Department of Mechanical Engineering

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Previous work on rigid splitter plates in the wake of a bluff body has shown that the primary vortex shedding can be suppressed for sufficiently long splitter plates. In the present work, we study the problem of a hinged-splitter plate in the wake of a circular cylinder. The splitter plate can rotate about the hinge at the base of the cylinder due to the unsteady fluid forces acting on it, and hence the communication between the two sides of the wake is not totally disrupted as in the rigid splitter plate case. In our study, we investigate this problem in the limit where the stiffness and internal damping associated with the hinge are negligible, and the mass ratio of the splitter plate is small. The experiments show that the splitter plate oscillations increase with Reynolds numbers at low values of Re, and are found to reach a saturation amplitude level at higher Re, Re > 4000. This type of saturation amplitude level that appears to continue indefinitely with Re, appears to be related to the fact that there is no structural restoring force, and has been observed previously for transversely oscillating cylinders with no restoring force. In the present case, the saturation tip amplitude level can be up to 0.45 D, where D is the cylinder diameter. For this hinged-rigid splitter plate case, it is found that the splitter plate length to cylinder diameter ratio (L / D) is crucial in determining the character and magnitude of the oscillations. For small splitter plate lengths (L / D ≤ 3.0), the oscillations appear to be nearly periodic with tip amplitudes of about 0.45 D nearly independent of L / D. The nondimensional oscillation frequencies (fD / U) on the other hand are found to continuously vary with L / D from fD / U ≈ 0.2 at L / D = 1 to fD / U ≈ 0.1 at L / D = 3. As the splitter plate length is further increased beyond L / D ≥ 4.0, the character of the splitter plate oscillations suddenly changes. The oscillations become aperiodic with much smaller amplitudes. In this long splitter plate regime, the spectra of the oscillations become broadband, and are reminiscent of the change in character of the wake oscillations seen in the earlier fixed-rigid splitter plate case for L / D ≥ 5.0. In the present case of the hinged-splitter plate, the sudden transition seen as the splitter plate length (L / D) is increased from 3 to 4 may be attributed to the fact that the wake vortices are no longer able to synchronize with the plate motions for larger splitter plate lengths. Hence, as observed in other vortex-induced vibration problems, the oscillations become aperiodic and the amplitude reduces dramatically. © 2009 Elsevier Ltd. All rights reserved.

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Journal of Fluids and Structures

Flow over a cylinder with a hinged-splitter plate

In this work the effect of the application of an alternating magnetic field on the large transverse vibration of a cantilever beam with tip mass is investigated. The governing equation of motion is derived using D'Alembert's principle, which is reduced to its nondimensional temporal form by using the generalized Galerkin method. The temporal equation of motion of the system contains nonlinearities of geometric and inertial types along with parametric excitation and nonlinear damping terms. Method of multiple scales is used to determine the instability region and frequency response curves of the system. The influences of the damping, tip mass, amplitude of magnetic field strength, permeability, and conductivity of the beam material on the frequency response curves are investigated. These perturbation results are found to be in good agreement with those obtained by numerically solving the temporal equation of motion and experimental results. This work will find extensive applications for controlling vibration in flexible structures using a magnetic field. © 2009 by ASME.

Journal of Vibration and Acoustics, Transactions of the ASME

Nonlinear vibration of a magneto-elastic cantilever beam with tip mass

We propose a nonconforming spectral/hp element method for solving elliptic systems on non smooth domains using parallel computers. A geometric mesh is used in a neighbourhood of the corners and a modified set of polar coordinates, as defined by Kondratiev Diff. Equations 6: 1392 - 1401, 1970, is introduced in these neighbourhoods. In the remaining part of the domain Cartesian coordinates are used. With this mesh we seek a solution which minimizes the sum of a weighted squared norm of the residuals in the partial differential equation and the squared norm of the residuals in the boundary conditions in fractional Sobolev spaces and enforce continuity by adding a term which measures the jump in the function and its derivatives at inter-element boundaries, in fractional Sobolev norms, to the functional being minimized. The set of common boundary values consists only of the values of the spectral element functions at the vertices of the polygonal domain. Since the cardinality of the set of common boundary values is so small, a nearly exact Schur complement matrix can be computed. The method is exponentially accurate and asymptotically faster than the h-p finite element method. The normal equations obtained from the least-squares formulation can be solved by the preconditioned conjugate gradient method using a parallel preconditioner. The algorithm is implemented on a distributed memory parallel computer with small inter- processor communication. Numerical results for scalar problems and the equations of elasticity are provided to validate the error estimates and estimates of computational complexity that have been obtained. © 2009 de Gruyter.

Fulltext

Journal of Numerical Mathematics

Nonconforming spectral/hp element methods for elliptic systems

Flight test data of helicopters indicate that vibratory levels in the fuselage exhibit a wide spectrum of frequencies including the dominant blade passage frequency and its integer multiples. The present work attempts to understand the reason for the existence of several frequencies in the response of the fuselage and possible cause for this observed phenomenon by formulating a computational aeroelastic model. In this theoretical study, a systematic approach has been undertaken to identify the effects of inflow modeling and sectional aerodynamic load evaluation, on helicopter trim, rotor blade response, and hub loads. Five different combinations of aerodynamic models of increasing complexity, representing rotor inflow and sectional aerodynamic loads, have been proposed. The differential equations of motion are solved in time domain in a sequential manner to obtain the response of all the blades in the rotor system, the inflow variables, and the sectional loads at every time step. The results of the present study show that the aerodynamic model incorporating dynamic wake and dynamic stall effects introduces a wide spectrum of harmonics in the hub loads including blade passage frequency and its integer multiples. The influence of aerodynamic modeling on the variation of trim parameters with forward speed has also been brought out. It is observed that the aerodynamic model incorporating dynamic wake and dynamic stall effects predicts the trim parameters whose variation with forward speed resemble qualitatively similar to those obtained in flight test. A comparison of the variation of blade sectional lift for various aerodynamic models indicates that in the advancing side of the rotor, a dynamic stall model introduces a shift in the azimuth angle at which the minimum lift occurs. The effect of structural flap - lag coupling due to blade pretwist on trim and rotor loads has been studied, and these results are compared with those pertaining to a straight blade configuration.

Journal of the American Helicopter Society

Influence of dynamic stall and dynamic wake effects on helicopter trim and rotor loads

Resonance

Editorial

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is 'zero'. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6-7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2 Sc1/2, and the Reynolds number would scale as Ra1/2 Sc-1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh-Bénard (R-B) convection for similar density differences. © 2009 Cambridge University Press.

Journal of Fluid Mechanics

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

Fluid mechanics of fish swimming : 11. Lift-based propulsion

This paper studies the non-linear dynamics of a soft magneto-elastic Cartesian manipulator with large transverse deflection. The system has been subjected to a time varying magnetic field and a harmonic base excitation at the roller-supported end. Unlike elastic and viscoelastic manipulators, here the governing temporal equation of motion contains additional two frequency forced, and linear and non-linear parametric excitation terms. Method of multiple scales has been used to solve the temporal equation of motion. The influences of various system parameters such as amplitude and frequency of magnetic field strength, amplitude and frequency of support motion, and the payload on the frequency response curves have been investigated for three different resonance conditions. With the help of numerical results, it has been shown that by using suitable amplitude and frequency of magnetic field, the vibration of the manipulator can be significantly controlled. The developed results and expressions can find extensive applications in the feed-forward vibration control of the flexible Cartesian manipulator using magnetic field. © 2009 Elsevier Ltd. All rights reserved.

International Journal of Non-Linear Mechanics

Non-linear dynamics of a soft magneto-elastic Cartesian manipulator

An experimental study is carried out to elucidate the structure of a high Reynolds number (∼105) turbulent pulsed jet. Particle image velocimetry measurements showed that the near flow field is dominated by a series of vortex rings with jet-like flows in between. The data show that the vortex rings convect at nearly constant speed of 0.6 Uj (Uj: mean jet exit velocity) and the spacing between the rings assumes a value of about 0.6/St (St: Strouhal number = fd/Uj, where f is the pulsing frequency and d is the nozzle exit diameter). With increasing Strouhal number, the rings are closely spaced and the flow tends to assume a steady jet character at five diameters downstream of the nozzle exit. At lower Strouhal numbers there is a distinct region of jet flow in between the rings. Many of the global characteristics, entrainment, mass and momentum flux are essentially determined by the strength and spacing of the rings which, in turn, depend on St. We show that the increase in momentum is due to both increased momentum flux and overpressure at the exit in accordance with Krueger &amp; Gharib (AIAA J., vol. 43 (4), 2005, p. 792). This increase in momentum comes at the expense of higher energy required to produce the jet. We also present results of organized and random components of the fluctuations and production of the random turbulence in a pulsed jet. The two regions of dominant turbulence production are identified with the ring and the trailing jet shear layers. © 2009 Cambridge University Press.

An experimental study of an axisymmetric turbulent pulsed air jet

Water flow through point-of-use porous ceramic water treatment filters have been theoretically analyzed in this technical paper. Filters tested were manufactured by combining low cost materials namely, clay and sawdust. Three filters with distinct volume fractions of clay to sawdust (75:25, 65:35 and 50:50) were tested. Sintered clay filters casted in frustum shapes were structurally characterized using mercury intrusion porosimetry. A linear increase in porosity with volume fraction of sawdust was observed. Flow experiments were carried out at constant room temperature and pressure. Potable tap water was used in these studies. Flows through filters occurring with drop in the head of water under gravity were statistically analyzed. Discharges through the filters were predicted with respect to independent variables of time for cumulative discharge and volume fraction of sawdust used for manufacturing the filters. The experimental data analysis predicts a multiplicative influence of time and volume fraction of sawdust respectively, on discharge from the filters. The results demonstrate a new theoretical approach for prediction of flow in similar types of heterogeneous porous media as discussed in this technical paper. © 2009 Tech Science Press.