Plane Wall Research Articles

An Effect of Gap Ratios at Four Circular Cylinders in a Staggered Configuration Near a Plane Wall

The flow that crosses the arrangement of four circular cylinders will form a certain flow pattern according to the geometry of the body contour, the distance between the cylinders, and the flow orientation (α), and generated aerodynamic forces, such as lift force, drag force, as well as induced vibration on the body. The force coefficients on four circular cylinders in an equispaced arrangement with a staggered configuration located near a plane wall were calculated through the pressure distributions measurement. The pressure distributions on each cylinder surface and the plane wall were measured for various gap ratio values of G/D= 0.0 and 0.2 (G, the gap between cylinder to the plane wall; D, diameter) and L/D= 2.7 (L, gap spacing between cylinders) in a uniform flow at a Reynolds Number of 1.743 x 104. The results show that the drag and lift coefficients on the cylinders depend on the gap ratio value of G/D. The drag coefficient decreases, when the amount of G/D increases, especially on the upstream cylinders. The lift coefficient on the upper-downstream cylinders has a significant value more than other cylinders at a small spacing ratio.

Reappraisal of plane wall jet self-similarity

There is a general consensus that the characteristic velocity and length scales for a plane wall jet exhibit power law with distance downstream of the jet nozzle/slot, x; however, no definitive values are given for the power-law exponents. In view of this, plane wall jet self-similarity is reappraised using a compilation of experimental and direct numerical data of plane wall jets. The plots of compensated distributions of the maximum velocity Umax and length y1/2, the location where the velocity is equal to Umax/2 in the outer part of the flow, reveal that these variables follow the power laws Umax∼y1/2n and y1/2∼xm, where n∼−1/2 and m∼1, which comply with self-similarity solutions. While n∼−1/2 is in agreement with the existing results, the linear growth of y1/2 contrasts with the common belief that m should be less than 1. It is argued that the limited ranges of x and Reynolds numbers (Re) used in the previous studies prevent this latter behavior to be observed. This behavior emerges when these data are compiled into a single set, allowing a reasonable range of x and Re. It is further observed that only one velocity scale, either Umax or uτ, the friction velocity, is needed for the outer region, which complies with a requirement imposed by self-similarity under a linear growth y1/2. In the inner region, either ν/uτ or y1/2,in (the location where the velocity is equal to Umax/2 in the inner part) can be used as a scaling velocity, while uτ should be the adequate scaling velocity. The present analysis provides some support to the argument that scaling could be universal, at least when the Reynolds number is large enough and the flow is allowed to evolve over a very long distance.

Thin and thick bubble walls II: expansion in the wall width

We study the dynamics of a cosmological bubble wall beyond the approximation of an infinitely thin wall.In a previous paper, we discussed the range of validity of this approximationand estimated the first-order corrections due to the finite width.Here, we introduce a systematic method to obtain the wall equation of motion and its profile at each order in the wall width.We discuss in detail the next-to-next-to-leading-order terms.We use the results to treat the growth of spherical bubbles and the evolution of small deformations of planar walls.

Ab initio generalized Langevin equation

We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multiscale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of CVs by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.

Low-frequency vibration reduction of an underwater metamaterial plate excited by a turbulent boundary layer

Flow-induced structural noise is an important component of hydrodynamic noise of underwater structures. Local resonance metamaterials are considered to have excellent performance and enormous potential in the field of low-frequency vibration and noise control. To verify its potential, the paper derived the underwater band gap of a lateral local resonance (LLR) plate through the plane wave expansion (PWE). Then, utilizing the modal superposition approach and Rayleigh integral technique, the vibro-acoustic response of a LLR plate under a turbulent boundary layer (TBL) excitation is obtained. Finite element certification is also conducted through an uncorrelated wall plane wave technique. Parametric study is conducted to analyse the factors which influence the control effects. The result shows that the plate exhibits excellent suppression performance for flow-induced vibration at band gap frequencies. The band gaps and suppression ranges generated by the underwater metamaterial plate, are dramatically narrowed due to the thick fluid load. The paper provides theoretical guidance for the control of flow-induced structural vibration and the application of acoustic metamaterials.

Steady laminar stagnation flow NH[formula omitted]-H[formula omitted]-air flame at a plane wall: Flame extinction limit and its influence on the thermo-mechanical stress and corrosive behavior of wall materials

The steady laminar stagnation flow flame of NH3-H2-air gas mixture stabilized at a plane wall is numerically investigated. Its interaction with the wall with the consideration of heat loss is the focus of this work. The numerical study of the combustion system is performed by using the full chemical mechanism and detailed transport model including the differential diffusion and Soret effect. The simulation of the solid mechanics is based on the theory of isotropic linear thermo-elasticity. With the numerical simulation, it will be discussed how the wall material would change the flame stability in terms of extinction limit, and how the combustion system such as mixture composition, flame strain rate, and pressure would vary the thermo-mechanical stresses in the solid wall and the corrosive behavior at the surface of the wall.

Cryogenic strengthening of Fe27Co24Ni23Cr26 high-entropy alloys via hierarchical nanotwin-driven mechanism

FCC-based high entropy alloys (HEAs) with exceptional cryogenic mechanical properties have the potential for use in strategic applications. In this regard, we have studied via transmission electron microscopy (TEM) the microstructural evolution of hierarchical nanotwins in tensile-strained Fe27Co24Ni23Cr26 HEA alloys as a function of true strain at cryogenic temperature and compared the behavior at room temperature. At cryogenic temperature, the alloy had a high strength of ∼1211 MPa and large elongation of 87.2% compared to the room temperature tensile strength of 746 MPa and elongation of ∼61%. At 25 °C, the deformation initiated with the entanglement of wavy dislocations, which transformed into planar configuration and dislocation walls, and lastly to deformation nanotwins. In striking contrast, at −150 °C, numerous nanotwin bundles were formed through the coalescence of deformation nanotwins, which divided the matrix into microscale closed blocks. At higher strain, dense deformation nanotwins refined annealing twins into nanoscale closed blocks. Subsequently, in the interior of annealing twins, deformation nanotwin variants interpenetrated, producing serrated/curved interfacial structures. These interfaces are envisaged to promote the formation of ultra-fine deformation nanotwins and closed blocks that facilitate accommodation of a higher degree of deformation strain at cryogenic temperatures. The study provides new insights and guidelines in the futuristic design of FCC high entropy alloys for use at cryogenic temperatures by embracing the hierarchical nanotwin-driven mechanism.

Controlled transport of fluid particles by microrotors in a Stokes flow using linear transfer operators

The manipulation of a collection of fluid particles in a low Reynolds number environment has several important applications. As we demonstrate in this paper, this manipulation problem is related to the scientific question of how fluid flow structures direct Lagrangian transport. We investigate this problem of directing the transport by manipulating the flow, specifically in the Stokes flow context, by controlling the strengths of two rotors fixed in space. We demonstrate a novel dynamical systems approach for this problem and apply this method to several scenarios of Stokes flow in unbounded and bounded domains. Furthermore, we show that the time-varying flow field produced by the optimal control can be understood in terms of dynamical structures such as coherent sets that define Lagrangian transport. We model the time evolution of the fluid particle density using finite-dimensional approximations of the Liouville operators for the microrotor flow fields. Using these operators, the particle transport problem is framed as an optimal control problem, which we solve numerically. This framework is then applied to the problem of transporting a blob of fluid particles in domains with different boundary conditions: free space, near to a plane wall, in a circular confinement, and the transport of two distributions of particles to a common target. These examples demonstrate the effectiveness of the proposed framework and also shed light on the effects of boundaries on the ability to achieve a desired fluid transport using a rotor-driven flow.

Planar wall plumes bounded by vertical and inclined surfaces

Planar wall plumes are gravity-driven flows where a fluid of lower (or higher) density than the ambient rises (or lowers) along a vertical or inclined wall. This study investigates planar wall plumes at five different wall slopes, ranging from a vertical wall (θ=90°) to a shallow inclination of θ=3°, using highly resolved direct numerical simulations. The three-dimensional turbulent structure of these supercritical flows is investigated in detail along with the streamwise evolution of the depth-averaged quantities. Simulations were performed in very large domains in order to focus attention on the behavior of the plumes in the near self-similar state, far downstream of the inlet. In the self-similar state, key quantities such as the entrainment rate, the basal drag coefficient, the Richardson number (or equivalently the Froude number), and the shape factors reach constant values, which dependent only on the slope. The present simulations, along with earlier results for subcritical currents at shallower slopes, provide a complete description of this dependency.

Domain walls in Horndeski gravity

The Horndeski gravity yields domain wall solutions that connect asymmetric vacua for a certain region of parameters. In the thin wall limit there exist BPS domain walls that connect stable vacua. That is, the false vacua in this theory follows the same effect obtained in supergravity vacua, i.e., it does not decay according to Coleman-de Luccia theory and the BPS solutions interpolating different vacua, e.g., non-degenerate AdS vacua, are static infinite planar domain walls separating vacua associated with different spacetimes.

Wetting and Spreading Behavior of Axisymmetric Compound Droplets on Curved Solid Walls Using Conservative Phase Field Lattice Boltzmann Method.

Compound droplets have received increasing attention due to their applications in many several areas, including medicine and materials. Previous works mostly focused on compound droplets on planar surfaces and, as such, the effects of curved walls have not been studied thoroughly. In this paper, the influence of the properties of curved solid wall (including the shape, curvature, and contact angle) on the wetting behavior of compound droplets is explored. The axisymmetric lattice Boltzmann method, based on the conservative phase field formulation for ternary fluids, was used to numerically study the wetting and spreading of a compound droplet of the Janus type on various curved solid walls at large density ratios, focusing on whether the separation of compound droplets occurs. Several types of wall geometries were considered, including a planar wall, a concave wall with constant curvature, and a convex wall with fixed or variable curvature (specifically, a prolate or oblate spheroid). The effects of surface wettability, interfacial angles, and the density ratio (of droplet to ambient fluid) on the wetting process were also explored. In general, it was found that, under otherwise identical conditions, droplet separation tends to happen more likely on more hydrophilic walls, under larger interfacial angles (measured inside the droplet), and at larger density ratios. On convex walls, a larger radius of curvature of the surface near the droplet was found to be helpful to split the Janus droplet. On concave walls, as the radius of curvature increases from a small value, the possibility to observe droplet separation first increases and then decreases. Several phase diagrams on whether droplet separation occurs during the spreading process were produced for different kinds of walls to illustrate the influences of various factors.

Radiation of a short linear antenna above a topologically insulating half-space

The topological magnetoelectric effect is a unique macroscopic manifestation of quantum states of matter possessing topological order and it is described by axion electrodynamics. In three-dimensional topological insulators, for instance, the axion coupling is of the order of the fine structure constant, and hence, a perturbative analysis of the field equations is plenty justified. In this paper, we use Green’s function techniques to obtain time-dependent solutions to the axion field equations in the presence of a planar domain wall separating two media with different topological order. We apply our results to investigate the radiation of a short linear antenna near the domain wall.

Critical behaviour of the contact angle within nonwetting gaps

Recent density functional theory and simulation studies of fluid adsorption near planar walls in systems where the wall–fluid and fluid–fluid interactions have different ranges, have shown that critical point wetting may not occur and instead nonwetting gaps appear in the surface phase diagram, separating lines of wetting and drying transitions, that extend up to the critical temperature Tc . Here we clarify the features of the surface phase diagrams that are common, regardless of the range and balance of the forces, showing, in particular, that the lines of temperature driven wetting and drying transitions, as well as lines of constant contact angle π>θ>0 , always converge to an ordinary surface phase transition at Tc . When nonwetting gaps appear the contact angle either vanishes or tends to π as t≡(Tc−T)/Tc→0 . More specifically, when the wall–fluid interaction is long-ranged (dispersion-like) and the fluid–fluid short-ranged we estimate π−θ∝t0.16 , compared with θ∝t0.77 when the wall–fluid interaction is short-ranged and the fluid–fluid dispersion-like, allowing for the effects of bulk critical fluctuations. The universal convergence of the lines of constant contact angle implies that critical point filling always occurs for fluids adsorbed in wedges.

Three-dimensional modelling of cavitation bubble collapse using non-orthogonal multiple-relaxation-time lattice Boltzmann method

In this study, we employ a three-dimensional (3D) non-orthogonal multiple relaxation time (MRT) pseudo-potential lattice Boltzmann (LB) model to simulate the dynamics of cavitation bubble evolution. We benchmark the model against the Laplace law and the Rayleigh–Plesset (R–P) equation, confirming its efficacy in accurately capturing cavitation phenomena. We then apply the model to examine the collapse dynamics of a singular bubble located near a plane wall boundary and right-angled wall corner. Additionally, the dynamic interactions among five cross-shaped bubbles revealed the dimensionless jet volume Vj*, which is the ratio of the jet volume to the maximum bubble volume, exhibits a power relationship with the bubble distance δ. The simulation results demonstrate the accuracy of the model in discerning the effect of the wall boundary and the protective mechanisms inherent to multi-bubble interactions. These results further validate the aptness of the model for cavitation bubble dynamics simulations. Moreover, the tested case studies provide a foundational basis for future research into more complex cavitation behaviours. In summary, the developed 3D non-orthogonal MRT pseudo-potential LB model is capable of reproducing fluid flows, capturing pressure waves, and measuring wall pressures. Our work provides a deep insight into cavitation bubble dynamics and a solid basis for both applied and fundamental research.

Viscous tubular-body theory for plane interfaces

Filaments are ubiquitous within the microscopic world, occurring in biological and industrial environments and displaying a varied dynamics. Their wide range of applications has spurred the development of a branch of asymptotics focused on the behaviour of filaments, called slender-body theory (SBT). Slender-body theories are computationally efficient and focus on the mechanics of an isolated fibre that is slender and not too curved. However, SBTs that work beyond these limits are needed to explore complex systems. Recently, we developed tubular-body theory (TBT), an approach like SBT that allows the hydrodynamic traction on any isolated fibre in a viscous fluid to be determined exactly. This paper extends TBT to model fibres near plane interfaces by performing a similar expansion on the single-layer boundary integrals (BIs) for bodies by a plane interface. This provides a well-behaved SBT inspired approach for fibres by interfaces with a similar versatility to the BIs but without the singular kernels. The derivation of the new theory, called tubular-body theory for interfaces (TBTi), also establishes a criterion for the convergence of the TBTi series representation. The TBTi equations are solved numerically using a approach similar to boundary element methods (BEMs), called TBTi-BEM, to investigate the properties of TBTi empirically. The TBTi-BEM is found to compare favourably with an existing BEM and the lubrication singularity on a sphere, suggesting TBTi is valid for all separations. Finally, we simulate the hydrodynamics of helices beneath a free interface and a plane wall to demonstrate the applicability of the technique.

Local Structure of Nonuniform Fluid Mixtures Containing Associating and Chainlike Molecules from a Multilayer Quasichemical Model.

In this work, we develop a theory for predicting details of the local structure in nonuniform multicomponent fluids that may contain chainlike and associating components. This theory is an extension─to the fluid interfaces and mesoscopic structures of different geometry─of the multilayer quasichemical model originally proposed by Smirnova to describe liquid solution in the vicinity of a planar solid wall. The basis of the theory is the "cut-and-bond" approach, much in spirit of SAFT, where an infinite attraction between the separated monomeric units of a chainlike molecule mimics the chemical bonds of the chain. We describe the equilibrium structure of the mixture, including the spatial distribution of the monomeric units and the local orientation of the chemical bonds in chainlike molecules, and discuss the contribution of chemical bonds to the local chemical potential in a nonuniform fluid. To test the new theory, we apply it to mixtures containing combinations of model components: a strongly associating solvent, an inert substance of varying chain length, and a chainlike amphiphile. To compare predictions from the multilayer model with the results of continuous description of nonuniform fluids, we also address the square-gradient theory and derive an analytical expression for the influence parameter that takes into account pair correlations in the quasichemical approximation. The multilayer quasichemical model developed in this work predicts formation of aggregates in liquid solution and describes the local structure of the interfaces between the coexisting liquid phases in the mixture. Our theoretical predictions agree on a qualitative level with the accumulated knowledge about the structure of different types of systems studied in this work.

Thermal analysis of a turbulent wall jet over an adiabatic wavy surface

The impact of wavy wall amplitude on the turbulent characteristics of a wall jet has been investigated experimentally, where the wavy wall is given an adiabatic condition. In the experimental study, the mean and turbulent velocity are measured using a constant temperature anemometer manufactured by Dantec Dynamics. For temperature measurement over the wall and within the flow domain, the FLIR camera and k-type thermocouple are used, respectively. For the current study, uniformly heated at △T0 = (T0 − T∞) = 30 ± 1.2 0C with a Reynolds number of 15,000 is utilized to flow over a sinusoidal wavy wall (y = A*sin (ωx)), where “A = Amplitude ⁄ a” is the amplitude normalised by the nozzle height “a". The nozzle height is 20 mm and to maintain the Reynolds number 15,000 at the inlet, velocity is set at 10.95 ± 0.36 m ⁄ s. The amplitude of the wavy wall is varied between 0.2 and 0.6 and the results are compared to those of the plane wall jet. The current problem is also numerically solved using the k − ε RNG and k − ω SST models. Based on the results, it is concluded that the k − ε RNG model predicts the wavy wall results quite well. It is also discovered that the thermal self-similar profile deviates from the Gaussian curve at the crest of the wavy wall. The influence of the wavy surface on the thermal characteristics of the turbulent wall jet is more pronounced in the near flow field. It is observed that the bottom wall temperature, fluctuating temperature and turbulent heat flux decrease with the increase in amplitude. This indicates that for the higher amplitude, the turbulence increases, which increases the intermixing of jet fluid with the colder ambient fluid. The present results can be used as a benchmark for validating numerical models working in this area.

Wall effect on the wake characteristics of a transversely rotating sphere

In the present work, the flow over a transversely rotating sphere placed at varying separation from a plane wall at a Reynolds number Re=U∞Dν of 300 is numerically investigated using Open Source Field Operation and Manipulation, where Re is defined based on the free stream velocity (U∞) and the diameter (D) of the sphere. Three values of the non-dimensional rotational speed ω*=ωD2U∞, viz., −1, 0 and 1, have been chosen with ω being the dimensional rotation rate with anticlockwise rotation being positive. The non-dimensional separation gap G=gD between the sphere and the wall is varied from 0.25 to 3.0. Here, g is the dimensional gap between the sphere and the wall. At ω*=0 and G = 0.25, the wall completely suppresses vortex shedding from the sphere, whereas flow is found to be unsteady for other values of ω* and G. As compared to the case in the absence of the wall, the presence of the wall causes an increase in vortex shedding frequency for ω*=0 and 1 and decrease for ω*=−1. Hilbert spectrum reveals that the wake nonlinearity remains unchanged with an increase in G for ω*=0. On the other hand, it increases for ω*=−1 and decreases for ω*=1. Similar to the observation made for vortex shedding, the presence of wall increases drag force on the sphere for ω*=0 and 1 and decreases for ω*=−1. In order to reveal the spatial and temporal behavior of the coherent structures in the unsteady wake, dynamic mode decomposition (DMD) has been performed. For all the values of G, DMD mode 1 is found to be the primary vortex shedding mode.

Effect of Prestressing on Shear Strengths of Cylindrical and Planar Walls with Low Aspect Ratio

Effect of Prestressing on Shear Strengths of Cylindrical and Planar Walls with Low Aspect Ratio

Chemotactic behavior for a self-phoretic Janus particle near a patch source of fuel.

Many biological microswimmers are capable of chemotaxis, i.e., they can sense an ambient chemical gradient and adjust their mechanism of motility to move towards or away from the source of the gradient. Synthetic active colloids endowed with chemotactic behavior hold considerable promise for targeted drug delivery and the realization of programmable and reconfigurable materials. Here, we study the chemotactic behavior of a Janus particle, which converts "fuel" molecules, released at an axisymmetric chemical patch located on a planar wall, into "product" molecules at its catalytic cap and moves by self-phoresis induced by the product. The chemotactic behavior is characterized as a function of the interplay between the rates of release (at the patch) and the consumption (at the particle) of fuel, as well as of details of the phoretic response of the particle (i.e., its phoretic mobility). Among other results, we find that, under certain conditions, the particle is attracted to a stable "hovering state" in which it aligns its axis normal to the wall and rests (positions itself) at an activity-dependent distance above the center of the patch.