Steady-state Analytical Model Research Articles

An analytical study of facemask performance to mitigate respiratory diseases transmission through coughs and sneezes

Upper respiratory infectious diseases are often transmitted through ejected droplets and aerosols at high velocity by coughs or sneezes. In its early stages, the rapid spread of the COVID-19 virus could not be fully controlled without face masks and social distancing, and the measures' effectiveness was in doubt due to the uncertainty of air leakage around the mask edges. This study aims to analytically investigate the effect of wearing face masks on the contamination distance around a coughing infected person in still air. The effect of mask design and the presence of gaps around the mask edges was also investigated in this study. A steady-state analytical model was developed to estimate the contamination distance as a function of mask properties and the gap width around the mask edges. The model was validated against experimental observations, showing good agreement. Results revealed that the effectiveness of a face mask in reducing contamination distances is highly dependent on the tightness of the mask fit around the wearer's face. Masks with high packing density, such as N95, were found to be ineffective with gap widths wider than 0.2 mm around the mask edges due to their high resistance, which diverts most of the flow to leak around the edges. For such wide gaps, more permeable cloth masks with packing densities below 1 % reduce the contamination distance more effectively, despite having a low filtration capacity, by impeding the inertia of the ejected particles.

Comparison of steady-state analytical wake models implemented in wind farm analysis software

A common set of mathematical wind turbine wake models are implemented in a few, well-adopted computational tools for wind farm wake modelling. Although the referenced mathematical formulations are common, implementation details may lead to differences in results. This study presents a systematic comparison of the implementation of mathematical wake models in open source, Python-based wind turbine wake modelling software, and a set of the models are directly compared. Despite aligning only the mathematical model parameters and retaining the default computational model parameters, good agreement is found across most of the model implementations, and additional agreement is expected upon further parameters alignment.

Electrical performance enhancement of MHD microgenerators through the longitudinal shaping of the cross-section

In the present work, the impact that the longitudinal shape of channels has on the current produced in the flow of a magneto-hydrodynamic microgenerator (MHDMG) is studied. The goal is to find the micro-channel geometry via modeling to maximize the current output for low Reynolds and Mach regimes. To carry out this study, a 3D dynamic numerical tool relying on the finite volume method was handled with the open-source software OpenFOAM. It is the base model to study the impact of intricate geometries on the ability to produce energy. An additional steady-state 2D analytical model was also developed to check some basic modeling assumptions. Both models have been experimentally validated on the simplest flow system having a constant square cross-section throughout. The results produced by both models cross-check very well and compare favorably with respect to experimental data. Hence, using the validated numerical tool, three shapes have been further investigated, namely, progressive (linear decrease of the cross-section), arc (parabolic decrease of the cross-section), and wavy (sinusoidal shape). It was found that the arc channel provides the greatest current output for the same volumetric flow. It is therefore the preferred choice for developing high current gain and more efficient MHDMG used in micro-scaled actuators and sensors.

A 2D steady state analytical model for atmospheric pressure RF plasma jet

This paper presents a 2-dimensional analytical model for plasma inside the discharge tube of an RF atmospheric pressure plasma jet (APPJ) in coaxial geometry. Since the model is a steady state one, it requires that the frequency of the applied RF be high enough so that the formation of streamers and plasma bullets is suppressed and that continuous plasma is present throughout the RF cycle. It is also assumed that power absorption is due to electron-atom collisions in the bulk plasma. The model takes into account gas flow, yielding a flow-diffusion axial flux that aids the exit of the plasma into the atmosphere. The inputs to the model are the reactor dimensions, average power fed (P av ) and the flow velocity of the gas (ug) using which the model yields the plasma density along with its radial and axial profiles, electron temperature, axial and radial particle fluxes, gas heating, flux, and energy of the plasma particles escaping from the discharge tube into the ambient air. Experiments were undertaken on an RF-powered jet at 13.56 MHz. Substituting the average RF power, measured using voltage and current probes, into the model gives the plasma density n ≈ 3.9 × 1017(≅2.8 × 1019)m−3 at for He (Ar). The corresponding electron temperature given by the model is for He (Ar). It is hoped that the developed model would be able to provide a comprehensive methodology for analyzing APPJs.

Seasonal scour and siltation induced spatiotemporal variations in riverbed sediment leakage coefficients as measured via the thermal tracer method

Riverbed scour and siltation can change the hydraulic conductivity and thickness of sediments, leading to notable spatiotemporal variations of groundwater–surface water interaction. However, correlated quantitative research on the dynamic leakage coefficient (LC) remains lacking under riverbed scour and siltation. Based on dynamic monitoring and analysis of sediment medium properties, river-groundwater levels, and temperature profiles in the section of Liao River, this study compared the applicable conditions of different thermal analytical models and identified spatiotemporal variations in the LC values induced by riverbed scour and siltation. The results showed that: (1) The thermal tracer method combined with river-groundwater level monitoring can effectively quantify spatiotemporal variations in the LCs of riverbed sediment. Based on the sediment temperature presents diurnal fluctuations and gradient characteristics in different seasons, the LCs in summer, spring, and autumn compared to winter in seasonally frozen regions should be calculated using transient and steady-state analytical solution models, respectively. (2) The LCs ranged from 0.47 to 24.90 × 10-6 s−1, showed larger temporal variability than spatial, increased from the river bank to the center, and had larger values in autumn and winter. (3) Distinct from previous findings, the riverbed underwent a scouring process associated with reductions in the incoming sediment coefficient as the river stage shifted from high to low, eroding the surface 4–8 cm of sediment. During this process, the LC increased by 40 to 420%. Further, the influence of riverbed scour and siltation on the LC varied by river section. Near the riverbank, the sediment LC was primarily controlled by hydraulic conductivity related to the coarsening of sediment lithology; however, it was influenced by variations in both sediment thickness and hydraulic conductivity near the riverbed center. Collectively, these results further understand the mechanisms underlying changes in the sediment LC induced by riverbed scour and siltation, as well as provide a scientific basis for ensuring the sustainable development of riverside water sources under such changes.

EXPERIMENTAL AND THEORETICAL STUDY OF TWO-PHASE HEAT PIPE

In this study, thermal characteristics of a two-phase closed heat pipe were investigated experimentally and theoretically. A two-phase closed heat pipe (copper container, Fluorocarbon FC-72 (C6F14) working fluid) was fabricated to examine its performance under the effect of input heat flux range of 250–1253 W/m2 , 70% fill charge ratio and various tilt angles. The temperature distribution along the heat pipe, input heat to evaporator section, and output heat from condenser were monitored. A comprehensive mathematical model was developed to investigate the steadystate heat transfer performance of a two-phase closed heat pipe. A steady state analytical model, is presented to determine important parameters on the design of two-phase closed heat pipe, including temperature levels and heat transfer coefficients for condenser and evaporator. The experimental and simulation results of this work are found in good agreement. The experimental boiling heat transfer coefficients were compared with existing previously reported correlations.

Outflow geometry for electrochemical desalination cells

Electrochemical desalination approaches continue to gain in application. Here, we introduce an electrochemical desalination system utilizing a novel flow geometry with symmetric, porous Ag/AgCl electrodes. The system takes advantage of advection to continuously deliver input solution to the surface of the electrodes and reduce depletion that limits throughput and energy efficiency of many desalination systems. We explore the system behavior using steady-state analytical and transient numerical models along with experimental characterization of a small (1 cm2 active area) cell. Desalination performance is explored in terms of degree of separation, throughput, charge efficiency, and energy usage. Optimal flowrate corresponding to minimum energy per mole of salt removed is found based on steady state models when advective separation and system resistive loss is balanced. As an example, for idealized flow, with 65% removal and 50% recovery from a 50 mM NaCl solution, system energy usage at optimum velocity is predicted to be 16.5x the thermodynamic minimum. A gradual tradeoff between energy efficiency and cell throughput exists, potentially allowing vastly higher superficial velocities (e.g., > 0.1 mm/s) and more compact systems than comparable techniques such as reverse osmosis. At example experimental operating conditions, the test cell provides 83% removal of NaCl from a 50 mM input solution at 0.32 V cell voltage with 50% recovery.

A steady-state analytical model for coupled methane transport and oxidation in vegetated landfill cover soil

The biologically active soils covered by plants are widely applied in landfill final covers for controlling the emission of methane from municipal solid waste. The current study focuses on developing alternative formulations of steady-state analytical modeling for coupled methane transport and oxidation in vegetated landfill cover systems considering the effect of mass exchange via plants’ roots. The proposed analytical frameworks are validated by a set of experimental data. The varied examples of coupled methane transport and oxidation are evaluated by the proposed solution to discuss the effects of the properties of roots and soils on the overall performance of vegetated landfill covers. It was shown that the increment of the root depth or root density can effectively contribute to the reduction of CH4 emission from landfill cover systems while coupled effects of advection/diffusion and oxidation rate may influence the overall performance of CH4 transport. For example, increasing root density from 100 m/m3 to 3 × 103 m/m3 can lead to a reduction of CH4 emission rate by a factor of 1.3. This is mainly attributed to the increase of aerobic zone with the root density growing. It is found that the methane removal efficiency is more sensitive to variations of the saturation outside the root zone (S2) than that in the root zone (S1) as gases inlet fluxes are largely reduced and the role of the plant is weakened for a larger S2. The present analytical models may provide an easy-to-use tool for performance evaluation of cover systems, benchmark studies, parameter identification and sensitivity analysis.

Estimation of erosion phenomena within helicon plasma sources through a steady-state explicit analytical model

Helicon plasma sources produce high-density discharges without the need of electrodes in direct contact with the plasma, which is thought to provide them with long operational lifetimes. An explicit steady-state analytical model is described with the capability of depicting the 2D plasma density distribution, the sheath potentials and the estimated sputtering and etch rates along the plasma-facing components of the source. The individual constituting submodels are fitted against available experimental data, and the model is used to predict erosion rates within the VX-CR research helicon plasma source. Erosion within these components is dependent on the value of plasma density along the boundaries, the electron temperature and the particular ion-target material combination. The highest erosion rates are found along the upstream system boundary, followed by the regions near the helicon antenna straps where a capacitive RF sheath is formed. The assumptions and limitations of the model are discussed, and future improvements are proposed.

Analytical modelling of power production from Un-moored Floating Offshore Wind Turbines

To avoid the limitations of floating offshore wind turbines (FOWTs) in deep water, and with the increasing push for renewable power to X (PtX) systems, un-moored wind turbine concepts are now being considered. Un-moored floating offshore wind turbines (UFOWTs) are still in the conceptual design stage, but they represent a unique way of harnessing the abundant far-offshore wind resource in deep waters. We examine an UFOWT with bottom-mounted thrusters for station-keeping from an analytic perspective. A one-dimensional steady-state analytical model is constructed to estimate the net power that can be extracted using such a system. Results of the model are consistent with existing literature in that a significant amount of power is lost to the thrusters for course-/station-keeping. Sensitivity of the net power to substructure design and relative size of the rotors is examined. Model predictions suggest that UFOWTs can produce more power by moving either upwind or downwind as opposed to remaining stationary. Optimal vessel speed and direction is also found to be sensitive to system design parameters. Although major concessions are made for the sake of model simplicity, the results serve to motivate and guide further modelling efforts for mobile wind energy systems (MWES).

The impact of sea-level rise on saltwater intrusion for barrier-island aquifers in North Carolina

Saltwater intrusion is an increasing problem for coastal aquifers due to rising sea levels, especially in areas of low hydraulic gradient, such as barrier-island aquifer systems. Large-scale studies are particularly useful for identifying trends in the effects of sea-level rise, especially for relatively understudied barrier-island aquifers. The barrier islands of coastal North Carolina, U.S.A., lie in a hot spot of sea level rise, where rates are projected to exceed global means throughout this century. Herein, we present a study of the effects of sea-level rise using four primary study sites, each with varying hydraulic properties, island width, and rates of sea-level rise. We use these sites to understand the viability of barrier-island aquifers in North Carolina, but also to understand in general the factors that are most important to the future viability of all barrier-island aquifers. We utilize a one-dimensional steady-state analytical model that allows the calculation of the position of the toe of the saltwater wedge at the base of the aquifer while limiting a rise in the water table. We determine the position of the toe for various sea-level projections up to the year 2100 and utilize this parameter as an assessment of the viability of the aquifer. Our findings suggest that higher island width and lower hydraulic conductivity are the most sensitive parameters and help to limit the effects of sea-level rise on aquifer viability. Aquifer risk maps calculated for the entire North Carolina coast, which equate risk with the position of the toe relative to island width, demonstrate that sea-level rise is projected to have increasing impact on aquifer viability over time, but that areas with narrower width and higher sea-level rise rates are the most vulnerable.

Effect of turbidity on choice of zonal thicknesses in solar ponds under various performance evaluation criteria

A turbid solar pond is investigated to study how turbidity in the insulating zone affects the optimum dimensions of the pond, that suit a concerned design criterion. Four different criteria for the optimization have been undertaken, namely: minimizing the maturation time period, maximizing the extraction power under no constraint, maximizing the extraction power under constraint of fixed pond volume and maximizing the extraction power while simultaneously minimizing the volume. Transient numerical solution is sought for the first criterion, whereas for remaining three, a steady-state analytical model is employed that assesses the year-round extraction performance. Simplified versions of the respective models have been validated with data obtained experimentally and with theoretical data available in the literature. It is revealed that turbidity in the salinity gradient zone can lead to considerable alterations in the optimal pond dimensions, regardless of what the criterion used for optimization. The maximum errors in the optimal insulating zone and heat storage zone thickness values, arising from neglect of turbidity are observed to be about 125% and 60%, respectively. Hence, either attempts should be made to make solar ponds free of any foreign agents that cause turbidity, or if not, then they should be designed considering this factor into account, for which this work can serve as a guiding study.

Two-dimensional steady-state thermal analytical model of permanent-magnet synchronous machines operating in generator mode

PurposeThermal analysis of electrical machines is usually performed by using numerical methods or lumped parameter thermal networks depending on the desired accuracy. The analytical prediction of temperature distribution based on the formal resolution of thermal partial differential equations (PDEs) by the harmonic modeling technique (or the Fourier method) is uncommon in electrical machines. Therefore, this paper aims to present a two-dimensional (2D) analytical model of steady-state temperature distribution for permanent-magnet (PM) synchronous machines (PMSM) operating in generator mode.Design/methodology/approachThe proposed model is based on the multi-layer models with the convolution theorem (i.e. Cauchy’s product theorem) by using complex Fourier’s series and the separation of variables method. This technique takes into the different thermal conductivities of the machine parts. The heat sources are determined by calculating the different power losses in the PMSM with the finite-element method (FEM).FindingsTo validate the proposed analytical model, the analytical results are compared with those obtained by thermal FEM. The comparisons show good results of the proposed model.Originality/valueA new 2D analytical model based on the PDE in steady-state for full prediction of temperature distribution in the PMSM takes into account the heat transfer by conduction, convection and radiation.

Kinematic synergy analysis of crouch cerebral palsy gait reveals a reduced locomotor strategy based on movement primitives

This paper proposes an analytical method to design thermoelectric heat pumps (THPs), in order to meet a given thermal power demand with a maximum coefficient of performance (COP). The method returns the optimal thermoelectric element (TE) design (leg length, leg section and number of legs) and optimal electric current, assuming that the hot and cold operating temperatures, the thermal power demand and the material properties are known. The optimal operating conditions are derived analytically from steady-state analytical models in the literature. Analytical development leads to defining an equivalent Seebeck coefficient when the Thomson effect is taken into account. Given that the optimal variables are closely related, many designs can meet the two performance criteria: (i) meeting thermal demand and (ii) maximizing the COP. To define a single optimal design, two additional manufacturing criteria are also considered: (iii) minimizing the material volume and (iv) minimizing the number of electrical junctions. This approach leads to the following recommendations:- identify the maximum THP area acceptable, depending on the application targeted, in order to decrease the thermal flux density and thus increase THP performance;- minimize the leg length in order to reduce the material volume and thus the THP cost;- maximize the leg section (leading to work with the maximal electric current achievable) in order to reduce the number of junctions, thus facilitating the manufacturing process.Finally, the optimal number of legs and electrical current can be calculated via simple ratios.

Transient pigging dynamics in gas pipelines: Models, experiments, and simulations

The bypass hole lowers the traditional pig velocity and brings significant uneven pig velocity which rises the pigging stuck risks. Aiming to give the quick evaluations of the uneven pig motion, this paper first proposed a transient steady-state analytical model to describe the trend and the fluctuation range of the uneven pig velocity, then developed the stoppage model to estimate the stoppage time as the result of inlet mass flow, friction force, and bypass character. The accuracy of the analytical model was verified by the consistency between the model calculated velocity, experimental data and the simulated velocity trend. And the stoppage model was verified by the simulated velocity trends. On considering the gas compressibility effect and the variation in friction profile, this paper studied the occurrence of pig stoppage and the extent of slippage with the designed abnormal friction section in simulation procedure. The variation in friction aggravates the slippage and stimulates the occurrence of stoppage. The positive friction deviation is largely responsible for the sudden deceleration and then stoppage. While, the gas compressibility is primarily responsible for the occasional stoppage after the pig acceleration-deceleration procedure when the pig travels into the lower friction region.

Simulation of methane steam reforming in a catalytic micro-reactor using a combined analytical approach and response surface methodology

In this study, a steady-state analytical model for heat and mass transfer in a 2D micro-reactor coated with a Nickel-based catalyst is developed to investigate microscale hydrogen production. Appropriate correlations for each species’ net rate of production or consumption, mass diffusivity, and the heat of reactions are developed using a detailed reaction mechanism of methane steam reforming. The energy and species conservation equations are then solved for the reactive mixture coupled with the wall energy equation. Finally, the response surface methodology (RSM) is employed to study the effects of channel height, inlet velocity and temperature, wall thickness and conductivity, and external heat flux on CH4 conversion. It is found that the inlet gas temperature, among different parameters, has the most influence on the overall performance of the microchannel hydrogen production. Also, the maximum necessary heat of reforming reaction increases by 84% and 26% if the CH4 conversion changes from 50% to 60% and 60% to 70%, respectively. The developed analytical simulation can be a useful tool for designing experiments in micro-scale hydrogen production.

Modeling and Simulation of Ultrahigh Sensitive AlGaN/AlN/GaN HEMT-Based Hydrogen Gas Detector With Low Detection Limit

Presented through this work is a steady state analytical model of the GaN HEMT based gas detector. GaN with high chemical and thermal stability provides promises for detectors in hazardous environments. However, HEMT sensor resolution must be improved to develop high precision gas sensors for automotive and space applications. The proposed model aids in systematical study of the sensor performance and prediction of sensitivities. The linear relation of threshold voltage shift at thermal equilibrium is used in predicting the sensor response. Numerical model for the reaction rates and the electrical dipole at the adsorption sites at the surface and metal/semiconductor interface have been developed and the sensor performance is analyzed for various gas concentrations. The validation of the model has been achieved through surface and interfacial charge adsorption-based gate electrode work function, Schottky barrier, 2DEG and threshold voltage deduction using MATLAB and SILVACO ATLAS TCAD. Further the applicability of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{g}_{d}$ </tex-math></inline-formula> (channel conductance) as gas sensing metric is also presented. With high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{I}_{D}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{g}_{d}$ </tex-math></inline-formula> percentile sensitivities of 118.5% and 92 % for 10 ppm hydrogen concentration. The sensor shows capability for detection in sub-ppm levels by exhibiting a response of 0.043% for 0.01ppm (10 ppb) hydrogen concentration. The detection limit of the sensor (1% sensitivity) presented here is 169 ppb and the device current increases by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$34.2~\mu \text{A}$ </tex-math></inline-formula> for 1ppb hydrogen concentration.

Temperature dynamics and its effects on gas influx handling during managed pressure drilling operations

With Managed Pressure Drilling (MPD) becoming increasingly important to oil and gas well construction, there has been a growing demand for comprehensive models that can accurately describe the well hydraulic dynamics, especially for complex well geometries, High-Pressure High-Temperature (HPHT) conditions, during well control events, etc. To meet this demand, new multi-phase hydraulic models have been developed. However, despite their improvement over the traditional lumped parameter models, these models typically do not consider detailed temperature effects, which markedly influence well hydraulics and need to be explicitly considered for accurate MPD control.The development of a new integrated multi-phase thermal and hydraulic modeling framework is presented in this paper. This integrated model can estimate the mud temperature in the drillstring and the annulus, as well as the temperature variations of the formation during complex well control situations. The model uses a semi-implicit finite volume approach and solves the mixture energy equation for the wellbore fluids, assuming that all the phases are in thermal equilibrium. Heat transfer between the drillstring and wellbore fluids, and between the wellbore fluids and the formation is calculated using thermal resistance networks.The steady-state and transient temperature behaviors during mud circulation are compared to the steady-state analytical model by Hasan and Kabir and commercial software. These comparisons show good agreement for both steady-state and transient cases. To demonstrate the importance of accurate temperature estimation of the drillstring and annulus fluids in HPHT conditions, offshore kick scenarios for non-aqueous drilling fluids and dynamic kick control methods are simulated. Simulation results indicate that the model enables real-time estimation of crucial parameters during well control, such as the wellbore pressure and temperature profiles, increased outflow and pit gain during kicks, gas thermodynamic behavior including solubility and unloading behavior at low pressure conditions, gas rising velocity, and temperature-dependent formation strength.

Analytical solution for quenching of hot rolled aluminium plates without passing through C-curve

At the end of the hot rolling process, quenching is deployed for obtaining the desired microstructure and mechanical properties. During the quenching of aluminium plates, it is essential to optimize the process parameters such as the plate speed and cooling intensity for surpassing the C-curve. In this study, 1-D steady-state analytical model has been developed with the constant heat transfer boundary condition. The Eulerian computational domain contains the precooling and water cooling regions. Temperature drop starts in the precooling region itself due to back diffusion of heat, which originates from the water cooling region. Based on the analytical solution, the effect of plate speed and heat transfer coefficient on the cooling time has been investigated with the three non-dimensional parameters such as Peclect, Biot, and Fourier numbers. Typically, for the 2xxx (Al–Cu) alloys, every material point in the plate has to reach 350 °C within 0.2 s, which surpasses the nose of the C-curve where the phase transformation (CuAl2) severity can be reduced. This sets the limit for the maximum Fourier number and while keeping Peclect number as the independent variable, the minimum required water cooling in terms of Biot number is identified. The presented analytical solution provide the guidelines for selecting the appropriate combinations of plate speed and heat transfer coefficient for the quenching of continuously moving hot rolled plates. The results indicate that the nose of the C-curve can be surpassed easily by increasing the plate speed instead of reducing which contradicts the common notion.

Assessment of proposed maximum power point tracking–unity power factor algorithms for optimum operation permanent magnet synchronous generator–based wind turbine

It is very important to select proper maximum power point tracking algorithm in order to achieve best performance and low cost for wind turbine–generator combination. A permanent magnet synchronous generator steady-state unity power factor analytical model based on a current source—equivalent circuit is provided. Validation of the identified load angle effect in current source as compared with that of the commonly used voltage source permanent magnet synchronous generator is presented. Then three new maximum power point tracking–load angle control algorithms based on current source model are presented. They all apply magnitude and frequency control techniques for Digital Signal Processor control systems. The first one presents maximum power point tracking–unity power factor applying constrained load angle control algorithm. The merits of the next two developed schemes are quickly and precisely tracking the maximum power output of the wind turbine; thus, the second and third algorithms are then characterized with linear control systems. The linearity of the second scenario is between load angle and reference speed while the third one has a load angle–torque linear relationship which shows its optimality. Finally, the controlled characteristics and implementation for the optimum case are presented for both stationary and synchronous reference frames (for vector control purposes). Simulation modeling for optimum case is provided and its results match well with the proposed predictive control algorithm.