Multiphysics Processes Research Articles

Development of Mathematical Models and Computational Framework for Multi-physics Interaction Processes

This paper presents development of mathematical models for multi-physics interaction processes in which the physics of solids, liquids and gases are described using conservation laws, appropriate constitutive equations and equations of state in Eulerian description. The use of conservation laws in Eulerian description for all media of an interaction process and the choice of the same dependent variables in the resulting governing differential equations (GDEs) for solids, liquids and gases ensure that their interactions are intrinsic in the mathematic model. In the development of the constitutive equations and the equations of state, the same dependent variables are also utilized as those in the conservation laws. The dependent variables of choice due to the Eulerian description (which is necessary for liquids and gases) are density, pressure, velocities, temperature, heat fluxes and stress deviations. For solid, liquids and gases the development of constitutive equations is based on rate constitutive equations utilizing convected time derivatives of the chosen stress and strain measures. The resulting GDEs from these mathematical models are a system of non-linear partial differential equations in space coordinates and time. The hpk mathematical and computational finite element framework with space-time variationally consistent (STVC) integral forms is utilized to obtain the numerical solutions of the associated initial value problems. The proposed computational methodology permits higher order global differentiability approximations, and ensures time accuracy of evolutions as well as unconditional stability of computations during the entire evolution. The methodology presented here for multi-media interaction processes is rather natural and lends itself naturally to accurate finite element computations in hpk framework when the integral forms are STVC. In most of the currently used methodologies, the interaction between the different media is established using constraint equations at the interfaces between the media. Thus these approaches are error prone and the validity and accuracy of the computed solution is highly dependent on the physics described by the constraint equations. In the proposed methodology, the constraint equations are completely eliminated.

Mathematical modeling analysis of regenerative solid oxide fuel cells in switching mode conditions

A 2D transient mathematical model is developed for regenerative solid oxide cells operated in both SOFC mode and SOEC mode. The steady state performance of the model is validated using experimental results of in-house prepared NiO–YSZ/YSZ/LSM cell under different operating temperatures. The model is employed to investigate complicated multi-physics processes during the transient process of mode switching. Simulation results indicate that the trend of internal parameter distributions, including H 2/O 2/H 2O and ionic potentials, flip when the operating cell is switched from one mode to another. However, the electronic potential shows different behaviors. At H 2 electrode, electronic potential keeps at zero voltage level, while at O 2 electrode, it increases from a relatively low level in SOFC mode to a relatively high level in SOEC mode. Transient results also show that an overshooting phenomenon occurs for mass fraction distribution of water vapor at H 2 side when the operating cell switches from SOFC mode to SOEC mode. The mass fractions of O 2 and H 2 as well as charge (electrons and ions) potentials may quickly follow the operating mode changes without over-shootings. The simulation results facilitate the internal mechanism understanding for regenerative SOFCs.

A dynamic multi-timescale method for combustion modeling with detailed and reduced chemical kinetic mechanisms

A new on-grid dynamic multi-timescale (MTS) method is presented to increase significantly the computation efficiency involving multi-physical and chemical processes using detailed and reduced kinetic mechanisms. The methodology of the MTS method using the instantaneous timescales of different species is introduced. The definition of the characteristic time for species is examined and compared with that of the computational singular perturbation (CSP) and frozen reaction rate methods by using a simple reaction system. A hybrid multi-timescale (HMTS) algorithm is constructed by integrating the MTS method with an implicit Euler scheme, respectively, for species with and without the requirement of accurate time histories at sub-base timescales. The efficiency and the robustness of the MTS and HMTS methods are demonstrated by comparing with the Euler and VODE solvers for homogenous ignition and unsteady flame propagation of hydrogen, methane, and n-decane–air mixtures. The results show that both MTS and HMTS reproduce well the species and temperature histories and are able to decrease computation time by about one-order with the same kinetic mechanism. Compared to MTS, HMTS has slightly better computation efficiency but scarifies the stability at large base time steps. The results also show that with the increase of mechanism size and the decrease of time step, the computation efficiency of multi-timescale method increases compared to the VODE solver. In addition, it is shown that the integration of the multi-timescale method with the path flux analysis based mechanism reduction approach can further increase the computation efficiency. Unsteady simulations of outwardly propagating spherical n-decane–air premixed flames demonstrate that the multi-timescale method is rigorous for direct numerical simulations with both detailed and reduced chemistry and can dramatically improve the computation efficiency.

Multi-physical processes in geomechanics

ABSTRACT This paper is the basis for a course dedicated to the geomechanics modelling, taking into account multiphysics couplings. A number of different coupling are discussed, with respectively the fluid flow (saturated and unsaturated) and the thermal transfers in deformable porous media. Eventually some aspects on the numerical modelling with the finite element method are discussed.

Multi-physical processes in geomechanics An introduction to constitutive modelling and coupling aspects

Multi-physical processes in geomechanics An introduction to constitutive modelling and coupling aspects

Multi-physical processes in geomechanics An introduction to constitutive modelling and coupling aspects

This paper is the basis for a course dedicated to the geomechanics modelling, taking into account multiphysics couplings. A number of different coupling are discussed, with respectively the fluid flow (saturated and unsaturated) and the thermal transfers in deformable porous media. Eventually some aspects on the numerical modelling with the finite element method are discussed.

Computational Fluid Dynamic Analysis of a Seal-Less Solid Oxide Fuel Cell Stack

Combined heat and power generation systems accommodating intermediate temperature (600–800°C) solid oxide fuel cell (SOFC) modules have been developed by Mitsubishi Materials Corporation and The Kansai Electric Power Co., Inc. High overall efficiency system units are designed in such a way that their output power can be modularized by altering the number of stacks inside the SOFC modules. The seal-less design concept is adopted to build generic stacks made up of stainless steel separators and disk-type planar electrolyte-supported cells. Innovative stack design together with its precise integration with the hot balance of plant components inside the SOFC module requires a number of design iterations supported by carefully planned experiments. In order to achieve improved levels of efficiency and reliability via optimum number of iterative cycles, we believe that the computational techniques offer significant advantages. In this work, a commercial computational fluid dynamics code is employed for solving the conservation of mass, momentum, and energy equations with an additional electrochemical submodel to simulate the coupled multiphysics processes in a generic SOFC stack. This approach proved to be effective in providing necessary guidance for identifying problem areas in the stack design and estimating the stack performance via less expensive numerical experiments. The results of the computational model are also compared with data obtained by experimental measurements.

Advances in simulation of wave interactions with extended MHD phenomena

The Integrated Plasma Simulator (IPS) provides a framework within which some of the most advanced, massively-parallel fusion modeling codes can be interoperated to provide a detailed picture of the multi-physics processes involved in fusion experiments. The presentation will cover four topics: 1) recent improvements to the IPS, 2) application of the IPS for very high resolution simulations of ITER scenarios, 3) studies of resistive and ideal MHD stability in tokamk discharges using IPS facilities, and 4) the application of RF power in the electron cyclotron range of frequencies to control slowly growing MHD modes in tokamaks and initial evaluations of optimized location for RF power deposition.

Consistency of iterative operator‐splitting methods: Theory and applications

AbstractIn this article, we describe a different operator‐splitting method for decoupling complex equations with multidimensional and multiphysical processes for applications for porous media and phase‐transitions. We introduce different operator‐splitting methods with respect to their usability and applicability in computer codes. The error‐analysis for the iterative operator‐splitting methods is discussed. Numerical examples are presented. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

An On-Grid Dynamic Multi-Timescale Method with Path Flux Analysis for Multi-Physics Detailed Modeling of Combustion

Combustion is a kinetic and multi-physical-chemical process involving many time and length scales from atomic excitation to turbulent mixing. This paper presents an overview of the recent progress of numerical modeling using detailed and reduced chemical kinetic mechanisms for multi-scale combustion problems. A particular focus of this review is to introduce two new methods, an on-grid dynamic multi-time scale (MTS) method and a path flux analysis (PFA) to increase the computation efficiency involving multi-physical chemical processes using large kinetic mechanisms. Firstly, the methodology of the on-grid dynamic MTS method using the instantaneous time scales of different reaction groups is introduced. The definition of species timescales and the algorithm to generate species groups are presented. Secondly, a concept of hybrid multi-time scale (HMTS) method to selectively remove time histories of uninterested fast modes is introduced to increase the algorithm flexibility and efficiency. The efficiency and the robustness of the MTS and HMTS methods are demonstrated by comparing with the Euler and ODE solvers for ignition and flame propagation of hydrogen, methane, and n-decane-air mixtures. Thirdly, the PFA method to generate a comprehensive reduced mechanism by using the reaction path fluxes in multiple generations is summarized. The results are compared with that of the direct relation graph (DRG) method for n-decane and n-heptane-air ignition delay time. The PFA method shows a significant improvement in the accuracy of mechanism reduction over the DRG method in a broad range of species number and physical properties. Finally, the PFA method is integrated with MTS and HMTS methods to further increase the computation efficiency of combustion with large mechanisms. The new algorithm is used to predict unsteady flame propagation of n-decane-air mixtures in a spherical chamber. Excellent computation accuracy and efficiency are demonstrated.

A model-coupling framework for nearshore waves, currents, sediment transport, and seabed morphology

This paper presents a framework for synchronously coupling wave, current, sediment transport, and seabed morphology for the accurate simulation of multi-physics coastal ocean processes. The governing equations, which represent models that are commonly adopted in practical simulations, are discretized using finite-difference methods. The resulting system is validated against analytical solutions. In order to test the performance of the proposed framework and the numerical methods, dam-break flow over a mobile-bed and evolution of a wave-driven sand dune are simulated. The interactions among waves, currents, and seabed morphology are illustrated.

Increased Storage Capacity at Yucca Mountain Favors Thermal Management for a Cold Repository

The nuclear waste storage concept according to the baseline design of the proposed high-level nuclear waste repository at Yucca Mountain is analyzed. The high-temperature storage concept, in which the emplacement area is heated above the boiling temperature of water, is subject to criticism on the basis of uncertainties due to nonlinear multiphysics processes in the rock mass and in the storage airspace. The storage environment around the nuclear waste containers is reexamined using a new thermal-hydrologic airflow model. The complex nature of the thermal-hydraulic behavior in a superheated waste repository is described with fewer simplifying assumptions than those used in the baseline design. The emplacement area in the mountain is described as an open system, in which the air pressure is connected to the barometric pressure through fractures, faults, and partially sealed drifts. The cyclic variation of the atmospheric pressure that affects the heat and mass transport processes in the near-field rock mass is also modeled. The implications of evaporation into the drift airspace are discussed, and a hypothesis of salt accumulation in the near-field rock mass is established. Model calculation is also presented for a below-boiling temperature storage concept that is easier to predict and has fewer anomalies. The price for a below-boiling temperature storage is the extended preclosure ventilation time period. However, as demonstrated for a trade-off, it is possible to design a repository with below-boiling temperatures and doubled waste inventory at the same time.

Analysis of processes in planar solid oxide fuel cells

In this paper, a platform for solid oxide fuel cell (SOFC) simulation has been developed and the corresponding algorithms are presented. The platform is capable of dealing with fully coupled multiphysical processes and simulating the behaviors of three flow configurations. “Border effects” were revealed and it is important to understand the scale-up topic in SOFC development. The determining steps in cell performance are proposed and respective schemes are provided to enhance cell performance according to the determining steps. The characteristics of the three flow configurations were analyzed and compared. The cross-flow configuration was given negative recommendations for its unsatisfactory performance in uniformly distributing cell temperature and current density. The co-flow configuration could intrinsically obtain a uniform current density distribution with the disadvantage of steadily increasing cell temperature from fuel inlet to outlet. The counter-flow configuration had “localized enhancement effects” near the fuel inlet and cell performance substantially benefited from these effects. But the operating conditions of the counter-flow configuration should be deliberately adjusted to avoid an excessively high cell temperature.

Modélisation de l'élasticité d'une pâte de ciment au jeune âge

ABSTRACT Concrete is a complex multi-scale composite involving multi-physics processes. As it is the only evolving component, the cement paste has a major influence on the mechanical properties of concrete at early age. The homogenization theory for disordered media is used in order to model the development of the elastic properties of a cement paste during its hydration. The morphological model refers to two types of C-S-H distinguished by many authors: high density C-S-H or inner products build up layers surrounding the anhydrous particles, while low density C-S-H or outer products play the role of a porous matrix. The effective Young's modulus evolution with respect to the degree of hydration proves to be in excellent agreement with the experimental results available in the literature.

Modélisation de l'élasticité d'une pâte de ciment au jeune âge

ABSTRACT Concrete is a complex multi-scale composite involving multi-physics processes. As it is the only evolving component, the cement paste has a major influence on the mechanical properties of concrete at early age. The homogenization theory for disordered media is used in order to model the development of the elastic properties of a cement paste during its hydration. The morphological model refers to two types of C-S-H distinguished by many authors: high density C-S-H or inner products build up layers surrounding the anhydrous particles, while low density C-S-H or outer products play the role of a porous matrix. The effective Young's modulus evolution with respect to the degree of hydration proves to be in excellent agreement with the experimental results available in the literature.

Modelling elasticity of a hydrating cement paste

Concrete is a complex multi-scale composite involving multi-physics processes. As it is the only evolving component of concrete, the cement paste has a major influence on the mechanical properties of concrete at early age. This paper focuses on the increase of the elastic properties of a cement paste during its hydration. The homogenization theory for disordered media is used in order to estimate the evolution of the effective elastic moduli of the hydrating paste. The morphological model refers to two types of C-S-H (calcium silicate hydrates, main hydration products of Portland cements) distinguished by many authors: inner products or high density C-S-H build up layers surrounding the anhydrous particles, while the outer products or low density C-S-H play the role of a porous matrix. The simulations of the effective Young's modulus at late age during hydration and at the end of hydration prove to be in excellent agreement with the experimental results available in the literature.

Direct numerical simulation of turbulent counterflow nonpremixed flames

This paper presents our recent progress in terascale three-dimensional simulations of turbulent nonpremixed flames in the presence of a mean flow strain and fine water droplets. Under the ongoing university collaborative project supported by the DOE SciDAC Program [1] along with the INCITE 2007 Project [2], the study aims at bringing the state-of-the-art high-fidelity simulation capability to the next level by incorporating various advanced physical models for soot formation, radiative heat transfer, and lagrangian spray dynamics, to an unprecedented degree of detail in high-fidelity simulation application. The targeted science issue is fundamental characteristics of flame suppression by the complex interaction between turbulence, chemistry, radiation, and water spray. The high quality simulation data with full consideration of multi-physics processes will allow fundamental understanding of the key physical and chemical mechanisms in the flame quenching behavior. In this paper, recent efforts on numerical algorithms and model development toward the targeted terascale 3D simulations are discussed and some preliminary results are presented.

Adaptive mesh simulations of multi-physics processes during pellet injection in tokamaks

We present the results of fully 3D adaptive mesh MHD simulations of fueling pellets injected into tokamaks. The Chombo framework for block structured local adaptive mesh refinement (AMR), extended to use the equilibrium magnetic coordinates, is employed to mitigate the problems due to the large range of spatial scales. Generalized upwinding techniques are employed to deal with sharp gradients. The modeling includes a semi-analytical kinetic treatment of the transport of electron energy flux which drives the ablation. We discuss the phenomenology of the mass redistribution processes involving the density equilibrating along field lines and transport across surfaces (in the large-major-radius direction).

Computational modelling of polymer electrolyte membrane (PEM) fuel cells: Challenges and opportunities

Fuel cells are still undergoing intense development, and the combination of new and optimized materials, improved product development, novel architectures, more efficient transport processes, and design optimization and integration are expected to lead to major gains in performance, efficiency, reliability, manufacturability and cost-effectiveness. Computational fuel cell engineering (CFCE) tools that allow systematic simulation, design and optimization of fuel cell systems would facilitate the integration of such advances, allow less heavy reliance on hardware prototyping, and reduce development cycles. CFCE requires the robust integration of models representing a variety of complex multi-physics transport processes characterized by a broad spectrum of length and time scales. These processes include a fascinating, but not always well understood, array of phenomena involving fluidic, ionic, electronic and thermal transport in concert with electrochemical reactions. In this paper, we report on some progress in both fundamental modelling of these phenomena, as well as in the development of integrated, computational fluid dynamics (CFD) based models for polymer electrolyte membrane (PEM) fuel cells. A new rational model for coupled protonic and water transport in PEMS, as well direct numerical simulations of two-phase flow in porous gas diffusion electrodes are discussed. Illustrative applications of CFD-based simulations are presented for conventional fuel cells and novel micro-structured fuel cells. The paper concludes with a perspective on some of the remaining theoretical, experimental and numerical challenges to achieve truly functional CFCE tools.

Multiphysics processes in concrete

Multiphysics processes in concrete