Boundary Conditions Research Articles

Contribution of wall-attached momentum transfer structures to the skin friction in slip channel flows

Reducing the skin-friction drag in wall turbulence is crucial for minimizing energy consumption in various industrial applications. Although numerous studies have proposed strategies for skin-friction reduction, their effectiveness generally degrades at high Reynolds numbers (Re) owing to the multiscale nature of wall turbulence. To address this challenge, it is necessary to understand coherent structures that span a wider range at high Re, particularly those that extend down to the wall. Hence, we explore wall-attached momentum transfer structures in drag-reduced flows and investigate the associated Re effects on the skin-friction reduction. We perform direct numerical simulations of drag-reduced flows at two bulk Re of 10,000 and 20,000 by employing the Navier slip boundary condition. For comparison, we conduct no-slip cases at the same bulk Re. We extract clusters of intense ejections and sweeps responsible for momentum transfer in instantaneous flow fields. We observe that wall-attached momentum transfer structures play a dominant role in the turbulent skin friction quantified through the FIK identity (Fukagata et al., 2002). These structures are classified into buffer-layer, self-similar, and non-self-similar ones according to their height. The self-similar structures not only exhibit geometrical self-similarity but also maintain their Reynolds shear stress distribution relative to the local Reynolds shear stress under slip conditions. Moreover, these self-similar structures show nearly identical skin-friction reduction across all heights. In contrast, the non-self-similar structures exhibit a significant difference under slip conditions, especially at a high Re. The reduced area fraction and volume of non-self-similar structures, along with decreased wall-normal transport under slip conditions, result in a greater skin-friction reduction compared to that observed at the low Re. Our findings advance the understanding of the scale-dependent behavior of wall-attached structures in drag-reduced flows, paving the way for the development of new drag-reduction methods through the strategic manipulation of these structures.

Stability and related zero viscosity limit of steady plane Poiseuille-Couette flows with no-slip boundary condition

We study the existence and stability of smooth solutions to the steady Navier-Stokes equations near plane Poiseuille-Couette flow in the absence of any external force in two-dimensional domain Ω=(0,L)×(0,2). Under the assumption 0<L≪1, we prove that there exist smooth solutions to the steady Navier-Stokes equations which are stable under infinitesimal perturbations of plane Poiseuille-Couette flow. In particular, if the basic flow is the Couette flow, then through a formal asymptotic expansion including the Euler correctors and weak boundary layer correctors with different scales near the rigid walls y=0 and y=2, we can prove that for any finite disturbance o(1) of the Couette flow in horizontal direction, there still exist stable smooth solutions to the steady Navier-Stokes equations. Finally, based on the same linear estimates, we establish the zero viscosity limit of the solutions obtained above to the solutions of the steady Euler equations.

Carroll dilaton supergravity in two dimensions

We construct and discuss generic N = 1 and N = 2 Carroll dilaton supergravity in two dimensions. We apply our general results to the supersymmetric Carroll-Jackiw-Teitelboim model, including a discussion of specific boundary conditions. For N = 2 Carroll dilaton supergravity, we find two versions, dubbed “democratic” and “despotic”.

INFLUENCE OF DIFFERENT FACTORS ON THE STABILITY BY ROLLING PROCESS IN THE WIRE BLOCK

One of the leading trends in the development of modern metallurgical manufacturing is the improvement of wire rod production using wire blocks. For existing continuous rolling mills, it is important to maximize the use of equipment capabilities both to improve the quality of products and to reduce the loss of metal and other resources for the adjustment and realize of technological modes at production. Effective technical solutions require scientific justification based on research results. To assess the boundary conditions of the stable rolling process, the average integral of the longitudinal forces at the plastically deformed metal is used. In physical terms, the vector of this force, which opposes the movement of the metal, cannot be directed along the motion of the sample, so the values of the force itself cannot be positive. The assessment of the longitudinal stability of the strip in the rolls (the possibility of a stable rolling process) is as follows: the process is implemented at negative values of the force value, zero value is the limit, at positive values the process is impossible. Analysis of the deformation process in the wire block of rolling mill 200 proved that the specific stresses in the stands should be insignificant because the resource of the forces that draw the metal into the rolls is limited. A more significant influence on the longitudinal stability of the process is the back tension. To ensure the stability of the process, especially in the first passes, the grip angle must be close in value to the coefficient of friction. With an increase in the coefficient of friction, the rolling of wire rod in the wire block becomes more stable. The results of the research show that in the case of external actions on the object, it is theoretically possible to find the limits of self-regulation for the rolling process in a wire block.Whenimplemented, thetechnique makes it possible to assess the limits of self-regulation not only by changes in the size of the workpiece, but by the amount of gauges wear in the rolls, in accordance with changes in friction conditions, temperature of the strip and other parameters.

Static and dynamic responses of point-fixing laminated glass plates under out-of-plane loading

In canopy and façade panel applications where glass elements are utilized, support is typically provided through small point-fixed steel hinges, which can enhance transparency but introduce notable structural challenges. To ensure structural integrity over time, the design of these systems must be supported by experimental evidence or its response monitored during its lifetime. A common approach involves continuous structural monitoring via accelerometers, which theoretically enables the detection of stiffness variations, indicative of potential damage, within the monitored components.The paper examines the static and dynamic responses of point-fixed, two-ply laminated glass panels, both heat-strengthened and thermally toughened (tempered), to assess their elastic and post-breakage behavior. Experimental data are compared directly with results from numerical simulations. The findings demonstrate that: (i) conventional monitoring systems for damage detection in glass panels are effective only with thermally toughened glass; (ii) point-fixed boundary conditions represent the most structurally disadvantageous support configuration; (iii) simplified numerical models offer a preliminary but informative framework for understanding the post-breakage response of glass panels.

Thermoelastic damping in bi-layered micro/nanobeam resonators using the dual-phase-lag generalized heat conduction model

The existing analytical investigations on thermoelastic damping (TED) in laminated micro/nanobeam resonators have generally neglected the thermal axial force and rarely considered the time lagging in the heat transfer. However, laminated beams will very likely exhibit stretching-bending coupling deformation due to the deviation of the physical neutral surface from the beam mid-surface. Furthermore, the TED in layered beams has been predicted by using the energy rather than the complex frequency approach. In this presentation, TED in bi-layered micro/nanobeams is analyzed based on the Euler-Bernoulli beam theory and the dual-phase-lag (DPL) generalized heat conduction theory by considering the thermal axial force. Analytical solutions for the TED in bi-layered micro/nanobeams are developed by using both the complex frequency approach and the energy method. Numerical results are presented to examine the effects of the thermal axial force and DPL relaxation times on the TED in the laminated beam resonators for different physical and geometrical parameters, vibration modes and mechanical boundary conditions, which reveal that the thermal axial force will increase (decrease) the TED in metal/ceramic (ceramic/ceramic, metal/metal) bi-layered beams. The maximum underestimation for the TED due to neglecting the thermal axial force will reach about 7 % in Ag/Si beam and 15 % in Cu/Si3N4 beam. The DPL effect on the TED is closely related to the material properties of the laminas and their volume fractions. For the Ag/Si beam with the thickness less than 1nm, influence of the DPL relaxation on the TED becomes significant which changes continuously from the negative contribution to the positive one with the increase in the volume fraction of the Si from 0 to 1. However, the DPL effect can be ignored in the bi-layered beams with micrometer size.

Complexity and isotropization based extended models in the context of electromagnetic field: an implication of minimal gravitational decoupling

This paper formulates three different analytical solutions to the gravitational field equations in the framework of Rastall theory by taking into account the gravitational decoupling approach. For this, the anisotropic spherical interior fluid distribution is assumed as a seed source characterized by the corresponding Lagrangian. The field equations are then modified by introducing an additional source which is gravitationally coupled with the former fluid setup. Since this approach makes the Rastall equations more complex, the MGD scheme is used to tackle this, dividing these equations into two systems. Some particular ansatz are taken into account to solve the first system, describing initial anisotropic fluid. These metric potentials contain multiple constants which are determined with the help of boundary conditions. On the other hand, the solution for the second set is calculated through different well-known constraints. Afterwards, the estimated data of a pulsar 4U 1820-30 is considered so that the feasibility of the developed models can be checked graphically. It is concluded that all resulting models show physically acceptable behavior under certain choices of Rastall and decoupling parameters.

Evaluation of Bonding Strength of Pipeline Coating Based on Circumferential Guided Waves

The anti-corrosion layer of the pipe provides corrosion resistance and extends the lifespan of the whole pipeline. Heat-shrinkable tape is primarily used as the pipeline joint coating material bonded to the pipeline weld connection position after heating. Delineating the bonding strength and assessing the quality of the bonded structure is crucial for pipeline safety. A detection technology based on nonlinear ultrasound is presented to quantitatively evaluate the bonding strength of a steel-EVA-polyethylene three-layer annulus bonding structure. Using the Floquet boundary condition, the dispersion curves of phase velocity and group velocity for a three-layer annulus bonding structure are obtained. Additionally, wave structure analysis is employed in theoretical study to choose guided wave modes that are appropriate for detection. In this paper, guided wave amplitude, frequency attenuation, and nonlinear harmonics are used to evaluate the structural bonding strength. The results reveal that the detection method based on amplitude and frequency attenuation can be used to preliminarily screen the poor bonding, while the acoustic nonlinear coefficient is sensitive to bonding strength changes. This study introduces a comprehensive and precise pipeline joint bonding strength detection system leveraging ultrasonic-guided wave technology for pipeline coating applications. The detection system determines the bonding strength of bonded structures with greater precision than conventional ultrasonic inspection methods.

Chebyshev Polynomials in the Physics of the One-Dimensional Finite-Size Ising Model: An Alternative View and Some New Results

For studying the finite-size behavior of the Ising model under different boundary conditions, we propose an alternative to the standard transfer matrix technique approach based on Abelès theorem and Chebyshev polynomials. Using it, one can easily reproduce the known results for periodic boundary conditions concerning the Lee–Yang zeros, the exact position-space renormalization-group transformation, etc., and can extend them by deriving new results for antiperiodic boundary conditions. Note that in the latter case, one has a nontrivial order parameter profile, which we also calculate, where the average value of a given spin depends on the distance from the seam with the opposite bond in the system. It is interesting to note that under both boundary conditions, the one-dimensional case exhibits Schottky anomaly.

How can microfinance institutions successfully navigate a competitive advantage and financial performance? Exploring the role of ambidextrous leadership and intellectual capital

The main objective of this study was to investigate how ambidextrous leadership contributes to competitive advantage and financial performance in Indonesia's microfinance institutions (MFIs). A secondary aim was to analyze the moderating effect of intellectual capital on the relationship between ambidextrous leadership and competitive advantage and the mediating role of competitive advantage in the indirect link between ambidextrous leadership and financial performance. Data were collected from 88 firms in the MFI sector through purposive sampling. The Moderation-Mediation (MODMED) procedure was used to assess four proposed relationships. The results indicated that ambidextrous leadership is crucial for achieving competitive advantage, with intellectual capital as a moderator in this relationship. Furthermore, competitive advantage was found to significantly explain financial performance and serve as an intermediary in the connection between ambidextrous leadership and financial performance. This study addresses the existing literature gap by examining ambidextrous leadership's influence on competitive advantage. It also introduces a fresh perspective by suggesting that intellectual capital acts as a boundary condition in the link between ambidextrous leadership and competitive advantage. The findings offer pragmatic insights for organizations, particularly MFIs in Indonesia, to enhance their competitive advantage through effective leadership and strategic management of intellectual resources.

Li diffusion in plagioclase crystals and glasses – implications for timescales of geological processes

Abstract. The growing interest in Li diffusion as a tool to determine timescales of short-time magmatic events, such as magma ascent during eruption, increases the necessity to better understand Li diffusion in common mineral phases. In this context, well-constrained diffusion coefficients and understanding of kinetic processes specific to mineral phases are of crucial importance. To gain further insight especially into the kinetic processes in plagioclase, we investigated the diffusion of Li between natural An61 plagioclase crystals and synthetic glasses of An80 plagioclase composition. Experiments were conducted at 200 MPa in rapid-heat/rapid-quench cold-seal pressure vessels (RH/RQ CSPVs) and internally heated pressure vessels (IHPVs) at temperatures between 606 and 1114 °C. Concentration and isotope profiles of Li were measured using femtosecond laser ablation multicollector inductively coupled plasma mass spectrometry (fs-LA-MC-ICP-MS). We adopted a multispecies diffusion model and specified boundary conditions for plagioclase of labradoritic composition. Using this model, we were able to distinguish between an interstitial (DLii) and a vacancy process (DLiA), with the interstitial process being 0.2–1 orders of magnitude faster than the vacancy process, depending on temperature. DLii=10-3.76±0.58exp⁡-180.0±12.0kJmol-1RTm2s-1DLiA=10-5.53±0.16exp⁡-151.7±3.2kJmol-1RTm2s-1 Our data indicate charge compensation of Li by Na in both the crystal and the glass. Chemical Li diffusion coefficients in An80 glass are up to 3 orders of magnitude slower compared to Li tracer diffusion in silicate and aluminosilicate glasses and melts, which is attributed to slow Na diffusion at high An content. Our results for chemical diffusion of Li in plagioclase crystals are 1.5–2 orders of magnitude slower than Li tracer diffusion in An- and Ab-rich plagioclase determined in previous studies. This indicates that earlier studies on natural intermediate plagioclase compositions have underestimated timescales by up to 2 orders of magnitude. For accurate determination of timescales from Li diffusion in plagioclase we suggest further exploring the role of Na and a possible dependence on An content.

Reference map technique for Lagrangian exploration of coherent structures

We explore the application of the reference map technique, originally developed for Eulerian simulation of solid mechanics, in Lagrangian kinematics of turbulent flows. Unlike traditional methods based on explicit particle tracking, the reference map facilitates the calculation of flow maps and gradients without the need for particles. This is achieved through an Eulerian update of the reference map, which records the take-off positions of fluid particles. This approach is found to be mathematically equivalent to the work of Leung (J. Comput. Phys., vol. 230, issue 9, 2011, pp. 3500–3524), who computed the flow map of simple two-dimensional flows using an Eulerian approach. We discuss important modifications necessary for its first application to complex three-dimensional turbulent flows, including the conservative, low-dissipation update of the flow map and the treatment of periodic boundary conditions. We first demonstrate the accuracy of finite-time Lyapunov exponent (FTLE) calculations based on the reference map against the standard particle-based approach in a two-dimensional Taylor–Green vortex. Then we apply it to turbulent channel flow at $Re_\tau =180$ , where Lagrangian coherent structures identified as ridges of the backward-time FTLE are found to bound vortical regions of flow, consistent with Eulerian coherent structures from the $Q$ -criterion. The reference map also proves suitable for material surface tracking despite not explicitly tracking particles. This capability can provide valuable insights into the Lagrangian landscape of turbulent momentum transport, complementing Eulerian velocity field analysis. The evolution of initially wall-normal material surfaces in the viscous sublayer, buffer layer and log layer sheds light on the Reynolds stress-generating events from a Lagrangian perspective.

Stabilization of a weak viscoelastic wave equation in Riemannian geometric setting with an interior delay under nonlinear boundary dissipation

The stabilization of a weak viscoelastic wave equation with variable coefficients in the principal part of elliptic operator and an interior delay is considered. The dynamics is subject to a nonlinear boundary dissipation. This leads to a non-dissipative dynamics. The existence of solution is demonstrated by means of Faedo–Galerkin method combined with monotone operator theory in handling nonlinear boundary conditions. The main result pertains to exponential decay rates for energy, which depend on the geometry of the spatial domain, viscoelastic effects, the strength of delay and the strength of mechanical boundary damping. An important feature of the model is the fact that the delay term and stabilizing mechanism are not collocated geometrically — in contrast with many other works on the subject. This aspect of the problem requires the appropriate tools in order to exhibit propagation of the dissipation from one location to another. The precise ranges of admissible parameters characterizing the model and ensuring the stability are provided. The methods of proofs are routed in Riemannian geometry.

Polynomial stability of a Kirchhoff plate equation in the presence of a frictional damping, a fractional time delay, and a source term

We investigate the asymptotic behavior of a Kirchhoff plate equation with free boundary conditions in a bounded domain of R2. The model involves frictional internal damping, a time delay condition of fractional type and a source term. We derive a polynomial decay estimate for the associated semigroup by using the frequency domain method.

Combustion and Emission Characteristics of Methanol–Diesel Dual Fuel Engine at Different Altitudes

Currently, in the two technological approaches for using diesel pilot injection to ignite methanol and partially substituting diesel fuel with methanol, neither can fully achieve carbon neutrality in the context of internal combustion engines. Compression-ignition direct-injection methanol marine engines exhibit significant application potential because of their superior fuel economy and lower carbon emissions. However, the low cetane number of methanol, coupled with its high ignition temperature and latent heat of vaporization, poses challenges, especially amidst increasingly stringent marine emission regulations. It is imperative to comprehensively explore the impacts of the engine geometry, intake boundary conditions, and injection strategies on the engine performance. This paper first investigates the influence of the compression ratio on the engine performance, subsequently analyzes the effects of intake conditions on methanol ignition characteristics, and finally compares the combustion characteristics of the engine under different fuel injection timings. When the compression ratio is set at 13.5, only an injection timing of −30 °CA can initiate methanol compression ignition, but the combustion is not ideal. For compression ratios of 15.5 and 17.5, all the injection timings studied can ignite methanol. Reasonable increases in the intake pressure and intake temperature are beneficial for methanol compression ignition. However, when the intake temperature rises from 400 K to 500 K, a decrease in the thermal efficiency is observed. Particularly, at an injection timing of −30 °CA, both the peak cylinder pressure and peak cylinder temperature are higher, the ignition occurs earlier, the combustion process shifts forward, and the combustion efficiency and indicated thermal efficiency are at higher levels. Furthermore, the overall emissions of NOX, HC, and CO are relatively low. Therefore, selecting an appropriate injection timing is crucial to facilitate the compression ignition and combustion of methanol under low-load conditions.

Dispersion analysis of grounded dielectric slab coated with double positive (DPS) / double negative (DNG) material

The present work investigates the dispersion characteristics both for TM and TE modes in a grounded dielectric slab coated with double positive (DPS) material and double negative (DNG) material. The outermost dielectric layer is assumed to be free space. By employing proper boundary conditions at interfaces, dispersion relations for the aforementioned structure for both TM and TE modes are derived. Additionally, surface waves at the interface of free space and DPS/DNG coating are investigated. Existence of mode degeneracy for DNG/DPS combination has been discussed based on dispersion analysis.

The Response of Tropopause-Overshooting Convection over North America to Climate Change

Abstract Recent field campaigns, observational studies, and modeling work have demonstrated that extratropical tropopause-overshooting convection has a substantial and previously underestimated impact on stratospheric water vapor concentrations. This necessitates improved understanding of how tropopause-overshooting convection will respond to a warming climate. A growing body of research indicates that environments conducive to severe thunderstorms will occur more often and be increasingly unstable in the future, but no study has examined how this may be related to increased overshooting. To rectify this, this study leverages an existing pseudo–global warming (PGW) experiment to evaluate potential future changes in tropopause-overshooting convection over North America. We examine two 10-yr simulations consisting of 1) a retrospective period (2003–12) forced by ERA-Interim initial and boundary conditions (the control simulation) and 2) the same retrospective period with CMIP5 ensemble-mean high-end emission scenario climate changes added to the initial and boundary conditions (the PGW simulation). Tropopause-overshooting convection in the control simulation is validated against observed overshoots from both ground-based radar observations in the United States and GOES observations over North America. The model is shown to effectively simulate the observed regional distribution, annual cycle, and diurnal cycle of tropopause-overshooting convection. In the PGW simulation, tropopause-overshooting convection is found to increase more than 250% across the model domain, and the projected seasonal period of frequent tropopause-overshooting convection is shown to extend into late summer. Additionally, tropopause-overshooting convection with extreme tropopause-relative heights (&gt;4 km) is more frequent in a warmed climate scenario.

Magnetohydrodynamics of couple stress Casson fluid flow in a channel with stretching wall in the presence of dissipative and radiative heat transfer

AbstractThis paper investigates the unsteady magnetohydrodynamic flow of a couple stress Casson fluid between two parallel sheets where the heat transfer mechanism is incorporated with the influences of heat radiation, viscous dissipation, and Joule heating. The fluid flow is induced due to bi‐directional stretching of the lower sheet of the channel. The mathematical model of the physical problem is governed by highly nonlinear coupled partial differential equations with boundary conditions that are then transformed into highly nonlinear ordinary differential equations with boundary conditions using well‐defined similarity variables. The authors have used the well‐known computational technique called the spectral successive linearization method (SLM) to solve the obtained ordinary differential equations subject to the boundary conditions. Graphs and tables show the effects of non‐dimensional parameters on the important physical quantities such as the velocity and temperature profiles, and coefficients of skin‐frictions and heat transfer. The quadratic regression method is used to perform statistical analysis of Nusselt number and skin friction coefficients. The present investigation has significant applications in different problems of biomedical engineering, clinical sciences, industrial manufacturing processes, and so forth.

Thermocapillary stability of a viscoelastic liquid film falling down above or below an inclined thick wall with slip

Background:Thin viscoelastic liquid films falling down walls have been investigated theoretically since many years ago due to their applications in coating and cooling of substrates. They may also be subjected to temperature gradients and have been investigated under a variety of boundary conditions. In particular, the Navier slip boundary condition has been the subject of recent research. This condition is used when at the interface between the liquid and the wall the no-slip boundary condition does not apply due to different reasons like wall small topography, chemical coatings, etc. Methods:The small wavenumber approximation is used to derive a nonlinear evolution equation to describe the free surface deformations of the viscoelastic liquid film falling down an inclined wall. This equation is linearized and its linear stability is investigated using normal modes. The nonlinear free surface deformations are calculated numerically by means of a normal modes expansion substituted into the nonlinear evolution equation. Significant Findings:The thermocapillary stability of a thin viscoelastic film falling down a thick wall of finite thermal conductivity is investigated. Linear and nonlinear flows are examined when the interface of the liquid and the wall presents slip effects. The stability of the flow above and below (Rayleigh–Taylor) the wall is also explored. The lubrication approximation is used to derive a nonlinear evolution equation for the free surface deformation. The curves of linear growth rate, maximum growth rate and critical Marangoni number are calculated for different viscoelastic Deborah numbers. The film will be subjected to destabilizing and stabilizing Marangoni numbers. It is found that from the point of view of the linear growth rate the flow destabilizes with slip in a wavenumber range k<k+. However slip stabilizes for larger wavenumbers k>k+ up to the critical (cutoff) wavenumber. The results show that the Deborah number displaces k+ to the right. When k+ reaches the critical wavenumber by an increase of the Deborah number, slip is unable to stabilize. The corresponding critical Deborah number is derived. On the contrary, when the Deborah number is zero these slip stabilizing regions k>k+ correspond to Newtonian fluids investigated in previous works. From the point of view of the maximum growth rate slip may stabilize or destabilize increasing the slip parameter depending on the magnitude of the Marangoni, Galilei and Deborah numbers. Explicit formulas were derived for the intersections where slip may change its stability properties. Numerical solutions of the free surface nonlinear evolution equation show that slip can decrease the amplitude and may stimulate the appearance of subharmonics. The effects of different wall properties are also investigated.

Boundary element method for hypersingular integral equations: Implementation and applications in potential theory

The main objective of this paper is to develop effective numerical methods to solve hypersingular integral equations arising in various physical and mechanical applications. Both surface and contour integrals are considered. The novelty of the proposed approach lies in the exact formulas obtained for an arbitrary planar polygon in hypersingular integral estimations. A one-dimensional hypersingular integral equation is derived for axially symmetrical configurations, and analytical formulas are established for calculating the hypersingular parts. It is proved that the hypersingular component of the surface integral is equal to its hypersingular component along the tangent plane. These exact formulas enable the development of an effective numerical method based on boundary element implementation. Benchmark tests are considered, and the convergence of the proposed methods is demonstrated. Problems in crack analysis are formulated and solved using both surface and contour hypersingular integral equations. A comparison of the results is made between boundary element methods and finite element methods for penny-shaped cracks. Boundary value problems in fluid-structure interaction are considered, and numerical simulations are performed. An estimation of modes and frequencies of panel and blade vibrations when interacting with liquids is carried out.