, such as hydrogen generation rate, were investigated using response surface methodology (RSM). According to the obtained results of the RSM prediction, maximum hydrogen generation rate (53.69 L. min^?1g_cat^-1) was obtained at temperature of 281.18 K, pH of 5.97, reducing agent concentration of 31.47 NaBH₄/water and reduction rate of 7.16 ml min^?1. Consequently, after validation studies it was observed that the RSM together with Taguchi methods are efficient experimental designs for parameter optimization.     

Heat treatment method for making high strength and conductivity Cu–Cr–Zr alloy

Abstract

In this paper, the heat treatment called ‘a two-step aging process’ with the feature of the first step aging at a low temperature for a long time and the second step aging at a higher temperature for a short time has been proposed. Applying this process, the Cu–Cr–Zr alloy possessing both high strength and high conductivity can be acquired due to the formation of numerous tiny particles precipitated fully out from Cu matrix.     

Immersed boundary method for the simulation of heat transfer and fluid flow based on vorticity–velocity formulation

ABSTRACT

The present paper, based on the vorticity–velocity formulation of the Navier–Stokes equations, proposes an immersed boundary method for the simulation of heat transfer problems within a geometrically complex domain. The desired boundary conditions are imposed by the direct modification of the initial conditions of vorticity transport and energy equations using smooth interpolations. The time advancement of both transport equations is performed by the explicit fourth-order Runge–Kutta method. One of the main objectives of this paper is to present global smooth interpolations to evaluate the local Nusselt number. The forced convection of moving and fixed circular cylinders, natural convection problem in complex geometries, and the mixed convection between two concentric cylinders—at various Reynolds numbers—are studied.