Transient Case Research Articles

Structure-Preserving and Helicity-Conserving Finite Element Approximations and Preconditioning for the Hall Mhd Equations

We develop structure-preserving finite element methods for the incompressible, resistive Hall magnetohydrodynamics (MHD) equations. These equations incorporate the Hall current term in Ohm's law and provide a more appropriate description of fully ionized plasmas than the standard MHD equations on length scales close to or smaller than the ion skin depth. We introduce a stationary discrete variational formulation of Hall MHD that enforces the magnetic Gauss's law exactly (up to solver tolerances) and prove the well-posedness and convergence of a Picard linearization. For the transient problem, we present time discretizations that preserve the energy and magnetic and hybrid helicity precisely in the ideal limit for two types of boundary conditions. Additionally, we present an augmented Lagrangian preconditioning technique for both the stationary and transient cases. We confirm our findings with several numerical experiments.

Comparative performance assessment of methods for operational modal analysis during transient order excitation

Machinery with rotating components poses a challenge to Operational Modal Analysis (OMA) due to its periodic inputs, i.e. orders. Transient (acceleration or deceleration) runs represent a relevant test condition for structures, which experience a low amount of broadband (noise) excitation during operation. In these cases, orders present themselves as a favourable source of excitation. However, this type of excitation can result in distortions of the response spectrum at the ending frequencies of individual orders. These “end-of-order” distortions can introduce spurious or biased modal estimations. Order-based Modal Analysis (OBMA) is an OMA method, which was developed specifically for the transient test case and is not affected by end-of-order distortions. However, some downsides are associated with OBMA because it performs modal analysis for each relevant order individually. In addition to the associated analysis effort, this produces multiple sets of modal estimations with ambiguous results. This paper introduces an extension of OBMA to address these issues. The proposed method, called Averaged Order-based Modal Analysis (AOBMA), applies scaling and (weighted) averaging to extracted orders prior to the modal estimation step. A Monte-Carlo simulation study is introduced to compare the modal estimation performance of traditional OMA, OBMA and AOBMA. Different ratios of harmonic and random excitation amplitudes are simulated to gauge the impact of the excitation's composition. In addition, all methods are also applied to operational measurements from a turbofan casing during run-up. The results indicate that AOBMA produces a lower variance in the estimated modal parameters compared to OBMA. Moreover, while OMA was more successful in the estimation of closely spaced modes, it was surpassed by AOBMA and OBMA regarding the accuracy of mode shape estimations.

Comparison of the parasitic impedances from the drain‐source path of power transistor packages at up to 2 GHz

AbstractIn this article, we compare several concepts for gallium‐nitride (GaN) power high electron mobility transistor (HEMT) packages in terms of their drain‐to‐source parasitic inductance and resistance values. Unlike in previous studies, however, due to several fast transient use cases the investigated frequencies are extended to 2 GHz. Since the device's dimensions are already a significant fraction of the corresponding wavelength at 2 GHz, full wave simulation tools have been employed to more accurately assess the problem. The results reveal how the considered package concepts affect the overall parasitic device impedances and show a clear improvement of the parasitic impedance over each generation of package implementation. Furthermore, full wave analysis results are compared to method of moments results to emphasize the necessity of full wave simulations at these frequencies.

Application of a mixed variable physics-informed neural network to solve the incompressible steady-state and transient mass, momentum, and energy conservation equations for flow over in-line heated tubes

The prohibitive cost and low fidelity of experimental data in industry-scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding the physics equations in the construction of the neural network loss function. In the present paper, the mixed-variable PINN methodology is applied to develop steady-state and transient surrogate models of incompressible laminar flow with heat transfer through a 2D internal domain with obstructions. Automatic spatial and temporal differentiation is applied to the partial differential equations for mass, momentum and energy conservation, and the residuals are included in the loss function, together with the boundary and initial values. Good agreement is obtained between the PINN and CFD results for both the steady-state and transient cases, but normalization of the PDEs proves to be crucial. Although this proves the ability of the PINN approach to solve multiple physics-based PDEs on a single domain, the PINN takes significantly longer to solve than the traditional finite volume numerical methods utilized in commercial CFD software.

A procedure to predict solar receiver damage during transient conditions

The successful deployment of solar-power-towers lies in the reliable design of solar receivers, assuring the lifetime under high heat flux and cloud passages. Two main damage mechanisms appear during central-receiver operation: creep, during hold times at high temperatures and stresses, and fatigue, caused by transient operation. This work aims to determine the extent of each damage on a Haynes 230 receiver. It is analyzed using transient DNI of a whole year, controlling the operation to guarantee the receiver preheat and minimize the start-ups. The molten-salt flow-rate during cloud passages or hazy days remains as the clear-sky scheduled one, to avoid tube overheat, preventing salt degradation and stress reset, when the clouds cleared.The results show that creep dominates, with a minimum share of 73.8% for the transient case. High creep is motivated by the long operating (6 h per day on average), mostly at high DNI, while the low number of average start-ups per day (1.4) do not increase much the fatigue, barely affected by small transients. The use of clear-sky, instead of the transient DNI, constitutes a conservative estimation, with the creep greatly increasing, showing a minimum share of 82%. Consequently, the predicted lifetime is lower, going from 45 years to 27.8. Intermediate mass-flow control modes fall in-between them. Clustering the days according to their DNI features shows that the high-energy days, with high creep, are the most common, highlighting the creep interest and that the fatigue can be estimated taking only the strain range produced by the start-up.

Numerical constraints and non-spatial open boundary conditions for the Wigner equation

We discuss boundary value problems for the characteristic stationary von Neumann equation (stationary sigma equation) and the stationary Wigner equation in a single spatial dimension. The two equations are related by a Fourier transform in the non-spatial coordinate. In general, a solution to the characteristic equation does not produce a corresponding Wigner solution as the Fourier transform will not exist. Solution of the stationary Wigner equation on a shifted k-grid gives unphysical results. Results showing a negative differential resistance in IV-curves of resonant tunneling diodes using Frensley’s method are a numerical artefact from using upwinding on a coarse grid. We introduce the integro-differential sigma equation which avoids distributional parts at k=0 in the Wigner transform. The Wigner equation for k=0 represents an algebraic constraint needed to avoid poles in the solution at k=0. We impose the inverse Fourier transform of the integrability constraint in the integro-differential sigma equation. After a cutoff, we find that this gives fully homogeneous boundary conditions in the non-spatial coordinate which is overdetermined. Employing an absorbing potential layer double homogeneous boundary conditions are naturally fulfilled. Simulation results for resonant tunneling diodes from solving the constrained sigma equation in the least squares sense with an absorbing potential reproduce results from the quantum transmitting boundary with high accuracy. We discuss the zero bias case where also good agreement is found. In conclusion, we argue that properly formulated open boundary conditions have to be imposed on non-spatial boundaries in the sigma equation both in the stationary and the transient case. When solving the Wigner equation, an absorbing potential layer has to be employed.

Modelling and performance analysis of a recuperated gas turbine with low-Btu fuel

• A gas turbine model was estabilished considering recuperator, fuel, and generator. • The recuperator is the dominant component for thermal inertia of smallgas turbine. • 1-D heat soakage model was more proper for radial rotor than 0-D lumped model. • The thermal inertia and volume effect are good for gas turbine with sudden load change. • Overspeed in load shedding and surge in deceleration need to be studied case by case. Low-Btu fuels such as land fill gas and bio-gas are good alternatives to high priced natural gas. Due to the limited production of low-Btu fuel, small gas turbines are widely applied in such applications. For higher power efficiency at full and part load conditions, the small gas turbine is always equipped with a recuperator and a high-speed generator. Due to low shaft inertia, a small gas turbine’s speed response is quick. Therefore, for standard simple cycle gas turbine, control lags from instruments, actuators, thermal inertia, or volume effect may induce control instabilities during transient loading, and resulting in over speed, flow instabilities, and even mechanical failure. However, for recuperated engine burning low BTU fuel, other factors including the large volume of the combustor and recuperator, the thermal inertia of the rotor and recuperator, lags in the fuel valve lags, and efficiency changes caused by rectifiers of the high-speed generators could all induce visible changes and lags in the engine’s transient operations. This paper summarizes the influences of the gas turbine engine itself, the recuperator, and the high-speed generator in one model. It is believed that this is the first time that all these effects and interactions have been analysed together. Heat soakage, volume dynamics, recuperator transient characteristics, and the rectifier model were combined and tuned in detail to understand the separate effects. From the analysis of transient cases such as, load shedding and acceleration, conclusions are drawn made regarding overspeed and recovery time. The recuperator thermal inertia, low-Btu fuel, and combustor and recuperator volume effect interact with each other to produce more than three times larger overspeed or nearly five times more recovery time compared to a natural gas engine with recuperator. The fuel valve with a 0.02 s-time constant was found to be adequate even for the most severe case described in this paper. The recuperated gas turbine did not necessarily lead to lower compressor surge margin and should be investigated on a case-by-case basis. Rectifier system efficiency variation should be taken into account especially for the acceleration process. To convert a natural gas turbine engine into low-Btu gas turbine, the matching point of the gas turbine components needs to be carefully selected for efficiency, surge margin, and transient manoeuvre behaviour.

An efficient and accurate numerical method for the heat conduction problems of thermal metamaterials based on edge-based smoothed finite element method

Thermal metamaterials are a class of artificial composite structures with special thermal conduction properties. Due to the existence of complex multi-phase materials arrangement and interfaces in the thermal metamaterials, an efficient and accurate numerical method is on-demand to predict their temperature distribution and performances. In this paper, we studied the edge-based smoothed finite element method (ES-FEM) for simulating the heat conduction of thermal metamaterials in both steady-state and transient circumstances. Benefit from the adopted smoothing technique, the numerical errors caused by the complex interface are further eliminated. The most significant advantage of the proposed method is that one can directly use the automatically generated coarse triangle mesh to reduce the computational costs while ensuring accuracy. Two numerical examples are presented, in which two typical thermal metamaterials, the thermal cloak and thermal concentration device, are considered respectively in both steady-state and transient cases. The results illustrate that the ES-FEM based approach has good efficiency and accuracy in the heat conduction simulation of the thermal metamaterials.

A Computational Analysis of Heat Transfer in an Air-Cooled Proton Exchange Membrane Fuel Cell for Unsteady Flow Conditions Using a Reynolds Stress Turbulence Model

Within telecom applications, the air-cooled fuel cell, as a backup power system, has recently been gaining popularity. These fuel cells are cost effective, simple, and additionally they do not require a secondary coolant loop. However, since airflow is used as coolant, the heat generated by the fuel cell limits the current density and thus the power density. A turbulence inducing grid is placed in front of the cathode channel to make the airflow turbulent and hence increase the convective cooling effect from the air. The turbulence inducing grid is placed 2.5mm from the cathode channel since previous studies have shown this distance to be most effective.In this study, a three dimensional CFD analysis on the effect of a transient boundary conditions on the cooling effect of the turbulence grid has been conducted. Special emphasis has been on using the comprehensive Reynolds Stress Model as turbulence model. Additional analysis has been made on the cooling effect of pulsating flow with a period of 10 seconds excluding the turbulence inducing grid. At an electrode heat flux of 2600 W/m2, the results indicate that the convective cooling effect increases when using transient boundary conditions compared to steady state boundary conditions. Furthermore, results show that the start-up time is seven minutes, and the time-averaged peak temperature in the transient case is two degrees Celsius below the peak temperature of the steady state case. The CFD analysis show an additional cooling effect due to accelerated-decelerated flow conditions. Figure 1

Transient high thyroid stimulating hormone and hypothyroidism incidence during follow up of subclinical hypothyroidism.

Objectives. Given the high prevalence of subclinical hypothyroidism (SCH), defined as high thyroid stimulating hormone (TSH) and normal free thyroxine (FT4), and uncertainty on treatment, one of the major challenges in clinical practice is whether to initiate the treatment for SCH or to keep the patients under surveillance. There is no published study that has identified predictors of short-term changes in thyroid status amongst patients with mild elevation of TSH (4.5-10 mIU/L). Subjects and Results. A cohort study was conducted on patients with SCH detected through a general population screening program, who were followed for six months. This project identified factors predicting progression to hypothyroid status, persistent SCH and transient cases. A total of 656 participants joined the study (431 controls and 225 were patients with SCH). A part of participants (12.2%) developed biochemical hypothyroidism during the follow-up, while 73.8% of the subjects became euthyroid and the remained ones (13.4%) stayed in the SCH status. The incidence of overt hypothyroidism for participants with TSH above 6.9 mIU/L was 36.7%, with incidence of 42.3% for females. Anti-thyroid peroxidase antibodies (TPO) positivity is an important predictor of development of hypothyroidism; however, it could be also positive due to transient thyroiditis. Conclusions. It can be concluded that females with TSH above 6.9 mIU/L, particularly those with free triiodothyronine (FT3) and FT4 in the lower half of the reference range, are more likely to develop biochemical hypothyroidism. Therefore, it is recommended to give them a trial of levothyroxine replacement. It is also recommended to repeat TSH after six months for male subjects and participants with baseline TSH equal or less than 6.9 mIU/L.

A locking-free finite element formulation for a non-uniform linear viscoelastic Timoshenko beam

In this paper we use a modified constitutive law in a hereditary integral form to analyze the response of an isotropic non-uniform linear viscoelastic Timoshenko beam. A mixed method framework is used to provide stability and semi-discrete error estimates that do not deteriorate as the thickness parameter becomes small. Numerical experiments for both quasi-static and transient cases are presented.

Voltage Stability Analysis of Large Scale PV Plant Reactive Power Control Methods

The increasing integration of photovoltaic (PV) plants in conventional power systems has led to the need to examine the effects of these plants on the system dynamics. In this study, a well-known IEEE-9 bus power system is modified by integrating PV plant in DigSilent Powerfactory environment. Then, 3 transient cases are tested by using PV plant control units designed by Western Electricity Coordinating Council (WECC). The effect of load and line transient disconnections and 3-phase short circuit fault on modified power system are investigated as case-I, case-II, and case-III, respectively. In all cases, two sub-cases are considered according to the location. As a result, comparison of PV system reactive power control methods (RPCM) is analyzed in terms of voltage stability in these 3 cases.

Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems

In this paper, a new reliability measure, named sequential interval reliability, is introduced for homogeneous semi-Markov repairable systems in discrete time. This measure is the probability that the system is working in a given sequence of non-overlapping time intervals. Many reliability measures are particular cases of this new reliability measure that we propose; this is the case for the interval reliability, the reliability function and the availability function. A recurrent-type formula is established for the calculation in the transient case and an asymptotic result determines its limiting behaviour. The results are illustrated by means of a numerical example which illustrates the possible application of the measure to real systems.

CFD Analyses for the Upgrade Divertor System of KSTAR

The Korea Superconducting Tokamak Advanced Research (KSTAR) device, constructed in 2008, is a world-class superconducting tokamak fusion research device for the development of fusion energy. The expected heating power goal has been set to 12 MW by using an additional heating system, i.e., the second neutral beam injection (NBI) system NBI-2. As the heating power increases, resistance to high heat flux and cooling capacity at the divertor should be improved to exhaust power in the scrape-off-layer domain. Therefore, an upgrade of the divertor system for KSTAR was launched in 2019, and the upgrade divertor will be installed by 2022. The peak heat flux on the divertor target in steady-state operation is set to 10 MW/m2, and the ITER-like divertor type, the water-cooled tungsten monoblock, has been applied. The upgrade KSTAR divertor system comprises 64 cassette divertor modules. A divertor module consists of the inner target, the central target, the outer target, and the cassette body with supports to connect each part. In this study, thermal analyses were carried out to confirm the design’s thermal robustness for a whole divertor module. The temperature distribution and pressure drop were calculated by computational fluid dynamics analyses. Based on the response surface optimization method, the optimized tungsten monoblock design was derived. The optimized monoblock design showed that all materials, tungsten, Cu, and CuCrZr, comprising the divertor target, are operated within their allowable temperature windows. For the global divertor model applying the optimized monoblock design, steady-state and transient analyses were carried out for heat fluxes of 10 and 20 MW/m2. At 10 MW/m2, all composing materials were operated within the allowable temperature, while the maximum temperatures of tungsten, Cu, and CuCrZr exceeded the allowable temperature range of 20 MW/m2. However, the results were acceptable since the temperatures are sufficiently lower than the melting temperatures, and the slow transient case occurs quickly.

A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam

The accurate description of the flow of water in porous media is of the greatest importance due to its numerous applications in several areas (groundwater, soil mechanics, etc.). The nonlinear Richards equation is often used as the governing equation that describes this phenomenon and a large number of research studies aimed to solve it numerically. However, due to the nonlinearity of the constitutive expressions for permeability, it remains a challenging modeling problem. In this paper, the stationary form of Richards’ equation used in saturated soils is solved by two numerical methods: generalized finite differences, an emerging method that has been successfully applied to the transient case, and a finite element method, for benchmarking. The nonlinearity of the solution in both cases is handled using a Newtonian iteration. The comparative results show that a generalized finite difference iteration yields satisfactory results in a standard test problem with a singularity at the boundary.

Application of the generalised fully Lagrangian approach to simulating polydisperse gas-droplet flows

In this paper, we demonstrate the application of a generalised fully Lagrangian approach to the simulation of polydisperse gas-evaporating droplet flows. The paper focuses on the proposed methodology for modelling the dispersed phase, droplets, in both steady and transient cases. To account for polydispersity, the set of Lagrangian variables is extended to include the droplet size, and the droplet size distribution function is introduced to the droplet parameter set. According to the Lagrangian approach, all the droplet parameters, including the distribution function, are found along the droplet trajectories. An interpolation scheme to convert droplet parameter fields from a Lagrangian to an Eulerian framework for visualising droplet distribution is proposed. The developed methodology was applied to simple 1D and 2D stationary cases for verification, after which it was incorporated into OpenFOAM to simulate steady and periodic flows around a cylinder. In the case of a steady flow, a region devoid of droplets is formed behind the cylinder. From the droplet distribution plots, it was observed that small and medium sized droplets reach a region near to the axis of the symmetry of the flow. In the case of periodic flow, the analysis of droplet distribution is based on instantaneous pictures of the droplet parameters rather than their values along droplet trajectories. In this flow, strongly influenced by vortices, a strong droplet segregation is shown; at various locations one can see a full droplet size spectrum, only small or large droplets, and/or droplets from a narrow size interval. In all cases, the effect of the evaporation is to decrease the maximum value of the droplet distribution function shifted towards smaller-sized droplets.

PILLAR: Integral test facility for LBE-cooled passive small modular reactor research and computational code benchmark

An integral test facility, PILLAR, was commissioned, aiming to provide valuable experimental results which can be referenced by system and component designers and used for the performance demonstration of liquid-metal-cooled, passive small modular reactors (SMRs) toward their licensing. The setup was conceptualized by a scaling analysis which allows the vertical arrangements to be conserved from its prototypic reactor, scaled uniformly in the radial direction achieving a flow area reduction of 1/200. Its final design includes several heater rods which simulate the reactor core, and a single heat exchanger representing the steam generators in the prototype. The system behaviors were characterized by its data acquisition system implementing various instruments. In this paper, we present not only a detailed description of the facility components, but also selected experimental results of both steady-state and transient cases. The obtained steady-state test results were utilized for the benchmark of a system code, achieving a capability of accurate simulations with ±3% of maximum deviations. It was followed by qualitative comparisons on the transient test results which indicate that the integral system behaviors in passive LBE-cooled systems are able to be predicted by the code.

Unsteady conjugate heat transfer with combined effects of MHD and moving conductive elliptic object in CNT-water nanofluid with ventilation ports

PurposeThe purpose of this paper is to analyze the unsteady conjugate mixed convective heat transfer characteristics in a vented porous cavity under the combined effects of moving conductive elliptic object and magnetic field.Design/methodology/approachThe finite element method and arbitrary Lagrangian-Eulerian (ALE), impacts of Reynolds number, Hartmann number, aspect ratio of the conductive ellipse and moving speed of the object on the hydro-thermal performance are analyzed.FindingsIt was observed that the dynamic characteristics of the local and average Nu number of each hot wall are different. Magnetic field strength increment resulted in the enhancement of average Nu number for bot steady and transient case while the optimum case for best hydro-thermal performance is achieved for highest Ha number and non-dimensional time of 10. Higher value of average Nu and lower pressure coefficient are achieved for aspect ratio of 4 and non-dimensional time of 10. When the moving velocity of the conductive ellipse is considered, 42% enhancement in the average Nu is obtained at non-dimensional time of 20 and object velocity equals to 0.012 times entering fluid velocity in the negative y direction while the pressure coefficient is higher. The moving object is used as a useful tool to control the dynamic features of heat transfer in a vented cavity.Originality/valueThe present method of convective heat transfer control inside a vented cavity with a moving elliptic object is novel and can be used as an effective tool with magnetic field effects owing to diverse use of convection in cavities with vented ports in many practical thermal engineering systems.

A computational method to solve for the heat conduction temperature field based on data-driven approach

In this paper, a computational method for solving for the 1-D heat conduction temperature field is proposed based on a data-driven approach. The traditional numerical solution requires algebraic processing of the heat conduction differential equations, and necessitates the use of a complex mathematical derivation process to solve for the temperature field. In this paper, a temperature field solution model called hidden temperature method is proposed. This model uses an artificial neural network to establish the correspondence relationship of the node temperature values during the iterative process, so as to obtain the ?Data to Data? solution. In this work, one example of 1-D steady-state and three examples of 1-D transient state are selected, and the calculated values are compared to those obtained by traditional numerical methods. The mean-absolute error of the steady-state is only 0.2508, and among the three transient cases, the maximum mean-square error is only 2.6875, indicating that the model is highly accurate in both steady-state and transient conditions. This shows that the hidden temperature method simulation can be applied to the solution of the heat conduction temperature field. This study provides a basis for the further optimization of the hidden temperature method algorithm.

Numerical investigation on turbulent penetration and thermal stratification for the in-surge case of the AP1000 pressurizer surge line

The transient three-dimensional in-surge case of the AP1000 pressurizer surge line is investigated by conjugating multi-physics fields under the ANSYS Workbench platform. Through analysis, it is found that there is a notable temperature oscillation in the fluid domain. The frequency of temperature fluctuation at cross sections near the hot leg is around 4.4 Hz, however, there are two peaks in the frequency spectrum at cross sections away from the hot leg. Due to the existence of turbulent penetration, the thermal stratification effect of the surge line under the in-surge case is not drastic, and the temperature difference along paths is less than 10 K. In order to determine the depth of turbulent penetration, four detective methods based on rapid temperature drop, temperature isosurfaces, the swirling strength isosurface and the step change of stress are introduced in this study. At the same time, some sections of interest along which may cracks occur are discussed, which provides a reference for the maintenance of the AP1000 pressurizer surge line.