Transient Solution Research Articles

Transient Analysis of Two-Dimensional State M/M/2 Queueing Model with Multiple Vacations, Catastrophes and Feedback

This study obtains transient solution of two-dimensional state Markovian queueing model with homogenous servers, multiple vacations, catastrophes and feedback. Inter-arrival and service times follow an exponential distribution with parameters ? and ?, respectively. Units are ejected from the system when catastrophes occur. Servers get deactivated for a moment and are ready for service when new units arrive. Occurrence of catastrophes follows Poisson distribution with rate. After receiving the service, the units either exit or rejoin the system immediately at the early end of the queue; this is known as ?feedback?. Laplace transform approach has been used to find transient solution and discover some quantifiable results.. KEYWORDS :Markovian queue, Laplace transform, Multiple vacations, Catastrophes, Feedback

FSI simulation of a high-head pump-turbine during load rejection process

Abstract High-head pump-turbine suffers large centrifugal and hydraulic forces due to large rotational speed and severe pressure pulsations during transient processes, and the strong vibration may increase the risk of runner failure. Load rejection transient process is crucial for pumped-storage hydropower stations, and the evolution laws of the runner dynamic stress during this process need profound research. In this study, the evolution of the runner dynamic stress of a prototype pump-turbine during a load rejection transient process was simulated using the one-dimensional and three-dimensional coupling (1D-3D) method and the fluid-structure interaction (FSI) method. The results of this dynamic transient process were compared to the results of the static working points. It is shown that the rotational speed dominates the mean value of stress while the fluctuating amplitude of stress is dominated by pressure fluctuations, which are larger in the S-shaped region of characteristics. Compared with the static working point solutions, the transient process solutions can better reflect the stress fluctuations and should be used for safety assessment.

Applications of Asymptotic Solutions of the Diffusivity Equation to Infinite Acting Pressure Transient Analysis

Summary Understanding how pressure propagates in a reservoir is fundamental to the interpretation of pressure and rate transient measurements at a well. Unconventional reservoirs provide unique technical challenges as the simple geometries and flow regimes [wellbore storage (WBS) and radial, linear, spherical, and boundary-dominated flow] applied in well test analysis are now replaced by nonideal flow patterns due to complex multistage fracture completions, nonplanar fractures, and the interaction of flow with the reservoir heterogeneity. In this paper, we introduce an asymptotic solution technique for the diffusivity equation applied to pressure transient analysis (PTA), in which the 3D depletion geometry is mapped to an equivalent 1D streamtube. This allows the potentially complex pressure depletion geometry within the reservoir to be treated as the primary unknown in an interpretation, compared with the usual method of interpretation in which the depletion geometry is assumed and parameters of the formation and well are the unknown properties. The construction is based upon the solution to the Eikonal equation, derived from the diffusivity equation in heterogeneous reservoirs. We develop a Green’s function that provides analytic solutions to the pressure transient equations for which the geometry of the flow pattern is abstracted from the transient solution. The analytic formulation provides an explicit solution for many well test pressure transient characteristics such as the well test semi-log pressure derivative (WTD), the depth of investigation (DOI), and the stabilized zone (SZ) (or dynamic drainage area), with new definitions for the limit of detectability (LOD), the transient drainage volume, and the pseudosteady-state (PSS) limit. Generalizations of the Green’s function approach to bounded reservoirs are possible (Wang et al. 2017) but are beyond the scope of the current study. We validate our approach against well-known PTA solutions solved using the Laplace transform, including pressure transients with WBS and skin. Our study concludes with a discussion of applications to unconventional reservoir performance analysis for which reference solutions do not otherwise exist.

A Modified Enthalpic Lattice Boltzmann Method for Simulating Conjugate Heat Transfer Problems in Non-Homogeneous Media

A Modified Enthalpic Lattice Boltzmann Method for Simulating Conjugate Heat Transfer Problems in Non-Homogeneous Media

Specific, nondestructive, and durable adhesion primer for polyolefins

Gluing polyolefins [e.g., polyethylene (PE) and polypropylene (PP)] results in a very challenging task. The main reason relies on their low surface energy, which reduces the affinity between the polyolefin surface and the chosen adhesive. To tackle this problem, the most commonly used solutions are physical surface treatments, such as plasma, corona, and flame, which introduce hydrophilic moieties on the plastics surface, thus increasing their surface energy. These approaches require special setups, are unspecific, and can induce material degradation. Furthermore, they provide a transient solution, making the storage of pretreated substrates not recommended. In this work, we developed an easy-to-apply primer for durable bonding of adhesives on PE and PP, as robust alternative to physical treatments. Our primer contains a surface-anchoring moiety and an adhesive-binding group to covalently react with the polyolefin substrate and with the glue. As a surface-anchoring moiety, we chose the perfluorophenylazide (PFPA), which is known to undergo a C–H insertion reaction upon UV activation, while as adhesive-binding groups, we selected OH functions, which can covalently react with the most common commercially available glues. When these two features (i.e., PFPA and OH) are combined in a single molecule, the reaction with the substrate does not occur and the molecule is only physisorbed, inducing no adhesion improvement. Chemisorption only occurs with bicomponent formulations, comprising a hydrophobic trifunctional PFPA and a polymer bearing OH and PFPA groups. Those induced improved adhesion on PP compared to the golden standard plasma with polyurethane-based and two-component epoxy adhesives. Storing the coated substrates at room temperature for up to two months did not alter the adhesion performance, thus further ascribing the developed primers as a promising alternative to plasma treatment.

Numerical prediction of mean flow and acoustic field of a supersonic impinging jet

The three-dimensional turbulent mean flow and acoustic field of a supersonic jet impinging on a solid plate is studied computationally using the general purpose CFD code Ansys Fluent. A pressure-based coupled solver formulation with the second order weighted central-upwind spatial discretization is applied to compute transient solutions. Cold and hot jet thermal conditions are considered. Mean flow characteristics are investigated by a steady-state modeling approach. Acoustic radiation of impingement tones is simulated using a transient time-domain formulation. The effects of turbulence in steady-state are modeled by the SST k-ω turbulence model. The Wall-Modeled Large-Eddy Simulation (WMLES) model is applied to compute transient solutions. The near-wall mesh on the impingement plate is fine enough to resolve the viscosity-affected near-wall region all the way to the laminar sublayer. Nozzle-to-plate distance is parameterized in the model for automatic re-generation of the mesh and results. Steady-state predictions of hover lift loss and mean jet velocity distributions are compared with experimental data, and favorable agreement is reported. The transient solution reproduces the mechanism of impingement tone generation by the interaction of large scale vortical structures with the impingement plate. The acoustic near-field is directly resolved by Computational Aeroacoustics (CAA) to accurately propagate impingement tone waves to near-field microphone locations. Calculated impingement tone frequencies and sound pressure levels agree with experimental values.

Direct vs. staged TAVI in the acute management of decompensated severe aortic stenosis

Abstract Funding Acknowledgements None. Background Transcatheter aortic valve implantation (TAVI) has emerged as a preferred treatment for severe aortic stenosis across a spectrum of surgical risks, potentially diminishing the role of balloon aortic valvuloplasty (BAV) as a transient solution or a bridge to definitive intervention. With advancements in TAVI technology and expertise, patients even in unstable conditions are increasingly receiving direct, definitive TAVI, avoiding the risks associated with staged, multiple procedures. Aims The study set out to assess whether immediate TAVI is safer and more effective than BAV followed by elective aortic valve replacement (AVR) in acute severe aortic stenosis. Methods Conducted as a retrospective analysis at a single center, this study encompassed a cohort of consecutive patients who received either urgent or emergency BAV, as bridge to AVR, or TAVI to manage decompensated severe aortic stenosis from May 2012 to May 2023. The primary outcomes were mortality rates at both 30 days and one year following the procedures. Results In this cohort, 258 cases of urgent or emergent percutaneous aortic valvuloplasty were evaluated. BAV was performed in 47 patients, whereas 211 received direct TAVI. A significantly higher proportion of the BAV group (36%) was treated due to cardiogenic shock as the primary indication, compared with just 11% in the TAVI group (p< 0.001). Demographic parameters and comorbid condition profiles were equivalently balanced across both groups. The median age was 81 years (interquartile range: 74-85, p= 0.40), and males constituted 56% of the patient population (p= 0.72). Most patients (65%) presented with left ventricular systolic dysfunction, and nearly half (49%) were diagnosed with obstructive coronary artery disease. The reduction in peak aortic valve gradient was significantly more pronounced in the TAVI group (-56±25 mmHg) compared to the BAV group (-27±19 mmHg, p< 0.001). TAVI recipients also had a higher incidence of VARC-2 minor and major bleeding events (26% versus. 6% for BAV, p<0.001), and a greater occurrence of advanced atrioventricular block necessitating temporary pacing (19% vs. 9% for BAV, p= 0.02). Thirty-day survival rates favored the TAVI group (93%) over BAV (86%). This trend persisted at the one-year mark, with survival rates of 84% for TAVI and 70% for BAV. Furthermore, the one-year hazard ratio for mortality among patients undergoing BAV was 2.01 (95% confidence interval: 1.34–3.01, p< 0.001). Conclusion The data from this retrospective analysis indicate that for patients with decompensated severe aortic stenosis, immediate TAVI may confer a mortality benefit over BAV followed by elective procedures. Despite a higher rate of procedural complications, the direct TAVI approach was associated with better survival rates at both 30 days and one year. These outcomes suggest a potential reevaluation of treatment strategies in acute settings may be warranted.

Theoretical and numerical study on transient acoustic wave propagation across ice layers in the Arctic Ocean.

The study of transient acoustic wave propagation across the Arctic Ocean ice layer provides theoretical guidance for the design of trans-ice acoustic communication systems. In this study, the Arctic Ocean was modeled as an ice-water composite structure, where the ice and water are regarded as an elastic solid and liquid, respectively. An analytical transient solution for acoustic wave propagation in this structure was derived using the eigenfunction expansion method. Further, the numerical procedures were presented and used to analyze the acoustic wave propagation characteristics across the ice layer. The results show that waveforms corresponding to the radial displacements are more severely distorted than the axial displacements. The amplitudes of the radial and axial displacements decreased rapidly with increasing propagation distance. The ice thickness had a greater impact on the radial displacement than axial displacement; the thicker the ice, the greater the distortion for both radial and axial displacements.

Semi-analytical solutions for forced and free vibration of damped fluid-conveying pipe systems based on complex modal superposition method

In this paper, the response solutions of the damped fluid-conveying pipe system with elastic torsion constraints at both ends are analyzed. The pipe system considering gyroscopic effect induced by internal flow and damping effect is a typical damped gyroscopic system. This system cannot be decoupled in the modal space by the traditional modal analysis, and then the semi-analytical response solutions cannot be obtained by the classical modal superposition method. In order to remedy this problem, this paper proposes a new method based on complex modal superposition method and state-space method to give the semi-analytical response solutions of the damped fluid-conveying pipe system. The adjoint system is introduced through the concept of adjoint operator, and the orthogonality conditions of the damped fluid-conveying pipe system are derived in the state-space by using the eigenvalue relationship between the original system and the adjoint system. The Laplace transformation method is used to solve the eigenvalue problems of the original system and the adjoint system, and the implicit function equations about the eigenvalues and analytical eigenfunctions are obtained. According to the obtained orthogonality conditions, the semi-analytical response solutions of the system under arbitrary initial conditions and excitations are given, and the obtained solutions include transient and steady-state response solutions. In the numerical discussion part, the reliability and accuracy of the present method are verified. This research has positive significance for the dynamic analysis of fluid-conveying pipe systems, and the obtained orthogonality conditions have potential value for the nonlinear dynamics research.

Research on transient temperature rise characteristics of composite cylindrical roller bearings

Composite roller bearings have received extensive attention from bearing design engineers because of their good contact and running performance. According to the contact mechanical characteristics of composite cylindrical roller, a bearing heat generation power calculation model is established. Then, using the local heat source analysis method, and considering the heat conduction mode, the transient temperature solution model of bearings is established. The influence of filling ratio, radial force, angular velocity and roller numbers on the heat generation power and steady-state temperature of the bearing components is calculated and analyzed. The calculated results are in good agreement with the experimental results, which verifies the correctness of the model. The model can accurately predict the temperature distribution of bearings, providing new ideas and methods for temperature rise analysis, and laying the foundation for temperature analysis of bearings.

EFFECTS OF ANTI-PREDATOR BEHAVIOR ON A STOCHASTIC PREDATOR-PREY SYSTEM

An ecosystem with anti-predator behavior is established in both deterministic and stochastic environments. This means that adult prey could attack weak predators. Bifurcation diagrams are used to analyze the deterministic case, while a tool called the most probable trajectory, defined by the spatial extreme point of the probability density function (PDF), is employed to explore the stochastic case. The Fokker-Planck equation is solved using the stochastic averaging method of energy envelope, which provides an analytical expression for the PDF. The results show that in the deterministic case, effective anti-predator behavior can dampen predator-prey oscillations and mitigate negative effects caused by the time delay. Additionally, it can accelerate the transient solution to reach a steady state and reduce the ratio of predator-to-prey densities in coexistence. In the stochastic case, effective anti-predator behavior can raise the noise threshold that leads to population extinction. Furthermore, it can also reduce the randomness of solutions. It’s worth noting that appropriate anti-predator behavior can ensure that the most probable solution in the stochastic system approximates the solution in the deterministic system. Monte Carlo simulations verify the accuracy of these analytical results.

Optimisation-based strategies to identification of material parameters of hygro-thermo-mechanical problems

Applications involving hygro-thermo-mechanical models are found in engineering fields as diverse as electronic packaging, concrete structures, composite materials and wood structures. Within the framework of wood processing, hygro-thermo-mechanical problems account for the cross-dependence of moisture content, temperature and dimensional changes of wooden components. Numerical simulation plays an important role in predicting the behaviour of wooden structures and, therefore, use of appropriate process and material parameters is essential for a successful prediction. The present work is inserted in this context and addresses application of optimisation techniques to identification of heat transfer, moisture diffusion and moisture-dependent swelling/shrinkage parameters. The direct problem is formulated based on a fully coupled transient solution of the energy, moisture and momentum transfer conservation laws. A global–local hybrid optimisation technique is proposed combining swarm intelligence and deterministic approaches, respectively based on particle swarm optimisation and the Nelder–Mead (NM) technique. The first stage aims at reducing the search space, so that the NM algorithm is able to determine the global minimum with acceptable accuracy. The strategy is both robust and efficient, being able to avoid local minima with reduced number of fitness computations. An illustrative example featuring a moisture-gaining process is also discussed, in which special attention is placed on the elastic and material swelling coupled effects caused by moisture transfer.

A three-dimensional numerical well-test model for pressure transient analysis in fractured horizontal wells with secondary fractures

During oil and gas reservoir development, multi-stage horizontal wells (MFHWs) and hydraulic fracturing techniques can effectively increase estimated ultimate recovery. However, there still lacks an understanding of the three-dimensional (3D) pressure transient behaviors of multi-stage fractured horizontal wells with secondary fractures. To narrow this gap, a three-dimensional numerical well-test model based on a discrete fracture model and unstructured tetrahedral grids is developed to study the pressure transient behaviors of MFHWs with secondary fractures. The pressure transient solutions of MFHWs with secondary fractures have been demonstrated by model verifications. The results show that the proposed model can accurately capture the complex transient flow around fractures, including early radial flow that is not easily captured by two-dimensional numerical well test models. The proposed model classifies the flow regimes of a MFHW as: wellbore storage and skin effects, early radial flow, bilinear flow, linear flow, elliptical flow, pseudo radial flow, and pseudo-boundary dominated flow. It is found that the fracture geometry has a relatively large effect on the shape of the pressure derivative curve in this work. The hydraulic fracture half-length has the greatest impact on the pressure transient behaviors of the MFHW, followed by fracture height and secondary fracture half-length, as found in this study. Additionally, fracture parameters are evaluated, and actual well testing data are interpreted, taking into account the fracture height. This work is meaningful to understand the three-dimensional pressure transient behaviors of MFHWs with secondary fractures.

A semi-analytical pressure and rate transient analysis model for inner boundary and propped fractures exhibiting dynamic behavior under long-term production conditions

The loss of hydrocarbon production caused by the dynamic behavior of the inner boundary and propped fractures under long-term production conditions has been widely reported in recent studies. However, the quantitative relationships for the variations of the inner boundary and propped fractures have not been determined and incorporated in the semi-analytical models for the pressure and rate transient analysis. This work focuses on describing the variations of the inner boundary and propped fractures and capturing the typical characteristics from the pressure transient curves.A generalized semi-analytical model was developed to characterize the dynamic behavior of the inner boundary and propped fractures under long-term production conditions. The pressure-dependent length shrinkage coefficients, which quantify the length changes of the inner zone and propped fractures, are modified and incorporated into this multi-zone semi-analytical model. With simultaneous numerical iterations and numerical inversions in Laplace and real-time space, the transient solutions to pressure and rate behavior are determined in just a few seconds. The dynamic behavior of the inner boundary and propped fractures on transient pressure curves is divided into five periods: fracture bilinear flow (FR1), dynamic PFs flow (FR2), inner-area linear flow (FR3), dynamic inner boundary flow (FR4), and outer-area dominated linear flow (FR5). The early hump during FR2 period and a positive upward shift during FR4 period are captured on the log-log pressure transient curves, reflecting the dynamic behavior of the inner boundary and propped fractures during the long-term production period.The transient pressure behavior will exhibit greater positive upward trend and the flow rate will be lower with the shrinkage of the inner boundary. The pressure derivative curve will be upward earlier as the inner boundary shrinks more rapidly. The lower permeability caused by the closure of un-propped fractures in the inner zone results in greater upward in pressure derivative curves. If the permeability loss for the dynamic behavior of the inner boundary caused by the closure of un-propped fractures is neglected, the flow rate will be overestimated in the later production period.

Transient versus steady-state solutions: a qualitative study

In view of the ultimate goal of producing long-lasting quasi-stationary discharges required for future fusion power stations, the numerical study of steady-state solutions of equations describing the particle and energy balance rightfully gets ample attention. Transient states may, however, differ significantly from the steady state ultimately reached and will – in practice – impact on the actual fate of the discharge. Using brutally simple models, the present paper highlights a number of aspects to illustrate this dynamics. It e.g. shows the different signature of wave and beam heating, potentially giving room to transiently trigger desirable effects that may allow us to better steer a discharge.

Numerical simulation and experimental study on the heat and mass transfer behavior during the pulsed laser cladding process

Compared with continuous wave (CW), pulse wave (PW) perturbation results in a larger temperature change rate inside the cladding layer, which leads to a higher quality cladding layer. In this paper, a three-dimensional numerical model of laser cladding Fe60 powder was established. The multiphysics field coupling transient evolution and solute distribution under PW and CW operating modes were studied. The problem of lack of theoretical support for laser cladding process under different working modes in heat source was solved. Calculations show that at 1970 ms when the temperature is stable, the maximum temperature, flow rate, and stress under the PW mode are 2660 K, 0.34 m/s, and 354 MPa, respectively, which are smaller than those under the CW mode. The four solute distributions at stable temperature are as follows: The minimum mass fractions of Fe and Mn are 87% and 0.49% in the CW mode, and the maximum mass fractions of Cr and Ni are 11% and 5%. In the PW mode, the minimum mass fractions of Fe and Mn are 82% and 0.44%, and the maximum mass fractions of Cr and Ni are 14% and 5%. PW has a smaller heat input than CW, resulting in a smaller molten pool, so the elements in the molten pool are more fully mixed with other alloying elements. Metallographic experiments were performed using a scanning electron microscope to examine the mechanical properties on the fusion cladding layer, and the accuracy of the model was verified by combining numerical simulations with experimental studies for comparative analysis.

Investigation of diabatic imparity involving asymmetric convection in two-dimensional longitudinal fins using lattice Boltzmann solver

This manuscript investigates the effect of diabatic imparity on two-dimensional (2-D) transient fins having naturally obtained non-linear variation of temperature-dependent conductivity. The diabatic imparity arises due to asymmetrical convection coefficient on the surfaces, implemented using different Biot numbers on each respective surface of the fin, which resembles pragmatic industrial applications. The transient solution of 2-D fin has been obtained using a Lattice Boltzmann (LB) solver, firstly, the suitability of 2-D LB formulation is established with the validity of the existing results, and subsequently extending the LB formulation for the present study. The numerical solution is determined under the two types of step-changing boundary conditions at the fin root having (i) heat flow and (ii) temperature. Results have been plotted graphically, and these include instantaneous isotherms, equilibrium isotherms, and threshold iso-temporal lines. Reported results facilitate the fin designer to examine the effect of diabatic imparity on the attainment of steady-state and occurrence of transverse temperature gradient on 2-D transient fin. The reported results provided are pertinent to the pragmatic application and are seldom reported in the literature. The outcomes of the present investigation are eminently informative to practising engineers and will serve as design monograms.

Elastic moduli prediction of a short fiber composite with interface debonding at fiber ends

This work deals with the fiber ends debonding-induced elastic moduli degradation of a short fiber reinforced composite (SFRC). The strain fields of the matrix in a representative volume element (RVE) of the SFRC are determined from an imaginary fiber technique. By using the debonding boundary conditions, the debonded modulus of the composite is derived, which is affected by not only the far-field but also the transient solutions for the longitudinal strain of the matrix. Particularly, the imaginary fiber technique provides unbounded solution for a moderately large fiber aspect ratio. This is resolved by separating the RVE along the fiber direction into two domains. Combining the longitudinal strains in both domains, the longitudinal modulus is determined, and the longitudinal bridging tensor element in the micromechanics Bridging Model is amended. Five elastic moduli of an SFRC after the fiber end debonding are obtained on the amended Bridging Model. The effects of the fiber volume fraction, fiber aspect ratio, and fiber-to-matrix modulus ratio on the end-debonded longitudinal modulus, transverse modulus, and longitudinal Poisson’s ratio are investigated.

Study of the Effect of Static Eccentricity on Vibration Damping Properties of Squeeze Film Dampers Considering the Two-Phase Flow Case

To analyze the effect of static eccentricity on the air ingestion distribution and vibration damping properties of the SFD, a numerical simulation study of SFDs considering two-phase flow was carried out based on CFD using a transient solution method and dynamic mesh technique. The results show that the angle between the static eccentricity direction and the circumferential direction of the oil supply hole increases and the air ingestion area in the oil film expands. In contrast, the oil film damping decreases, and the larger the static eccentricity distance, the greater its effect on the air ingestion area in the oil film. When the circumferential angle is small, the oil film damping increases with the increase of static eccentricity distance, and when the circumferential angle is large, the oil film damping decreases with the increase of static eccentricity distance and then increases. With the increase of static eccentricity distance, the air ingestion area at both ends of the oil film increases. At the same time, studying the effect of dynamic eccentricity shows that as the dynamic eccentricity increases, the oil film damping first decreases and then increases, and the air ingestion area increases. Comparing the 1 hole, the 2 hole, and the 3 hole oil supplies, the air ingestion area is significantly larger in the 1 hole oil supply than in the 2 hole or the 3 hole oil supplies, and the oil film damping of the 1 hole oil supply is smaller than the oil film damping of the 2 hole or the 3 hole oil supplies. It can be seen from the present study that in the actual installation of the SFD, when the circumferential angle is less than 60°, the static eccentricity can be increased appropriately. When the circumferential angle is greater than 60°, the static eccentricity can be appropriately reduced.

Nonsurgical Treatment of Postburn Hypopigmentation: A Literature Review.

The treatment of postburn hypopigmentation was primarily surgical before the advent of new technologies. Medical devices and therapies are emerging to manage scar sequelae that can be disfiguring and associated with severe psychosocial impact. These innovations have been poorly investigated for hypopigmentation, but they represent a real hope. We reviewed all articles published on Pubmed up to June 2022. Included studies had to specifically focus on treating postburn hypopigmented scars. All articles evaluating transient solutions such as make-up, and articles describing inflammation-linked hypopigmentation with no etiological details or no burn injury history were excluded. Through this review, we have highlighted 6 different types of nonsurgical treatments reported in postburn leukoderma potentially allowing definitive results. Electrophoto-biomodulation or E light (combining intensive pulsed light, radiofrequency, and cooling), topical daylight psoralen UVA therapy, and lasers (fractional lasers using pulse energies or CO2FL devices, lasers-assisted drug delivery as local bimatoprost and tretinoin or pimecrolimus) have been explored with encouraging results in hypopigmented burns. Finally, other promising medical strategies include using FK506, a nonsteroidal anti-inflammatory drug, to induce melanogenesis or using melanocyte-stimulating hormones with fractional laser-assisted drug deliveries, which are expected to emerge soon.