Time-dependent Analytical Model Research Articles

A novel time-dependent analytical model for optimizing efficiency and valve timing in Ericsson engines

In this work, a novel analytical time-sensitive model for Ericsson engines was developed taking into account the heat transfer phenomena between the working gas and the cylinder walls in the compressor and the expander. For the calculation of the mass flow entering/exiting each cylinder, another dedicated flow model was developed to account for the pressure drop at the valves. From the energy equilibrium taking into consideration the time-dependent thermal response of the cylinder walls and the enthalpy entering/exiting each cylinder through the valves, an analytical solution of the working gas pressure and temperature can be obtained for every time step and consequently, the thermal efficiency of the engine can be calculated. A case study was performed where the thermal efficiency of an Ericsson engine was calculated for different rotational speeds and heat exchanger gas temperatures. It was observed that with higher temperatures thermal efficiency maintained a more stable behaviour with a weak dependence on rotational speed. The thermal efficiency of the engine in the performed case studies was found in the range of 10% to 14%. The valve timing of the Ericsson engine was optimized in order to achieve the highest thermal efficiency possible. The thermal efficiency of the engine could be increased up to 26% as a percentage after a thorough optimization of the valve timing. Finally, backflow phenomena accounting for thermal efficiency drop were studied. The developed model can also be applied to other types of external combustion engines such as Stirling engines.

Time-dependent reliability analysis of wellbore stability during drilling in hydrate exploitation

Methane hydrates is regarded as an important alternative energy in the future. Due to the complexity of marine environment, the mechanical parameters and initial stress state of formation have great uncertainties which can affect the wellbore stability in hydrate exploitation. In this study, a new time-dependent analytical model is proposed, considering the influence of hydrate dissociation on the mechanical properties and the partial coupling among pore pressure/temperature/mechanical field. The analytical solutions are verified and validated by numerical solutions. Based on the analytical solution and Mogi-Coulomb failure criterion, the reliability of wellbore stability during drilling in hydrate exploitation is analyzed by the Response Surface Method. Through the reliability analysis, the probability of wellbore instability increases and the safe drilling fluid pressure window range is narrowed with time, and finally tended to be stable at t = 12 h. Hydrate dissociation would lead to a more narrowed pressure window range, about by −38.75%. The most significant parameter whose uncertainty affects the instability probability is initial in-situ stress, followed by the initial internal friction angle and Biot’s coefficient.

An analytical model of time-dependent elastoplasticity with hydraulic–mechanical coupling for wellbore stability in hydrate exploitation

Natural gas hydrates have potential economic and environmental significance. However, wellbore instability likely occurs during drilling due to the deterioration in the geomechanical properties of formation caused by hydrate dissociation. In this study, a time-dependent elastoplastic analytical model for wellbore stability is proposed under overbalanced and underbalanced drilling, considering the hydrate dissociation-induced changes in the geomechanical properties and full coupling between hydraulic–mechanical fields. The analytical solutions are verified with the finite element results under the same conditions and validated with the results from complex numerical simulations. According to the analytical solutions, the difference in pore pressure relative to the initial pore pressure decreases, and accordingly, the incremental displacement decreases (by approximately 39.54% for the maximum displacement) after the influence of the mechanical field on pore pressure is considered. The influence is greater far from the wellbore and smaller around the wellbore due to the constant drilling fluid pressure. The risk of wellbore instability increases with time, and the safe drilling window of drilling fluid pressure will be narrowed by hydrate dissociation (by −5.90%), the increase in the drilling fluid temperature (by −12.64% from the temperature of 20 °C to 30 °C) and the reduction in cohesion (by −47.43% at most).

An Analytical Fourier Transformation Model for the Production of Hard and Soft X-Ray Time Lags in Active Galactic Nuclei: Application to 1H 0707-495

The variability of the X-ray emission from active galactic nuclei is often characterized using time lags observed between soft and hard energy bands in the detector. The time lags are usually computed using the complex cross-spectrum, which is based on the Fourier transforms of the hard and soft time series data. It has been noted that some active galactic nuclei display soft X-ray time lags, in addition to the more ubiquitous hard lags. Hard time lags are thought to be produced via propagating fluctuations, spatial reverberation, or via the thermal Comptonization of soft seed photons injected into a hot electron cloud. The physical origin of the soft lags has been a subject of debate over the last decade. Currently, the reverberation interpretation is recognized as a leading theory. In this paper, we explore the alternative possibility that the soft X-ray time lags result partially from the thermal and bulk Comptonization of monochromatic seed photons which, in the case of the narrow-line Seyfert 1 galaxy 1H 0707-495, may correlate with fluorescence of iron L-line emission. In our model, the seed photons are injected into a hot, quasi-spherical corona in the inner region of the accretion flow. We develop an exact, time-dependent analytical model for the thermal and bulk Comptonization of the seed photons based on a Fourier-transformed radiation transport equation, and we demonstrate that the model successfully reproduces both the hard and soft time lags observed from 1H 0707-495.

A new vision of short-time and long-time AC loss measurement and modelling: A superconducting power electronic circuit

This paper provides a new vision of loss measurement and modelling for superconducting coils, with both the short-time test and long-time test, as the behaviour of the AC loss in superconductors is actually a dynamic process with the temperature and time dependence, particularly for the medium-to-high frequency AC operation. A single-pancake High temperature superconducting (HTS) coil was tested in a power electronic circuit (DC-AC inverter). The operating current was from 15 A to 50 A, and the operating frequency was from 1 kHz to 5 kHz. The AC loss measurements were carried out using the function of fully decoupling power by a commercial power analyzer. This method was able to measure the real-time AC loss, and the loss measuring process is much easier than the conventional electrical and magnetic method. As expected, for short-time loss tests, the experiment, the FEM H-formulation model, and the conventional analytical model agree with each other. However, the AC losses in long-time tests are found having power-law relations with the operating time (above kHz level). As the accumulated heat in the HTS coil as well as the interrelation between the critical current and temperature, the real-time AC losses are strongly time-dependent. A new time-dependent analytical model is developed, for the purpose of accurately modelling the real-time loss in the HTS coil. The new analytical model well matches the AC loss tests over both the long and short testing time. The experimental method and new analytical model offer a new sight at the AC loss of superconducting coil for both the short-time and long-time operation in a power electronic circuit, which is able to explore more reasonable guidelines of safe operating area (SOA) during the practical AC operation of superconducting applications.

Seebeck coefficient’s comparative evaluation by cross-examination of time-dependent analytical model, numerical simulation and experimental measurement applied to germanium surface

A time dependent evaluation method is presented in order to visualize the changing behavior of several parameters such as temperature, electron concentration and electrical potential in semiconductor materials. If well-known experimental standard methods enable solid measurements and results, animated time-dependent simulations enable a good step-by-step follow-up of the mechanisms. An original combination of three complementary methods (analytical, numerical and experimental) is presented here as an exhaustive package to extract the Seebeck coefficient of Germanium using the Hot-Probe experiment.

A Soft Material Flow Sensor for Micro Air Vehicles.

To control and navigate micro air vehicles (MAVs) efficiently, there is a need for small, lightweight, durable, sensitive, fast, and low-power airspeed sensors. When designing sensors to meet these requirements, soft materials are promising alternatives to more traditional materials due to the large deformations they can withstand. In this article, a new concept of a soft material flow sensor is presented based on elastic filament velocimetry, which fulfills all necessary criteria. This technique measures flow velocity by relating it to the strain of a soft ribbon suspended between two static supports and subjected to a flow of interest. The ribbon is manufactured from polydimethylsiloxane and can be made piezoresistive by the addition of silver nanowires. With the described manufacturing method, the sensor can be made using common laboratory tools, outside of a clean room, significantly reducing its complexity. Furthermore, it can be operated using a simple and lightweight circuit, making it a convenient alternative for MAVs. Using a piezoresistive material allows for the flow velocity to be calibrated to the resistance change of the strained ribbon. Although certain challenges remain unsolved, such as polymer creep, the sensor has demonstrated its ability to measure flow velocities down to 4 m/s in air through experiments. A time-dependent analytical model is also provided. The model shows that the current sensor has a bandwidth of 480 Hz. Most importantly, the sensitivity and the bandwidth of the sensor can be varied strictly by modifying the geometry and the material properties of the ribbon.

Probabilistic analysis on time-dependent mechanical behavior of post-tensioned self-centering concrete connections

This paper presents a probabilistic assessment on the time-dependent mechanical behavior of post-tensioned (PT) self-centering (SC) concrete connections. First, the prestress loss in PTSC frames induced by the shrinkage and creep effects of concrete is estimated according to the probabilistic analysis with the inclusion of possible sources of uncertainties. The finite element models of PTSC subassemblies with different structural parameters are developed and utilized to investigate the impacts of span number, reinforcement ratio and initial prestress level on the loss degree of prestress. Subsequently, a time-dependent analytical model is proposed for the PTSC concrete connections. The long-term performance of PTSC joints is analyzed with the incorporation of prestress loss and other time-dependent effects, such as the continuing hydration of cement. Finally, the key indicators for the mechanical properties of PTSC connections are extracted and quantitatively evaluated.

Excitation of decay-less transverse oscillations of coronal loops by random motions

Context. The relatively large-amplitude decaying regime of transverse oscillations of coronal loops has been known for two decades and has been interpreted in terms of magnetohydrodynamic kink modes of cylindrical plasma waveguides. In this regime oscillations decay in several cycles. Recent observational analysis has revealed so-called decay-less, small-amplitude oscillations, in which a multi-harmonic structure has been detected. Several models have been proposed to explain these oscillations. In particular, decay-less oscillations have been described in terms of standing kink waves driven with continuous mono-periodic motions of loop footpoints, in terms of a simple oscillator model of forced oscillations due to harmonic external force, and as a self-oscillatory process due to the interaction of a loop with quasi-steady flows. However, an alternative mechanism is needed to explain the simultaneous excitation of several longitudinal harmonics of the oscillation. Aims. We study the mechanism of random excitation of decay-less transverse oscillations of coronal loops. Methods. With a spatially one-dimensional and time-dependent analytical model taking into account effects of the wave damping and kink speed variation along the loop, we considered transverse loop oscillations driven by random motions of footpoints. The footpoint motions were modelled by broad-band coloured noise. Results. We found the excitation of loop eigenmodes and analysed their frequency ratios as well as the spatial structure of the oscillations along the loop. The obtained results successfully reproduce the observed properties of decay-less oscillations. In particular, excitation of eigenmodes of a loop as a resonator can explain the observed quasi-monochromatic nature of decay-less oscillations and the generation of multiple harmonics detected recently. Conclusions. We propose a mechanism that can interpret decay-less transverse oscillations of coronal loops in terms of kink waves randomly driven at the loop footpoints.

Corrosive Environment Assessment and Corrosion-Induced Rockbolt Failure Analysis in a Costal Underground Mine

As an effective ground-reinforcing system, rockbolts have been widely used in underground excavations. Corrosion of rockbolts has been one of the most reasons for rockbolts system failure. In this paper, the chemical composition and pH values of the groundwater in Sanshandao Gold mine are first tested. Corrosion of the slotted rockbolts used in roadways of the mine is analysed. The corrosion rate of rockbolts is evaluated based on experimental results from similar corrosive conditions. A time-dependent analytical model on anchoring force degradation caused by corrosion of the rockbolt is developed. Furthermore, the effects of corrosion rate and geometric parameters of the slotted rockbolts on anchoring force degradation are discussed. Suggestions on rockbolts support design in corrosive conditions are given. It has been found that, with the corrosion time increasing, the anchoring force between the rock and the rockbolt gradually decreases. The larger the corrosion rate is, the faster the anchoring force decreases. For long-term service roadways under corrosive conditions, a slotted rockbolt with a smaller radius and thicker wall can enhance the anchoring force.

Time-dependent Electron Acceleration in Pulsar Wind Termination Shocks: Application to the 2007 September Crab Nebula Gamma-Ray Flare

Abstract In 2007 September, the Crab Nebula exhibited a bright γ-ray flare in the GeV energy range that was detected by AGILE. The observed emission at ≳160 MeV indicates that the radiating electrons had energies above the classical synchrotron radiation-reaction limit, thus presenting a serious challenge to classical models for electron acceleration in astrophysical environments. In this paper, we apply our recently developed time-dependent self-similar analytical model describing electrostatic acceleration in the explosive reconnection region around the pulsar wind termination shock to the 2007 September flare. This event was unique in that it displayed both long-duration “wave” and short-duration “subflare” features. The unusual temporal variation makes this flare an especially interesting test for our model. We demonstrate that our model can reproduce the time-dependent γ-ray spectrum for this event, as well as the associated γ-ray light curve, obtained by integrating the spectrum for photon energies ≥100 MeV. This establishes that our time-dependent electrostatic acceleration model can explain both wave and subflare transients, which lends further support to the theoretical framework we have developed. We also further examine the validity of the self-similar electric and magnetic field evolution implied by our model. We conclude that strong electrostatic acceleration driven by shock-induced magnetic reconnection is able to power the Crab Nebula γ-ray flares by energizing the electrons on sub-Larmor timescales.

Time Dependent Analytical Diffusion Model of Air Pollutant in a Protected Zone due to Point Source with Wet Deposition

Time Dependent Analytical Diffusion Model of Air Pollutant in a Protected Zone due to Point Source with Wet Deposition

Chaotic motion and the evolution of morphological components in a time-dependent model of a barred galaxy within a dark matter halo

Studies of dynamical stability (chaotic versus regular motion) in galactic dynamics often rely on static analytical models of the total gravitational potential. Potentials based upon self-consistent N-body simulations offer more realistic models, fully incorporating the time-dependent nature of the systems. Here we aim at analysing the fractions of chaotic motion within different morphological components of the galaxy. We wish to investigate how the presence of chaotic orbits evolves with time, and how their spatial distribution is associated with morphological features of the galaxy. We employ a time-dependent analytical potential model that was derived from an N-body simulation of a strongly barred galaxy. With this analytical potential we may follow the dynamical evolution of ensembles of orbits. Using the Generalized Alignment Index (GALI) chaos detection method, we study the fraction of chaotic orbits, sampling the dynamics of both the stellar disc and of the dark matter halo. Within the stellar disc, the global trend is for chaotic motion to decrease in time, specially in the region of the bar. We scrutinized the different changes of regime during the evolution (orbits that are permanently chaotic, permanently regular, those that begin regular and end chaotic, and those that begin chaotic and end regular), tracing the types of orbits back to their common origins. Within the dark matter halo, chaotic motion also decreases globally in time. The inner halo (r < 5 kpc) is where most chaotic orbits are found and it is the only region where chaotic orbits outnumber regular orbits, in the early evolution.

Development of a time-dependent energy model to calculate the mining-induced stress over gates and pillars

Generally, longwall mining-induced stress results from the stress relaxation due to destressed zone that occurs above the mined panel. Knowledge of induced stress is very important for accurate design of adjacent gateroads and intervening pillars which helps to raise the safety and productivity of longwall mining operations. This study presents a novel time-dependent analytical model for determination of the longwall mining-induced stress and investigates the coefficient of stress concentration over adjacent gates and pillars. The model is developed based on the strain energy balance in longwall mining incorporated to a rheological constitutive model of caved materials with time-varying parameters. The study site is the Tabas coal mine of Iran. In the proposed model, height of destressed zone above the mined panel, total longwall mining-induced stress, abutment angle, induced vertical stress, and coefficient of stress concentration over neighboring gates and intervening pillars are calculated. To evaluate the effect of proposed model parameters on the coefficient of stress concentration due to longwall mining, sensitivity analysis is performed based on the field data and experimental constants. Also, the results of the proposed model are compared with those of existing models. The comparative results confirm a good agreement between the proposed model and the in situ measurements. According to the obtained results, it is concluded that the proposed model can be successfully used to calculate the longwall mining-induced stress. Therefore, the optimum design of gate supports and pillar dimensions would be attainable which helps to increase the mining efficiency.

On the construction of low-energy cislunar and translunar transfers based on the libration points

There exist cislunar and translunar libration points near the Moon, which are referred to as the LL 1 and LL 2 points, respectively. They can generate the different types of low-energy trajectories transferring from Earth to Moon. The time-dependent analytic model including the gravitational forces from the Sun, Earth, and Moon is employed to investigate the energy-minimal and practical transfer trajectories. However, different from the circular restricted three-body problem, the equivalent gravitational equilibria are defined according to the geometry of the instantaneous Hill boundary due to the gravitational perturbation from the Sun. The relationship between the altitudes of periapsis and eccentricities is achieved from the Poincaré mapping for all the captured lunar trajectories, which presents the statistical feature of the fuel cost and captured orbital elements rather than generating a specified Moon-captured segment. The minimum energy required by the captured trajectory on a lunar circular orbit is deduced in the spatial bi-circular model. The idea is presented that the asymptotical behaviors of invariant manifolds approaching to/traveling from the libration points or halo orbits are destroyed by the solar perturbation. In fact, the energy-minimal cislunar transfer trajectory is acquired by transiting the LL 1 point, while the energy-minimal translunar transfer trajectory is obtained by transiting the LL 2 point. Finally, the transfer opportunities for the practical trajectories that have escaped from the Earth and have been captured by the Moon are yielded by the transiting halo orbits near the LL 1 and LL 2 points, which can be used to generate the whole of the trajectories.

Nucleation on a stepped surface with an Ehrlich–Schwöbel barrier

During deposition on a stepped surface the growth mode depends on the conditions such as temperature T, deposition rate F and width of the terraces w. In this work we studied the influence of all the above mentioned characteristics using the kinetic Monte Carlo (kMC) technique. We concentrated on the conditions on the terrace at the moment of the first nucleation. The critical density of monomers for nucleation ηm decreases with the width of the terrace and the nucleation starts at surprisingly low densities of monomers. We tested several definitions of the critical width for nucleation wc used in various articles in the past and we compared our results with results of the analytical steady-state mean-field model (Ranguelov and Altman 2007 Phys. Rev. B 75 245419). To check how the simplified assumption about the steady-state regime during deposition influences the resulting dependence of wc ≃ (D/F)κ, we set and also solved a time-dependent analytical model. This analytical model as well as kMC predict that wc ≃ (D/F)1/5. kMC simulation also shows that the Ehrlich–Schwöbel barrier has only limited influence on the nucleation on the stepped surface at conditions close to the nucleation regime. For all widths of terraces there is a critical value of the Ehrlich–Schwöbel barrier ( eV at T = 175 K), and only below this critical value does the Ehrlich–Schwöbel barrier affect the final value of the density of nuclei. The results of the kMC are summarized in a semi-empirical analytical formula which describes the dependence of the step-flow growth and nucleation on the terrace width w, diffusion coefficient D and deposition rate F. In our simulations we tested two models of the stepped surface with different thicknesses of the step, both with an Ehrlich–Schwöbel barrier on the edge of the terrace.

Impact Loading on Glass/Epoxy Composite Laminates with Nano Clay

This paper presents various energy absorbing modes in nano composite laminates when subjected to impact loading. Composite laminates, made of 610 gsm WRM(Woven Roving Mat), are prepared by hand lay-up and compression molding technique.Nano clay is dispersed in epoxy and is used as a matrix. Clay dispersion in epoxy is varied from 1% to 5% by weight. A gas gun set up is used to impact the composite laminates with spherical nose cylindrical projectile of diameter 9.5 mm and mass 7.6g.The laminates are subjected to different velocities, which vary from below ballistic limit to above ballistic limit.The vibration response of the laminate at different impact velocities is studied. A time dependent analytical model is used to predict the projectile energy during penetration, and is used to determine the ballistic limit of the laminate. The ballistic limit obtained from experiment is validated with analytical model and good agreement is found.

A Time-Dependent Collisional Sheath Model for Dual-Frequency Capacitively Coupled RF Plasma

A time-dependent analytical model for capacitive sheath is developed for describing collisional radio-frequency sheath driven by two sinusoidal sources. In this model, it has been assumed that ion motion and velocity are time varying and sheath is collisional. The time-dependent terms in ion-fluid equations are ignored. Based on the assumption of steplike electron density profile model, analytical expressions for instantaneous sheath motion and sheath potential have been developed. The plasma-sheath motion and sheath potential are compared with a time-dependent model for collisionless and a time-independent model for collisional capacitively coupled plasma.

Analytical model of transient temperature and thermal stress in continuous wave double-end-pumped laser rod: Thermal stress minimization study

A time-dependent analytical thermal model of the temperature and the corresponding induced thermal stresses in continuous wave double-end-pumped laser rod are derived from the first principle using the integral transform method. The aim of the paper is to study the effect of increasing the pumping powers while the laser crystals are still in the safe zone (i.e. far away from failure stress) and to suitably choose a crystal that achieves this task. The result of this work is compared with a well-verified finite element solution and a good agreement has been found. Some conclusions are obtained: Tm:YAP crystal, which has high thermal conductivity, low expansion coefficient, low absorption coefficient, low thermal factor and low product of γE/(1− υ), is the best choice to reduce induced stress although it is responded and brought to thermal equilibrium faster than the other types of crystal usually used in the end-pumped solid-state laser.

SU-E-T-294: Maximizing the Availability of Positron Emitting Nuclei for Proton Therapy Verification Using Different Beam Irradiation Sequences.

To demonstrate that the amount of nuclei available for post- irradiation proton treatment verification using positron emission tomography (PET) can be enhanced by reversing the beam delivery sequence in proton scanning beam irradiations. A time-dependent analytical model is used to calculate the distributions of positron emitting nuclei for three different irradiation sequences: a scattered beam and a scanning beam in both the conventional sequence, distal edge first, and reverse sequence, distal edge last. The simulated geometry emulates reference dosimetry measurements conducted at the Paul Scherrer Institute (PSI). The reference measurements irradiate a 10 ×10 cm2 field, delivering about 1 Gy to a 10 cm wide spread-out Bragg peak (SOBP). Positron emitter availability with different beam sequence and imaging times and the impact of the different irradiation sequences on the statistical error on a range extrapolation were investigated. The ratio of the amount of positron emitters from the distal last beam sequence to that from the distal first sequence was 2.22 in the last centimeter of the SOBP. The comparison between distal last and a scattered beam gave a ratio of about 1.7 in the same region. In the distal last irradiation, more isotopes decay within a 120 second window, than in a 240 second window using a distal first irradiation. The statistical fluctuation on a range extrapolation was also smallest in the distal last beam sequence. We demonstrated the effect of the irradiation beam sequence on the isotope production relevant for the verification of proton spot scanning therapy with PET. The largest amount of isotopes is available by irradiating the distal edge last. This new beam sequence reduces the PETmeasurement time while still offering higher counts and accuracy compared with both the conventional beam sequence and the scattering method. This project was supported by JSPS Core-to-Core Program.