Simplified Semi-analytical Model Research Articles

Vibroacoustics Analysis of Plates with Bioinspired Surface Modifications

This study presents a simplified semi-analytical model to analyze the dynamic behavior of a plate with shark skin biomimetic surface modifications. The base plate is considered to be thin isotropic homogeneous and modeled using a Kirchhoff–Love plate theory, whereas the dermal denticles are modeled as a distributed array of point mass and replicated using a Dirac delta function. A semi-analytical formulation, which takes into account closed-form beam mode shapes, with the Galerkin technique to minimize errors is utilized to study the free and forced vibration response of modified plates. Harmonic analysis is carried out to understand the dynamic behavior of the modified plate both quantitatively as well as qualitatively. A parametric study varying the array spacing and the boundary conditions is carried out to understand the effect of surface modification on power radiation characteristics. It appears that adding dermal denticles reduces the peak velocity amplitude and peak radiated power at all resonance frequencies. A separate study by varying the base plate material reveals that a higher reduction in the dynamic response and the radiated power can be achieved by increasing the mass ratio. Hence, surface modification using such a shark skin layer may prove beneficial to reduce acoustic radiation and dynamic response and to optimize the design.

Diffusiophoresis of a Charged Droplet in Asymmetric as Well as Mixed Electrolytes through Numerical and Semianalytic Models

A numerical study on the diffusiophoresis of a droplet in an electrolyte medium is carried out by solving the full set of coupled governing equations, which are based on the conservation principle. Diffusiophoresis is considered for monovalent as well as non-z:z electrolytes and mixed electrolytes. The numerical model is supplemented with a semianalytic simplified model based on first-order perturbation analysis, which agrees with the numerical model for a low to moderate range of surface potential. The mobility for a low-viscosity fluid at a thinner Debye length is dominated by the chemiphoresis part, which creates the mobility to become an even function of the surface charge density for a monovalent electrolyte. Such a pattern in mobility does not appear in a non-z:z asymmetric electrolyte. At a thinner Debye length, diffusiophoresis becomes independent of the diffusion field, hence the mobility is independent of the composition of electrolytes in a mixed monovalent electrolyte solution. Our results show that the size-based sorting of droplets is efficient when a mixed electrolyte is considered. We have also addressed the finite ion size effects by considering a modified ion transport equation. One of the key features of the present study is the simplified semianalytical model for the diffusiophoresis of a droplet in a z:z electrolyte as well as in non-z:z and mixed electrolytes, which is shown to be valid up to a moderate range of surface potential for a finite Debye length.

A Simplified 2D Semi-Analytical Model for the Analysis of Dispersion Behavior in Functionally Graded Material Plates

A Simplified 2D Semi-Analytical Model for the Analysis of Dispersion Behavior in Functionally Graded Material Plates

Study on the simplified model of vertical double U-pipe ground heat exchanger

A simplified semi-analytical model of vertical double U-pipe ground heat exchanger was established. The validity of the established model is examined by contrasting the figured outcomes with experiment data, emulation results of 3-D numerical model and calculation results of infinite line-source model for different inlet boundary conditions and configurations. After one hour, the semi-analytical model?s relative error is less than 0.32% under the boundary condition of given inlet fluid temperature. Under the boundary condition of given total heat input rate, the semi-analytical model?s relative error after ten hours is less than 0.11%, while the infinite line-source model?s relative error is less than 0.60%. The semi-analytical model is in good agreement with experiment and numerical model, and has higher calculation accuracy than infinite line-source model.

Shark skin biomimetic surface modification for plates: influence on free vibration response

Denticle microstructures in shark skin have intrigued researchers since they can be prospective for various marine applications due to their inherent properties which help in reducing drag as well as do not allow barnacles to form on its surface. However, any such alterations to create surface rivulets will invariably lead to changes in mass and stiffness, and thereby natural frequencies. Subsequently, the dynamic response will also be influenced as these hydrodynamic phenomena are strongly dependent on the natural frequencies. Therefore, in this work, an investigation of the effect of shark skin type biomimetic surface modifications on the free vibration response is investigated. The free vibration response of plates with shark skin is computed first using a high-fidelity numerical simulation in a commercial finite element package ABAQUS and then compared against a simplified semi-analytical model proposed herein. Results from both these methods agreed quite well. It is observed that shark skin denticles significantly influence the natural frequency without altering its mode shapes. It appears that adding shark skin like dermal denticles on the surface of a bare plate as an appendage helps in reducing the natural frequencies in each mode. The study also reveals that the reduction in the spacing between denticles reduces natural frequency even further. Therefore, the effect of these wettability altercations on free vibration response should be known apriori for efficient design.

A simplified semi-analytical model for predicting the global and local responses of hybrid honeycomb-like sandwich panel

The hybrid honeycomb-like sandwich panel (hybrid HSP) is composed of FRP facesheets and an aluminum/steel honeycomb-like core, which has excellent mechanical properties and lower cost. This paper presents a fast and accurate semi-analytical model for evaluating the mechanical behavior of hybrid HSP based on the variational asymptotic theory and considering two small parameters: thickness-to-width ratio and heterogeneity. The original HSP is decomposed into 2-D equivalent plate model (2D-EPM) analysis at the macro level and 2-D unit cell constitutive modeling at the micro level to obtain the equivalent stiffness matrix. The static and dynamic analysis is carried out by using the 2-D panel with the equivalent stiffness matrix, and the local stress, strain, and displacement fields are recovered by using the recovery relationship. Finally, the effects of material and geometric parameters on the effective performance of hybrid HSPs are systematically analyzed. Numerical examples show that the static and dynamic results of 2D-EPM are in good agreement with the 3D finite element results, with a relative error of less than 5%. Most importantly, calculation efficiency has been considerably improved. Compared with the traditional finite element model, the novelties of cell tailoring and local field recovery within the unit cell are very important features, which significantly facilitate the effective analysis of hybrid HSPs.

Effect of T-shaped micro-fins on pool boiling heat transfer performance of surfaces

The saturated pool boiling heat transfer performance on the surface of T-shaped micro-fins was investigated with deionized water as working medium. Ten different T-shaped micro-fins surfaces were fabricated by machining method and the pool boiling experiments were carried out. By comparing the influence of varios parameters on the boiling heat transfer performance, the results showed that reducing the width of upper fin, increasing the gap or height of upper fin can improve the boiling heat transfer coefficient. With the increase of the width of the lower fins, the boiling heat transfer performance showed a different trend, that is, it increased at first and then decreased. The maximum boiling heat transfer coefficient of the surface S1 to the smooth surface was 184.7%. The visualization results showed that the merging of bubbles on the outside of the channel surface could strengthen the vertical and horizontal replenishment of the liquid to dry spot in the channel, thereby delaying the occurrence of critical heat flux and effectively reducing the wall temperature. The simplified semi-analytical model to determine the total heat flux of the micro channeal was proposed, which provided a heat flux prediction with an error of ± 40%.

Pressure behavior of multi-stage fractured horizontal well in a laterally non-uniform reservoir

Formation heterogeneity is very common in practice, where the reservoir usually consists of several regions with dissimilar properties separated by discontinuities. Because of the effect of the heterogeneity, there are few literatures studying the pressure response of multi-stage fractured horizontal (MSFH) wells in a laterally non-uniform reservoir. In this work, considering the linearity of the governing equations for describing fluid flows, the Laplace-domain point-source solution for three-region linear composite reservoirs is derived, based on which seepage model for an MSFH well in a laterally non-uniform reservoir is established. Fracture discrete scheme and Stehfest algorithm are used to solve the established model for an MSFH well. The validation of the proposed model is conducted by comparing with the simplified semi-analytical models in literatures and the commercial numerical simulator, which shows that our results match well with both analytical results and numerical results. Pressure behavior of an MSFH well in laterally non-uniform reservoirs is analyzed thoroughly based on the proposed model. It is found that the pressure behavior is significantly influenced by formation heterogeneity, well location, and well properties. The study provides a point-source function method for calculating pressure solutions of MSFH wells in three-region linear composite reservoirs, which can be easily extended to other complex well types besides MSFH wells, such as MSFH wells with stimulated reservoir volume, and fractured vertical wells with multiple fracture wings.

Semi-analytical modeling for multi-wing fractured vertical wells in a bilaterally heterogeneous gas reservoir

Many prolific hydrocarbon reservoirs show the lateral heterogeneity of rock properties, where the formation is composed of several regions with different rock properties separated by linear interfaces. Although there have been many studies on laterally heterogeneous reservoirs by linear composite models, most of them focus on vertical well without hydraulic fracturing. The modeling for fractured vertical wells in laterally heterogeneous reservoirs remains limited. The goal of this study is to develop a semi-analytical three-region linear composite model for multi-wing fractured vertical (MWFV) wells in a bilaterally heterogeneous gas reservoir. This model can take into account the common situation in practice, where the heterogeneity occurs on both sides of the reservoir region with the MWFV well. Based on the point-source function method, a semi-analytical modeling for an MWFV well in a bilaterally heterogeneous gas reservoir is developed by using pressure drop superposition, fracture wing discretization, and Stehfest algorithm. Compared with the simplified semi-analytical and numerical models, the correctness of the present model is verified. Log-log type curves for MWFV wells in a bilaterally heterogeneous gas reservoir are drawn. The flow regimes of the MWFV well in a bilaterally heterogeneous gas reservoir are identified. The influences of some well and reservoir parameters on the pressure response and rate decline of MWFV wells are investigated thoroughly. It is found that the pressure response and rate decline of MWFV wells are significantly affected by the well location, fracture wing properties, and reservoir heterogeneity.

Dynamics of Deep Ocean Eastern Boundary Currents

AbstractThe long‐standing paradigm for the large‐scale time‐averaged ocean circulation in the world oceans includes intensified currents at the western boundary, and a much slower interior flow elsewhere. However, poleward deep boundary currents in the eastern limits of the deep South Pacific, Atlantic, and Indian Oceans have been observed repeatedly at 2‐ to 4‐km depth. They carry up to a third of the total deep ocean transports, implying a significant role in climate, yet their dynamics are still not well understood. Here we develop a theoretical understanding for these currents, using a hierarchy of realistic and idealized models, focusing on the South Pacific Ocean. The deep eastern boundary current there is shown to be driven by a traditional interior balance together with a narrow boundary layer scale near the eastern boundary, which exists only when stratification and topography are both included. A simplified semianalytical vorticity model is developed for the deep eastern boundary current.

Comparison of pool boiling performance for plain micro-fins and micro-fins with a porous layer

The paper focuses on the comparison of pool boiling heat transfer on micro-fin enhanced structures with and without porous covering. The purpose of the present study was to find the optimal parameters of the perforated foil or wire mesh sintered to the micro-fin tips to provide the highest heat transfer coefficient. Additionally, a simplified model was proposed for determining total heat flux for investigated surfaces.Three types of structured surface were used: 1.0 mm high plain micro-fins (designated as MF), enhanced surfaces made by sintering micro-fin tips with the copper perforated foil (MF+F) and structured surfaces formed by sintering the woven copper wire mesh to the micro-fin tips (MF+M).The experiments were carried out for water, ethanol, Novec-649 and FC-72 at atmospheric pressure. At medium and high heat fluxes for water, low and medium heat fluxes for ethanol and medium heat fluxes for FC-72, surfaces with micro-fins covered with wire mesh produced the highest heat transfer coefficient. The plain micro-fin surfaces helped obtain the increase in the heat transfer coefficient value about two times higher than that of the micro-fins with perforated foil at FC-72 boiling for high heat fluxes. The simplified semi-analytical model was proposed for determining total heat flux for the studied surfaces. The model provided a heat flux prediction with a ±30–40% margin of error.

Comparison of models to evaluate microbial sulphide generation and transport in the near field of a SF/HLW repository in Opalinus Clay

In a deep geological repository for radioactive waste in the Opalinus Clay, disposal canisters may be corroded due to sulphide produced by sulphate reducing bacteria (SRB). This paper presents two computational models, a reactive transport model (RTM) and a simplified semi-analytical model (SM), to evaluate the potential of SRB to generate elevated sulphide concentrations, to assess sulphide fluxes to the canister and, in a simplified manner, the resulting canister corrosion.Calculations performed in the context of the repository's safety assessment based on a shared conceptual model reveal that the two computational models are complementary. The reactive transport model incorporates state-of-the-art understanding of the system's geochemistry, but is currently too computationally demanding to be applied in probabilistic safety assessment sensitivity analyses. The simplified model is fast and efficient, but some of its assumptions need to be verified, and some parameter values need to be calibrated using the more complete reactive transport model. Nonetheless, given the same set of assumptions, the two models predict comparable magnitudes of sulphide fluxes to the canister and comparable canister corrosion depths.

Latitudinal variations of charged dust in co-orbital resonance with Jupiter

AbstractThe interplanetary magnetic field may cause large amplitude changes in the orbital inclinations of charged dust particles. In order to study this effect in the case of dust grains moving in 1:1 mean motion resonance with planet Jupiter, a simplified semi-analytical model is developed to reduce the full dynamics of the system to the terms containing the information of the secular evolution dominated by the Lorentz force. It was found that while the planet causes variations in all orbital elements, the influence of the magnetic field most heavily impacts the long-term evolution of the inclination and the longitude of the ascending node. The simplified secular-resonant model recreates the oscillations in these parameters very well in comparison to the full solution, despite neglecting the influence of the magnetic field on the other orbital parameters.

A simplified semi-analytical model for the filling and cooling process in plastic molding

The effects of the operational conditions on the filling and cooling process in plastic molding are studied. First, a semianalytical model is developed to study the effects of thermal boundary conditions and imposed pressure on the velocity profile and blocking time in the filling stage of the molding process. To do so, a lubrication approximation type model is developed in which the shear viscous heating terms are neglected to simplify the governing equations. Using an equipped mold, molding experiments are conducted to validate the model predictions by using a well-controlled injection molding machine. Comparing the model and experimental results shows a reasonable agreement among them. Second, regarding the cooling process, a modified Avrami equation is used to capture the polymer crystallization in variable cooling rates. The model results show that the cooling time and the final solid fraction decrease by increasing the cooling rate.

New transient simplified model for radiant heating slab surface temperature and heat transfer rate calculation

A new simplified model based on a semi-analytical correlation is proposed in this paper to evaluate the heating radiant slab surface temperature and to examine its thermal behavior under dynamic solicitations. In fact, the surface temperature is a normative design parameter and shall be kept under an upper limit whatever are the running conditions. Experimental measurements and a two-dimensional finite difference model (2D FDM) were carried out to validate the developed simplified model based on two characteristic parameters that are the time constant and the delay time. A Design of Experiments (DoE) method is employed to derive meta-models for the time constant and the delay time in order to compute the surface temperature. The sensitivity analysis shows that the specific heat capacity of the slab material and the heating water flow rate affect significantly the time constant compared to the thermal conductivity and the heating water pipe inner diameter. Moreover, it was found that all these parameters, except the heating water flow rate, have a substantial impact on the delay time. Compared to the experimental results, the maximum relative deviations from the computed surface temperature are within 2.4% for the numerical model and 1.75% for the simplified semi-analytical model. Consequently, the proposed simplified model may be utilized by engineers and designers to quickly estimate the radiant slab surface temperature and heat flux as well as to study its thermal behavior under dynamic running conditions. This model may also be integrated in the thermal building simulation software.

Simplified 0-D semi-analytical model for fuel draining in molten salt reactors

A key feature of molten salt reactors is the possibility to reconfigure the fuel geometry (actively or passively driven by gravitational forces) in case of accidents. In this regard, the design of reference molten salt reactor of Generation IV International Forum, the MSFR, foresees the Emergency core Draining System (EDS). Therefore, the research and development of MSFRs move in the direction to study and investigate the dynamics of the fuel salt when it is drained in case of accidental situations. In case of emergency, the salt could be drained out from the core, actively or passively triggered by melting of salt plugs, and stored into a draining tank underneath the core. During the draining transient, it is relevant from a safety point of view that thermal and mechanical damages to core internal surfaces and to EDS structure – caused by the temperature increase due to the decay heat – are avoided. In addition, the subcriticality of the fuel salt should be granted during all the draining transients. A simplified zero-dimensional semi-analytical model is developed in this paper to capture the multiphysics interactions, to separate and analyse the different physical phenomena involved and to focus on time evolutions of temperature and system reactivity. Results demonstrate that the fuel draining occurs in safe conditions, both from the thermal (temperature-related internal surface damages) and neutronic (sub-critical states dominate the transient) view points and show which are the main characteristics of the fuel salt draining transient.

Average Opacity Calculation for Core-collapse Supernovae

Abstract Supernovae (SNe) are among the most intensely studied objects of modern astrophysics, but due to their complex physical nature, theoretical models are essential to better understand these exploding stars, as well as the properties of the variation of the emitted radiation. One possibility for modeling SNe light curves (LCs) is the construction of a simplified semianalytic model, which can be used for getting order-of magnitude estimates of the SN properties. One of the strongest simplifications in most of these LC models is the assumption of the constant Thomson-scattering opacity that can be determined as the average opacity of the ejecta. Here we present a systematic analysis for estimating the average opacity in different types of core-collapse supernovae that can be used as the constant opacity of the ejecta in simplified semianalytic models. To use these average opacities self-consistently during LC fit, we estimate their values from hydrodynamic simulations. In this analysis, we first generate MESA stellar models with different physical parameters (initial mass, metallicity, and rotation), which determine the mass-loss history of the model star. Then we synthesize SN LCs from these models with the SNEC hydrodynamic code and calculate the Rosseland mean opacity in every mass element. Finally, we compute the average opacities by integrating these Rosseland mean opacities. As a result, we find that the average opacities from our calculations show adequate agreement with the opacities generally used in previous studies.

Structure of the Balmer jump

Context.The spectrum of the hydrogen atom was explained by Bohr more than one century ago. We revisit here some of the aspects of the underlying quantum structure, with a modern formalism, focusing on the limit of the Balmer series.Aims.We investigate the behaviour of the absorption coefficient of the isolated hydrogen atom in the neighbourhood of the Balmer limit.Methods.We analytically computed the total cross-section arising from bound-bound and bound-free transitions in the isolated hydrogen atom at the Balmer limit, and established a simplified semi-analytical model for the surroundings of that limit. We worked within the framework of the formalism of Landi Degl’Innocenti & Landolfi (2004, Astrophys. Space Sci. Lib., 307), which permits an almost straight-forward generalization of our results to other atoms and molecules, and which is perfectly suitable for including polarization phenomena in the problem.Results.We analytically show that there is no discontinuity at the Balmer limit, even though the concept of a “Balmer jump” is still meaningful. Furthermore, we give a possible definition of the location of the Balmer jump, and we check that this location is dependent on the broadening mechanisms. At the Balmer limit, we compute the cross-section in a fully analytical way.Conclusions.The Balmer jump is produced by a rapid drop of the total Balmer cross-section, yet this variation is smooth and continuous when both bound-bound and bound-free processes are taken into account, and its shape and location is dependent on the broadening mechanisms.

Galactic Disk Winds Driven by Cosmic Ray Pressure

Abstract Cosmic ray pressure gradients transfer energy and momentum to extraplanar gas in disk galaxies, potentially driving significant mass loss as galactic winds. This may be particularly important for launching high-velocity outflows of “cool” (T ≲ 104 K) gas. We study cosmic ray-driven disk winds using a simplified semi-analytic model assuming streamlines follow the large-scale gravitational potential gradient. We consider scaled Milky Way–like potentials including a disk, bulge, and halo with a range of halo velocities V H = 50–300 and streamline footpoints with radii in the disk R 0 = 1–16 kpc at a height of 1 kpc. Our solutions cover a wide range of footpoint gas velocity u 0, magnetic–to–cosmic ray pressure ratio, gas–to–cosmic ray pressure ratio, and angular momentum. Cosmic ray streaming at the Alfvén speed enables the effective sound speed C eff to increase from the footpoint to a critical point where C eff,c = u c ∼ V H; this differs from thermal winds, in which C eff decreases outward. The critical point is typically at a height of 1–6 kpc from the disk, increasing with V H, and the asymptotic wind velocity exceeds the escape speed of the halo. Mass-loss rates are insensitive to the footpoint values of the magnetic field and angular momentum. In addition to numerical parameter space exploration, we develop and compare to analytic scaling relations. We show that winds have mass-loss rates per unit area up to , where Π0 is the footpoint cosmic ray pressure and u 0 is set by the upwelling of galactic fountains. The predicted wind mass-loss rate exceeds the star formation rate for V H ≲ 200 and u 0 = 50 , a typical fountain velocity.

Electron heating in the laser and static electric and magnetic fields

A 2D slab approximation of the interactions of electrons with intense linearly polarized laser radiation and static electric and magnetic fields is widely used for both numerical simulations and simplified semi-analytical models. It is shown that in this case, electron dynamics can be conveniently described in the framework of the 3/2 dimensional Hamiltonian approach. The electron acceleration beyond a standard ponderomotive scaling, caused by the synergistic effects of the laser and static electro-magnetic fields, is due to an onset of stochastic electron motion.