Present Analytical Model Research Articles

A novel membrane-based absorber for sorption heat transformers: A comparative experimental study of a thin-film absorbent and salt-impregnated adsorbents

The present study proposes a novel membrane-based sorber bed with stationary solution film for oscillatory sorption heat transformers. A custom-built gravimetric large pressure jump setup is used to experimentally compare the performance of the novel membrane-based sorber bed with a Lithium Bromide/Silica gel solid composite sorbent synthesized using the salt-impregnation method. It is shown that the current membrane-based sorber bed provides up to about four times the specific cooling power and more than twice the cooling power density of solid sorbents, demonstrating the capability of the present sorber bed as a promising alternative to solid sorbents. The specific cooling power, cooling power density, and energy storage density of about 2.8 kW/kg, 470 kW/m3, and 269 MJ/m3 are experimentally obtained, respectively. According to experimental results, it is observed that the film thickness plays a significant role in sorption dynamics, while the effect of membrane mass transfer resistance on sorption dynamics is less than 10%. In addition, the present membrane-based sorber bed is analytically modeled, and the results are validated with present experimental data. The present analytical model is also used to investigate the effects of design parameters on the performance metrics.

Dynamic response of clamped sandwich beams with foam-filled sinusoidal corrugated core subjected to low-velocity impact

Sandwich structure is a lightweight structure with high specific strength and specific stiffness, as well as excellent energy absorption and load-carrying capacity. Sandwich structures are widely used in aerospace, high-speed rail and marine applications. Low-velocity impact of a sandwich beam with foam-filled sinusoidal corrugated core is investigated by means of theoretical derivations and numerical calculations. A yield criterion is used to obtain an analytical solution of the dynamic behavior of champed sandwich beams with foam-filled sinusoidal corrugated cores under low-velocity impact. Numerical calculations are performed. The analytical results are in excellent accordance with the finite element results. Influences of the amplitude, half-wavelength and thickness of the sinusoidal corrugated plate, foam strength, metal-sheet strength, and the impact location on the dynamic behavior of the sandwich beams with foam-filled sinusoidal corrugated cores under low-velocity impact are discussed. The present analytical model can predict reasonably well the dynamic behavior of foam-filled sinusoidal corrugated core sandwich beams under low-velocity impact.

Cutting failure behavior of foam core sandwich plates

During the ship, collisions with reefs or grounding may cause damage to the hull of ships made of sandwich plates. The cutting failure mechanism of sandwich panels is still not fully understood. In this paper, the failure behavior of metal foam sandwich plates under cutting load by a wedge-shaped indenter is studied through analytical, experimental, and numerical methods. An analytical model is proposed to describe the cutting failure behavior of foam core sandwich plates. Based on experimental results, three distinct failure modes of foam sandwich plates with varying thicknesses are observed. Numerical simulations are performed, and analytical and numerical results capture experimental results reasonably. The effects of core thickness, face-sheet thickness, and tip angle and cutting angle of wedge indenter on the failure mode, load-carrying capacity and energy absorption performance of the sandwich plates are explored. The present analytical model can effectively predict the cutting failure behavior of sandwich plates.

Nonlinear vibrations analysis of two-directional functionally graded porous cylindrical shells resting on elastic substrates in a thermal environment based on Donnell nonlinear shell theory

The primary objective of this study is to investigate the nonlinear free vibrational characteristics of temperature-dependent two-directional functionally graded porous (TDFGP) cylindrical shells resting on elastic substrates in a thermal environment. To accomplish this, the thermomechanical equations are derived based on the Donnell nonlinear shell theory framework in conjunction with the von Kármán assumption. Two-directional functionally graded porous cylindrical shell models have mechanical properties that can change smoothly and continuously across the length and thickness of the shell. Additionally, it is assumed that the internal porosities in the matrix materials can be dispersed into two independent patterns, either even or uneven porosity distribution. The nonlinearity in free vibration assessed via the nonlinear-to-linear frequency ratio concerning the central deflection amplitude can be gained employing the Galerkin discretization approach and modified Poincare–Lindstedt (P-L) method. The accuracy and effectiveness of the present analytical model are indicated through comparison with existing solutions. Finally, some comprehensive parametric investigations are carried out to gain insight into the impacts of several factors on the nonlinear free vibration characteristics of structures under different conditions. The results of this article demonstrate that parameters such as gradient indices, volume fraction, distribution pattern of porosity, geometric parameters, and ambient temperature rise significantly influence the structure’s nonlinear frequency and free vibration response.

Evaluation of modulus of elasticity of concrete containing both natural and recycled concrete aggregates

There is growing requirement to use recycled aggregate in concrete to demote industrial wastes produced by construction sectors. Thus, to develop simple but meaningful formulations to assess the mechanical properties of concrete, when it is mixed with both natural and recycled aggregates, becomes essential. In the present study an analytical approach to calculate the elastic modulus of concrete containing both natural and recycled concrete aggregates is proposed. The approach is developed on the concept of effective medium approximation but considering the effect of Poisson's ratio. Two analytical formulas are derived. One is for the two-phase concrete (mortar and aggregate) that is mixed with 100% natural aggregate or 100% recycled concrete aggregate. The other is for the three-phase concrete (mortar, natural aggregate, and recycled concrete aggregate) that is mixed with both natural and recycled aggregates. The analytical formulations are validated using the results obtained from both the numerical simulations and experimental tests. The present analytical model not only provides the simple and meaningful formulations to calculate the effective elastic modulus but also can be used to directly examine the influence of mortar, natural aggregate, recycled concrete aggregate and its replacement ratio to natural aggregate on the elastic modulus of the mixed concrete.

Insights Into Frictional Brush Seal Hysteresis

Abstract Brush seals offer a superior sealing effectiveness compared to labyrinth seals. However, widespread use of brush seals is constrained by deleterious behaviors such as pressure-stiffening and hysteresis. For the latter, the bristles bend during the shaft incursion process and do not fully recover during the shaft retraction process. An opening gap is created, which increases seal leakage unless the pressure load drops to a certain level. In this work, analytical and numerical models based on a single bristle are proposed to capture the seal's response to shaft displacement with and without pressure loading. The models are validated using static stiffness tests at an unpressurized condition from literature. The main results show that modeling of the backing ring friction is essential to capture the bristle hang-up behavior. Shaft friction dominates at unpressurized conditions, while backing ring friction dominates at high pressure loading. An expression for shaft hang-up displacement has been derived. A sensitivity study shows that seals with shallow lay angle, short bristle length, and large bristle diameter are less prone to hang-up problems. The models developed in the present framework have been shown to qualitatively capture the pressure stiffening, hysteresis, bristle hang-up, and shaft rotation effects.

Machine-learning enhanced photometric analysis of the extremely bright GRB 210822A

ABSTRACT We present analytical and numerical models of the bright long GRB 210822A at z = 1.736. The intrinsic extreme brightness exhibited in the optical, which is very similar to other bright GRBs (e.g. GRBs 080319B, 130427A, 160625A 190114C, and 221009A), makes GRB 210822A an ideal case for studying the evolution of this particular kind of GRB. We use optical data from the RATIR instrument starting at T + 315.9 s, with publicly available optical data from other ground-based observatories, as well as Swift/UVOT, and X-ray data from the Swift/XRT instrument. The temporal profiles and spectral properties during the late stages align consistently with the conventional forward shock model, complemented by a reverse shock element that dominates optical emissions during the initial phases (T < 300 s). Furthermore, we observe a break at T = 80 000 s that we interpreted as evidence of a jet break, which constrains the opening angle to be about θj = (3–5) degrees. Finally, we apply a machine-learning technique to model the multiwavelength light curve of GRB 210822A using the afterglowpy library. We estimate the angle of sight θobs = (6.4 ± 0.1) × 10−1 degrees, the energy E0 = (7.9 ± 1.6) × 1053 erg, the electron index p = 2.54 ± 0.10, the thermal energy fraction in electrons ϵe = (4.63 ± 0.91) × 10−5 and in the magnetic field ϵB = (8.66 ± 1.01) × 10−6, the efficiency χ = 0.89 ± 0.01, and the density of the surrounding medium n0 = 0.85 ± 0.01 cm−3.

Analytic solution and numerical validation of the transient regime in dry surface grinding

In the framework of Samara–Valencia model for heat transfer in dry surface grinding, analytical expressions for the time-dependent temperature field of the workpiece during the transient regime in which the wheel is engaged (cut-in) and disengaged (cut-out) from the workpiece are calculated. The main assumption we consider is a constant heat flux profile along the contact zone between the wheel and the workpiece. According to the analytical expression obtained for the temperature field, a closed-form expression for the maximum temperature during the cut-in transient regime has been obtained. Further, a very rapid method for the numerical evaluation of maximum temperature during the cut-out is described. This maximum temperature is responsible of the thermal damage of the workpiece. Experimental evidence shows that the thermal damage risk is greater during the cut-out transient regime. The present analytical model reproduces this experimental feature. Finally, the analytical results have been numerically validated using FEM analysis and are intended to be very useful for the monitoring of the online grinding process in order to avoid thermal damage.

A new analytical model of condensation outside low-finned tubes for refrigerants at low temperatures and high heat flux

In this paper, a new analytical model is developed for the condensation of refrigerants outside low-finned tubes. It is based on the flow and heat transfer characteristics at low saturation temperatures and high heat flux, such as those in the LNG intermediate fluid vaporizer (IFV). Due to the increase of viscous effect at lower saturation temperature and higher heat flux, the previous condensate retention angle models are modified by adding the viscous term. At high heat flux and condensate rate, the condensate profile at the fin root is simplified to be arc-shaped and obtained directly by force analysis. Furthermore, considering the heat transfer enhancement caused by the circumferential flow at high heat flux, the convective mechanism is included for the heat transfer through the thick liquid film between the fins. The distributions of liquid film and fin surface temperature are also predicted. The present analytical model is in good agreement with different experimental and numerical results, while most deviations are within 10% for predicting the heat transfer coefficients at high heat flux. Because of the increased flow viscosity and surface tension, the optimal fin spacing and fin height increase as the heat flux increases and the saturation temperature decreases.

Investment timing and length choice for a rail transit line under demand uncertainty

This paper is motivated by the inadequate treatment of uncertainty in public transit infrastructure investments. As observed in the past, rare but dramatic events can heavily disrupt public transit system operations and negatively affect the transit riders. For example, the COVID-19 pandemic caused an 80%-90% transit demand decline in March 2020 in the U.S. However, the existing transit infrastructure planning studies have not modeled such sudden demand shocks. We thus improve the modeling realism of uncertain transit demand by formulating demand evolution as a jump-diffusion process, which is a combination of continuous-time Brownian motion and a discrete counting process, namely Poisson process, and present analytical optimization models for the development of a rail transit line under such uncertainty. We jointly optimize two related decisions, namely the timing for introducing rail transit to a commuter corridor and length choice for the rail line. We refute a misconception that investment in a project should always start immediately if a positive cost saving over the planning horizon is expected. We also find that investment timing and sizing decisions are closely related and behave quite differently for the same change in some parameters, such as the infrastructure construction period. The developed modeling and analysis framework should be transferable to other civil infrastructure development and investment problems under uncertainty.

Dynamic response of foam-filled X-type sandwich beam under low-velocity impact

The dynamic response of a fully clamped foam-filled X-type sandwich beam under low-velocity impact is studied analytically and numerically. The analytical model is developed for the dynamic response of the sandwich beam with foam-filled X-type core under low-velocity impact based on the yield criterion. The numerical calculations are carried out, and analytical results are in good agreement with numerical ones. The effects of face-sheet thickness, X-type folding plate thickness and foam strength on the impact resistance of the foam-filled X-type sandwich beam are discussed. It is shown that face-sheet thickness, X-type folding plate thickness, and foam strength have noticeable effects on the low-velocity impact response of the foam-filled X-type sandwich beam. The present analytical model can be used to predict the low-velocity impact of the foam-filled X-type sandwich beam.

Bandgap formation and low-frequency structural vibration suppression for stiffened plate-type metastructure with general boundary conditions

Metastructures with unique mechanical properties have shown attractive potential application in vibration and noise reduction. Typically, most of the metastructures deal with the vibration bandgap properties of infinite structures without considering specific boundary condition and dynamic behaviors, which cannot be directly applied to the engineering structures. In this research, we design a Stiffened Plate-type Metastructure (SPM) composed of a plate with periodic stiffeners and cantilever beam-type resonators subjected to general boundary conditions for low-frequency vibration suppression. The effects of boundary conditions and the number and orientation of the stiffeners on Locally Resonant (LR) type bandgap properties in SPM are further investigated. An analytical modeling framework is developed to predict the bandgap formations and vibration behaviors of SPMs in finite-size configuration. The governing equations of the SPM reinforced by various arrangements of stiffeners are derived based on the first-order shear deformation theory and Hamilton’s principle, and a Fourier series combined with auxiliary functions is employed to satisfy the arbitrary boundary conditions. Finite element analysis and experimental investigations of vibration behaviors for the SPM are carried out to validate the accuracy and reliability of the present analytical model. For practical designs of the SPMs with specific boundary conditions, it is found that there exist optimal numbers of stiffeners and resonators which can produce the significant LR-type bandgap behaviors. Furthermore, various arrangements of stiffeners and resonators are explored for different boundary conditions by breaking the requirement of spatially periodicity. It is shown that for the designed SPM, the vibration modes of its host structure should be considered to widen the frequency range in which the resonators transfer and store energy, and hence improve the performance of low-frequency vibration suppression. The present work can provide a significant theoretical guidance for the engineering application of metamaterial stiffened structures.

Dynamic response of multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores under low-velocity impact

The paper focuses on the dynamic response of multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores under low-velocity impact with heavy-mass using analytical and numerical methods. Based on the yield criterion for the multilayer sandwich structure, the circumscribing and inscribing loci of sandwich structure are obtained. Considering the interaction of bending and stretching, the analytical solution and “bound” solution for the dynamic response of multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores are developed. The numerical calculations are used to verify the analytical solutions, and all lie within the analytical “bound” predications. Then, the influences of impact position, foam strength and face-sheet thickness on the dynamic response of multilayer sandwich beams are discussed in detail by theoretical model. For a given deflection, the impact force decreases with impact position closer to the midspan, the impact force increases with the increase of foam strength and face-sheet thickness. The present analytical model can effectively predict the dynamic response of fully clamped multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores under low-velocity impact.

On scalar transport in an oscillatory Couette–Poiseuille flow under the effects of heterogeneous and bulk chemical reactions: A multi-scale approach

This research presents an analytical solution to explore a two-dimensional concentration transport of solute in an oscillatory Couette–Poiseuille flow between two parallel plates in the presence of homogeneous and heterogeneous reactions. Mei's homogenization method up to second order approximation is used to find the multi-dimensional concentration distributions, namely, transverse concentration distribution, longitudinal concentration distribution, mean concentration distribution, Taylor dispersion coefficient, and the transverse uniformity simultaneously for three different flow conditions: steady, periodic, and the joint effect of steady and periodic Couette–Poiseuille flow for the first time. The distribution of transverse concentration of solute is studied due to its importance in oil lubrication and industrial applications. The transverse variation rate shows that the introduction of heterogeneous reactions cause transverse non-uniformity, but it is significant to note that homogeneous reaction has no effect on it. Furthermore, the maximum variation rate of the concentration cloud is obtained along the upstream and downstream directions when the boundary absorption is considered at steady and moving plates, respectively. To validate the present analytical model, a comparison is performed with the numerical solution and has achieved an excellent agreement. The outcomes of the present study may be helpful to develop a better understanding of the process of contamination and to prevent the pollution in the flow.

Analytical Model of Wellbore Stability Analysis of Inclined Well Based on the Advantageous Synergy among the Five Strength Criteria

The proper drilling mud density is vital for wellbore stability maintenance, which relies on both stress distribution on the borehole wall and rock strength. Thus, the selection of rock strength criterion is vital for wellbore stability analysis (WSA), and several strength criteria have been developed and employed to perform WSA, but the real collapse pressure does not comply with any single strength criterion. Therefore, to accurately predict the critical mud weight against wellbore collapse, an analytical model of WSA was proposed for inclined wells based on the advantageous synergy among the five types of strength criteria, such as the Mohr-Coulomb criterion, Mogi-Coulomb criterion, Drucker-Prager criterion, modified Wiebols-Cook criterion, and modified Lade criterion. The predicted results among these analytical and five conventional models were compared under three kinds of typical stress regimes, such as normal, strike-slip, and reverse faults. Finally, five kinds of typical oil and gas field data were collected to further verify the accuracy of this new model. The results indicated that different models predicted different collapse pressure, owing to the Mohr-Coulomb criterion ignoring the intermediate principal stress ( σ 2 ), so as to always give the greatest collapse pressure, followed by the present analytical model and the Mogi-Coulomb criterion, while the other three types of strength criteria gave different results, because of the difference in the influence of σ 2 , while the present analytical model integrated the advantageous synergy among the five strength criteria. The prediction error of the conventional analytical model ranges from 9.4 to 34.2% with an average of 22.1%, while the prediction error of this new model ranges from 2.3 to 12.5% with an average of 7.1%, so that the present analytical model has much higher accuracy than that of any single strength criterion. In addition, this new analytical model can be simplified as the conventional analytical model by adjusting the weight coefficients.

A semi-analytical solution for water wave scattering by partially immersed perforated and solid barriers with a quadratic pressure discharge condition

Partially immersed perforated and/or solid barriers in the ocean are often considered as important components of many marine applications, and they have received significant attentions by ocean engineering research community with potential flow methods. In this study, water wave interaction with a system that consists of a vertical perforated front barrier and a vertical impermeable rear barrier, as a representative unit, is investigated based on the linear potential flow theory. A semi-analytical solution for this problem is derived using an eigenfunction expansion method and an iterative resolution method. To model the flow passing through the perforated barrier, a quadratic pressure discharge condition of practical validity is applied. The reflection coefficient predicted by the present analytical model agrees well with the published theoretical result. The validated model is used to perform a parametric study to examine the effects of the width, submergence depth, porosity, incident wave steepness and wave frequency on the hydrodynamic characteristics of the perforated system. It is found that larger incident wave steepness can result in smaller transmission coefficient and dimensionless horizontal wave force acting on the impermeable rear barrier and larger dimensionless horizontal wave force acting on the perforated front barrier due to the nonlinear nature of the quadratic pressure discharge condition. By examination over a broad range of circumstances, we find that the partially immersed perforated system is more effective when the ratio of the width to the incident wavelength B/L is located between 0.2+0.5n and 0.35+0.5n (n=1,2,…). The present study can be utilized for a range of marine applications in wave preventing and wave energy absorption or conversion.

Analytical solution for heat and mass transfer in desiccant coated heat exchangers

• Heat and moisture transfer in a desiccant-coated heat exchanger (DC-HX) is studied. • A new closed-form analytical solution is proposed. • Linear and exponential profiles are assumed for air temperature and humidity ratio. • A new DC-HX coated with AQSOA™-FAM-Z02 is also fabricated and tested. Due to the complicated nature of desiccant-coated heat exchangers (DC-HXs), solving the highly-coupled transient heat and mass transfer equations using numerical simulations are rather time-consuming and as a result may be impractical for real-time system optimization and seasonal simulations. On the other hand, the approach of majority of studies associated with DC-HXs is numerical and experimental analyses and there is no analytical model that can accurately predict the heat and moisture transfer in a DC-HX in the literature. Thus, in this paper, a new closed-form analytical solution is proposed to accurately predict the heat and moisture transfer in a DC-HX for the first time. The governing equations are simplified to a set of linear ordinary differential equations with initial conditions and then solved analytically. In the present analytical model, both linear and exponential profiles are assumed for the air temperature and humidity ratio along the DC-HX and the results are compared to experimental data collected in our lab. A new DC-HX coated with AQSOA™-FAM-Z02 is also fabricated and tested in our custom-built testbed under a wide range of operating conditions for model validation and performance assessment. Our results indicate that the present analytical solution with exponential profile assumption predicts the experimental data with an average relative difference of less than 10%, while the linear profile assumption results in a relative difference of ∼ 20% with the experimental data. The new analytical solution is capable of predicting the performance of DC-HXs, which is crucial for design, optimization and operating dehumidification systems in a variety of applications.

An analytical model for thermoelastic damping in laminated microring resonators

Predicting thermoelastic damping (TED) is crucial in the design of micro-resonators with high quality factors. Until now, some analytical models have been developed to evaluate the TED effect on microrings which are widely used in many micro-resonators. However, most previous works are limited to microrings with single homogeneous material. This paper develops an analytical model for investigating the TED in the laminated microrings. The temperature fields along the thickness and circumferential directions in the laminated microring are presented using the generalized orthogonal expansion technique. The analytical model for the TED is obtained by computing the dissipated energy and the maximum elastic energy in each layer. The present analytical model for evaluating the TED is validated by comparing with the previously published result and the finite element method (FEM). The effects of the thickness and the property of the metallic layer on the TED characteristics of two- and three-layered microrings are analyzed. The present model can be used to optimize the design of the microring resonators with high quality factors.

Squeeze-Film Damping of Microbeam and Microplate Resonators in the Free Molecular Regime

Background: Correct modeling of squeeze-film damping (SFD) is an important consideration in the design of high-Q microresonators. In 2002, using the molecular dynamics (MD) approach, Bao et al. developed an analytical MD model for the evaluation of the SFD of a parallel-plate device in the free molecular regime. Their model was based on the energy exchange between the oscillating plate and gas molecules. Bao’s model is now widely used in microsystem design. However, Bao’s model cannot reduce to the air damping model in free space and is unsuitable for flexible microbeams. Objective: This paper first presents a more accurate analytical model for the evaluation of the SFD of the parallel plate. Then the present analytical model is extended to model the SFD of flexible microbeams with deformed shapes. Methods: This paper is based on the momentum transfer between the vibration plate and gas molecules. Results: The analytical results of the present model have shown a good agreement with the available experimental results. Conclusion: The limitations in the previous model are overcome.

Electrocatalytic rate constants from DFT simulations and theoretical models: Learning from each other

Electrochemical interfaces present an extraordinarily complex reaction environment and several, often counter-acting, interactions contribute to rate constants of electrocatalytic reactions. We compile a short review on how electrode potential, solvent, electrolyte, and pH effects on electrocatalytic rates can be understood and modelled using computational and theoretical methods. We address the connections between computational models based on DFT and (semi)analytical model Hamiltonians to extract physical or chemical insights, identify some omissions in present DFT simulation approaches and analytic models, and discuss what and how simulations and models could learn from each other.