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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:50:24 +0000The Analogy Between Surface Shock Waves in a Liquid and Shocks in Compressible Gases
https://resolver.caltech.edu/CaltechTHESIS:10312023-182234590
Authors: {'items': [{'id': 'Crossley-Harry-Eastwood', 'name': {'family': 'Crossley', 'given': 'Harry Eastwood'}}]}
Year: 1950
DOI: 10.7907/grgr-zs89
It has been known for some time that an analogy exists between t he flow of a liquid with a free surface and the flow of a compressible gas. A less accurate analogy has been shown to obtain between hydraulic jumps and compression shocks. The interaction of shocks can occur in two forms, the regular or two-shock configuration and the Mach or three-shock configuration. The latter configuration is not yet completely understood, either in the case of hydraulic jumps in a free-surface liquid or in the case of shocks in a compressible gas. This experimental study was primarily concerned with the Mach interactions of hydraulic jumps. The conclusions of this study are: (a) there is a definite disagreement between experiment and existing theory; (b) a depth discontinuity, or wave, rather than a velocity discontinuity separates the region behind the Mach wave from the region behind the reflected wave; (c) there is evidence t hat, for interactions of weak hydraulic jumps, there is a deviation from constant depth between waves; ( d) the Mach wave is convex for the interaction of the stronger hydraulic jumps, but is concave for the interaction of weak hydraulic jumps (e) measurements should not be made so as to allow for curvature of the Mach without considering the curvature of the incident and reflected waves in the neighborhood of the triple point.https://thesis.library.caltech.edu/id/eprint/16223Perturbation Effects in Cavitation Bubble Dynamics
https://resolver.caltech.edu/CaltechETD:etd-04242009-141438
Authors: {'items': [{'id': 'Rattray-Maurice', 'name': {'family': 'Rattray', 'given': 'Maurice'}, 'show_email': 'NO'}]}
Year: 1951
DOI: 10.7907/NJDD-ZN16
Previous theoretical investigations of cavitation bubble dynamics have failed to consider the effect of a nearby wall or of translatory motion of the bubble.
It is shown that these effects are not small, but actually the analysis based on this assumption finally breaks down due to the large deformation of the bubble in the later stages of collapse. However, as the major portion of the time of collapse is spent in the low velocity motion, a meaningful time of collapse is obtained which, for the case of a bubble against a wall, is 20% longer than in the symmetric case. This agrees with the experiments performed in the Hydrodynamics Laboratory at the California Institute of Technology. The time of collapse is not appreciably affected by a translatory motion of the bubble of the magnitude encountered in the above experiments.https://thesis.library.caltech.edu/id/eprint/1493The Dynamics of Condensation and Vaporization
https://resolver.caltech.edu/CaltechETD:etd-12152003-104652
Authors: {'items': [{'id': 'Gilmore-Forrest-Richard', 'name': {'family': 'Gilmore', 'given': 'Forrest Richard'}, 'show_email': 'NO'}]}
Year: 1951
DOI: 10.7907/K9PG-JT41
The condensation process in supersaturated vapors is analyzed with the help of thermodynamics and kinetic theory. The simplifying approximations which make the problem tractable are carefully examined. Results are obtained for the steady rate of condensation which constitute a theoretical improvement over Becker and Doring's values. The uncertainties in the values of the free energy for very small droplets, which are only partially removed by Tolman's theory on the variation of surface tension with curvature, limit this improvement in the condensation theory.
Nonsteady condensation situations are also treated in detail by means of numerical and graphical integrations. It is found that the condensation in such situations generally approaches a steady rate in time periods of the order of 1 to 100 microseconds. Such time periods are negligible in many physical situations, but may be significant in the case of condensation shocks in wind tunnels.
A similar analysis is carried out for the boiling of superheated liquids and the rupture of liquids under tension. Approximations reduce the analysis of these processes to mathematical relations very similar to those for the condensation process. Nonsteady solutions are obtained by numerical integration. It is found that the solutions ordinarily approach a steady rate of bubble formation in less than a microsecond.https://thesis.library.caltech.edu/id/eprint/5002Scale Effects in Cavitating Flow
https://resolver.caltech.edu/CaltechETD:etd-03302009-081459
Authors: {'items': [{'id': 'Parkin-Blaine-Raphael', 'name': {'family': 'Parkin', 'given': 'Blaine Raphael'}, 'show_email': 'NO'}]}
Year: 1952
DOI: 10.7907/DWKE-J388
Scale effects in cavitating flow are considered for the so-called limited cavitation flow regime. The roles of nuclei and air diffusion in ordinary water and the kinetic theory of liquids for pure water are considered as to their bearing on cavitation scale effects.
The attack on the problem is concentrated in three general areas. First, dynamic similarity considerations for individual bubble growth show that no useful scaling laws can be established from such arguments. Aside from changes due to Reynolds number, it is concluded that scale effects are dependent upon the time required for a nucleus to grow from its original microscopic size to a macroscopic size. Second, a series of experiments shows that the cavitation behaves in a systematic way as the scale of the immersed body is changed. In certain instances, the inception of cavitation depends on both model size and free stream velocity. Third, a theoretical study is made to gain insight into the relationships that must hold between the parameters which affect the inception of cavitation. A simplified theory gives only rough qualitative agreement with experiment.https://thesis.library.caltech.edu/id/eprint/1209The Rate of Growth of Vapor Bubbles in Superheated Water
https://resolver.caltech.edu/CaltechETD:etd-03262007-112120
Authors: {'items': [{'id': 'Dergarabedian-Paul', 'name': {'family': 'Dergarabedian', 'given': 'Paul'}, 'show_email': 'NO'}]}
Year: 1952
DOI: 10.7907/M5Q9-M126
Calculations are presented for the dynamic stability of vapor and air bubbles in superheated water. These calculations indicate that the values of the bubble radii for which the equilibrium is unstable are restricted to a finite range of radii whose values are governed by the temperature of the water and the initial air content in the bubble.
Two theoretical solutions for the rate of growth of these unstable bubbles are considered. The first, is a solution of the equation of motion of the bubble radius with the assumption that there is no heat diffusion across the bubble wall. The second, is a solution which includes the effect of heat diffusion. The two solutions differ appreciably.
These two solutions are then compared with the experimental data on the growth of the vapor bubbles in superheated water. This comparison shows agreement with the solution with the effect of heat diffusion included.https://thesis.library.caltech.edu/id/eprint/1142Observations on Cavitation Bubble Collapse
https://resolver.caltech.edu/CaltechETD:etd-05142003-140023
Authors: {'items': [{'id': 'Ellis-Albert-Tromly', 'name': {'family': 'Ellis', 'given': 'Albert Tromly'}, 'show_email': 'NO'}]}
Year: 1953
DOI: 10.7907/EWJ4-R705
<p>Experimental observations are made on collapsing cavitation bubbles. Bubbles generated by two different methods are studied. The first method consists of bubble generation and collapse by flow over a submerged body. This work is done in the High-Speed Water Tunnel of the Hydrodynamics Laboratory. Existing photographic equipment and experimental techniques are employed. The second method consists of bubble generation and collapse by variation of the hydrostatic pressure. Much improved time and space resolution of the collapse is obtained in the latter case by design and construction of a high-speed photographic system. Bubble collapse pictures are taken at 105 frames per sec and an effective exposure time of 5 x 10<sup>-8</sup> sec. A magnification of eight diameters from object to image is attained. This equipment reveals new details of cavitation bubble collapse.</p>
<p>Numerical solutions of the spherical bubble collapse equations are compared with experimental results. A consistently longer collapse time is observed in all cases. Observed bubble asymmetries are shown to be caused by pressure gradients. A large degree of coupling is shown to exist between the radial motion and the translational motion of the bubble centroid. Bubble collapse is observed to be much less stable than bubble growth.</p>https://thesis.library.caltech.edu/id/eprint/1790Investigation of Boundaries for Transitions from Axial to Two-Dimensional Flow by Electrical Analogy
https://resolver.caltech.edu/CaltechETD:etd-04242003-094814
Authors: {'items': [{'id': 'Kampé-de-Fériet-Marc', 'name': {'family': 'Kampé de Fériet', 'given': 'Marc'}, 'show_email': 'NO'}]}
Year: 1953
DOI: 10.7907/RRZH-NR37
<p>A study on a series of axially symmetric potential flows in radial-flow impeller channels has been made with the aid of an electrical analogy. An electrolytic tank was built and tested with flows for which the mathematical solution was known. The experimental determination of velocity along the boundaries was within one percent of the exact value.</p>
<p>Velocity distributions on families of impeller channels with ellipsoidal boundaries were then obtained. The parameters varied were inlet to outlet area ratio and eccentricity of the bounding ellipses. These results are presented as graphs and in addition the maximum velocity along the front shroud is given as a function of the various parameters.</p>
<p>This analogy was also applied to a well designed commercial impeller channel and the results compared to the preceding study.</p>https://thesis.library.caltech.edu/id/eprint/1488On the Flow of Vapor Between Liquid Surfaces
https://resolver.caltech.edu/CaltechETD:etd-05062003-114142
Authors: {'items': [{'id': 'Mathews-Warren-Edward', 'name': {'family': 'Mathews', 'given': 'Warren Edward'}, 'show_email': 'NO'}]}
Year: 1953
DOI: 10.7907/EHV7-1W20
An analysis of the one-dimensional flow of vapor between parallel liquid surfaces of identical composition but different temperatures is presented. The low velocity steady flow analysis reported previously by Plesset is extended to steady flows in which the Mach number approaches unity, and to low velocity flows in which the liquid surface spacing and temperatures are allowed to vary slowly with time. More important among the new results obtained are 1) an exact solution in closed form of the (non-linear) steady-flow equations, subject only to the condition [gamma]M[superscript 2] <= 1, and 2) a relatively simple approximate form of the nonsteady-flow perturbation solution which applies whenever the product of liquid surface spacing and unperturbed current density is not unusually small.
The perturbation technique developed for the one-dimensional problem is extended also to cylindrically symmetric two-dimensional and spherically symmetric three-dimensional flows. In addition, an alternative solution for the pressure perturbation is obtained by a method which, while clearly non-exact, does not explicitly involve a neglect of higher order terms.https://thesis.library.caltech.edu/id/eprint/1645Hydrodynamic Forces on Prolate Ellipsoidal Bodies
https://resolver.caltech.edu/CaltechETD:etd-12122003-093537
Authors: {'items': [{'id': 'Stallkamp-John-Albert', 'name': {'family': 'Stallkamp', 'given': 'John Albert'}, 'show_email': 'NO'}]}
Year: 1954
DOI: 10.7907/D5TA-HR09
The hydrodynamic forces and moment on submerged bodies of prolate ellipsoidal shape are investigated for two dimensional motion. The specific motion consisted of constant relative linear velocity of the fluid and body and small angular oscillation of the body about its geometric center. The average position of the long axis of the body was in the direction of constant linear motion. The components of the lateral force and of the moment proportional to angular position, velocity, and acceleration are measured for motion in water. These reactions are compared with the reactions derived from perfect fluid theory. It is concluded that the force proportional to angular position is the principal real fluid reaction not predicted by the perfect fluid theory. The deviations of the other components from the theoretical values are small.https://thesis.library.caltech.edu/id/eprint/4954The Growth and Collapse of Cavitation Bubbles
https://resolver.caltech.edu/CaltechETD:etd-01142004-112130
Authors: {'items': [{'id': 'Zwick-Stanley-Alan', 'name': {'family': 'Zwick', 'given': 'Stanley Alan'}, 'show_email': 'NO'}]}
Year: 1955
DOI: 10.7907/QP9J-PJ94
<p>A theory is developed which describes the behavior of a vapor bubble in a liquid. Its physical basis is the assumption that the heat transfer effects which accompany the evaporation occurring at the bubble wall when the bubble grows, or the condensation that occurs there when the bubble collapses, are dynamically important. The basic equations of hydrodynamics are shown to reduce, for the problem under consideration, to a dynamic equation which describes the behavior of the bubble wall, and a heat convection equation for the liquid which is coupled to the dynamic equation by a boundary condition at the bubble surface. A solution for the heat problem is obtained under the assumption that significant temperature variation in the liquid occurs only in a thin thermal boundary layer surrounding the bubble wall. An estimate of the correction to the temperature solution is also derived. Once the temperature at the bubble wall is given, the vapor pressure within the bubble is known and the dynamic problem becomes determinate.</p>
<p>The theory is applied to the cases of the growth of a vapor bubble in a superheated liquid, and the collapse of a vapor bubble in a liquid below its boiling temperature at the external pressure. The simplifying physical assumptions made in the course of the investigation are justified for the specific example of vapor bubble behavior in water.</p>
<p>A comparison of the theory with experiment is given for the observable range of bubble growth in superheated water, and the agreement is found to be very good.</p>https://thesis.library.caltech.edu/id/eprint/163A Study of the Application of Photoelasticity to the Investigation of Stress Waves
https://resolver.caltech.edu/CaltechETD:etd-12122003-094948
Authors: {'items': [{'id': 'Sutton-George-Walter', 'name': {'family': 'Sutton', 'given': 'George Walter'}, 'show_email': 'NO'}]}
Year: 1955
DOI: 10.7907/ZQCE-ZN61
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The object of this investigation is to determine the suitability of photoelasticity for the purpose of quantitatively investigating stress waves in solids. Specifically, procedures for determining the dynamic mechanical and optical properties of a common photoelastic plastic, CR-39, were investigated, as well as the techniques for recording dynamic fringe lines.
The dynamic mechanical properties of CR-39 were determined from the frequency and decay of free-free longitudinal vibrations of bars. It was found that CR-39 is a viscoelastic plastic whose wave speed, complex modulus, and damping depends on frequency. The stress-strain relationship for CR-39 was found to be slightly nonlinear.
The birefringent properties of CR-39 were determined from impact tests in which the fringe order was detected by a phototube, and strain was measured by means of bonded wire strain gages. The results show that CR-39 has a strain-fringe constant of 3.42 x 10[superscript -4] in/fringe [plus or minus] 3%, which is the same as the static value within experimental error. Thus this constant is independent of the rate of loading. CR-39 is not stress-birefringent, which is the usual law quoted for photoelastic plastics.
An approximate theory of longitudinal stress waves in elastic bars is derived, which shows that the Boussinesq theory, if used to calculate the stress-fringe constant from sharp impacts, leads to serious error.
Using the Ellis camera, strain wave isochromatics can be photographed at framing rates up to 400, 000 per second. An RCA. 1P21 multiplier phototube was found to be extremely sensitive to optical retardation, by using it to detect the time duration of transient strains caused by cavitation. The tube has a frequency response of at least 18 megacycles.https://thesis.library.caltech.edu/id/eprint/4957I. The Propagation of Shock Waves in Non-Uniform Gases. II. The Stability of the Spherical Shape of a Vapor Cavity in a Liquid
https://resolver.caltech.edu/CaltechETD:etd-06142004-153608
Authors: {'items': [{'id': 'Mitchell-Thomas-Patrick', 'name': {'family': 'Mitchell', 'given': 'Thomas Patrick'}, 'show_email': 'NO'}]}
Year: 1956
DOI: 10.7907/PDMS-YT82
I. The one-dimensional propagation of shock waves in a perfect gas in which the pressure and the density are not necessarily uniform is investigated by seeking similarity solutions of the equations describing the non-isentropic motion of the gas. It is shown that such solutions can be found and that they can be related to specific types of compressive piston motion. In particular, the propagation of the shock resulting from the uniform compressive motion of a piston in a non-uniform gas is studied. For this case a first order, ordinary, non-linear differential equation which determines the shock strength as a function of distance is derived. An analytic solution of this equation is obtained for a gas in which the pressure is constant but the density varies, and for which the ratio of the specific heats, [gamma], is 3/2. There is no restriction placed upon the permissible density variations. In situations in which the pressure and the density distributions are variable, and in which general values of [gamma] are allowed, numerical results are presented. It is not possible in such cases to derive analytic solutions of the equation. The discussion of the shock propagated by the non-uniform motion of a piston is more difficult. However, some details are given in the case of strong and weak shocks resulting from a decelerative piston motion.
II. The stability of the spherical shape of a gas bubble in a liquid is investigated for the case in which the difference between the pressure in the bubble, P[subscript i] and the pressure in the liquid, P[subscript o], is constant. These conditions apply approximately to a vapor bubble growing, (P[subscript i] > P[subscript o]), or collapsing, (P[subscript i] < P[subscript o]), in a liquid at constant external pressure. The general solution for the behavior of a small deformation in the spherical shape of the cavity is readily determined when surface tension is neglected. For a growing bubble the deformation increases slowly and monotonically; for a collapsing bubble the deformation oscillates with small amplitude until the mean radius of the bubble approaches zero, when the magnitude of the deformation increases rapidly. The consistency and applicability of the small amplitude theory is thus demonstrated. A solution is also obtained which includes the effect of surface tension. In this case the distortion amplitude decreases with increasing radius for the expanding bubble and the singularity in the distortion amplitude for the collapsing bubble at zero radius persists.https://thesis.library.caltech.edu/id/eprint/2581The Hydrodynamics of Spherical Cavities in the Neighborhood of a Rigid Plane
https://resolver.caltech.edu/CaltechETD:etd-07132004-143023
Authors: {'items': [{'id': 'Green-Joseph-Matthew', 'name': {'family': 'Green', 'given': 'Joseph Matthew'}, 'show_email': 'NO'}]}
Year: 1957
DOI: 10.7907/3R56-N749
The velocity potential in a perfect fluid is found for a sphere which is translating in a direction normal to a rigid plane and which is simultaneously undergoing a change in its radius. The solution of the problem is conveniently pursued in the bispherical coordinate system. The kinetic energy of the fluid is determined.
The dynamics of the motion of the translating sphere of variable radius is then described in terms of a Lagrangian which is formed from the kinetic energy of the fluid field and from the potential energy of the spherical cavity. The general equations of motion are exhibited and are solved in two cases of physical interest where approximations may be applied: (1) the case of an air bubble undergoing small oscillations because of a time varying external pressure, and (2) the case of a cavitation bubble collapsing so rapidly that the translational velocity may be neglected.
For the cases in which the dynamics of the problem are specifically determined, pressure effects on the rigid plane are expressed in terms of the dynamic variables of the cavity. It is suggested that these results will serve to aid in the further quantitative experimental investigation of cavitation damage.
The most important functions are evaluated numerically and are presented in a series of tables.https://thesis.library.caltech.edu/id/eprint/2870Some Experiments in Cavitation Bubble Dynamics
https://resolver.caltech.edu/CaltechETD:etd-09222004-134550
Authors: {'items': [{'id': 'Fabula-Andrew-George', 'name': {'family': 'Fabula', 'given': 'Andrew George'}, 'show_email': 'NO'}]}
Year: 1958
DOI: 10.7907/942V-N588
Observations of the shape distortion during collapse of individual cavitation bubbles with maximum radii of about 0.5 to 1 cm have been made for collapse times of three to fourteen milliseconds; these observations are compared with theory. The bubbles were produced in superheated water and photographed at 3000 or 5000 frames per second. Growth was triggered by electrolysis and collapse was produced by pressurization. The distortions of bubble shape from spherical were found to be fairly well predicted by the theory of M. Rattray, when his perturbation parameter was adapted in a simple manner to the conditions used. A large variation in the collapse noise, due to bubble distortion caused by translational velocity, was observed to occur over the range of conditions tested.https://thesis.library.caltech.edu/id/eprint/3684Hydromagnetic Stability of a Streaming Cylindrical Plasma
https://resolver.caltech.edu/CaltechETD:etd-02272006-080626
Authors: {'items': [{'id': 'Zabusky-Norman-Julius', 'name': {'family': 'Zabusky', 'given': 'Norman Julius'}, 'show_email': 'NO'}]}
Year: 1959
DOI: 10.7907/91N3-4M47
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Dispersion relations for hydromagnetic stability were found for three related problems in which the effects of plasma motion were considered. The hydromagnetic differential equations and boundary conditions were linearized in an analysis which assumes small amplitude perturbations about an equilibrium configuration. This configuration consists of a dissipationless plasma flowing in an infinite cylinder with internal and external longitudinal and azimuthal magnetic field components.
Problem 1 is an extension of earlier work and includes electromagnetic radiation and compressibility effects. Problems 2 and 3 assume that the plasma is bound by a non-conducting compressible medium in addition to the magnetic fields. The equilibrium magnetic and velocity field vary as [...], [...] where [...]. In problem 2 incompressibility is assumed, while in 3 the assumption of compressibility is made where [...] sonic speed of the plasma. This allows a matrix-perturbation expansion about the incompressible solution. The effects of the moving boundary were included. It was found convenient to use the hydromagnetic pressure [...] as the basic dependent variable and to use the hydromagnetic equations in symmetric form. The equations were extended to a quasi-symmetrical form for treating the compressible medium.
An analytical-numerical study was made in which the dispersion relation for incompressible flow was treated as a function of a complex variable. In each of ten different physical situations the flow parameter, [...], was varied over the range [...] and the following conclusions were reached:
1. The oscillation frequencies are symmetrically distributed about the origin with [...] = 0. When [...] > 0 the mode frequencies are all shifted toward the negative and vary monotonically with [...].
2. The growth rates are larger for large wave number disturbances.
3. The oscillation frequency for complex modes increases with increasing [...].
4. Increasing the flow ([...]) removes sausage instabilities and enhances (the magnitude of) kink instabilities.
5. Adding a strong longitudinal magnetic field intensifies the sausage instabilities by increasing the magnitude of their growth rate and requiring a larger flow to remove them. Kink instabilities are removed.
https://thesis.library.caltech.edu/id/eprint/780Problems in Effusion
https://resolver.caltech.edu/CaltechETD:etd-02072006-131514
Authors: {'items': [{'id': 'Stockmair-Wilfried', 'name': {'family': 'Stockmair', 'given': 'Wilfried'}, 'show_email': 'NO'}]}
Year: 1959
DOI: 10.7907/KH55-XN11
The flow of rarefied gases from a vessel through an orifice into vacuum is studied here. Special conditions of this study are that the mean free path of the molecules is of the same order of magnitude as the hole diameter; furthermore the thickness of the wall is neglected. Knudsen [1,2] investigated this effusion problem for constant conditions throughout the gas, assuming Maxwellian velocity distribution and very large mean free paths. In the present study the influence of a one-dimensional temperature gradient extending from the wall upstream into the gas is investigated. Formulae for the massflux and the spatial intensity distribution of the outflowing molecules are calculated for steady flow conditions. Finally the behavior corresponding to a nonstationary temperature gradient (according to suddenly heated or cooled wall) is studied.https://thesis.library.caltech.edu/id/eprint/535A Study of Exploding Wires
https://resolver.caltech.edu/CaltechETD:etd-08022006-104759
Authors: {'items': [{'id': 'Turner-Ben-Robert', 'name': {'family': 'Turner', 'given': 'Ben Robert'}, 'show_email': 'NO'}]}
Year: 1960
DOI: 10.7907/JER9-AS18
Experimental observations were made of exploding wires of different sizes and types. Explosions in air and vacuum were studied. Kerr cell pictures were taken in air and the time dependent energy imput obtained. The shock wave was photographed and compared with theoretical calculations from which estimates of other quantities were made. The time integrated spectral energy density was determined for the wave length region 2300 [angstroms] - 5500 [angstroms] for 3 mil diameter iron wire. Photographs of the exploding wires in a vacuum of 10(-5) Hg are presented and discussed.
The maximum energy which could be stored was 7500 joules. Most of the experimental work was done using 3.75 microfarads charged to 40 kv with a circuit resonance frequency of 50 kc. Pictures were taken at the rate of 4 x 10(5) frames per second in most cases with exposure times of about 1/20 microsecond.https://thesis.library.caltech.edu/id/eprint/2998Theory of Gas Bubble Dynamics in Oscillating Pressure Fields
https://resolver.caltech.edu/CaltechETD:etd-06152006-093844
Authors: {'items': [{'id': 'Hsieh-Din-Yu', 'name': {'family': 'Hsieh', 'given': 'Din-Yu'}, 'show_email': 'NO'}]}
Year: 1960
DOI: 10.7907/3VCA-FH77
The behavior of a permanent gas bubble in liquids under oscillating pressure fields is studied by a linearized theory. The derived thermodynamic relation tends to indicate average isothermality for high frequency limit, contrary to the usual intuitive reasonings. The growth of the gas bubble under the oscillating pressure fields due to the effect of rectification of mass is also investigated. The effect is small, being of second order, but accumulating. The absence of resulting large bubbles is explained briefly by the considerations on the stability of spherical shape of the bubbles.https://thesis.library.caltech.edu/id/eprint/2610I. Acoustic Radiation and Reflection from Spheres. II. Some Effects of Thermal Conduction and Compressibility in the Collapse of a Cavity in a Liquid
https://resolver.caltech.edu/CaltechETD:etd-08182006-160354
Authors: {'items': [{'id': 'Hickling-Robert', 'name': {'family': 'Hickling', 'given': 'Robert'}, 'show_email': 'NO'}]}
Year: 1963
DOI: 10.7907/N27T-0Y47
This thesis presents the results of computations for four problems: two in the field of acoustics and two on the collapse of a cavity in a liquid. The first is an analysis of echoes from a solid homogeneous sphere in water, and demonstrates that the vibrations induced in the solid material by incident sound waves have an important effect on the form of the echo. Various materials are examined and the theory is shown to provide a satisfactory explanation for echoes observed in sonar work. The second problem deals with the far-field radiation patterns formed by different types of source distributions on the surface of a rigid sphere, and demonstrates the effect of the shape of a transducer and its housing on such radiation patterns. The problem of the binaural localization of sound sources is also considered. The third problem is concerned with the behavior of a thermally conducting gas inside a collapsing cavity in a liquid. It is shown that, for bubbles of an appropriate size, thermal conduction in the gas can account for the varying intensities of sonoluminescence which have been observed when different gases are dissolved in water. In the final problem, the shock waves which form in the liquid as a result of a cavity collapse are investigated. It is estimated that such shock waves could be a potent cause of cavitation damage.https://thesis.library.caltech.edu/id/eprint/3167I. Fluid flow in a precessing spherical cavity. II. Electromagnetic radiation from an expanding sphere in a magnetic field
https://resolver.caltech.edu/CaltechETD:etd-01222004-095044
Authors: {'items': [{'id': 'Venezian-G', 'name': {'family': 'Venezian', 'given': 'Giulio'}, 'show_email': 'NO'}]}
Year: 1965
DOI: 10.7907/CVPG-CK78
In Part I the flow of an incompressible fluid inside a precessing spherical cavity is studied. The precession angle is assumed small and the equations of motion are linearized. For the case of large viscosity an expansion is developed in inverse powers of the viscosity by expanding the velocity field in vector spherical harmonics. The flow obtained is essentially rigid body motion. The case of low viscosity is also studied. At low precession rates difficulties arise in the boundary layer treatment and the inviscid equations. A modified boundary layer equation is derived and an approximate solution obtained. The flow consists essentially of rotation about the average axis of rotation. Some geophysical aspects of the problem, and in particular its relevance to dynamo theories of the earth's magnetic field are discussed.
Part II deals with the electromagnetic fields about a perfectly conducting sphere which is placed in a uniform magnetic field. The radiation fields that result when the radius of the sphere is allowed to change are investigated. Explicit expressions are obtained for the cases of a sphere expanding or collapsing at a uniform rate. In the latter case it is found that wave propagation and energy propagation are in opposite directions. Constant speed oscillations are also investigated and the effect of the amplitude on the power radiated is considered. The case of arbitrary motions of the radius is also discussed.
https://thesis.library.caltech.edu/id/eprint/266Multiple Scattering of Acoustical Waves
https://resolver.caltech.edu/CaltechETD:etd-10012002-153230
Authors: {'items': [{'id': 'McCloskey-David-James', 'name': {'family': 'McCloskey', 'given': 'David James'}, 'show_email': 'NO'}]}
Year: 1967
DOI: 10.7907/HC3V-M545
The general theory of the multiple scattering of acoustical waves by a random distribution of isotropic point scatterers is considered. Configurational averages are taken of the equations of multiple scattering and integral equations governing these configurational averages are obtained; the physical consequences of these equations are examined in detail. A complete theoretical picture is obtained of the propagation of the coherent and incoherent radiation and of the connections between the coherent and incoherent contributions to the average sound intensity and current.
The problem of the transmission of sound from a plane sound source into a scattering half-space is studied; numerical results are presented for the average sound intensity and current. The reflection of an incident plane wave, inclined at an arbitrary angle to a scattering half-space is considered; an expression for the reflection coefficient, including both the coherent and incoherent reflection of sound, is obtained. The foregoing results are then applied to sound propagation in a liquid containing a large number of small gas bubbles.https://thesis.library.caltech.edu/id/eprint/3854Nonspherical Vapor Bubble Collapse
https://resolver.caltech.edu/CaltechTHESIS:04142011-083038797
Authors: {'items': [{'id': 'Chapman-Richard-Bruce', 'name': {'family': 'Chapman', 'given': 'Richard Bruce'}, 'show_email': 'NO'}]}
Year: 1970
DOI: 10.7907/TDCB-D645
Vapor bubble collapse problems lacking spherical symmetry are solved using a method of simulation designed especially for these problems. Viscosity and compressibility in the liquid are neglected. The method of simulation uses finite time steps and features an iterative technique for applying the boundary conditions at infinity directly to the liquid a finite distance from the free surface. Two cases of initially spherical bubbles collapsing near a plane solid wall were simulated, a bubble initially in contact with the wall and a bubble initially half its radius from the wall. at the closest point. In both cases the bubble developed a jet directed towards the wall. Free surface shapes and velocities are presented at various stages in the collapses. Velocities are scaled like √^(∆p)/_ ρ where p is the density of the liquid and ∆p is the difference between the ambient liquid pressure and the vapor pressure. For ^(∆p)/_ ρ = 10^6 (^(cm)/_(sec))^2 ≈ ^(1 atm.)/_(density of water) the jet had a speed of about 130m/ sec in the first case and 170 m/ sec in the second when it struck the opposite side of the bubble. Collapse in a homogeneous liquid was simulated for bubbles with nonspherical initial shapes described by the radii r_s = R_o [1 + 1/10 P_2(cos θ)] and r_s = R_o [l – 1/10 P_2(cos θ)] where P_2 (cos θ) is the second degree Legendre polynomial. Bubble shapes in both cases were close to those predicted by linearized theory. A simple perturbation study of the effect of a small pressure gradient on a collapsing bubble shows that gravity is ordinarily negligible for bubbles initially one cm. in radius or less.
https://thesis.library.caltech.edu/id/eprint/6327Phase transitions from the solid state of monatomic elements
https://resolver.caltech.edu/CaltechTHESIS:08072015-110010138
Authors: {'items': [{'id': 'Kerber-R-L', 'name': {'family': 'Kerber', 'given': 'Ronald L.'}}]}
Year: 1970
DOI: 10.7907/7B4C-H074
<p>The principle aims of this thesis include the development of
models of sublimation and melting from first principles and the application
of these models to the rare gases.</p>
<p>A simple physical model is constructed to represent the sublimation
of monatomic elements. According to this model, the solid
and gas phases are two states of a single physical system. The nature
of the phase transition is clearly revealed, and the relations between
the vapor pressure, the latent heat, and the transition temperature
are derived. The resulting theory is applied to argon, krypton, and
xenon, and good agreement with experiment is found.</p>
<p>For the melting transition, the solid is represented by an anharmonic
model and the liquid is described by the Percus-Yevick approximation.
The behavior of the liquid at high densities is studied
on the isotherms kT/∈ = 1.3, 1.8, and 2.0, where k is
Boltzmann's constant, T is the temperature, and e is the well depth
of the Lennard-Jones 12-6 pair potential. No solutions of the PercusYevick
equation were found for ρσ<sup>3</sup> above 1.3, where ρ is the
particle density and σ is the radial parameter of the Lennard-Jones
potential. The liquid structure is found to be very different from the
solid structure near the melting line. The liquid pressures are about
50 percent low for experimental melting densities of argon. This
discrepancy gives rise to melting pressures up to twice the experimental
values.</p>https://thesis.library.caltech.edu/id/eprint/9086Surface effects in simple molecular systems
https://resolver.caltech.edu/CaltechTHESIS:04042016-133123395
Authors: {'items': [{'id': 'Chapyak-Edward-Jay', 'name': {'family': 'Chapyak', 'given': 'Edward Jay'}}]}
Year: 1972
DOI: 10.7907/F4N2-0732
<p>This thesis examines two problems concerned with surface effects in simple molecular systems. The first is the problem associated with the interaction of a fluid with a solid boundary, and the second originates from the interaction of a liquid with its own vapor.</p>
<p>For a fluid in contact with a solid wall, two sets of integro-differential equations, involving the molecular distribution functions of the system, are derived. One of these is a particular form of the well-known Bogolyubov-Born-Green-Kirkwood-Yvon equations. For the second set, the derivation, in contrast with the formulation of the B.B.G.K.Y. hierarchy, is independent of the pair-potential assumption. The density of the fluid, expressed as a power series in the uniform fluid density, is obtained by solving these equations under the requirement that the wall be ideal.</p>
<p>The liquid-vapor interface is analyzed with the aid of equations that describe the density and pair-correlation function. These equations are simplified and then solved by employing the superposition and the low vapor density approximations. The solutions are substituted into formulas for the surface energy and surface tension, and numerical results are obtained for selected systems. Finally, the liquid-vapor system near the critical point is examined by means of the lowest order B.B.G.K.Y. equation.</p>
https://thesis.library.caltech.edu/id/eprint/9647Viscous and nonlinear effects in the oscillations of drops and bubbles
https://resolver.caltech.edu/CaltechETD:etd-11072006-111631
Authors: {'items': [{'email': 'prosperetti@jhu.edu', 'id': 'Prosperetti-A', 'name': {'family': 'Prosperetti', 'given': 'Andrea'}, 'show_email': 'YES'}]}
Year: 1974
DOI: 10.7907/FRDP-DV27
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The thesis is divided into three parts. In Part I the nonlinear oscillations of a spherical gas bubble in an incompressible, viscous liquid are investigated analytically by means of an asymptotic method. The effect of surface tension is included, and it is shown that thermal and acoustic damping can be accounted for by the suitable redefinition of one parameter. Approximate analytical solutions for the steady state oscillations are presented for the fundamental mode as well as for the first and second subharmonic and for the first and second harmonic. The transient behaviour is also briefly considered. The first subharmonic is studied in particular detail, and a new explanation of its connection with acoustic cavitation is proposed. The approximate analytical results are compared with some numerical ones and a good agreement is found.
In Part II the characteristics of subharmonic and ultraharmonic modes appearing in the forced, steady state oscillations of weakly nonlinear systems are considered from the physical, rather than mathematical, viewpoint. A simple explanation of the differences between the two modes, and in particular of the threshold effect usually exhibited by subharmonic oscillations, is presented. The principal resonance in the case of weak excitation is also briefly considered.
Finally, in Part III the problem of two viscous, incompressible fluids separated by a nearly spherical free surface is considered in general terms as an initial value problem to first order in the perturbation of the spherical symmetry. As an example of the applications of the theory, the free oscillations of a viscous drop are studied in some detail. In particular, it is shown that the normal mode analysis of this problem available in the literature does not furnish a solution correct for all times, but only an asymptotic one valid as [...].https://thesis.library.caltech.edu/id/eprint/4443Extension of Rayleigh-Taylor Instability Theory with Applications
https://resolver.caltech.edu/CaltechTHESIS:02032021-213518907
Authors: {'items': [{'id': 'Whipple-Christopher-George', 'name': {'family': 'Whipple', 'given': 'Christopher George'}, 'show_email': 'NO'}]}
Year: 1974
DOI: 10.7907/5bc3-w217
<p>A theoretical derivation is presented for interfacial waves, both stable and unstable, which includes viscosity and surface tension. This result is extended to the case where one fluid has a finite thickness and is bounded by a rigid boundary or a free surface. As these solutions present formidable algebraic difficulties, approximate forms of solutions, which are motivated by physical arguments, are also given, and, through the use of a computer, the full theoretical result is shown to be fairly accurately reproduced by these approximations. The theory is used to give an explanation of the bioconvection patterns which have been observed with cultures of microorganisms which have negative geotaxis. Since such organisms tend to collect at the surface of a culture and since they are heavier than the culture medium the conditions for Rayleigh-Taylor instability are met. It is shown that the observed patterns are quite accurately explained by the theory. Similar observations with a viscous liquid loaded with small glass spheres are described. A behavior similar to the bioconvective patterns with microorganisms is found and the results are also explained quantitatively by Rayleigh-Taylor instability theory with viscosity. Further physical considerations of the bioconvection demonstrate the validity of the Rayleigh-Taylor instability model, and describe the steady state circulation of microorganisms. An approximate solution to a viscous fluid of finite depth with an exponential density gradient is developed, and the applicability of this result to certain bioconvective situations is discussed.</p>https://thesis.library.caltech.edu/id/eprint/14075I. Experimental observations of the microlayer in vapor bubble growth on a heated solid. II. An investigation of the theory of evaporation and condensation
https://resolver.caltech.edu/CaltechETD:etd-12082006-131228
Authors: {'items': [{'email': 'larry.koffman@srnl.doe.gov', 'id': 'Koffman-L-D', 'name': {'family': 'Koffman', 'given': 'Larry Douglas'}, 'show_email': 'NO'}]}
Year: 1980
DOI: 10.7907/M1H1-S690
Two fundamental problems related to the evaporation of the microlayer formed beneath growing vapor bubbles on a solid surface are investigated. First, experimental measurements of microlayer formation and evaporation have been obtained for nucleate boiling of water and ethanol using laser interferometry combined with high speed photography. For pool boiling of water at atmospheric pressure with low subcooling, the initial microlayer profile is wedge-like with a thickness of 1.85 µm at a radius of 0.25 mm; the thickness for ethanol is approximately 1.6 times that for water. The measured evaporation rates from the microlayer correspond to local heat fluxes of the order of 1000 kW/m2 over the bubble lifetime. The measurement technique of laser interferometry is discussed in detail with emphasis on the difficulties encountered in interpretation of the fringe patterns. In the second investigation, the theory of evaporation and condensation is considered from a kinetic theory approach. The moment method of Lees is used to solve the problem of the flow of vapor between a hot liquid surface and a cold liquid surface. A result of the theory is that the temperature profile in the vapor for the continuum problem is inverted from what would seem physically reasonable. Because of this behavior, the theory is questioned on physical grounds leading to the conclusion that the usually assumed boundary conditions for emission of molecules from a liquid surface are probably incorrect.https://thesis.library.caltech.edu/id/eprint/4869