Stationary Boundary Research Articles

Effect of Cr segregation on grain growth in nanocrystalline [formula omitted]-Fe alloy: A multiscale modeling approach

We present a multiscale modeling framework that integrates density functional theory (DFT) with a phase-field model (PFM) to explore the intricate dynamics of grain growth in nanocrystalline α-Fe single-phase alloy in the presence of chromium (Cr) segregation. Simulated results for equilibrium segregation in stationary grain boundary (GB) agree with the Mclean isotherm, validating our model. Polycrystal simulations featuring nanocrystalline grains at different temperatures reveal that the grain growth kinetics depends on the ratio of Cr diffusivity to intrinsic GB mobility. Without Cr segregation at GB, the relationship between the square of average grain size (d2) and time (t) demonstrates a linear correlation. With Cr segregation at GB, the d2 vs. t plot initially follows the same linear growth trajectory as observed without segregation up to a threshold grain size, beyond which it deviates with a decreasing slope. The threshold grain size decreases with increasing temperature from 700K to 900K. Notably, at 1000K, grain growth without and with Cr segregation both follow a linear trajectory, the latter having a smaller slope from the beginning. We develop an analytical formulation based on Cahn’s solute drag theory to predict grain growth in the presence of solute segregation at GB and use it to validate our simulation results.

Degenerate Parabolic Equation with Zero-flux Boundary Condition and its Approximations

We study a degenerate parabolic-hyperbolic equation with zero-flux boundary condition. The aim of this paper is to prove convergence of numerical approximate solutions towards the unique entropy solution. We propose an implicit finite volume scheme on admissible mesh. We establish fundamental estimates and prove that the approximate solution converge towards an entropy-process solution. Contrarily to the case of Dirichlet condition, in zero-flux problem unnatural boundary regularity of the flux is required to establish that entropyprocess solution is the unique entropy solution. In the study of well-posedness of the problem, tools of nonlinear semigroup theory (stationary, mild and integral solutions) were used in order to overcome this difficulty. Indeed, in some situations including the one-dimensional setting, solutions of the stationary problem enjoy additional boundary regularity. Here, similar arguments are developed based on the new notion of integral-process solution that we introduce for this purpose.

Extreme Convective Gusts in the Contiguous USA

Most damage to buildings across the contiguous United States of America (USA) is caused by gusts in convective events associated with thunderstorms. Design rules for structures to resist these events rely on the integrity of meteorological observations and the methods of assessment. These issues were addressed for the US Automated Surface Observation System (ASOS) in six preliminary studies published in 2022 and 2023, allowing this present study to focus on the analysis and reporting of gust events observed between 2000 and 2023 at 642 well-exposed ASOS stations distributed across the contiguous USA. It has been recently recognized that the response of buildings to convective gusts, which are non-stationary transient events, differs in character from the response to the locally stationary atmospheric boundary gusts, requiring gust events to be classified and assessed by type. This study sorts the mixture of all observed gust events exceeding 20 kn, but excluding contributions from hurricanes and tropical storms, into five classes of valid meteorological types and two classes of invalid artefacts. The valid classes are individually fitted to optimal sub-asymptotic models through extreme value analysis. Classes are recombined into a joint mixture model and compared with current design rules.

Impacts of thermally stratified medium on transient convective heat transfer between co‐axial horizontal fixed pipes: Applications of the thermal stratification

AbstractThermal stratification improves coaxial pipe systems’ efficiency and stability. Thermal stratification enables accurate temperature maintenance, reduces thermal stress, optimizes heat transmission performance, and minimizes usage of energy to guarantee the system's long‐term performance. The main aim of the current study is to investigate the impacts of thermal stratification on buoyancy force flow and thermal transmission between coaxial fixed pipes. In the present research, the applications of thermally stratified medium on transient convective heat transfer between two coaxial fixed pipes are studied. A two‐dimensional mathematical formulation in terms of mutually nonlinear partial differential equations is used to analyze the unsteady flow and temperature field between the co‐axial pipes, when the internal pipe is uniformly heated and the outer wall of the external pipe is placed at infinity from the surface of the inner fixed pipe. Flow is assumed along the axial direction of the internal pipe and stationary boundary condition is assumed at the surface of the inner pipe. The coupled equations of the simulated model are solved numerically by applying the Implicit Finite Difference Technique. The computed outcomes in the form of geometrical interpretation are highlighted by using the technically advanced software TECHPLOT‐360. Comprehensive detail of the obtained results for the non‐dimensional parameters included in the flow formulation is predicted for steady state velocity, temperature distribution, time‐dependent surface shearness and time‐dependent energy shearness in results and discussion section of the manuscript. The emphasis is placed on the thermal stratification parameter in the above mentioned chief quantities. From the obtained results, it is predicted that the fluid flow pattern and thermal distribution are both reduced for rising values of the thermal stratification parameter S = 0.001, 0.03, 0.05, and 0.07. Minimum flow and thermal profile are observed at S = 0.07. Further, the amplitude of the time‐dependent surface shearness is uniformly distributed throughout the medium and the amplitude of the time‐dependent energy shearness is reduced effectively for S = 1.0, 5.0, and 10.0.

Observation of discrete-light temporal refraction by moving potentials with broken Galilean invariance

Refraction is a basic beam bending effect at two media’s interface. While traditional studies focus on stationary boundaries, moving boundaries or potentials could enable new laws of refractions. Meanwhile, media’s discretization plays a pivotal role in refraction owing to Galilean invariance breaking principle in discrete-wave mechanics, making refraction highly moving-speed dependent. Here, by harnessing a synthetic temporal lattice in a fiber-loop circuit, we observe discrete time refraction by a moving gauge-potential barrier. We unveil the selection rules for the potential moving speed, which can only take an integer v = 1 or fractional v = 1/q (odd q) value to guarantee a well-defined refraction. We observe reflectionless/reflective refractions for v = 1 and v = 1/3 speeds, transparent potentials with vanishing refraction/reflection, refraction of dynamic moving potential and refraction for relativistic Zitterbewegung effect. Our findings may feature applications in versatile time control and measurement for optical communications and signal processing.

A wall-modeled immersed boundary/large eddy simulation method and its application to simulating heart valve flows

In this work, a wall-modeled immersed boundary (IB)/large eddy simulation (LES) method is extended to the simulation of moving-boundary flows. The used non-equilibrium algebraic wall model is based on an assumed velocity profile, the coefficients of which are determined from physical constraints provided by the full turbulent-boundary-layer equations. To implement the wall model in an IB method named the local domain-free discretization (DFD) method, a local coordinate system fixed on the moving body is introduced. Thus, wall modeling is transformed into a local two-dimensional problem and the complexity of implementation of the wall model is reduced. In the present LES-DFD method, the tangential velocity at an exterior dependent node is determined via wall shear stress prescribed by the wall model. To reduce computational cost for simulating an internal flow with moving boundaries, the stationary boundaries are handled by the body-fitted-grid method and the moving boundaries by the local DFD method. There is no need of an auxiliary grid for solving the non-equilibrium algebraic wall model. Therefore, the inbuilt advantage of an IB method can be retained when simulating moving-boundary problems, and the economy of equilibrium wall models can also be preserved. The present method is applied to simulating the pulsatile flows through a bileaflet mechanical heart valve implanted in a model aorta. The predicted results show an acceptable agreement with the referenced experimental measurements or numerical results at much higher resolution and the applicability of the non-equilibrium wall model to LES of complex moving-boundary flows is verified.

Role of turbulent separatrix tangle in the improvement of the integrated pedestal and heat exhaust issue for stationary-operation tokamak fusion reactors

The magnetic separatrix surface is designed to provide the final and critical confinement to the hot stationary-operation core plasma in modern tokamak reactors in the absence of an external magnetic perturbation (MP) or transient magneto-hydrodynamic perturbation, while diverting the exhaust heat to divertor plates. All the stationary operational boundary plasma studies and reactor designs have been performed under this assumption. However, there has been a long-standing suspicion that a stationary-operation tokamak plasma even without external MPs or edge localized modes (ELMs) activities may not have a stable closed separatrix surface, especially near the magnetic X-point. Here, the first gyrokinetic numerical observation is reported that the divertor separatrix surface, due to homoclinic tangles caused by intrinsic electromagnetic turbulence, is not a stable closed surface in a stationary operation phase even without MPs or ELMs. Unlike the MP- or ELM-driven homoclinic tangles that could cause deleterious effects to core confinement or divertor plates, it is found that the micro-turbulence driven homoclinic tangles could connect the divertor plasma to the pedestal plasma in a constructive way by broadening the divertor heat-exhaust footprint and weakening the pedestal slope to the ELM-safe direction. Micro-turbulent homoclinic tangles can open a new research direction in understanding and controlling these two most troublesome and non-locally connected edge-plasma issues in a tokamak fusion reactor.

Enhanced Aerodynamic Performance of a Two-Dimensional Airfoil Using Moving Boundaries

The effects of moving boundary conditions on the aerodynamic performance of a two-dimensional NACA 0012 airfoil at different angles of attack (α) in a uniform freestream at a Reynolds number of 10,000 are numerically studied. The moving boundary conditions are motivated by inviscid potential flow around the airfoil, which also satisfies the viscous equations of motion. In this study, the wall is moved at the slip velocity of the inviscid flow, or a fraction of it. These prescribed moving boundary conditions are shown to suppress vortex shedding, thus allowing the drag to go toward zero and the lift coefficient toward 2πα over a wide range of angles of attack (α≤20°) even in the separated flow regime. It is shown that moving boundary conditions are effective over a wide range of their strengths with respect to the overall power required (required to overcome aerodynamic drag and move the airfoil boundary). This power is shown to attain a minimum near the inviscid flow moving boundary condition, which is around 10% or less of the power required for the stationary boundary condition. Finally, the effectiveness of the moving boundary conditions is demonstrated for fully turbulent flow regimes at Re=6 million as well.

SIMULATION OF DYNAMIC PROCESSES IN A p - i - n DIODE BY THE METHODS OF PERTURBATION THEORY

In the paper a mathematical model of the dynamic process of the electron-hole plasma formation in the active region ( i - region) of a semiconductor p - i - n - diode in the direct bias mode with a harmonic signal fed on the diode is developed. The basis of the model is a nonlinear nonstationary sin- gularly perturbed boundary value problem for a system of continuity equations of electron-hole currents and Poisson's equation. The algorithm for searching the charge carrier concentration distributions and the potential distribution is based on the asymptotic method of boundary functions and the Fourier method. In the course of the research, a technique for decomposing a nonlinear problem based on the development of perturbation theory me- thods was proposed. The initial nonlinear problem is reduced to a recurrent sequence of linear stationary boundary value problems, solved by classical and partially original analytical-numerical methods. The identification of the boundary functions in the solution of the problem provides, in particular, in contrast to the classical approximation of ambipolar diffusion, an adequate description of the electric field strength behavior in the active region of p - i - n - diodes. The obtained research results shed light on the peculiarities of the formation of the impedance characteristics of p - i - n - structures. The results of the work reveal more deeply the nature of the physical processes in the studied technical system and are aimed at improving the methodology for modeling and designing control semiconductor devices.

A new born‐approximation approach to compute the effects of motion on the solution of electromagnetic problems involving moving materials with stationary boundaries

AbstractThe non‐relativistic motion of media induces very weak effects on electromagnetic fields. For this reason, it is extremely difficult to compute such effects with traditional techniques. To overcome this difficulty, a novel approach is introduced in this work. It is based on the Born approximation of the solution of electromagnetic problems involving media in motion. The formulation of these problems makes use of equivalent field sources and is specifically tailored to find the effects of motion on the electromagnetic field. The new methodology exploits traditional simulators able to deal with media at rest. The motion of the materials has to be managed by specific programs performing simple algebraic calculations. The simplest of the methods proposed does not present any additional complexity with respect to more traditional approaches to the same problems. All methods deal with time‐harmonic electromagnetic fields and, for this reason, they can manage materials in motion with stationary boundaries. A complete set of simulations for cylinders moving in the axial direction show that the new methods outperform traditional numerical approaches and, in some significant cases, traditional approaches based on semi‐analytical techniques. The good features of the new methodology are shown to hold true for a range of velocity values spanning 11 decades; such a range covers most of the applications of practical interest.

Effect of surface roughness on large-scale downburst-like impinging jets

Downbursts are cold descending winds that develop from thunderstorm clouds and, after impingement on the ground, produce an intense low-level horizontal front characterized by an axisymmetric toroidal vortex structure. Surface roughness is a key factor in the characterization of mean and turbulent wind speed features of synoptic-scale stationary atmospheric boundary layer winds. The goal of the present research is to physically assess whether the same can apply to the surface layer produced during thunderstorms, which are non-stationary, highly time-transient, and spatially limited phenomena. Downburst-like flows were produced through the impinging jet technique at the WindEEE Dome, at Western University in Canada. Three different surfaces were tested, and an equivalent full-scale roughness length (z0,eq) was determined. Experimental records are made publicly available. The large geometric and kinematic scales produced high Reynolds numbers, which enabled us to classify the flow as “fully turbulent” and therefore representative of full-scale downbursts. Results indicate a weak dependency on the Reynolds number, which suggests no relevant flaws in extending the results to the natural environment. The overall wind speed maxima weakly depend on z0, whereas a sharp velocity decrease is observed beyond the radial position of the maxima with increasing z0. Surface roughness enhances the boundary layer separation and consequently elevates the height of maximum wind speed above the surface. Vertical profiles of the horizontal velocity return a quite clear nose shape. Turbulence intensity shows a C-like shape with maxima in the near proximity of the ground that increase with z0.

PEGASUS Centrifugal Particle Receiver CentRec300S - Optimization, Manufacturing and Test

The centrifugal particle receiver (CentRec®) developed by DLR for high-temperature solar applications, previously tested on sun in a 500 kWth prototype at the solar tower in Jülich was further developed and tested at slightly smaller scale of 300 kWth. The test with artificial sunlight provided more stationary and controllable boundary conditions. Outlet temperature of 681 °C was reached at an irradiating input power of 214 kW. The performance was determined with particle mass flow and temperature measurement systems. The data confirms the thermodynamic model for this receiver, indicating an extrapolated performance of 81% at nominal conditions.

Physics-informed neural networks for incompressible flows with moving boundaries

Physics-informed neural networks (PINNs) employed in fluid mechanics deal primarily with stationary boundaries. This hinders the capability to address a wide range of flow problems involving moving bodies. To this end, we propose a novel extension, which enables PINNs to solve incompressible flows with time-dependent moving boundaries. More specifically, we impose Dirichlet constraints of velocity at the moving interfaces and define new loss functions for the corresponding training points. Moreover, we refine training points for flows around the moving boundaries for accuracy. This effectively enforces the no-slip condition of the moving boundaries. With an initial condition, the extended PINNs solve unsteady flow problems with time-dependent moving boundaries and still have the flexibility to leverage partial data to reconstruct the entire flow field. Therefore, the extended version inherits the amalgamation of both physics and data from the original PINNs. With a series of typical flow problems, we demonstrate the effectiveness and accuracy of the extended PINNs. The proposed concept allows for solving inverse problems as well, which calls for further investigations.

SELECTION OF A BOARD LOCATION FOR OIL COLLECTION IN THE EVENT OF A POSSIBLE ACCIDENT AT THE UNDERWATER OIL PIPELINE CROSSING

The article is devoted to the substantiation of technical solutions for choosing a stationary line for collecting oil for an underwater crossing of an operator of main oil pipelines in the Republic of Belarus. To study the landscape conditions of the territory selected as the proposed stationary boundary for the localization and collection of oil on the river, a tacheometric survey of the area was carried out. The result of geodetic and hydrometric works was a topographic plan of the area with plotted elevation lines of the relief section, including the bottom of the river, and hydroisotates of the watercourse flow velocities. The selected boundary provides optimal conditions for localizing a possible oil spill.

Erratum to: Stationary Boundary Problems of Coupled Thermoelasticity for a Half-Plane and Their Solution

Erratum to: Stationary Boundary Problems of Coupled Thermoelasticity for a Half-Plane and Their Solution

Cavity evolution of ventilated vehicle launch under a rolling condition

The unsteady development of the tail cavity of a vehicle after it leaves a tube often causes adverse effects, most notably an impact load on the vehicle when the cavity ruptures. The rolling of the launch platform can alter the development of the tail cavity, significantly altering the influence of the impact load on the motion and attitude of the vehicle. The present study employs the shear stress transport k-w model, the volume of fluid multiphase flow model, the Schnerr–Sauer cavity model, and the overlapping mesh technique to conduct numerical simulations of the underwater launching process of a ventilated vehicle under both stationary and rolling boundaries. A comparative analysis is conducted to examine the evolution of the cavity shape, pressure distribution, and collapse-induced load in the tail cavity under various conditions after vehicle launch. The findings suggest that the rolling of the tube induces an asymmetrical development of the shoulder cavity lengths and widths on both the windward and leeward sides, with the result of a lower peak pressure at the cavity closure position compared with that under stationary conditions. The rolling of the tube reduces the internal velocity within the tail cavity, elevates the rupture position of the tail cavity, delays the tail cavity rupture, impacts the timing of the force peak occurrence in the vertical direction of the vehicle, reduces the high pressure at the point of tail cavity rupture, and modifies the post-rupture structural characteristics of the tail cavity.

MATHEMATICAL MODELING OF DIFFUSION BOUNDARY PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS USING MATLAB AND C++ FOR NUMERICAL AND ANALYTICAL SOLUTIONS

The article examines a second-order parabolic partial differential equation of a three-dimensional (3D) non-stationary boundary problem with constant diffusion coefficients and periodic boundary conditions in the x and y directions. The method for reducing the (3D) non-stationary boundary problem to the corresponding one-dimensional (1D) non-stationary boundary problem using periodic boundary conditions in the x and y directions is discussed. The stationary (analytical) solution of the obtained (1D) stationary boundary problem is also obtained. The numerical solutions of the 1D boundary problem are obtained using the Matlab package "pdepe" and the C++ programming language. As a practical application of the developed mathematical model, the article discusses calculating the concentration of heavy metal Ca in a peat layer based on the obtained experimental data (measurements).

Two-phase kinematic evolution of the Qilian Shan, northern Tibetan Plateau: Initial Eocene−Oligocene deformation that accelerated in the mid-Miocene

The Cenozoic growth of the Tibetan Plateau and the distribution of deformation across it are a consequence of India-Asia collision and continued convergence, which have implications for studies of continental tectonics. The spatio-temporal development of Cenozoic deformation along the northern margin of the plateau is an important issue that can be better understood by testing various models of plateau growth. The northern Tibetan Plateau is bounded by the Cenozoic Qilian Shan thrust belt and the Haiyuan left-slip fault. We conducted geologic mapping, field observations, electron spin resonance (ESR) dating, and apatite (U-Th)/He (AHe) and apatite fission-track (AFT) analysis in the Qilian Shan thrust belt to improve our understanding of the timing of brittle faulting and range exhumation in the northern Tibetan Plateau. We document the first direct age constraints for Oligocene deformation within the central Qilian Shan via ESR dating, which correlates with AHe-AFT cooling ages in adjacent ranges. We demonstrate that the Qilian Shan thrust belt experienced a two-phase growth history, including Eocene−Oligocene fault-related uplift shortly after the India-Asia convergence, and mid-Miocene regional overprinting deformation that reactivated the proximal thrust faults. This deformational pattern suggests that the Qilian Shan thrust belt has experienced out-of-sequence development since the Eocene−Oligocene and has persisted as the stationary northeastern boundary of the Himalayan-Tibetan Orogen throughout the Cenozoic. The Paleozoic Qilian suture systems acted as a pre-existing weakness and played a decisive role in controlling the lithospheric rheology, which therefore impacted the timing, pattern, and strain distribution of Cenozoic deformation across the northern Tibetan Plateau.

Long-lived Cenozoic positive relief of the south-Eastern Tian Shan: Insights from provenance analyses of the northwestern Kuqa Depression sediments

The Eastern Tian Shan, one of the most active intracontinental orogenic belts, should bear important information on the mechanisms of intracontinental mountain building. In this study, detrital zircon U-Pb geochronological analysis of the Cenozoic Tiereke section succession in the northern Tarim Basin-Eastern Tian Shan convergence zone, combined with stratigraphic results, reveals the provenance histories of the Cenozoic sediments in the northwestern Kuqa Depression of northern Tarim Basin. Nine Cenozoic samples obtained from the strata of the Kumugeliemu Group to the lowest Kangcun Formation of the Tiereke section exhibit high resemblance to provenances of the south-Eastern Tian Shan, indicating existence of a prolonged eroding relief within this mountain since the early Cenozoic (∼54 Ma). This prolonged state of eroding relief requires continuous intracontinental deformation of the Eastern Tian Shan to sustain a provenance region, implying immediate deformation responding to the initial Indian-Eurasian collision. Furthermore, the south-Eastern Tian Shan served as the only source region for the northwestern Kuqa Depression of northern Tarim Basin, demonstrating that the upper-crustal boundary between the south-Eastern Tian Shan and the northern Tarim Basin was possibly stationary during most of the Cenozoic Era (∼54 Ma to ∼9.7 Ma). Such a stationary basin-orogenic boundary would favor the predictions of the pure-shear-like thickening model for the intracontinental mountain building during this period. We suggest that the long-lived mountain building of the Eastern Tian Shan may be due to its small convergence rate.

Stationary Boundary Problems of Coupled Thermoelasticity for a Half-Plane and Their Solution

Stationary Boundary Problems of Coupled Thermoelasticity for a Half-Plane and Their Solution