Multiphysics Systems Research Articles

Port-Hamiltonian modeling and reduction of a burning plasma system

In this contribution, we develop a structured port-Hamiltonian model for a class of irreversible distributed parameter systems and exploit the obtained formulation for model reduction from dimension 3 to dimension 1 in space. The proposed methodology is motivated by the control of burning plasma profiles in Tokamak reactors. The burning plasma is viewed as a multi-physics system built on Maxwell equations and total mass, species, momentum, energies, and entropy balance equations. Moreover, the system presents nonlinear couplings, especially through transport coefficients, and its dynamic evolves over multiple time scales. The main couplings considered here are the Joule effect, the Lorentz forces, and the fusion reaction kinetics. The port-based modeling formulation and reduction rely on the use of the Gibbs relation, Onsager linear transport theory, Stokes–Dirac structures, and energy preserving geometric reduction.

Component-based modelling of PEM fuel cells with bond graphs

A polymer electrolyte membrane (PEM) fuel cell is a power generation device that transforms chemical energy contained within hydrogen and oxygen gases into useful electricity. The performance of a PEMFC unit is governed by three interdependent physical phenomena: heat, mass, and charge transfer. When modelling such a multi-physical system it is advantageous to use an approach capable of representing all the processes in a unified fashion.This paper presents a component-based model of PEMFCs developed using the bond graph (BG) technique in Modelica language. The basics of the BG method are outlined and a number of relevant publications are reviewed. Model assumptions and necessary equations for each fuel cell component are outlined. The overall model is constructed from a set of bond-graphic blocks within thermal, pneumatic and electrical domains.The model output was compared with the experimental data gathered from a two-cell stack and demonstrated a good accuracy in predicting system behaviour. In the future the designed model will be used for fuel cell reliability studies.

Universal DLL based components for simulations of multiphysical electro-thermal systems

Universal DLL based components for simulations of multiphysical electro-thermal systems

Thermo-electro-mechanical vibration analysis of piezoelectric nanoplates resting on viscoelastic foundation with various boundary conditions

Based on the nonlocal Kirchhoff plate theory, the thermo-electro-mechanical vibration responses are studied for a rectangular piezoelectric nanoplate resting on viscoelastic foundation with various boundary conditions. In doing this, the governing equations of motion are first derived for vibration analysis, where thermo-electro-mechanical loadings, nonlocal effect, piezoelectric effect and viscoelastic foundation have been taken into consideration. Subsequently, the Galerkin strip distributed transfer function method is proposed to solve the governing equations, which enables one to obtain the semi-analytical solutions of natural frequencies for piezoelectric nanoplates with arbitrary boundary conditions. Here, the developed mechanics model is first validated by comparing the obtained results with those available in the literature. Also, the effects of nonlocal parameter, boundary conditions, viscoelastic foundation, external electric voltage, increment temperature, biaxial force and geometric dimensions on the vibration behaviors are carefully examined for the piezoelectric nanoplate. The results demonstrate the efficiency and robustness of the developed model for vibration analysis of a complicated multi-physics system comprising piezoelectric nanoplates, viscoelastic foundation and thermo-electro-mechanical loadings.

Comprehensive global optimization of an implicit constrained multi-physics system for electric vehicles with in-wheel motors

This study establishes an implicit constrained global optimization approach for electric vehicles with in-wheel motors. Limited wheel space and specified vehicle performance make the traditional global optimization algorithms ineffective. An innovative optimization approach is proposed to provide a full understanding of the design space and to find the optimal implicit constrained global solution. First, an in-wheel motor is modeled as a multi-physics system considering structural mechanics, electromagnetism and thermal physics. Then, an optimization problem is built by applying structural geometry and vehicle performance to the multi-physics system as constraints. The structural geometric relationships between the wheel and motor are applied as linear constraints. Vehicle performance derived from typical load cases is treated as an implicit constraint that cannot be satisfied directly in typical optimization algorithms. An innovative procedure is then suggested to explore the design space governed by implicit constraints. Finally, feasible subspaces are distinguished and illustrated in detail. Optimizations based on feasible subspaces are performed. The accuracy and computational costs of the proposed approach are also discussed. The results showed that the proposed approach provides a better solution for the implicit constrained global optimization of multi-physics systems, such as electric vehicle driving systems and energy management, at the same computational cost as that of existing approaches.

Domain-Independent Thermoviscoelastic Modeling Framework: A Physical Approach on Thermoelasticity by Bond Graph

Controlling the thermomechanical behavior of a multiphysical system has always been a challenging issue, because the general behavior of the system in this case is a result of complex energetic transactions between the system’s existing physical subdomains. In this study, a novel thermoviscoelastic modeling framework is proposed in which the thermomechanical behavior of the system is generated from the interactive dynamics of its involving subdomains. To this aim, by means of the Bond graph approach, the dynamic behavior of each subdomain is first generated separately with respect to the interactions of its own energetic components. The dynamics of all involving subdomains are then coupled via generating reversible and irreversible interactions between the counterpart energetic components of different subdomains. The impacts of geometrical and material changes on the system dynamics are finally added to the model via the compatibility consideration of the energetic components of different subdomains. The proposed modeling framework provides an energetic structure with which the general dynamics of the system are obtained from the constructive dynamics of each of the subdomains. This special capability of the proposed modeling framework leads to an automatic capture of the thermomechanical phenomena inside the system. The obtained simulation results for a simple beam structure demonstrate the impacts of the internal dynamics on the observable behavior of the system and prove the applicability of the proposed approach to the modeling of a wide range of thermomechanical behaviors, including material softening, vibrational heating, dilation, relaxation, conduction, and damping.

Inverse Predictive Modeling of Radiation Transport Through Optically Thick Media in the Presence of Counting Uncertainties

Using the problem of inverse prediction from detector responses in the presence of counting uncertainties of the thickness of a homogeneous slab of material containing uniformly distributed gamma-emitting sources, this work investigates the possible reasons for the apparent failure of the traditional inverse-problem methods based on the minimization of chi-square-type functionals to predict accurate results for optically thick slabs. This work also compares the results produced by such methods with the results produced by applying the Predictive Modeling of Coupled Multi-Physics Systems (PM-CMPS) methodology for optically thin and thick slabs. For optically thin slabs, this work shows that both the traditional chi-square-minimization method and the PM-CMPS methodology predict the slab’s thickness accurately. However, the PM-CMPS methodology is considerably more efficient computationally, and a single application of the PM-CMPS methodology predicts the thin slab’s thickness at least as precisely as the traditional chi-square-minimization method, even though the measurements used in the PM-CMPS methodology were ten times less accurate than the ones used for the traditional chi-square-minimization method. For optically thick slabs, the results obtained in this work show that: (1) the traditional inverse-problem methods based on the minimization of chi-square-type functionals fail to predict the slab’s thickness; (2) the PM-CMPS methodology underpredicts the slab’s actual physical thickness when imprecise experimental results are assimilated, even though the predicted responses agree within the imposed error criterion with the experimental results; (3) the PM-CMPS methodology correctly predicts the slab’s actual physical thickness when precise experimental results are assimilated, while also predicting the physically correct response within the selected precision criterion; and (4) the PM-CMPS methodology is computational vastly more efficient while yielding significantly more accurate results than the traditional chi-square-minimization methodology.

Sensitivity and Uncertainty Analysis of Counter-Flow Mechanical Draft Cooling Towers—II: Predictive Modeling

Based on the adjoint sensitivity models for the saturated case of the counter-flow cooling tower developed in the accompanying Part I, this work computed and analyzed the sensitivities, with respect to all of the 52 model parameters, of the following responses (i.e., model outputs of interest): the outlet air temperature, outlet water temperature, outlet water mass flow rate, and outlet air relative humidity. The sensitivity results indicate that, in general, all these response of interest are mostly sensitive to the boundary-related parameters (e.g., , , , , , and ) and also somewhat sensitive to those parameters (e.g., , , , , , , and ) that directly relate to the heat and mass transfer terms in the cooling tower model. The rankings of these parameters depend on the respective model responses. With the sensitivities known, the propagation of the uncertainties in the model parameters to the uncertainties in the model outputs are readily obtained. The uncertainties associated with the model outputs were reduced by applying the “predictive modeling for coupled multiphysics systems” (PM_CMPS) methodology. For a typical case studied in this work, the uncertainties associated with the model outputs of the outlet air temperature, outlet water temperature, and outlet air relative humidity, are reduced by 22%, 38%, and 68%, respectively. Moreover, the PM_CMPS methodology also generated optimal best-estimate nominal values for the model parameters and model responses. It also improved (i.e., reduced) the uncertainties associated with model parameters through the process of model calibration, as shown in the paper. The results presented in this work demonstrate that the PM_CMPS methodology reduces the predicted standard deviations to values that are smaller than either the computed or the experimentally measured ones, even for responses (e.g., the outlet water flow rate) for which no measurements are available. These improvements stem from the global characteristics of the PM_CMPS methodology, which combines all of the available information simultaneously in phase-space, as opposed to combining it sequentially, as in current data assimilation procedures.

Sensitivity and Uncertainty Analysis of Counter-Flow Mechanical Draft Cooling Towers—I: Adjoint Sensitivity Analysis

For counter-flow mechanical draft cooling towers, the air in the fill can reach the point of saturation before leaving the fill section. The heat and mass transfer to the saturated air by evaporative cooling inside the fill are modeled with some assumptions and with over 50 parameters for boundary conditions, cooling tower geometries, heat and mass transfer correlations, water and air thermal properties, etc. Because of the parameter uncertainties and modeling assumptions, the accuracy and reliability of the cooling tower model need to be evaluated by quantifying the uncertainties associated with the model output. First, sensitivities of the model output with respect to all the model parameters need to be analyzed. Based on the cooling tower model, this work developed adjoint sensitivity models for the saturated case to compute efficiently and exactly the sensitivities of the model responses to all model parameters by applying the general adjoint sensitivity analysis methodology for nonlinear systems. The solution of the adjoint sensitivity models are independently verified. With the sensitivities known, the model parameters can be ranked in their importance for contributing to response uncertainties. The propagation of the uncertainties in the model parameters to the uncertainties in the model outputs can be evaluated. By further applying the predictive modeling for coupled multiphysics systems methodology, the cooling tower model for the saturated case can be improved by reducing the model prediction uncertainties through assimilation of experimental measurements and calibration of model parameters.

Safeguarding against Inactivation Temperatures during Plasma Treatment of Skin: Multiphysics Model and Phase Field Method

One of the most appealing applications of cold plasmas is medical treatment of the skin. An important concern is the capability to safeguard the non-targeted cells against inactivation temperatures during the plasma treatment. Unfortunately, it is problematic to experimentally determine the highest transient temperatures in these cells during the plasma treatment. In the present work, a complete multiphysics model was built based on finite element analysis using phase field method coupled with heat transfer and fluid dynamics to study the discharge phenomenon of cold plasma with helium carrier gas ejected out of a tube for skin treatment. In such plasmas with carrier gas, the fractions of plasma constituents are small compared to the carrier gas, so thermofluid analysis is needed for the carrier gas as the major contributor to the fluid and heat flow. The phase field method has been used to capture the moving helium gas in air, which has enabled us to compute fluid dynamics parameters for each phase individually. In addition to computational fluid dynamic analyses, we have also considered heat transfer in the fluids and to the skin using the Fourier law of heat conduction, which led to a multiphysics system. In the present paper, various flow velocities and tube-to-target distances (TTDs) have been considered to reveal the dependence of the fluid discharge output parameters on the flow and efficiency of heat transfer to the skin and the surrounding environment. The built model is a useful tool for future development of plasma treatment devices and to safeguard the non-targeted cells against inactivation temperatures.

Study on Fluid-Induced Vibration Power Harvesting of Square Columns under Different Attack Angles

A model of the flow-vibration-electrical circuit multiphysical coupling system for solving square column vortex-induced vibration piezoelectric energy harvesting (VIVPEH) is proposed in this paper. The quasi steady state theory is adopted to describe the fluid solid coupling process of vortex-induced vibration based on the finite volume method coupled Gauss equation. The vibrational response and the quasi steady state form of the output voltage are solved by means of the matrix coefficient method and interactive computing. The results show that attack angles play an important role in the performance of square column VIVPEH, of which α=45° is a relatively ideal attack angle of square column VIVPEH.

An Overview of the Main Topics and Applications of Graph Theoretic Problems in Multiphysics Engineering

Graph-theoretic concepts are mostly used to study different applications in various areas such as electrical and mechanical engineering, generally multi-physics systems. The interest of researchers on this theory has importantly increased in the last decade. The main goal of this paper is to provide an overview of the use and applications of graph theoretic concept in modelling and analysis of systems in different fields. Therefore, the research topics discussed in this review are going to respect all the mentioned domains and the countries that apply this theory formulation in addition to the community of researchers who are identified by their publishers.

Backbone: A Multiphysics Framework for Coupling Nuclear Codes Based on CORBA and MPI

Recent trends in nuclear reactor performance and safety analyses increasingly rely on multiscale multiphysics computer simulations to enhance predictive capabilities by replacing conventional methods that are largely empirically based with a more scientifically based methodology. Through this approach, one addresses the issue of traditionally employing a suite of stand-alone codes that independently simulate various physical phenomena that were previously disconnected. Multiple computer simulations of different phenomena must exchange data during runtime to address these interdependencies. Previously, recommendations have been made regarding various approaches for piloting different design options of data coupling for multiphysics systems (Seydaliev and Caswell, 2014, “CORBA and MPI Based “Backbone” for Coupling Advanced Simulation Tools,” AECL Nucl. Rev., 3(2), pp. 83–90). This paper describes progress since the initial pilot study that outlined the implementation and execution of a new distribution framework, referred to as “Backbone,” to provide the necessary runtime exchange of data between different codes. The Backbone, currently under development at the Canadian Nuclear Laboratories (CNL), is a hybrid design using both common object request broker architecture (CORBA) and message passing interface (MPI) systems. This paper also presents two preliminary cases for coupling existing nuclear performance and safety analysis codes used for simulating fuel behavior, fission product release, thermal hydraulics, and neutron transport through the Backbone. Additionally, a pilot study presents a few strategies of a new time step controller (TSC) to synchronize the codes coupled through the Backbone. A performance and fidelity comparison is presented between a simple heuristic method for determining time step length and a more advanced third-order method, which was selected to maximize configurability and effectiveness of temporal integration, saving time steps and reducing wasted computation. The net effect of the foregoing features of the Backbone is to provide a practical toolset to couple existing and newly developed codes—which may be written in different programming languages and used on different operating systems—with minimal programming effort to enhance predictions of nuclear reactor performance and safety.

Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano

This paper deals with the time-domain simulation of an electro-mechanical piano: the Fender Rhodes. A simplified description of this multi-physical system is considered. It is composed of a hammer (nonlinear mechanical component), a cantilever beam (linear damped vibrating component) and a pickup (nonlinear magneto-electronic transducer). The approach is to propose a power-balanced formulation of the complete system, from which a guaranteed-passive simulation is derived to generate physically-based realistic sound synthesis.Theses issues are addressed in four steps. First, a class of Port-Hamiltonian Systems is introduced: these input-to-output systems fulfill a power balance that can be decomposed into conservative, dissipative and source parts. Second, physical models are proposed for each component and are recast in the port-Hamiltonian formulation. In particular, a finite-dimensional model of the cantilever beam is derived, based on a standard modal decomposition applied to the Euler-Bernoulli model. Third, these systems are interconnected, providing a nonlinear finite-dimensional Port-Hamiltonian System of the piano. Fourth, a passive-guaranteed numerical method is proposed.This method is built to preserve the power balance in the discrete-time domain, and more precisely, its decomposition structured into conservative, dissipative and source parts. Finally, simulations are performed for a set of physical parameters, based on empirical but realistic values. They provide a variety of audio signals which are perceptively relevant and qualitatively similar to some signals measured on a real instrument.

Energy management strategy for a fuel cell hybrid vehicle based on maximum efficiency and maximum power identification

This paper addresses the energy management strategy (EMS) for a fuel cell hybrid electric vehicle (FC-HEV). The fuel cell system (FCS) is a multi-physics system, and consequently, its energetic performances depend on the degradation and on the operating conditions. The maximum power (MP) and the maximum efficiency (ME) points of the FCS are unique but they move with operating condition variations. Thus, developing an extremum seeking process (ESP) for both MP and ME tracking is a challenging task. In the ESP, models are identified online by using an adaptive recursive least square (ARLS) method to seek a variation in the FCS performances. Then an optimisation algorithm is used on the updated model to find the MP and the ME points. The ESP is incorporated into a hysteresis power splitting control (HPSC). A MP mode or a ME mode can be set based on the energy storage level (battery pack). The effectiveness of the proposed MP- and ME-ESP EMS is demonstrated by conducting experimental studies on two FCSs with different levels of degradation. It was demonstrated that the classical EMS based on maps are not valid when the operating parameters vary because of the level of degradation change.

Geometric methods and formulations in computational multibody system dynamics

Multibody systems are dynamical systems characterized by intrinsic symmetries and invariants. Geometric mechanics deals with the mathematical modeling of such systems and has proven to be a valuable tool providing insights into the dynamics of mechanical systems, from a theoretical as well as from a computational point of view. Modeling multibody systems, comprising rigid and flexible members, as dynamical systems on manifolds, and Lie groups in particular, leads to frame-invariant and computationally advantageous formulations. In the last decade, such formulations and corresponding algorithms are becoming increasingly used in various areas of computational dynamics providing the conceptual and computational framework for multibody, coupled, and multiphysics systems, and their nonlinear control. The geometric setting, furthermore, gives rise to geometric numerical integration schemes that are designed to preserve the intrinsic structure and invariants of dynamical systems. These naturally avoid the long-standing problem of parameterization singularities and also deliver the necessary accuracy as well as a long-term stability of numerical solutions. The current intensive research in these areas documents the relevance and potential for geometric methods in general and in particular for multibody system dynamics. This paper provides an exhaustive summary of the development in the last decade, and a panoramic overview of the current state of knowledge in the field.

A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.

Vibration analysis of horn-shaped single-walled carbon nanotubes embedded in viscoelastic medium under a longitudinal magnetic field

Based on nonlocal Euler-Bernoulli beam theory, vibration characteristics are investigated for a horn-shaped single-walled carbon nanotube (SWCNT) which is embedded in a viscoelastic medium and subjected to a longitudinal magnetic field. Governing equations of motion are derived for vibration analysis of horn-shaped SWCNTs, where the Lorentz magnetic force, the surrounding viscoelastic medium and variable cross-section have been taken into consideration. Subsequently, perturbation method (PM) and transfer function method (TFM) are employed to compute the natural frequencies and the corresponding mode shapes for horn-shaped SWCNTs with arbitrary boundary conditions. The obtained results are first compared with the results available in the literature, where good agreement is achieved. The validation of the model is followed by a detailed parametric study of the effects of nonlocal parameter, taper parameter and longitudinal magnetic field on the vibration of horn-shaped SWCNTs. The results demonstrate the efficiency of the developed model for vibration analysis of a complicated multi-physics system comprising horn-shaped SWCNTs, viscoelastic medium and a magnetic field in longitudinal direction.

Predictive Modeling of a Paradigm Mechanical Cooling Tower Model: II. Optimal Best-Estimate Results with Reduced Predicted Uncertainties

This work uses the adjoint sensitivity model of the counter-flow cooling tower derived in the accompanying PART I to obtain the expressions and relative numerical rankings of the sensitivities, to all model parameters, of the following model responses: (i) outlet air temperature; (ii) outlet water temperature; (iii) outlet water mass flow rate; and (iv) air outlet relative humidity. These sensitivities are subsequently used within the “predictive modeling for coupled multi-physics systems” (PM_CMPS) methodology to obtain explicit formulas for the predicted optimal nominal values for the model responses and parameters, along with reduced predicted standard deviations for the predicted model parameters and responses. These explicit formulas embody the assimilation of experimental data and the “calibration” of the model’s parameters. The results presented in this work demonstrate that the PM_CMPS methodology reduces the predicted standard deviations to values that are smaller than either the computed or the experimentally measured ones, even for responses (e.g., the outlet water flow rate) for which no measurements are available. These improvements stem from the global characteristics of the PM_CMPS methodology, which combines all of the available information simultaneously in phase-space, as opposed to combining it sequentially, as in current data assimilation procedures.

Dimensional analysis and surrogate models for the thermal modeling of Multiphysics systems

This paper presents an original form of surrogate models and the associated construction procedure adapted to the thermal modeling of Multiphysics systems. This method of meta-modeling, which uses dimensional analysis, extracts compact models suitable for preliminary design from finite element simulations. The mathematical expression used for the model is a product of variable power laws of dimensionless numbers. Compared to traditional surrogate models (polynomial response surfaces, kriging and radial basis functions), it has the advantage of giving light, compact forms with good predictive accuracy over a wide range of the design variables (several orders of magnitude). The general regression process is first explained and illustrated with a study of the Marangoni effect. Then the methodology is used to build thermal models of an electromechanical actuator (EMA) which are used to size an aileron EMA for two different cooling strategies. Finally the models are also used to discuss the effect of confinement on the actuator’s overall thermal resistance.