C. Samuel Martin

Analysis of transient pressures in bubbly, homogeneous, gas-liquid mixtures

Flow of a gas-liquid mixture in a piping system may be treated as a pseudo-fluid flow if the mixture is homogeneous and the void fraction is small. The governing equations for such flows are a set of nonlinear partial differential equations with pressure dependent coefficients. Shocks may be produced during transient state conditions. For numerical integration of these equations, two second-order explicit finite-difference shemes are introduced

Cavitation Inception in Spool Valves

Cavitation has been investigated in directional control valves in order to identify damage mechanisms characteristic of components of aircraft hydraulic systems. Tests have been conducted in a representative metal spool valve and in a model three times larger. Data taken under non-cavitating conditions with both valves showed that the position of the high-velocity annular jet shifts orientation depending upon valve opening and Reynolds number. By means of high-frequency response pressure transducers strategically placed in the valve chamber cavitation could be sensed by the correlation of noise with a cavitation index. The onset of cavitation can be detected by comparing energy spectra for a fixed valve opening and a constant discharge. Another sensitive indicator of cavitation inception is the ratio of cavitating to non-cavitating spectral densities. The incipient cavitation number as defined in this investigation is correlated with the Reynolds number for both valves.

Pressure Pulse Propagation in Two-Component Slug Flow

The simple model of pressure pulse propagation in slug flow proposed by Henry, Grolmes, and Fauske has been extended by considering wave reflection and wave transmission at gas-liquid interfaces. A frequency-response model applied to a series of idealized gas and liquid slugs yields a pulse propagation speed that approaches the homogeneous model value as the number of slugs is increased for a given void fraction. All characteristic roots from the solution to a three-equation drift-flux model are related to the velocity of the center of mass of the mixture. The pulse propagation speed relative to this velocity is exactly equal to the homogeneous model value, however. Measured pulse propagation speeds in vertically downward slug flow are, as anticipated, much less than those predicted by the simple model of Henry, Grolmes, and Fauske, but slightly greater than the homogeneous model value. Measured pressure surges produced by the rapid closure of a downstream valve in a pipeline are reasonably well predicted by the drift-flux model. For the range of void fractions, pressures, and velocities encountered in this study, it is concluded that pressure pulse speeds and the magnitude of pressure surges in slug flow can be adequately predicted by a homogeneous model.

Shock-wave formation in flowing bubbly mixtures by steepening of compression waves

Abstract The formation and propagation of shock waves in a two-component flowing bubbly mixture has been investigated experimentally. The structure of shock waves formed by steepening of compression waves is compared with the corresponding features of shocks produced spontaneously in shock tubes. Experimentally determined values of the speed of propagation of the shock compare favorably with the Hugoniot relationship based upon a homogeneous two-phase model. The effect of the gravitational and frictional pressure gradients on the shock characteristics is also examined.

Secondary Flow and Hydraulic Losses Within Sinuous Conduits of Rectangular Cross Section

This paper describes the relationship between hydraulic losses and secondary flow within sinuous conduits with complicated bends. It has been found that the nature of secondary flow present in the bends is quite sensitive to the geometric configuration of the bend and the actual aspect ratio of the conduit section. Indeed, many different secondary flow patterns have been found to exist as the bend geometry is altered. A wide range of experiments has been conducted for various aspect ratios of a rectangular conduit with different curvatures.

Pressure Wave Propagation in Two-Component Flow

The one-dimensional equations of motion for a two-component mixture are expressed in conservation form. For numerical analyses, the equations are reduced to that of a one-dimensional homogeneous bubbly model which neglects any relative motion between the two phases. Hence, the three conservation relationships --conservation of the gas mass, of the liquid mass, and the mixture momentum --yield a set of differential equations that can be solved by various numerical methods. Comparison of the theoretical and measured speed of sound is made for both bubbly-and slug-flow. Finally, various numerical schemes are compared with existing experimental results in the literature.

Rolling motion of a sphere on a plane boundary in oscillatory flow

The rolling motion of a sphere on a smooth plane boundary in a simple-harmonic water motion has been analytically and experimentally investigated. For spheres having specific gravities ranging from 0·09 to 15·18 the sphere motion was found to be sinusoidal for both low and high values of the period parameter defined by Keulegan & Carpenter. The knowledge of the sphere motion, and hence the resultant force, allowed the determination of inertia and drag coefficients from Fourier-averaging techniques. Experiments in the inertial range yielded an added-mass coefficient of 1·2, compared with 0·67 from inviscid theory for translating spheres. For values of the period parameter greater than 30 the drag coefficient is reported to be approximately 0·74.

Application of signal analysis to cavitation

The diagnostic facilities of the cross power spectrum and the coherence function have been employed to enhance the identification of not only the inception of cavitation, but also its level. Two piezoelectric pressure transducers placed in the downstream chamber of a model spool valve undergoing various levels of cavitation allowed for the use of both functions - the phase angle of the complex cross spectrum and the dimensionless coherence function - to sense clearly the difference between noise levels associated with a noncavitating jet from those once cavitation inception is attained. The cavitation noise within the chamber exhibited quite a regular character in terms of the phase difference between instruments for limited cavitation. Varying cavitation levels clearly illustrated the effect of bubble size on the attendant frequency range for which there was an extremely high coherence or nearly perfect causality.

Waterhammer in a Horizontal Pipe Induced by Slug Formation and Rapid Condensation

The phenomenon of condensation-induced waterhammer in an ammonia refrigeration system was investigated experimentally. Waterhammer was generated by introducing warm ammonia gas over static subcooled ammonia liquid placed in a horizontal 146.3 mm diameter carbon steel pipe approximately 6.0 m long. By means of fast response piezoelectric pressure transducers and a high speed data acquisition system rapid dynamic pressures were recorded whenever a condensation-induced event occurred. Employing top-mounted diaphragm pressure transducers to sense gas pressure the speed of liquid slugs propagating along the pipe was determined.The occurrence of condensation-induced waterhammer depended upon three major variables; namely, (1) initial liquid depth, (2) liquid temperature, and (3) mass flow rate of warm gas. For given liquid depth and temperature, once the warm gas threshold conditions were exceeded, shocks occurred with greater magnitude as the mass flow rate of warm gas input was increased. With adequate subcooling condensation-induced waterhammer occurred for initial liquid depths ranging from 25% to 95% of internal pipe diameter. The threshold mass flow rate of warm gas necessary to initiate waterhammer was greater as the initial liquid depth was lowered. For numerous tests with sufficient gas mass flow rate a condensation-induced shock occurred at the end cap of the test pipe, generating an acoustic (pressure) wave that propagated at a modified speed of sound toward the gas-liquid interface at the back of the slug. Peak shock pressures could be correlated with the gas mass flow rate for various initial liquid depth and suction pressures and temperatures. As the initial liquid temperature and pressure were increased the hydraulic shocks became lower because of smaller subcooling.Copyright

Dynamic Response of Ductwork Laboratory Exhaust Systems

A numerical model based on the method of characteristics is developed to analyze unsteady flows in laboratory ductwork systems. Damper opening and/or closing initiate time-variable boundary conditions at hood inlets. Minor losses and ductwork friction are included, as well as interaction with fans. Extensive data are obtained from two university laboratory systems for purposes of code verification. Comparisons between experiments and simulations demonstrate the accuracy and versatility of the numerical model.