A general nonconvex large deviation result II

We refine the conditions for the lower bound in an abstract large deviation result with nonconvex rate function we had previously introduced. We apply the results to certain stochastic recursive schemes.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000044

A Note on Partial Cavitation of Flat Plate Hydrofoils

Recently Tulin and Wu have treated the problem of fully developed cavitation on flat plate and cambered foils. In these treatments, the length of the cavity is always greater than the chord of the hydrofoil and the cavity is assumed to start at the leading edge of the plate. The purpose of this note is to extend Tulin's work to account for partial cavitation, i.e., when the cavitation bubble is less than the hydrofoil chord

Experimental study of the spray characteristics of a research airblast atomizer

Airblast atomization was studied using a especially designed atomizer in which the liquid first impinges on a splash plate, then is directed radially outward and is atomized by the air passing through two concentric, vaned swirlers that swirl the air in opposite directions. The effect of flow conditions, air mass velocity (mass flow rate per unit area) and liquid to air ratio on the mean drop size was studied. Seven different ethanol solutions were used to simulate changes in fuel physical properties. The range of atomizing air velocities was from 30 to 80 m/s. The mean drop diameter was measured at ambient temperature (295 K) and atmospheric pressure

Separation and Surface Nuclei Effects in a Cavitation Susceptibility Meter

This work is concerned with the effects of flow separation and surface nuclei on the operation of a fixed geometry Cavitation Susceptibility Meter (CSM) with laminar flow. Cavitation is induced under controlled conditions at the throat of a glass venturi tube for the measurement of the active nuclei concentration in water samples as a function of the applied tension. Both cavitation and flow velocity are monitored optically by a Laser Doppler Velocimeter. The throat pressure is determined indirectly from the upstream pressure and the local flow velocity. The results show that laminar flow separation and surface nuclei effects are the most stringent operational limitations. Separation in the diffuser increases the minimum attainable throat pressure above the susceptibility of most cavitation nuclei commonly found in technical waters. Surface nuclei can generate extensive sheet or spot cavitation at relatively high tensions even on optically finished glass surfaces. These phenomena are difficult to eliminate and bring therefore into question the practical utility of CSM's with laminar flow and fixed geometry for the measurement of the dependence of the cavitating nuclei concentration over wide ranges of the applied tension, as required for cavitation studies

A Cavitation Susceptability Meter with Optical Cavitation Monitoring-Part One: Design Concepts

This work is concerned with the design of a Cavitation Susceptibility Meter based on the use of a venturi tube for the measurement of the active cavitation nuclei concentration in water samples as a function of the applied tension. The operation of the Cavitation Susceptibility Meter is analyzed and the main considerations leading to the proposed design are illustrated and critically discussed. The results of this analysis indicate that the operational range is mainly limited by nuclei interference, flow separation and saturation (choking), and suggest to develop a Cavitation Susceptibility Meter where; (1) the flow possesses a laminar potential core throughout the venturi throat section in all operational conditions; (b) the pressure at the venturi throat is determined from the upstream pressure and the local flow velocity; (c) the detection of cavitation and the measurement of the flow velocity are carried out optically by means of a Laser Doppler Velocimeter; (d) a custom-made electronic Signal Processor incorporating a frequency counter is used for real time data generation and temporary storage; (e) a computerized system performs the final acquisition and reduction of the data

A Note on the Calculation of Supercavitating Hydrfoils with Rounded Noses

Practical supercavitating hydrfoils have rounded leading edges for mechanical strength. The prediction of pressures near the leading edge of such hydrofoils by linearized free streamline theory fails because singularities are usually required there by the theory. A simple method based on singular perturbations of avoiding these difficulties for hydrofoils which have parabolic noses but an arbitrary profile downstream of the leading edge is presented. The results of such a computation on a hydrofoil with a parabolic profile and with fixed cavity separation near the leading edge radius are shown and are compared with an exact free-streamline theory. The agreement is excellent

A Brief Note on Linearized, Unsteady, Supercavitating Flows

Three different models for the unsteady fluctuations of a slender cavity in the limit of small reduced frequency are compard with the results of quasi-steady calculations. Tullin's kinematically closed model in unsteady flow in soon to tend smoothly to a limiting quasi-steady motion having the same value for the compliance of the cavitating flow, unlike other models that have been used in the past

A Note on the Unsteady Cavity Flow in a Tunnel

The unsteady internal cavitating flow such as the one observed in a pump or a turbine is studied for a simple two-dimensional model of a base-cavitating wedge in an infinite tunnel and it is shown how the cavitation compliance can be calculated using the linearized free streamline theory. Numerical values are obtained for the limiting case of a free jet. Two important features are: First, the cavitation compliance is found to be of complex form, having additional resistive and reactive terms beyond the purely inertial oscillation of the whole channel in "slug flow." Second, the compliance has a strong dependence on frequency

Unsteady Flow in Cavitating Turbopumps

Unsteady flow in a cavitating axial inducer pump is analyzed with the help of a simple two-dimensional cascade model. This problem was motivated by a desire to study the effect of unsteady cavitation on the so-called POGO instability in the operation of liquid rocket engines. Here, an important feature is a closed loop coupling between several different modes of oscillation, one of which is due to the basic unsteady characterisitcs of the cavitation itself. The approaching and leaving flow velocities up- and downstream of the inducer oscillate, and the cavity-blade system participates dynamically with the basic pulsating flow. In the present work, attention is focused on finding a transfer matrix that relates the set of upstream variables to those downstream. This quantity, which is essentially equivalent to cavitation compliance in the quasistatic analyses, is found to be complex and frequency dependent. It represents the primary effect of the fluctuating cavity in the system. The analysis is based on a linearized free streamline theory