CaltechTHESIS advisor: Monograph
https://feeds.library.caltech.edu/people/Cole-J-D/combined_advisor.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 26 Jun 2024 12:54:27 -0700On Problems of Heat Conduction in a Compressible Fluid
https://resolver.caltech.edu/CaltechETD:etd-06032004-135328
Year: 1952
DOI: 10.7907/G8DW-K988
The present work starts with a study of heat conduction in a non-viscous compressible fluid based on a linearized theory which is similar to that used in the theory of sound. Important features of exact equations of motion and their corresponding linearized equations are studied briefly. For this linear system, which preserves many of the features of the original non-linear system, the fundamental solutions are found and discussed. The additional role played by viscosity in the heat conduction problem is then investigated. The fundamental solutions for this compressible, viscous, heat-conducting flow problem are found and compared with the non-viscous case. The problem of heat conduction in a two-dimensional stationary flow of a viscous compressible fluid is further studied by finding the fundamental solutions and discussing the result in some detail. As an example proposed to show how a superposition of these fundamental solutions can be used to solve a boundary value problem, the problem of the anemometry of a heated flat plate is solved for both large and small values of the Reynolds number. The result obtained herein is discussed and compared with some existing theories and experiments. The causes of the discrepancy resulting from this linearized theory are briefly explained.https://resolver.caltech.edu/CaltechETD:etd-06032004-135328Transonic Flow Past Cone-Cylinders
https://resolver.caltech.edu/CaltechETD:etd-05122003-103200
Year: 1953
DOI: 10.7907/DE4W-ZJ43
Experimental results are presented for transonic flow past cone-cylinder, axially symmetric bodies. The drag coefficient, surface Mach number, etc. are studied as the free stream Mach number is varied and, wherever possible, the experimental results are compared with theoretical predictions. Interferometric results for several typical flow configurations are shown and an example of shock-free supersonic to subsonic compression is experimentally demonstrated.
The theoretical problem of transonic flow past finite cones is discussed briefly and an approximate solution of the axially symmetric transonic equations, valid for a semi-infinite cone, is presented.https://resolver.caltech.edu/CaltechETD:etd-05122003-103200The Lift of Thin Airfoils at High-Subsonic Speeds
https://resolver.caltech.edu/CaltechETD:etd-01222004-114509
Year: 1954
DOI: 10.7907/DFFC-8041
Experimental results are presented for the lift characteristics of thin, two-dimensional airfoils at high-subsonic speeds and small angles of attack. Symmetrical airfoils with different locations of maximum thickness were investigated using a surface pressure probe technique which should find use in other applications.
The flow fields over each airfoil are discussed and the quantitative results for the lift and location of the center of lift are compared with theory whenever possible. The effects of flow separation caused by boundary-layer shock-wave interaction are noted and discussed. In particular, the possibility of the forced oscillation of control surfaces due to boundary layer separation is mentioned.https://resolver.caltech.edu/CaltechETD:etd-01222004-114509Similarity Solution for Transonic Flow Past a Cone
https://resolver.caltech.edu/CaltechETD:etd-06282004-095155
Year: 1956
DOI: 10.7907/74PX-HS89
By applying a transonic expansion procedure to a conical flow field, a system of approximate transonic equations, boundary conditions, and shock relations is derived. A similarity law for the pressure coefficient on the surface of slender cones is established. The surface pressure is computed by solving the approximate equations.
By use of similarity, the second order differential equations of the first two steps of the approximation scheme are reduced to first order equations. The solution of the first step is carried out numerically in great detail for different transonic parameters; the procedure for solving the latter is explained in the Appendix.
The results are compared with the exact solution, and a highly satisfactory agreement is reached.https://resolver.caltech.edu/CaltechETD:etd-06282004-095155Expansion Procedures and Similarity Laws for Transonic Flow
https://resolver.caltech.edu/CaltechETD:etd-07152004-091254
Year: 1957
DOI: 10.7907/4HK0-K279
The transonic flow past slender bodies and thin wings is investigated with the use of a general theory of expansion procedures. It is assumed that the solutions for the velocity components possess asymptotic expansions of a very general form, and the differential equations and boundary conditions for the first and higher approximations are obtained by applying appropriate limiting procedures to the full equations. The following cases are treated: 1) bodies of revolution at zero incidence; 2) bodies of nearly circular cross-section, at zero incidence; 3) bodies of revolution at an angle of attack; and 4) thin wings at zero incidence. Certain first-order similarity laws are derived for these problems, and the order of magnitude of the error is stated in each case.https://resolver.caltech.edu/CaltechETD:etd-07152004-091254Problems in Effusion
https://resolver.caltech.edu/CaltechETD:etd-02072006-131514
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://resolver.caltech.edu/CaltechETD:etd-02072006-131514Transonic Flow Over a Non-Lifting Slender Body of Revolution
https://resolver.caltech.edu/CaltechETD:etd-01092006-153522
Year: 1959
DOI: 10.7907/NFVH-YH92
Sonic flow past a non-lifting, slender body of revolution is investigated by the use of small disturbance theory. An approximation for the local Mach number distribution is used to linearize the transonic potential equation. Solutions for the velocity components, pressure distribution, and drag are obtained in terms of simple integrals involving the body geometry. An extension to other Mach numbers in the transonic range is given. The theoretical pressure distribution and drag are found to give good agreement with experimental data.https://resolver.caltech.edu/CaltechETD:etd-01092006-153522On Magnetohydrodynamic Flow over Solids
https://resolver.caltech.edu/CaltechETD:etd-12162005-083621
Year: 1960
DOI: 10.7907/5AMT-CM66
The steady flow of a viscous, incompressible and electrically conducting fluid over a solid, in the presence of an applied magnetic field parallel to the main flow, is considered. The equations of magnetohydrodynamics (MHD) are linearized by assuming that the solid only slightly perturbs the velocity and magnetic field. Fundamental solutions of the linearized equations are derived, and they are used to construct MHD flows over solids. The MHD drag formulas for the finite flat plate and the sphere are derived. The special cases of zero viscosity and infinite conductivity are studied, and general formulas for MHD forces on a solid are presented. The problem is generalized to include an electrical generator in the body.
Steady flow over a flat, circular, broadside-on disk in the presence of a parallel magnetic field is solved as a boundary value problem. The flow solution and drag formulas are valid for all values of the three parameters, Reynolds number, Magnetic Reynolds number, and Alfven number. The drag is calculated for large and small magnetic interaction; in the latter case the drag is proportional to the Alfven number. A special diffusion model applicable for large Hartmann number flows is also presented.https://resolver.caltech.edu/CaltechETD:etd-12162005-083621Motion of a Current Element Through a Fluid of Low Electrical Conductivity
https://resolver.caltech.edu/CaltechETD:etd-12072005-131316
Year: 1960
DOI: 10.7907/B0AW-TR02
Two-dimensional flow of an incompressible, viscous, electrically conducting fluid past a current element is studied. A solution in the form of an asymptotic development is obtained, valid as a certain dimensionless parameter (essentially the product of the electrical conductivity and the current) tends to zero. An expression for the drag on the current element is computed, and is found to be independent of viscosity.https://resolver.caltech.edu/CaltechETD:etd-12072005-131316Isentropic Plane Waves in Magnetohydrodynamics
https://resolver.caltech.edu/CaltechETD:etd-12082005-134709
Year: 1961
DOI: 10.7907/K49C-2N76
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Plane waves propagating in a perfectly electrically conducting polytropic gas of otherwise uniform state in the presence of an arbitrarily oriented uniform magnetic field are studied; they correspond to plane simple waves in magnetohydrodynamics. Riemann invariants across finite amplitude waves in ordinary gasdynamics are generalized herein to take into account all possible magnetohydrodynamics effects. There exist totally seven types of waves, namely, contact surfaces, forward and backward facing transverse simple waves and forward and backward facing coupled (fast and slow) simple waves. But of these only coupled waves are genuinely nonlinear and receive most of our attention. The mathematical theory of simple waves is discussed first to give a general picture of the underlying structure of solutions. Contact surfaces and transverse simple wave solutions are given next with particular emphasis on the case of the contact surface adjacent to a vacuum, region. An exact analytical solution of coupled waves for gases of arbitrary value of [...] is obtained in terms of generalized Riemann invariants; some of these invariants are expressed in terms of definite integrals of a parameter [...]. The invariant relations among several physical quantities are thus expressed in a parametric form. An alternative method of solving coupled waves by graphical means is proposed and some detailed calculations are presented. General properties of physical variables across coupled waves are mentioned. For the special case of gas in a purely transverse magnetic field, a scheme of solving arbitrary flow problems is discussed briefly. The corresponding case of coupled wave solutions is given in terms of a hypergeometric function. Finally, some examples are shown to illustrate the application of the solutions to actual physical problems.https://resolver.caltech.edu/CaltechETD:etd-12082005-134709Some Flow Problems in Rarefied Gas Dynamics
https://resolver.caltech.edu/CaltechETD:etd-11042003-095050
Year: 1961
DOI: 10.7907/1S8T-QA38
This thesis discusses three rather loosely connected problems in free molecule and nearly free molecule flow. First the expansion of a gas cloud into perfect vacuum is considered on the basis of the collision-less Boltzmann equation, and it is shown that if the initial distribution is an isothermal Maxwellian, the density obeys a diffusion equation with a diffusion coefficient proportional to the time. This leads to the description of the free expansion of symmetric clouds in terms of a thick 'diffusion front' traveling at the initial isothermal speed of sound. The expansion of asymmetric clouds and the flow due to sources and jets are also studied.
Second, a method of iteration proposed by Willis for calculating nearly free molecular flow is extended to general unsteady flows; it is then applied to the flow through an orifice to show that the correction to the mass flow is of the first order in the inverse Knudsen number. The coefficient, estimated by making some reasonable assumptions about the three-dimensional nature of the flow, is found to agree quite well with Liepmann's measurements.
Finally a physical basis is suggested for Krook's collision model used in the above calculations. Several consequences of the model are then derived, including the important one that, in the Navier-Stokes limit, the model implies a Stokesian gas with a Prandtl number of unity. The value to be given to the parameter in the model is also discussed at some length.https://resolver.caltech.edu/CaltechETD:etd-11042003-095050Perturbations on Hypersonic Wedge Flow
https://resolver.caltech.edu/CaltechETD:etd-12152005-133232
Year: 1962
DOI: 10.7907/KE9Q-XN81
The hypersonic inviscid flow over a configuration representing a small perturbation about a two-dimensional wedge is analyzed. Equations and boundary conditions are obtained for a class of general perturbations within the framework of Hypersonic Small Disturbance Theory. A specialization of this formulation is made to the case where the resultant perturbation consists of semi-infinite flat plates of slightly different incidence to the freestream. The flow over such a shape is divided into an outlying uniform region and a central conefield. Here, the outlying, uniform region solution is found to be trivial. The determination of the conefield gives rise to an elliptic boundary value problem which is solved with the aid of the Tschaplygin transformation and other conformal mappings.
Calculations are presented using the Fourier series solution for the perturbation pressure indicating the surface loads associated with the perturbation as well as the shock distortion function. Integral representations are obtained for the downwash and sidewash perturbations using the pressure solution.
The results are compared qualitatively with an analogous linear supersonic flow.
Finally, a solution for more general profiles is obtained under the further restriction that the specific heat ratio [gamma] is close to one. This solution is specialized to the case considered previously and a qualitative evaluation of the physical significance of the results is made.https://resolver.caltech.edu/CaltechETD:etd-12152005-133232Studies on the Propagation of Elastic Waves in Solid Media
https://resolver.caltech.edu/CaltechETD:etd-09192002-160252
Year: 1964
DOI: 10.7907/EW57-KB61
Several aspects of three basic problems concerned with the propagation of elastic waves in solid media are explored.
Stress and displacement correction terms resulting from application of a subsonically moving point load to the free surface of the infinite half-space are obtained using Fourier transform techniques (the load moves subsonically with respect to the longitudinal and transverse wave speeds). It is shown, for the supersonically travelling point load, that the solution is given, in the limit as the load velocity becomes large, by the well known solution of Sauter for the impulsive point load.
Analytic function theory is used to predict the existence of Rayleigh waves on the free surface of the infinite halfspace and Stoneley waves along the welded interface between two dissimilar solid media. A brief analysis shows that free-running waves are also possible on the interior surface of an infinitely long cylindrical cavity. These waves are dispersive, however, because of the introduction of a characteristic length.
The early and long time approximations for the hoop stress generated through scattering of a plane dilatational wave by a cylindrical cavity in an infinite medium are developed. Use is made of Friedlandler's Riemann surface representation (early time) and expansion in Fourier series (long time).https://resolver.caltech.edu/CaltechETD:etd-09192002-160252On the Viscous Hypersonic Blunt-Body Problem
https://resolver.caltech.edu/CaltechETD:etd-09102002-143008
Year: 1964
DOI: 10.7907/QCBK-ZD50
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The viscous hypersonic flow past an axisyrnmetric blunt-body is analyzed based upon the Navier-Stokes equations for a perfect gas having constant specific heats, a constant Prandtl number, P, whose numerical value is of order one, and a viscosity varying as a power, [...], of the absolute temperature, as the free-stream Mach number, M, and the freestream Reynolds number based on the body nose radius, R, go to infinity, and [...] (where [gamma] is the ratio of the specific heats) and [...] go to zero.
Through the use of strict asymptotic expansions, the behavior of the flow in the three distinct regions that comprise the interior of the "shock structure" is found, as well as for the one, two, or three regions that make up the "shock layer" depending on whether the quantity [...] is equal to [...], equal to [...], or greater than [...], respectively.https://resolver.caltech.edu/CaltechETD:etd-09102002-143008A Class of Three-Dimensional Optimum Wings in Hypersonic Flow
https://resolver.caltech.edu/CaltechETD:etd-11302005-135648
Year: 1967
DOI: 10.7907/X1J8-JK85
The idea of using streamlines of a certain known flow field to construct generally three-dimensional lifting surfaces together with the method of evaluating the aerodynamic forces on the surfaces, developed by Nonweiler, Jones and Woods, has been extended and applied to axisymmetric hypersonic flow fields associated with a class of slender power-law shock waves of the form r ~ τx<sup>n</sup> in the limit of infinite free stream Mach number. For this purpose, the basic flow fields associated with concave shocks (n > 1) have first been calculated numerically at a fixed value of the ratio of specific heats γ = 1.40, and the results are presented in tabulated form, covering a wide range of values of n. The method of constructing a lifting surface either by prescribing its leading edge shape on the basic shock or by specifying its trailing edge shape in the plane x = 1 is then discussed. Expressions for lift and drag on the surface are derived. A class of optimum shapes giving minimum pressure drag at a fixed value of lift has been determined for every basic flow field with n ranging from 1/2 to 10 at γ = 1.40.
https://resolver.caltech.edu/CaltechETD:etd-11302005-135648Steady Laminar Compressible Magneto-Fluid-Dynamic Gas Flows in Channels.
https://resolver.caltech.edu/CaltechETD:etd-09172002-144944
Year: 1967
DOI: 10.7907/5T8X-8S80
Numerical computations are carried out for the core flow of subsonic MFD generator channels with a large length-to-height ratio and fine electrode segmentation. The working fluid is taken as potassium seeded argon. Variable transport properties and radiation effects are considered. It is shown that transverse variations in fluid properties are very important in Faraday generators; a one-dimensional analysis of the flow is not adequate. Axial currents in nonequilibrium flows can be kept low if the right value of the Hall parameter can be obtained; this also depends critically on the Mach number and load parameter. Mach numbers much less than one and high load parameters are to be avoided. Attainment of very large Hall parameters and fields cannot be expected.https://resolver.caltech.edu/CaltechETD:etd-09172002-144944Nearly free molecular heat transfer from a sphere
https://resolver.caltech.edu/CaltechTHESIS:04052013-154128630
Year: 1968
DOI: 10.7907/KZ16-1X08
Consider a sphere immersed in a rarefied monatomic gas with
zero mean flow. The distribution function of the molecules at infinity
is chosen to be a Maxwellian. The boundary condition at the body is
diffuse reflection with perfect accommodation to the surface temperature.
The microscopic flow of particles about the sphere is modeled
kinetically by the Boltzmann equation with the Krook collision term.
Appropriate normalizations in the near and far fields lead to a perturbation
solution of the problem, expanded in terms of the ratio of
body diameter to mean free path (inverse Knudsen number). The distribution
function is found directly in each region, and intermediate
matching is demonstrated. The heat transfer from the sphere is then
calculated as an integral over this distribution function in the inner
region. Final results indicate that the heat transfer may at first
increase over its free flow value before falling to the continuum level.https://resolver.caltech.edu/CaltechTHESIS:04052013-154128630Construction of solutions to partial differential equations by the use of transformation groups
https://resolver.caltech.edu/CaltechETD:etd-04082005-155822
Year: 1968
DOI: 10.7907/X1E8-1E61
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
A systematic approach is given for finding similarity solutions to partial differential equations by the use of transformation groups.
If a one-parameter group of transformations leaves invariant a partial differential equation and its accompanying boundary conditions, then the number of variables can be reduced by one. In order to find the group of a given partial differential equation, the "classical" and "non-classical" methods are discussed. Initially no special boundary conditions are imposed since the invariances of the equation are used to find the general class of invariant boundary conditions.
New exact solutions to the heat equation are derived. In addition new exact solutions are found for the transition probability density function corresponding to a particular class of first order nonlinear stochastic differential equations. The equation of nonlinear heat conduction is considered from the classical point of view.
The conformal group in n "space-like" and m "time-like" dimensions, C(n, m), which is the group leaving invariant [...], is shown to be locally isomorphic to S O (n+l, m+l) for n + m >= 3. Thus locally compact operators, besides pure rotations, leave invariant Laplace's equation in n >= 3 dimensions. These are used to find closed bounded geometries for which the number of variables in Laplace's equation can be reduced.
https://resolver.caltech.edu/CaltechETD:etd-04082005-155822A Perturbation Procedure for Nonlinear Oscillations: The Dynamics of Two Oscillators with Weak Nonlinear Coupling
https://resolver.caltech.edu/CaltechTHESIS:04102013-145406345
Year: 1969
DOI: 10.7907/HXVR-7T87
<p>This thesis considers in detail the dynamics of two oscillators with weak nonlinear coupling. There are three classes of such problems: non-resonant, where the Poincaré procedure is valid to the order considered; weakly resonant, where the Poincaré procedure breaks down because small divisors appear (but do not affect the O(1) term)
and strongly resonant, where small divisors appear and lead to O(1) corrections. A perturbation method based on Cole's two-timing procedure is introduced. It avoids the small divisor problem in a straightforward manner, gives accurate answers which are valid for long times, and appears capable of handling all three types of problems with no change in the basic approach.</p>
<p>One example of each type is studied with the aid of this
procedure: for the nonresonant case the answer is equivalent to the Poincaré result; for the weakly resonant case the analytic form of the answer is found to depend (smoothly) on the difference between the initial energies of the two oscillators; for the strongly resonant case
we find that the amplitudes of the two oscillators vary slowly with time as elliptic functions of ϵ t, where ϵ is the (small) coupling parameter.</p>
<p>Our results suggest that, as one might expect, the dynamical behavior of such systems varies smoothly with changes in the ratio of the fundamental frequencies of the two oscillators. Thus the pathological behavior of Whittaker's adelphic integrals as the frequency ratio is
varied appears to be due to the fact that Whittaker ignored the small divisor problem. The energy sharing properties of these systems appear to depend strongly on the initial conditions, so that the systems not ergodic.</p>
<p>The perturbation procedure appears to be applicable to a wide variety of other problems in addition to those considered here.</p>https://resolver.caltech.edu/CaltechTHESIS:04102013-145406345