Department of Mechanical Engineering

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A circular hydraulic jump is commonly seen when a circular liquid jet impinges on a horizontal plate. Measurements of the film thickness, jump radius and the wave structure for various jet Reynolds numbers are reported. Film thickness measurements are made using an electrical contact method for regions both upstream and downstream of the jump over circular plates without a barrier at the edge. The jump radius and the separation bubble length are measured for various flow rates, plate edge conditions, and radii. Flow visualization using high-speed photography is used to study wave structure and transition. Waves on the jet amplify in the film region upstream of the jump. At high flow rates, the waves amplify enough to cause three-dimensional breakdown and what seems like transition to turbulence. This surface wave induced transition is different from the traditional route and can be exploited to enhance heat and mass transfer rates.

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Experiments in Fluids

Wave structure in the radial film flow with a circular hydraulic jump

This paper presents a study on the effect of non-linearities of an elastomeric bearing on isolated lag dynamics and coupled rotor/fuselage ground resonance stability of an idealized bearingless rotor blade. The rotor blade is modelled as an elastic beam with a non-linear elastomer and a rigid torque tube. First, amplitude dependent natural frequency of the blade in lag mode is analysed using numerical perturbation technique. Then the problem of amplitude-dependent stability of the coupled rotor/fuselage system under ground resonance condition is investigated. The results of the study indicate that the effect of amplitude seems to be more dominant on the progressive lag mode damping than on regressive lag mode damping. It is also observed that so far as the stability in ground resonance is concerned, there exists optimum locations for the attachment of both the elastomer and torque tube. ©2000 The American Institute of Aeronautics and Astronautics Inc. All rights reserved.

41st Structures, Structural Dynamics, and Materials Conference and Exhibit

Influence of nonlinear elastomer on isolated lag dynamics and rotor/fuselage aero mechanical stability

This paper deals with turbulent free convection in a horizontal fluid layer above a heated surface. Experiments have been carried out on a heated surface to obtain and analyze the planform structure and the heat transfer under different conditions. Water is the working fluid and the range of flux Rayleigh numbers (Ra) covered is 3 × 107 - 2 × 1010. The different conditions correspond to Rayleigh-Bénard convection, convection with either the top water surface open to atmosphere or covered with an insulating plate, and with an imposed external flow on the heated boundary. Without the external flow the planform is one of randomly oriented line plumes. At large Rayleigh number Ra and small aspect ratio (AR), these line plumes seem to align along the diagonal, presumably due to a large scale flow. The side views show inclined dyelines, again indicating a large scale flow. When the external flow is imposed, the line plumes clearly align in the direction of external flow. The nondimensional average plume spacing, R1/3λ, varies between 40 and 90. The heat transfer rate, for all the experiments conducted, represented as Ra-1/3δT, where δT is the conduction layer thickness, varies only between 0.1-0.2, showing that in turbulent convection the heat transfer rates are similar under the different conditions. © 2000 American Institute of Physics.

Physics of Fluids

Planform structure and heat transfer in turbulent free convection over horizontal surfaces

The trajectory of a laminar buoyant jet discharged horizontally has been studied. The experimental observations were based on the injection of pure water into a brine solution. Under certain conditions the jet has been found to undergo bifurcation. The bifurcation of the jet occurs in a limited domain of Grashof number and Reynolds number. The regions in which the bifurcation occurs has been mapped in the Reynolds number-Grashof number plane. There are three regions where bifurcation does not occur. The various mechanisms that prevent bifurcation have been proposed.

Journal of Fluid Mechanics

Bifurcation in a buoyant horizontal laminar jet

The phenomenon of limit cycle in bearingless rotor blades was investigated by examining the transient response of the blade with two different models of elastomer. The response characteristics of the blade exhibited a totally different nature. Overall, the results indicate that the phenomenon of limit-cycle oscillation is highly dependent on elastomer model.

Journal of Aircraft

Elastomeric damper model and limit cycle oscillation in bearingless helicopter rotor blade

The intermittency profile in the turbulent flat-plate zero pressure-gradient boundary-layer and a thick axisymmetric boundary-layer has been computed using the Reynolds-averaged k - ϵ - γ model, where k denotes turbulent kinetic energy, e its rate of dissipation, and g intermittency. The Reynolds-averaged model is simpler compared to the conditional model used in the literature. The dissipation equation of the Reynolds-averaged model is modified to account for the effect of entrainment. It has been shown that the model correctly predicts the observed intermittency of the flows. © 2000 by ASME.

Journal of Fluids Engineering, Transactions of the ASME

Use of k - ϵ - γ model to predict intermittency in turbulent boundary-layers

In this paper we give a procedure to obtain analytical solutions for unsteady laminar flow in an infinitely long pipe with circular cross section, and in an infinitely long two-dimensional channel, created by an arbitrary but given volume flow rate with time. In the literature, solutions have been reported when the pressure gradient variation with time is prescribed but not when the volume flow rate variation is. We present some examples: (a) the flow rate has a trapezoidal variation with time, (b) impulsively started flow, (c) fully developed flow in a pipe is impulsively blocked, and (d) starting from rest the volume flow rate oscillates sinusoidally.

Journal of Applied Mechanics, Transactions ASME

Unsteady laminar duct flow with a given volume flow rate variation

We present experimental results of free convection in a vertical tube due to an unstable density difference imposed between the two (open) ends of the tube. Two tanks of fluids connect the two ends of the tube with the top-tank fluid heavier than the bottom-tank fluid. We use salt mixed with water to create the density difference. The convection in the tube is in the form of relatively heavier fluid going down and lighter fluid going up simultaneously; the mean flow at any cross section of the tube is zero. Depending on the Rayleigh number we observe different types of flow, with turbulent flow being observed at the higher Rayleigh numbers. We believe this is a new type of turbulent flow - a nearly homogeneous, buoyancy-driven flow with zero mean shear.

Current Science

Convection in a long vertical tube due to unstable stratification - A new type of turbulent flow?

This paper presents a study on the effect of non-linearities of an elastomeric bearing on isolated lag dynamics and coupled rotor/fuselage ground resonance stability of an idealized bearingless rotor blade. The rotor blade is modelled as an elastic beam with a non-linear elastomer and a rigid torque tube. First, amplitude dependent natural frequency of the blade in lag mode is analysed using numerical perturbation technique. Then the problem of amplitude-dependent stability of the coupled rotor/fuselage system under ground resonance condition is investigated. The results of the study indicate that the effect of amplitude seems to be more dominant on the progressive lag mode damping than on regressive lag mode damping. It is also observed that so far as the stability in ground resonance is concerned, there exists optimum locations for the attachment of both the elastomer and torque tube.

Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

Influence of nonlinear elastomer on isolated lag dynamics and rotor/fuselage aeromechanical stability

A vertical jet of water impinging on a horizontal surface produces a radial film flow followed by a circular hydraulic jump. We report a phenomenon where fairly large (1 ml) drops of liquid levitate just upstream of the jump on a thin air layer between the drop and the film flow. We explain the phenomenon using lubrication theory. Bearing action both in the air film and the water film seems to be necessary to support large drops. Horizontal support is given to the drop by the hydraulic jump. A variety of drop shapes is observed depending on the volume of the drop and liquid properties. We show that interaction of the forces due to gravity, surface tension, viscosity and inertia produces these various shapes.