Temperature-explicit formulation of energy equation for thermal–hydraulic analyses

A temperature equation which is derived from an enthalpy transport equation by using an assumption of a constant specific heat is very attractive for analyses of heat and fluid flows. It can be used for an analysis of a solid–fluid conjugate heat transfer, and it does not need a numerical method to obtain temperature from a temperature–enthalpy relation. But its application is limited because of the assumption. A new method is derived in this study, which is a temperature-explicit formulation of the energy equation. The enthalpy form of the energy equation is used in the method. But the final discrete form of the equation is expressed with temperature. The discretized equation from the temperature-explicit formulation can be used for a heat transfer analysis in a solid–fluid coupled region without any special treatment at the solid–fluid interface. And it can be applied for multiphase flows with a real gas effect. It is found by numerical tests in this study that the proposed method is very efficient and as accurate as the standard enthalpy formulation.     

Influence of evaporation on spray flamelet structures

The structure of laminar spray flames considerably differs from their gaseous counterpart. However, most often flamelet models employed in the simulation of turbulent spray combustion are based on laminar gas flame structures neglecting the influence of spray evaporation in the laminar spray flamelets. In this work, a combined theoretical and numerical study of the impact of spray evaporation on the structure of laminar spray flames is presented. Spray flamelet equations are derived, which explicitly take into account evaporation effects – the classical gas flamelet equations are recovered for non-evaporating conditions. Two new terms accounting for evaporation and for combined mixing and evaporation, respectively, are identified, and their relative importance is evaluated by means of numerical simulations of an axisymmetric laminar mono-disperse ethanol/air counterflow spray flame. The results show that the distribution of the spray evaporation rate plays a key role in the characterization of the spray flame structure. The new source terms overweigh the dissipation term of the gas phase in most situations even for non-evaporating species. Therefore, spray evaporation should always be considered. The relevance of the present formulation for turbulent spray modeling is evaluated and discussed, and a novel spray flamelet formulation is suggested.     

A numerical method for lower bound limit analysis of 3-D structures with multi-loading systems

The determination of lower bound limit load of 3-D structures is by no means an easy task, especially for complex configurations and loading systems. In our previous work, a numerical method of upper bound limit analysis for 3-D structures with multi-loading systems was proposed. This method combines FEM and mathematical programming technique in an iterative procedure. In the present article, on the basis of the nature of the iterative procedure for upper bound limit analysis, the statically admissible stress fields, which satisfies the equilibrium equation and boundary conditions, are constructed using some intermediate variables obtained by upper bound limit analysis procedure. Moreover, a mathematical programming formulation is set up for the static limit analysis of 3-D structures under multi-loading systems and a direct iterative algorithm used to determine the lower bound limit load multiplier is proposed, which depends on the static theorem of plasticity. The numerical examples are given to demonstrate the applicability of the procedure.     

Modeling and hybrid simulation of slow discharge process of adsorbed methane tanks

The slow discharge process of a methane tank filled with porous carbonaceous adsorptive material is modelled and solved by the Integral Transform Method, yielding a hybrid numerical-analytical solution of the related energy equation. A transient one-dimensional nonlinear formulation is adopted, which includes the compressed and adsorbed gas thermal capacitances, the reservoir wall thermal capacitance effect and the gas compressibility influence. The overall mass balance is employed to determine the pressure field evolution, here assumed as spatially uniform. A thorough covalidation analysis is performed, with both numerical and experimental data available in the literature, and the relative importance of some terms in the energy equation formulation is inspected. Finally, different possibilities for the reduction of the adverse effect of the heat of adsorption on storage capacity are proposed and investigated.     

Effective boundary conditions for buoyancy-driven flows and heat transfer in fully open-ended two-dimensional enclosures

The present work achieves an accurate representation of the effective boundary conditions at the aperture plane of a two-dimensional open-ended structure for wide range of pertinent parameters. The presented effective boundary conditions are correlated in terms of Rayleigh number, Prandtl number, and the aspect ratio of the open-ended geometry. The numerical procedure used in this work is based on the Galerkin weighted residual method of finite-element formulation. Comprehensive comparisons between the present investigation using the effective boundary conditions for the anticipated closed-ended model and the results for the fully extended computational domain confirm successful implementation of the proposed model. Implementation of this representation reduces the main difficulties associated with specifying the open-ended boundary conditions and results in very substantial savings in CPU and memory usage. The present work plays an important role on modeling a basic and generic set of effective boundary conditions at the aperture plane for several applications of practical interest.     

Variational multiscale methods for premixed combustion based on a progress-variable approach

In this study, novel computational techniques for the numerical simulation of premixed combustion based on a progress-variable formulation are proposed. Two new variational multiscale methods within a finite element framework are developed for the system of mass, momentum and progress-variable equations: a purely residual-based variational multiscale method and an algebraic variational multiscale-multigrid method. The proposed methods are tested for the numerical example case of a flame–vortex interaction using Arrhenius chemical kinetics. This actually laminar reactive flow problem may serve as a model problem for interactions of turbulent flows and (premixed) flames. The results obtained from this test case show that both methods are capable of accurately predicting the features expected during the progression of the flame–vortex interaction. The evolution of both a pocket of unburned gas and a secluded, drop-like structure, which detaches itself and moves upwards, are accurately predicted already for a relatively coarse discretization.     

Dimensionless lumped formulation for performance assessment of adsorbed natural gas storage

Adsorbed natural gas (ANG) has been emerging as an attractive alternative to compressed natural gas or liquefied natural gas, on various circumstances. However, in spite of the advantages associated with ANG over other storage modes, there are some issues that need be properly addressed in order to ensure a viable employment of such alternative. One major problem is that the thermal effects associated with the sorption phenomena tend to diminish the storage capacity, thereby resulting in poorer performance. Hence, in order to design commercially viable storage vessels, the heat and mass transfer mechanisms that occur in these devices must be carefully understood and controlled. With the purpose of improving the understanding of mass and energy transport within ANG vessels, dimensionless groups associated with this problem have been developed in this study, resulting in an innovation to the ANG literature. Along with the dimensionless groups, a lumped-capacitance formulation has been also proposed. Although this type of formulation is limited compared to the multi-dimensional formulations present in the literature, its computational solution is remarkably faster. Numerical solution results using the proposed lumped formulation are compared with those of a previous study, suggesting that the simpler model can be applied to larger process times. The process of charging and discharging ANG vessels was then simulated employing the proposed formulation for different combinations of the developed dimensionless groups. In order to properly assess charge and discharge processes, a performance coefficient was employed. The results show that increasing the heat capacity ratio and dimensionless heat transfer coefficient tend to augment the performance coefficient, whereas an increase in the dimensionless heat of sorption worsens performance. The proposed normalization scheme is applicable to both multi-dimensional and spatially-lumped formulations, thereby facilitating the analysis of heat transfer enhancement in these storage vessels.     

A dual-porosity dual-permeability model for acid gas injection process evaluation in hydrogen-carbonate reservoirs

The Pre-Caspian basin is one of the most prolific in terms of oil and gas exploration and hydrogen and carbon compounds energy production around the world. The major hydrogen and carbon compounds reservoirs are Carboniferous reef and platform hydrogen-carbonate rocks. The original fluids under subsurface conditions contain 15% hydrogen sulfide and 4% carbon dioxide. Acid hydrogen and carbon compounds reinjection is not only an environmentally friendly solution for disposal of produced greenhouse gases but also enhances oil recovery and supplies more fuel energy. On the other hand, the presence of fractures makes hydrogen-carbonate reservoir characteristics nature more complicated than conventional sandstone reservoirs, which leads to a tremendous challenge to evaluate the gas injection process. In this work, a dual-porosity dual-permeability formulation was used to model the dual-medium nature incorporating matrix system with high porosity and low permeability and fracture network with low porosity and high permeability. After matching PVT experiments, a ten pseudo-components fluid model was generated for running compositional simulation. The miscible hydrogen and carbon compounds injection was simulated as an effective enhanced oil recovery approach. Sensitivity analysis such as timing of injection gas, injection rate, well spacing and completion interval have proposed the optimal condition for the miscible hydrogen and carbon compounds flooding. The recommended optimum hydrogen and carbon compounds injection scenario is twice higher oil recovery compared with natural depletion. The results of this study illustrate further the practicability of pseudo-components splitting and lumping for compositional simulation to evaluate the performance of hydrogen and carbon compounds injection processes, and are of great importance using the dual-porosity dual-permeability method performing numerical simulation of naturally fractured hydrogen-carbonate reservoirs.     

A New Inundation Correlation for the Prediction of Heat Transfer in Steam Condensers

A new correlation used to account for the inundation effect on the prediction of heat transfer between steam vapor and cooling water in tube-and-shell condensers is proposed in this work. The proposed correlation is validated by comparing the predicted results with the experimental data of a steam surface condenser. A modified k–ε turbulence model for gas–liquid two-phase flows with distributed flow resistance is used in the numerical simulation. The predicted results using the proposed correlation agree better with the experimental data than those obtained using the existing correlations for inundation.     

Experimental validation of a lumped model of single droplet deformation,oscillation and detachment on the GDL surface of a PEM fuel cell

Proton Exchange Membrane Fuel Cell (PEMFC) performance significantly depends on electrodes water content. Liquid water emerging from the Gas Diffusion Layer (GDL) micro-channels can form droplets, films or slugs in the Gas Flow Channel (GFC). In the regime of droplets formation, the interaction with the gas flow leads to an oscillating mechanisms that is fundamental to study the detachment from the GDL surface. In this work, a numerical model of a droplet growing on the GDL surface is developed to describe the interaction between droplet and gas flow. Therefore, a lumped force balance is enforced to determine the center of mass motion law. Oscillation frequencies during growth and at detachment are found as a function of droplet size. The model is also exploited to find the relationship between droplet critical detachment size and gas velocity. The numerical results are compared with the experimental data previously published by the authors as well as with other experimental results available in the literature. The matching between the numerical and experimental data is very good. The low computational burden and the conciseness of the proposed approach make the model suitable for applications such as control and optimization strategies development to enhance PEMFC performance. Additionally, the model can be exploited to implement monitoring and diagnostic algorithm as well.     

Improved configuration of supported nickel catalysts in a steam reformer for effective hydrogen production from methane

The heat and mass transfer characteristics in a steam reformer are investigated via experimental and numerical approaches and a new configuration of packed catalysts is proposed for effective hydrogen production. Prior to the numerical investigation, parametric studies are carried for the furnace temperature, steam-to-carbon (S:C) ratio, and gas flow rate. After validation of the developed code, numerical work is undertaken to determine the relationship of the operating parameters. Based on the experimental and numerical results, and with the goal of obtaining optimum heat transfer characteristics and an efficient catalyst array, a new configuration for the packed bed is proposed and numerically investigated taking into account the endothermicity of the steam reforming reaction. A bed packed repeatedly with inert and active catalysts is found to be an efficient means to obtain the same, or better, hydrogen production with small amounts of the active catalysts compared with a typical steam reformer.     

An axisymmetric method of creep analysis for primary and secondary creep

A general axisymmetric method for elastic–plastic analysis was previously proposed by Jahed and Dubey [ASME J Pressure Vessels Technol 119 (1997) 264]. In the present work the method is extended to the time domain. General rate type governing equations are derived and solved in terms of rate of change of displacement as a function of rate of change in loading. Different types of loading, such as internal and external pressure, centrifugal loading and temperature gradient, are considered. To derive specific equations and employ the proposed formulation, the problem of an inhomogeneous non-uniform rotating disc is worked out. Primary and secondary creep behaviour is predicted using the proposed method and results are compared to FEM results. The problem of creep in pressurized vessels is also solved. Several numerical examples show the effectiveness and robustness of the proposed method.     

Numerical and Experimental Modelling of Gas Flow and Heat Transfer in the Air Gap of an Electric Machine

This work deals with the cooling of high-speed electric machines, such as motors and generators, through an air gap. It consists of numerical and experimental modeling of gas flow and heat transfer in an annular channel. Velocity and temperature profiles are modeled in the air gap of a high-speed test machine. Friction and heat transfer coefficients are presented in a large velocity range. The goals are reached acceptably using numerical and experimental research. The velocity field by the numerical method does not match in every respect the estimated flow mode. The absence of secondary Taylor vortices is evident when using time averaged numerical simulation.     

A simple moisture transfer model for drying of sliced foods

The mathematical formulation of mass transfer in drying processes is often based on the nonlinear unsteady diffusion equation. In general, numerical simulations are required to solve these equations. Very often, however, indirect and simplified methods neglecting fundamentals of the processes are used. In this work, a new mathematical model approach for the mass transfer occurring during drying of sliced foods is proposed. The model considers fundamentals of the drying process and takes internal resistance to moisture transfer into account. The parameters in the formulation have physical meaning and permit giving clear view of the moisture depletion process occurring during drying. The proposed model has an analytical solution and allows finding effective diffusion coefficient accurately. The verification of the model is made with basic drying experiments performed for chili red peppers sliced in slab form. The results reveal that there is nearly perfect match between the drying curves obtained by the model and the experiments.     

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.     

Performance analysis of a new tank configuration applied to the natural gas storage systems by adsorption

This work presents a numerical study of a new tank configuration applied to natural gas storage systems by adsorption. The traditional tanks employed in natural gas storage by adsorption reveal serious limitations for use in fast charge systems because of their inefficiency in the dissipation of adsorption heat. In order to eliminate the detrimental effects of adsorption heat, and to make viable the fast charge of gas in automotive tanks, a vessel made up of several tubes, compacted with activated carbon, was proposed. In the charge process, the gas circulates through the tank and all non-adsorbed gasses pass through an external heat exchanger installed close to the gas source of the refueling station. The numerical results obtained in the present work showed that the charge time of the new system can vary from 50 to 200 s, depending on the applied mass flow rate. These time periods are considered satisfactory for fast charge conditions. Another advantage of this new system is that there will be no need to include the accessories employed in traditional tanks, such as: fins, perforated tube in the tank center and a cooling external jacket, which would increase the complexity of the vessel design.     

MULTIPLE TRANSIENT POINT HEAT SOURCES IDENTIFICATION IN HEAT DIFFUSION: APPLICATION TO NUMERICAL TWO- AND THREE-DIMENSIONAL PROBLEMS

This article deals with an inverse problem, which consists of the location and strength identification of multiple-point heat sources in transient heat conduction. The identification procedure is based on a boundary integral formulation using space and time Green functions. The discretized problem is nonlinear if the location of the point heat sources is unknown. In order to reduce the sensitivity of the solution to errors, we use the future time step procedure associated to a Tikhonov regularization procedure. The proposed numerical approach is applied to numerical two- and three-dimensional examples.     

Nonlinear reduction of combustion composition space with kernel principal component analysis

Kernel principal component analysis (KPCA) as a nonlinear alternative to classical principal component analysis (PCA) of combustion composition space is investigated. With the proposed approach, thermo-chemical scalar’s statistics are reconstructed from the KPCA derived moments. The tabulation of the scalars is then implemented using artificial neural networks (ANN). Excellent agreement with the original data is obtained with only 2 principal components (PCs) from numerical simulations of the Sandia Flame F flame for major species and temperature. A formulation for the source and diffusion coefficient matrix for the PCs is proposed. This formulation enables the tabulation of these key transport terms in terms of the PCs and their potential implementation for the numerical solution of the PCs’ transport equations.     

Nonunitary Lewis Number Effects on the Combustion of a Linear Array of Gaseous Fuel Pockets

The numerical solution for the combustion of an infinite linear array of gaseous fuel pockets in a stagnant oxidizing environment under microgravity conditions is discussed. The gas pocket combustion is described using the generalized Shvab-Zel'dovich formulation with nonunitary Lewis number. The combustion process is considered isobaric and the flow is induced by density gradients due to the heat and mass transfer processes (Stefan flow). The model is based on mass, momentum, excess enthalpy, and mixture fraction conservation equations and considers the Burke-Schumann reaction mechanism and ideal gas behavior. The thermophysical properties, except the density, are assumed constant. The finite-volume method is employed in the numerical solution, using a generalized system of coordinates. A nonstaggered grid is used and the SIMPLEC algorithm is employed to solve the modified pressure-velocity coupling. Nonunitary Lewis number and interaction effects on flame behavior and on the fuel consumption are analyzed. Results show that the nonunitary Lewis number can modify the interaction effects on gas pocket linear array combustion. During the combustion process, the flame can evolve from individual flames around each gas fuel pocket to a merged flame, surrounding the merged fuel region. However, under certain conditions, the merged flame and the merged fuel region can be broken, returning to individual flames around each gas fuel pocket.     

CONTROLLED VARIATION SCHEME IN A SEQUENTIAL SOLVER FOR RECIRCULATING FLOWS,PART I: THEORY AND FORMULATION

The formalism of the total variation diminishing (TVD) schemes is utilized to design a convection scheme for incompressible recirculating flows. The scheme has been named the controlled variation scheme (CVS). Even though the CVS does not possess the TVD property for sequential solution algorithms, due to the appearance of source terms, the concept of controlled variation fluxes can be effective in suppressing spurious oscillations that commonly occur in convection-dominated viscous flows, by injecting a nonlinear numerical diffusion, similar to the original TVD schemes, into the central difference scheme. This is demonstrated by using the one-dimensional linear convection-diffusion equation with and without a source term as model problems. The formulation and an efficient implementation of the CVS in a sequential pressure-based solver for incompressible steady-state Navier-Stokes equations is presented in this work. The applications of the CVS for two-dimensional laminar and turbulent flows is presented in Part II of the present work.