Thermal Solver Research Articles

Advances in Multiphysics Modeling for Parallel Finite-Element Code Suite ACE3P

Developed by SLAC, the advanced computational electromagnetics three-dimensional parallel (ACE3P) code suite is a comprehensive set of parallel finite-element codes for multiphysics modeling of particle accelerators. Running on massively parallel computer platforms for high fidelity and high accuracy simulation, ACE3P enables rapid virtual prototyping of accelerator and radio frequency (RF) component design, optimization, and analysis. Recent advances of ACE3P have been focused on the implementation of advanced numerical algorithms, enhancement of multiphysics capabilities, and integration of ACE3P with other particle beams and plasmas codes toward end-to-end simulations in accelerators, and improvement of code performance on the state-of-the-art high-performance computing (HPC) platforms for large-scale RF modeling in accelerator applications and beyond. In this article, we will present a nonlinear electromagnetic (EM) eigensolver for damping calculation of resonant modes for cavities coupled with waveguides, the thermal solver for accurate evaluation of heat loads in superconducting RF (SRF) cavity power coupler, the elastic solver for investigation of SRF cavity cryomodule (CM) bowing due to thermal effect, the frequency-domain mechanical solver for studying SRF cavity mechanical oscillation modes, the particle tracking code for dark current simulation in SRF CM using a hybrid MPI+OpenMP parallel programming model, and the time-domain solver for high-fidelity modeling of EM wave propagation for powering midfield medical devices in human body. All the simulations have been performed on the computing resources at the National Energy Research Scientific Computing Center, and the impact of HPC on multiphysics modeling will be discussed.

A new microwave applicator for laparoscopic and robotic liver resection

Purpose: Bleeding from parenchyma transection during a robotic hepatic surgery remains the most critical point affecting postoperative recovery and long-term survival. Various robotic devices with different types of energies have been proposed; however, each of these lack in steerability, efficacy, or accuracy. The aim of this work is to evaluate the feasibility and performance of a new steerable microwave resection device intended for minimizing intraoperative blood loss during laparoscopic and robotic liver resections.Methods: The new device operating at 2.45 GHz was designed to accommodate the engineering constraints derived from its use for robotic surgery or laparoscopy, in which a steerable head is required and the internal cooling of forced gas or water is undesirable. The device design, analysis, and optimization were addressed using the most advanced commercial electromagnetic and thermal solvers to achieve the best results. To experimentally validate the results of the numerical analysis, many ablations were performed on a freshly explanted bovine liver by using a single device prototype with three levels of energy supplied to the tissue. During the ablation procedures, the time, temperature, and shape of the thermal lesion were recorded using thermocouples and an infra-red thermos camera.Summary: Ex vivo tests showed good agreement with the numerical simulations, demonstrating the validity of the simplifications adopted to deal with the complex phenomena involved in the extreme hyperthermia of a living tissue. The high performance, thermal reliability, and robustness of the developed device were also demonstrated along with the possibility of reducing operation time and blood loss.

Fully coupled multi-physics nonlinear analysis of structural space frames subjected to fire using the direct stiffness method

This article develops a fully coupled hydro-thermo-mechanical formulation based on the direct stiffness method for analysis of steel and reinforced concrete structural space frames. The superiority of the developed formulation lies in developing the direct stiffness method for fire analysis, which enables use of a much coarser spatial mesh when compared to existing fire analysis frameworks. Effects of temperature-dependent material properties, damage due to fire and pore pressure, nonlinear thermal gradients, and large deformations of structural members are directly integrated into the stability and bowing functions in the construction of the member stiffness matrix. This alleviates the need to perform element-level numerical quadrature, typically required by all existing finite element–based approaches. Full coupling between the pore pressure, thermal and mechanical solvers is considered through a two-level spatial discretization strategy with a staggered scheme for the numerical solution procedure. Five numerical examples are presented to demonstrate the accuracy and efficacy of the developed formulation in analysis of steel and reinforced concrete structural members and frames.

Multiphysics modelling approach to microwave heating of cerium oxide particles in diverse packing situations

In this work, a single-mode resonant microwave cavity (2.45 GHz) is loaded with spherical particles. A weakly coupled electromagnetic (EM)–thermal solver is used iteratively to determine how the microscopic geometry (local curvatures between the particles, grain size and neck size) modifies the EM field, and in turn the thermal field in the particles and also to quantify the microwave effect for an experimental process. The modelling is performed with the conformal finite element solver COMSOL Multiphysics. Moreover, this study will show that the electric field norm increases for one spherical particle of ceria with different sizes and consequently the temperature increases. In addition, the electric field and heating behaviour have been studied in the case of three particles with different neck sizes. Finally, the effect of the configuration versus the E-field direction has been studied for three particles and has a significant result.

Integrated Aerothermoelastic Analysis Framework with Application to Skin Panels

This study describes the development of an integrated aerothermoelastic computational framework. The framework consists of a Navier–Stokes aerodynamic solver based on an Automatic Differentiation flow solver code; a finite element structural solver for moderate deflection of a composite, doubly curved, shallow shell with thermal stress; and a finite element thermal solver for heat transfer in composite shallow shells with nonlinear material properties. The solvers are loosely coupled using a partitioned scheme. An analytical approach is developed to determine the time accuracy and the so-called energy accuracy of a loosely coupled scheme, which serves as a guide for designing schemes having a high convergence rate. The aeroelastic and aerothermoelastic behaviors of two-dimensional and three-dimensional panels are investigated using the computational framework. The effects of the aspect ratio and boundary-layer thickness are found to have significant influence on the critical flutter parameter and the onset time of aerothermoelastic instability.

Efficient Fluid-Thermal-Structural Time Marching with Computational Fluid Dynamics

This study focuses on the development of time-marching procedures for efficient and accurate fluid-thermal-structural analysis with time-accurate computational fluid dynamics. The developed procedures are based on a loosely coupled, partitioned framework for the fluid, thermal, and structural solvers—each with different second-order time integrators. The procedures also implement subcycling, where disparate time scales between the solvers are leveraged to minimize communication between solvers. The first scheme uses a second-order predictor of fluid loads, along with second-order interpolations of structural and thermal solutions. The second scheme is an extension that adds a corrector step to the structural and thermal solvers. The two schemes are benchmarked against both a strongly coupled approach with subiterations and a basic loosely coupled approach that omits the use of predictors/correctors. The schemes are examined in the context of the aerothermoelastic response of a panel in high supersonic flow, and are found to maintain second-order time accuracy with and without subcycling. Furthermore the approaches compare favorably against a strongly coupled approach at significantly reduced computational times, with the predictor-corrector approach yielding speedups of 2–4 times. In comparison, a basic scheme can yield characteristically different behavior.

Flame–wall interaction effects on the flame root stabilization mechanisms of a doubly-transcritical LO2/LCH4 cryogenic flame

High-fidelity numerical simulations are used to study flame root stabilization mechanisms of cryogenic flames, where both reactants (O2 and CH4) are injected in transcritical conditions in the geometry of the laboratory scale test rig Mascotte operated by ONERA (France). Simulations provide a detailed insight into flame root stabilization mechanisms for these diffusion flames: they show that the large wall heat losses at the lips of the coaxial injector are of primary importance, and require to solve for the fully coupled conjugate heat transfer problem. In order to account for flame–wall interaction (FWI) at the injector lip, detailed chemistry effects are also prevalent and a detailed kinetic mechanism for CH4 oxycombustion at high pressure is derived and validated. This kinetic scheme is used in a real-gas fluid solver, coupled with a solid thermal solver in the splitter plate to calculate the unsteady temperature field in the lip. A simulation with adiabatic boundary conditions, an hypothesis that is often used in real-gas combustion, is also performed for comparison. It is found that adiabatic walls simulations lead to enhanced cryogenic reactants vaporization and mixing, and to a quasi-steady flame, which anchors within the oxidizer stream. On the other hand, FWI simulations produce self-sustained oscillations of both lip temperature and flame root location at similar frequencies: the flame root moves from the CH4 to the O2 streams at approximately 450 Hz, affecting the whole flame structure.

Computational study on focused microwave thermotherapy for knee pathological treatment

This study is a computational study on focused microwave thermotherapy for knee pathological treatment using the time reversal (TR) principle in musculoskeletal disorders. The authors presented a modified TR algorithm with amplitude compensation for an accurate beam focusing of the knee tumour location in a lossy medium. Furthermore, they proposed a new approach called the truncated threshold method, which could be used to apply an effective beam focusing on a tumour location in the knee while the unwanted hot spots are controlled in the normal tissue region. Compared to the other existing methods, this new approach has the advantages of being implemented simply in the unwanted hot spot control and having a similar performance to the beam focusing on the target location. The application of the proposed algorithm and the new hot spot control method to knee pathological tissue achieved acceptable electromagnetic (EM) and thermal results. The anatomical based two-dimensional (2D) knee model for the simulation analysis was implemented using a segmentation result of the Korean human body model obtained from magnetic resonance imaging. 2D finite-difference time-domain electromagnetic and thermal solvers were developed and applied to conduct the 915 MHz focused microwave thermotherapy for knee pathological treatment.

Surface thermochemical effects on TPS-coupled aerothermodynamics in hypersonic Martian gas flow

This paper deals with the surface thermochemical effects on TPS-coupled aerothermodynamics in hypersonic Martian gas flow. An interface condition with finite-rate thermochemistry was established to balance the three-dimensional Navier-Stokes solver and TPS thermal response solver, and a series of coupled simulations of chemical non-equilibrium aerothermodynamics and structure heat transfer with various surface catalycities were performed for hypersonic Mars entries. The analysis of surface thermochemistry reveals that the surface chemical reactions have great contribution to aerodynamic heating, and the temperature-dependence of finite-rate catalysis highly influences the evolution of the coupling aerodynamic heating in the coupling process. For fixed free stream parameters with proper catalytic excitation energy, a “leap” phenomenon of the TPS-coupled heat flux with the coupling time appears in the initial stage of the coupling process, due to the strong thermochemical effects on the TPS surface.

Nonlinear multiphysics and multiscale modeling of dynamic ferromagnetic–thermal problems

A coupled ferromagnetic–thermal solver is developed for the multiphysics and multiscale modeling and simulation of nonlinear magnetic materials in the time domain. By adopting a temperature-dependent dynamic hysteresis model, the power loss is characterized and calculated from the solution of Maxwell's equations, which serves as the heat source for the thermal problem. By solving the thermal problem, the temperature change is obtained, and its effect on the magnetic material property can be quantified, which is then coupled back to Maxwell's equations. Due to different temporal characteristics of the electromagnetic fields and the thermal response, the resulting coupled ferromagnetic–thermal system has two significantly different time scales. Such a temporal multiscale issue is addressed with a proposed multiscale time integration method to account for the multiscale coupling between the two physics. With the proposed multiphysics and multiscale modeling method, both the electromagnetic fields and the thermal responses can be captured accurately in a dynamic operation.

Development of an efficient gas kinetic scheme for simulation of two-dimensional incompressible thermal flows.

In this work, an efficient gas kinetic scheme is presented for simulation of two-dimensional incompressible thermal flows. In the scheme, the macroscopic governing equations for mass, momentum, and energy conservation are discretized by the finite volume method and the numerical fluxes at the cell interface are reconstructed by the local solution of the Boltzmann equation. To compute these fluxes, two distribution functions are involved. One is the circular function, which is used to calculate the numerical fluxes of mass and momentum equations. Due to the incompressible limit, the circle at the cell interface can be approximately considered to be symmetric so that the expressions for the conservative variables and numerical fluxes at the cell interface can be given explicitly and concisely. Another one is the D2Q4 model, which is utilized to compute the numerical flux of the energy equation. By following the process for derivation of numerical fluxes of mass and momentum equations, the numerical flux of the energy equation can also be given explicitly. The accuracy, efficiency, and stability of the present scheme are validated by simulating several thermal flow problems. Numerical results showed that the present scheme can provide accurate numerical results for incompressible thermal flows at a wide range of Rayleigh numbers with less computational cost than that needed by the thermal lattice Boltzmann flux solver (TLBFS), which has been proven to be more efficient than the thermal lattice Boltzmann method (TLBM).

A new coupled thermomechanical framework for modeling formability in transformation induced plasticity steels

Transformation induced plasticity (TRIP) steels have significant volume fractions of retained austenite that can undergo a strain induced transformation into martensite. This transformation, known as the TRIP effect, produces a high hardening capacity that can lead to enhanced formability, which can result in weight reduction and improved vehicle fuel efficiency for automakers. In this paper, a phenomenological framework for TRIP steel is integrated into a Marciniak-Kuczynski (MK) model coupled with a thermal solver to create a new fully coupled thermomechanical formulation to evaluate formability. The constitutive model was calibrated to capture the kinematics of martensite and flow stress dependence on strain rate, temperature, triaxiality, and stress asymmetry for TRIP 800 steel. Several sensitivity and exploratory studies are performed to highlight critical mechanisms for modeling TRIP in formability. Kinematic effects of transformation are shown to have a minor effect on formability compared to the hardening and evolving yield surface effects. Thermal effects, such as conduction, convection, and radiation heat transfer, are shown to be crucial for the formability of TRIP 800 at elevated sheet temperatures with room temperature external boundaries, but not for elevated external boundaries. By modifying the sheet initial thermal conditions, martensite transformation could be controlled to be able to delay localization and enhance formability in the plane strain and uniaxial formability by 25% and 35% respectively.

Accelerate Battery Safety Simulations Using Composite Tshell Elements

Computational modeling has been widely used to evaluate battery performance and safety due to its efficiency and low cost. One challenge of conducting large-scale battery simulations is the computational intensity as the size of a battery pack can be several orders of magnitude larger than the thickness of individual layers in a cell and resolving each layer is computationally expensive. Here we present an approach that can accelerate battery simulations significantly without sacrificing much accuracy, which can be critical to extend battery simulations from cell level to module/pack level. In this approach, a newly developed element formulation, composite tshell element, is applied to mesh battery cells. One composite tshell element may contain multiple layers of materials so that local behavior can be captured. In the meanwhile, using such elements in a model reduces the number of elements and therefore computational time considerably. Case studies show that compared with models that resolve each layer using solid elements, using composite tshell elements can achieve comparable results in multiple solvers with much less time. Implementation of composite tshell elements in mechanical, electromagnetic and thermal solvers is presented. Benefits, constraints and future development of composite tshell elements in battery safety simulations are discussed.

Multi-Physics Modeling of Impact Safety of Lithium-Ion Batteries

As lithium-ion batteries are more and more widely used in electrical vehicles and hybrid electrical vehicles, their safety has become a primary concern due to their high energy densities and wide-range working conditions. Previously, experiments such as crush tests, have attempted to mimic the failure process of batteries under abuse conditions, but they usually only give binary pass/fail results and provide limited details of the root causes of failure. Recently, computational modeling has gained a lot of interest because it provides an efficient tool to capture fundamental mechanisms of battery failure. Nevertheless, most of existing models of battery safety either treat the battery as a homogeneous solid and only consider its mechanical response, or focus on the thermal-electrical coupling without consideration of mechanical influence. Here we present a three-dimensional multi-physics model of battery safety that is able to predict coupled mechanical, thermal, electrical and electrochemical responses of automobile lithium-ion batteries under mechanical abuse. This model resolves each component in unit cells of a large format Li-ion cell and applies one-way coupling between mechanical and other types of responses to accommodate the significant differences in time scales. In particular, the mechanical solver predicts the onset of internal or external short circuit at the initial stage of an impact, and then the coupled thermal and electrical solver captures the evolution of temperature and current distribution after short circuit initiation. The electrochemical response is captured by a spatially distributed equivalent circuit model, where empirical parameters are obtained from experimental data. This model has been applied to capture internal and external short circuits and subsequent thermal and electrical responses in different types of cells and modules. Various element formulations have been evaluated to achieve the computational efficiency that will be required for future pack simulations. Model predictions have been compared with experiment data, demonstrating the model capacity and providing insights into the failure mechanisms of batteries during an impact process.

Douglas–Gunn Method Applied to Dosimetric Assessment in Magnetic Resonance Imaging

This work analyses the thermal effects produced by the time-varying magnetic fields of a Magnetic Resonance Imaging scanner in the patient's body, also considering the case of a metallic implant. The computations are performed by the successive solution of an electromagnetic field and a thermal problem. In particular, the performances of a transient thermal solver, implemented according to the Douglas-Gunn scheme, are discussed and compared with other computational procedures. An example of application is finally presented.

Virtual Solar Field - Validation of a detailed transient simulation tool for line focus STE fields with single phase heat transfer fluid

Simulation models enable designers and operators to test different settings of the real systems while avoiding the large costs associated with experimental or practical systems. However, creating models that resemble the real physical system with acceptable accuracy and computational time remains a challenge for developers of such tools. With this motivation, a new simulation tool, the Virtual Solar Field (VSF), has been developed for line-focus power plants with single-phase heat transfer fluid (HTF) to assist in plant control during transient processes. VSF is a whole-field model based on an efficient coupling of hydraulic and thermal solvers that take into account the flow distribution in the parallel loops, as well as the transient conditions in the field.In this paper, some validation cases for VSF using data from Andasol-3 power plant are shown. Five test cases are examined, which include normal operation, start-up and evening operation during clear-sky and strong transients. The results show very good agreement with the real plant and some discrepancies are discussed and studied. The main sources of discrepancies are associated with difficulties in modelling all fine details of reality using the current technologies in some commercial power plants. For example, small cloud passage are not detected by the few weather stations in the power plant, as well as knowing the exact loop valve settings is not possible in Andasol-3. In addition, an overview of the potential applications of VSF are mentioned and briefly discussed. VSF offers a suitable platform for testing novel control strategies and assessing the performance of the solar fields.

Compact modeling approach for microchannel cooling and its validation

This paper presents a new compact modeling technique to describe the convective heat transfer realized by laminar flow of coolant in integrated microchannels used for thermal management of 3D ICs—with the aim of being able to implement this model for fast thermal simulators used in logi-thermal simulation frameworks. This model works only on laminar flow in straight channels. The compact model represents the convective heat transfer with a special resistor network representing one directional heat transfer realized by the flow of the coolant. The implementation of this model in a thermal field solver based on the successive node reduction (SUNRED) algorithm is also presented. The validation of the model is based on two examples. First, we compare the result obtained with the new model with the results provided by a commercially available CFD software for a simplified test case. The other pivot of the validation is an actual measurement of the thermal resistances of microfluidic cooling system under different flow-rates of coolant. The errors were calculated as the difference of the results of the direct implementation of the alternating resistors model, the modified SUNRED model and the result of a detailed CFD simulation for the test case. The error of the simulation of the cooling device is based on the difference of the directly measured and simulated thermal resistances. The comparison showed that the error of our new compact model was close to 5%.

Multi-Scale Modeling of Self Heating Effects on Power Consumption in Silicon CMOS Devices

This work pursues a multi-scale modeling approach to combine interconnect and device level simulation in order to study the effects of carrier self-heating and thermal transport on device performance. More specifically, this work will focus on power consumption and heat dissipation in silicon CMOS technology. As device dimensions decrease to the nanometer scale, current density in the device active regions and the circuit interconnects increases [4]. This increase in current density leads to substantial increases in operating temperatures in critical regions of nano-scale electronic devices. We have already shown these effects in n-channel MOSFETs [2], and will continue to explore how this phenomenon affects p-channel MOSFETs and CMOS circuits. This paper presents the methodology used for the study, multi-scale results from the n-channel MOSFET simulations, and preliminary results from the device level p-channel MOSFET simulation. The modeling approach combines an electro-thermal device simulation with a thermal transport solver at the circuit level. The electrical simulation solves Poisson's equations self-consistently coupled with an ensemble Monte Carlo to determine internal electric fields and model electron and hole transport in the device [3]. The thermal simulation solves the energy balance equations for acoustic and optical phonons and uses the phonon energy to determine the lattice temperature [5]. The electro-thermal solver couples these two processes by introducing temperature dependent scattering to the carrier transport solver. Thermal transport can be modeled in a variety of ways: phonon Monte Carlo simulations are necessary for modeling extreme nano-scale and hot-carrier devices, energy balance modeling is used in this study to model thermal transport at the device level, and the Joule heating method commonly used in commercial device simulators is used in this study to model thermal transport at the interconnect level. The thermal modeling in the device and the interconnects is coupled using the device structure itself as an interface: the electro-thermal simulator provides Joule heating terms throughout the device to be used in the Joule heating simulator which in turn gives the temperature profile in the interconnects to be used as a boundary condition in the electro-thermal solver. These simulations are repeated in a self-consistent loop until convergence is achieved [2]. This modeling approach has been successfully applied to n-channel MOSFET devices and the results have been confirmed using a novel experimental approach. Two identical MOSEFTs in either common source or common drain configuration can be biased such that one device is in saturation and one device is in cut-off or sub-threshold region. The device in saturation heats up and the device in sub-threshold is used as a sensor; the temperature in the sensor can be determined using the subthreshold slope [2]. Confirming the simulation results with experimental results for the temperature in the subthreshold device substantiates the accuracy of the methodology for determining the temperature throughout the device [2]. This methodology, now verified by comparison with experimental results for n-channel MOSFETS, will be applied to the study of CMOS circuits.

Fluid-thermal analysis of aerodynamic heating over spiked blunt body configurations

When flying at hypersonic speeds, the spiked blunt body is constantly subjected to severe aerodynamic heating. To illustrate the thermal response of different configurations and the relevant flow field variation, a loosely-coupled fluid-thermal analysis is performed in this paper. The Mesh-based parallel Code Coupling Interface (MpCCI) is adopted to implement the data exchange between the fluid solver and the thermal solver. The results indicate that increases in spike diameter and length will result in a sharp decline of the wall temperature along the spike, and the overall heat flux is remarkably reduced to less than 300W/cm2 with the aerodome mounted at the spike tip. Moreover, the presence and evolution of small vortices within the recirculation zone are observed and proved to be induced by the stagnation effect of reattachment points on the spike. In addition, the drag coefficient of the configuration with a doubled spike length presents a maximum drop of 4.59% due to the elevated wall temperature. And the growing difference of the drag coefficient is further increased during the accelerating process.

Virtual method for the determination of an optimum thermal design of hot stamping tools

This work presents a new virtual method for the optimised thermal design of hot stamping tools. It provides optimal positions of the tool's tempering ducts with respect to the average working temperature and its homogeneous distribution on the surface of a tool. It consists of a specific procedure for hot stamping tool design and a software framework in order to interconnect three domains: (I) a parametrised CAD tool model, (II) a linear thermal solver using a fast boundary element method and (III) an optimisation algorithm. This enables the automated set-up, simulation and optimisation of a duct topology. The boundary conditions for the simulations are derived from a reduced model of the thermal loading of the tool. The virtual method proposed is demonstrated on simplified tool segment geometries. The results are transferred to complex tool designs used in industry. For a selected use case, the number of ducts could be reduced by 50% through the application of the proposed method. These results are validated virtually based on an existing design. Hence, the new virtual method contributes to a CAE-driven tool design and a more efficient tool manufacturing.