Non-slip Boundary Condition Research Articles

A techno-economic investigation of 2D and 3D configurations of fins and their effects on heat sink efficiency of MHD hybrid nanofluid with slip and non-slip flow

The mixed convection heat transfer (MCHT) as a combination of forced and natural convection is studied in this paper. A rectangular enclosure with heatsink is considered that is filled with a hybrid nanofluids (HNFs). The assumed magnetic field (MF) applied the Lorentz force to the enclosure with heatsink. For the enclosure with heatsink, the boundary conditions are assumed as moving upper wall and lower wall with high temperature; Other both walls are well insulated to avoid heat transfer (HT) from them. There was a heat sink on the lower wall with the same temperature of the wall. The Flow could slip over the moving wall, and the non-slip boundary condition is violated on this wall. The governing equations of fluid flow and boundary conditions are discretized using the control volume formulation of the finite difference method and SIMPLE algorithm is used to solve the coupled equations. The effects of fin's length and different types of heat sinks with various lengths on the entropy generation rate (EGR) and Nusselt number (Nu) are investigated at different Richardson numbers (Ri) considering slip and non-slip conditions. The results showed that the HT and EGR increase by increasing the height of the fins. When the length of the heatsink blades was 1, it had the lowest manufacturing cost and at the same time the highest heat transfer per unit blade length, and economically, it was the most economical mode of the heatsink among the various models. The Nu and EGR are decreased using the slip boundary condition. Based on the results, The Nu per length reaches the maximum value for the lowest length of fin.

A semi‐implicit stabilized particle Galerkin method for incompressible free surface flow simulations

SummaryA new particle Galerkin method is introduced to solve the Naiver‐Stokes equations in a Lagrangian fashion. The present method aims to suppress key numerical instabilities observed in the strong form Lagrangian particle methods such as smoothed particle hydrodynamics (SPH), incompressible SPH, and moving particle semi‐implicit for incompressible free surface flow simulations.It is well‐known that strong form Lagrangian particle methods usually rely on ad hoc particle stabilization techniques based on particle shifting, artificial viscosity, or density‐invariant condition due to some formulation inconsistency issues. In the present method, we introduce a momentum‐consistent velocity smoothing algorithm which is used to combine with the second‐order rotational incremental pressure‐correction scheme to stabilize the pressure field as well as to enforce the consistency of Neumann boundary condition. To further impose slip‐free or nonslip boundary conditions for the fluid flow, a penalty method which is free of ghost or dummy particles is developed. Finally, a particle insertion‐deletion adaptive scheme is proposed when the violent fluid flow is considered. Four numerical examples are studied to validate the accuracy and stability of the present method.

Analysis of heat transfer of spilling fire spread over steady flow of n-butanol fuel

The continuously spilling n-butanol fire is systematically investigated in steady flow state. The influence of thermal conductivity of substrate on spilling fire is revealed. According to the temperature distribution and spreading characteristics, the spilling fire over concurrent steady flow n-butanol is separated into the heat transfer dominant stage in low-discharge rate and the forced flow dominant stage in high-discharge rate with the critical discharge rate Q = 141.5 ml/min. The low-discharge rate spilling fire spread depends on the coupled effects of subsurface flow preheating and intrinsic dragging of flowing fuel, whereas the high-discharge rate spilling fire depends mainly on the dragging effect of non-slip boundary condition on the liquid surface. The temperature distribution of liquid surface proves that the behavior of thermal fluid diffusion occurs in high-discharge rate. The velocity of spilling fire decreases with an increase in thermal conductivity of substrate. The magnitudes of heat transfer involving spilling fire spread over n-butanol inside the subsurface flow namely gas conduction, liquid conduction, liquid convection, sensible heat and heat dissipation from substrate and walls of spilling trench are quantitatively calculated. The sum of sensible heat and convective heat loss accounts for more than 80% of total heat flux.

The rates of convergence for the chemotaxis-Navier–Stokes equations in a strip domain

ABSTRACT In this paper, we study the long-time behavior of the chemotaxis-Navier–Stokes system posed in a strip domain . In Peng-Xiang (Math. Models Methods Appl. Sci., 28 (2018), 869-920), the authors have established the global existence of strong solutions to this system with non-flux boundary conditions for n and c and non-slip boundary conditions for . Our main purpose is to establish the time-decay rates for such solutions. This will be done by using the anisotropic interpolation and the iterative techniques.

Lieb–Thirring inequalities on the sphere

We prove on the sphere $\mathbb{S}^2$ the Lieb--Thirring inequalities for orthonormal families of scalar and vector functions both on the whole sphere and on proper domains on $\mathbb{S}^2$. By way of applications we obtain an explicit estimate for the dimension of the attractor of the Navier--Stokes system on a domain on the sphere with Dirichlet non-slip boundary conditions.

Initial-boundary layer associated with the 3-D Boussinesq system for Rayleigh-Benard convection

This article concerns the initial-boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh-Benard convection with ill-prepared initial data. We consider a non-slip boundary condition for the velocity field and inhomogeneous Dirichlet boundary condition for the temperature. By means of multi-scale analysis and matched asymptotic expansion methods, we establish an accurate approximating solution for the viscous and diffusive Boussinesq system. We also study the convergence of the infinite Prandtl number limit.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/31/abstr.html

Vorticity transport in laminar steady rotating plumes

A steady laminar rotating thermal plume was investigated by the numerical solution of the 3D momentum and energy equations. The flow originated from a low momentum hot jet (Richardson number Ri = 173 and Grashof number Gr = 5000) issued from a small inlet in the bottom wall of a cylindrical domain with a permeable lateral surface that is rotating (Ekman number Ek = 12). Second order accurate calculations of the structure and dynamics of the buoyant vortex were investigated, with specific emphasis on the evolution of the vorticity distributions and their effects on the ensuing vortex. Budgets of the vorticity transport equations were investigated to analyze the genesis of the developed axial vorticity, explaining how the whirling flow was generated. Nonslip and slip bottom boundary conditions allowed the investigation of the impact of the boundary layer on the axial vorticity generation. The results showed that there is a conversion of radial vorticity into axial vorticity. The radial vorticity was found to be generated not only in the boundary layer but also by tilting of the tangential vorticity, which results from buoyancy. Additionally, the boundary layer was found to have a strong impact on the generation of axial vorticity, but not to be necessary to generate the whirl. In fact, a stronger whirl was originated without the effect of the boundary layer, since the axial vorticity was generated closer to the inlet, where additional stretching is provided by the acceleration of the flow.

On optimal boundary control of Ericksen–Leslie system in dimension two

In this paper, we consider the boundary value problem of a simplified Ericksen-Leslie system in dimension two with non-slip boundary condition for the velocity field $u$ and time-dependent boundary condition for the director field $d$ of unit length. For such a system, we first establish the existence of a global weak solution that is smooth away from finitely many singular times, then establish the existence of a unique global strong solution that is smooth for $t>0$ under the assumption that the image of boundary data is contained in the hemisphere $\mathbb S^2_+$. Finally, we apply these theorems to the problem of optimal boundary control of the simplified Ericksen-Leslie system and show both the existence and a necessary condition of an optimal boundary control.

Sobre la solución numérica de una esfera ascendente en un fluído Newtoniano con viscosidad dependiente de la temperatura

In this work, we present some numerical results about the problem of a rising hot solid sphere immersed in a Newtonian fluid which viscosity depends on the temperature. The model formulated to solve the problem considers two dimensionless parameters: The Peclet number, Pe and a parameter related with the viscosity, e. Small and large variations on e lead to interesting results segregated into two regimes which exhibit an asymptotic structure.To carry out the computations to solve the proposed model, the element finite method was used along with a non-slip boundary condition for the contact surface between the sphere and the fluid and the results obtained were compared to those shown recently in papers related wherein contact surface has a slip-boundary condition prescribed.

Zero-Viscosity Limit of the Navier–Stokes Equations in a Simply-Connected Bounded Domain Under the Analytic Setting

In this paper, we consider the zero-viscosity limit of the 2-D Navier–Stokes equations in a simply-connected bounded domain with non-slip boundary condition. Based on the energy method in Wang et al. (Arch Ration Mech Anal 224(2):555–595, 2017), we justify the zero-viscosity limit under the analytic setting.

MHD natural convective flow of [formula omitted] ferrofluids in an inclined partial open complex-wavy-walls ringed enclosures using non-linear Boussinesq approximation

In the current contribution, a numerical investigation of natural convection with nonlinear Boussinesq approximation is considered for a ferrofluid flows inside an inclined, and partial open cavity. The vertical walls of the cavity are wavy where the aperture part lies in the right one. The left wall is considered to be uniformly heated whereas the remaining parts of the cavity are adiabatic. The nonslip boundary condition is assumed for all the boundaries except the aperture part where the directional do-nothing boundary condition is introduced to ensure the theoretical studies which leads to a conservative kinetic energy. The problem is modeled and the resulting partial differential equation system, after converting it to a non-dimensional form using a suitable transformation variables, is solved based on the Galerkin finite element method. The entropy generation analysis is presented for the local entropy generation due to heat transfer, local entropy generation due to fluid friction as well as their contribution to Bejan number. An intensive computation is carried out for wide ranges of the governing parameters namely; the Rayleigh number Ra, Hartmann number Ha, nanoparticle volume fraction ϕ, amplitudes of the two superimposed sinusoidal functions αi, non-linear Boussinesq parameter ξ, length of the aperture BR and its position bR. The obtained results are shown in terms of the streamlines, isotherms, local entropy generation due to heat transfer, local entropy generation due to fluid friction contours as well as average Bejan and Nusselt number. Over all, most of the governing parameters have a significant impacts in the flow and heat transfer rate as shown in the discussion section.

Boundedness and asymptotic behavior to a chemotaxis-fluid system with singular sensitivity and logistic source

In this paper, we consider the following chemotaxis-fluid model with singular sensitivity and logistic source{nt+u⋅∇n=Δn−χ∇⋅(nc∇c)+rn−μnk,x∈Ω,t>0,ct+u⋅∇c=Δc−c+n,x∈Ω,t>0,ut+λ(u⋅∇)u=Δu+∇P+n∇ϕ,x∈Ω,t>0,∇⋅u=0,x∈Ω,t>0 in a bounded domain Ω⊂RN(N=2,3) with smooth boundary ∂Ω. Under the non-flux boundary conditions for n and c, and the non-slip boundary condition for u, we establish the global boundedness and the time-decay rates of the classical solutions for any k>1 provided that χ satisfies suitable restrictions.

Integrating thermal‐concentration smoothed profile with lattice Boltzmann methods for simulating sedimentation of nonisothermal circular particles

SummaryA thermal‐concentration smoothed profile‐lattice Boltzmann method is proposed to study the effect of the concentration field on the dynamic behavior of nonisothermal cylindrical particles during the sedimentation process. The velocity, temperature, and concentration equations are solved using the lattice Boltzmann method. Moreover, the smoothed profile method is employed to enforce the nonslip boundary condition as well as constant temperature and constant concentration boundary conditions at the particles surfaces. Moreover, the Boussinesq approximation is used to couple the velocities, temperatures, and concentrations fields. The proposed combined method is validated by comparing the present numerical results with those found in the literature, showing good consistency. Then, the effect of the concentration buoyancy on the behavior of nonisothermal particles is discussed. In addition, the effect of Prandtl, Schmidt, and thermal Grashof numbers on the settling process is investigated. The results show that, by adding the effect of concentration, the maximum settling velocity of hot particles is reduced more relative to the cold ones; accordingly, the cold particles are settled faster than the hot ones. Finally, the sedimentation of two particles in a container at high thermal Grashof is investigated. It is shown that, at high thermal Grashof, there is an intense competition between the buoyancy force and gravity for the hot particles. The buoyancy flow generated leads to the reversal of the drafting‐kissing‐tumbling motion of the hot particles, making the particles move upward.

Multiscale flow characteristics of droplet spreading with microgravity conditions

In this paper, mesoscopic lattice–Boltzmann method (LBM) and microscopic molecular dynamics simulation method were used to simulate droplet dynamic wetting under microgravity. In terms of LBM, the wetting process of a droplet on a solid wall surface was simulated by introducing the fluid–fluid and solid–fluid interactions. In terms of molecular dynamics simulation, the spreading process of water on gold surface was simulated. Calculation results showed that two kinds of calculation methods were based on the microscopic molecular theory or mesoscopic kinetics theory, and such models could effectively overcome the contact line paradox issue, which results from the macro-continuum assumption and non-slip boundary condition assumption. The spreading exhibits two-stage behavior: fast spreading and slow spreading stages. For the two simulation methods, the ratio of fast spreading stage duration to slow spreading duration, spreading capacity (equilibrium contact radius/initial radius), and the spreading exponent of the rapid stage were very close. However, the predictive spreading index of the slow spreading stage was different, owing to the different spreading mechanisms between meso- and nanoscales.

Direct simulation of pore-scale two-phase visco-capillary flow on large digital rock images using a phase-field lattice Boltzmann method on general-purpose graphics processing units

We describe the underlying mathematics, validation, and applications of a novel Helmholtz free-energy—minimizing phase-field model solved within the framework of the lattice Boltzmann method (LBM) for efficiently simulating two-phase pore-scale flow directly on large 3D images of real rocks obtained from micro-computed tomography (micro-CT) scanning. The code implementation of the technique, coined as the eLBM (energy-based LBM), is performed in CUDA programming language to take maximum advantage of accelerated computing by use of multinode general-purpose graphics processing units (GPGPUs). eLBM’s momentum-balance solver is based on the multiple-relaxation-time (MRT) model. The Boltzmann equation is discretized in space, velocity (momentum), and time coordinates using a 3D 19-velocity grid (D3Q19 scheme), which provides the best compromise between accuracy and computational efficiency. The benefits of the MRT model over the conventional single-relaxation-time Bhatnagar-Gross-Krook (BGK) model are (I) enhanced numerical stability, (II) independent bulk and shear viscosities, and (III) viscosity-independent, nonslip boundary conditions. The drawback of the MRT model is that it is slightly more computationally demanding compared to the BGK model. This minor hurdle is easily overcome through a GPGPU implementation of the MRT model for eLBM. eLBM is, to our knowledge, the first industrial grade–distributed parallel implementation of an energy-based LBM taking advantage of multiple GPGPU nodes. The Cahn-Hilliard equation that governs the order-parameter distribution is fully integrated into the LBM framework that accelerates the pore-scale simulation on real systems significantly. While individual components of the eLBM simulator can be separately found in various references, our novel contributions are (1) integrating all computational and high-performance computing components together into a unified implementation and (2) providing comprehensive and definitive quantitative validation results with eLBM in terms of robustness and accuracy for a variety of flow domains including various types of real rock images. We successfully validate and apply the eLBM on several transient two-phase flow problems of gradually increasing complexity. Investigated problems include the following: (1) snap-off in constricted capillary tubes; (2) Haines jumps on a micromodel (during drainage), Ketton limestone image, and Fontainebleau and Castlegate sandstone images (during drainage and subsequent imbibition); and (3) capillary desaturation simulations on a Berea sandstone image including a comparison of numerically computed residual non-wetting-phase saturations (as a function of the capillary number) to data reported in the literature. Extensive physical validation tests and applications on large 3D rock images demonstrate the reliability, robustness, and efficacy of the eLBM as a direct visco-capillary pore-scale two-phase flow simulator for digital rock physics workflows.

Three-dimensional numerical study on rotating detonation engines using reactive Navier-Stokes equations

Three-dimensional simulations on the rotating detonation engine (RDE) are conducted by solving the Navier-Stokes equations in stoichiometric hydrogen/air mixtures. Free-slip wall and non-slip wall boundary conditions are considered. The emphasis is placed on the effects of the viscosity, mass diffusion and thermal conduction on the detonation wave in the RDE, especially in the boundary layer. The simulation results show that the detonation wave propagates with a lower velocity in the Navier-Stokes solutions compared with that in the Euler solutions. This is mainly due to the effects of mass diffusion and thermal conduction. Meanwhile, the two effects above reduce the pressure of the detonation wave in the mainstream. Moreover, the detonation wave height is higher in the Navier-Stokes solutions than that in the Euler solutions. The temperature behind the detonation wave near the walls is much higher than that inside the chamber due to the existence of the boundary layer. Therefore, the viscosity, mass diffusion and thermal conduction impact the detonation velocity, pressure, the detonation wave height and temperature in the RDE.

Numerical simulation of hydrodynamic and heat transfer characteristics of slug flow in serpentine microchannel with various curvature ratio

A numerical investigation is carried out to study hydrodynamic behavior and thermal performance of slug flow in serpentine microchannel with different curvature ratio and wall properties. By using coupled Level Set and Volume of Fluid (CLSVOF) method implemented in Fluent, gas-liquid interface shows good consistency with experimental results especially for slug flow. Distribution of sectional velocity profile in curved microchannel with various curvature ratios was investigated. On the basis of fluid flow in microchannel with non-slip boundary condition, by means of user defined function (UDF), influence of slip velocity on hydrodynamic characteristics was performed numerically. For a better prediction on thermal performance, further analysis of combined effect of wall properties and curvature ratio on fluid flow characteristics was also conducted. As a consequence, the increasing slip velocity on channel wall can reduce hydraulic resistance. Both the contact angle and the curvature ratio have an appreciable influence on thermal performance of gas-liquid two-phase flow in serpentine microchannel.

Immersed boundary-lattice Boltzmann simulation of a rotating flat plate interacting with laminar flows

To make an insight into the interaction characteristics of a flat plate rotating in laminar flows, the immersed boundary (IB)-lattice Boltzmann (LB) method combined with the multiple-relaxation-time (MRT) collision model in two dimensions is presented. Furthermore, an implicit velocity-correction IB method is proposed to deal with the interface of moving solid boundary interacting with fluid flows. Two valuable sub-issues are particularly highlighted in the research. One is the multiple-relaxation-time immersed boundary-lattice Boltzmann (MRT-IB-LB) implementation of the fluid-structure interface enforcing the nonslip boundary condition, and the other is the effects of rotating velocities associated with aspect ratios on the plate interacting with the flows. The model is validated with the benchmark case: the flow around a cylinder asymmetrically placed in a channel. Then the effects of different rotating velocities and aspect ratios are researched. With the increasing of aspect ratios, the vortex shedding frequency increases and the multiple dominant frequencies of the hydrodynamic force occur. The formed vortices are driven downstream and amalgamated into the dominant vortices in the biased flow. The average values of hydrodynamic forces can be enlarged by increasing aspect ratio. Additionally, the drag coefficient can be decreased but the lift coefficient is increased by increasing the rotating velocity.

A Smooth Dissipative Particle Dynamics method for nonisothermal liquid and gas flows in bounded domains

A Smoothed Dissipative Particle Dynamics formulation with dynamic virtual particle allocation (SDPD-DV) is developed for the simulation of mesoscale nonisothermal flows with non-slip, constant temperature and constant heat flux boundary conditions. For liquids, the particle internal energy is evaluated through a first-order expansion from an initial volume and entropy state. For liquids, the particle pressure and temperature are evaluated using the coefficients of adiabatic compressibility, volumetric thermal expansion and heat capacity. For monatomic and diatomic gases, the fluid particle internal energy is evaluated through a Sackur-Tetrode type of equation. For both liquids and gases, the viscosity and thermal conductivity are modeled by a power law. Integration of position and momentum equations is performed with a velocity-Verlet method and bounce-forward reflection. Integration of the entropy equation is performed with a Runge-Kutta method. Verification of SDPD-DV is performed for planar isothermal Couette, planar Fourier, and planar nonisothermal Couette flows of liquid H2O and gaseous N2, and for a nonisothermal planar Poiseuille flow of a fluid with an exponential temperature-depended viscosity. SDPD-DV simulations for liquid H2O, gaseous Ar and N2 systems under thermal equilibrium assess the impact of the ratio of particle mass (mi) over the real molecular mass and the size of smoothing length (h) on fluid properties, hydrodynamic fluctuations and transport coefficients. For liquid systems the density fluctuations exhibit scatter about the analytical estimates and the temperature fluctuations follow the analytical estimates for mass ratios smaller than 10,000. The velocity fluctuations are in excellent agreement with theoretical estimates. For gases, the density fluctuations exhibit scatter about the analytical estimates and the pressure fluctuations agree with the analytical estimates for mass ratios smaller than 10,000. The temperature and velocity fluctuations are in excellent agreement with the analytical estimates. The self-diffusivity evaluated from SDPD-DV simulations for liquid and gases is shown to increase with smoothing length for a given mass ratio, scales with h2/mi and is in excellent agreement with analytical estimates. The shear viscosity evaluated from SDPD-DV simulations for liquid and gases exhibits scatter around the experimental values and is shown to be scale free.

Effect of Lateral End Plates on Flow Crossing a Yawed Circular Cylinder

Numerical simulation is carried out to investigate the effect of the boundary condition of two lateral end-plate walls on the flow structure in the wake of a flow crossing a yawed circular cylinder. Two typical boundary conditions, nonslip and periodic, are investigated. It is revealed that the boundary condition of the two end-plates has a significant effect on the flow behaviors in the wake. Under the nonslip boundary condition, the vortex structure in the wake exhibits a tapering shape to the tip end. The flow pattern is formed in the wake as the streamlines on the tip side are becoming denser while the streamlines on the base end are becoming sparser. Spectral power analysis of the local lift coefficient shows that the frequency distribution exhibits axial variation. On the base side, the frequency distribution is broadband. On the tip side, there are two peak frequencies: the larger one corresponds to the value predicted by the independence principle, and the smaller one is generated by the secondary axial flow separation from the rear cylinder wall. Under the periodic condition, the numerical results show that organized Strouhal vortex is shed in the wake in the same way as to the flow orthogonally passing a cylinder and the independence principle is still applicable.