Quasi Two-dimensional Model Research Articles

Examining the effects of a pre-noon annular Solar Eclipse on equatorial electrodynamics: Evidence for a subsequent post-noon enhancement in plasma density

On 26 December 2019, an annular solar eclipse occurred in the southern part of the Indian subcontinent, which falls within the Equatorial ElectroJet (EEJ) region. This presented an opportunity to study the effects of a high-obscuration annular solar eclipse (93.3%) and of the special tides that accompany an eclipse. Eclipses are known to affect the electrodynamics of the equatorial region and the distribution of plasma in the low-latitude ionosphere. On December 26, 2019, different phenomena were indeed seen over different time scales. Around the time of the eclipse, there was a depletion in the total electron content (TEC) of the ionosphere, as inferred from GNSS receiver systems placed along the eclipse path in and around the EEJ region. Magnetometer measurements indicated a weakening of the EEJ current in this area not just when the eclipse took place but for the rest of the day as well. Observations from a digital-ionosonde located in Trivandrum (8.52°N, 76.94°E; 0.33°N dip-latitude) revealed that the ionospheric F-layer moved downwards just after obscurity maximum. Shortly after the F region was observed to move back upward, a one-hour long strong blanketing sporadic E-layer was triggered even though there was only a weakening of the EEJ but no reversal in the associated magnetic perturbations. Simulations from our quasi-two dimensional model clearly show that though there was no Counter Electrojet, there was indeed a weakening of the zonal field on 26 December 2019 during the eclipse and the post-eclipse period. The overall weakening trend lasted until late afternoon. Other notable features were uncovered on a time scale of several hours after the passage of the eclipse. While the day-long weakening of the EEJ is consistent with special tides related to the lunar trajectory, we also observed unusually large amplitude undulations in both vertical-TEC and F2-region peak plasma density over a five-hour time scale, starting around 2:00 PM LT. These undulations were consistent with the zonal electric field variations reconstructed from the magnetometer data.

Validation and verification of a quasi two-dimensional turbulence model and an eddy detection method for liquid metal magnetohydrodynamics flows

The flow of liquid metals in straight rectangular channels with an externally applied transverse magnetic field is considered for breeding blankets in tokamak fusion reactors. Under the tokamak magnetic field, the liquid metal experiences the magnetohydrodynamic (MHD) effect that enhances the laminarization of the flow. In geometric singularities, or under certain flow conditions, the combination of Lorentz forces, momentum, and buoyant forces may trigger the formation of vortical structures. The generated vortices will align with the direction of the magnetic field, and therefore the use of a quasi-two-dimensional (Q2D) model is convenient to study them assuming that the walls are electrically insulating and the Hartmann number is high enough. Using this model is computationally affordable, allowing extensive parametric analyses. To identify the presence of eddies in the two-dimensional domain, the application of the bi-dimensional fast Fourier transform (FFT2) is foreseen as an adequate detection method. This work presents a methodology to systematically calculate liquid metal MHD flows with a Q2D model and evaluate the formation of eddies in the flow domain. The work includes a description of the validation and verification of the Q2D MHD model and of the FFT2 method proposed to automatically identify eddies. The sensitivity of the detection method is analyzed to subsequently apply it in parametric analyses.

The scaled-invariant Planckian metal and quantum criticality in Ce1−xNdxCoIn5

The mysterious Planckian metal state, showing perfect T-linear resistivity associated with universal scattering rate, 1/τ = αkBT/ℏ with α ~ 1, has been observed in the normal state of various strongly correlated superconductors close to a quantum critical point. However, its microscopic origin and link to quantum criticality remains an outstanding open problem. Here, we observe quantum-critical T/B-scaling of the Planckian metal state in resistivity and heat capacity of heavy-electron superconductor Ce1−xNdxCoIn5 in magnetic fields near the edge of antiferromagnetism at the critical doping xc ~ 0.03. We present clear experimental evidences of Kondo hybridization being quantum critical at xc. We provide a generic microscopic mechanism to qualitatively account for this quantum critical Planckian state within the quasi-two dimensional Kondo-Heisenberg lattice model near Kondo breakdown transition. We find α is a non-universal constant and depends inversely on the square of Kondo hybridization strength.

Development of model-based simulation and optimization software for electron beam melting and refining

In this paper the development of a software for electron beam melting and refining (EBMR) of different materials is presented. It has the following functional characteristics: simulation of the temperature distributions in the cast ingots, investigation and optimization of the form of the liquid pool during the process of EBMR and estimation of the inclusion refining rates, depending on the EBMR process parameters. The temperature distributions in the cast ingots are simulated by the implementation of quasi steady-state two-dimensional heat model and three-dimensional time-dependent thermal model for different refined metals. Empirical models are estimated, integrated in the developed software and used for the investigation of the molten pool geometry parameters, the content of impurities after the electron beam refining process, refining rate, overall inclusion removal efficiency and the material losses. The influence of EBMR process parameters such as electron beam power, casting velocity, refining time, and electron beam radius are considered. Multicriterial optimization software functions can be implemented for solving concrete technological requirements for each practical use-case.

Signature of the midnight temperature maximum in thermospheric oxygen airglow emissions: Results from the ship-borne airglow measurements from the Indian region

This paper discusses the results from the aeronomy experiment carried out using a multiwavelength photometer operated onboard Sagar Kanya ship from the Indian region, which covered a latitude region from 14.5 N to 2S (7° to −10° Dip latitudes) along the same longitude region (∼72-75E). It has been found that the thermospheric airglows, especially the OI 630.0 nm emission near to the geographic equator exhibits ‘Midnight Brightness’ on different days of observations. Though the magnitudes were found to be less, the OI 777.4 nm and OI 557.7 nm emissions also exhibited intensity variations on those days, indicating a common causative mechanism for the same. The simulation studies using a quasi-two dimensional ionospheric model, revealed that such an enhancement could be due to the F-region collapse associated with the Midnight Temperature Maximum (MTM) phenomenon.

Optimized two-dimensional networks with edge-crossing cost: Frustrated antiferromagnetic spin system.

We consider a quasi-two-dimensional network connection growth model that minimizes the wiring cost while maximizing the network connections, but at the same time edge crossings are penalized or forbidden. This model is mapped to a dilute antiferromagnetic Ising spin system with frustrations. We obtain analytic results for the order-parameter or mean degree of the optimized network using mean-field theories. The cost landscape is analyzed in detail showing complex structures due to frustration as the crossing penalty increases. For the case of strictly no edge crossing is allowed, the mean-field equations lead to a new algorithm that can effectively find the (near) optimal solution even for this strongly frustrated system. All these results are also verified by Monte Carlo simulations and numerical solution of the mean-field equations. Possible applications and relation to the planar triangulation problem is also discussed.

Effect of magnetic field on the steady nanofluid flow past obstacle

The fluid flow and heat transfer of a nanofluid past a circular cylinder in a rectangular duct under a strong transverse magnetic field is studied numerically using a quasitwo-dimensional model. Transition from laminar flow with separation to creeping laminar flow is determined as a function of Hartmann number and the volume fraction of nanoparticle, as are critical Hartmann number, and the heat transfer from the heated wall to the fluid. Downstream cross-stream mixing induced by the cylinder wake was found to increase heat transfer. The successive changes in the flow pattern are studied as a function of the Hartmann number. Suppression of vortex shedding occurs as the Hartmann number increases.

Numerical optimisation of a micro-wave rotor turbine using a quasi-two-dimensional CFD model and a hybrid algorithm

Wave rotors are unsteady flow machines that exchange energy through pressure waves. This has the potential for enhancing efficiency over a wide spectrum of applications, ranging from gas turbine topping cycles to pressure-gain combustors. This paper introduces an aerodynamic shape optimisation of a power generating non-axial micro-wave rotor turbine and seeks to enhance the shaft power output while preserving the wave rotor’s capacity to function as a pressure-exchanging device. The optimisation considers six parameters including rotor shape profile, wall thickness, and number of channels and is done using a hybrid genetic algorithm that couples an evolutionary algorithm with a surrogate model. The underlying numerical model is based on a transient, reduced-order, quasi-two dimensional computational fluid dynamics model at a fixed operating condition. The numerical results from the quasi-two-dimensional optimisation indicate that the best candidate design increases shaft power by a factor of 1.78 and imply a trade-off relationship between torque generation and pressure exchange capabilities. Further evaluation of the optimised design using three-dimensional computational fluid dynamics simulations confirms the increase in power output at the cost of increased entropy production. It is further disclosed that increased incidence losses during the initial opening of the channel to the high-pressure inlet duct compromise the shock strength of the primary shock wave and account for the decrease in pressure ratio. Finally, the numerical trends are validated using experimental data.

Novel fan configuration for distributed propulsion systems with boundary layer ingestion on an hybrid wing body airframe

The performance benefits of directly ingesting the boundary layer (BLI) on air vehicles with distributed propulsion (DP) systems has been documented and explored extensively. However, numerous investigations have demonstrated that the increase of the flow distortion in the inlets of conventional propulsors can dramatically reduce the expected benefits. Hence, this work presents an alternative fan configuration to re-energize the boundary layer, and at the same time, to perform properly in a distorted and non-uniform flow-field. This conceptual design utilizes a two-dimension idealized fan and replaces the rotational movement with linear displacement, avoiding the undesired effects of circumferential distortion on the propulsor operation. A quasi two-dimensional model based on the Discretized Miller approach has been used to compare the proposed configuration with a conventional axial fan. From the results obtained, it is observed that the thermal performance of the fan is less affected for the proposed configuration and furthermore, intake pressure losses are ameliorated by the use of a single mailbox shape inlet. The performance assessment of the proposed configuration coupled on the N3-X aircraft shows benefits of 4% in fuel savings compared with current BLI turbo-machinery configurations. The main contribution of this study lies on the definition of a preliminary design for an alternative propulsor configuration able to deal with circumferential distortion.

Quasi-2D Performance Analysis for Axial Compressors Based on Time-Marching Method

In order to get a fast performance analysis tool for multi-stage axial compressors, a quasi-two dimensional analysis model based on time-marching method is developed in this paper. The model is based on Euler equation, and several source terms, like inviscid blade force model and viscous force model, are added to simulate different phenomena of compressor internal flow. The flow line in blade area is adjusted to solve the discontinuity problem at blade leading edge. Two test cases-PW3S1, a 3.5-stage axial compressor and a 1.5-stage high-speed axial compressor, are presented to validate the quasi-2D model. The overall performance characteristics of two compressors at different rotation speed are calculated then. The computed results are compared with experimental data or 3D results. The average errors of pressure ratio and efficiency are 0.52% and 0.63% in PW3S1 case, 1.73% and 2.91% in 1.5-stage compressor case, and the model is able to capture shock wave and to predict choke condition.

Thermal-hydraulic analysis of the thermoelectric space reactor power system with a potassium heat pipe radiator

The thermoelectric space reactor power system conceptual design incorporates fast reactor, liquid-lithium primary coolant loops that transfer heat to potassium-filled high temperature heat pipes and thermoelectric generators. An integrated system analysis model was developed to study the operating characteristics of the space power system, which consisted of reactor thermal-hydraulic model, neutron kinetics model, thermoelectric energy conversion assembly (ECA) model, heat pipe radiator model etc. One-dimensional thermal-hydraulic model was applied to model the coolant circuit. Quasi two-dimensional analysis models for heat transfer of fuel element, ECA and the heat pipe fin were established. Considering the thermoelectric conversion phenomena, an equivalent electric efficiency model was inserted in the ECA model. Both finite element method and thermal resistance network were applied to simulate the potassium heat pipe system. The normal operation condition and two demonstration accident scenarios (unprotected inadvertent movement of a sliding reflector and loss of heat pipes) were calculated to prove the capabilities of the new system model.

Experimental study of the dryout of a 2D heat-generating model porous medium

Dryout experiments are performed in a quasi two-dimensional heat-generating model porous medium, with bottom flooding. The test section is composed of an array of heating cylinders placed between two ceramic plates. It is held vertically and a liquid (HFE-7000) is injected from bottom at a controlled flow rate, pressure and temperature. Dryout incipient power is investigated by applying an increasing thermal power to a bundle of heating cylinders until a dry zone is detected. The liquid inlet mass fluxes range from 1.0kgm-2s-1 to 10.5kgm-2s-1 and the heat fluxes are between 195kWm-2 and 1086kWm-2. Two kinds of dryout phenomenology are observed. First, at low liquid injection rate (below 4.2kgm-2s-1 inlet mass flux), reaching the dryout power results into a liquid front receding from the top of the test section to the upper limit of the heated zone, while downstream the heated zone, the porous medium is vapour-saturated. Second, at higher flow rate (over 5.2kgm-2s-1 inlet mass flux), the boiling crisis happens at the surface of a single heating element, resulting in a local film boiling, whereas a two-phase flow still go through the whole test section. In both cases, high-speed visualizations allow characterizing 8 boiling/flow regimes, depending on the inlet mass flux, the power released by the heated zone, and the location inside the porous medium. In particular, when reaching the dryout incipient power, the existence of a pulsed flow regime is highlighted. Such a characterization of boiling/flow regimes might be helpful in improving dryout models.

Prediction of Sediment Transport Capacity in Rivers Using Quasi Two-Dimensional Mathematical Model

Prediction of Sediment Transport Capacity in Rivers Using Quasi Two-Dimensional Mathematical Model

Assessment of Parametric Sensitivity Analysis Methods Based on A Quasi Two-Dimensional Groundwater Model

Parametric sensitivity analysis (SA) aims to select the sensitive parameters that most significantly affect the model output variables, which helps to improve model optimization efficiency by adjusting a small number of sensitive parameters instead of all adjustable parameters. The qualitative and quantitative SA methods have been commonly used to quantify the sensitive parameters of the models. However, the response surface model based quantitative SA method was rarely used. Taking the simulation of a quasi twodimensional (quasi-2D) groundwater model as an example, this study systematically assess eight SA methods divided into three categories (qualitative SA, quantitative SA, and the response surface model-based quantitative SA). The study validates the effectiveness of these methods by comparing the parameter sensitivity results, and also demonstrates the efficiency of these methods by determining the minimum sample size required. Using the minimum samples means the least number of model runs. The results show that P1 and P2 are the most sensitive parameters of the quasi-2D model for simulating groundwater table elevation. Except for local method, four global qualitative SA methods obtain reasonable parameter sensitivity rankings using 200 samples, but the parameter sensitivity scores fail. For obtaining accurate sensitivity scores, at least 2000 samples are required by the quantitative SA methods. However, for the response surface model-based quantitative SA method, 60 samples are sufficient to obtain accurate sensitivity scores, demonstrating that the method is an effective and highly efficient, and should be recommended as the primary parametric SA method, especially for the complex models with large computational demand.

A quasi two-dimensional friction-thermo-hydro-mechanical model for high-speed landslides

For deep-seated landslides, thermal pressurization in shear zone has been considered an important cause of high-speed collapse. To quantify this mechanism, this study proposed a quasi two-dimensional friction-thermo-hydro-mechanical (FTHM) model, concerning the mechanisms of material frictional softening and thermo-hydro-mechanical softening during the start-up phase of high-speed landslides. In this model, the intact slide mass was divided into a lot of small slide blocks. The dynamic equations of each block, and the heat equations, pore pressure equations of each shear band were established respectively. The model fully considered the morphological characteristics of landslides, and variables such as velocity, temperature, excess pore pressure varied along both the normal and the tangential direction of the whole shear band during the slide mass movement. The model was applied to back-analyze the Vaiont landslide and the results were compared with existing one-dimensional models. It can be concluded that the irregular spatial shape of slide mass makes a difference on mechanism of thermo-hydro-mechanical softening which promotes the collapse, and that the quasi two-dimensional model is valid.

Evaluation of aerodynamic forces acting on oscillating cantilever beams based on the study of the damped flexural vibration of aluminium test samples

The paper is devoted to study of the aerodynamic forces acting on flat cantilever beams performing flexural vibrations in a viscous fluid. Original method for the force evaluation is presented based on analysis of experimental measurements of a logarithmic decrement of vibrations and relative variation in frequency of duralumin test specimens. The theoretical core of the method is based on the classical theory of bending beam oscillations and quasi-two dimensional model of interaction between a beam and a gas. Using the proposed method, extensive series of experiments for a wide range of oscillations parameters were carried out. The processing of the experimental data allowed to establish the global influence of the aerodynamic effects on beam oscillations and the local force characteristics of each cross-section of the beam in the form of universal functions of dimensionless amplitude and dimensionless frequency of oscillation. The obtained estimates of the drag and added mass forces showed a good correspondence with the available numerical and experimental data practically in the entire range of the investigated parameters.

Analytical solution of non-uniform flow in compound channel

The present work investigates the analysis of depth-averaged velocity and boundary shear stress distribution in compound channels with non-uniform flow condition. A quasi two-dimensional model is proposed to assess the flow variables by accounting the physical processes that are specific to non-uniform flow. For analyzing the flow behavior, experimental data sets concerning compound channels with narrowing and enlarging floodplains of previous investigators are considered. The model accounts the influence of momentum transfer on the flow variables through additional shear stresses that are developed in non-uniform flow. Three types of effective stresses produced by molecular viscosity, turbulent and dispersion on the vertical planes are discussed. An analytical solution to the model is presented. Terms associated with the effective stresses are investigated relating them to the geometric and hydraulic parameters. The significance of lateral variation of energy slope is further investigated. For both homogenous and heterogeneous non-prismatic channels, the approach is examined to predict the flow variables with reasonable accuracy.

Electrochemical Modeling of HTPEM Fuel Cells Using Elementary Step Kinetics

High temperature polymer electrolyte fuel cells (HT-PEM) offer certain advantages over the low temperature polymer electrolyte membrane fuel cells (LT-PEM). Numerical modeling is a powerful tool to understand the thermo-chemical and physico-chemical processes that takes place within the gas diffusion layer (GDL) and the catalyst layer (CL) during the cell operation. The models reported in the literature varies from simple analytical expressions to 3D models. Most of these models are based on a general Butler-Volmer equation, without giving any importance to the underlying charge transfer mechanism, and therefore the exchange current densities are fitted to some arbitrary order with respect to hydrogen and oxygen concentrations. Furthermore, most of these models are validated by reproducing the IV curve often by a one dimensional model by resolving the electrode thickness. Whenever such as validation is done, the fuel and oxidant depletion along the cell length and hence the fuel utilization is not accounted for. To the best of our knowledge no attempt has been done to date to validate the experimentally measured axial current density profile. A predictive model should be capable of predicting the measured axial current density profile and the IV curves. The objective of the current work is to develop an electrochemical model based on elementary step charge transfer that occur at the anode and cathode of the HT-PEM fuel cell. In order to develop the mechanistic steps, dissociative adsorption of H2 and O2 is considered. In addition, to account for performance drop in presence of CO, adsorption of CO is also considered in the elementary step reactions. Assuming the protonation reaction to be rate limiting at the anode three phase interface and OH formation to be rate limiting at the cathode three phase interface, Butler-Volmer expressions are derived for the charge transfer reactions at the respective electrodes.The exchange current density at the anode follows i=ioa [exp (βafηa) - exp (-βcfη)], and at the cathode follows i=ioc [exp (-βcfηc) - exp ((1+βa)fηc)].Here, the exchange current densities at the anode and cathode are respectively given by i0a =i*x [(KH2pH2)1/4]/[1+(KCOpCO)+(KH2pH2)1/2)]andioc = i*x [(pH2/p0)1/4 (KO2pO2)3/8]/[1+(KO2pO2)1/2+(pH2/p0) exp (- ΔG*/RT)]. The equilibrium constants appearing the expression for the exchange current densities are evaluated from the adsorption desorption equilibrium of the reactant species (H2, O2, and CO). The adsorption rates are calculated from the sticking coefficients. The activation energy for the desorption reactions is calculated using Unity Bond Index Quadratic Exponential Potential method (UBI-QEP) and the frequency factor for the desorption reactions is calculated from transition state theory. The electrochemical model is incorporated into a quasi-two dimensional numerical transport model of the cell.The transport model accounts for the species transport in the flow channels and diffusive transport across the thickness of the electrode (GDL + CL). The diffusive transport in the porous electrode is modeled using Dusty Gas Model (DGM). The resulting governing equations for the species transport are solved using the ODE solver CVode. The electrochemical model, i.e., the Butler-Volmer equations and the cell voltage equation, forms a set of algebraic equations, which are solved using a damped Newton iteration for every call made by the CVode solver.The whole model is implemented in C++. The model developed can predict the current density and species profiles along the cell length and the thickness of the catalyst layer required to achieve best cell performance. The current density profile predicted by the model along the length is validated by comparing against the experimental measurements reported in the literature. For demonstrating the capability of the model, a comparison between the simulated IV curves and the experimental measurements (Li et. al, 2003 ECS) is given in the Figure. Figure 1

Electrochemical Modeling of HTPEM Fuel Cells Using Elementary Step Kinetics

High temperature PEM fuel cells (HT-PEMFC) offer several advantages over low temperature PEM fuel cells (LT-PEMFC). Numerical modeling is a powerful tool to understand the thermo-chemical and physico-chemical processes that take place within the gas diffusion layer (GDL) and the catalyst layer (CL) during the cell operation. The objective of the current work is to develop an electrochemical model based on the elementary step charge transfer reactions that occur at the anode and cathode of the HT-PEMFC. Elementary step reaction for adsorption of CO is also incorporated to account for performance drop in presence of CO. The electrochemical model is incorporated into a quasi-two dimensional numerical transport model of the cell. The diffusive transport in the porous electrode (GDL + CL) is modeled using Dusty Gas Model (DGM). The resulting governing equations for the species transport are solved using the ODE solver CVode. The whole model is implemented in C++.

IMPLICATIONS OF PLUME DISCHARGE FOR TIDAL CHANNELS MORPHODYNAMICS: A COUPLED ONSHORE AND OFFSHORE SYSTEM

This contribution investigates the morphodynamic equilibrium of a funnel-shaped, well-mixed tidal channel taking into account the existing dynamical coupling between the tidal channel itself and the related offshore sediment-laden plume. We use a quasi two-dimensional numerical model that resolves the fully nonlinear unsteady shallow water, sediment bed load transport and suspended sediment advection-diffusion equations along with the Exner equation for the bathymetric changes. We close this model by including a dynamic boundary condition at the channel mouth that transfers the offshore plume sediment concentration to the channel dynamics. This model reveals that the offshore plume reduces the timescales to reach equilibrium of the channel and plays a crucial role on shaping it. At equilibrium, the non-plume influence case attains a quasi-linear profile of constant slope in the seaward part. However, the bottom profile in the case that includes the offshore plume tends to increase the concavity of the bottom profile, reducing the final channel mouth depth. Finally, numerical results suggest that the plume characteristics are altered as a consequence of tidal channel evolution.