Transient Solution Research Articles

Effect of Dielectric Properties of Cochlea on Electrode Insertion Guidance Based on Impedance Variation

The cochlear neuromodulator provides substantial auditory perception to those with impaired hearing. The accurate insertion of electrodes into the cochlea is an important factor, as misplaced may lead to further damage. The impedance measurement may be used as a marker of the electrode insertion guidance. It is feasible to investigate the impact of the dielectric properties of the cochlea tissue layers on the electrode insertion guidance using sophisticated bio-computational methods that are impractical or impossible to perform in cochlear implant (CI) patients. Although previous modeling approaches of the cochlea argued that the capacitive impact of the tissue layer can be neglected using the quasi-static (QS) approximation method, it is widely accepted that tissue acts as a frequency filter. Thus, the QS method may not always be appropriate due to short-duration pulses. This study aimed to investigate the impact of the frequency-dependent dielectric properties of the cochlea tissue layers on the impedance variation by following a systematic approach. The volume conductor model of the cochlea layers was developed, the dielectric properties of each tissue layer were attained, and the cochlea neuromodulator settings were applied to obtain the results based on both QS and transient solution (TS) methods. The results based on the QS and TS methods were compared to define to what extent these parameters affect the outcome. It was suggested that the capacitive impact of the cochlea layers should be considered after a certain frequency level.

Neo-Hookean modeling of nonlinear coupled behavior in circular plates supported by micro-pillars

In the contemporary era, the enhancement of wearable capacitive sensors is achieved through the utilization of polymeric micropillars as filler materials between electrode plates. To gain a deeper understanding of the dynamic response of the system, nonlinear coupled governing equations of a circular microplate motion resting on an array of polymeric micropillars have been derived. These equations are used to model the system’s behavior. In addition, the squeezing motion of the micro-pillars is characterized using the incompressible Neo-Hookean model. Both static and dynamic responses, including transient and steady-state solutions, are investigated in detail by discretizing over spatial coordinates using a weak formulation approach. A frequency response analysis is conducted using a continuation-based method. This entails expanding the steady-state solution using a Fourier transform and employing the energy balance principle. The unknown coefficients of the expansion series are calculated using a gradient descent-based learning approach that is physically motivated. Furthermore, a dynamic step size strategy for frequency increments is employed to effectively follow the solution path. This strategy is implemented via the ARC length method. In this study, we examine the impact of varying PDMS (polydimethylsiloxane) hydrogel mechanical and geometrical configurations. It can be reasonably concluded that the mechanical properties of the pillars and the geometrical configuration of the circular plate and micropillars have a significant impact on the maximum tolerable pressure, fast transient response, and frequency response analysis.

Determining the constant diffusion coefficient by Fourier series solution of the diffusion equation

The purpose of this study was to obtain the diffusion coefficient by calculating directly from the Fourier series solution of the diffusion equation, which has not been studied so far. The Fourier series solution is the sum of a steady-state solution and a transient solution. The steady-state solution is a linear function of distance. The transient solution is the product of a distance function and a time function. The Fourier sine series solution, a function of distance only, is negative for the steady-state solution. For the sublimation diffusion of disperse dye in paste into polyethylene terephthalate (PET) film using the film-roll method, the constant surface concentration and the diffusion distance were determined from the quadratic regression curve for the concentration distribution at a long time. The concentration distribution of the transient solution is a downwardly convex curve with negative values. The concentration distribution of the Fourier series solution is also a downwardly convex curve. The diffusion coefficient in the exponential term, a function of time only, was determined from the value of the exponential term obtained by the surface concentration and the diffusion distance. The constant diffusion coefficients determined from the Fourier series solution are reliable because they are very similar to those obtained from the error function solution and have excellent linearity of the linear regression lines for their Arrhenius plots.

Analytical solution of a microrobot-blood vessel interaction model

AbstractThis study develops a dynamics model of a microrobot vibrating in a blood vessel aiming to detect potential cancer metastasis. We derive an analytical solution for microrobot’s motion, considering interactions with the vessel walls modelled by a linear spring-dashpot and a constant damping value for blood viscosity. The model facilitates instantaneous state transitions of the microrobot, such as contact with the vessel wall and free motion within the fluid. Amplitudes and phase angles from the transient solutions of dynamics model of the microrobot are solved at arbitrary moments, providing insights into its transient dynamics. The analytical solution of the proposed system is validated by experimental data, serving as a benchmark to examine the influence of pertinent parameters on microrobot’s dynamic response. It is found that the contact force transmitted to the vessel wall, assessed by system’s transmissibility function dependent on damping and frequency ratios, decreases with increasing damping ratio and intensifies when the frequency ratio is below $$\sqrt 2$$ 2 . At the frequency ratio is equal to 1, resonance phenomenon is dominated by the magnification factor linked to the damping ratio, increasing the amplitude of resonance as damping decreases. Finally, different sets of system parameters, including excitation frequency and magnitude, fluid damping, vessel wall’s stiffness and damping, reveal multi-periodic motions and fake collision of the microrobot with the vessel wall. Simulation results imply that these phenomena are minimally affected by vessel wall’s stiffness but are significantly influenced by other parameters, such as fluid damping coefficient and damping coefficient of the blood vessel wall. This research provides a robust theoretical foundation for developing control strategies for microrobots aimed at detecting cancer metastasis.

Comparison of formulas derived from Fourier series solution of diffusion equation

The first Fourier series solution satisfying the boundary condition of zero concentration at the diffusion distance was derived by assuming that the solution consists of a steady-state solution and a transient solution. The first total amount which has passed through the first layer surface was derived from the first Fourier series solution. When the diffusion distance is large, the exponential term in the first total amount cannot be zero. For the sublimation diffusion of disperse dye in paste into polyethylene terephthalate film using the film-roll method, the plot of the first total amount against time was in good agreement with the quadratic regression curve. The second Fourier series solution satisfying the boundary condition of constant concentration at the diffusion distance was derived by assuming that the diffusion distance is the thickness of the first layer. The second total amount which has passed through the second layer surface was derived from the second Fourier series solution and is a linear function of time because the exponential term is zero due to the very small diffusion distance, the thickness of the first layer. The plot of the second total amount against time was in good agreement with the linear regression line. The time-lag formula was derived from the second total amount. The diffusion coefficients determined from the second total amount are much larger than those of the other three types. All four types showed excellent linearity in Arrhenius plot, but the activation energy for the time-lag formula is somewhat greater than the rest.

Multi-physics simulation on transient thermal response of inductive power transfer pad

Inductive power transfer is an important technological alternative for charging infrastructure, crucial for accelerating the future adoption of electronic vehicles. The magnetic components of an inductive charging pad generate inevitable thermal losses, which, if not properly managed, can exceed the pad’s safe operating temperature. Accurate simulation of both steady-state and transient thermal responses is thus essential for evaluating the pad’s suitability for real-world applications. None of the state-of-the-art thermal prediction proposals in this field, however, are able to perform long-term transient analyses efficiently while being versatile enough to simulate generic case studies. This paper presents a multi-physics methodology that aims to address this gap. The numerical framework comprises three coupled modules: electromagnetic, fluid dynamics, and solid heat conduction. To solve the issue of time-scale discrepancies, only the latter module was solved as a transient problem, while the remaining were approximated as near steady-state physics, continuously updated at every time step. The appropriateness of the resultant hybrid transient solution was verified with a fully transient solution from an equivalent heat-conjugate problem. Finally, the prediction capability of the proposed method was validated by reproducing the thermal responses of a lab-scale charging pad energized at various excitation levels and ambient conditions, both outside of and flush-embedded inside an asphalt slab. The relative errors between the measured and simulated thermal responses were consistently within 10%, demonstrating that the multi-physics approach was able to accurately simulate the long-duration transient temperature rise and drop of the test pad.

Dynamic Analysis and Approximate Solution of Transient Stability Targeting Fault Process in Power Systems

Modern power systems are high-dimensional, strongly coupled nonlinear systems with complex and diverse dynamic characteristics. The polynomial model of the power system is a key focus in stability research. Therefore, this paper presents a study on the approximate transient stability solution targeting the fault process in power systems. Firstly, based on the inherent sinusoidal coupling characteristics of the power system swing equations, a generalized polynomial matrix description in perturbation form is presented using the Taylor expansion formula. Secondly, considering the staged characteristics of the stability process in power systems, the approximate solutions of the polynomial model during and after the fault are provided using coordinate transformation and regular perturbation techniques. Then, the structural characteristics of the approximate solutions are analyzed, revealing the mathematical basis of the stable motion patterns of the power grid, and a monotonicity rule of the system’s power angle oscillation amplitude is discovered. Finally, the effectiveness of the proposed methods and analyses is further validated by numerical examples of the IEEE 3-machine 9-bus system and IEEE 10-machine 39-bus system.

Interaction analysis between single pile and multilayered saturated soils under horizontal transient loading

This study employs the coupled finite element-boundary element method to investigate the dynamic response of single pile subjected to horizontal transient loading, which is a common scenario in high-rise building, transportation, and ocean engineering. Firstly, the single pile is modeled as a Timoshenko beam and then discretized with the finite element method (FEM). The transient solution for multilayered saturated soils due to a horizontal load, serving as the kernel function for the boundary element method (BEM), aids in the derivation of the flexibility matrix of the soils. Considering the pile-soil displacement coordination conditions, the coupled FEM-BEM equation is constructed and solved to characterize the pile-soil interaction. Since the pile discretization pattern is applied consistently to the soils, it is more effective than the discretization of infinite domain in the finite element analysis. The validity of the presented method is confirmed through comparison with the full FEM numerical simulations, demonstrating the correctness and enhanced computational efficiency. Finally, parametric studies are carried out to discuss the effects of pile's length-diameter ratio, soil's shear wave velocity and stratification.

Pressure Source Model of the Production Process of Natural Gas from Unconventional Reservoirs

This work is focused on developing a computational model to predict the production rate and pressure evolution of natural gas from unconventional reservoirs, particularly shale gas deposits. The model is based on the principle of conservation of mechanical energy and was developed from the transient solution of Bernoulli’s equation. This solution was obtained by computing the pressure evolution in the well resulting from the combined action of extracting the free gas and of gasification from kerogen. The transient behavior of gas production by hydraulic fracturing was calculated by numerically integrating Bernoulli’s equation. The curves representing gas flow evolution were considered as a series of stepwise steady states under a constant gas flow rate, similar to the pressure–time curves. These time steps were connected by instantaneous drops in pressure or gas flow rates. On the other hand, the delayed release of the adsorbed and dissolved gas in the kerogen was accurately calculated by introducing a semi-empirical gas pressure source term into the gas well pressure equation. The effect of this source is to gradually increase the gas pressure in the reservoir, emulating the gas release mechanisms from the organic matter. Model validation was based on production data from the unconventional reservoirs Eagle Ford, U.S.A., and Burgos basin, México. The initial measured gas production rate was used to determine a global friction factor of the gas flowing out from soil cracks and ducts. Additionally, measured production rate data were used to determine the coefficients of the source term function. Pearson correlation coefficients of 0.97 and 0.96 were obtained for Eagle Ford and Burgos basins data, respectively. In contrast, the corresponding coefficients calculated from the traditional Arps’ model were 0.89 and 0.5, respectively. The present pressure source model (PSM) represents a new approach to characterize the process of gas production from unconventional reservoirs, proving to be accurate in forecasting both the gas flow rate and pressure evolution during gas production. The postulated pressure source term was shown to mimic the desorption and diffusion kinetics, which release free gas from the kerogen.

Transient temperature analysis and engineering application of steel shell immersed tunnel protected by fireproof board

Based on the Shenzhen-Zhongshan Link, the transient analytical solution of the steel shell immersed tunnel under the protection of fireproof board was deduced and verified through fire test. Then, the variation of the maximum temperature of the bottom steel shell with the thickness and thermal conductivity of the fireproof board was analyzed and suggestions on the selection of fireproof boards were given. Finally, a fitting formula for the maximum temperature of bottom steel shell was proposed. The results show that: (1) When the thermal contact resistance of the steel-concrete interface and the thermal resistance of cavity are 0.01 m2 °C/W and 0.02 m2 °C/W respectively under the case of 25 mm thick fireproof board, the variation of the analytical solution is consistent with test results, and the peak value is similar. (2) Based on the three-dimensional diagram of d -λ-T, with 300 °C as the fire resistance limit of structure, the range of the fireproof board parameters is obtained: when λ reaches 0.14 and 0.4 respectively, d shall not be less than 10 mm and 28.38 mm (3) The scatter points obtained from analysis were fitted using quadratic polynomials and linear functions respectively. Considering the accuracy and simplicity, the linear fitting formula is given as T = 275.66–7.41*d+644.6*λ.

Consistent solutions for simultaneous dynamic water, solute, stable isotope and radon balances to estimate average exchange fluxes between surface water bodies and groundwater

Many papers show that water, conservative solute, stable isotope and radon balances can be applied to the study of surface water – groundwater interaction. When undertaken simultaneously, such analysis provides an even more powerful method for estimating groundwater inflows and outflows, i.e. the exchange fluxes that for most people are hardest to estimate. The overarching objective of this paper is to provide practitioners with a consistent conceptual and simulation modelling framework with which to achieve a rapid initial understanding of surface water – groundwater interaction, as well as to guide the efficient and targeted acquisition of field data. This paper makes several important contributions. First, after an introduction that explains the complexities of groundwater flow patterns near surface water bodies, a set of general balance equations is developed using consistent terminology and notation. Second, after focusing on a simple conceptual model with steady groundwater inflow I, groundwater outflow O, precipitation P and ever-present evaporation E, analytical solutions are developed for transient and steady state conditions: one water balance solution is found to apply in all situations; solutions for the solute balance equation are developed for 23 different subcases; a transient balance equation for stable isotopes written in terms of 1+δ is found to apply in all situations; and a new transient solution for radon is found in terms of the upper incomplete gamma function. On the path towards developing the isotope balance equation, we present a rigorous approach, based on coupled nonlinear balance equations for abundant and rare isotope pairs (1H and 2H, then 16O and 18O), using isotope ratios and the fractions of each isotope. Third, we describe a Lake Water Balance Calculator (LWBC) written using GoldSim simulation software, a tool to help others to conduct the simultaneous analyses that we promote; we use GoldSim’s numerical methods to solve the general balance equations, we implement the analytical solutions to demonstrate that both GoldSim’s numerical methods and the analytical solutions are correct, and we also show that the 1+δ approximation is equivalent to the rigorous coupled equations, at least for heavy stable isotopes with very low abundance. Fourth, we describe field studies: we provide three examples of applications of LWBC to short-term studies of Perry Lakes East, Lake Jasper and Georgetown Billabong in Australia; we then describe WSIBal, a simulation model based on the same balance equations and describe its application to Lake Jasper over a 19-year period; finally, we describe R-WSIBal, which evolved from WSIBal, and explain its application to 2500 km of the Murray River in Australia.

Pressure Transient Solutions for Unbounded and Bounded Reservoirs Produced and/or Injected via Vertical Well Systems with Constant Bottomhole Pressure

Various analytical solutions for computing production and injection-induced pressure changes in aquifers and oil reservoirs have been derived over the past century. All prior solutions assumed a constant well rate as the boundary condition. However, in many practical situations, the fluid withdrawal from and/or injection into such subsurface reservoirs occurs with the aid of pump devices that maintain a constant bottomhole pressure in the well. Until now, how the well rate will decline over time, based on the pressure difference in the well relative to the initial reservoir pressure, could not be rapidly computed analytically (using the diffusivity as the key governing system parameter), because no concise expression had been derived with the boundary condition of a constant bottomhole pressure. The present study shows how the pressure diffusion equation can be readily solved for wells acting as sinks and sources with a constant bottomhole pressure condition. We consider both fractured and unfractured completions, as well as injection and production modes. The new solutions do not require an elaborate time-stepped pressure-matching procedure as in nodal analysis, the only other physics-based analytical method currently available to compute the well rate decline when a constant bottomhole pressure production system is used, which unlike our new method proposed here is limited to single well systems.

NEUTRON POINT KINETICS MODEL WITH A DISTRIBUTED-ORDER FRACTIONAL DERIVATIVE

In this paper, the solutions of an extended form of the Fractional-order Neutron Point Kinetics (FNPK) equation in terms of Caputo-time derivatives of the same order are investigated. Instead of using a Caputo derivative, a distributed-order fractional derivative in the Caputo sense was employed in the term of the FNPK equation which is multiplied by the reactivity. This term plays an important role in the description of neutron kinetics during the start-up, shutdown, and steady-state processes in nuclear reactors. The extended (DFNPK) model was solved using the beta, normal, bimodal and Dirac delta distributions to investigate their effect on the transient state solutions of the neutron density. Regardless of the distribution used, the most significant finding is that a destabilizing effect on the neutron density is induced when the mode (or the instant of application of the Dirac delta) of the distribution tends to one while maintaining the orders of the Caputo-time derivatives constant. What defines the destabilizing effect are large magnitude oscillations, a rapid decay, and an oscillation-free steady state with a monotonic increase that is parallel to but somewhat above the trend determined by the FNPK equation. The extended model is anticipated to be effective for modeling neutron density dispersion in a highly heterogeneous medium that may be described using distributed derivatives.

Probabilistic maximization of time-dependent capacities in a gas network

AbstractThe determination of free technical capacities belongs to the core tasks of a gas network owner. Since gas loads are uncertain by nature, it makes sense to understand this as a probabilistic problem provided that stochastic modeling of available historical data is possible. Future clients, however, do not have a history or they do not behave in a random way, as is the case, for instance, in gas reservoir management. Therefore, capacity maximization becomes an optimization problem with uncertainty-related constraints which are partially of probabilistic and partially of robust (worst case) type. While previous attempts to solve this problem were devoted to models with static (time-independent) gas flow, we aim at considering here transient gas flow subordinate to the isothermal Euler equations. The basic challenge addressed in the manuscript is two-fold: first, a proper way of formulating probabilistic constraints in terms of the differential equations has to be provided. This will be realized on the basis of the so-called spherical-radial decomposition of Gaussian random vectors. Second, a suitable characterization of the worst-case load behaviour of future customers has to be found. It will be shown, that this is possible for quasi-static flow and can be transferred to the transient case. The complexity of the problem forces us to constrain ourselves in this first analysis to simple pipes or to a V-like structure of the network. Numerical solutions are presented and show that the differences between quasi-static and transient solutions are small, at least in these elementary examples.

A comprehensive review on the Dynamical behavior of heat and fluid flow mechanism: Thermal performance across different geometries

The prominent novelty of current review is to exhibit the fluctuating and oscillatory convective heat transfer properties along various geometries with magnetic force, variable density, Prandtl number, buoyancy force and magnetic Prandtl number effects. The significance of present work is to illustrate a comprehensive review on transient convective heat transfer. Transient convective heat transfer plays an essential role in various technological and environmental applications, including climate control, structure safety, engines, thermal control, computer heating and cooling, and energy safety. The literature primarily focuses on steady temperature and velocity domains, with few studies exploring time-varying fluid flow in forced, natural, or mixed convective mechanisms with different methods. In current review, justification of results was performed by using oscillating stokes conditions directly in partial differential models. The similarity variables and stream functions are used in literature but in current review, the primitive variable transformation is used with implicit form of finite difference method and Gaussian elimination technique through FORTRAN and Tecplot-360 programming tools. The governing model is reduced into steady, real and imaginary form to explore steady and oscillating convective heat transmission. Transient flows have gained significance due to their ability to achieve large oscillating convective heat transfer rates. Compared with steady movement, oscillating flows exhibit higher velocity variations along the heated surface. Periodic flow produces an improved transient surface heat transmission rate than steady flow. Predicting and controlling transients in thermal exchangers requires a concept of transient forced convection heat transport. Transient convective thermal transmission solutions are important for ensuring the effectiveness and reliability of electrical components, nuclear and thermal power stations, heat-generating engines, steam turbines, condensation systems, catalytic converters, heat shielding for spacecraft, electrical devices, internal combustion engines, air conditioning and refrigerator components, cooling networks for batteries, generators, and transformers. It is found that the frequency of convective heat transport enhances through periodic and oscillating stokes variables. It was depicted that the higher amplitude in convective heat transfer was displayed for each choice of magnetic force parameter around two angles π/4 and π of circular magnetized surface. It was depicted that the maximum transient convective heat transmission was reported along vertical angle π/2 with buoyancy force, Prandtl and magnetic Prandtl values.

Transient behavior of a plate partially immersed in the fluid subjected to impact loadings: Theoretical analysis and experimental measurements

This study aimed to investigate the transient behavior of a rectangular plate partially in contact with fluid subjected to a dynamic external force. To this purpose, a theoretical model was developed to analyze vibration characteristics and transient wave propagation. Based on superposition method, the dry mode shapes and natural frequencies of the plate under vacuum could be obtained. The dry mode shapes were treated as the fundamental function to construct the wet mode that describes the vibration behavior of the fluid-plate coupled system. The velocity potential and fluid pressure within a finite tank due to the plate deflection were derived using an equation governing the incompressible fluid. Based on the relationship between dry mode shape and wet mode shape, the fluid-plate coupled system's wet mode shape and resonant frequency could be determined from the frequency response function. Applying the normal mode method, the transient displacement of plate and fluid pressure can be obtained by solving a system of non-homogeneous differential equations. The theoretical predictions were verified by finite element method (FEM) and experimental measurements. Experiments were conducted using piezoelectric film sensors (polyvinylidene fluoride, PVDF) to measure the force history induced by a steel ball impact to quantitatively analyze the transient response. The comparison results proved that the theoretical predictions and experiments were in good agreement, including the transient responses of the displacement and in-plane strain of a plate partially submerged in the fluid. The results indicate that changes in water depth can induce resonance frequency shifts and wet mode shape distortions, which also illustrate that the vibrational properties of wet modes affect transient behavior. The proposed transient solution demonstrates an analytical approach that connects the physical significance of the dynamic behavior of the fluid-plate coupled system in time and frequency domains; it provides a connection between the transient behaviors and vibration characteristics.

Transient analytical solution for coupled water–gas transport in unsaturated soil cover of landfill

A new analytical solution for coupled water–gas transport in unsaturated landfill cover system is proposed, which can consider transient diffusive-advective transport of gas under transient water transport condition. The proposed analytical solution is first verified against the laboratory measurements and numerical simulations. Using the proposed solution, parametric studies are conducted on the coupled transient behaviors of water–gas transport. The results show that ignoring the coupling effect can lead to significant error in gas transport results under various conditions, e.g., the surface gas emission flux is underestimated by about 28.3%∼79.8% due to ignoring the spatial and temporal variations of water content induced by transient water transport. The influencing parameters (i.e., initial saturation degree, rainfall patterns, and evaporation rate) all have significant impact on the coupled water–gas transport behaviors. The magnitude of the error induced by ignoring the coupling effect increases with increasing initial saturation degree and increasing evaporation rate (e.g., for initial saturation degree increasing from 0.35 to 0.95, the accumulated percolation at cover bottom increases by 10.9 times and the gas emission flux at cover surface decreases by 64.7%). The results highlight that it’s imperative to consider the effect of transient water transport when one needs more accurate assessment of gas transport results in the cover. This analytical solution can also be utilized to aid landfill cover design and to verify other numerical models.

Predictions of transient vector solution fields with sequential deep operator network

The deep operator network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models in the branch of DeepONet to predict final solutions given time-dependent inputs. In the current work, the S-DeepONet architecture is extended by modifying the information combination mechanism between the branch and trunk networks to simultaneously predict vector solutions with multiple components at multiple time steps of the evolution history, which is the first in the literature using DeepONets. Two example problems, one on transient fluid flow and the other on path-dependent plastic loading, were shown to demonstrate the capabilities of the model to handle different physics problems. The use of a trained S-DeepONet model in inverse parameter identification via the genetic algorithm is shown to demonstrate the application of the model. In almost all cases, the trained model achieved an R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^2$$\\end{document} value of above 0.99 and a relative L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_2$$\\end{document} error of less than 10% with only 3200 training data points, indicating superior accuracy. The vector S-DeepONet model, having only 0.4% more parameters than a scalar model, can predict two output components simultaneously at an accuracy similar to the two independently trained scalar models with a 20.8% faster training time. The S-DeepONet inference is at least three orders of magnitude faster than direct numerical simulations, and inverse parameter identifications using the trained model are highly efficient and accurate.

Numerical study on collapsing cavitation bubble dynamics in cryogenic fluids

The paper addresses the implementation of a dual distribution function multiphase lattice Boltzmann method (DDF-MLBM) for studying the collapse of cavitation bubbles in cryogenic liquids. The present scheme incorporates the energy equation and imposes interparticle interactions and fluid–solid adhesive forces through the exact difference method (EDM). To accurately model phase changes and the molecular complexities of cryogenic fluids like liquid hydrogen (LH2) and liquid nitrogen (LN2), the Peng-Robinson (PR) equation of state is employed along with an acentric factor. The accuracy of the present numerical technique is evaluated using the Laplace law and the Maxwell equal area construction theorem for a two-phase liquid–vapor system in equilibrium. For transient solutions, the study compares results of heterogeneous cavitation with the analytical solution derived from the thermal Rayleigh-Plesset equation. The research investigates the impact of the distance between a cavitation bubble with an adjacent solid wall on velocity, pressure, temperature, and collapse time. Furthermore, it is assessed how surface wettability influences cavitation bubble collapse intensity. Additionally, the paper examines the collapse of a cavitation bubble cluster and evaluates the effects of different physical parameters on the collapse properties of the bubble cluster. The results underscore the significant influence of the distance between cavitation bubbles in the cluster, the distance between bubbles and the adjacent solid surface on the micro-jet velocity. Moreover, it is found that increasing the contact angle of the solid surface enhances the collapse intensity and micro-jet velocity of the collapsing bubble cluster.

Pump System Model Parameter Identification Based on Experimental and Simulation Data

In this paper, the entire downhole fluid-sucker rod-pump system is replaced with a viscoelastic vibration model, namely a third-order differential equation with an inhomogeneous forcing term. Both Kelvin’s and Maxwell’s viscoelastic models can be implemented along with the dynamic behaviors of a mass point attached to the viscoelastic model. By employing the time-dependent polished rod force measured with a dynamometer as the input to the viscoelastic dynamic model, we have obtained the displacement responses, which match closely with the experimental measurements in actual operations, through an iterative process. The key discovery of this work is the feasibility of the so-called inverse optimization procedure, which can be utilized to identify the equivalent scaling factor and viscoelastic system parameters. The proposed Newton–Raphson iterative method, with some terms in the Jacobian matrix expressed with averaged rates of changes based on perturbations of up to two independent parameters, provides a feasible tool for optimization issues related to complex engineering problems with mere information of input and output data from either experiments or comprehensive simulations. The same inverse optimization procedure is also implemented to model the entire fluid delivery system of a very viscous non-Newtonian polymer modeled as a first-order ordinary differential equation (ODE) system similar to the transient entrance developing flow. The convergent parameter reproduces transient solutions that match very well with those from fully fledged computational fluid dynamics models with the required inlet volume flow rate and outlet pressure conditions.