Dimensionless Oscillation Amplitude Research Articles

Evaluation of aerodynamic forces acting on oscillating cantilever beams based on the study of the damped flexural vibration of aluminium test samples

The paper is devoted to study of the aerodynamic forces acting on flat cantilever beams performing flexural vibrations in a viscous fluid. Original method for the force evaluation is presented based on analysis of experimental measurements of a logarithmic decrement of vibrations and relative variation in frequency of duralumin test specimens. The theoretical core of the method is based on the classical theory of bending beam oscillations and quasi-two dimensional model of interaction between a beam and a gas. Using the proposed method, extensive series of experiments for a wide range of oscillations parameters were carried out. The processing of the experimental data allowed to establish the global influence of the aerodynamic effects on beam oscillations and the local force characteristics of each cross-section of the beam in the form of universal functions of dimensionless amplitude and dimensionless frequency of oscillation. The obtained estimates of the drag and added mass forces showed a good correspondence with the available numerical and experimental data practically in the entire range of the investigated parameters.

Transition to turbulence in pulsating pipe flow

Fluid flows in nature and applications are frequently subject to periodic velocity modulations. Surprisingly, even for the generic case of flow through a straight pipe, there is little consensus regarding the influence of pulsation on the transition threshold to turbulence: while most studies predict a monotonically increasing threshold with pulsation frequency (i.e. Womersley number, $\unicode[STIX]{x1D6FC}$), others observe a decreasing threshold for identical parameters and only observe an increasing threshold at low $\unicode[STIX]{x1D6FC}$. In the present study we apply recent advances in the understanding of transition in steady shear flows to pulsating pipe flow. For moderate pulsation amplitudes we find that the first instability encountered is subcritical (i.e. requiring finite amplitude disturbances) and gives rise to localized patches of turbulence (‘puffs’) analogous to steady pipe flow. By monitoring the impact of pulsation on the lifetime of turbulence we map the onset of turbulence in parameter space. Transition in pulsatile flow can be separated into three regimes. At small Womersley numbers the dynamics is dominated by the decay turbulence suffers during the slower part of the cycle and hence transition is delayed significantly. As shown in this regime thresholds closely agree with estimates based on a quasi-steady flow assumption only taking puff decay rates into account. The transition point predicted in the zero $\unicode[STIX]{x1D6FC}$ limit equals to the critical point for steady pipe flow offset by the oscillation Reynolds number (i.e. the dimensionless oscillation amplitude). In the high frequency limit on the other hand, puff lifetimes are identical to those in steady pipe flow and hence the transition threshold appears to be unaffected by flow pulsation. In the intermediate frequency regime the transition threshold sharply drops (with increasing $\unicode[STIX]{x1D6FC}$) from the decay dominated (quasi-steady) threshold to the steady pipe flow level.

Quadrupole electromagnetic radiation of an oscillating charged droplet

Analytical calculations using the first order of smallness with respect to dimensionless amplitude of oscillations show that the intensity of electromagnetic radiation of a charged droplet is determined by time-dependent quadrupole moment.

Reduction of friction by normal oscillations. II. In-plane system dynamics

The influence of out-of-plane oscillations on friction is a well-known phenomenon that has been studied extensively with various experimental methods, e.g., pin-on-disk tribometers. However, existing theoretical models have yet achieved only qualitative correspondence with experiment. Here we argue that this may be due to the system dynamics (mass and tangential stiffness) of the pin or other system components being neglected. This paper builds on the results of a previous study [19] by taking the stiffness and resulting dynamics of the system into account. The main governing parameters determining macroscopic friction, including a dimensionless oscillation amplitude, a dimensionless sliding velocity and the relation between three characteristic frequencies (that of externally excited oscillation and two natural oscillation frequencies associated with the contact stiffness and the system stiffness) are identified. In the limiting cases of a very soft system and a very stiff system, our results reproduce the results of previous studies. In between these two limiting cases there is also a resonant case, which is studied here for the first time. The resonant case is notable in that it lacks a critical sliding velocity, above which oscillations no longer reduce friction. Results obtained for the resonant case are qualitatively supported by experiments.

Reduction of friction by normal oscillations. I. Influence of contact stiffness

The present paper is devoted to a theoretical analysis of sliding friction under the influence of oscillations perpendicular to the sliding plane. In contrast to previous works we analyze the influence of the stiffness of the tribological contact in detail and also consider the case of large oscillation amplitudes at which the contact is lost during a part of the oscillation period, so that the sample starts to “jump”. It is shown that the macroscopic coefficient of friction is a function of only two dimensionless parameters—a dimensionless sliding velocity and dimensionless oscillation amplitude. This function in turn depends on the shape of the contacting bodies. In the present paper, analysis is carried out for two shapes: a flat cylindrical punch and a parabolic shape. Here we consider “stiff systems”, where the contact stiffness is small compared with the stiffness of the system. The role of the system stiffness will be studied in more detail in a separate paper.

Numerical simulation of flow interaction between stationary and downstream elastically mounted cylinders in tandem at low Reynolds numbers

Despite the simplicity of the geometry of the circular cylinders, the uniform flow around them is complex, since it may induce unsteady forces on structures associated with vortex shedding. This paper describes the study of two circular cylinders (the downstream one is elastically mounted in transversal direction) in tandem arrangement subject to bi-dimensional uniform laminar flows at low Reynolds numbers. The academic numerical model Ifeinco, which is based on the finite element method and uses a partitioned scheme that considers two-way interaction of fluid flow and structure, has been employed to the analysis. Firstly, both stationary cylinders in tandem arrangement for Re = 100 are analysed for center to center distance between the cylinders, L/D, from 1.5 to 6.0. Results of lift and drag coefficients and Strouhal number are compared with other numerical results and good agreement is found. Secondly, numerical results for L/D = 5.25, considering downstream elastically mounted cylinder, are analysed for Reynolds numbers ranging from 100 to 140. It shows that the resonance occurs for Reynolds numbers between 115 and 120 and the maximum dimensionless amplitude of oscillation is 0.721 for Re = 118.

Stability of capillary waves on charged surface of water layer on electrically driven solid cylindrical rod

Analytically, in a linear approach on the dimensionless amplitude of oscillation, the dispersion equation for capillary waves is obtained on the charged liquid layer surfaces on a conductive cylindrical firm bar of the final thickness. It is shown that the firm core has a stabilization effect on capillary waves and reduces the destabilizing influence of a radial electric field. The influence of the core becomes substantial only at values of the radius comparable with the outer radius of the cover. The higher the density of the superficial charge, the wider the range of unstable wave numbers and the higher the values of the instability increase increments.

Radiation of electromagneticwaves by a spheroidal charged drop oscillating in a uniform electrostatic field

The dispersion relation is derived for a spheroidal charged drop oscillating in a uniform electrostatic field and radiating electromagnetic waves in the first and second orders with respect to the dimensionless oscillation amplitude and the steady-state deformation, respectively. For an individual drop and a model cloud the intensity of the electromagnetic radiation and the frequency bandwidth are estimated as functions of the drop dimensions and charge and the external electric field strength.

Induced two-body scattering resonances from a square-well potential with oscillating depth

In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism which does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the Bohr frequency for the transition to a two-atom bound state. The real part of the s-wave scattering length a has a resonance as a function of the oscillation frequency near the Bohr frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of a which arises predominantly because the oscillating field converts atom pairs into molecules. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.

Inducing Resonant Interactions in Ultracold Atoms with a Modulated Magnetic Field.

In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism that does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the transition frequency between the scattering atoms and a two-atom bound state. The real part of the resulting s-wave scattering length a is resonantly enhanced when the oscillation frequency is close to the transition frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of a, which arises because the oscillating field converts atom pairs into molecules. The real part of a can be made much larger than the background scattering length without introducing catastrophic atom losses from the imaginary part. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.

Oscillatory motion and wake of a bubble rising in a thin-gap cell

We investigate the characteristics of the oscillatory motion and wake of confined bubbles freely rising in a thin-gap cell ($h=3.1~\text{mm}$ width). Once the diameter $d$ of the bubble in the plane of the cell is known, the mean vertical velocity of the bubble $V_{b}$ is proportional to the gravitational velocity $(h/d)^{1/6}\sqrt{gd}$, where $g$ is the gravitational acceleration. This velocity is used to build the Reynolds number $Re=V_{b}d/{\it\nu}$ that characterizes the flow induced by the bubble in the surrounding liquid (of kinematic viscosity ${\it\nu}$), and which determines at leading order the mean deformation of the bubble given by the aspect ratio ${\it\chi}$ of the ellipse equivalent to the bubble contour. We then show that in the reference frame associated with the bubble (having a fixed origin and axes corresponding to the minor and major axes of the equivalent ellipse) the characteristics of its oscillatory motion in the plane of the cell display remarkable properties in the range $1200<Re<3000$ and $h/d<0.4$. In particular, the velocity of the bubble presents along its path an almost constant component along its minor axis (fluctuations in time of approximately 5 %), given by $V_{a}/V_{b}\simeq 0.92$ for all $Re$. The dimensionless amplitude of oscillation of the angular velocity is also constant for all $Re$, $\tilde{r}d/V_{b}\simeq 0.75$, while that of the transverse velocity of the bubble (along its major axis) is given by $\tilde{V}_{t}/V_{b}\simeq 0.32{\it\chi}$, reaching values comparable to those of the axial velocity $V_{a}$ for the most deformed bubbles (${\it\chi}\approx 3$). Furthermore, the frequency $f$ of oscillation scales with the inertial time scale based on the transverse velocity of the bubble $\tilde{V}_{t}$, corresponding to a constant Strouhal number $St^{\ast }=fd/\tilde{V}_{t}\simeq 0.27$. Using high-frequency particle image velocimetry, we investigate in detail the properties of the wake associated with the oscillatory motion of sufficiently confined bubbles. We observe that vortex shedding occurs for a maximal transverse velocity $V_{t}$ of the bubble, corresponding to a maximal drift angle of the bubble. Furthermore, the measured vorticity of the vortex at detachment corresponds to the estimation $V_{b}{\it\chi}^{3/2}/d$ of the vorticity produced at the bubble surface. Three stages then emerge concerning the evolution in time of the wake generated by the bubble. For one to two periods of oscillation $T_{x}$ following the release of a vortex, a rapid decay of the vorticity of the released vortex is observed. Meanwhile, the released vortex located initially at a distance of approximately one diameter from the bubble centre moves outwards from the bubble path and expands. At intermediate times, the vortex street undergoes vortex pairing. When viscous effects become predominant at a time of the order of the viscous time scale ${\it\tau}_{{\it\nu}}=h^{2}/(4{\it\nu})$, the vortex street becomes frozen and decays exponentially in place.

Heat Transfer Enhancement in a Corrugated Channel Using Oscillating Flow and Nanoparticles: An LBM Approach

The effects of flow pulsation and nanoparticles on convection heat transfer over a wavy channel are investigated using the lattice Boltzmann method. The effects of dimensionless frequency (0.05–0.25) and oscillation amplitude (0–0.25) of pulsating flow and volume fractions (0-0.05) of Cu and Al2O3 nanoparticles on convection rate and pressure drop are studied at various Reynolds numbers. (50–150). The results show that using oscillating velocity and added nanoparticles have significant effects on both flow and thermal fields, which lead to heat transfer enhancement. Considering values of convection rate and pressure drop, shows that Cu nanoparticles are more practical at comparison with Al2O3 nanoparticles.

Viscous dissipation effects on entropy generation and heat transfer in cylindrical packed beds subjected to reciprocating flow

A numerical study of the viscous dissipation effects on entropy generation for oscillating flow, within a cylinder filled with a porous medium and heated by a constant heat flux at the wall, was carried out in laminar flow regime. The flow is modelled by the Brinkman–Lapwood–Forchheimer–extended Darcy model (DBLF). The mathematical model for energy transport is based on the local thermal equilibrium assumption and takes into account the viscous dissipation effects. The obtained differential system equations are solved using the control volume–based finite element method (CVFEM) with an unequal order velocity-pressure interpolation. The numerical results of the flow, heat transfer and entropy generation are presented and discussed. The influence of physical parameters, such as the dimensionless oscillation amplitude, the Darcy number, the Reynolds number, the thermal conductivity ratio, the heat capacity ratio, the Eckert number, the Brinkman number and the dimensionless temperature, is presented and discussed throughout this paper.

On the structure of the velocity field under the free spheroidal surface of a viscous liquid drop oscillating in an electrostatic field

An asymptotic analytical solution to an initial boundary-value problem considering (i) the time evolution of the capillary oscillation amplitude as applied to a viscous spheroidal liquid drop placed in a uniform electrostatic field and (ii) the liquid flow velocity field inside the drop is found. The problem is solved in an approximation that is linear in two small parameters: the dimensionless oscillation amplitude and the dimensionless field-induced constant deformation of the equilibrium (spherical) shape of the drop. Terms proportional to the product of the small parameters are retained. In this approximation, interaction between oscillation modes is revealed. It is shown that the intensity of the eddy component of the oscillation-related velocity field depends on the liquid viscosity and the external uniform electrostatic field strength. The intensity of the eddy component decays rapidly with distance from the free surface. The depth to which the eddy flow (which is caused by periodical flows on the free surface) penetrates into the drop is a nonmonotonic function of the polar angle and increases with dimensionless viscosity and field strength.

Transient Temperature Involving Oscillatory Heat Source With Application in Fretting Contact

An analytical approach for treating problems involving oscillatory heat source is presented. The transient temperature profile involving circular, rectangular, and parabolic heat sources undergoing oscillatory motion on a semi-infinite body is determined by integrating the instantaneous solution for a point heat source throughout the area where the heat source acts with an assumption that the body takes all the heat. An efficient algorithm for solving the governing equations is developed. The results of a series simulations are presented, covering a wide range of operating parameters including a new dimensionless frequency ω¯=ωl2∕4α and the dimensionless oscillation amplitude A¯=A∕l, whose product can be interpreted as the Peclet number involving oscillatory heat source, Pe=ω¯A¯. Application of the present method to fretting contact is presented. The predicted temperature is in good agreement with published literature. Furthermore, analytical expressions for predicting the maximum surface temperature for different heat sources are provided by a surface-fitting method based on an extensive number of simulations.

The pulsatile motion of a semi-infinite bubble in a channel: flow fields, and transport of an inactive surface-associated contaminant

We investigate a theoretical model of the pulsatile motion of a contaminant-doped semi-infinite bubble in a rectangular channel. We examine the fluid mechanical behaviour of the pulsatile bubble, and its influence on the transport of a surfaceinactive contaminant (termed surfinactant). This investigation is used to develop a preliminary understanding of surfactant responses during unsteady pulmonary airway reopening. Reopening is modelled as the pulsatile motion of a semi-infinite gas bubble in a horizontal channel of width 2a filled with a Newtonian liquid of viscosity µ and constant surface tension γ . A modified Langmuir sorption model is assumed, which allows for the creation and respreading of a surface multilayer. The bubble is forced via a time-dependent volume flux Q(t) with mean and oscillatory components (QM and Qω, respectively) at frequency ω. The flow behaviour is governed by the dimensionless parameters: CaM = µQM /(2aγ), a steady-state capillary number, which represents the ratio of viscous to surface tension forces; CaΩ = µQω/(2aγ), an oscillatory forcing magnitude; Ω = ωµa/γ , a dimensionless frequency that represents the ratio of viscous relaxation to oscillatory-forcing timescales; and A =2 CaΩ /Ω ,a dimensionless oscillation amplitude. Our simulations indicate that contaminant deposition and retention in the bubble cap region occurs at moderate frequencies if retrograde bubble motion develops during the oscillation cycle. However, if oscillations are too rapid the ensuing large forward tip velocities cause a net loss of contaminant from the bubble tip. Determination of an optimal oscillation range may be important in reducing ventilator-induced lung injury associated with infant and adult respiratory distress syndromes by increasing surfactant transport to regions of collapsed airways.

Laminar Natural Convection Heat Transfer From a Vertical Baffled Plate Subjected to a Periodic Oscillation

Abstract The problem of laminar natural convection on a vertical baffled plate subjected to a periodic oscillation is investigated numerically. Of particular interest of this paper is the heat transfer characteristic with the oscillatory velocity being close to the flow velocity in the velocity boundary layer under nonoscillation condition. The results show that a sevenfold increase in space-time averaged Nusselt number is achieved. Three mechanisms that are responsible for the heat transfer enhancement are identified. In addition, the effects of the governing parameters on the heat transfer are studied over a wide range. The heat transfer enhancement is found to be increased with dimensionless oscillation frequency and amplitude, but decreased with the Grashof number. Another interest of this paper is to optimize the geometry of baffle plates and an optimal baffle height-spacing ratio 0.25–0.50 is found for higher heat transfer rate.

A numerical study of laminar reciprocating flow in a pipe of finite length

A numerical investigation has been carried out for a laminar incompressible reciprocating flow in a circular pipe with a finite length. An examination of the governing equations and boundary conditions indicates that a sinusoidally reciprocating flow is governed by three similarity parameters: the kinetic Reynolds number Reω, the dimensionless oscillation amplitude Ao, and the length to diameter ratio L/D. The numerical solution for the velocity profiles of a developing reciprocating flow shows that at any instant of time, there exist three flow regimes in the pipe, namely, an entrance regime, a fully developed regime and an exit regime. The numerical results for the fully developed region are shown to be in excellent agreement with the analytical solution. Based on the numerical results, a correlation equation of the space-cycle averaged friction coefficient for a laminar developing reciprocating pipe flow has been obtained in terms of the three similarity parameters.

Experimental studies on the onset of turbulence and frictional losses in an oscillatory turbulent pipe flow

Transition to turbulence and frictional losses in an oscillatory and reversing flow of air in a pipe have been studied experimentally. A hot-wire anemometer was employed to observe temporal axial velocity variations, while a differential pressure transducer was used to measure temporal variations of pressure drops across the pipe. In contrast to previous work, the similarity parameters chosen for the present study are the kinetic Reynolds number Re ω and the dimensionless oscillation amplitude of fluid A o . A correlation equation in terms of these two similarity parameters for the prediction of the onset of turbulence is obtained. The experimental data show that a change from a favorable pressure gradient to an adverse pressure gradient at high kinetic Reynolds numbers and large dimensionless fluid displacements is responsible for the onset of turbulence. Based on the measured data of pressure drops and cross-sectional mean velocities, a correlation equation for the cycle-averaged friction coefficient of a cyclically turbulent oscillatory flow has been obtained in terms of the two similarity parameters.

Generation and detection of photons in a cavity with a resonantly oscillating boundary.

The problem of photon creation from vacuum in an ideal cavity with vibrating walls is studied in the resonance case, when the frequency of vibrations equals twice the frequency of some unperturbed electromagnetic mode. Analytical solutions are obtained in two cases: for the one-dimensional model (scalar electrodynamics) and for the three-dimensional (3D) cavity. In the first example, we have a strong intermode interaction; nonetheless, an explicit solution in terms of the complete elliptic integrals is found. The rate of photon generation in the principal mode rapidly assumes a constant value proportional to the product of the frequency by the dimensionless amplitude of oscillations. The total amount of photons created in all the modes increases in time as ${\mathit{t}}^{2}$. In the second example, the eigenmode spectrum is nonequidistant and the problem can be reduced to the problem of a single harmonic oscillator with a time-dependent frequency. The number of photons in the resonant mode of a 3D cavity increases exponentially in time and the field appears in a highly squeezed state with a strongly oscillating photon distribution function. The problem of detecting the created photons is analyzed in the framework of a simplified model, when a detector is replaced with a harmonic oscillator. It turns out that the presence of the detector changes the picture drastically: both the detector and the field mode occur in highly mixed (nonthermal) quantum states, with identical nonoscillating photon distribution functions. The detector gains exactly half of the total energy of excitation inside the cavity. The estimations show a possibility of creating up to several hundred or even thousand photons, provided that the cavity's Q factor exceeds ${10}^{10}$ and the amplitude of the wall's oscillations is greater than ${10}^{\mathrm{\ensuremath{-}}10}$ cm at a frequency of the order of 10 GHz. \textcopyright{} 1996 The American Physical Society.