Non-slip Boundary Condition Research Articles

Asymptotic stability of rarefaction wave with non-slip boundary condition for radiative Euler flows

This paper is devoted to studying the initial-boundary value problem for the radiative full Euler equations, which are a fundamental system in the radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena, with the non-slip boundary condition on an impermeable wall. Due to the difficulty from the disappearance of the velocity on the impermeable boundary, quite few results for compressible Navier-Stokes equations and no result for the radiative Euler equations are available at this moment. So the asymptotic stability of the rarefaction wave proven in this paper is the first rigorous result on the global stability of solutions of the radiative Euler equations with the non-slip boundary condition. It also contributes to our systematical study on the asymptotic behaviors of the rarefaction wave with the radiative effect and different boundary conditions such as the inflow/outflow problem and the impermeable boundary problem in our series papers including [5,6].

Global gradient estimates for shear thinning-type Stokes system on the non-smooth domains

In this paper, we present the global $L^q$ estimates for the weak solution of the steady p-Stokes equations describing the motion of the shear-thinning flow under the nonslip boundary condition. Our interest is a non-smooth domain whose boundary can go beyond the Lipschitz category, and the coefficients belong to BMO(Bounded Mean Oscillation) space with sufficiently small BMO semi-norm.

Long time existence of the non-isentropic slightly compressible Navier-Stokes equations with boundary conditions

We investigate the long time existence of smooth solutions to the initial boundary value problem for the non-isentropic slightly compressible Navier–Stokes equations with slip or non-slip boundary conditions on the velocity. We verify that the compressible Navier–Stokes equations with boundary conditions admit a unique smooth solution on the time interval where the smooth solution of the incompressible Navier–Stokes equations exists, when the Mach number is sufficiently small. Moreover, we obtain the uniform convergence of smooth solutions for the compressible system toward those for the corresponding incompressible system on that time interval.

Asymptotic analysis for the homogeneous model of wind‐driven oceanic circulation in the small viscosity limit

In this paper, we study the asymptotic expansion for the homogeneous model of wind‐driven oceanic circulation with the nonslip boundary condition when both of the beta‐plane parameter and the Reynolds number go to infinity. By asymptotic analysis under certain constraints on wind tensor, we derive a formal expansion including the geophysical boundary layer in the large beta‐plane parameter and high Reynolds number limit, from which one sees that the external force, wind tensor, has an important effect on the behavior of the boundary layers. Moreover, when the external force and initial data satisfy certain constraints, to exclude the appearance of strong boundary layers, we construct approximate solutions with steady boundary layers to the homogeneous model of wind‐driven oceanic circulation in the large beta‐plane parameter and high Reynolds number limit. By using an energy method, we obtain the ‐stability of small perturbation around this approximate solutions, which verifies the validity of the asymptotic expansion of weak boundary layers in the large beta‐plane parameter and high Reynolds number limit.

3D CFD-DEM study on fine particle migration in packed proppant layers

Fine particle migration is a crucial issue in hydraulic fracturing-based production from unconventional reservoirs and can significantly affect the effective conductivity of the packed proppant layers. In this study, to investigate the conveying behavior of fine particles, a Eulerian-Lagrangian method, namely the computational fluid dynamics–discrete element method (CFD-DEM), is adopted for 3D simulations. Two types of particles are involved in this process: larger proppant particles and fine particles. Proppant particles form a background skeleton, and a two-phase flow of fine particles and fluid is constrained in the connected pore networks. We adopt a unified CFD-DEM framework to resolve the non-slip boundary condition on the proppant particle surface and track fine particles using a four-way coupling strategy. In particular, a forcing term based on the fictitious domain method is embedded in a regular volume-averaged Navier-Stokes equation to solve the fluid motion. A perfectly packed skeleton of a face-centered cube is designed for subsequent numerical studies. The results show that the fluid and particle flow velocities are higher near the fracture surfaces than inside the interlayers. In addition, it is found that as the fine particle concentration increases, the average horizontal velocity increases, whereas the settling velocity tends to decrease.

Translation-rotation coupling and the kinematics of non-slip boundary conditions: A rough sphere between two sliding walls.

A non-slip constraint between a particle and a wall is applied at the microscopic level of collision dynamics using the rough sphere model. We analyze the consequences of the translation-rotation coupling of a rough sphere confined between two parallel planar walls and establish that shearing the walls past each other (i) preferentially deposits energy into the rotational degree of freedom and (ii) results in a bounded oscillation of the energy of the confined particle.

Implementation of a direct-addressing based lattice Boltzmann GPU solver for multiphase flow in porous media

GPU accelerated lattice Boltzmann (LB) simulations of multiphase flow in porous media have become a powerful tool to study fluid displacement process in porous media. For porous structures with a very low porosity, indirect-addressing memory access methods are preferred due to significantly reduction of the memory footprint despite that those methods are more difficult to implement and the resulting performance may be more sensible to the computing architectures, such as cache hierarchy and size. The direct-addressing methods are straightforward to implement and are able to archive high throughput when the porosity is large, while the methods become less efficient when the structures are too sparse. Nevertheless, the direct-addressing methods combined with multi-block grid technique are promising for many applications. In this work, we present a hybrid-way to tackle multiphase flow simulations in porous media, where the direct-addressing method is employed for the main LB evolution while the indirect-addressing method is employed for the complex boundary conditions. The CSF-based LB color-gradient multiphase model and the geometry-based wetting model are employed to increase accuracy and stability. Thanks to the utilization of AA-pattern streaming scheme, non-slip boundary condition of arbitrary orientation can be enforced without extra cost. We perform comprehensive analysis of the computational performance of the present solver on NVIDIA GPUs. For typical sandstones, our results show that the present implementation is able to achieve over 1.5 speedup compared with other direct-addressing schemes on V100 and A100, respectively and, particularly, the computational performance of the boundary kernels is greatly increased thanks to the increased L2 cache size of the latest GPUs.

Local well-posedness to the thermal boundary layer equations in Sobolev space

<abstract><p>In this paper, we study the local well-posedness of the thermal boundary layer equations for the two-dimensional incompressible heat conducting flow with nonslip boundary condition for the velocity and Neumann boundary condition for the temperature. Under Oleinik's monotonicity assumption, we establish the local-in-time existence and uniqueness of solutions in Sobolev space for the boundary layer equations by a new weighted energy method developed by Masmoudi and Wong.</p></abstract>

Regularity criterion in terms of BMO-type norm of the pressure gradient for the Navier-Stokes equations on unbounded domains

In this note we consider the initial-boundary value problem for the incompressible Navier-Stokes equations on unbounded domains in Rd by imposing the non-slip boundary condition. Then for locally uniform domains, introduced by Jones [20], we present a sufficient condition in terms of the BMO-type norm of the gradient of the pressure for the regularity of Leray-Hopf weak solutions.

Effects of spanwise length and side-wall boundary condition on plunging breaking waves

A systematic study of the effect of the spanwise length and the sidewall boundary condition of a numerical wave flume (NWF) on direct numerical simulation of a plunging breaking wave is performed. To deal with the topological changes of free surfaces, a high-fidelity numerical model is employed to solve the Navier–Stokes equations together with the volume of fluid function. After verification by two-dimensional (2D) simulations of a plunging breaker on a sloping beach, ten NWFs with different spanwise extents and sidewall boundary conditions are studied. Special attention is devoted to the three-dimensionality of the plunging breaker. Compared with three-dimensional (3D) models, the 2D model accurately reproduces the dynamics of a breaking solitary wave in the early stage, but it is inadequate for the study of the post-breaking process. For a 3D NWF with nonslip sidewall boundary condition, the wave domain can be divided into two regions with different physical properties. In the near-wall region, the nonslip boundary condition on the sidewall plays a crucial role in the wave hydrodynamics, while in the central region, the properties of the breaking wave are similar to those for the periodic boundary condition, which provide a closer representation of the real sea environment. The spanwise length of the NWF plays only a minor role in simulations under the periodic boundary condition. Furthermore, lateral boundaries and spanwise length show more influences on a plunging breaker with larger incident wave steepness. This study provides valuable support for the design of numerical simulations of wave breaking.

Application of Gas-Kinetic Scheme for Continuum and Near-Continuum Flow on Unstructured Mesh

A gas-kinetic scheme (GKS) with kinetic boundary condition based on unstructured mesh is present here. In the GKS method, the solid wall boundary conditions can be constructed by virtue of the gas distribution function, which is similar to the diffuse-scattering rule used in the other kinetic schemes. The kinetic boundary condition has a concise form and easy to implement. The use of unstructured mesh expands the adaptability of GKS to simulate the flows with complex geometry. The kinetic boundary condition can recover to the non-slip boundary condition in the continuum regime. In the slip regime, the slip velocity can be accurately predicted by kinetic boundary condition, which turns into the slip boundary condition. The use of kinetic boundary condition improves the calculation results of GKS in near-continuum flow. A series of test cases, from incompressible to compressible flow with a wide range of Knudsen number, are investigated to demonstrate the performance of kinetic boundary condition in near-continuum flow, which can provide a reference for the construction and optimisation for GKS-based multi-scale hybrid algorithms.

Accuracy improvement of immersed boundary-lattice Boltzmann and finite element method by iterative velocity correction

In an analysis of the fluid–structure interaction (FSI) problem, the non-slip boundary condition at solid walls cannot be accurately satisfied by the conventional immersed boundary-lattice Boltzmann coupling schemes due to insufficient interpolation accuracy. To solve this problem, an improved iterative velocity correction procedure for the immersed boundary-lattice Boltzmann coupling scheme is proposed by introducing a modified velocity operator. The particle distribution function was modified at each time step, and the evolution governing equation of the multiple relaxation time-lattice Boltzmann method was performed. A numerical framework for coupling lattice Boltzmann and finite element methods for transient problems involving FSI was established, and the iterative velocity correction immersed boundary method was used for the partitioned approach. The solid structure was discretized with the finite element method, while the single-component fluid flows were simulated with the lattice Boltzmann method. An FSI benchmark model was employed to verify the efficiency of the proposed coupling method. The results show that the developed method guarantees the non-slip boundary condition and maintains the convergence rate of the conventional immersed boundary method. In viscous flow and strong shearing flow, the accuracy of both stationary and moving solid boundaries is obviously improved.

Enthalpy-based immersed boundary-lattice Boltzmann model for solid-liquid phase change in porous media under local thermal non-equilibrium condition

Heat transfer enhancement structures are adopted to improve the performance of latent heat thermal energy storage (LHTES) systems, such as metallic porous matrix, multi-tube, and fin. The metallic porous matrix and complex geometries of the structures bring difficulties to the numerical studies of the solid-liquid phase transition in the enhanced LHTES system. In this work, an enthalpy-based immersed boundary (IB)-lattice Boltzmann (LB) model is proposed for solid-liquid phase change problems in porous media under the local thermal non-equilibrium (LTNE) condition. In this model, to reduce the numerical diffusion across the solid-liquid interface, a two-relaxation-time (TRT)-LB model is developed to obtain the temperature field of phase change material (PCM). Two single-relaxation-time (SRT)-LB equations (LBEs) are employed for the velocity field of the liquid PCM and the temperature field of the porous matrix, respectively. The partially saturated method is used for the non-slip boundary condition on the moving solid-liquid interface. Different discrete source term schemes are employed for source terms induced by surface heat transfer and IB. Based on the source term treatment, the multi-direct-forcing IB-LB method is employed for the implementation of velocity, enthalpy and temperature boundary conditions on the complex boundary. The proposed model is verified by four cases: one-dimensional conduction melting under the LTNE condition, natural convection in a metallic porous matrix-filled cavity, conduction melting in an annulus filled with metallic porous matrix, and constrained melting in an isothermal circular cylinder without porous media. As an example of application, a metallic porous matrix-enhanced LHTES system with different multi-tube arrangements at different Rayleigh numbers (Ra) and porosities is investigated.

Numerical investigation of latent heat thermal energy storage unit with different configurations and phase change materials

In this work melting behavior of PCMs inside the LHTES (latent heat thermal energy storage) unit for six different cases has been numerically investigated by Comsol Multiphysics and Simulation Software. Two different PCMs (phase change materials), namely lauric acid and n-octadecane, have been used in the analysis for two different configurations. When configuration-1 has only one region for PCM, configuration-2 contains two regions. Simulations show that melting is completed at the upper side of the LHTES unit first due to the natural convection effects. On the other hand, it has been shown that LHTES unit in the form of configuration-1 with n-octadecane completes phase change earliest and absorbs most heat at the end of the process. This also demonstrates that not only latent heats of the PCMs, but also parameters affecting natural convection have an important effect on the heat transfer. Because when PCM with a lower melting temperature is used, buoyancy force, consequently absorbed heat increases. Inside boundaries also inversely affect absorbed heat by PCMs due to the non-slip boundary condition on these boundaries. The maximum efficiency of the LHTES unit is obtained for the configuration-1 with lauric acid due to not only high value of absorbed heat as a result of fewer obstacles of the geometry, but also the smaller values of latent heat and specific heat of lauric acid affecting Emax.

A Three-Dimensional Slip Velocity Model for Water-Lubricated Hydrodynamic Journal Bearings

Hydrodynamic journal bearings, coated with polytetrafluoroethylene (PTFE) and lubricated by water, have been widely used in ships and large-scale pumps, and the function is to maintain the stability of rotor system. However, slip velocity exists on the PTFE-coated surface, whose effect is still an open question. This study aims to investigate the static characteristics of water-lubricated hydrodynamic journal bearings under three-dimensional slip velocity boundary conditions. Firstly, under the non-slip boundary condition, the CFD (computational fluid dynamics) method with ANSYS Fluent is verified based on the Reynolds lubrication equation and the open literature. Then, a three-dimensional slip velocity equation that is based on the Navier slip velocity boundary condition is proposed and embedded into Fluent. Finally, the effects of slip length on the static characteristics are analyzed. Under the same eccentricity ratio, with the increase in slip length, the load capacity decreases due to the decrease of the pressure circumferential gradient, and the friction power decreases. Under the same eccentricity ratio and the same slip length, with the increase in the attitude angle, the load capacity and friction power increase. However, under the non-slip boundary condition, the effects of attitude angle on the load capacity and friction power are insignificant. This paper could provide a reference for studying slip velocity in the hydrodynamic journal bearing.

Fully resolved simulations of viscoelastic suspensions by an efficient immersed boundary-lattice Boltzmann method

An efficient immersed boundary-lattice Boltzmann method (IB-LBM) is proposed for fully resolved simulations of suspended solid particles in viscoelastic flows. Stress LBM based on Giesekus and Oldroyd-B constitutive equation are used to model the viscoelastic stress tensor. A boundary thickening-based direct forcing IB method is adopted to solve the particle–fluid interactions with high accuracy for non-slip boundary conditions. A universal law is proposed to determine the diffusivity constant in a viscoelastic LBM model to balance the numerical accuracy and stability over a wide range of computational parameters. An asynchronous calculation strategy is adopted to further improve the computing efficiency. The method was firstly applicated to the simulation of sedimentation of a single particle and a pair of particles after good validations in cases of the flow past a fixed cylinder and particle migration in a Couette flow against FEM and FVM methods. The determination of the asynchronous calculation strategy and the effect of viscoelastic stress distribution on the settling behaviors of one and two particles are revealed. Subsequently, 504 particles settling in a closed cavity was simulated and the phenomenon that the viscoelastic stress stabilizing the Rayleigh–Taylor instabilities was observed. At last, simulations of a dense flow involving 11001 particles, the largest number of particles to date, were performed to investigate the instability behavior induced by elastic effect under hydrodynamic interactions in a viscoelastic fluid. The elasticity-induced ordering of the particle structures and fluid bubble structures in this dense flow is revealed for the first time. These simulations demonstrate the capability and prospects of the present method for aid in understanding the complex behaviors of viscoelastic particle suspensions.

New Thought on Matsumura–Nishida Theory in the L_p–L_q Maximal Regularity Framework

This paper is devoted to proving the global well-posedness of initial-boundary value problem for Navier–Stokes equations describing the motion of viscous, compressible, barotropic fluid flows in a three dimensional exterior domain with non-slip boundary conditions. This was first proved by an excellent paper due to Matsumura and Nishida (Commun Math Phys 89:445–464, 1983). In [10], they used energy method and their requirement was that space derivatives of the mass density up to third order and space derivatives of the velocity fields up to fourth order belong to L_2 in space-time, detailed statement of Matsumura and Nishida theorem is given in Theorem 1 of Sect. 1 of context. This requirement is essentially used to estimate the L_infty norm of necessary order of derivatives in order to enclose the iteration scheme with the help of Sobolev inequalities and also to treat the material derivatives of the mass density. On the other hand, this paper gives the global wellposedness of the same problem as in [10] in L_p (1 <p le 2) in time and L_2cap L_6 in space maximal regularity class, which is an improvement of the Matsumura and Nishida theory in [10] from the point of view of the minimal requirement of the regularity of solutions. In fact, after changing the material derivatives to time derivatives by Lagrange transformation, enough estimates obtained by combination of the maximal L_p (1 <p le 2) in time and L_2cap L_6 in space regularity and L_p–L_q decay estimate of the Stokes equations with non-slip conditions in the compressible viscous fluid flow case enable us to use the standard Banach’s fixed point argument. Moreover, one of the purposes of this paper is to present a framework to prove the L_p–L_q maximal regularity for parabolic-hyperbolic type equations with non-homogeneous boundary conditions and how to combine the maximal L_p–L_q regularity and L_p–L_q decay estimates of linearized equations to prove the global well-posedness of quasilinear problems in unbounded domains, which gives a new thought of proving the global well-posedness of initial-boundary value problems for systems of parabolic or parabolic-hyperbolic equations appearing in mathematical physics.

Exponential mixing by orthogonal non-monotonic shears

Non-monotonic velocity profiles are an inherent feature of mixing flows obeying non-slip boundary conditions. There are, however, few known models of laminar mixing which incorporate this feature and have proven mixing properties. Here we present such a model, alternating between two non-monotonic shear flows which act in orthogonal (i.e. perpendicular) directions. Each shear is defined by an independent variable, giving a two-dimensional parameter space within which we prove the mixing property over open subsets. Within these mixing windows, we use results from the billiards literature to establish exponential mixing rates. Outside of these windows, we find large parameter regions where elliptic islands persist, leading to poor mixing. Finally, we comment on the challenges of extending these mixing windows and the potential for a non-exponential mixing rate at particular parameter values.

Performance of a Propeller Coated with Hydrophobic Material

Computational and experimental methods were used to study a propeller coated with hydrophobic material and a propeller with a conventional surface for comparison. In CFD simulations, the blade surface mesh was arranged in a way to set non-slip or free slip wall boundary conditions with different proportions to define the level of surface slip. The conventional and the hydrophobic material propellers defined by different surface slip rates were simulated under different advance speed coefficients and different rotational speeds. Propeller performance results, blade pressure, and the Liutex vorticity distribution were studied. An experimental platform was established to study the velocity field around the propeller using a Particle Image Velocimetry (PIV) device. The CFD calculation results were compared with the PIV results. It was found that the calculation results using a 75% surface slip rate were closer to the experimental results. The calculation results show that the propeller coated with hydrophobic material has improved thrust and efficiency compared with the propeller with conventional material. The hydrophobic material can significantly reduce the low-speed region downstream of the propeller hub. The hub and the tip vortices shown by the Liutex are also significantly reduced. Those changes help to improve the propulsion efficiency.

On fluid flow regime transition in rough rock fractures: Insights from experiment and fluid dynamic computation

The influence of roughness, aperture and asperity irregularity on fluid flow regimes in rough rock fractures was investigated by performing coupled triaxial water flow tests and fluid dynamic computation. Ten sets of fabricated curved wedges were developed to obtain different fracture surface roughness by splitting under compression. Three fluid flow regimes were identified in mated rock fractures: pre-linear flow at low flow velocity, linear Darcy’s flow at the medium flow velocity and post-linear flow at high flow velocity. In pre-linear flow regime, the increasing rate of flow rate increased with water pressure gradient, but it decreased in post-linear flow regime. The pre-linear flow is ascribed to the slippage effect of water-fracture interfaces, while the post-linear flow is mainly due to inertial effects. The critical hydraulic gradient for fluid flow regime transition from pre-linear to linear flow increased with the increase of confining stress. The numerical modeling shows that the asperity irregularity influences the flow regime. For low-speed flow in fracture under slip boundary condition, the slip flux per unit width in the fracture with triangular asperity is largest, while that of rectangular asperity is smallest. For high-speed flow in fracture with non-slip boundary condition, the rectangular asperity element causes more severe nonlinearity when compared to the fractures of trapezoidal and triangular asperity elements.