The steady streaming generated by a vibrating plate parallel to a fixed plate

A viscous fluid is sandwiched between two parallel plates. The top plate performs both normal and lateral small translatory oscillations. The unsteady Navier-Stokes equations are solved using perturbations. The nonlinear Reynolds stress causes a secondary steady streaming. It is found that the normal oscillations induce a steady lift while the interaction between normal and lateral oscillations causes a directional net flux. The system thus operates as a valveless pump with rigid walls.     

Unsteady flow of an Oldroyd-B fluid generated by a constantly accelerating plate between two side walls perpendicular to the plate

The velocity field and the adequate tangential stresses corresponding to the unsteady flow of an Oldroyd-B fluid induced by a constantly accelerating plate between two side walls perpendicular to the plate are established by means of Fourier sine transforms. The solutions corresponding to Maxwell, second grade and Newtonian fluids, performing the same motion, appear as limiting cases of the solutions obtained here. In the absence of the side walls, namely when the distance between walls tends to infinity, all solutions that have been determined reduce to those corresponding to the flow over an infinite plate. Finally, for comparison, the velocity field at the middle of the channel as well as the shear stress on the bottom wall is plotted as a function of y for several values of t and of the material constants. The influence of the side walls on the motion of the fluid is also emphasized by graphical illustrations.     

Permeable plate at angle of attack in steady flow of a viscous fluid

An approximate solution is presented for the problem of the resistance of a permeable plate of widthl at an angle of attack in a steady plane flow of an incompressible viscous fluid for the case of both small and very large Reynolds numbers with different permeability laws. The results obtained in the case of large Reynolds numbers are compared with the corresponding results for flow past plane rod grids.     

On the forces transmitted to a vibrating cylinder by a blowing fluid

Summary The measuring apparatus used for experimental wind tunnel studies is described together with the test procedure and salient results. After an analysis of the results, a mechanical model is developed to explain the nature of the phenomenon.

---

Sommario Si descrive l'apparato di misura utilizzato per le ricerche sperimentali eseguite in camera a vento al fine di determinare le forze esercitate da una vena fluida su un cilindro libero di vibrare. Si espongono le modalità di prova ed i risultati più salienti. Dopo un'analisi dei risultati si elabora un modello meccanico per interpretare la natura del fenomeno.

---

---

This study forms part of a project that has been carried out jointly by A. Salvi & C. SpA and the Institute of Applied Mechanics, Milan Polytechnic. The Institute of Applied Mechanics received a CNR subsidy to take part in this project.     

Ion slip effect on a steady flow through a circular pipe of a dusty conducting Oldroyd 8-constant fluid

In this paper, a steady magnetohydrodynamic (MHD) flow of a dusty incompressible electrically conducting Oldroyd 8-constant fluid through a circular pipe is examined with considering the ion slip effect. A constant pressure gradient in the axial direction and an external uniform magnetic field in the perpendicular direction are applied. A numerical solution is obtained for the governing nonlinear momentum equations by using finite differences. The effect of the ion slip, the non-Newtonian fluid characteristics, and the particle-phase viscosity on the velocity, volumetric flow rates, and skin friction coefficients of both the fluid and particle phases is reported.     

The steady and vibrating statuses of tulip tree leaves in wind

The study of tree leaf aerodynamics is useful to tree protection,solar panel design and development of new power generation technology.73 tulip leaves were tested in suspended condition and with front as well as back surface of the lamina facing wind.Three types of vibrating statuses,two types of steady statuses,and five critical wind speeds were observed.The existence probabilities of the statuses and criticals,the probability density distribution of every critical over the range of wind speed 0–27     

Motion of a liquid droplet in a vibrating fluid

The motion of a liquid droplet in a liquid with density different from that of the liquid composing the droplet and subjected to harmonic excitations is investigated. Nonlinear equations are obtained that describe the translational motion of the droplet and its oscillations. It is shown by numerical means that, under the essential resonance conditions, the droplet ascends by a cascade method if the value of the load coefficient is small.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 7, pp. 78–83, July, 1995.     

Axisymmetric convective boundary layer in a vibrating fluid

A vibrating convective flow around a uniformly heated sphere in weightlessness conditions is studied theoretically for circularly polarized vibrations. It is found that the fluid motion has the form of two jets spreading from the sphere in opposite directions along the symmetry axis, perpendicular to the vibration polarization plane. For large characteristic temperature gradients, the flow becomes self-similar. The equations describing thermovibrational convection in the boundary layer approximation are derived. A class of self-similar solutions for a point heat source is found. The results obtained on the basis of the full equations and in the boundary layer approximation are compared.     

Pulsatile electroosmotic flow of a Maxwell fluid in a parallel flat plate microchannel with asymmetric zeta potentials

The pulsatile electroosmotic flow (PEOF) of a Maxwell fluid in a parallel flat plate microchannel with asymmetric wall zeta potentials is theoretically analyzed. By combining the linear Maxwell viscoelastic model, the Cauchy equation, and the electric field solution obtained from the linearized Poisson-Boltzmann equation, a hyperbolic partial differential equation is obtained to derive the flow field. The PEOF is controlled by the angular Reynolds number, the ratio of the zeta potentials of the microchannel walls, the electrokinetic parameter, and the elasticity number. The main results obtained from this analysis show strong oscillations in the velocity profiles when the values of the elasticity number and the angular Reynolds number increase due to the competition among the elastic, viscous, inertial, and electric forces in the flow.     

Excitation,inertia, and drag forces on a cylinder vibrating transversely to a steady flow

We present a computational study of the forces on a cylinder oscillating harmonically in the direction perpendicular to a uniform flow. The two-dimensional Navier–Stokes equations are solved on a coordinate system fixed on the cylinder. The Reynolds number is equal to 400. Several oscillation frequencies are considered: (a) resonant forcing, (b) forcing at frequency below the natural frequency of the wake, and (c) forcing at frequency above the natural frequency of the wake. Once the flow has reached a statistical steady state, the lift and drag forces on the cylinder are computed. The lift force in particular is decomposed into one component that is in phase with the velocity (excitation force), and one component that is ${180}^{\circ }$ out of phase with the acceleration (inertia or added mass force). The variation of the forces as a function of the amplitude-over-diameter-ratio is studied in detail. It is found that the scaling of the so-called inertia component of the force with the acceleration of the cylinder can lead to serious problems at small amplitudes of oscillation, and that it is overall preferable to scale both components of the force with the dynamic pressure of the fluid. Through extensive flow visualization, it is shown that changes in the state of the flow are related to the abrupt changes of the forces with the amplitude-over-diameter-ratio. Moreover, qualitative differences are found between the results for the below resonance and the resonant or above resonance forcing. The former are characterized by smooth variation of the hydrodynamic force coefficients and spatially ordered vortex streets. The latter are characterized by continuous and sharp, even jump-like, changes of the forces, and a variety of vortex patterns in the wake, resulting for some combinations of frequency and amplitude of oscillation to spatially disordered vortex streets.     

Visco-elastic flow due to a plate which starts oscillating in the presence of a parallel stationary plate

In this paper, the flow of a visco-elastic liquid between two parallel plates has been studied when one plate is stationary and the other plate suddenly starts oscillating. Both finite Fourier sine transform and Laplace transform technique have been employed to solve the basic differential equations. The flow phenomenon has been characterized by the parameters, and and the effects of these on the flow characteristics have been studied through several graphs.Late professor of the department, who died in an accident on 7th July 1978.     

Starting flow in a rotating parallel plate channel

The starting flow due to a suddenly applied pressure gradient in a parallel plate channel which is rotating as a system is studied. Exact analytic series solutions to the unsteady Navier-Stokes equations are found by both the Laplace transform method and the separation of parameters method, the latter is shown to be superior. Rotation not only induces a secondary transverse flow but also alters the character of the transient flow rate and velocity profiles. Back flow and inertial oscillations occur, especially at higher rotation rates.     

Natural convection enhancement by a discrete vibrating plate and a cross-flow opening: a numerical investigation

In this study, a unique combination of a vibrating plate and a cross-flow passage is proposed as a means of enhancing natural convection cooling. The enhancement potential was estimated based on numerical studies involving a representative model which includes a short, transversely oscillating plate, placed over a transverse cross-flow opening in a uniformly heated vertical channel wall dividing two adjacent vertical channels. The resulting velocity and temperature fields are analyzed, with the focus on the local thermal effects near the opening. The simulation indicates up to a 50% enhancement in the local heat transfer coefficient for vibrating plate amplitudes of at least 30% of the mean clearance space and frequencies of over 82 rad/s.     

Temperature profiles in a controlled-stress parallel plate rheometer

Actual melt temperatures are rarely measured directly when conducting rheological characterisations of materials in non-ambient conditions despite the potentially large influence temperature may have on the rheological data. For rheometers that use only a temperature-regulated lower plate, it is likely that the set point and true melt temperatures differ, an effect that becomes significant when characterising melts or suspensions close to phase-change events like crystallisation. This work investigates the magnitude of these effects for a controlled-stress rheometer featuring a temperature-controlled lower plate. The lower plate was fitted with a serrated cover disc that was found to exacerbate temperature deviations from the desired set point. Steady-state radial and vertical temperature profiles within the sample were measured and compared with the predictions of a finite element analysis model. The deviations between set point and measured temperatures were successfully predicted by the simulation for two typical gap heights for a thermoplastic, ceramic paste. The non-ideal heat transfer characteristics were also investigated numerically for a representative polymer system that demonstrated the increased deviations from ideal values for lower thermal conductivity materials.

Asymptotic solution to the problem of drag of a fluid by a moving plate

An analogy is established between the formulations of the problem of the drag of a fluid by a moving plate [1–3] and the problem of propagation of a stationary flame [4, 5]. The theory of singular perturbations is used to a find a two-term asymptotic expression for the film thickness h₀. The expansion parameter is the Bond number Bo 1. The limited applicability of the well-known formula of [1, 2] is estimated quantitatively. Such an estimate has been obtained earlier experimentally [3]. The approach used in the present paper should also be fruitful for the solution of other problems in capillary hydrodynamics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 52–56, November–December, 1980.