Conventional Boundary Conditions Research Articles

Near-wall turbulence alteration with the transpiration-resistance model

A set of boundary conditions called the transpiration-resistance model (TRM) is investigated in altering near-wall turbulence. The TRM was proposed by Lacis et al. (J. Fluid Mech., vol. 884, 2020, p. A21) as a means of representing the net effect of surface micro-textures on their overlying bulk flows. It encompasses conventional Navier-slip boundary conditions relating the streamwise and spanwise velocities to their respective shears through the slip lengths $\ell _x$ and $\ell _z$ . In addition, it features a transpiration condition accounting for the changes induced in the wall-normal velocity by expressing it in terms of variations of the wall-parallel velocity shears through the transpiration lengths $m_x$ and $m_z$ . Greater levels of drag increase occur when more transpiration takes place at the boundary plane, with turbulent transpiration being predominately coupled to the spanwise shear component for canonical near-wall turbulence. The TRM reproduces the effect of a homogeneous and structured roughness up to $k^{+}\approx 18$ , encompassing the regime of smooth-wall-like turbulence described using virtual origins (Luchini, 1996 Reducing the turbulent skin friction. In Computational Methods in Applied Sciences’ 96 (Paris, 9–13 Sept. 1996), pp. 465–470. Wiley; Ibrahim et al., J. Fluid Mech., vol. 915, 2021, p. A56) and slightly beyond it. The transpiration factor is defined as the product of the slip and transpiration lengths, i.e. $(m\ell )_{x,z}$ . This factor contains the compound effect of the wall-parallel velocity occurring at the boundary plane and increased permeability, both of which lead to the transport of momentum in the wall-normal direction. A linear relation between the transpiration factor and the roughness function is observed for regularly textured surfaces in the transitionally rough regime of turbulence. This shows that such effective flow quantities can be suitable measures for characterizing rough surfaces in this flow regime.

Development of a Phase-Field Method for Phase Change Simulations Using a Conservative Allen–Cahn Equation

Abstract Two-phase flows including a phase change such as liquid–vapor flows play an important role in many industrial applications. A deeper understanding of the phase change phenomena is required to improve performance and safety of nuclear power plants. For this purpose, we developed a phase change simulation method based on the phase-field method (PFM). Low computational efficiency of the conventional PFM based on the Cahn–Hilliard equation is an obstacle in practical simulations. To resolve this problem, we presented a new PFM based on the conservative Allen–Cahn equation including a phase change model. The wettability also needs to be considered in the phase change simulation. When we apply the conventional wetting boundary condition to the conservative Allen–Cahn equation, there is a problem that the mass of each phase is not conserved on the boundary. To resolve this issue, we developed the mass correction method which enables mass conservation in the wetting boundary. The proposed PFM was validated in benchmark problems. The results agreed well with the theoretical solution and other simulation results, and we confirmed that this PFM is applicable to the two-phase flow simulation including the phase change. We also investigated the computational efficiency of the PFM. In a comparison with the conventional PFM, we found that our proposed PFM was more than 100 times faster. Since computational efficiency is an important factor in practical simulations, the proposed PFM will be preferable in many industrial simulations.

Non-Hermitian pseudo mobility edge in a coupled chain system

In this work, we explore interesting consequences arising from the coupling between a clean non-Hermitian chain with skin localization and a delocalized chain of the same length under various boundary conditions (BCs). We reveal that in the ladder with weak rung coupling, the nonHermitian skin localization could induce a pseudo mobility edge in the complex energy plane, which separates states with extended and localized profiles yet allowing unidirectional transport of signals. We also demonstrate the gradual takeover of the non-Hermitian skin effect in the entire system with the increase of the rung coupling under conventional open BC. When taking open BC for the nonHermitian chain and periodic BC for the other, it is discovered that a quantized winding number defined under periodic BC could characterize the transition from the pseudo mobility edge to the trivial extended phases, establishing a "bulk-defect correspondence" in our quasi-1D non-Hermitian system. This work hence unveils more subtle properties of non-Hermitian skin effects and sheds light on the topological nature of the non-Hermitian localized modes in the proximity to systems with dissimilar localization properties.

Addressing Surface Effects at the Particle-Continuum Interface in a Molecular Dynamics and Finite Elements Coupled Multiscale Simulation Technique.

Atomistic-to-continuum coupling methods are used to unravel molecular mechanisms of polymers and polymer composites. These multiscale techniques advantageously combine the computational efficiency of continuum approaches while keeping the accuracy of particle-based methods. The Capriccio method [Pfaller et al. Comput. Methods Appl. Mech. Eng. 2013, 260, 109-129.] is a well-proven multiscale technique, which connects finite elements (FE) with molecular dynamics (MD) in a partitioned-domain approach. A vital aspect of these multiscale methods is to provide physically sound boundary conditions to the particle domain suppressing any interface effects at the domain boundary occurring due to the coupling. These interfacial coupling artifacts still pose a significant problem, especially for amorphous polymers due to their highly irregular microstructure. We solve this problem by extending the particle-continuum interface by a layer of passive atoms which move with the outer continuum, thereby providing the missing interactions with a surrounding polymer bulk to the inner particle region. This solution allows us to successfully reproduce structural and mechanical properties obtained under conventional periodic boundary conditions, like density, stress, Young's modulus, and Poisson's ratio. Furthermore, we demonstrate the application of a nonaffine deformation by means of a simple bending test. In general, our revised method provides a framework to apply complex deformations for molecular scientists, while it allows the engineering community to examine challenging phenomena such as fracture behavior at a molecular level.

Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization

This work aims to prove a Hardy-type inequality and a trace theorem for a class of function spaces on smooth domains with a nonlocal character. Functions in these spaces are allowed to be as rough as an [Formula: see text]-function inside the domain of definition but as smooth as a [Formula: see text]-function near the boundary. This feature is captured by a norm that is characterized by a nonlocal interaction kernel defined heterogeneously with a special localization feature on the boundary. Thus, the trace theorem we obtain here can be viewed as an improvement and refinement of the classical trace theorem for fractional Sobolev spaces [Formula: see text]. Similarly, the Hardy-type inequalities we establish for functions that vanish on the boundary show that functions in this generalized space have the same decay rate to the boundary as functions in the smaller space [Formula: see text]. The results we prove extend existing results shown in the Hilbert space setting with p = 2. A Poincaré-type inequality we establish for the function space under consideration together with the new trace theorem allows formulating and proving well-posedness of a nonlinear nonlocal variational problem with conventional local boundary condition.

Effect of slip boundary condition and non-newtonian rheology of lubricants on the dynamic characteristics of finite hydrodynamic journal bearing

In the present study, the influence of various slip zone locations on the dynamic stability of finite hydrodynamic journal bearing lubricated with non-Newtonian and Newtonian lubricants has been investigated. Linearized equation of motion with free vibration of rigid rotor has been used to find the optimum location of the slip region with maximum stability margin limit. It has been observed that bearing with interface of slip and no-slip region near the upstream side of minimum film-thickness location is effective in improving the direct and cross stiffness coefficient, critical mass parameter, and critical whirling speed. The magnitude of dynamic performance parameters with slip effect is highly dependent on the rheology of lubricant. Shear-thinning lubricants combined with slip boundary condition shows higher dynamic stability as compared to the Newtonian lubricants under the conventional boundary condition. For all considered rheology of lubricants, the dynamic stability of bearing with slip effect is improving by increasing the eccentricity ratio.

Lubrication\u2013Contact Interface Conditions and Novel Mixed/Boundary Lubrication Modeling Methodology

Under severe conditions, solid contacts take place even when parts are lubricated. Precise mathematical conditions are needed to describe the interior interface between fluid lubrication and solid-contact zones. In order to distinguish the conditions for this interface from conventional lubrication boundary conditions, they are named lubrication–contact interface conditions (LCICs). In this work, mathematical LCICs are derived with local flow continuity from the continuum mechanics point of view and pressure inequality across the interface. Numerical implementations are developed and tested with problems having simple geometries and configurations, and they are integrated into a new mixed/boundary elastohydrodynamic lubrication solver that uses a new method to determine solid-contact pressures. This solver is capable of capturing film thickness and pressure behaviors involving solid contacts.

Development of a Phase-Field Method for Phase Change Simulations Using a Conservative Allen–Cahn Equation

Abstract Two-phase flows including a phase change such as liquid–vapor flows play an important role in many industrial applications. A deeper understanding of the phase change phenomena is required to improve the performance and safety of nuclear power plants. For this purpose, we developed a phase change simulation method based on the phase-field method (PFM). The low computational efficiency of the conventional PFM based on the Cahn–Hilliard equation is an obstacle in practical simulations. To resolve this problem, we presented a new PFM based on the conservative Allen–Cahn equation including a phase change model. The wettability also needs to be considered in the phase change simulation. When we apply the conventional wetting boundary condition to the conservative Allen–Cahn equation, there is a problem that the mass of each phase is not conserved on the boundary. To resolve this issue, we developed the mass correction method which enables mass conservation in the wetting boundary. The proposed PFM was validated in benchmark problems. The results agreed well with the theoretical solution and other simulation results, and we confirmed that this PFM is applicable to the two-phase flow simulation including the phase change. We also investigated the computational efficiency of the PFM. In a comparison with the conventional PFM, we found that our proposed PFM was more than 100 times faster. Since computational efficiency is an important factor in practical simulations, the proposed PFM will be preferable in many industrial simulations.

Diffusion of Lipid Nanovesicles Bound to a Lipid Membrane Is Associated with the Partial-Slip Boundary Condition.

During diffusion of nanoparticles bound to a cellular membrane by ligand–receptor pairs, the distance to the laterally mobile interface is sufficiently short for their motion to depend not only on the membrane-mediated diffusivity of the tethers but also in a not yet fully understood manner on nanoparticle size and interfacial hydrodynamics. By quantifying diffusivity, velocity, and size of individual membrane-bound liposomes subjected to a hydrodynamic shear flow, we have successfully separated the diffusivity contributions from particle size and number of tethers. The obtained diffusion-size relations for synthetic and extracellular lipid vesicles are not well-described by the conventional no-slip boundary condition, suggesting partial slip as well as a significant diffusivity dependence on the distance to the lipid bilayer. These insights, extending the understanding of diffusion of biological nanoparticles at lipid bilayers, are of relevance for processes such as cellular uptake of viruses and lipid nanoparticles or labeling of cell-membrane-residing molecules.

Unsteady squeezing flow of a magnetized nano-lubricant between parallel disks with Robin boundary conditions

The aim of the present work is to examine the impact of magnetized nanoparticles (NPs) in enhancement of heat transport in a tribological system subjected to convective type heating (Robin) boundary conditions. The regime examined comprises the squeezing transition of a magnetic (smart) Newtonian nano-lubricant between two analogous disks under an axial magnetism. The lower disk is permeable whereas the upper disk is solid. The mechanisms of haphazard motion of NPs and thermophoresis are simulated. The non-dimensional problem is solved numerically using a finite difference method in the MATLAB bvp4c solver based on Lobotto quadrature, to scrutinize the significance of thermophoresis parameter, squeezing number, Hartmann number, Prandtl number, and Brownian motion parameter on velocity, temperature, nanoparticle concentration, Nusselt number, factor of friction, and Sherwood number distributions. The obtained results for the friction factor are validated against previously published results. It is found that friction factor at the disk increases with intensity in applied magnetic field. The haphazard (Brownian) motion of nanoparticles causes an enhancement in thermal field. Suction and injection are found to induce different effects on transport characteristics depending on the specification of equal or unequal Biot numbers at the disks. The main quantitative outcome is that, unequal Biot numbers produce significant cooling of the regime for both cases of disk suction or injection, indicating that Robin boundary conditions yield substantial deviation from conventional thermal boundary conditions. Higher thermophoretic parameter also elevates temperatures in the regime. The nanoparticles concentration at the disk is boosted with higher values of Brownian motion parameter. The response of temperature is similar in both suction and injection cases; however, this tendency is quite opposite for nanoparticle concentrations. In the core zone, the resistive magnetic body force dominates and this manifests in a significant reduction in velocity, that is damping. The heat build-up in squeeze films (which can lead to corrosion and degradation of surfaces) can be successfully removed with magnetic nanoparticles leading to prolonged serviceability of lubrication systems and the need for less maintenance.

Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model

In the present paper, a refined trigonometric higher-order shear deformation theory has been presented with the conjunction of nonlocal theory for the vibrational response of functionally graded (FG) porous nanoplate. The displacement field is chosen based on assumptions that the out of the plane displacement consists of bending and shear components whereas the transverse shear-strain has nonlinear variation along the thickness direction. The number of unknown variables is four, as against five in other renowned shear deformation theories. The governing equations have been derived using Hamilton's principle. A generalized porosity model has also been developed to accommodate both even and uneven type of distribution of porosity in the FG nanoplates. The closed-form solution of simply-supported FG porous nanoplates is obtained and the results are compared with the available reported results. In finite element solution, a C0 continuous isoparametric quadrilateral element has been used with various conventional and unconventional boundary conditions. The effects of various parameters like small-scale effect, aspect ratio, volume fraction index, porosity volume fraction, and thickness ratio have been investigated. The significant influence of small-scale effects and porosity inclusions have been observed in the reported results. It has been reported that both closed-form and finite element solutions with the present theory can make accurate predictions of the free vibration response.

Thermal Analysis of Journal bearing with controlled slip/no-slip boundary condition and Non-Newtonian Rheology of lubricant

This paper discusses the combined effect of Non-Newtonian rheology of lubricants and slip boundary condition on the static performance characteristics of finite hydrodynamic journal bearings. A modified JFO model with an adiabatic energy equation has been used for calculating the variation of performance parameters. It has been observed that shear-thinning lubricant with slip effect on partial circumferential region shows a significant percentage of improvement in load-carrying capacity and coefficient of friction. Further, For eccentricity ratio of less than 0.2, these lubricants give maximum tribological performance as compared to Newtonian lubricants under conventional boundary condition.

Intra-pore tortuosity and diverging-converging pore geometry controls on flow enhancement due to liquid boundary slip

The liquid boundary slip, in contrast to the conventional no-slip boundary condition, exists due to a less wetting or the non-wetting nature of sediment grains, which can significantly control fluid hydraulics of porous media, specifically which consists of smaller pore-throats, e.g., siltstones and mudstones. Most studies to date presume a no-slip boundary condition and a few who have investigated the aspects of slip-boundary presume a simplified straight tube or a non-tortuous pore shape. Therefore, how the degree of tortuosity and pore-geometry control flow enhancement in porous media remains underexplored. In this computational study, we design a set of diverging-converging staggered tortuous (DCST) pores, which account for a variable amount of intra-pore tortuosity. To compare, a set of capillary pores are designed that can account for tortuosity by taking the form of sinusoidal and helical shapes. Our results quantify how the diverging-converging nature of pore geometry and its intra-pore tortuosity alone have a significant impact on modifying the microscopic flow behavior -accounting of which is a key in upscaling these effects to a macroscopic continuum or the Darcy-scale. We find, DCST pores contribute to an asymptotic flow enhancement behavior in response to boundary slip.In comparison, capillary pores lead to a linearly ‘unlimited’ flow enhancement. This unlimited nature of flow enhancement can lead to differences over several orders in magnitude. We test theoretical models to predict flow enhancement from all pores. We determine constitutive relations that can predict flow enhancement as a function of intra-pore tortuosity and hydraulic shape factor. We examine the physical mechanisms of energy dissipation and find that the microscopic fluid-structure interactions can contribute to significant variation in how intra-pore geometry and boundary slip manifest as the flow enhancement factor relevant to the continuum-scale. We find that the ‘asymptote’ in the flow enhancement factor of DCST pores manifests as a result of an equilibrium between energy dissipation and enhancing flow due to boundary slip, at least in the laminar flow regime.

Effect of slippery boundary on solute transport in rough-walled rock fractures under different flow regimes

Fundamental understanding of solute transport behaviors in rock fractures is of great importance to many hydrogeological processes. The fate of fluid-borne solutes is inherently linked to fluid flow process in rock fractures, which is usually theoretically and numerically analyzed under the assumption of classic no-slip boundary condition. However, fluid slippage at rock surfaces is possibly present in some geological environments, such as hydrophilicity change in rock surfaces exposed to organic substances, or the immobile wetting film covering rock surfaces. These situations would induce a non-zero velocity at the boundary walls for flowing fluid, i.e., fluid slippage, which leads to a violation of the no-slip assumption. Nonetheless, the effect of slippery boundary on fluid-borne solute transport is poorly understood for rock fractures. This study systematically investigated the slippery boundary effect on solute transport in rough-walled rock fractures under different flow regimes. A series of pore-scale simulation results showed that the slippery boundary has a profound influence on both microscale and macroscale solute transport behaviors in rock fractures. Such an influence became more significant with increasing hydraulic gradient, accompanied by the flow regime transitioning from Darcy to non-Darcian. For Darcy flow regime, the slippery boundary exerted its influence on solute transport by altering velocity distribution pattern in rock fracture; while for non-Darcian flow regime, the enlarged eddy volume and promoted mass transfer process by the slippery boundary profoundly affected solute transport behaviors. Further discussion indicated that the predictive models with parameters estimated from the conventional no-slip boundary condition cannot directly apply to the slip one. Moreover, the effect of slippery boundary would possibly have an impact on larger-scale fractured rock aquifers which requires further verification. The results and findings enrich the understanding of solute transport in fractured rocks where the slippery boundary is prevalently present, and contribute to developing predictive models for complex geological environments.

OpenMandible: An open-source framework for highly realistic numerical modelling of lower mandible physiology

ObjectiveComputer modeling of lower mandible physiology remains challenging because prescribing realistic material characteristics and boundary conditions from medical scans requires advanced equipment and skill sets. The objective of this study is to provide a framework that could reduce simplifications made and inconsistency (in terms of geometry, materials, and boundary conditions) among further studies on the topic. MethodsThe OpenMandible framework offers: 1) the first publicly available multiscale model of the mandible developed by combining cone beam computerized tomography (CBCT) and μCT imaging modalities, and 2) a C++ software tool for the generation of simulation-ready models (tet4 and hex8 elements). In addition to the application of conventional (Neumann and Dirichlet) boundary conditions, OpenMandible introduces a novel geodesic wave propagation - based approach for incorporating orthotropic micromechanical characteristics of cortical bone, and a unique algorithm for modeling muscles as uniformly directed vectors. The base intact model includes the mandible (spongy and compact bone), 14 teeth (comprising dentin, enamel, periodontal ligament, and pulp), simplified temporomandibular joints, and masticatory muscles (masseter, temporalis, medial, and lateral pterygoid). ResultsThe complete source code, executables, showcases, and sample data are freely available on the public repository: https://github.com/ArsoVukicevic/OpenMandible. It has been demonstrated that by slightly editing the baseline model, one can study different “virtual” treatments or diseases, including tooth restoration, placement of implants, mandible bone degradation, and others. SignificanceOpenMandible eases the community to undertake a broad range of studies on the topic, while increasing their consistency and reproducibility. At the same time, the needs for dedicated equipment and skills for developing realistic simulation models are significantly reduced.

Thermal conductivity of a thick 3D textile composite using an RVE model with specialized thermal periodic boundary conditions

Finite element analysis is performed to virtually measure homogenized thermal conductivity of a thick 3D woven textile composite (T3DWC). Temperature-dependent thermal and mechanical properties of constituents are considered for the measurements over a wide range of temperature. A two-step homogenization approach is adopted here to simplify the analysis at the microscopic level without losing heterogeneity of the material at the macroscopic scale. First-step homogenization is carried out at a tow level using an analytical homogenization scheme. Fiber tows are homogenized and assigned with effective elastic and thermal properties. The solid tows are then implemented into a representative volume element considering the unique in-plane periodic fiber architecture of the thick composite material. Due to the unique in-plane periodicity, conventional periodic boundary conditions for thermal and mechanical loading conditions are reformulated. Anisotropic thermal conductivity of T3DWC is obtained from the second-step homogenization based on virtual thermal tests performed at ambient to elevated temperatures.

On the far-field boundary condition treatment in the framework of aeromechanical computations using ANSYS CFX

This numerical study aims at predicting the reflective behavior of different conventional inlet and outlet far-field boundary conditions as well as available non-reflecting boundary conditions (NRBC) implemented in the commercial CFD solver ANSYS CFX. An isolated rotor model of an axial turbine stage with prescribed blade displacement is applied as test case to consider a representative application case, while at the same time provoke an unsteady flow field featuring pronounced flow perturbations in the far-field. Since the reflective behavior of the implemented boundary conditions was found inadequate in the given application case, a zonal treatment of the inlet and outlet far-field, based on a modification of the governing Navier-Stokes equations, is investigated. The applied approach has proven its capability to suppress spurious reflections reliably, while at the same time ensures a preservation of the reference flow conditions within the required domain extensions. The results of a case study considering calculation domains of different spatial extent and different treatments of their respective far-fields suggest variations in the steady flow aerodynamics to be of moderate influence on the predicted aerodynamic damping, while spurious reflections were found to falsify the unsteady aerodynamics considerably.

Analytical solution of deflection of multi-cracked beams on elastic foundations under arbitrary boundary conditions using a diffused stiffness reduction crack model

Crack can significantly affect the performance of structures and is one of the crucial indicators of damage in structural health monitoring. In this paper, the deflection behaviors of Euler–Bernoulli beams with arbitrary open edge cracks under arbitrary elastic boundary conditions are investigated. A continuous diffused stiffness reduction crack model is implemented to simulate the cracks in beams, which can incorporate multiple cracks and consider the stiffness reduction effect in the vicinity of a crack. With the proposed diffused stiffness reduction model, the fourth-order differential equation governing the deflection behavior of the multi-cracked Euler–Bernoulli beam is constructed. The powerful variational iteration method is applied to obtain the analytical solution of the multi-cracked beams on elastic foundations. Five shape functions are introduced, based on which the deflection of the multi-cracked beam is proposed. Both the solutions corresponding to the general elastic boundary conditions and the conventional boundary conditions are presented explicitly. The deflection solution is benchmarked and verified against the literature, and encouraging agreements are obtained. Parametric studies are carried out to investigate the influences of crack position, crack ratio, stiffness of the elastic foundation, and boundary conditions on the deflection of the cracked beams. The proposed crack model and the deflection solution overcome some of the limitations in the literature.

Propagation Operator Based Boundary Condition for Finite Element Analysis

A new efficient boundary condition of finite element method (FEM) by using propagation operator is proposed. In this method, input, and output ports are terminated on their own boundaries instead of using perfectly matched layer (PML) which requires expanding the computational window. Moreover, this boundary condition can consider all modes including radiation modes without mode expansion. The propagation operator is efficiently calculated by Denman-Beavers iteration (DBI). The electromagnetic field on the POM boundary can be accurately propagated outside the boundary by using the propagation operator. In addition, we present a technique based on scattering operator method which can reduce the computational complexity of FEM. Three numerical results show that the present scheme is more accurate, and stable than conventional approximate boundary conditions such as using Pade approximation in both TE, and TM modes.

Free Vibrations of Symmetric Arch: Boundary Conditions of Stress Resultants Revisited

This paper deals with analyzing free vibrations of the symmetric arch. The boundary conditions of the stress resultants are newly derived, which can be replaced by the conventional boundary conditions of the deflections. All solutions of the natural frequency with the mode shape, using the new boundary conditions, are the same as those of the conventional deflections. The boundary conditions mixed with new and conventional conditions act correctly to calculate natural frequencies. The mode shapes of the stress resultants using the new boundary conditions are reported in two types: symmetric and anti-symmetric modes.