Energy Transport Model Research Articles

Review of social dynamics in complex energy systems models

The problem of techno-economic approaches to evaluating energy transition pathways has been constantly reported in the literature. Existing research recognises the critical role played by social aspects in energy systems models. System dynamics (SD) has been pointed out among modelling techniques as a suitable tool to evaluate the interdisciplinary nature of energy transitions. This paper explores how energy system-related SD models have incorporated social aspects through a literature review. Models were assessed based on their geographical resolution, time horizon, methodological approach, and main themes: supply-demand, energy-economy-environment (3E), energy-transport, water-energy-food (WEF) nexus, and consumer-centric and socio-political dynamics. Social aspects considered include behaviour and lifestyle changes, social acceptance, willingness to participate, socio-economic measures, among others. As expected, the representation of social aspects was not standard among the papers analysed. Socio-economic aspects were most commonly included in supply-demand and 3E models. Energy-transport and WEF models mainly incorporated changes in travel and consumption habits, respectively. The last theme had a more diverse approach to social aspects that deserves further attention, especially for energy access and justice issues. Other research lines include modelling approaches combination, enhanced participatory and transparent processes during model development, and use of SD models in policy-aiding and stakeholders’ information processes.

A comparison of a commercial hydrodynamics TCAD solver and Fermi kinetics transport convergence for GaN HEMTs

Various simulations of a GaN HEMT are used to study the behaviors of two different energy-transport models: the Fermi kinetics transport model and a hydrodynamics transport model as it is implemented in the device simulator Sentaurus from Synopsys. The electron transport and heat flow equations of the respective solvers are described in detail. The differences in the description of electron flux and the discretization methods are highlighted. Next, the transport models are applied to the same simulated device structure using identical meshes, boundary conditions, and material parameters. Static simulations show the numerical convergence of Fermi kinetics to be consistently quadratic or faster, whereas the hydrodynamic model is often sub-quadratic. Further comparisons of large-signal transient simulations reveal the hydrodynamic model produces certain anomalous electron ensemble behaviors within the transistor structure. The fundamentally different electron dynamics produced by the two models suggest an underlying cause for their different numerical convergence characteristics.

Review of magnetic islands from the divertor perspective and a simplified heat transport model for the island divertor

Magnetic islands in toroidal confinement devices are reviewed from the viewpoint of their divertor potential. Divertor-relevant geometric parameters are derived analytically, and the relationships among them are revealed. We explain how the island geometry limits the target length and demonstrate the importance of an appropriate numerical tool to minimize the risk of thermal overload of plasma-facing components in the divertor design. The currently available three-dimensional (3D) models are briefly discussed, and their strengths and weaknesses are evaluated. The highlight will be the introduction of a new energy transport model recently developed within the framework of the EMC3 code (Feng et al 2004 Contrib. Plasma Phys. 44 57)—the so-called EMC3-Lite version—primarily for the design and optimization of 3D divertors involving thermal overload concerns. While still undergoing experimental validation with the current graphite divertor of W7-X, it is already being used to develop a subsequent tungsten divertor for W7-X.

Effects of rotation on the spectra of brown dwarfs

ABSTRACT Measured rotational speeds of giant planets and brown dwarfs frequently constitute appreciable fractions of the breakup limit, resulting in centrifugal expansion of these objects at the equator. According to models of internal energy transport, this expansion ought to make the poles of a rotator significantly hotter than the equator, so that inclination of the rotational axis greatly affects both spectral shape and total flux. In this paper, we explore the dependence of a substellar object’s observables on its rotational speed and axis inclination. To do so, we combine picaso (Planetary Intensity Code for Atmospheric Spectroscopy Observations) with software pars (Paint the Atmospheres of Rotating Stars). The former computer program models radiative transfer within plane-parallel planetary atmospheres, while the latter computes disc-integrated spectra of centrifugally deformed gaseous masses. We find that the specific flux of a typical fast-rotating brown dwarf can increase by as much as a factor of 1.5 with movement from an equator-on to a pole-on view. On the other hand, the distinctive effect of rotation on spectral shape increases toward the equator-on view. The latter effect also increases with lower effective temperature. The bolometric luminosity estimate for a typical fast rotator at extreme inclinations has to be adjusted by as much as ${\sim} 20{{\ \rm per\ cent}}$ due to the anisotropy of the object’s observed flux. We provide a general formula for the calculation of the corresponding adjustment factor in terms of rotational speed and inclination.

A solution to the simplified multi-dimensional energy-transport model with a general conductivity for semiconductors

The Dirichlet–Neumann mixed boundary value problem of a simplified multi-dimensional energy-transport model for semiconductors with the conductivity κ(n,θ)=nθ is studied. It consists of a drift–diffusion equation for carrier’s density, involving temperature gradients, a nonlinear heat equation for the carrier’s temperature, and the Poisson equation for the electric potential. The existence of weak solution and zero energy relaxation time limit for the problem are proved. For a small variation of the lattice temperature, the resulting limit for the problem is well-known drift–diffusion model. The proofs are based on the analysis of a time-discrete approximate system for the transient problem with the Stampacchia’s truncation approach and some careful calculations concerning the stability estimates needed for convergence of the scheme. Under some regularity assumption of the solution, the uniqueness of solution is shown.

Exploitation of the Maximum Entropy Principle in the Study of Thermal Conductivity of Silicon, Germanium and Graphene

In this paper, we review the application of a recent formula for the lattice thermal conductivity to silicon and germanium, which are two of the most commonly used materials in electronic devices, and to graphene, one the most promising new materials. The formula, which is based on a hierarchy of macroscopic models that generalize the Cattaneo equation, is capable of reproducing the results achieved by means of the well-known Callaway formula. In semiconductors, energy transport is largely due to acoustic phonons, therefore one can choose suitable moments of their occupation numbers as variables of the models. Equations determining the time evolution of these state variables are derived from the Boltzmann–Peierls transport equation by integration, while the maximum entropy principle (MEP) is used to obtain closure relations for the extra variables. All relevant phonon scattering mechanisms are taken into account. We present numerical results regarding the steady-state and dynamical thermal conductivities of silicon, germanium, and graphene, showing their main characteristics and how these are affected by the various scatterings. The results are in good qualitative and quantitative agreement with those in the literature, confirming that MEP is a valid method for developing macroscopic models of charge and energy transport in semiconductor materials.

Modeling fission spikes in nuclear fuel using a multigroup model of electronic energy transport

In fission based nuclear reactors the fuel is subject to an intense neutron environment that drives the fission chain reaction. Due to this process fission fragments are created with energies reaching 1 MeV/amu that lose energy primarily through inelastic interactions with the electronic structure producing electronic excitations. Subsequently, these excitations thermalize through electron-phonon interactions resulting in the formation of a high temperature thermal spike and associated pressure spike. This process promotes atomic mobility that is expected to evolve lattice defects, including the annealing of latent ion tracks. In this work, a multigroup model for electron energy transport is developed and applied to molecular dynamics simulations in the LAMMPS code to examine fission energy deposition and fission effects in nuclear fuel. This technique utilizes MCNP Monte Carlo electron transport calculations to determine the initial injection of fission energy. To provide a more predictive approach than semi-empirical two-temperature models, the electron-phonon interactions are defined to include multiphonon energy transfer as a function of atomic and electron temperature, and are evaluated from electronic structure calculations using the VASP density functional theory code and PHONON lattice dynamics code. Application of this model to fission energy deposition in uranium dioxide predicts ion track formation and fission enhanced atomic mobility behavior within reasonable agreement of experimental trends. Furthermore, simulations of fission fragment interactions with latent ion tracks demonstrate an annealing effect due to this enhanced mobility.

Transport and modeling of subgrid-scale turbulent kinetic energy in channel flows

To develop a more convenient subgrid-scale (SGS) model that performs well even in coarse grid cases, we investigate the transport and modeling of SGS turbulent kinetic energy (hereafter SGS energy) in turbulent channel flows based on the stabilized mixed model (SMM). In this paper, we try to increase the convenience of the SMM by replacing the modeled transport equation for the SGS energy with an algebraic model. The SMM quantitatively adequately predicts the total turbulent kinetic energy of the direct numerical simulation (DNS) even in coarse grid cases. For both the filtered DNS (fDNS) and large-eddy simulation (LES), the statistically averaged production term balances with the dissipation in the region away from the wall in the SGS energy transport equation. In contrast, we reveal that the correlation coefficient between the production and dissipation terms is high for the modeled transport equation in LES, whereas that for the fDNS is low. Based on the high correlation or local equilibrium between the production and dissipation observed in the LES, we demonstrate the reduction of the SMM into a zero-equation SMM (ZE-SMM). We construct a new damping function based on the grid-scale Kolmogorov length to reproduce the near-wall behavior of the algebraic model for the SGS energy. The ZE-SMM provides quantitatively the same performance as the original SMM that employs the SGS energy transport model. This result suggests that the local equilibrium model for the SGS energy provides the equivalent performance as the transport model in wall-bounded turbulent flows even in coarse grid cases.

Hydrodynamics and transport in the long-range-interacting φ 4 chain

We present a simulation study of the one-dimensional φ 4 lattice theory with long-range interactions decaying as an inverse power r −(1+σ) of the intersite distance r, σ > 0. We consider the cases of single and double-well local potentials with both attractive and repulsive couplings. The double-well, attractive case displays a phase transition for 0 < σ ⩽ 1 analogous to the Ising model with long-range ferromagnetic interactions. A dynamical scaling analysis of both energy structure factors and excess energy correlations shows that the effective hydrodynamics is diffusive for σ > 1 and anomalous for 0 < σ < 1, where fluctuations propagate superdiffusively. We argue that this is accounted for by a fractional diffusion process and we compare the results with an effective model of energy transport based on Lévy flights. Remarkably, this result is fairly insensitive on the phase transition. Nonequilibrium simulations with an applied thermal gradient are in quantitative agreement with the above scenario.

Potential bottleneck in the energy transition: The case of cobalt in an accelerating electro-mobility world

Within the context of the energy transition, decarbonization of the transport sector is the cornerstone of many public policies. As a key component in the cathodes of lithium-ion batteries and nickel metal hydride batteries used in electric or hybrid vehicles, cobalt is expected to face a dynamic demand in the coming decades. Numerous questions are arising regarding the criticality risks of this key metal of the energy transition. In order to assess the availability of cobalt until 2050, we rely on our linear programming world energy-transport model, TIAM-IFPEN. Two climate scenarios were considered (2 °C and 4 °C), each with two different mobility scenarios (Business-as-Usual mobility and Sustainable mobility) and for each mobility scenario, three lithium-ion battery chemistry mix trajectories were considered (high, central and low cobalt content) by 2050. Results show that in the most stringent scenario 83,2% of cobalt resources identified in 2013 would be extracted from the ground by 2050 to satisfy global consumption. Two Thirds of world production is from Africa while China consumes 1/3 of the total demand by 2050. We identify several ways to meet the increasing demand for cobalt resources. Public policies must therefore focus on 3 complementary axes: promoting the development of sustainable mobility; prioritizing low cobalt content batteries in electric vehicles; and concentrating efforts on the implementation and the deployment of a system for recovering, sorting and recycling waste.

Numerical analysis of DDFV schemes for semiconductors energy-transport models

This article addresses the construction and the numerical analysis of implicit Discrete Duality Finite Volume schemes for a semiconductors’ energy-transport model. The considered energy-transport model is presented in its scaled version as well as in a symmetrized form which involves entropy variables. We propose implicit in time numerical schemes for both the original system and its symmetrized form. As in the continuous framework, the numerical analysis is based on the reformulation of the PDE system using the set of entropic variables. The equivalence of both schemes allows to establish a discrete entropy inequality and consequently an priori estimates. As a by-product, existence of solutions to the schemes is proved by means of a Leray–Schauder argument. Numerical evidences allow to compare the performances of both schemes on the test case of a 2D ballistic diode.

Coupled Schrödinger equations as a model of interchain torsional excitation transport in the DNA model

In this report we consider two weakly coupled Schrödinger equations as a reduced model of interchain energy transport in the DNA double-helix torsional model. We employ a reduction of the Yakushevich-type model that considers the torsional dynamics of the DNA as effective chains of pendula. In previous works, only small amplitude excitations and stationary dynamics were investigated, whereas we focus on the nonstationary dynamics of the double helix. We consider the system to be a model of two weakly interacting DNA strands. Assuming that initially only one of the chains is excited in the form of a breather, we demonstrate the existence of an invariant that allows us to reduce the order of the problem and examine the system of the phase plane. The analysis demonstrates the utility of an analytical tool for predicting the periodic interchain excitation transitions of its localisation on one of the chains. The technique also takes into account the spreading of the excitations over time.

Quantum energy-transport and drift-diffusion models for electron transport in graphene: an approach by the wigner function

The present work aims at formulating quantum energy-transport and drift-diffusion equations for charge transport in graphene from a quantum hydrodynamic model proposed in Luca and Romano (Ann. Phys. 406:30–53, 2019), obtained from the Wigner-Boltzmann equation via the moment method. Here, we only sketch the main ideas and show the most relevant formulas. Further developments are under current investigation by the authors. The interested reader can find the omitted details in the references. In analogy with the semiclassical case, we are confident that the energy-transport and drift-diffusion models have mathematical properties which allow an easier numerical treatment.

Transport electrification at all environmental costs? The case of large passenger duty-vehicles

Electrification is often highlighted as the future for transportation sector as it is considered as a zero-tailpipe emission. However, environmental impacts related to battery electric vehicles (BEVs) exist. The aim of this article is to identify the trade-off between batteries’ weight and vehicle’s autonomy from an environmental perspective in the BEVs’ development as electrified mobility will consume more critical materials but reducing tailpipe emissions. Thus, a focus on climate change and resources has been done using a life cycle assessment (LCA) methodology. Large vehicles (D-segment) for BEVs and their fossil thermic counterparts have been assessed for two time horizons (2019, 2030) in Europe. Our linear programming world energy-transport model, TIAM-IFPEN, has been used in order to assess demand and import dependency on materials through to 2050. Results show that BEVs can generate higher impacts than their inherent conventional ones and that criticality assessment should be done in order to get a complete view of BEVs’ deployment.

Adaptation and validation of a voxel based energy transport model for conifer species

A spatially explicit energy balance model previously developed for deciduous trees was extended to account for physical differences in conifer species. These differences include the emission and scattering of radiation in needles compared to leaves as well as the boundary-layer conductance for needles. To validate the model, an array of sensors was placed in and around two separate isolated Picea pungens trees in a heterogeneous urban environment. Model validation examined components of the local-volume averaged needle energy budget utilizing radiative and turbulent fluxes as the forcing inputs. Analysis focused on the model's ability to reproduce integrated upward shortwave and longwave radiation, local radiation attenuation through the tree crown, and local needle surface temperature. The model performed quite well with R2 values above 0.9 for calculated versus measured integrated upward longwave and shortwave radiation and above 0.87 for needle surface temperature. The high level of agreement with experimental measurements was only possible with the modifications made to the boundary layer conductance for needles.

Stability analysis of the thermocline thermal energy storage system during high flow rates for solar process heating applications

The thermal energy storage system is a pivotal system for solar thermal plants for improving reliability. The stability in the thermocline is more significant to clarify and improve the performance of thermal energy storage tank which legitimately shows the quality of the thermocline. In this stability analysis investigation, the modern engineering energy storage material concrete was used as a filler material for high-temperature thermal energy storage applications as a result of the intrinsic properties. A comprehensive laminar and k-ε turbulent flow energy transport model accounts for the heat transfer fluid and filler material with adiabatic and non-adiabatic conditions using LTNE (Local Thermal Non-Equilibrium model). The axial, radial, and diagonal temperature differences were identified which was used to calculate the stability of the thermocline. A thermal energy storage tank size of 1 m height and 0.250 m diameter with a 0.030 m size of filler material packed with an average porosity of 0.3 for the storage capacity of 150 kWh/m3 is used for solar process heating applications considered for the present study. The thermocline stabilities are performed with Reynolds numbers, Re varied from 1 to 3000. It is found that the Re = 1 provides better stability in the axial and radial direction as well as diagonal than other Reynolds number. It is observed that Re = 1 provides superior discharging efficiency for nearly 5.84 hrs which is highly suitable for solar process heating applications and the discharging efficiency consistently drops, when Re increases from 1 to 3000. The wall condition of the tank and velocity of the heat transfer fluid is highly disturbing the thermocline in the radial direction and it creates a ‘spike’ profile in the axial direction. Based on the newly introduced stability scale, the effective length of packing and timing to achieve stability is identified for H/D = 4. From that result, the top and bottom layer of the thermocline tank porosity is also found which is used to decide the porosity of the packed bed distributors. The identified porosity for the top and bottom distributors in the ɛ = 0.3 thermal energy storage tank is less than 0.3 is more suitable for provide the uniform flow in the tank.

Thermal non-equilibrium natural convection in a trapezoidal porous cavity with heated cylindrical obstacles

Thermal and flow analysis is performed for natural convection in a porous trapezoidal cavity considering a non-equilibrium thermal energy transport model. The model study comprises a partially and fully heated bottom wall while obstacles are placed inside the cavity to examine the thermal behavior. However, governing energy and momentum equations exhibit an unsteady state, but the numerical outcomes are obtained after employing the steady-state condition. The physical problem is expressed in a mathematical model and numerically simulated using the finite difference scheme. The results are presented in graphical sets, while a comparative tabular analysis with existing literature is also reported. It is demonstrated that the parameters γ and H affect thermal non-equilibrium and that the isotherms and streamlines are symmetrically distributed around the obstacles. The local Nusselt number and average Nusselt numbers show a dominant enhancement for both fluids and solid phases assisted by Rayleigh numbers while decreased with an increase in the heating domains. The reported study will be useful in analyzing the natural convection thermal non-equilibrium models in curvilinear geometries.

Analysis of numerical schemes for semiconductor energy-transport models

Some finite volume schemes for unipolar energy-transport models are introduced. Using a reformulation in dual entropy variables, we can show the decay of a discrete entropy with control of the discrete entropy dissipation. We establish a priori estimates which lead to the existence of a solution to the scheme. Similarly to the continuous framework, we prove the exponential decay of the discrete relative entropy towards the thermal equilibrium. Numerical results assess the good behavior of the whole numerical scheme.

It Is Still Possible to Achieve the Paris Climate Agreement: Regional, Sectoral, and Land-Use Pathways

It is still possible to comply with the Paris Climate Agreement to maintain a global temperature ‘well below +2.0 °C’ above pre-industrial levels. We present two global non-overshoot pathways (+2.0 °C and +1.5 °C) with regional decarbonization targets for the four primary energy sectors—power, heating, transportation, and industry—in 5-year steps to 2050. We use normative scenarios to illustrate the effects of efficiency measures and renewable energy use, describe the roles of increased electrification of the final energy demand and synthetic fuels, and quantify the resulting electricity load increases for 72 sub-regions. Non-energy scenarios include a phase-out of net emissions from agriculture, forestry, and other land uses, reductions in non-carbon greenhouse gases, and land restoration to scale up atmospheric CO2 removal, estimated at −377 Gt CO2 to 2100. An estimate of the COVID-19 effects on the global energy demand is included and a sensitivity analysis describes the impacts if implementation is delayed by 5, 7, or 10 years, which would significantly reduce the likelihood of achieving the 1.5 °C goal. The analysis applies a model network consisting of energy system, power system, transport, land-use, and climate models.

A Mountain‐Front Recharge Component Characterization Approach Combining Groundwater Age Distributions, Noble Gas Thermometry, and Fluid and Energy Transport Modeling

AbstractMountain‐front recharge (MFR), or all inflow to a basin‐fill aquifer with its source in the mountain block, is an important component of recharge to basin‐fill aquifer systems. Distinguishing and quantifying the surface from subsurface components of MFR is necessary for water resource planning and management, particularly as climate change may impact these components in distinct ways. This study tests the hypothesis that MFR components can be distinguished in long‐screened, basin‐fill production wells by (1) groundwater age and (2) the median elevation of recharge. We developed an MFR characterization approach by combining age distributions in six wells using tritium, krypton‐85, argon‐39, and radiocarbon, and median recharge elevations from noble gas thermometry combined with numerical experiments to determine recharge temperature lapse rates using flow and energy transport modeling. We found that groundwater age distributions provided valuable information for characterizing the dominant flow system behavior captured by the basin‐fill production wells. Tracers indicated the presence of old (i.e., no detectable tritium) water in a well completed in weathered bedrock located close to the mountain front. Two production wells exhibited age distributions of binary mixing between modern and a small fraction of old water, whereas the remaining wells captured predominantly modern flow paths. Noble gas thermometry provided important complementary information to the age distributions; however, assuming constant recharge temperature lapse rates produced improbable recharge elevations. Numerical experiments suggest that surface MFR, if derived from snowmelt, can locally suppress water table temperatures in the basin‐fill aquifer, with implications for recharge elevations estimated from noble gas thermometry.