One-dimensional Analytical Model Research Articles

Free Vibration of Inclined Twisted Cables

This paper is aimed at simulating and investigating the coupled translational and rotational vibrations occurring simultaneously in inclined sagged cables. The three-dimensional behavior of the single-layered six wires strand stiffness results are reduced to effective one-dimensional behavior from the elasticity-based finite element behavior analyses under axial tension and torsional loads. These are directly compared with multiple one-dimensional analytical model results. The effective stiffness coefficients agreed well for the actual lay angle of the cable and at angles below 20 degrees with finite element models where internal contact was not considered. To find the cable natural frequency and corresponding modal shapes the derived primary stiffness and mass matrices are discretized over the inclined sagged cable using a finite element model where the two-node cable element has three translational and three rotational degrees of freedom. The vibration behavior is also studied using extensive experimental tests using the same cable geometry and material used in the numerical calculations. In addition to the physical experiments, the finite element model accuracy was also compared with results from a well-known analytical model available from the literature for horizontal cables, and the influence of the inclination angle variation was also investigated and compared with the computer finite element software ABAQUS for the same purpose. The results found confirm the correctness of the derived formulation, mathematical, and psychical importance of the six-degrees of freedom finite element model developed and the efficiency in evaluating the coupled cable dynamic behavior. It addition, the results highlight the fundamental dynamics of inclined cables and the role of the inclination angle, sag, and weight of the cable.

Influence of advection on the soil gas radon deficit technique for the quantification of LNAPL

The Radon (Rn) deficit technique is a rapid, low-cost, and non-invasive method to identify and quantify light non-aqueous phase liquids (LNAPL) in the soil. LNAPL saturation is typically estimated from Rn deficit using Rn partition coefficients, assuming equilibrium conditions. This work examines the applicability of this method in the presence of local advective fluxes that can be generated by groundwater fluctuations or biodegradation processes in the source zone. To this end, a one-dimensional analytical model was developed to simulate the steady-state diffusive-advective transport of soil gas Rn in the presence of LNAPL. The analytical solution was first validated against an existing numerical model adapted to include advection. Then a series of simulations to study the effect of advection on Rn profiles were carried out. It was found that in high-permeability soils (such as sandy soils), advective phenomena can significantly affect Rn deficit curves in the subsurface compared with those expected, assuming either equilibrium conditions or a diffusion-dominated transport. Namely, in the presence of pressure gradients generated by groundwater fluctuations, applying the traditional Rn deficit technique (assuming equilibrium conditions) can lead to an underestimation of LNAPL saturation. Furthermore, in the presence of methanogenesis processes (e.g., in the case of a fresh LNAPL of petroleum hydrocarbons), local advective fluxes can be expected above the source zone. In such cases, Rn concentrations above the source zone can be higher than those above background areas without advective phenomena, resulting in Rn deficits higher than 1 (i.e., Rn excess), and thus leading to a wrong interpretation regarding the presence of LNAPL in the subsurface if advection is not considered. Overall, the results obtained suggest that advection should be considered in the presence of pressure gradients in the subsurface to ensure an effective application of the soil gas Rn-deficit technique for quantitative estimation of LNAPL saturation.

Temperature distribution of an SG-DBR laser cooled by a thermoelectric cooler

We introduce a one-dimensional analytical model to determine the steady-state thermal behavior of a sampled grating distributed Bragg reflector laser coupled to a thermoelectric element cooler. The governing equations are a system of ordinary differential equations that can be solved analytically. This method can easily be used when the laser is integrated with more functional elements, e. g., semiconductor optical amplifiers and amplitude modulators. The results are verified by the numerical finite element method and experimental data reported by other researchers. A comparison between the results of the analytical and numerical methods reveals the high consistency between them.

Analysis and Experimental Investigation of High-Frequency Magnetic Flux Distribution in Mn-Zn Ferrite Cores

This article presents a comprehensive investigation of the high-frequency magnetic flux distributions in manganese-zinc ferrite ring cores. New experimental characteristics are presented and used in the flux modeling. The flux distribution is predicted by a one-dimensional analytical model, a transmission-line model, and finite-element analysis. The models are used to investigate the high-frequency effects, such as skin depth and dimensional resonance. A complete experimental validation is presented. The nonuniform magnetic flux distributions are experimentally validated for two Mn-Zn materials: 3F36 and 3E10. The low permeability 3F36 material performance can be significantly degraded by dimensional resonance. However, the high permeability 3E10 material degrades due to the skin effect. The presented analytical methods show a very good correlation with the measurements.

Electric control of a phononic crystal constituted of Piezoelectric layers using Schottky diode

A one-dimensional piezoelectric phononic crystal (PPC) consisting of a periodic pattern made of two perfectly bonded materials: one active (piezoelectric), the other passive (elastic) and exhibiting a strong acoustic impedance contrast is studied. We are interested in the tunability of piezoelectric inclusions in order to control the propagation of ultrasonic waves in the MHz range from a nonlinear electrical component connected to the terminals of the piezoelectric elements. After modeling the dynamic resistance of the Schottky diode, based on the piezoelectricity equations, a one-dimensional analytical model is proposed to take into account the resistive impedance effect of this diode connected to the electrodes of the active plate. Thus, we have shown that the application of various electrical boundary conditions (EBCs) on the electrodes (open-circuit, short-circuit, connecting an electrical load) allows to change the effective properties of the piezoelectric plate in particular and those of the PPC in general. The dispersion of the waves is then electrically tuned and, depending on the applied EBCs, we have demonstrated numerically the possibility of opening Bragg or hybridization gaps in the PPC band structure.

Quantitative Characterization of Interfacial Defects in Thermal Barrier Coatings by Long Pulse Thermography

The non-contact long pulse thermography method is commonly used to detect the defects in thermal barrier coatings (TBCs). The profile of interfacial defect in TBCs can be monitored by infrared camera under the irradiation of the excitation source. Unfortunately, the defect profile is always blurry due to heat diffusion between the defect area and the intact area. It is difficult to quantify the size of defect size in TBCs. In this work, combined with derived one-dimensional heat conduction analytical model, a non-contact long pulse thermography (LPT) method is applied to quantitatively investigate the interface defects in TBCs. Principal component analysis (PCA) and background subtraction method are used to improve the contrast of the defect profile in collected thermal images. By fitting the results between the profile of the interface defect in thermal images and the predicted shape of the model, the interface defect size can be determined. Furthermore, a simple extension of proposed method for interfacial defects with irregular shape is presented. The predicted errors for round defect with diameters of 3 mm, 5 mm and 7 mm are roughly distributed in the range of 3%~6%, which are not affected by the defect diameter.

A position-dependent acoustic model relevant for some active noise control applications

This paper focuses on acoustic modeling for active noise control applications. The desired model must be finite dimensional and efficient numerically to meet implementation requirements. It must also be parameterized by the position considered inside the cavity. This additional characteristic is desirable for addressing specific active noise control applications such as optimizing microphone placement, estimating acoustic pressure at different positions of the considered cavity, and finally attenuating noise level in a subarea of the cavity. The main contribution of this paper is to propose a finite-dimensional, low-order, and parameterized acoustic model of a cavity, suitable for active noise control applications. The resulting model is defined as a gray box that combines a one-dimensional analytical model of acoustic propagation, which handles the physical parameterization, and a black-box model that copes with actuator and sensor dynamics as well as modeling errors. The parameters of the proposed model are optimized in order to reproduce the frequency behavior of the real system (LS2N active noise control platform) in a frequency range. This model allows one to accurately reproduce the dynamics at any position in the considered cavity. The prediction performance of the proposed model was compared to a classical black-box model (usually used for active noise control applications) and validated experimentally using the LS2N active noise control platform. The analysis highlighted that the proposed gray-box model can predict the acoustic behavior in a great range of positions.

Anti-blast analysis and design of a sacrificial cladding with graded foam-filled tubes

Foam-filled tubes are excellent energy absorption structures for impact resistance, and graded foam may have superiority for the design of anti-blast sacrificial cladding. The anti-blast response of density-graded foam-filled tubes as a core layer is investigated numerically and theoretically. Mesoscopic finite element models for graded foam-filled tubes are constructed, and their constant-velocity compression and anti-blast performance are simulated. One-dimensional analytical shock models based on an empirical force–displacement relationship are developed to analyze the axial collapse wave propagation in graded foam-filled circular tubes. Single-/double-wave deformation patterns are observed for graded foam-filled tubes under blast loading, especially the negatively graded foam-filled tubes with gradient parameters close to zero may also show a single-wave deformation pattern. The results demonstrate that the negatively graded foam-filled tube with a small density gradient is a good choice to design anti-blast sacrificial cladding with a small critical length and a low transmitted force. A contour map of the critical length required to absorb the impulse of blast loading for different gradient parameters and diameter-thickness ratios of the outer tube is established. This study proposes a new design guideline for superior blast resistance structures in engineering applications.

Laser-structured microarray electrodes for durable stretchable lithium-ion battery

Stretchable lithium-ion batteries (SLIBs) hold great potential as a power source for wearable electronics. A major challenge in the development of SLIBs is fabricating stable and reliable stretchable electrodes. Herein, we develop a novel laser-structured microarray electrodes based SLIBs. An active material film adhered to a planar stretchable current collector is ablated by ultrafast laser into an independent microscale square array, enabling electrodes stretchable. A one-dimensional elastic analytical model is developed to evaluate the stretchability of the microarray electrodes under tensile conditions. The microscale square array adheres to the current collector and keeps intact if the shear stress is less than the adhesion force as well as the tensile stress is less than the tensile strength of the active material. The demonstrated electrodes have a mass active material loading of 10 mg cm−2 and maintain robust electrochemical performance when stretched beyond 500 cycles at 100 % strains. The fabricated SLIBs show a stable capacity of 1.2 mAh cm−2, and over 70 % of initial capacity can be maintained at 100 % strain.

Analytical model of free charge transfer in charge-coupled devices

A one-dimensional analytical model of charge transfer in charge-coupled devices, which describes the spatial–temporal behavior of the charge carrier density in a potential well, is presented. The general solution of this model considers the transfer dynamics in terms of the electric drift field, i.e., self-induced drift and fringing-field drift, and yields an analytical solution for the total number of charge carriers. A comparison of the transfer efficiency for various electric drift fields is presented. The modulation transfer function in dependence on the transfer efficiency is analyzed, aiming especially at time-delay integration (TDI) applications. Finally, the results of this model are concluded and discussed in detail.

Transient and Quasi-Steady-State Analytical Methods for Simulating a Vertical Gas Flow in a Landfill with Layered Municipal Solid Waste

The exploration of gas pressure and its distribution in landfills is a principal concern for the design and management of municipal solid waste (MSW) landfills. A one-dimensional analytical model was proposed to simulate a vertical gas flow in a landfill with layered MSWs. The transient analytical solution was obtained by the method of superposition and eigenfunction expansion and verified by a semi-analytical solution and numerical simulation. According to the results of a parametric analysis by the transient analytical solution, a vertical gas flow in landfills can be simplified to a quasi-steady-state flow. A quasi-steady-state analytical solution for simulating a vertical gas flow in a landfill with layered MSW is proposed. The quasi-steady-state analytical solution showed good agreement with the transient solution. Both temporal and spatial variations of the gas generation rate in MSW landfills were considered in the transient and quasi-steady-state analytical methods. A comparison between the proposed quasi-steady-state solution and the previously described steady-state solution showed that using the average gas generation rate or the gas generation rate corresponding to the average age of the MSW layer in the steady-state solution resulted in an error in the estimation of the gas pressure in landfills. The proposed solutions are reliable and can provide a reference for the design, management, and subsequent restoration of landfills.

Response of cylindrical tubes subjected to internal blast loading

Cylindrical metallic tubes are commonly used as a protective structure to contain explosives. This study focused on the response of single walled and sandwich walled cylindrical tubes subjected to an internal explosion. Firstly, real-life detonation experiments were performed to obtain the basic deformation patterns. Finite element (FE) simulations were then conducted in ANSYS and LS-DYNA to obtain the simulated data for deformation pattern. Those simulated results were then validated against the experimentally obtained data. Next, a parametric study was performed in order to obtain the main parameters in an explosive process while keeping the failure strain of the material constant. For single-walled tubes, these were namely found to be the mass of the PE4 explosive used (M), the thickness of the tube wall (h) and the stand-off distance (R). A non-dimensional empirical formula was obtained. Then the response of sandwich-walled tube filled with the closed-cell aluminum foam under PE4 charge was investigated numerically. The numerical results revealed that the deformation or failure, and the energy absorption of the sandwich tubes were significantly affected by the PE4 charge, and also the mass ratio of the tube to the foam. As a first step, a simplified one-dimensional axisymmetric analytical model was presented where the filled foam was assumed to have an initial rigid regime, followed by a perfectly-plastic stage and locking densification (R-PP-L). Comparison with the numerical model gives a fairly good agreement.

Study on supercritical CO2 critical flow through orifices under power cycle operating conditions

For prediction of critical flow occurring under supercritical carbon dioxide (S-CO2) condition, one-dimensional (1-D) analytical critical flow models are evaluated in this study. Specifically, homogeneous equilibrium model (HEM) and a newly proposed non-equilibrium model are evaluated. The new non-equilibrium model adopts Moody’s slip ratio for mechanical non-equilibrium and a newly proposed correlation of supercooling for thermal non-equilibrium. For evaluation of the models over various thermodynamic states, S-CO2 critical flow experiment through an orifice is conducted to supplement and expand a range of previously published S-CO2 critical flow experiment data. From the evaluation results with the expanded S-CO2 critical flow experiment database, the new non-equilibrium model shows better prediction performance than HEM in terms of the prediction of critical mass flux and critical pressure. For practical applications, discharge coefficients for each 1-D analytical critical flow model are suggested for the orifice geometry.

Thermodynamic performance comparison of organic Rankine flash cycle with and without ejector for geothermal power output

To improve the matching between heat source and working fluid and alleviate the problem of high pump power and low system efficiency in small-scale organic Rankine cycle (ORC), an organic Rankine flash cycle with ejector (EORFC) was proposed. In this paper, the theoretical analysis of the EORFC is conducted based on one-dimensional global model of the ejector and one-dimensional analytical thermodynamic model of the system. A parametrical analysis on the EORFC with R245fa is conducted, the influences of the entrainment ratio and area ratio on the ejector mechanism and system performance are investigated in turn. Then, a comparative analysis is further carried out, which mainly focus on the comparison between the thermodynamic performance of the EORFC and organic Rankine flash cycle (ORFC) by analyzing the influences of the system operating parameters, including overall efficiency of the pump, flashing temperature, condensing temperature and dryness degree at the evaporator outlet. The results show that with the decrease of the entrainment ratio and the area ratio, the pressure lift and ejector efficiency increase, thereby improving the performance of the EORFC. The temperature at the ejector outlet is also inversely proportional to the entrainment ratio, while it is almost unaffected by the area ratio. Meanwhile, the four system operating parameters have positive influence on the net power output of the EORFC and ORFC. When the overall efficiency of the pump is lower than 30% and the condensing temperature is higher than 30 °C, the EORFC can put more net power. Compared with the ORFC, the EORFC always has higher thermal efficiency and exergetic efficiency due to the heating effect of the ejector, besides the EORFC is superior at low cycle efficiencies.

A Reduced-Order Modeling Framework for Simulating Signatures of Faults in a Bladed Disk

This paper reports a reduced-order modeling framework of bladed disks on a rotating shaft to simulate the vibration signature of faults like cracks in different components aiming towards simulated data-driven machine learning. We have employed lumped and one-dimensional analytical models of the subcomponents for better insight into the complex dynamic response. The framework seeks to address some of the challenges encountered in analyzing and optimizing fault detection and identification schemes for health monitoring of rotating turbomachinery, including aero-engines. We model the bladed disks and shafts by combining lumped elements and one-dimensional finite elements, leading to a coupled system. The simulation results are in good agreement with previously published data. We model the cracks in a blade analytically with their effective reduced stiffness approximation. Multiple types of faults are modeled, including cracks in the blades of single and two-stage bladed disks, Fan Blade Off (FBO), and Foreign Object Damage (FOD). We have applied aero-engine operational loading conditions to simulate realistic scenarios of online health monitoring. The proposed reduced-order simulation framework will have applications in probabilistic signal modeling, machine learning toward fault signature identification, and parameter estimation with measured vibration signals.

Hybrid Monte Carlo-Diffusion Studies of Modeling Self-Heating in Ballistic-Diffusive Regime for Gallium Nitride HEMTs

Abstract Exact assessment of self-heating is of great importance to the thermal management of electronic devices, especially when completely considering the cross-scale heat conduction process. The existing simulation methods are either based on convectional Fourier's law or limited to small system sizes, making it difficult to deal with noncontinuum thermal transport efficiently. In this paper, a hybrid phonon Monte Carlo diffusion method is adopted to predict device temperature in ballistic–diffusive regime. Heat conduction around the heat generation region and boundaries are simulated by phonon Monte Carlo (MC) method, while the other domain is by Fourier's law. The temperature of the hybrid method is higher than that of Fourier's law owing to phonon ballistic transport, and the calculation efficiency of the hybrid method is remarkably improved compared with phonon MC simulation. Furthermore, the simulation results indicate that the way of modeling self-heating has a remarkable impact on phonon transport. The junction temperature of the heat source (HS) scheme can be larger than that of the heat flux (HF) scheme, which is opposite to the result under Fourier's law. In the HS scheme, the enhanced phonon-boundary scattering counteracts the broadening of the heat source, leading to a stronger ballistic effect and higher temperatures. The conclusion is verified by a one-dimensional analytical model. This work has opened up an opportunity for the fast and extensive thermal simulations of cross-scale heat transfer in electronic devices and highlighted the influence of heating schemes.

Modeling of machining of EB-PVD ceramic coatings using smoothed particle hydrodynamics method

In this work, an improved Smoothed Particle Hydrodynamics (SPH) based model for simulating the machining process of the thermal barrier coatings is presented. The columnar grain microstructure in the electron-beam physical vapor deposition (EB-PVD) coating is constructed. The Johnson-Holmquist 2 (JH-2) material model coupled with the Johnson-Holmquist plasticity damage model is used for the ceramic coating. The model validation is conducted by the comparison between the SPH model and qualitative agreement with experimental observation, and a quantitative agreement with the one-dimensional stress wave analytical model. In the SPH model, the cutting processing parameters, such as cutting depth, cutting speed, cutting tool's edge radius, rake angle on the cutting force, and temperature change are studied. The results show that the fracture of the columnar grains during the cutting process is done through deflection and fracture of the grains, followed by pushing against neighboring grains. Both the cutting force and temperature of the coating increase with cutting depth due to increased cutting work which is transferred to heat. The cutting forces from the SPH model at the stable stage are in excellent agreement with the fracture mechanics analytical solution. The cutting force and temperature increase are higher for a larger edge radius, due to increased friction between the cutting tool and coating. The SPH model result follows the same trend as the main cutting force calculated by the analytical expression. The SPH cutting model developed in this work can be used as a design tool to optimize the coating machining process.

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.

One-dimension frequency–wavenumber-domain based model for ultrasonic waves generated by dual-array transducers

Array transducers can allow wavelength and frequency selectivity and can be used to generate different types of waves, such as ultrasonic bulk or guided waves. Dual-array transducers consist of two interlaced arrays, where the elements of each array are electrically connected. Therefore, by driving each array with a pair of phased pulses one can achieve a degree of wave generation control that allows unidirectional generation, unlike single array transducers that generate waves in both 0° and 180° directions with respect to the array’s longitudinal axis. In this paper, we present a one-dimensional analytical model to determine the ultrasonic waves generated by dual-array transducers based on the excitability of the array in the frequency–wavenumber domain, the so-called operation region, determined by the joint spatial and temporal spectrum of the dual-array. We further exploited it to analyse the effectiveness of unidirectional generation with time-delayed excitation signals that provide ideal constructive or destructive interferences. The model also provides the time-domain received waveforms, which were compared to experimentally generated shear-horizontal ultrasonic guided waves, with a dual periodic permanent magnet array electromagnetic acoustic transducer, showing very good agreement. The adequate selection of the excitation signal allowed one to obtain up to about 40 dB unidirectionality experimentally.