Total Energy Equation Research Articles

Driven wave generated electric field in the solar corona

We investigate the evolution of waves driven by the linearly polarized Alfvén wave in the magnetic field‐aligned cross‐field shear flow. The generated electric field is derived in ideal MHD using analytical solutions for the driven waves. A single particle dynamics in the generated electromagnetic field is considered and governing equations for the particle's total kinetic energy and particle parallel velocity are obtained. Our goal is to show how the driven wave inclusion modifies the evolution of these quantities. It is shown that the total kinetic energy of the particle as well as the particle's parallel velocity is not conserved in the driven wave fields and there is a force exerted on particles. A specific example is considered using solar coronal hole plasma parameters. The process presented in this work might also be important in the laboratory, terrestrial and astrophysical plasma processes where the inhomogeneous flows are present.

A multiphase segregation model for multicomponent alloys with a peritectic transformation

A multiphase microsegregation model for the solidification of multicomponent alloys that experience a peritectic transformation is developed. It is based on a volume averaging method. Coupling is achieved among the conservation equations for total mass, solute mass and energy. The diffusion in extradendritic and several interdendritic liquid and solid phases, the growth kinetics of the dendritic and peritectic solidifying microstructures, as well as the velocities of the solid/liquid and solid/solid phase interfaces are considered in the model. The model is applied to the dendritic and peritectic solidification of a Fe-C-Cr alloy. Equilibrium between phases at the interface is taken into account and computed using a thermodynamic software. The occurrence of several recalescences due to the growth of the microstructure and the peritectic transformation are predicted and the solidification behaviors near recalescence are evaluated. By adjusting the parameters, the lever rule (LR), Gulliver-Scheil (GS) and partial equilibrium (PE) approximations are retrieved.

BADA를 활용한 4-D 경로 모델링법 개발

Four dimensional(4-D) trajectory modeling is conducted based on flight plan. The flight plan is divided into several segments which represent certain operating flight modes. Thrust, drag and fuel consumption rate of an aircraft are calculated using BADA provided by Eurocontrol. The trajectory is modeled with the rate of climb/descent calculated with Total-Energy Equation. The simulation results with a typical aircraft and its flight plan indicate that the trajectory modeled corresponds well with the suggested flight plan. The performance profiles including total endurance time and time history for speed, thrust, drag and fuel consumption were also appropriately generated.

Dynamic -equation model for large-eddy simulation of compressible flows

AbstractThis paper presents a dynamic one-equation eddy viscosity model for large-eddy simulation (LES) of compressible flows. The transport equation for subgrid-scale (SGS) kinetic energy is introduced to predict SGS kinetic energy. The exact SGS kinetic energy transport equation for compressible flows is derived formally. Each of the unclosed terms in the SGS kinetic energy equation is modelled separately and dynamically closed, instead of being grouped into production and dissipation terms, as in the Reynolds averaged Navier–Stokes equations. All of the SGS terms in the filtered total energy equation are found to reappear in the SGS kinetic energy equation. Therefore, these terms can be included in the total energy equation without adding extra computational cost.A prioritests using direct numerical simulation (DNS) of decaying isotropic turbulence show that, for a Smagorinsky-type eddy viscosity model, the correlation between the SGS stress and the model is comparable to that from the original model. Also, the suggested model for the pressure dilatation term in the SGS kinetic energy equation is found to have a high correlation with its actual value. Ina posterioritests, the proposed dynamic$k$-equation model is applied to decaying isotropic turbulence and normal shock–isotropic turbulence interaction, and yields good agreement with available experimental and DNS data. Compared with the results of the dynamic Smagorinsky model (DSM), the$k$-equation model predicts better energy spectra at high wavenumbers, similar kinetic energy decay and fluctuations of thermodynamic quantities for decaying isotropic turbulence. For shock–turbulence interaction, the$k$-equation model and the DSM predict similar evolutions of turbulent intensities across shocks, owing to the dominant effect of linear interaction. The proposed$k$-equation model is more robust in that local averaging over neighbouring control volumes is sufficient to regularize the dynamic procedure. The behaviour of pressure dilatation and dilatational dissipation is discussed through the budgets of the SGS kinetic energy equation, and the importance of the dilatational dissipation term is addressed.

Total-variation-diminishing implicit–explicit Runge–Kutta methods for the simulation of double-diffusive convection in astrophysics

We put forward the use of total-variation-diminishing (or more generally, strong stability preserving) implicit–explicit Runge–Kutta methods for the time integration of the equations of motion associated with the semiconvection problem in the simulation of stellar convection. The fully compressible Navier–Stokes equation, augmented by continuity and total energy equations, and an equation of state describing the relation between the thermodynamic quantities, is semi-discretized in space by essentially non-oscillatory schemes and dissipative finite difference methods. It is subsequently integrated in time by Runge–Kutta methods which are constructed such as to preserve the total variation diminishing (or strong stability) property satisfied by the spatial discretization coupled with the forward Euler method. We analyse the stability, accuracy and dissipativity of the time integrators and demonstrate that the most successful methods yield a substantial gain in computational efficiency as compared to classical explicit Runge–Kutta methods.

Thermal Buckling of Axially Functionally Graded Thin Cylindrical Shell

In the present research, thermal buckling of shell made of functionally graded material (FGM) under thermal loads is investigated. The material properties of functionally graded materials (FGMs) are assumed to be graded in the axial direction according to a simple power law distribution in terms of the volume fractions of the constituents. In the previous articles that published, these properties are assumed to be graded in the thickness direction. Nonlinear kinematic (strain-displacement) relations are considered based on the first order shear deformation shell theory. By substituting kinematic and stress-strain relations of functionally graded shell in the total potential energy equation and employing Euler equations, the equilibrium equations are obtained. Applying Euler equations to the second variation of total potential energy equation leads to the stability equations. Then, buckling analysis of functionally graded shell under three types of thermal loads is carried out resulting into closed-form solutions.

Non linear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure

Abstract. The present paper addresses the nonlinear response of a FG square plate with two smart layers asa sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relationbased on the Von-Karman assumption. All the mechanical and electrical properties except Poisson’s ratio canvary continuously along the thickness of the plate based on a power function. Electric potential was assumedas a quadratic function along the thickness direction and trigonometric function along the planar coordinate.By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect toamplitude of displacements and electrical potential. The effect of non homogenous index was investigated onthe responses of the system. Obtained results indicate that with increasing the non homogenous index, thedisplacements and electric potential tend to an asymptotic value. Displacements and electric potential can bepresented in terms of planar coordinate system. A linear analysis was employed and then the achieved resultsare compared with those results that are obtained using the nonlinear analysis. The effect of the geometricnonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis.Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can bepresented as novelty of this study. Keywords: plate; mechanical properties; electrical properties; nonlinear; functionally graded material;piezoelectric; sensor.

A Theory of Vertical Modes in Multilayer Stratified Fluids

AbstractA theory of vertical modes in multilayer stratified fluids is proposed. A matrix notation is introduced to generalize the theory to an arbitrary number of layers. The properties of vertical modes including their orthogonality are derived. The linearized shallow-water equations and total energy equation are then decomposed into vertical modal components in the presence of large horizontal variations in bottom elevation and stratification, which induce linear interactions among vertical modes. The theory is applied to the derivation of vertical modes in three-layer stratified fluids and an internal tide generation problem under two-layer stratification. It is shown that the proposed theory correctly approaches the continuous counterpart as the number of layers increases.

Fluid’s Flow Parameters Research of Piping Bifurcation Layout

The junction and flow distributing of Yangtze River’s main stream or branch, the underground gate valve of every interception and reservoir are all placed branch. In order to find flow parameters of algorithms when the water system needs the pipeline bifurcation layout, the fluid energy equation was built based on the differential equation of fluid motion because it force only the steady flow and the gravity in the quality. By further analysis of the equation, derive that fluid total energy equation when merging flow bifurcation layout in a underground drainage piping as an example, demonstrate the use of the equation. Theoretical calculations were consistent with actual measurements and provided a theoretical basis for the engineering design and calculation.

Switching Windows for a Nanostructured Cell of Synthetic Ferrimagnets

The magnetization switching window of nanostructured synthetic ferrimagnets with lateral dimension of 160 nm x 80 nm under combined in-plane magnetic fields along the longitudinal and transverse directions is investigated by numerical calculation using an analytical equation for the total energy. The considered total energy equation precisely accounts for the magnetostatic energy, which is significantly large in nanostructured magnetic cells. Due to the complex magnetization alignment of synthetic ferrimagnets, a different switching criterion based on the reversibility of magnetization process is used, instead of the simple criterion frequently used for single magnetic layers. Synthetic ferrimagnets with various thickness asymmetries are considered, and switching windows are calculated both in static and dynamic conditions. The static switching windows show a smaller dependence on the thickness asymmetry than the dynamic switching windows do. The dynamic switching window at a large thickness asymmetry resembles that of a single magnetic layer. The results are discussed in terms of energy profiles that can be obtained by locating the lowest energy path linking the two stable states from the total energy surface.

Calculation of hysteresis loops in face-centered cubic thin films

A total energy equation for a single-crystalline face-centered cubic thin film with its close-packed (111) plane parallel to the film plane is used to calculate in-plane and out-of-plane hysteresis loops at various values of the cubic magnetocrystalline anisotropy constant ( K 1). In-plane loops show that the easy and hard axes are the <112> and <110> directions, respectively, and that the coercivities, which are nearly independent of the sign of K 1, are quite low over the K 1 values due to the small variation of the magnetocrystalline anisotropy energy during the field sweep. The out-of-plane loops are similarly shaped to those of typical thin films, except for the appearance of a small hysteresis loop near the origin, which is attributed to an irreversible magnetization jump from one easy axis to another in the (111) plane. The magnetic parameters such as K 1 are estimated by comparing the theoretical results for in-plane and out-of-plane hysteresis loops with the experimental results measured for an epitaxial Co thin film. The value of K 1 is estimated to be − 1.2 × 10 6 erg/cm 3, which is significantly higher than that of − 6×10 5 erg/cm 3 for bulk Co, but is in good agreement with the values of − 1.3 to − 1.6 × 10 6 erg/cm 3 reported for Co thin films.

An eddy closure for potential vorticity

It is now over 40 years since a closure for the effects of mesoscale eddies in terms of Ertel potential vorticity was first proposed. The consequences of the closure that treats potential vorticity exactly the same as a passive tracer in isopycnal coordinates are explored in this paper. This leads to a momentum equation to predict the mean velocity. While the momentum equation is not unique due to the presence of an undefined potential function, the total energy equation is used to constrain its functional form. The inviscid form of the proposed eddy closure nearly conserves total energy; the error in conservation of total energy is proportional to the time derivative of the bolus velocity. The proposed eddy closure retains Kelvin’s circulation theorem with mean potential vorticity conserved along particle trajectories following the transport (mean + bolus) velocity field. The relative vorticity component of the potential vorticity being diffused along isopycnals leads to terms that look like viscous stress, but these terms do not satisfy two important conditions of standard viscous closures. A numerical model based on this closure is developed, and idealized simulations in a re-entrant zonal channel are conducted to evaluate the merit of the proposed closure. When comparing various eddy closures to an eddy-resolving reference solution, the closure that both transports and diffuses potential vorticity performs marginally better than its peers, particularly with respect to the core zonal jet structure and position. However, these favorable results are obtained only if a potential vorticity diffusion coefficient is used that is smaller than the coefficient used to compute the bolus velocity. Based on these results, we conjecture that extending eddy-closures to include potential vorticity dynamics is possible, but will require the use of a closure parameter that varies temporally and spatially.

Electrofluid dynamic (EFD) energy conversion in gas flows with suspended nanoparticles

This work presents simulations of the Electrofluid Dynamic energy conversion process in slender channel devices having very small particles (in both micro and nano scales) as charge carriers. Solutions are discussed for a system composed by coupled differential equations, which includes the equation for the total current along the channel, the equations for total energy and momentum of the mixture (gas and solid particles), the continuity equation and the equations for energy and momentum of a single particle. Results for suspended particles of higher diameters have been previously published in the Literature, but the simulations here presented exhibit an appreciable increase in the values for output currents.

Phase diagram of magnetization switching in a nanostructured magnetic thin film

The magnetization switching behavior in a nanostructured magnetic thin film, under combined in-plane fields along the longitudinal and the transverse directions, is investigated both analytically and numerically. Two critical curves under a static and a dynamic condition are calculated analytically by using an equation for the total energy. The analytically calculated critical curves are compared with the micromagnetic simulation results for the switching phase diagrams of nonswitching, incoherent switching, and coherent switching. The comparison indicates that the dynamic critical curve is the boundary separating the nonswitching from the incoherent switching, while the static critical curve acts as the boundary between the incoherent switching and the coherent switching. The present results indicate that the switching phase diagram can be constructed analytically with the use of a total energy equation. The analytically calculated critical curves are less accurate in the presence of the simplifying assumptions of a single and in-plane domain state for a small angle between the applied magnetic field and the easy axis. In this case, an accurate value of the anisotropy energy, an input to the total energy equation, must be accurately estimated by micromagnetic simulation.

A physical model of exchange bias in [Pd/Co]5/FeMn thin films with perpendicular anisotropy

A physical model of perpendicular exchange bias (PEB) has been established based on the total energy equation per unit area of an exchange bias system by assuming coherent rotation of the magnetization. The anisotropy energy of antiferromagnetic (AFM) layer, KAFM×tAFM, as well as ferromagnetic (FM) multilayers, KFM,eff×tFM, and the interfacial exchange coupling energy, Jex were considered as primary physical parameters in building up the physical model of PEB phenomenon. It was proposed that the PEB is a result of the energy competition between KAFM×tAFM, KFM,eff×tFM, and Jex; where KAFM×tAFM≥Jex, is a critical condition to observe exchange bias in the system. In particular, it was revealed that Jex is directly relevant to the net magnetization of FM and AFM spin structure, Jex∝cos αAFM×cos βFM, in the perpendicular direction rather than the magnetization angle difference observed in an in-plane system. The physical role of perpendicular anisotropy energy, KFM,eff×tFM was also found to be significant to enhance the PEB. These physical characteristics are completely different from those are observed from an exchange bias system with in-plane anisotropy. The physical validity of the proposed PEB model was confirmed using different structures of exchange biased [Pd/Co]5/FeMn thin films with perpendicular anisotropy. The experimentally analyzed results demonstrated that the physical model of PEB proposed in this work is agreed well with the experimentally observed PEB phenomenon. Furthermore, the proposed model was found to be effective to design and to predict a new PEB system for the advanced spintronics applications.

Energy and temperature relaxation described by nonequilibrium green's functions

A quantum kinetic approach is presented to investigate the energy relaxation of dense strongly coupled two-temperature plasmas. We derive a balance equation for the mean total energy of a plasma species including a quite general expression for the transfer rate. An approximation scheme is used leading to an expression of the transfer rates for systems with coupled modes relevant for the warm dense matter regime. The theory is then applied to dense beryllium plasmas under conditions such as realized in recent experiments. Special attention is paid to the influence of correlation and quantum effects on the relaxation process.

Prediction of Solidification Paths for Fe–C–Cr Alloys by a Multiphase Segregation Model Coupled to Thermodynamic Equilibrium Calculations

A microsegregation model for the solidification of multicomponent alloys is developed. It couples the volume-averaged conservation equations for total mass, solute mass and energy assuming a uniform temperature. The diffusion in the liquid and solid phases, the growth kinetics of the solidifying microstructures and the velocity of the solid/liquid and solid/solid phase interfaces are considered in the model. Equilibrium between phases is taken into account and computed using dedicated thermodynamic software. The thermodynamic properties and their evolutions during solidification are directly retrieved from a database. Illustration is provided by the solidification of a Fe–C–Cr alloy. The occurrence of the recalescence due to the growth of the microstructure and the progress of solidification are predicted. The solidification behavior near to recalescence is evaluated. By adjusting the cooling intensity and the solute diffusivities, extreme approximations are retrieved. The model shows potentials to be coupled with a macrosegregation model for application to the solidification of multicomponent alloys.

A high-order cell-centered Lagrangian scheme for compressible fluid flows in two-dimensional cylindrical geometry

The goal of this paper is to present high-order cell-centered schemes for solving the equations of Lagrangian gas dynamics written in cylindrical geometry. A node-based discretization of the numerical fluxes is obtained through the computation of the time rate of change of the cell volume. It allows to derive finite volume numerical schemes that are compatible with the geometric conservation law (GCL). Two discretizations of the momentum equations are proposed depending on the form of the discrete gradient operator. The first one corresponds to the control volume scheme while the second one corresponds to the so-called area-weighted scheme. Both formulations share the same discretization for the total energy equation. In both schemes, fluxes are computed using the same nodal solver which can be viewed as a two-dimensional extension of an approximate Riemann solver. The control volume scheme is conservative for momentum, total energy and satisfies a local entropy inequality in its first-order semi-discrete form. However, it does not preserve spherical symmetry. On the other hand, the area-weighted scheme is conservative for total energy and preserves spherical symmetry for one-dimensional spherical flow on equi-angular polar grid. The two-dimensional high-order extensions of these two schemes are constructed employing the generalized Riemann problem (GRP) in the acoustic approximation. Many numerical tests are presented in order to assess these new schemes. The results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of our new schemes.

KINETIC THEORY OF PLASMAS: TRANSLATIONAL ENERGY

In the present study, we derive from kinetic theory a unified fluid model for multicomponent plasmas by accounting for the electromagnetic field influence. We deal with a possible thermal nonequilibrium of the translational energy of the particles, neglecting their internal energy and reactive collisions. Given the strong disparity of mass between the electrons and heavy particles, such as molecules, atoms, and ions, we conduct a dimensional analysis of the Boltzmann equation and introduce a scaling based on a multiscale perturbation parameter equal to the square root of the ratio of the electron mass to a characteristic heavy-particle mass. We then generalize the Chapman–Enskog method, emphasizing the role of the perturbation parameter on the collisional operator, the streaming operator, and the collisional invariants of the Boltzmann equation. The system is examined at successive orders of approximation, each corresponding to a physical timescale. At the highest approximation order investigated, the multicomponent Navier–Stokes regime is reached for the heavy particles and is coupled to first-order drift-diffusion equations for the electrons. The transport coefficients are then calculated in terms of bracket operators whose mathematical structure allows for positivity properties to be determined and Onsager's reciprocal relations to hold. The transport coefficients exhibit an anisotropic behavior when the magnetic field is strong enough. We also give a complete description of the Kolesnikov effect, i.e. the crossed contributions to the mass and energy transport fluxes coupling the electrons and heavy particles. Finally, the first and second laws of thermodynamics are proved to be satisfied by deriving a total energy equation and an entropy equation. Moreover, the purely convective system of equations is shown to be hyperbolic.

Code development for ITER edge modelling – SOLPS5.1

Most ITER divertor modelling work to date used the B2–EIRENE (SOLPS4) code package, coupling a 2D fluid description of the charged plasma species (B2) to a Monte-Carlo kinetic description of the neutrals (EIRENE). In recent years, the emphasis at ITER has been on completing the neutral model, including neutral-neutral collisions, opacity effects, radiation transport, etc. Elsewhere, new physics, numerics, and algorithmic improvements, such as E × B and diamagnetic drifts, electric currents, ion and neutral heat and particle flux limits, wall material mixing and surface temperature evolution, and bundling of heavy ions species, as well as switching to cell-centred velocities and using an internal energy instead of a total energy equation, gave birth to the B2.5 code, combined with EIRENE as SOLPS5. We report on work in progress to merge these advances with the ITER-specific model of the edge and divertor.