No-slip Boundary Research Articles

Theoretical exploration of heat transport in a stagnant power-law fluid flow over a stretching spinning porous disk filled with homogeneous-heterogeneous chemical reactions

The distinction between homogeneous and heterogeneous chemical reactions is crucial because many chemically reactive systems, such as hydrometallurgical processes, cooling towers, biological systems, fog dispersion, catalysis, etc., involve both types of reactions. Thus, this study analyzes the heat transmission (HT) characteristics in an MHD stagnant flow of power-law fluid caused by a spinning disk that is stretched and saturated in a porous medium. The study considers homogeneous-heterogeneous (HH) reactions and nonlinear thermal radiation subject to no-slip and convection boundary conditions. The leading equations are switched into ordinary differential equations (ODEs) employing similarity variables. The study focuses on the dimensionless concentration, velocity, temperature, Nusselt number, and skin friction coefficient, which are discussed in detail in the results and discussion section. The study observes that for power-law fluids with an index value less than 1, the skin friction coefficient decays as the power-law index grows. It also notes that the dimensionless skin friction of power-law fluids decreases as the velocity ratio increases. The dimensionless concentration increases with Schmidt and modified Prandtl numbers for both power-law fluids over a stretching spinning porous disk. The HH reaction parameters decline the concentration of power-law fluids.

Spike formation theory in three-dimensional flow separation

We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in three-dimensional flows with arbitrary time dependence. Based on the exact evolution of the largest principal curvature on near-wall material surfaces, our theory identifies fixed and moving separation. Our approach is effective over short time intervals and admits an instantaneous limit. As a byproduct, we derive explicit formulas for the evolution of the Weingarten map and the principal curvatures of any surface advected by general three-dimensional flows. The material backbone we identify acts first as a precursor and later as the centrepiece of Lagrangian flow separation. We discover previously undetected spiking points and curves where the separation backbones connect to the boundary and provide wall-based analytical formulas for their locations. We illustrate our results on several steady and unsteady flows.

Mathematical Model of the Flow in a Nanofiber/Microfiber Mixed Aerosol Filter

A new mathematical model of an aerosol fibrous filter, composed of a variety of nano- and microfibers, is developed. The combination of nano- and microfibers in a mixed-type filter provides a higher overall quality factor compared with filters with monodisperse fibers. In this paper, we propose a mathematical model of the flow of an incompressible fluid in a porous region consisting of a set of cylinders of various diameters in the range of nano- and micrometers to describe a mixed-type aerosol filter. The flow domain is a rectangular periodic cell with one microfiber and many nanofibers. The motion of the carrier medium is described by the boundary value problem in Stokes flow approximation with the no-slip boundary condition for microfibers and the slip condition for nanofibers. The boundary element method taking into account the slip and non-slip conditions is developed. The calculated velocity field, streamlines, vorticity distribution, and drag of separate fibers and the entire periodic cell are presented. Numerical results for the drag force of the porous medium of a mixed-type filter for the various ratios of mass proportion of nano- and microfibers, porosity, and filtration velocity are presented. The obtained results are compared with the analytical formulas based on the approximate theory of filtration of bimodal filters and with known experimental data. It is shown that with an increase in the mass fraction of nanofibers, the total drag force of the cell increases, while the relative contribution of nanofibers to the total drag force tends toward the value that is less than unity. An approximate analytical formula for the drag coefficient of a mixed aerosol filter is derived. The developed flow model and analytical formulas allow for estimating the aerodynamic drag of a mixed filter composed by nano- and microfibers.

Observation of a Large Slip Effect in the Nanoscale Flow of Highly Viscous Supercooled Liquid Metals.

Understanding and controlling the flow of materials confined in channels play important roles in science and engineering. The general no-slip boundary condition will result in it being more challenging to drive the flow as the channel size decreases to the nanoscale, especially for highly viscous liquids. Here, we report the observation of a large boundary slip in the nanoscale flow of highly viscous supercooled liquid metals (with viscosities of ≲108 Pa s), enabled by the hydrophobic treatment of smooth nanochannels. The slip length significantly depends on the pressure, which can be rationalized by the shear-dependent viscosity. Our findings provide not only new insights into the field of nanofluidics but also a practical technique for resolving the challenge in the net formation of highly viscous supercooled liquid metals at the nanoscale.

Lift force in odd compressible fluids.

When a body moves through a fluid, it can experience a force orthogonal to its movement called lift force. Odd viscous fluids break parity and time-reversal symmetry, suggesting the existence of an odd lift force on tracer particles, even at vanishing Reynolds numbers and for symmetric geometries. It was previously found that an incompressible odd fluid cannot induce lift force on a tracer particle with no-slip boundary conditions, making signatures of odd viscosity in the two-dimensional bulk elusive. By computing the response matrix for a tracer particle, we show that an odd compressible fluid can produce an odd lift force. Using shell localization, we provide analytic expressions for the drag and odd lift forces acting on the tracer particle in a steady state and also at finite frequency. Importantly, we find that the existence of an odd lift force in a steady state requires taking into account the nonconservation of the fluid mass density due to the coupling between the two-dimensional surface and the three-dimensional bulk fluid.

Vanishing dissipation limit of solutions to initial boundary value problem for three dimensional incompressible magneto-hydrodynamic equations with transverse magnetic field

In this paper, we study the vanishing dissipation limit of solutions to the initial boundary value problem of three-dimensional incompressible viscous magnetohydrodynamic equations in the upper half space where the magnetic field is assumed to be transverse to the boundary. When the tangential component of the magnetic field is imposed the zero Neumann boundary condition, we can establish the uniform energy estimates of the solutions to the initial boundary value problem in the conormal Sobolev spaces even if the velocity field satisfies the no-slip boundary condition. Then the vanishing dissipation limit of solutions to the initial boundary value problem can be achieved in L∞ sense based on some compactness arguments. Compared with the previous results, our results show that the strong boundary layer can still be prevented by the transverse magnetic field even with the magnetic diffusion.

Oscillations of the total kinematic momentum vector for viscous fluid dynamics in pipes of arbitrary section

We derive the oscillatory exact solutions to the Navier–Stokes equations that describe z-invariant viscous fluid flows in a general cylindrical pipe C=D×ℝ1 with section D having an arbitrary geometry and a piece-wise smooth boundary ∂D. Exact viscous fluid flows are presented that satisfy the no-slip boundary condition at the pipe's boundary ∂D×ℝ1 and have an arbitrary number of oscillations of the total kinematic momentum vector on any given interval of time [T1,T2]. The stability of the oscillations with respect to small perturbations of infinitely many parameters is proven. The new method for the generation of a hierarchy of exact solutions with oscillating kinematic momentum is developed. Exact solutions to the Navier–Stokes equations without external forces (in addition to the friction forces at the pipes's boundary ∂D×ℝ1) are derived, which have any number of oscillations of the average shift of viscous fluid.

On augmented finite element formulations for the Navier–Stokes equations with vorticity and variable viscosity

In this work, we propose and analyse an augmented mixed finite element method for solving the Navier–Stokes equations describing the motion of incompressible fluid. The model is written in terms of velocity, vorticity, and pressure, and takes into account non-constant viscosity and no-slip boundary conditions. The weak formulation of the method includes least-squares terms that arise from the constitutive equation and the incompressibility condition. We discuss the theoretical and practical implications of using augmentation in detail. Additionally, we use fixed–point strategies to show the existence and uniqueness of continuous and discrete solutions under the assumption of sufficiently small data. The method is constructed using any compatible finite element pair for velocity and pressure, as dictated by Stokes inf-sup stability, while for vorticity, any generic discrete space of arbitrary order can be used. We establish optimal a priori error estimates and provide a set of numerical tests in 2D and 3D to illustrate the behaviour of the discretisations and verify their theoretical convergence rates. Overall, this method provides an efficient and accurate solution for simulating fluid flow in a wide range of scenarios.

Yield stress fluid flows in superhydrophobic channels: From creeping to inertial regime

In this work, inertial flows of a yield stress fluid in a channel equipped with a superhydrophobic groovy wall are studied through numerical computations. Assuming an ideal Cassie state, the superhydrophobic wall is modeled via arrays of slip, quantified using the Navier slip law, and arrays of stick, corresponding to the no-slip boundary condition. The viscoplastic rheology is modeled using the Bingham constitutive model, implemented via the Papanastasiou regularization technique. The focus is on inertial flows in the thin channel limit, where the groove period is much larger than the half-channel height. The effects of the flow parameters are quantified on the flow variables of interest, including the slip and axial velocity profiles, unyielded plug zones, regime classifications, flow asymmetry indices, effective slip lengths, and friction factors. In particular, an increase in the flow inertia quantified via the Reynolds number affects the flow in several ways, such as reducing the dimensionless slip velocity and effective slip length, increasing the friction factor, inducing an asymmetry in the velocity profile, and showing a non-monotonic effect on the yielding of the center plug. The present work addresses the complex interplay between the yield stress fluid rheology, the wall superhydrophobicity, and the flow inertia, and it can find applications in macro-/micro-transports of non-Newtonian fluids, from oil and gas to health-related industries.

Numerical simulations of the flows past two parallel square columns by MPS method

The hydrodynamic interactions between an offshore platform and surrounding water mainly occurs in way of the pile legs, and the flow past the pile legs can be simplified to the flow past the columns. This is the reason why it is of great significance to simulate the flow around multiple columns with accuracy. In this paper, based on a mesh-less method, Moving Particle Semi-implicit (MPS) method, the MLParticle-SJTU solver is used to simulate the flow past two parallel square columns. Firstly, the reliability and accuracy of the solver is verified by simulating the Poiseuille flow, in which the no-slip boundary condition is applied. Then, the flow past two parallel square columns with different spacing between the two columns is simulated when the Reynold number is 40. The influence of spacing on flow pattern, force on columns and the vortex shedding frequency is analyzed. It is found that when the spacing is relatively small, small vortices will be attached to the surface of the columns. As the spacing ratio increases, periodic shedding of vortices will occur.

Imposing slip conditions on curved boundaries for 3D incompressible flows with a very high-order accurate finite volume scheme on polygonal meshes

The conventional no-slip boundary condition does not always hold in several fluid flow applications and must be replaced with appropriate slip conditions according to the wall and fluid properties. However, not only slip boundary conditions are still a subject of discussion among fluid dynamicists, but also their numerical treatment is far from being well-developed, particularly in the context of very high-order accurate methods. The complexity of these conditions significantly increases when the boundary is not aligned with the chosen coordinate system and, even more challenging, when the fluid slips along a curved boundary. The present work proposes a simple and efficient numerical treatment of general slip boundary conditions on arbitrary curved boundaries for three-dimensional fluid flow problems governed by the incompressible Navier–Stokes equations. In that regard, two critical challenges arise: (i) achieving very high-order of convergence with arbitrary curved boundaries for the classical no-slip boundary conditions and (ii) extending the developed numerical techniques to impose general slip boundary conditions. The conventional treatment of curved boundaries relies on generating curved meshes to eliminate the geometrical mismatch between the physical and computational boundaries and achieve high-order of convergence. However, such an approach requires sophisticated meshing algorithms, cumbersome quadrature rules on curved elements, and complex non-linear transformations. In contrast, the reconstruction for off-site data (ROD) method handles arbitrary curved boundaries approximated with linear piecewise elements while employing polynomial reconstructions with specific linear constraints to fulfil the prescribed boundary conditions. For that purpose, the general slip boundary conditions are reformulated on a local orthonormal basis to allow a straightforward application of the ROD method with scalar boundary conditions. The Navier–Stokes equations are discretised with a staggered finite volume method, and the numerical fluxes are computed solely on the polygonal mesh elements. Several benchmark test cases of fluid flow problems in non-trivial three-dimensional curved domains are addressed and confirm that the proposed method effectively achieves up to the eighth-order of convergence.

Direct numerical simulation of an unsteady wall-bounded turbulent flow configuration for the assessment of large-eddy simulation models

A new benchmark case for the evaluation of direct numerical simulation (DNS) and large-eddy simulation (LES) models and methods is presented in this study. The known Taylor–Green vortex is modified by replacing the periodic boundary conditions in one direction with a no-slip boundary. A passive scalar is added and transported from the wall into the fluid. The addition of walls allows for the study of transient-instationary flows in a simple geometry with clean boundary and initial conditions, which is a key requirement for the assessment of LES modeling strategies. The added scalar mimics heat transfer through the wall. The case features reasonable computational cost for highly-resolved LES and DNS calculations. Simulations of the wall-bounded Taylor–Green vortex are easy to setup and do not require additional modeling. The proposed modification of the case is compared to the default Taylor–Green vortex and the difference in flow-physics is discussed. A detailed convergence study with four meshes, each of them refined by a factor of 2, has been conducted. The results reveal that converged second-order statistics can be obtained up to a dimensionless time of t/t_0 = 20. Beyond that, due to the unsteady chaotic nature of the flow, some uncertainties remain. The results show that the case features challenging (near-wall) flow dynamics, which cannot be covered using the default Taylor–Green vortex and hence, justify the proposed case as a useful benchmark.

Magnetohydrodynamic forced convection and heat transfer of a Casson fluid flow in an anisotropic porous channel with Isoflux boundaries

Theoretical analysis of magnetohydrodynamic fully developed forced convective flow and heat transfer characteristics of a non-Newtonian electrically conducting Casson fluid through a porous channel filled with anisotropic porous material bounded by two impermeable horizontal walls subject to constant heat flux applied to the outer walls is investigated. The extended Darcy-Brinkmann model govern the flow inside the porous channel and accounts for the presence of the inertia term, which allows for the no-slip boundary conditions at the walls. The principal axis of anisotropic permeability is oriented from to radians. The equations governing the system are solved using the inbuilt “DSolve” in Mathematica 11.1 for the velocity and temperature profiles as well as the Nusselt number (Nu), which characterizes the rate of heat transfer in the system. The effects of various parameters on the velocity, temperature and heat transfer profiles are displayed through graphs and discussed quantitatively. From the results we observed that the velocity profile reduced as the Casson parameter (ß), anisotropic ratio (Kr), orientation angle (), and Hartmann number (Ha) increased, whereas the velocity profile increased when the Darcy number (Da) and apparent viscosity () increased. Similarly, these variables also had similar effect on the temperature profile of the fluid. On the other hand, the heat transfer profile, as measured by Nusselt number, increased when the Casson parameter (ß), anisotropic ratio (Kr) and Hartmann number (Ha) increased, while increasing the orientation angle () and apparent viscosity ( ) decreased the Heat Transfer Profile. Upon further investigation, the heat transfer profile was shown to be maximum along the path of least permeability in the anisotropic porous media under investigation.

Hierarchical conductive metal-organic framework films enabling efficient interfacial mass transfer

Heterogeneous reactions associated with porous solid films are ubiquitous and play an important role in both nature and industrial processes. However, due to the no-slip boundary condition in pressure-driven flows, the interfacial mass transfer between the porous solid surface and the environment is largely limited to slow molecular diffusion, which severely hinders the enhancement of heterogeneous reaction kinetics. Herein, we report a hierarchical-structure-accelerated interfacial dynamic strategy to improve interfacial gas transfer on hierarchical conductive metal-organic framework (c-MOF) films. Hierarchical c-MOF films are synthesized via the in-situ transformation of insulating MOF film precursors using π-conjugated ligands and comprise both a nanoporous shell and hollow inner voids. The introduction of hollow structures in the c-MOF films enables an increase of gas permeability, thus enhancing the motion velocity of gas molecules toward the c-MOF film surface, which is more than 8.0-fold higher than that of bulk-type film. The c-MOF film-based chemiresistive sensor exhibits a faster response towards ammonia than other reported chemiresistive ammonia sensors at room temperature and a response speed 10 times faster than that of the bulk-type film.

Exploring the influence of span-wise boundary conditions on the wake of a thin flat plate using Fourier-Averaged Navier–Stokes equations

The wake of a thin normal flat plate with different end conditions is numerically analyzed at a Reynolds number of 250. Periodic, slip, and no-slip boundary conditions are considered for the spanwise boundaries in order to analyze the effect of spanwise flow constraints using a new technique: Fourier-Averaged Navier–Stokes equations (FANS). The results of cases with periodic and slip end conditions were similar in both mean and unsteady fields. However, no-slip boundary conditions, which could represent the case of experimental setups with end plates, significantly reduce the velocity, drag and lift fluctuations in the flow. FANS analysis confirmed that loss of the nominal two-dimensional behavior due to the no-slip end condition relates to the presence of a spanwise flow coherence at the vortex shedding frequency (mode). Interactions between the rollers and boundary layer induces large-scale spanwise fluctuations that are absent without the end plates. In this way, the boundary layer due to the end plate serves as a flow control mechanism that suppresses fluctuations in the flow and reduces stresses in the center-plane, alongside increasing coherence in the spanwise flow.

Influence of Variable Viscosity on Entropy Generation Analysis Due to Graphene Oxide Nanofluid Flow

Conventional investigations on fluid flows are undertaken with an assumption of constant fluid properties. But in reality, the properties such as viscosity and thermal conductivity vary with temperature. In such cases, considering these variabilities aids in modelling the flows with accuracy. Particularly, studying the flow of graphene based nanofluids with variable properties makes the best of both the advantageous thermophysical properties of graphene nanoparticles in heat transfer and the variable fluid properties in accuartely modelling the flow. In this article, the flow of graphene oxide nanofluid along a linearly stretching cylinder under no-slip and convective boundary conditions is investigated, by taking the base fluid viscosity to be a temperature dependant function. Buongiorno model is adapted to develop the flow of graphene nanofluids including the influence of variable heat source, cross-diffusion effects and the effects of nanoparticle characteristics such as thermophoresis and Brownian motion. The modelled equations are transformed and are numerically solved using linearization method. The impacts of embedded parameters including the Dufour and Soret numbers on temperature, concentration and velocity profiles of the chosen nanofluid and their consequent impacts on the predominant cause for the generated entropy are studied. The obtained results are depicted and interpreted in detail. From the tabulated values of skin friction and the values of Sherwood and Nusselt numbers, it is inferred that the conductive heat and mass transfer can be enhanced by variable viscosity parameter and skin friction can be reduced by Soret number. Furthermore, entropy generation is analysed and Bejan number is calculated to be lesser than 0.5, thus demonstrating the dominance of irreversibilty to fluid friction and mass transfer.

Review of Jackson Herring’s Early Work on Thermal Convection

Jack Herring had three mid-1960s numerical papers on Rayleigh-Bénard thermal convection that might seem primitive by today’s standards, but already encapsulated many of the questions that are still being asked. All of them use severely truncated versions of the incompressible Navier–Stokes–Boussinesq equations with only one, or just a few, horizontal Fourier modes. In the first two papers, 1963 and 1964, the presented results used only one Fourier mode α and three variables. The single mode’s variables are its vertical velocity profile wα(z,t), its temperature profile θα(z,t) and the horizontally uniform vertical profile of the background temperature ψ(z,t). All of the second- and third-order terms are ignored except the convective heat flux wθ¯. The objective was to find asymptotic steady-state solutions. Each paper found evidence for the one-third Nusselt versus Rayleigh scaling of Nu∼Ra1/3, originally derived from Malkus’ maximum flux principle. The 1963 paper uses free-slip upper and lower boundaries, with magnitudes of Nu that are a factor of three larger than the experiments. In the 1964 paper, by introducing no-slip/rigid boundary conditions, the magnitude of Nu dropped to within 20% of the experimental values. Both Nu(Ra) relations are in good agreement with circa-1990 direct numerical simulations (DNS). This dependence upon the boundary condition at the walls suggests that to obtain physically realistic scaling, no-slip boundary conditions are necessary. The third paper is discussed only in terms of what it might have been aiming to accomplish and its relation to the earlier free-slip results.

No-Slip Boundary Condition for Vorticity Equation in 2D Exterior Domain

In this article we derive the no-slip boundary condition for a non-stationary vorticity equation. This condition generates the affine invariant manifold and no-slip integral relations on vorticity can be transferred to a Robin-type boundary condition.

Global bounded solution of a 3D chemotaxis-Stokes system with nonlinear doubly degenerate diffusion

The paper considers the following chemotaxis-Stokes system with nonlinear doubly degenerate diffusion{nt+u⋅∇n=∇⋅(|∇nm|p−2∇nm)−χ∇⋅(n∇c),x∈Ω,t>0,ct+u⋅∇c=Δc−cn,x∈Ω,t>0,ut+∇P=Δu+n∇Φ,x∈Ω,t>0,∇⋅u=0,x∈Ω,t>0 in a bounded domain Ω⊂R3 with zero-flux boundary conditions and no-slip boundary condition. In this paper, we proved that global bounded weak solutions exist whenever m>1 and p≥2. It removes the restrict 8mp−8m+3p>15 and improves the result of paper Lin (2022) [15].

Novel Schemes of No-Slip Boundary Conditions for the Discrete Unified Gas Kinetic Scheme Based on the Moment Constraints.

The boundary conditions are crucial for numerical methods. This study aims to contribute to this growing area of research by exploring boundary conditions for the discrete unified gas kinetic scheme (DUGKS). The importance and originality of this study are that it assesses and validates the novel schemes of the bounce back (BB), non-equilibrium bounce back (NEBB), and Moment-based boundary conditions for the DUGKS, which translate boundary conditions into constraints on the transformed distribution functions at a half time step based on the moment constraints. A theoretical assessment shows that both present NEBB and Moment-based schemes for the DUGKS can implement a no-slip condition at the wall boundary without slip error. The present schemes are validated by numerical simulations of Couette flow, Poiseuille flow, Lid-driven cavity flow, dipole-wall collision, and Rayleigh-Taylor instability. The present schemes of second-order accuracy are more accurate than the original schemes. Both present NEBB and Moment-based schemes are more accurate than the present BB scheme in most cases and have higher computational efficiency than the present BB scheme in the simulation of Couette flow at high Re. The present Moment-based scheme is more accurate than the present BB, NEBB schemes, and reference schemes in the simulation of Poiseuille flow and dipole-wall collision, compared to the analytical solution and reference data. Good agreement with reference data in the numerical simulation of Rayleigh-Taylor instability shows that they are also of use to the multiphase flow. The present Moment-based scheme is more competitive in boundary conditions for the DUGKS.