Time-averaged Force Research Articles

Analytical solution for an acoustic boundary layer around an oscillating rigid sphere

Analytical solutions in fluid dynamics can be used to elucidate the physics of complex flows and to serve as test cases for numerical models. In this work, we present the analytical solution for the acoustic boundary layer that develops around a rigid sphere executing small amplitude harmonic rectilinear motion in a compressible fluid. The mathematical framework that describes the primary flow is identical to that of wave propagation in linearly elastic solids, with the difference being the appearance of complex instead of real valued wave numbers. The solution reverts to the well-known classical solutions in special limits: the potential flow solution in the thin boundary layer limit, the oscillatory flat plate solution in the limit of large sphere radius, and the Stokes flow solutions in the incompressible limit of infinite sound speed. As a companion analytical result, the steady second order acoustic streaming flow is obtained. This streaming flow is driven by the Reynolds stress tensor that arises from the axisymmetric first order primary flow around such a rigid sphere. These results are obtained with a linearization of the non-linear Navier–Stokes equations valid for small amplitude oscillations of the sphere. The streaming flow obeys a time-averaged Stokes equation with a body force given by the Nyborg model in which the above-mentioned primary flow in a compressible Newtonian fluid is used to estimate the time-averaged body force. Numerical results are presented to explore different regimes of the complex transverse and longitudinal wave numbers that characterize the primary flow.

DEM study of dry and wet granular flows in a vertical bladed mixer

In this work, numerical simulations of both dry and wet granular flows inside a vertical cylindrical mixer were performed using discrete element method (DEM). Two different cases were considered by using four-bladed and two-bladed mixer setups. Effects of blade rake angle, blade rotational speed and number of blades on mixing characteristics for both dry and wet flows were examined under different conditions. It was found that blade rake angle of 90° produces low velocity but with relatively high time-averaged mean interparticle forces. Moisture content also influences the flow and mixing behavior. It was found that dry particles have higher mixing efficiencies than wet particles but only with higher moisture contents like 4% (vol%) used in this study. The same is not true when lower moisture contents of less than 1% (vol%) are used and show better mixing performance at these low moisture contents. It was also found that a two-bladed mixer is a better choice for mixing at these moisture contents in comparison to a four-bladed mixer. Our results suggest that all these factors must be considered carefully for each specific application.

Lift Enhancement of a Stationary Wing in a Wake

A stationary wing placed in the wake of a bluff body experiences lift enhancement. The quasi-periodic flow in the wake causes excitation of the separated flow in the poststall conditions. The increase in the time-averaged lift force is associated with the flow separation, leading-edge vortex formation, and subsequent reattachment in a process similar to the dynamic stall of oscillating wings. The lift enhancement is maximum for an optimal offset distance from the wake centerline. At the optimal location, potential flow oscillations, rather than the direct impingement of large vortices in the wake, provide the excitation. The smaller amplitude flow oscillations lead to a large separation bubble in the time-averaged sense in the poststall regime. The delayed flow separation in the wake has a similar mechanism and frequency to those of the active flow control methods for separation. The degree of the lift enhancement is remarkable, given that the wake at a Reynolds number of 50,000 is expected to be highly three-dimensional.

Radiation force and torque on a two-dimensional circular cross-section of a non-viscous eccentric layered compressible cylinder in acoustical standing waves

The purpose of this study is to develop an analytical formalism and derive series expansions for the time-averaged force and torque exerted on a compound coated compressible liquid-like cylinder, insonified by acoustic standing waves having an arbitrary angle of incidence in the polar (transverse) plane. The host medium of wave propagation and the eccentric liquid-like cylinder are non-viscous. Numerical computations illustrate the theoretical analysis with particular emphases on the eccentricity of the cylinder, the angle of incidence and the dimensionless size parameters of the inner and coating cylindrical fluid materials. The method to derive the acoustical scattering, and radiation force and torque components conjointly uses modal matching with the addition theorem, which adequately account for the multiple wave interaction effects between the layer and core fluid materials. The results demonstrate that longitudinal and lateral radiation force components arise. Moreover, an axial radiation torque component is quantified and computed for the non-absorptive compound cylinder, arising from geometrical asymmetry considerations as the eccentricity increases. The computational results reveal the emergence of neutral, positive, and negative radiation force and torque depending on the size parameter of the cylinder, the eccentricity, and the angle of incidence of the insonifying field. Moreover, based on the law of energy conservation applied to scattering, numerical verification is accomplished by computing the extinction/scattering energy efficiency. The results may find some related applications in fluid dynamics, particle trapping, mixing and manipulation using acoustical standing waves.

Addendum: Radiation force and torque of light-sheets (2017 J. Opt. 19 065403)

The purpose of this Addendum is to provide some clarifications and additional discussions related to the formalism of the generalized Lorenz–Mie theories in two-dimensions presented in the manuscript (Mitri F G 2017 J. Opt. 19 065403). The generalized formalism provides exact mathematical expressions that are used to compute the optical scattering, and time-averaged radiation force and torque of any light-sheets of arbitrary wavefront illuminating a homogeneous dielectric cylindrical particle of arbitrary geometrical cross-section, suspended in a lossless medium of wave propagation. In particular, it is emphasized here that concerning the analytical derivations and calculations based on far-field limits of the scattering, the Poynting vector formalism can only be utilized to determine the optical radiation force vector and its components, a result that is commensurate with the same outcome of an analysis based on the integration of the time-averaged Maxwell stress tensor. Nevertheless, in the far-field, the Poynting vector formalism is not valid to evaluate the optical radiation torque because it is radial, and the integration of its moment over a surface of large radius enclosing the particle leads to a zero torque, not in agreement with the derivation based on Maxwell’s stress tensor. Therefore, the analytical expression required to derive the optical radiation torque component (either in the near-field or far-field limits of the scattering, which lead to equivalent expressions without any approximations in the case of a lossless medium of wave propagation) should always involve the integration of the moment of the time-averaged Maxwell stress tensor.

Magnetohydrodynamic self-propulsion of active matter agents

Self-propelled particles, based on the magnetohydrodynamic acceleration of the surrounding fluid, are proposed for application as active matter agents. When the particles are resonantly excited by an electromagnetic wave, the scattered electric field induces currents in the surrounding fluid, which interact with the scattered magnetic field, thus producing a thrust. The time-averaged force is generally non-zero and can provide steady motion. Both the orientation of the particle and the direction of motion can be controlled by the radiation frequency and polarization. The concept has been studied analytically and through simulations showing its feasibility.

Numerical study of unsteady viscoelastic flow past two side-by-side circular cylinders

In this study, numerical simulation is conducted to understand the two-dimensional viscoelastic flows past two side-by-side circular cylinders at a Reynolds number of 100. The Peterlin approximation of the finitely extensible nonlinear elastic model is adopted to describe the non-linear modulus of elasticity and the finite extendibility of polymer macromolecules. The flow behavior and time-averaged forces that act on the two cylinders are investigated over a wide range of parameter space, i.e., the Weissenberg number (We), from 0 to 8, and the spacing between the two cylinders (LD), from 0.1D to 3.0D (D denotes the diameter of each cylinder). Similar to the corresponding Newtonian flow, the viscoelastic flow gradually undergoes six transitions as LD increases. However, these transitions are delayed in the viscoelastic flow, particularly at a high We. As a result, three distinct flow modes remain within the above-mentioned LD range at a high We. With increasing We, the total drag acting on the two cylinders increases for all LD values, and the repulsive force between the two cylinders gradually decreases for a lower LD value but increases for a higher LD value. Both the intensity and frequency of force fluctuation decrease as We increases. The findings of the present study may provide new insight into the multi-body wake dynamics in the viscoelastic flow.

Quasi-stationary modeling of the DBD plasma flow control around airfoil

This paper presents the results of numerical simulation of a dielectric barrier discharge (DBD) plasma actuator and shows its effectiveness to control air flow around the NACA(National Advisory Committee for Aeronautics)0015 airfoil. The actuator consists of two tape electrodes separated by a dielectric layer, and it is mounted on the suction side of the airfoil at 18% of the chord length. An alternating voltage with 20 kV magnitude and 10 kHz frequency is applied between both electrodes. The physical model of the DBD includes the drift of two ionic species, positive and negative, and the Poisson equation for the electric potential distribution. The spatio-temporal distribution of the electric field, the space charge density in the ambient air, and the surface charge density on the dielectric layer have been determined. The time average electric body force was entered into the air flow model, which was solved using the Spalart–Allmaras turbulence technique. The simulation of the air flow was performed for the free-stream velocities between 5 m/s and 20 m/s (Reynolds numbers 1.65 × 105–6.61 × 105 based on the chord length). The results of computations show the effect of the electrohydrodynamic actuation on the flow pattern, the lift and drag coefficients, the pressure coefficient, and the flow fluctuation near the airfoil. The ability of the DBD actuation to effectively control the aerodynamic airfoil characteristics has been confirmed, and its limitations for the discussed case have been determined.

Acoustic radiation force on a cylindrical particle near a planar rigid boundary II. – Viscous fluid cylinder example and inherent radiation torque

ObjectiveThis study extends the scope of a previous analysis on the time-averaged acoustic radiation force on a rigid (sound impenetrable) cylinder near a flat boundary [F.G. Mitri, J. Phys. Commun. 2 (2018) 045019] to the case of a viscous compressible fluid (sound penetrable) particle, and determine the time-averaged acoustic radiation torque as well. Motivation and noveltyPrevious analytical formalisms did not consider the case of a sound penetrable cylindrical particle insonified at an arbitrary angle of incidence (in the polar plane) near a reflecting boundary. This work fills this gap, and provides exact expressions and computations for the acoustic radiation force and torque components. MethodThe partial-wave series expansion method, in conjunction with the method of images and the translational addition theorem of cylindrical wave functions are used to derive the analytical expressions for the longitudinal and transverse acoustic radiation force components. Moreover, the emergence of a radiation torque that causes the particle to rotate around its center of mass is computed using an exact partial-wave series expression. Results, key conclusion and some perspectivesAttractive (pulling), repulsive (pushing) and neutral (zero) forces arise depending on the particle-boundary distance, the cylinder size parameter as well as the angle of incidence (in the polar plane) of the insonifying waves. Emphasis is also given on the emergence of an acoustic radiation torque (that vanishes for a rigid or non-viscous circular cylinder). Computations for the axial radiation torque efficiency anticipate the generation of positive radiation torque, its reversal, in addition to a zero efficiency, leading, respectively, to counter-clockwise, clockwise or lack of particle rotation as the angle of the incident waves deviates from normal incidence with respect to the boundary surface. The extension to the case of an elliptical/oval cylinder near a boundary is mentioned, and replies to some misleading and obtuse comments on the paper [F.G. Mitri, Phys. Fluids 28 (2016) 077104] are provided.

Interparticle acoustic radiation force between a pair of spherical particles in a liquid exposed to a standing bulk acoustic wave

We elucidate the interparticle force between a pair of particles suspended in a liquid exposed to a standing bulk acoustic wave. A three-dimensional model based on the perturbation technique and tensor integral method is employed to predict the interparticle force by subtracting the time-averaged primary radiation force due to the scattering effect from the time-averaged total radiation force due to combined scattering and re-scattering effects. The results show that irrespective of the sizes of particles at the nodal plane, interparticle force Fs* is attractive and symmetric and scales with the product of wavenumber (k) and interdistance (δx) as Fs*∼kδx−4. By studying the interparticle force between a pair of particles located out of the nodal plane, we unravel that the interparticle force is independent of their positions and depends on the horizontal (parallel to the nodal plane) and vertical interdistances. Our results reveal interparticle force changes from attractive to repulsive at a critical interdistance, attributed to the competition between time-averaged second-order pressure and velocity terms. We found that for a pair of particles parallel to the nodal plane, the interparticle force is independent of their distance from the nodal plane. Considering the total radiation force as the sum of the interparticle force, axial primary force, and drag force, we demonstrate a methodology for experimental quantification of the interparticle force. The interparticle force predicted from the model shows good agreement with experimental data (within 5%). Our study sheds light on interparticle forces that will facilitate more accurate estimation of forces on particles in an acoustic field.

Influences of marshalling length on the flow structure of a maglev train

In this paper, transient numerical simulations of maglev trains of different marshalling lengths (2, 4, and 8-car group trains) were conducted in the open air and without wind. This was done by solving the three-dimensional incompressible Navier-Stokes equations using an SST K-ω double-equation IDDES turbulence model. The results were compared with the results of wind tunnel experiments to verify the feasibility of numerical simulation. The results show an increase in the marshalling lengths of the train affects the flow above and below the train. With the increase of the marshalling length, the position of the flow separation in the tail car is advanced. The turbulence generated by the average shear on the x, y-plane and the x, z-plane as a component of the turbulence of the wake region increases. The region that produces non-vorticial vorticity in the main vortex becomes narrow and moves towards tail car. The structural analysis of the wake indicates that the wake structure of the 8-car group train is quite different from the other two groups. Both the time-averaged slipstream and the gust analysis show that the maximum expected slipstream velocity at the track-side increases as the train marshalling length increases. At the platform height, the change in vertical position of the wake vortex structure of the 2, 4, and 8-car group trains caused the difference of the shear flow regions. This is why the maximum expected slipstream velocity generated by the 4-car group train at this position is largest. As the marshalling length of the train increases, the time-average drag and lift force coefficient of the tail car have a significant negative correlation.

Optical TM ⇄ TE mode conversion contribution to the radiation force on a cylinder exhibiting rotary polarization in circularly polarized light

Circularly polarized light can induce additional mode conversion when it interacts with a material that rotates the orientation of the plane of polarization, which is known as “optical rotation” or “rotary polarization”. The effect of this additional mode conversion phenomenon is studied in the framework of the optical radiation force theory. The time-averaged force (per-length) acting on an infinitely long perfect electromagnetic conductor (PEMC) circular cylinder is considered. The multipole modal expansion method in cylindrical coordinates is utilized to derive exact series expansions for the components of the longitudinal radiation force per-length (i.e. acting along the direction of wave propagation) applicable to any range of frequencies. Numerical predictions for the radiation force function (which is the radiation force per unit energy density and cross-sectional surface) and its components clearly demonstrate the contribution of the co-polarized and cross-polarized waves. It is shown that the total radiation force is not the mere sum of the TM and TE mode components in a circularly polarized wave-field. There is an additional cross-interference term describing the contributions of TM ⇄ TE mode conversion to the total force that cannot be neglected. The computations show that the interference term can be positive, null or negative as the dimensionless size parameter ka and admittance M of the cylinder vary (where k is the wavenumber in the medium of wave propagation and a is the radius of the cylinder). The results show that the total force is always positive and acts in the direction of wave propagation (i.e., force of repulsion). The analysis is further extended to compute the energy efficiencies, demonstrating the validity of the results from the standpoint of energy conservation. This work generalizes the radiation force formalism for linearly polarized fields by introducing additional terms corresponding to TM ⇄ TE mode conversions in the series expansion for the longitudinal radiation force on cylindrical materials exhibiting rotary polarization in circularly polarized plane progressive waves.

Investigation of asymmetrically pitching airfoil at high reduced frequency

The expanding application in micro-air vehicles has encouraged many researchers to understand the unsteady flow around a flapping foil at a low Reynolds number. We numerically investigate an incompressible unsteady flow around a two-dimensional pitching airfoil (SD7003) at high reduced frequency (k ≥ 3) in the laminar regime. This study interrogates the effect of different unsteady parameters, namely, amplitude (A), reduced frequency (k), Reynolds number (Re), and asymmetry parameter (S) for pitching motion on the force coefficients. The inviscid theoretical model is utilized to calculate the lift coefficient for sinusoidal motion in the viscous regime, and a comparison is made with the numerical results. The theoretical analysis identifies the influence of the non-circulatory lift over circulatory lift at a high reduced frequency. Furthermore, the results indicate that the reduced frequency (k) and asymmetry parameter (S) have a significant impact on the instantaneous and time-averaged force coefficients as well as on the vortex structure in the wake. Finally, the fast Fourier transformation analysis is carried out over a simulated case with fixed amplitude and Reynolds number for distinct k and S values. The findings confirm that the dominant frequency in the flow (k*) has a direct correlation to the airfoil pitching frequency (k).

Influences of flapping modes and wing kinematics on aerodynamic performance of insect hovering flight

A numerical investigation into the effects of flapping modes on the aerodynamic performance of insect hovering flight is carried out through the solution of the two-dimensional unsteady Navier-Stokes equations. Four types of idealized flapping modes with the identical quasi-steady lift force are compared, and the influences of the Reynolds number (Re), the translational duration and the rotational duration on the aerodynamic characteristics of the hovering are systematically analyzed flight. It is found that the instantaneous aerodynamic forces of the wing differ significantly in each flapping mode. The mode with harmonic translation and harmonic rotation leading the highest lifting efficiency is suitable for long-time flight while the mode with harmonic translation and trapezoid rotation giving the largest instantaneous forces is suitable for maneuvering flight. When Re increases from 100 to 1000, the lift force and lifting efficiency of the wing are increased significantly with the increasing Re first, and then slow down with the further increase in Re. In addition, the fast-translational mode with short translational duration will reduce the time-averaged lift force and the efficiency, whereas the fastrotational mode with short rotational duration can enhance the time-averaged lift force with the sustained efficiency.

Flow Interactions Between Low Aspect Ratio Hydrofoils in In-line and Staggered Arrangements.

Many species of fish gather in dense collectives or schools where there are significant flow interactions from their shed wakes. Commonly, these swimmers shed a classic reverse von Kármán wake, however, schooling eels produce a bifurcated wake topology with two vortex rings shed per oscillation cycle. To examine the schooling interactions of a hydrofoil with a bifurcated wake topology, we present tomographic particle image velocimetry (tomo PIV) measurements of the flow interactions and direct force measurements of the performance of two low-aspect-ratio hydrofoils () in an in-line and a staggered arrangement. Surprisingly, when the leader and follower are interacting in either arrangement there are only minor alterations to the flowfields beyond the superposition of the flowfields produced by the isolated leader and follower. Motivated by this finding, Garrick’s linear theory, a linear unsteady hydrofoil theory based on a potential flow assumption, was adapted to predict the lift and thrust performance of the follower. Here, the follower hydrofoil interacting with the leader’s wake is considered as the superposition of an isolated pitching foil with a time-varying cross-stream velocity derived from the wake flow measurements of the isolated leader. Linear theory predictions accurately capture the time-averaged lift force and some of the major peaks in thrust derived from the follower interacting with the leader’s wake in a staggered arrangement. The thrust peaks that are not predicted by linear theory are likely driven by spatial variations in the flowfield acting on the follower or nonlinear flow interactions; neither of which are accounted for in the simple theory. This suggests that unsteady potential flow theory that does account for spatial variations in the flowfield acting on a hydrofoil can provide a relatively simple framework to understand and model the flow interactions that occur in schooling fish. Additionally, schooling eels can derive thrust and efficiency increases of 63-80% in either a in-line or a staggered arrangement where the follower is between two branched momentum jets or with one momentum jet branch directly impinging on it, respectively.

Practical assessment of manoeuvrability in adverse conditions

The introduction of EEDI raised the need for norming (standardising) of ship's manoeuvrability under adverse conditions. Besides the necessary criteria, measures and standards, developed in several research projects and described elsewhere, also procedures and methods for the practical evaluation of the proposed criteria in design and regulatory approval are required, which are addressed in this paper. The idea is to develop a flexible assessment framework, ranging from advanced assessment procedures, necessary in cases with large uncertainties and near the acceptance boundary, to simple procedures, which are sufficient for the majority of conventional vessels. The paper outlines the background of three levels of assessment procedures and describes in detail possible approaches towards level 2 and level 1 assessment procedures for propulsion and steering criteria. The proposed assessment procedures require definition of multiple input components: time-average wave-induced forces and moments, wind forces, calm-water reactions, rudder-induced forces and propeller characteristics. The paper discusses the availability of different methods (experimental, numerical or empirical) for these components and, besides, proposes and validates several simple empirical formulae developed specifically for the simplified assessment to further reduce its complexity.

Numerical Investigation on Flapping Aerodynamic Performance of Dragonfly Wings in Crosswind

Numerical simulations are performed to investigate the influence of crosswind on the aerodynamic characteristics of rigid dragonfly-like flapping wings through the solution of the three-dimensional unsteady Navier-Stokes equations. The aerodynamic forces, the moments, and the flow structures of four dragonfly wings are examined when the sideslip angleϑbetween the crosswind and the flight direction varied from 0oto 90o. The stability of the dragonfly model in crosswind is analyzed. The results show that the sideslip angleϑhas a little effect on the total time-average lift force but significant influence on the total time-average thrust force, lateral force, and three-direction torques. An increase in the sideslip angle gives rise to a larger total time-average lateral force and yaw moment. These may accelerate the lateral skewing of the dragonfly, and the increased rolling and pitching moments will further aggravate the instability of the dragonfly model. The vorticities and reattached flow on the wings move laterally to one side due to the crosswind, and the pressure on wing surfaces is no longer symmetrical and hence, the balance between the aerodynamic forces of the wings on two sides is broken. The effects of the sideslip angleϑon each dragonfly wing are different, e.g.,ϑhas a greater effect on the aerodynamic forces of the hind wings than those of the fore wings. When sensing a crosswind, it is optimal to control the two hind wings of the bionic dragonfly-like micro aerial vehicles.

Dynamic double layer force between charged surfaces

The authors develop a theory for the dynamic double layer force between charged surfaces in an electrolyte under a time dependent voltage. For a suddenly applied voltage, the surface force jumps to a dielectric value followed by an exponential decay to its equilibrium value, due to the formation of electric double layers adjacent to the surfaces. A non-zero time-averaged force is predicted even under a purely oscillatory voltage.

Analysis of a model for longitudinal electromagnetic stirring in the continuous casting of steel

A recent three-dimensional (3D) model that revisited earlier theoretical work for longitudinal electromagnetic stirring in the continuous casting of steel blooms is analyzed further to explore how the bloom width interacts with the pole pitch of the stirrer to affect the magnetic flux density. Whereas the first work indicated the presence of a boundary layer in the steel near the interface with the stirrer, with all three components of the magnetic flux density vector being coupled to each other, in the analysis presented here we find that the component along the direction of the travelling wave decouples from those in the other two directions and can even be determined analytically in the form of a series solution. Moreover, it is found that the remaining two components can be found via a two-dimensional computation, but that it is not possible in general to determine these components without taking into account the surrounding air. The validity of the asymptotically reduced model solution is confirmed by comparing it with the results of 3D numerical computations. Moreover, the asymptotic approach provides a way to compute the time-averaged Lorentz force components that requires two orders of magnitude less computational time than the fully 3D approach.

Dielectric or plasmonic Mie object at air–liquid interface: The transferred and the traveling momenta of photon**Project supported by the World Academy of Science (TWAS) research grant 2018 (Ref: 18-121 RG/PHYS/AS I-FR3240303643) and North South University (NSU), Bangladesh, internal research grant 2018-19 & 2019-20 (approved by the members of BOT, NSU, Bangladesh).

Considering the inhomogeneous or heterogeneous background, we have demonstrated that if the background and the half-immersed object are both non-absorbing, the transferred photon momentum to the pulled object can be considered as the one of Minkowski exactly at the interface. In contrast, the presence of loss inside matter, either in the half-immersed object or in the background, causes optical pushing of the object. Our analysis suggests that for half-immersed plasmonic or lossy dielectric, the transferred momentum of photon can mathematically be modeled as the type of Minkowski and also of Abraham. However, according to a final critical analysis, the idea of Abraham momentum transfer has been rejected. Hence, an obvious question arises: whence the Abraham momentum? It is demonstrated that though the transferred momentum to a half-immersed Mie object (lossy or lossless) can better be considered as the Minkowski momentum, Lorentz force analysis suggests that the momentum of a photon traveling through the continuous background, however, can be modeled as the type of Abraham. Finally, as an interesting sidewalk, a machine learning based system has been developed to predict the time-averaged force within a very short time avoiding time-consuming full wave simulation.