No-slip Wall Research Articles

Wall-to-wall optimal transport in two dimensions

Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of velocity fields by a P\'eclet number $\text{Pe}$ proportional to their root-mean-square rate-of-strain, the schemes are applied to compute two-dimensional flows optimizing convective enhancement of diffusive heat transfer, i.e., the Nusselt number $\text{Nu}$ up to $\text{Pe} \approx 10^5$. The resulting transport exhibits a change of scaling from $\text{Nu}-1 \sim \text{Pe}^{2}$ for $\text{Pe} < 10$ in the linear regime to $\text{Nu} \sim \text{Pe}^{0.54}$ for $\text{Pe} > 10^3$. Optimal fields are observed to be approximately separable, i.e., products of functions of the wall-parallel and wall-normal coordinates. Analysis employing a separable ansatz yields a conditional upper bound $\lesssim \text{Pe}^{6/11} = \text{Pe}^{0.\overline{54}}$ as $\text{Pe} \rightarrow \infty$ similar to the computationally achieved scaling. Implications for heat transfer in buoyancy-driven Rayleigh-B\'enard convection are discussed.

Comparison of the flow-field characteristics of a slot synthetic jet with and without sidewalls

In this paper, experimental investigation of the flow-field of a slot synthetic jet (SJ) with and without sidewalls, issuing into a quiescent environment is systematically reported. Two parallel sidewalls were mounted along the shorter side of the slot extending in the streamwise direction to constrain the flow along the slot span. Hot-wire anemometry was used to explore the flow-field characteristics of both configurations at a Reynolds number of 4000 based on the slot-width and slot average exit velocity during the ejection phase. The present work is a first step towards the investigation of the SJ flow-field characteristics in a bounded region. In a number of generic situations, this work is of high importance as the SJ is deployed in constrained environments (e.g., in cooling applications) where sidewalls may be present. The relative difference in the magnitude of the distinct peaks in the near-field spanwise velocity profiles for both configurations reveals that the vortex does not get curled up towards the centerline in the case of the synthetic jet with sidewalls due to the presence of the no-slip walls. Spectral analysis in the near-wall region further confirms the absence of the phenomenon of axis-switching in the case of the synthetic jet with sidewalls. This behavior is also demonstrated with the help of the relative spreading rate in both configurations, where the unbounded synthetic jet spreads rapidly compared to the bounded one, due to greater entrainment of the surrounding fluid. The statistically two-dimensional region for a synthetic jet with sidewalls is found to extend over a longer axial distance in the downstream. The other jet properties such as turbulence intensity, skewness, and flatness factors further reveal the differences in the flow-field of the two configurations. The results show that the presence of the sidewalls strongly influences the SJ flow-field and hence, it would significantly impact the heat transfer capacity of the SJ.

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

We propose a Finite Volume Method for the simulation of elastoviscoplastic (EVP) flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154–161]. The method is applicable to cell-centred grids of arbitrary geometry by the introduction of new stabilisation techniques of the “momentum interpolation” and “both sides diffusion” types, for pressure and velocity, respectively. Adaptive time stepping is employed. The method is used to perform benchmark simulations of lid-driven cavity flow, which also serve to explore certain aspects of this EVP constitutive equation in a two-dimensional setting. The model parameters are chosen so as to represent Carbopol, and simulations are performed for different lid velocities and with either slip or no-slip wall boundaries. The results are compared against those obtained with the classic Herschel-Bulkley model. It is noticed that different initial conditions for stress lead to different steady states. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted; it is found that, contrary to the classic Herschel-Bulkley predictions, the EVP flow does not cease in finite time. Rather, the flow decays very slowly while the material oscillates as kinetic energy is converted to elastic energy and vice versa. Flow decay is much faster under slip conditions due to the friction between the material and the walls.

Solid wall and open boundary conditions in hybrid recursive regularized lattice Boltzmann method for compressible flows

Complex geometries and open boundaries have been intensively studied in the nearly incompressible lattice Boltzmann method (LBM) framework. Therefore, only few boundary conditions for the high speed fully compressible LBM have been proposed. This paper deals with the definition of efficient boundary conditions for the compressible LBM methods, with the emphasis put on the newly proposed hybrid recursive regularized D3Q19 LBM (HRR-LBM) with applications to compressible aerodynamics. The straightforward simple extrapolation-based far-field boundary conditions, the characteristic boundary conditions, and the absorbing sponge layer approach are extended and estimated in the HRR-LBM for the choice of open boundaries. Moreover, a cut-cell type approach to handle the immersed solid is proposed to model both slip and no-slip wall boundary conditions with either isothermal or adiabatic behavior. The proposed implementations are assessed considering the simulation of (i) isentropic vortex convection with subsonic to supersonic inflow and outflow conditions, (ii) two-dimensional (2D) compressible mixing layer, (iii) steady inviscid transonic flow over a National Advisory Committee for Aeronautics (NACA) 0012 airfoil, (iv) unsteady viscous transonic flow over a NACA 0012 airfoil, and (v) three-dimensional (3D) transonic flows over a German Aerospace Center (DLR) F6 full aircraft configuration.

An X-lattice cored rectangular honeycomb with enhanced convective heat transfer performance

This paper proposes a new periodic cellular material (PCM) by integrating the X-lattice into a rectangular honeycomb. Convective heat transfer in this new PCM is explored. For a given Reynolds number, the overall Nusselt number of the new PCM is up to 360% and 55% higher than the parent honeycomb and X-lattice sandwich panel, respectively. The introduction of the honeycomb walls to the X-lattice sandwich panel enlarges or induces new separation vortices near the four corners of each rectangular passage, which weakens the tangential flow perpendicular to the mainstream; the no-slip honeycomb walls and the modification of the separation vortices change the counter-rotating vortex pair behind the ligaments, significantly reduce the bulk turbulent kinetic energy magnitude and limit the convective transport of the high turbulent kinetic energy to the endwalls, due to severe dissipation of the energy by the viscous sub-layer. Corresponding to the flow pattern variations, local heat transfer on the endwall and the X-lattice ligaments is deteriorated. However, the X-lattice induced spiral flow and secondary flows enhance the heat transfer on the honeycomb walls by approximately 230%. For a given pumping power, the new PCM exhibits up to 42% higher heat removal than the parent X-lattice sandwich.

Analytical solutions for two-dimensional singly periodic Stokes flow singularity arrays near walls

New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from a concentric annulus (or a disc) to a rectangle and a complex variable formulation of Stokes flow to derive the solutions. The form of the solutions is amenable to fast and accurate numerical computation without the need for Ewald summation or other fast summation techniques.

Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: Implications for the hydrodynamics of an active microswimmer near an elastic interface.

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future for biomedical and technological applications. These microswimmers move autonomously through aqueous media, where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than those due to shear resistance. Bending can enhance (suppress) the velocities resulting from higher-order singularities whereas the shear related contribution decreases (increases) the velocities. Most prominently, we find that near an elastic interface of only energetic resistance toward shear deformation, such as that of an elastic capsule designed for drug delivery, a swimming bacterium undergoes rotation of the same sense as observed near a no-slip wall. In contrast to that, near an interface of only energetic resistance toward bending, such as that of a fluid vesicle or liposome, we find a reversed sense of rotation. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.

Improved treatment of wall boundary conditions for a particle method with consistent spatial discretization

In recent years, consistent spatial discretization schemes for meshfree particle methods to numerically simulate incompressible flow have been studied by many researchers. This study is focused on the treatment of solid wall boundary conditions for one of those schemes, namely the least squares MPS (LSMPS) scheme, and proposes a new technique to deal with no-slip and free-slip wall boundary conditions. With the proposed treatment, wall geometries are expressed by surface meshes, i.e. polygons in 3D and line segments in 2D. Thus, complicated geometries can be handled easily. Based on a Taylor series expansion, wall boundary conditions are incorporated into the differential operators acting on fluid particles located in the vicinity of a wall, through a least squares approach. As a consequence, Neumann boundary conditions can be treated quite efficiently. To verify consistency of the proposed discretization scheme, a convergence study was carried out. As numerical examples, Couette flow, plane Poiseuille flow, gravity-driven flow in a 3D square duct, a rigid rotation problem, Taylor–Green vortices and lid-driven cavity flow have been calculated using the proposed boundary treatment, with both no-slip and free-slip conditions applied. As a result, the present method agreed well with the reference solutions, which verified its computational accuracy.

Direct numerical simulation of low-Prandtl fluid flow over a confined backward facing step

The paper presents the direct numerical simulation (DNS) of a confined backward facing (BFS) step geometry with a flow of two fluids with Prandtl numbers 0.005 and 0.1. The expansion ratio of the BFS geometry is equal to 2.25 and the outflow of the geometry has a shape of a rectangle. The geometry is surrounded by no-slip walls and has no periodic boundaries. Additionally, a step wall and a heater are simulated, which are thermally coupled with each other and to the fluid domain. A recycling boundary condition is used to achieve a fully turbulent inflow boundary condition with a constant mass flow rate. The friction Reynolds number of the flow in the channel before the step is around 207 and the Reynolds number based on the bulk velocity at the inflow and the hydraulic diameter of the inflow is approximately 7100. The reattachment zone was found at about 7.9 step heights downstream of the step. Because the step is confined in the span-wise direction, the average flow exhibits strong 3D features. These features significantly increase the averaging times to achieve sufficiently low statistical uncertainties of flow properties. The DNS is performed with moderate spatial resolution on 30 million grid points, however, it took very long averaging time and 8 million time steps to obtain acceptable statistical uncertainties. In the paper we explore the 3D features and give first and second order statistics for flow and thermal fields, which are relevant for the validation of RANS modelling approach. To this regard, an advanced and well calibrated turbulent heat flux model, called AHFM-NRG+, is selected for validation in this paper.

Competing chemical and hydrodynamic interactions in autophoretic colloidal suspensions.

At the surfaces of autophoretic colloids, slip velocities arise from local chemical gradients that are many-body functions of particle configuration and activity. For rapid chemical diffusion, coupled with slip-induced hydrodynamic interactions, we deduce the chemohydrodynamic forces and torques between colloids. For bottom-heavy particles above a no-slip wall, the forces can be expressed as gradients of a nonequilibrium potential which, by tuning the type of activity, can be varied from repulsive to attractive. When this potential has a barrier, we find arrested phase separation with a mean cluster size set by competing chemical and hydrodynamic interactions. These are controlled, in turn, by the monopolar and dipolar contributions to the active chemical surface fluxes.

MHD Free Convection in a Partially Heated Open-Ended Square Cavity: Effect of Angle of Magnetic Field and Heater Location

A computational analysis based upon the kinetic, mesoscopic numerical tool is adapted for elucidating the buoyancy-driven convection in the square shaped open cavity having the partially active wall under the influence of the uniform magnetic field (B). A heater (size- half of the height of the cavity) is positioned along the vertical, no-slip wall of the cavity (while another vertical end is open to the atmosphere). Other regions of no-slip partially heated vertical wall, as well as top and bottom walls, are thermally insulated. The significance of heater location (bottom, middle and top), the angle of magnetic field (0°, 45° and 90°), Hartmann number (0–100) and Rayleigh number (103–105) on natural convection have been illustrated. The interpretation of results have been carried out by studying the streamlines, isotherms, centreline variation of temperature; velocity component profiles and Nusselt number (local, average). The dependence of the Nusselt number with the magneto-convective parameter is presented and discussed. Heat transfer rate increases with the angle of the magnetic field.

Magneto-hydrodynamic flow of squeezed fluid with binary chemical reaction and activation energy

The present exploration is conducted to describe the motion of viscous fluid embedded in squeezed channel under the applied magnetics effects. The processes of heat and mass transport incorporate the temperature-dependent binary chemical reaction with modified Arrhenius theory of activation energy function which is not yet disclosed for squeezing flow mechanism. The flow, heat and mass regime are exposed to be governed via dimensionless, highly non-linear, ordinary differential equations (ODEs) under no-slip walls boundary conditions. A well-tempered analytical convergent procedure is adopted for the solutions of boundary value problem. A detailed study is accounted through graphs in the form of flow velocity field, temperature and fluid concentration distributions for various emerging parameters of enormous interest. Skin-friction, Nusselt and Sherwood numbers have been acquired and disclosed through plots. The results indicate that fluid temperature follows an increasing trend with dominant dimensionless reaction rate σ and activation energy parameter E. However, an increment in σ and E parameters is found to decline in fluid concentration. The current study arises numerous engineering and industrial processes including polymer industry, compression and injection shaping, lubrication system, formation of paper sheets, thin fiber, molding of plastic sheets. In the area of chemical engineering, geothermal engineering, cooling of nuclear reacting, nuclear or chemical system, bimolecular reactions, biochemical process and electrically conducting polymeric flows can be controlled by utilizing magnetic fields. Motivated by such applications, the proposed study has been developed.

Characteristic scales of Townsend's wall-attached eddies.

Townsend (The Structure of Turbulent Shear Flow, 1976, Cambridge University Press) proposed a structural model for the logarithmic layer (log layer) of wall turbulence at high Reynolds numbers, where the dominant momentum-carrying motions are organised into a multiscale population of eddies attached to the wall. In the attached-eddy framework, the relevant length and velocity scales of the wall-attached eddies are the friction velocity and the distance to the wall. In the present work, we hypothesise that the momentum-carrying eddies are controlled by the mean momentum flux and mean shear with no explicit reference to the distance to the wall and propose new characteristic velocity, length and time scales consistent with this argument. Our hypothesis is supported by direct numerical simulation of turbulent channel flows driven by non-uniform body forces and modified mean velocity profiles, where the resulting outer-layer flow structures are substantially altered to accommodate the new mean momentum transfer. The proposed scaling is further corroborated by simulations where the no-slip wall is replaced by a Robin boundary condition for the three velocity components, allowing for substantial wall-normal transpiration at all length scales. We show that the outer-layer one-point statistics and spectra of this channel with transpiration agree quantitatively with those of its wall-bounded counterpart. The results reveal that the wall-parallel no-slip condition is not required to recover classic wall-bounded turbulence far from the wall and, more importantly, neither is the impermeability condition at the wall.

DEM/CFD Simulations of a Pseudo-2D Fluidized Bed: Comparison with Experiments

The present work investigates the performance of a mesoscopic LaGrangian approach for the prediction of gas–particle flows under the influence of different physical and numerical parameters. To this end, Geldart D particles with 1 mm diameter and density of 2500 kg/m 3 are simulated in a pseudo-2D fluidized bed using a Discrete Element Method (DEM)/Large-Eddy Simulation (LES) solver called YALES2. Time-averaged quantities are computed and compared with experimental results reported in the literature. A mesh sensitivity analysis showed that better predictions regarding the particulate phase are achieved when the mesh is finer. This is due to a better description of the local and instantaneous gas–particle interactions, leading to an accurate prediction of the particle dynamics. Slip and no-slip wall conditions regarding the gas phase were tested and their effect was found negligible for the simulated regimes. Additional simulations showed that increasing either the particle–particle or the particle–wall friction coefficients tends to reduce bed expansion and to initiate bubble formation. A set of friction coefficients was retained for which the predictions were in good agreement with the experiments. Simulations for other Reynolds number and bed weight conditions are then carried out and satisfactory results were obtained.

Bifurcation theory for vortices with application to boundary layer eruption

We develop a bifurcation theory describing the conditions under which vortices are created or destroyed in a two-dimensional incompressible flow. We define vortices using the $Q$-criterion and analyse the vortex structure by considering the evolution of the zero contours of $Q$. The theory identifies topological changes of the vortex structure and classifies these as four possible types of bifurcations, two occurring away from boundaries, and two occurring near no-slip walls. Our theory provides a description of all possible codimension-one bifurcations where time is treated as the bifurcation parameter. To illustrate our results, we consider the early stages of boundary layer eruption at moderate Reynolds numbers in the range from $Re=750$ to $Re=2250$. By analysing numerical simulations of the phenomenon, we show how to describe the eruption process as sequences of the four possible bifurcations of codimension one. Our simulations show that there is a single codimension-two point within our parameter range. This codimension-two point arises at $Re=1817$ via the coalescence of two codimension-one bifurcations which are associated with the creation and subsequent destruction of one of the vortices that erupt from the boundary layer. We present a theoretical description of this process and explain how the occurrence of this phenomenon separates the parameter space into two regions with distinct evolution of the topology of the vortices.

Universality in statistics of Stokes flow over a no-slip wall with random roughness

Stochastic roughness is a widespread feature of natural surfaces and is an inherent byproduct of most fabrication techniques. In view of the rapid development of microfluidics, the important question is how this inevitable problem affects the low-Reynolds-number flows that are common for micro-devices. Moreover, one could potentially turn the flaw into a virtue and control the flow properties by means of specially ‘tuned’ random roughness. In this paper we investigate theoretically the statistics of fluctuations in fluid velocity produced by the waviness irregularities at the surface of a no-slip wall. Particular emphasis is laid on the issue of the universality of our findings.

Effect of residual air bubbles on diesel spray structure at the start of injection

Experimental and numerical analyses of the effect of residual air bubbles in a single-hole high-pressure diesel injector nozzle are presented. Detailed information on spray structures and dynamics near nozzle exit at the Start of Injection(SOI) is described. Experimental measurements are performed using a laser-based backlit imaging technique through a long distance microscope by injecting diesel fuel into a constant volume high-pressure spray chamber. Numerical investigation of, in and near-nozzle fluid dynamics is conducted in an Eulerian framework using a Volume of Fluid(VOF) interface capturing technique integrated with Large Eddy Simulation(LES) turbulence modelling. The present flow setup includes residual air bubbles remaining from a previous injection event, in-nozzle turbulence with no-slip wall conditions. Experimental images show a toroidal starting vortex near the nozzle exit suggesting a partially filled nozzle; transparency in the emerging jet demonstrates the presence of air trapped inside the nozzle liquid from the previous injection event. The numerical model provides insight into the influence of residual air bubbles on the spray morphology and dynamics of the emerging jet at the SOI. A mathematical code is developed to replicate the backlit imaging approach with the numerical results. The virtual images demonstrate a transparent liquid jet emerging into the pressurized chamber gas showing improved agreement with experimental images. The inclusion of air bubbles in the nozzle liquid prior to injection in the numerical model also yields improved agreement in the penetration velocity profile of the jet. These results explain how inclusion of residual air bubbles inside the nozzle liquid affects the physics of the penetrating jet at the SOI. The air bubbles inclusion also provides an explanation for the transparency of the emerging jet, rough interfacial surfaces, and enhanced necking behind the jet tip captured at the SOI.

Numerical study of crude oil batch mixing in a long channel

The main objective of this work is to predict the mixing of two different miscible oils in a very long channel. The background to this problem relates to the mixing of heavy and light oil in a pipeline. As a first step, a 2D channel with an aspect ratio of 250 is considered. The batch-mixing of two miscible crude oils with different viscosities and densities is modeled using an unsteady laminar model and unsteady RANS model available in the commercial CFD solver ANSYS-Fluent. For a comparison, a LES model was used for a 3D version of the 2D channel. The distinguishing feature of this work is the Lagrangian coordinate system utilized to set no-slip wall boundary conditions. The global CFD model has been validated against classical analytical solutions. Excellent agreement has been achieved. Simulations were carried out for a Reynolds number of 6300 (calculated using light oil properties) and a Schmidt number of ~10^4. The results show that, in contrast to the unsteady RANS model, the LES and unsteady laminar models produce comparable mixing dynamics for two oils in the channel. Analysis of simulations also shows that, for a channel length of 100 m and a height of 0.4 m, the complete mixing of two oils across the channel has not been achieved. We showed that the mixing zone consists of the three different mixing sub-zones, which have been identified using the averaged mass fraction of the heavy oil along the flow direction. The first sub-zone corresponds to the main front propagation area with a length of several heights of the channel. The second and third sub-zones are characterized by so-called shear-flow-driven mixing due to the Kelvin–Helmholtz vortices occurring between oils in the axial direction. It was observed that the third sub-zone has a steeper mass fraction gradient of the heavy oil in the axial direction in comparison with the second sub-zone, which corresponds to the flow-averaged mass fraction of 0.5 for the heavy oil.

Variable Fluid Property Effect on Heat Transfer and Frictional Flow Characteristics of Water Flowing through Microchannel

The effects of temperature-dependent viscosity and thermal conductivity on heat transfer and frictional flow characteristics of water flowing through a microchannel are numerically investigated in this work. The hydrodynamically and thermally developing flow with no-slip, notemperature jump, and constant wall heat flux boundary condition is numerically studied using 2D continuum-based conservation equations. A significant deviation in Nusselt number from conventional theory is observed due to flattening of axial velocity profile due to temperaturedependent viscosity variation. The Nusselt number shows a significant deviation from conventional theory due to flattening of the radial temperature profile due to temperature-dependent thermal conductivity variation. It is noted that the deviation in Nusselt number from conventional theory is maximum for combined temperature-dependent viscosity and thermal conductivity variations. The effects of temperature-dependent viscosity and thermal conductivity on the Fanning friction factor are also investigated. Additionally, the effects of variable fluid properties on Poiseuille number, Prandtl number, and Peclet number are also investigated.

Mobilities of polydisperse hard spheres near a no-slip wall

We have derived an analytical formulation for far-field hydrodynamic interactions among unequal size hard spheres near a no-slip wall and have implemented the formulation in a Stokesian dynamics model to simulate a suspension of polydisperse particles in a semi-bounded domain. The formulation is based on the multipole expansion of the boundary integral of Stokes flow, and the mobility tensors are deduced from Fáxen’s law together with Green’s function for Stokes flow near a no-slip wall. Lubrication approximation is incorporated to account for the close-distance interactions between any two particles and also between the particles and the wall. The implementation is validated against previous formulations for equal size particles and against a boundary-element code for unequal size particles. The code can be used to simulate the Stokesian or Brownian interaction of unequal particles in presence of a no-slip wall. In the current study, we applied the Stokesian dynamics model to investigate the trajectories of two unequal hard spheres and their redistribution during sedimentation parallel to a wall. We further used it to demonstrate the cases of many-particle sedimentation toward or parallel to a wall.