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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:39:56 +0000Higher Order Approximate Solutions for the Flow in Axial Turbomachines
https://resolver.caltech.edu/CaltechETD:etd-01282009-092006
Authors: Monroe, Gerald Morgan
Year: 1949
DOI: 10.7907/8BJW-AE38
The theory of the three-dimensional rotational flow of an incompressible and inviscid fluid through an axial turbomachine is described and the hydrodynamical equations are simplified by considering an infinite number of blades in each row. The forces of the blades on the fluid are treated as non-conservative body forces distributed uniformly about the axis.
Formulation of the mathematical problem leads to one non-linear partial differential equation and two integral equations for the three velocity components. A linearized solution of these simultaneous equations for any prescribed blade loading is based on the consideration that the vorticity generated by the blades is transported downstream by the mean axial velocity. An iteration process which leads to solutions of greater accuracy is developed by considering for each iteration that the vorticity is transported by the velocities found by the previous iteration.
The Bessel's functions which occur in the Green's function solution are replaced by their asymptotic values and the infinite series is summed to express the solution in closed form. The iteration process is then adapted to mechanical calculations by dividing the region of vorticity into small rings of rectangular cross-section and determining the influence on the velocity of a unit change of vorticity in each of these rings. Once this influence is established it is relatively easy to calculate the velocities in any axial flow machine with any prescribed blade loading.https://thesis.library.caltech.edu/id/eprint/391Some Potential Problems Arising in the Theory of Axial Turbomachines
https://resolver.caltech.edu/CaltechETD:etd-11122003-085608
Authors: Mandelbrot, Benoit B.
Year: 1949
DOI: 10.7907/QGD5-YD25
<p>Some potential problems raised by the trailing-vortex theory of axial turbomachines are solved in the cases of cylindrical semi-infinite and infinite helicoidal vortices and of trailing vortices in a cone. The analysis is carried out for the cylindrical doubly infinite case and the dynamical problems are set up.</p>
<p>The results are in a form where further applications to the physical problems may be undertaken and actual computations worked out.</p>
<p>It is hoped that this work will be completed in the future.</p>https://thesis.library.caltech.edu/id/eprint/4517Supersonic Nozzle Design for Viscous Fluids
https://resolver.caltech.edu/CaltechETD:etd-01262009-141501
Authors: Gompf, George Edward
Year: 1949
DOI: 10.7907/R422-S076
A method is presented for including the effects of viscosity in the design of supersonic wind tunnel nozzles, the effect being presented in the form of a modification to the non-viscous, or perfect fluid, nozzle shapes. The modification essentially consists of providing additional expansion area to compensate for the retarded flow near the wall, and is estimated from considerations of possible boundary layer growth along a heat insulated flat well with a pressure gradient, when both the velocity profile and friction coefficient are assumed.
It is shown that the modification to the perfect fluid shape becomes very pronounced for design Mach numbers above five and results in a shorter nozzle length for a given test section size than that predicted from perfect fluid theory. At a Mach number of 10, this method results in a nozzle length reduction of 50% indicating that the boundary layer occupies this percentage of the test section for the shortened nozzle.
Design curves are presented from which the modification to a specific perfect fluid nozzle shape may be computed for Mach numbers up to 10.https://thesis.library.caltech.edu/id/eprint/361Application of the Ram Jet to Vertical Ascent
https://resolver.caltech.edu/CaltechETD:etd-02112009-094718
Authors: Rowney, James Victor
Year: 1950
DOI: 10.7907/DRA1-DS60
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The purpose of this paper is to investigate the applicability of the ramjet to replace the first step of a two-step or multi-step rocket, with the hope of increasing the efficiency and performance of vertical ascent missiles of the present day. The ramjet is considered as a booster motor to boost the primary missile through the atmosphere. It is to be discarded from the primary missile after reaching its maximum velocity. To boost the ramjet to operating speed the second stage rocket must be operated for the first few seconds as a ducted rocket.
General ramjet performance is calculated graphically by using a step-by-step integration process to solve the differential equation of motion. The resulting flight velocity, fuel consumption per initial weight, and altitude are presented graphically in terms of time after launching the ramjet. It is assumed throughout the problem that gravity is constant and that the altitude necessary to start the ramjet is negligible. The acceleration of the missile is limited to 25 g's.
Important results present in this paper are: The most important factor that limits the performance of the ramjet is the air density ratio. The greatest increase in second-step launching altitude, by improved thrust and drag coefficients and increased ramjet cross-section area, is achieved at low ramjet launching velocities. The performance of the ramjet missile operating at a specific fuel consumption of .0007 [...] shows a marked increase of efficiency over a missile using a higher fuel consumption value. Missiles using a lower specific fuel consumption value, of the same order as the increased value, show negligible improvement in efficiency. When ramjet performance is compared to rocket performance; specifically, maximum velocity, altitude of maximum speed and altitude attained, the ramjet missile will burn only one third of the fuel required by a two-step rocket. Conversely, for the same fuel consumed, the ramjet missile will attain 65% more altitude than the two-step rocket.https://thesis.library.caltech.edu/id/eprint/605Analysis of an Inclined Thrust Axis as Applied to a Ramjet Propelled Aircraft
https://resolver.caltech.edu/CaltechETD:etd-03162009-142841
Authors: Welch, Frank
Year: 1950
DOI: 10.7907/T1QH-QJ51
The low values of lift-drag ratio attained by supersonic wing configurations provide the opportunity for the utilization of an inclined thrust axis. The exhaust jet of a ramjet propelled aircraft is inclined in order to use some of the jet force to supply additional lift. This has the effect of augmenting the lift by the relatively large sine component of the jet force whereas the thrust in the flight direction is reduced only by the smaller change in the cosine component.
It was found that this principle offers a substantial decrease in fuel consumption over that of a normal ramjet for probable values of lift-drag ratios above Mach number 1.5. Almost all of the possible decrease can be obtained with jet inclination angles of 15° or less.https://thesis.library.caltech.edu/id/eprint/971A Formulation of the Problem of Distributed Vorticity in the Shock Wave Boundary Layer Interaction process
https://resolver.caltech.edu/CaltechETD:etd-01292009-153901
Authors: Barker, William Cyrus
Year: 1950
DOI: 10.7907/H3PW-QF74
The problem of shock wave boundary layer interaction is reviewed and attention focused upon the role of vorticity in the process. In order to simplify the physical considerations the two phenomena exhibited by vorticity in the interaction process-reflection and refraction of the disturbance, and transport of the vorticity from its original distribution - are divorced from one another. The reflection and refraction process is then considered apart from the other, and it is found that a boundary value problem can be formulated for it and formally solved for small perturbations from the undisturbed flow.
The perturbation component, which is associated with the pressure variation over the bounding surface, is set up and carried through to a point involving evaluation of a contour integral. This integral is so complex that its analytical evaluation would require many months of effort, and at this point it is thought that a re-examination of the original problem would be in order.
Although numerical results would be desirable, the effort expended would have to be weighed against their relative contribution to an understanding of the overall problem.https://thesis.library.caltech.edu/id/eprint/403Determination of Temperature in a Low Pressure Flame
https://resolver.caltech.edu/CaltechETD:etd-03192009-114701
Authors: Lobdell, John Henry
Year: 1951
DOI: 10.7907/MTQ1-K461
The extended dimensions of a flame zone which result from reducing the ambient pressure below 10 mm. Hg provide possibility for detailed investigation of flame chemistry and thermodynamics. The present investigation constitutes the first part of a detailed survey of the temperature distribution in an oxy—acetylene flame and describes the instrumentation and development of the modified Schmidt Technique for measuring flame temperature and the measurement of the maximum temperature in the flame.
The results indicate the maximum flame temperature to be within plus or minus 30°C. of the equilibrium flame temperature at 4.3 mm. Hg. The technique developed, while laborious, may be used to determine flame temperature with a good degree of accuracy.
The work was carried on with the financial support of the U. S. Army Ordnance Corps and the U. S. Air Force Air Materiel Command as part of a study of low pressure combustion under way at the Jet Propulsion Laboratory.https://thesis.library.caltech.edu/id/eprint/1027I. On the Dust Devils. II. Linearized Theory of Conical Turbomachines
https://resolver.caltech.edu/CaltechETD:etd-03042009-142746
Authors: Michelson, Irving
Year: 1951
DOI: 10.7907/PZKM-9280
Dust devils are small-scale atmospheric motions of instability arising from the development of large thermal stratifications in the lowest layers above the surface of the earth. A theory is proposed in Part I to describe the conditions of formation of these motions and depends on the new result that shear provides a powerful stabilizing influence even in non-viscous fluid motions in which denser fluid is situated above less dense. Those features of the flow which can be predicted by the theory and compared with observations are found to be in reasonably good agreement, and it is therefore indicated that the theory, which is based on a highly simplified model of flow, furnishes at least a qualitatively correct correlation of the basic ideas involved in the stable flow of very slightly viscous fluids containing density inversions. Applications to technically interesting flows of this type, in large-scale atmospheric motions as well as in high speed aerodynamic boundary layers, are indicated but not analyzed in detail.
In Part II the perfect fluid flow is determined for a turbomachine of conical shape and prescribed blade loading. On the basis of the assumption that the stream surfaces are conical in shape, a linear, elliptic partial differential equation of the second order is obtained. The associated boundary value problem is of the Sturm-Liouville type and is solved completely. An asymptotic representation of the solution is determined which is convenient for computational purposes.https://thesis.library.caltech.edu/id/eprint/876An Analysis of a Compound Pendulum Rocket Suspension
https://resolver.caltech.edu/CaltechETD:etd-03162009-142423
Authors: Norris, James Caspar
Year: 1951
DOI: 10.7907/YDS1-JW02
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
This is an investigation of the equations of motion and physical parameters involved in stabilizing the initial flight of a vertically launched rocket by means of a booster rocket pin-connected below the main rocket. The system is designed to stabilize the flight in its early stage before the aerodynamic control surfaces become effective. Stability of the system is dependent on the pendulum action of the booster rocket.
The equations of motion were derived from Lagrange's generalized momentum equation. The differential equations thus obtained were not solved but were tested for stability by means of Routh's stability criteria. The ratio of the mass of the main rocket, M[subscript 1], to the mass of the booster rocket, M[subscript 2], was investigated for the two values [...] = 1.5 and [...] = 7.75.
The system involving a mass ratio [...] = 7.75 was found to be unstable under all conditions. However, the system involving a mass ratio [...] 1.5 was determined to be stable in the range 1.62 < β < 4.54 x 10[superscript 10], where β is defined as the ratio of the distance [...] from the center of gravity of the booster M[subscript 2] to the pin connecting the strut to the main rocket M[subscript 1], divided by the radius of gyration, k[subscript 2], of the booster M[subscript 2]. In this range, for any given value of, β, stability was uniquely determined by one value of the ratio α = [...], where [...], is the length of the strut from the main rocket M[subscript 1] to the booster rocket M[subscript 2]. Thus, for a given booster, stability is primarily a function of the ratio [...], and for any given [...], is uniquely determined.
Although the system was found to be theoretically stable for the mass ratio [...] = 1.5 , the ratio [...] turned out to be of such great magnitude as to make the system entirely impractical for this particular mass ratio.https://thesis.library.caltech.edu/id/eprint/970Effect of Small Variations of Parameters in the Turboprop Cycle
https://resolver.caltech.edu/CaltechETD:etd-12282005-104251
Authors: Holmquist, Carl Oreal
Year: 1951
DOI: 10.7907/B34Z-JX85
A cycle analysis of the turbine-propeller engine is given in terms of the parameters of the cycle and the component efficiencies of the engine with and without regeneration. By means of a Taylor expansion about the point of ideal efficiencies, total power output, specific fuel consumption, and optimum jet pressure ratio are given in terms of the ideal values plus corrections for small variations in the component efficiencies from 100%. In this way, the relative importance of component efficiencies in affecting the performance of the ideal turboprop cycle is demonstrated by means of simple analytical expressions involving the basic cycle parameters and the component efficiencies.
The analysis of the ideal turboprop cycles is given in terms of three basic parameters which are functions of the forward flight speed, the compressor pressure ratio, and the limiting combustion chamber temperature. For the ideal cycle, the jet pressure ratio for optimum division of power between propeller and jet results in the total work of the cycle being done by the propeller.
Of the component efficiencies, the turbine efficiency was found to be the most important in affecting the performance criteria of the ideal turboprop cycle. Since all work is done by the propeller in the ideal cycle, the propeller efficiency was also found to be important in affecting performance. Regeneration, as considered in this analysis, decreased the total power output and decreased the specific fuel consumption of the ideal turbine-propeller engine.https://thesis.library.caltech.edu/id/eprint/5151A Study of Compressible Perfect Fluid Motion in Turbomachines with Infinitely Many Blades
https://resolver.caltech.edu/CaltechETD:etd-03182009-151729
Authors: Monroe, Gerald Morgan
Year: 1951
DOI: 10.7907/HQD3-G406
A study is made of compressible perfect fluid motion in turbomachines having infinitely many blades and a general theory is developed. An underlying concept of the theory is that force fields which represent the action of infinitely many blades belong to a special class described as pseudo-conservative and can be expressed as the product of a scalar function and the gradient of a potential. The scalar function is simply the rate at which energy is imparted to the fluid by the blades, and the potential is simply the family of the equations for the blade surfaces. The introduction of these two functions to express the force field casts an entirely new light on problems of mixed-flow turbomachines having infinitely many blades of arbitrary shape.
In the formulation of the problem the non-linear action of rotationality and compressibility is regarded as a force tending to displace the streamsurfaces from their irrotational, incompressible position. It is shown that the character of the problem is determined by a governing velocity: the velocity relative to the blades where blades are present, or the meridional velocity, where blades are not present. Where the governing velocity is subsonic the problem is essentially elliptic, where supersonic, hyperbolic.
The theory and the examples lead to conclusions which are believed to explain in part the unexpected efficiencies observed for compressors having transonic governing velocities. These conclusions, which indicate that transonic compressors could perhaps be profitably developed, are as follows: The deflection of the streamsurfaces induced by a given strength of vorticity at a certain point in the flow has one sense when the governing velocity at the point is subsonic, the opposite sense when it is supersonic, and becomes zero as it becomes sonic. The deflection of the streamsurfaces brought about by a given distribution of vorticity in a region is less when the governing velocity in the region is transonic than when it is entirely subsonic or entirely supersonic.
Examples of incompressible flow through a mixed flow compressor with prescribed blades, and subsonic and transonic flow through actuator disks, were solved by the method of finite differences, applying simultaneously the relaxation technique and an iteration process.https://thesis.library.caltech.edu/id/eprint/1003Analytical Performance Study of Turbojet Cycle with Nearly Ideal Component Efficiencies
https://resolver.caltech.edu/CaltechETD:etd-03192009-161901
Authors: Hughes, Richard Frank
Year: 1951
DOI: 10.7907/Q2CP-J309
The performance of the turbojet engine for high component efficiency is approximated by an ideal expression (efficiencies equal unity) plus the first terms of a Taylor Series expansion for the purpose of isolating the individual effects of the components.
The analytical solution to two optimizations is presented; namely:
(A) For fixed burner outlet temperature, flight Mach number, and component efficiency, what is the compressor pressure ratio corresponding to maximum jet velocity (maximum thrust per unit mass flow)?
(B) For fixed flight Mach number, compressor pressure ratio and component efficiency, what is the burner outlet temperature corresponding to minimum specific fuel consumption?https://thesis.library.caltech.edu/id/eprint/1031Initial Motion of a Rocket Moving on a Stretched Cable
https://resolver.caltech.edu/CaltechETD:etd-03302009-090703
Authors: Weinberg, Warren E.
Year: 1952
DOI: 10.7907/NY23-GR26
The practicability of using a stretched cable for a rocket launching device is dependent primarily upon the transverse movement of the rocket and the stresses involved in the system. This requires analysis of the effects of the moving rocket mass on the cable from the instant of contact, and the problem reduces to one of wave propagation.
The analysis here is restricted essentially to developing a procedure by which the initial motion of the mass can be calculated, and an expression is obtained which permits determination of the deflections. The problem is approached by first assuming that the mass exerts a constant transverse force on the cable. Admittedly, this is a simplifying assumption, and the result is not valid for the instant the mass hits the cable or for a short time thereafter because the inertia of the mass is not considered.
Next, the problem is solved by taking into account the dynamics of the mass, and the solution reveals that the path of the actual mass deviates from the force path by as much as twenty percent during the initial motion but soon returns to the force path. The mass does not exert its full force on the cable at the instant of contact, but comes down on the cable with full force a short time later. Since maximum stresses on the system occur at this time, this factor is an important result of the analysis. Further, it is shown that increased velocity of the mass increases the deviation from the force path, and increased mass lengthens the time of return to the force path.https://thesis.library.caltech.edu/id/eprint/1216Stabilization of a Bipropellant Liquid Rocket Motor
https://resolver.caltech.edu/CaltechETD:etd-03192009-154303
Authors: Cox, Dale William
Year: 1952
DOI: 10.7907/4SBW-M406
The unstable burning of a bipropellant rocket combustion chamber is investigated and a study made of the requirements for an automatic closed loop control circuit to stabilize the motor.
The bipropellant combustion chamber equations developed by Dr. L. Crocco(1) are utilised as the analytical description of the rocket motor burning phenomena. Equations similar to those developed by Dr. H. S. Taiga(2) are used for the oxidizer and fuel supply systems and the two closed loop stabilizing circuits.
The stability or instability of the system is demonstrated by the use of a special plotting diagram in the complex plane suggested by M. Satche as a means of handling systems with time lag, and developed for this use by H. S. Tsien. This involves separating the transfer function into two parts. In the complex plane the first portion of the transfer function, the exponential variable containing the time lag, plots as a unit circle as the complex variable p is made to take a contour enclosing the positive half of the p—plane. If the remaining portion of the transfer function intersects this unit circle, the rocket motor can be unstable for large reduced time lag; if it does not intersect the unit circle, the system is generally stable, although the roots of the exponential coefficient in the positive half of the complex plane must be investigated. This latter requirement can be conveniently accomplished by the aid of a Nyquist Diagram.
The equations for the feedback circuit are developed and the oxidizer and fuel transfer function requirements are determined.
Two cases of stable combustion and two cases of unstable combustion are analyzed. One unstable case is stabilized by the addition of a feedback circuit.https://thesis.library.caltech.edu/id/eprint/1030Investigation of Flame Velocities at Low Pressures
https://resolver.caltech.edu/CaltechETD:etd-03232009-075003
Authors: Eriksen, George August
Year: 1952
DOI: 10.7907/NGNK-YA29
The purpose of this study is to investigate flame velocities of mixtures of oxygen and various fuel gases at low pressures. Acetylene and propane fuels were used, and flame velocities were measured by means of flat disc flames and by means of the geometry of cone-shaped flames. Flame front area was measured from the profile defined by the onset of luminosity. The pressure range from three to one hundred mm. of mercury was covered by using two burner inlet ducts of different diameters, 2.37 and 1.25 inches respectively. The equipment and characteristics of the low pressure flame limited the data in this range, so that restricted quantitative results were obtained in regard to the variation of flame velocities with pressure.
Qualitatively, very definite variations were noted. There is a marked decrease of flame velocity with decreasing pressures in the regime below forty mm. of mercury. The variation in flame speed for the same pressure increments becomes greater as the pressure decreases. This is attributed to the rapid increase of the quenching effect from the inlet duct rim at these low pressures and low flow velocities. It is also found that flame velocities from flat flames are consistently lower than those obtained through the geometry of the cone flames. Similarly, flame velocities measured with the smaller inlet duct are consistently lower than those measured with the larger duct for the same measuring criteria. Both these variations appear to be explained by the large quenching effect encountered.https://thesis.library.caltech.edu/id/eprint/1074An Experimental Investigation of Ignition and Flame Stabilization in a Turbulent Mixing Zone
https://resolver.caltech.edu/CaltechETD:etd-03252009-114335
Authors: Becker, Jack Lincoln
Year: 1952
DOI: 10.7907/BFQK-V510
The present investigation constituted the first part of an attempt to isolate the essentials of flame stabilization behind a bluff body. It is thought by many that such a flame is initiated and stabilized by heat transfer, the diffusion of active chemical species, and the chemistry of the combustible mixture involved.
The ignition of a fresh combustible mixture by a hot stream of gas provides possibility for detailed study of flame stabilization because of heat transfer.
Results indicate that the method followed herein to produce ignition resulted in the formation of two distinct types of flames. One flame seemed to be affected primarily by temperature, the other was affected by temperature, stream velocity and fuel-air ratio.
The work was carried on as part of a study of flame stabilization being conducted at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California.https://thesis.library.caltech.edu/id/eprint/1125Burning Rate for a Solid Propellant Ramjet Developing Constant Tthrust
https://resolver.caltech.edu/CaltechETD:etd-03232009-150232
Authors: Arbo, Paul Edward
Year: 1952
DOI: 10.7907/31B3-3W28
An analysis of a solid propellant ramjet which carries the propellant in the combustion chamber was made, and a procedure outlined for calculating the required burning rate of such a ramjet which develops constant thrust. The two factors which influenced this development were:
1) The solid propellant ramjet’s combustion chamber varies in size with time due to burning of the fuel.
2) The solid propellant ramjet develops constant thrust.
These factors were coordinated with the analysis of the internal flow system of the ramjet, and an expression for the required burning rate was derived.https://thesis.library.caltech.edu/id/eprint/1080An Approximate Method of Calculating Three-Dimensional Compressible Flow in Axial Turbomachines
https://resolver.caltech.edu/CaltechETD:etd-04232003-115022
Authors: Holmquist, Carl Oreal
Year: 1953
DOI: 10.7907/3FB2-G132
The two principal existing methods of calculating axially-symmetric compressible flow in turbomachines are: (1) a simplified one-dimensional analysis, and (2) numerical methods using the complete or linearized flow equations. The first is not satisfactory for multi-stage turbines with appreciable wall divergence; the second is very tedious and time consuming. The purpose of this investigation is to extend the approximate methods, successfully used in calculating incompressible flow in compressors with constant blade height, to the analysis of compressible flow in turbomachines with variable blade height. Assuming that the blades can be completely defined by the exit flow angle, and neglecting the influence of downstream blades, the analysis is made considering the flow between successive blade rows only. With these restrictions, subsonic and isentropic supersonic flow patterns can be determined for arbitrary boundary shapes as long as separation does not occur. Average losses can be accounted for by the use of a polytropic law, and the effect of radial variations in stagnation temperature can be included without difficulty. Examples illustrating the flexibility and practical value of the iteration method, and the rapid convergence of successive solutions are given.https://thesis.library.caltech.edu/id/eprint/1468Use of a Sampling Feedback System for Stabilization of Low Frequency Oscillations in Liquid Monopropellant Rocket Motors
https://resolver.caltech.edu/CaltechETD:etd-04232003-090202
Authors: Fernández, Raymond Caesar
Year: 1953
DOI: 10.7907/PZEC-N445
Instability in liquid monopropellant rocket motors may be corrected by the use of a feedback servomechanism. This mechanism consists essentially of a pressure pickup which senses pressure oscillations in the combustion chamber, an amplifier and a variable capacitance in the feed line. It is shown that a feedback system with an arbitrary sampling circuit which causes the capacitance in the line to complete its own cycle of variation once for every several cycles of combustion pressure oscillations can be made to stabilize the oscillations for all values of combustion time lag for a particular motor. It is believed that this system of stabilization may be applied to monopropellant motors in general.https://thesis.library.caltech.edu/id/eprint/1462Feedback Servo-Stabilization of a Rocket During Take-Off
https://resolver.caltech.edu/CaltechETD:etd-05092003-161730
Authors: Saxon, John Solon
Year: 1953
DOI: 10.7907/BV8Y-QT45
When a rocket is launched, there is a short initial period of acceleration during which the rocket is unstable. As the flight velocity increases, the aerodynamic forces acting on the fins and stabilizers become large enough to give stability. Various methods have been employed to stabilize the rocket during this launching period. Guide rails, "zero length" launchers, booster rockets which produce high initial acceleration, and auto-pilot controlled nozzles are typical devices that have been used.
This is an investigation of the requirements of a nozzle control which would stabilize the rocket during the launching period. The configuration investigated is unique in that the nozzle of the rocket is mounted as a compound pendulum, and the movement of the pendulum is utilized to furnish the signal for the nozzle control servo-mechanism, thereby eliminating the need for gyroscopic elements in the control system. The pendulum motion of the nozzle caused by a change in flight attitude of the rocket is introduced into a computer which produces an output signal proportional to the attitude of the rocket. This attitude signal is fed back to the nozzle control, which positions the nozzle.
The results of the analysis showed that the rocket was unstable during the take-off period when the nozzle control acted on the rocket attitude signal alone. Stability over a narrow range of feedback gains was indicated for the system using a simple lead circuit as a nozzle control, or in other words, when the nozzle control acted on both the attitude signal and the rate of change of attitude of the rocket. The damping characteristics of this system were poor. By changing the nozzle control function to include a response to the acceleration of the rocket attitude, the damping characteristics were improved and the range of feedback gains was widened.https://thesis.library.caltech.edu/id/eprint/1697Laminar Boundary Layer Problems Associated with Flow Through Turbomachines
https://resolver.caltech.edu/CaltechETD:etd-05122003-100849
Authors: Mager, Artur
Year: 1953
DOI: 10.7907/49CS-2731
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
This analysis deals with three-dimensional boundary layer flows which are of particular interest in the design of turbomachinery. By assuming only small lateral pressure gradients and applying perturbation procedure to the steady, laminar boundary layer equations of motion a set of zeroth and first order equations is found. While the zeroth order equations are just the two-dimensional ones for flow over flat plate, the first order equations retain the characteristic Blasius similarity for a family of external flows expressible by [?] (where U* [and] W* are the perturbation velocities, x [and] z are the coordinates and A [and] B are arbitrary constants). For various types of such external flows (which may or may not be rotational) boundary layer velocity distributions were found by a numerical solution.
The investigation is divided into two parts, the first one dealing with boundary layer flows over plane surfaces and the second one considering such flows over surfaces with very sharply varying lateral curvature. In order to obtain solutions in the second part it was necessary to expand the appropriate equations in terms of the product of the local surface curvature and the boundary layer thickness. In addition, the effects of compressibility and rotation (of the surface) on the flows over a plane surface were quantitatively evaluated.
Comparison of the present results with the more exact solutions of other investigators in certain special cases, and with the visual studies of three-dimensional boundary layer flow in cascades, indicates a fair qualitative agreement.https://thesis.library.caltech.edu/id/eprint/1731Variation of Burning Velocity with Pressure
https://resolver.caltech.edu/CaltechETD:etd-04292003-095800
Authors: Pardee, William McKnight
Year: 1953
DOI: 10.7907/C95P-BV39
A review of some of the recent theories of steady state flame propagation in gaseous mixtures reveals a considerable difference in their prediction of the effect of pressure on burning velocity. Furthermore, the experimental data obtained by various workers in the field indicate widely different trends. In some cases burning velocity appears to be independent of pressure whereas in other cases it appears to increase as the pressure is reduced below atmospheric. Hence, as a possible aid in discovering more about the mechanism of flame propagation, the burning velocity of several gaseous mixtures was studied over the general pressure range from 100 to 700 mm Hg absolute.
The mixtures used were acetylene-oxygen, acetylene-air, acetylene-oxygen-nitrogen, ammonia-oxygen, ammonia-oxygen-nitrogen, carbon monoxide-oxygen, carbon monoxide-air, and propane-air. Using the burner-visual cone-area method with burners of various sizes, the following results were obtained: for all the above mixtures, except propane-air, the burning velocity is independent of pressure; for propane-air mixtures, the burning velocity varies as P[superscript -.13]. These results are valid provided the burner size is large enough to nullify the effect of quenching.
It is concluded that these results definitely do not support the Tanford and Pease theory that burning velocity varies as P[superscript -.25].https://thesis.library.caltech.edu/id/eprint/1537An Experimental Study of the Stability of Laminar Flame
https://resolver.caltech.edu/CaltechETD:etd-04222003-101645
Authors: Curran, Donald Charles
Year: 1953
DOI: 10.7907/6W88-7713
Knowledge of laminar flame front structure is insufficient to make exact stability calculations possible. The analysis of Landau(1) indicated flame front instability under all conditions. Semi-empirical corrections to Landau's result by Markstein(2) demonstrated that a cellular flame front structure that Markstein observed experimentally might be a stable configuration. Karlovitz(3) has proposed that there is a significant additional amount of turbulence produced in turbulent flames over that found in the upstream flow. Of particular significance is the question of whether or not a flame may take on a turbulent structure in the absence of upstream turbulence.
Therefore explorations concerning the conditions under which a laminar flame might become unstable were undertaken by burning premixed propane and air using a spherical flame holder.
The resulting conical flame had annular waves develop in the flame front a short distance downstream from the flame holder. This distance decreased as fuel-air ratio was decreased and as gas mixture flow velocity increased. Lean high velocity flames showed a parallel result in the amplitude of the wave formed - the wave in this case developing to a large amplitude in a short distance with a tendency to roll up.
Another result of the investigation was that a fairly uniform wavelength of 0.27 in. was observed even though mixture, flame holder size and flow rate were varied.
The introduction of a small external turbulence source upstream of the flame front disturbed the flame - the amount of disturbance increasing with Reynolds' number of the turbulence source and with fuel-air equivalence ratio.https://thesis.library.caltech.edu/id/eprint/1446An Experimental Investigation of High Frequency Combustion Instability in a Fuel-Air Combustor
https://resolver.caltech.edu/CaltechETD:etd-12082003-111443
Authors: Rogers, Don Easterday
Year: 1954
DOI: 10.7907/65NM-7Q10
The results of an experimental investigation of high frequency combustion instability in a fuel-air combustor are described. The phenomenon is described in terms of alterations in the flame geometry and pressure changes associated with the flow field. Quantitative measurements of the pressure fluctuations are presented and the effects of various system parameters on the instability are indicated.
A possible mechanism for forcing and sustaining the oscillations as indicated by the experimental data is suggested and discussed.https://thesis.library.caltech.edu/id/eprint/4852An Experimental Investigation of the Recirculation Zone of Laminar Flames Stabilized on Bluff Bodies at Low Reynolds Numbers
https://resolver.caltech.edu/CaltechETD:etd-12022003-171942
Authors: von Gerichten, Robert Louis
Year: 1954
DOI: 10.7907/HHVW-Z921
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
As part of a program to explain the shift in the maximum blowoff velocity from stoichiometric mixture ratio for small flame holder sizes, laminar flame stabilization studies were made using cylindrical flame holders of 0.031 to 0.125 inches in diameter at Reynolds numbers in the range of 10[^3] to 10[^4]. Chemical samples of the gases in the recirculation region behind the flame holders were taken and analyzed to determine the composition of the burning gases at the flame front. Maximum temperature measurements were taken of this same region. It was found that at these low Reynolds numbers, the composition was different than in the unburned approach mixtures, and that this was apparently due to the difference in molecular diffusion of the fuel and air across the flame front. The variation in the composition of the burning gases appears to be a direct function of the approach fuel-air mixture ratio for each diameter and approach mixture velocity.https://thesis.library.caltech.edu/id/eprint/4715Ignition and Combustion in a Laminar Mixing Zone
https://resolver.caltech.edu/CaltechETD:etd-11202003-135437
Authors: Adamson, Thomas Charles, Jr.
Year: 1954
DOI: 10.7907/Q9A7-T088
<p>The equations describing combustion in a flow field are modified for use in laminar flows where the so called boundary layer approximations may be employed. These equations are transformed into a corresponding incompressible flow with the Howarth transformation.</p>
<p>As an example of the use of boundary layer concepts this analysis considers the ignition and combustion in the laminar mixing zone between two parallel moving gas streams. One stream consists of a cool combustible mixture, the second is hot combustion products. The two streams come into contact at a given point and a laminar mixing process follows in which the velocity distribution is modified by viscosity, and the temperature and composition distributions by conduction, diffusion and chemical reaction. The decomposition of the combustible stream is assumed to follow first-order reaction kinetics with temperature dependence according to the Arrhenius law. For a given initial velocity, composition, and temperature distribution, the questions to be answered are: (1) Does the combustible material ignite and (2) How far downstream of the initial contact point does the flame appear and what is the detailed process of development?</p>
<p>Since the hot stream is of infinite extent it is found that ignition always takes place at some point of the stream. However when the temperature of the hot stream drops below a certain value, the distance required for ignition increases so enormously that it essentially does not occur in a physical apparatus of finite dimension. The complete development of the laminar flame front is computed using an approximation similar to the von Karman integral technique in boundary layer theory.</p>
https://thesis.library.caltech.edu/id/eprint/4605A Study of the Effect of Boundary Layer Control on an Axial Flow Compressor Stage
https://resolver.caltech.edu/CaltechETD:etd-01152004-115145
Authors: Mertz, Charles
Year: 1954
DOI: 10.7907/AG0W-5T14
The problem of increasing the pressure ratio per stage of an axial flow compressor is studied in part by considering the effect of boundary layer control by area suction on the three dimensional turbulent boundary layer flow on the casing in one stage of a compressor.
The effect of this boundary layer control, on the prevention of separation is investigated. Crossflow and crosswise variation of crossflow in the boundary layer are factors contributing to the tendency toward separation and the effect of boundary layer control on this phenomenon is determined. This analysis is limited to the boundary layer on the casing and does not take into consideration the possible separation taking place at the blades.
The boundary layer equations are used to obtain the momentum integral equations with suction applied at the surface. The method of small perturbations is applied to the equations in order to simplify them so that a solution may be reached with relatively little effort. Expressions are assumed for the boundary layer profiles, flow path outside the boundary layer, and shear stresses. These are in a form which closely resembles the actual conditions.
In order to show what effect boundary layer control exerts, a simplified single stage compressor is studied. The results show that crossflow can be reduced by applying suction to the boundary layer with a resultant decreased tendency toward separation of the flow, but this is reached only after a certain minimum suction velocity is attained, If the suction velocity is less than this minimum, in spite of the decrease in boundary layer thickness the crossflow will be increased over that of a solid wall and likewise the tendency toward separation will increase.https://thesis.library.caltech.edu/id/eprint/187Flame Stabilization on Bluff Bodies at Low and Intermediate Reynolds Numbers
https://resolver.caltech.edu/CaltechETD:etd-01142004-105717
Authors: Zukoski, Edward Edom
Year: 1954
DOI: 10.7907/E9V0-GM76
The problem of attaining stable combustion in ramjet power plants and in afterburners of turbojet engines has led to rather extensive studies of the processes involved in stabilizing flames on bluff bodies. One of the results of these studies was to indicate that the flame stabilization mechanism changes significantly at low Reynolds Numbers; the velocity at which flames may be stabilized drops abruptly as the Reynolds Number is decreased, and the mixture ratio for which maximum velocity of flame holding occurs shifts markedly from the stoichiometric value.
This abrupt change in the mechanism of flame stabilization is investigated through photographic studies of the flame front near the flame holder. A transition from a laminar to a turbulent surface of the flame front immediately downstream from the flame holder is shown to account for the change in flame stabilization characteristics. This transition was found to occur independently of fuel type and flame holder geometry.
The behavior of the low Reynolds Number stabilization limits is attributed to a diffusion process; in particular, the shift found for the mixture ratio corresponding to the maximum blowoff velocity is explained on the basis of the difference in the diffusion rate of fuel and oxygen. Detailed experiments including blowoff results, chemical analysis of gas taken from the flame holder wake, and measurements of wake temperatures are shown to confirm the suggested diffusion mechanism.
Once the transition phenomenon is appreciated, re-examination of high Reynolds Number blowoff data is found possible. The results of previous experiments are found to show that the blowoff velocity depends on the square root of the characteristic dimension if the transition Reynolds Number is exceeded and if the flame holder is a bluff body of small fineness ratio.https://thesis.library.caltech.edu/id/eprint/162Variation of Burning Velocity of Laminar Flames with Pressure by the Burner-Area Method
https://resolver.caltech.edu/CaltechETD:etd-12022003-160702
Authors: Charles, John Morrison
Year: 1954
DOI: 10.7907/PVFG-9X18
Because of the disagreement in the published data on the effect of pressure on the burning velocity of laminar flames a general study was undertaken at the California Institute of Technology Jet Propulsion Laboratory to determine the variation of burning velocity with pressure by the burner-area method. This report is a portion of that study.
The mixtures utilized for this investigation were ethylene-air, isobutylene-air, propylene-oxygen-nitrogen, and propylene-air. Expressing the pressure dependence of burning velocity as p[superscript n], the value found for n is ?0.13 for ethylene-air, -0.186 for isobutylene-air, -0.153 for propylene-oxygen-nitrogen, and ?0.132 for propylene-air. The results compare reasonably well with the experimental findings of Pardee (10), Cullen (6), and Culshaw and Garside (5). At atmospheric pressure the values of burning velocity of the mixtures studied in this report are in close agreement with several experimental investigators.
Also investigated was the effect on the burning velocity of a mixture of acetylene-oxygen with the addition of helium. The trend found is that the burning velocity of an acetylene-oxygen mixture increases with the addition of helium up to a maximum at a certain percentage of helium and then decreases as more helium is added.https://thesis.library.caltech.edu/id/eprint/4710A Theory of Stall Propagation in Axial Compressors on the Basis of Airfoil Characteristics
https://resolver.caltech.edu/CaltechETD:etd-11242003-103851
Authors: Burggraf, Odus Roy
Year: 1955
DOI: 10.7907/HQV0-7S12
The process of stall propagation in an axial flow compressor is represented by nonlinear airfoil lift and drag characteristics, with a time lag associated with the stalling mechanism. A pair of nonlinear integro-differential equations express the lift and drag as a function of time for a given airfoil in an isolated plane cascade representing an annulus with only a finite number of blades. Approximate solutions of these integro-differential equations are obtained by considering only the fundamental frequency in the Fourier series representing the blade loadings. Qualitative results are obtained for three cases: (a) only blade circulation is considered to be of importance in the mechanism of propagating stall, (b) blade drag is of predominant importance, and (c) combined effects of lift and drag are considered. Comparisons are made of the propagating speeds calculated for a finite number of blades with the values obtained by the approximation of an infinite number of blades. The magnitudes of the fluctuations in lift and drag are calculated as well as limiting angles of attack for which stall propagation can occur.https://thesis.library.caltech.edu/id/eprint/4647Analysis of Optimalizing Control Systems witb Special Reference to Noise Interference Effects
https://resolver.caltech.edu/CaltechETD:etd-12112003-090547
Authors: Serdengecti, Sedat
Year: 1955
DOI: 10.7907/TMXZ-AJ80
The optimalizing control system is designed to search out automatically the optimum state of operation of the controlled system and to confine the operation to a region near this optimum state. The performance of the system is affected by the dynamics of the controlled system and by the noise interference.
The dynamic effects of the controlled system on the performance of a peak-holding optimalizing control is analyzed under the assumption that the controlled system dynamics may be represented by a first order input linear group and a first order output linear group. Design charts are constructed for determining the required input drive speed and consequent hunting loss with specified time constants of the input and output linear groups, the hunting period, and the critical indicated difference for input drive reversal.
The noise interference effects on the control system performance led to a new type of optimalizing control system which is a modification of the peak-holding optimalizing controller. Performance of the modified optimalizing controller is analyzed and several possible procedures are discussed for detecting and eliminating the incorrect operation modes. A statistical analysis is made to demonstrate the efficiency of a typical detection procedure, namely, the method of filtering through cross-correlation.
The modified optimalizing controller can utilize any periodically varying input. An example of this, a sinusoidal input controller, is analyzed to show the dynamic effects of the controlled system and to demonstrate the effect of noise interference on the performance of the modified optimalizing controller.https://thesis.library.caltech.edu/id/eprint/4939Secondary Flow in Compressor Cascades
https://resolver.caltech.edu/CaltechETD:etd-04022009-083759
Authors: Lindley, Charles Alexander
Year: 1956
DOI: 10.7907/2RYC-QB23
An experimental study was made of the secondary flow in a compressor cascade. Detailed surveys of the entire flow channel at various operating conditions are presented. The chief difference of the experimental results from those predicted by linearized theory was the presence of a turbulent separation region at the corner of the wall and the low pressure surface of the blade. While the actual losses involved were small, the effects on the succeeding stages of a turbomachine might be more severe.https://thesis.library.caltech.edu/id/eprint/1252The Interaction of Flow Discontinuities with Small Disturbances in a Compressible Fluid
https://resolver.caltech.edu/CaltechETD:etd-04142004-150412
Authors: Kerrebrock, Jack Leo
Year: 1956
DOI: 10.7907/9EN8-WZ61
The interaction of a random small disturbance field in a compressible fluid with shock waves and flame fronts is analyzed. The disturbance field, which may consist of fluctuations of pressure, entropy and vorticity, is found to be modified in passing through the shock or flame.
In the case of the shock wave, it is found that all of the the three types of disturbances are generated in comparable strength in the downstream flow by the presence of any of the three in the upstream flow. Moderate fluctuations of either vorticity (turbulence) or entropy will produce intense noise fields in the downstream flow. If the shock is normal, the frequency of this noise field is much lower for very weak shocks than for strong shocks, given the same upstream velocity and disturbance wave length. If the weak shock is oblique to the flow, the frequency of the noise is increased.
For the flame front, also, it is found that all three types of disturbances are generated in the downstream flow by the presence of one of them in the upstream flow. In this case, however, the normal propagation Mach number of the flame enters as a small parameter. It is found that the intensity of the downstream turbulence generated by sound waves inpinging on the upstream face of the flame is proportional to the reciprocal of this Mach number times the intensity of the upstream pressure fluctuation. Hence, rather strong turbulence may be generated downstream of a flame by comparatively weak sound upstream. The pressure amplitudes of the sound fields generated by entropy and vorticity fluctuations in the upstream flow are proportional, respectively, to the Mach number squared and cubed. For ordinary hydrocarbon flames, ten percent turbulent velocity fluctuations, or one percent entropy (temperature) fluctuations will cause audible sound to be emitted. The fequency is in the range of 20 to perhaps 100 cycles per second for an input disturbance wave length of one inch.
Although the analysis is carried out for an isolated infinite discontinuity, it is felt that the results are applicable, at least qualitatively, to the complicated configuration of shock waves found in under or over-expanded nozzles, and to the flame configurations found in actual combustion processeshttps://thesis.library.caltech.edu/id/eprint/1381Combustion in Laminar Mixing Regions and Boundary Layers
https://resolver.caltech.edu/CaltechETD:etd-03222004-162749
Authors: Dooley, Donald Allen
Year: 1956
DOI: 10.7907/MGTH-TS83
The governing relations for gaseous flow systems with chemical reaction are briefly discussed. A mixture of mechanically similar Maxwellian molecules is assumed and the general relations are then reduced to the simplified forms appropriate for reacting, laminar boundary layer type flow systems. One-step unopposed, "global" reactions following first-order, second-order, and third-order kinetics are considered.
The simplified governing relations are transformed to an equivalent constant density plane by application of the Howarth transformation. A similarity function relating the specie concentrations to the local temperature is found for the case of equal Prandtl and Schmidt numbers. The similarity function is shown to be equal to the dimensionless streamwise velocity when the Prandtl and Schmidt numbers are both equal to unity. The remaining governing relations are then transformed to the Blasius plane in which the velocity field has known solutions. The energy equation is solved by an iteration process; a general analytic solution for the N'th approximation is obtained.
The analytic techniques developed are applied to the problems of combustion within laminar mixing regions and boundary layers. Temperature and concentration profiles are calculated and the dependence of the characteristic stay time upon the parameters of the system is determined. The application of the similarity techniques to the problem of chemical reaction within a hypersonic boundary layer is briefly discussed in an Appendix.https://thesis.library.caltech.edu/id/eprint/1052An Analytical Investigation of the Ducted Propeller for Hydrodynamic Propulsion
https://resolver.caltech.edu/CaltechETD:etd-08172004-094413
Authors: Savage, Glenn Allen
Year: 1957
DOI: 10.7907/EBDR-SN58
An analytical investigation was carried out to determine the design conditions, for a ducted propeller unit operating in water, providing optimum suppression of cavitation when the forward speed, depth and body drag are given. The selection charts were constructed in detail for propellers using the NACA 65 series blades. The results indicate the pumps of generally higher flow rates are more desirable than those that have been employed in the few units actually constructed.https://thesis.library.caltech.edu/id/eprint/3149An Experimental Investigation of Flame Stabilization in a Heated Turbulent Boundary Layer
https://resolver.caltech.edu/CaltechETD:etd-07162004-110746
Authors: Turcotte, Donald Lawson
Year: 1958
DOI: 10.7907/XT75-T174
For a number of years the significant parameters governing flame stabilization in moving streams have been known. In high speed applications the chemical time delay plays a fundamental role. For the low speed problems the normal flame speed and quenching distance govern stabilization. Unfortunately the transition region between the two groups of problems has not been investigated. Also the actual relation between these parameters and the properties of the combustible mixture has not been established.
To investigate these fundamental questions an experiment was set up to study flame stabilization in heated turbulent boundary layers. For wall temperatures above about 1700[degrees]F. the chemical time delay, represented by the length of the heated flame holder wall required for stabilization, was found to be a systematic and reproducible variable. A rational explanation was made for the transition from the low speed stabilization mechanism known to be applicable in unheated turbulent boundary layers and heated laminar boundary layers to the ignition mechanism applicable in heated turbulent boundary layers.
An attempt was made to relate the observed stabilization measurements to a theoretical solution based on ignition in a laminar sub-layer. The present methods of solution for such problems were found to be inadequate. A similarity solution yielded an interesting result which agreed fairly well with experiments.https://thesis.library.caltech.edu/id/eprint/2897Experiments Concerning the Occurrence and Mechanism of High-Frequency Combustion Instability
https://resolver.caltech.edu/CaltechETD:etd-10072004-092728
Authors: Barker, Calvin LaRue
Year: 1958
DOI: 10.7907/F39S-MP16
The phenomenon of screeching combustion was examined experimentally with particular reference to the significance of the time lag proposed by Rogers and Marble.
This investigation was conducted in a 1- x 4-inch rectangular cross-section water-cooled combustor in which was burned a premixed air - fuel mixture. This combustor contained a 70 % blockage solid V-wedge flameholder.
Vortices were generated at the flameholder lips during smooth combustion by impinging a shock wave on the flamefront. These vortices were compared with those generated during screeching combustion and found to be similar to them in all major respects. Thus the common assumption that vortices are generated by the action of the oscillating velocity is a sound one.
The fact that screech excitation occurs in the shear layers immediately downstream of the flameholders was demonstrated by injection of air into this region. Such injection was found to suppress the tendency of the combustor to screech.
By comparison of observations of the screech limit with ignition time delay data obtained from bluff-body flameholding studies it was shown that the mechanism of screech excitation is indeed controlled by a characteristic time. A procedure, based on this result, was developed for determining in advance the behavior of the screech limit in a family of geometrically similar combustors under variations of fuel type and inlet temperature.https://thesis.library.caltech.edu/id/eprint/3960Performance of Axial Compressors with Asymmetric Inlet Flows
https://resolver.caltech.edu/CaltechETD:etd-11012004-143844
Authors: Katz, Robert
Year: 1958
DOI: 10.7907/5214-1S06
An experimental and analytical investigation was undertaken to determine the influence of asymmetric inlet flows on the performance of axial turbomachinery.
Overall performance measurements and circumferential surveys of total pressures, velocities and flow angles were obtained in an axial compressor with inlet disturbances covering approximately 25% of the inlet annulus area. Three configurations were tested to find the principal effects in a single rotor, a complete stage and a multi-stage machine. A two-dimensional linearized theory was developed which includes the effect of losses and leaving angle deviations in the blade rows. The analysis may also be applied to propagating stall so that this theory allows a unified treatment of the two phenomena.
Introducing the inlet disturbances did not alter the two-dimensional character of the flow in the compressor. Considerable attenuation of the disturbances occurred through a single rotor and the disturbances were almost completely attenuated downstream of a three stage configuration. The mutual interference of the blade rows with small axial spacing was responsible for significant stator losses. The overall performance deteriorated primarily due to losses occurring in the blade rows. In the three configurations tested the inception of propagating stall, as based on the mean flow rate, was essentially unchanged. The theory qualitatively described the flow behavior and a simple application of the theory would give an estimate of the blade forces.https://thesis.library.caltech.edu/id/eprint/4355Throughflow in Axial Turbomachines with Variable Wall Geometry
https://resolver.caltech.edu/CaltechETD:etd-02172006-093110
Authors: Oates, Gordon Cedric
Year: 1959
DOI: 10.7907/ZR3D-NR88
The theory of three-dimensional flow in axial turbomachines was extended to include the effects of variable hub and tip radii such as occur in the entrance stages of conventional axial flow compressors and, to a larger extent, in mixed flow compressors. The problem is simplified by assuming an infinite number of infinitely thin blades in each blade row, so that axially symmetric fluid motion results.
The effect of variable hub and tip radii of the annulus walls is investigated when the tangential velocities are small but arbitrary, and when they are large but of special form. The combined effect of heavily loaded inlet guide vanes and variable hub radius is also investigated for the case in which the inlet guide vanes impart a motion very nearly of the solid-body type. The boundary conditions for the variable hub radius require linearization, thus restricting the magnitude of perturbation to be induced by the wall. Finally, the effect of a loaded blade row placed behind the inlet guide vane is determined.
The local axial and tangential velocities induced by the variable wall radius were found to be of the same general magnitude as the velocities induced by a normal rotor or stator blade row. Although the forms of the solutions are somewhat complex for routine application in turbomachine design, a sufficiently simple approximate result is obtained for one case and it is indicated how the method of approximation may be extended.https://thesis.library.caltech.edu/id/eprint/657The Study of a Lifting Air Breathing Boost for Satellite Launch
https://resolver.caltech.edu/CaltechETD:etd-12282005-094057
Authors: Smith, Homer Leroy
Year: 1959
DOI: 10.7907/Q47F-X275
The effect on performance of variations in power plant, aircraft, and rocket parameters was calculated for a lifting air breathing boost system for launching satellites. A limited variation in aircraft flight plan was considered also. In addition, comparisons were made between the air breathing boost system and a three stage all rocket system. For the air breathing boost computations were made for launch Mach numbers ranging from two to five.
The air breathing boost was assumed to be a turbojet or dual cycle engine powered aircraft. The rocket used in conjunction with the boost had two stages. In computing aircraft performance thrust and engine specific fuel consumption were taken as constants. The lift to drag ratio was also considered constant for each portion of the flight profile which consisted of a take off and acceleration to climb speed, a two step climb, and a pull up to the maximum angle attainable for rocket launch.
In computing rocket performance burning times, effective exhaust velocities, payload weight ratios, and structural weight ratios were assumed to be the same for each stage. Drag was neglected in rocket calculations, and the acceleration of gravity was assumed constant. The calculations were made by computing the kinetic and potential energies for a sounding rocket and equating them to the energy required for orbit.https://thesis.library.caltech.edu/id/eprint/5149An Experimental Investigation of Unstable Combustion in Solid Propellant Rocket Motors
https://resolver.caltech.edu/CaltechETD:etd-02012006-132933
Authors: Brownlee, Wilmot Grant
Year: 1959
DOI: 10.7907/84XQ-AA28
Unstable combustion in solid propellant rocket motors is characterized by high frequency chamber pressure oscillations, often accompanied by changes in the mean burning rate. Experiments with case-bonded, cylindrically perforated motors were reproducible as a result of careful manufacturing control and extended propellant curing time. In these motors the oscillations were in the fundamental pseudo-standing tangential mode and were accompanied by increases in the average burning rate. At sufficiently high pressure levels all firings were stable. Reduction of the operating level led to mild instability. A sufficient further reduction produced a sudden change to maximum instability. Continued reduction in pressure level from this point resulted in a gradual decrease in degree of instability but it could not be experimentally verified that a low pressure stable region existed. The levels at which these events took place were frequency dependent and generally increased as the tangential frequency was reduced. At given operating level, the instability became less severe when the grain length was reduced below a critical value. Increasing the length above the critical value moved the point of maximum instability to somewhat higher levels but did not affect the level at which the motors became stable. The pressure levels for stability and for maximum instability moved to lower values with decreases in the propellant grain temperature in a manner not entirely accounted for by the effect of grain temperature on burning rate. Stable, mildly unstable and severely unstable operation was observed throughout the range -80°F to 180°F. The maximum instability decreased with grain temperature.
Slab motors with opposed-plane grain surfaces exhibited oscillations in the transverse sloshing mode but no accompanying changes in the burning rate. Tangential oscillation of equivalent amplitude strongly affected the burning rate in the cylindric motors; hence it appears that increases in the burning rate are associated with tangential velocities rather than pressure fluctuations.https://thesis.library.caltech.edu/id/eprint/433Applications of Linearized Flow Theory to Axial Compressors with Asymmetric Inlet Flows
https://resolver.caltech.edu/CaltechETD:etd-04042006-141510
Authors: Kreisberg, Harvey N.
Year: 1961
DOI: 10.7907/TV0R-NV88
An analytical investigation was undertaken to determine the applicability of a two-dimensional linearized flow theory to axial compressors with severe asymmetric distortions in the approach flow.
Using the assumption of zero axial gap between blade rows, the simplified theory was applied to three compressor configurations: an expanded single stage, a normal single stage and a three-stage configuration. The three-stage configuration was analyzed for two values of the mean flow coefficient and at two radial positions.
The simplified theory was not adequate for describing experimentally determined total pressure profiles in an expanded single stage subjected to strong asymmetric inlet flows. The theory gave good agreement with experimental data for a normal single stage subjected to small asymmetric inlet disturbances. Application of the simplified theory to a three-stage compressor with severe peripheral distortions in the inlet flow showed that good agreement could be obtained between theoretical and experimental total pressure profiles. However, the loss coefficient required to attain this agreement resulted in theoretical predictions for other flow functions which were in error by as much as 50 per cent at the circumferential position corresponding to maximum flow distortion.
The present theory is capable of providing fair qualitative agreement between theory and experiment for axial compressors with severe asymmetric inlet flow distortions. However, this simplified theory does not simulate the flow processes in such compressors accurately enough to provide good quantitative agreement.https://thesis.library.caltech.edu/id/eprint/1267I. Relaxation Time of One-Dimensional, Laminar Deflagration for First Order Reactions. II. Reflection and Transmission of Electromagnetic Waves at Electron Density Gradients
https://resolver.caltech.edu/CaltechTHESIS:07262011-115318209
Authors: Albini, Frank Addison
Year: 1962
DOI: 10.7907/TYH3-ZQ11
<p>Part I</p>
<p>The one-dimensional, time-dependent equations describing laminar deflagration are solved by an integral method, under the assumption of a physical model for the flame structure and behavior, with restrictions on the type of deviation from steady-state behavior. By virtue of application of a hot-boundary approximation of the von Kármán type, certain sensitive integrals are expressed in a form independent of the temperature profile assumed. Two cases are considered: the "thermal theory" neglecting diffusion, and the case of unity Lewis number (temperature/concentration similarity). Only first order reactions are considered. Arguments supporting the generality of the results are included, along with a discussion of accuracy, and some comparison with experimental work. Graphical display of the results anticipates the utility of the theory for correlating and cross-checking experimental data.</p>
<p>It is concluded that the relaxation time is closely related to the time required for the gas undergoing rapid chemical reaction to pass through the flame.</p>
<p>Part II</p>
<p>The interaction of an electromagnetic wave with a mildly ionized gas is described by an ensemble average treatment of electron motion, and under this description, electromagnetic wave propagation parameters derived. Motivated by the fact that mildly ionized gases in general exhibit inhomogeneous boundary regions, exemplary transition zones are described in terms of varying electron density but constant collision frequency, in order to simplify the solution of wave problems. The half-space reflection problem with a linear transition zone is solved exactly and under two approximations. It is discovered that the reflection and transmission coefficients are strong functions of zone thickness for thin zones. A piecewise-linear transition zone solution exemplifies the procedure for constructing an approximate solution to an arbitrary profile and illustrates the relative insensitivity of reflection and transmission coefficients to detailed zone structure. The "slab" reflection problem with symmetrical, linear transition zones is solved exactly, and it is discovered that the basic periodicity of reflection and transmission coefficients with slab thickness is unchanged, although shifted to higher values of slab thickness/wavelength. The text is supported by fairly extensive graphical presentation of results.</p>https://thesis.library.caltech.edu/id/eprint/6547Heat transfer in reacting gas mixtures with large pressure gradients
https://resolver.caltech.edu/CaltechTHESIS:08032011-150229292
Authors: Marxman, Gerald Albert
Year: 1962
DOI: 10.7907/61YR-1468
<p>Energy transport by conduction and diffusion is considered in chemically-reacting, gaseous mixtures which have a pressure gradient parallel to the temperature gradient. As a consequence of pressure diffusion and other mechanisms, the pressure gradient can influence energy transport, and this effect is given particular emphasis. The use of an idealized flow model and a perturbation technique makes it possible, with a relatively simple analysis, to deduce many of the features of energy transport in multicomponent, gaseous media.</p>
<p>The dissociation reaction of a diatomic gas, with the ratio (reaction rate/diffusion rate) either large or small, is studied. When the flow is chemically frozen, the extension of the analysis to include any number of components would be straightforward, in principle. However, when the gas is in local chemical equilibrium, the binary case is unique in that the diffusion velocities are then proportional to the local temperature gradient, but independent of the local pressure gradient. Consequently, there exists an effective thermal conductivity. The order of the governing set of equations is therefore the same as for a simple, single-component gas, and the effect of the wall surfaces on reaction rates is confined to reaction boundary layers. Two other examples illustrate that the order of the equations is higher when the equilibrium flow comprises more than two components, although there are still reaction boundary layers. The additional boundary conditions associated with the higher order are determined, through integral conditions, by the proportions of the chemical elements present.</p>
<p>The results show that in many high-temperature gasdynamics problems of current interest the presence of a pressure gradient may have an important influence on energy transport.</p>
https://thesis.library.caltech.edu/id/eprint/6573A Theoretical Investigation of Particle Trajectories Through a Prandtl-Meyer Expansion Fan
https://resolver.caltech.edu/CaltechETD:etd-12212005-145547
Authors: Johnson, Grant Reed
Year: 1962
DOI: 10.7907/FTNK-N998
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The equations of motion are developed and solved numerically for the trajectory of a spherical particle passing through a Prandtl-Meyer expansion fan. The effect of a change in [...] and n is shown, where [...] is the ratio of specific heats of the gas, and n/2 is the exponent in [...], the assumed viscosity temperature relationship.
It is demonstrated that for particles the order of a micron in diameter, slip flow will exist, and a proposed correction to the drag to account for this discontinuous nature of the flow is investigated.
The results are plotted showing particle trajectory profiles and the components of the relative velocity or slippage velocity of the particle for flow deflection angles up to 70 degrees.https://thesis.library.caltech.edu/id/eprint/5103On the structure of laminar diffusion flames
https://resolver.caltech.edu/CaltechETD:etd-12072005-134536
Authors: Linan, Amable
Year: 1963
DOI: 10.7907/JHTK-CA51
The structure of laminar diffusion flames is analyzed in the limiting case of large, although finite, reaction rates.
It is shown that the the chemical reaction takes place only in a very thin region or "chemical boundary layer" where convection effects may be neglected. Then the temperature and mass fraction distributions within the reaction zone are obtained analytically.
The flame position, rates of fuel consumption, and temperature and concentration distributions outside the reaction zone may be obtained by using the assumption of infinite reaction rates.
For large Reynolds numbers mixing and combustion take place in boundary layers and free mixing layers. And again analytical solutions are obtained for the temperature and mass fraction distributions outside of the reaction zone.https://thesis.library.caltech.edu/id/eprint/4833Problems in particle-fluid mechanics
https://resolver.caltech.edu/CaltechETD:etd-10172002-122957
Authors: Liu, Joseph Tsu Chieh
Year: 1964
DOI: 10.7907/11Y4-2H39
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The continuum equations describing the motion of a fluid containing small solid particles are discussed and stated. The examples considered fall into two categories: (1) when the fluid is incompressible and viscous, with simultaneous occurrence of particle-fluid momentum relaxation and fluid viscous diffusion; and (2) when the fluid can be considered as "inviscid" but compressible, with simultaneous occurrence of coupled particle-fluid momentum and thermal relaxations and fluid compressibility.
Under (1), the low Mach-number Rayleigh problem is studied. Many of the physical features of the non-linear steady (constant pressure) laminar boundary-layer problem are recovered from appropriate expansions from this exact solution. One obtains answers to questions about the modifications on the boundary layer growth and skin friction; particularly their transition from the "frozen" value near the leading edge, where the viscous layer is "thin" and the fluid viscous diffusion behaves as if in the absence of particles with the ordinary fluid kinematic viscosity,[.....], to the ultimate "equilibrium" value far downstream where the mixture then behaves as a single heavier fluid and viscous diffusion takes place with the "equilibrium" kinematic viscosity augmented by the particle density [.....].The uncoupled thermal Rayleigh problem (small relative temperature differences) is directly inferred, and this answers questions about the modifications on the surface heat-transfer rates and particularly about the possibility of similarity with the velocity boundary layer. Similarity of the two boundary layers is possible when, in addition to lateral diffusion effects being similar as indicated by Prandtl number unity, the streamwise relaxation processes must also be similar. The infinite flat plate oscillating in its own plane is studied, and appropriate expansions from the exact solutions point out how approximate treatment of periodic boundary layers in the absence of a mean flow may be made.
Under (2), the first-order small perturbation theory is discussed, leading from the equation for acoustic propagation to that for linearized supersonic flow. The two-dimensional steady case, or the Ackeret problem, is considered in detail. The Mach wave structure induced by a thin obstacle is deduced and shows a rapid damping of the disturbance along the "frozen" Mach wave (based on the sound speed of a gas in the absence of particles), both damping and diffusiveness along an intermediary Mach wave, and diffusiveness along the "equilibrium" Mach wave (based on the sound speed of an equilibrium mixture of gas and particles) and along which the bulk of the disturbance is carried to regions far from the obstacle. An exact form of the pressure coefficient is obtained for any surface shape (consistent with the linear theory), and involves a convolution integral of two Bessel functions with imaginary argument which is analytically evaluated. When the particle-fluid density ratio is small, the "frozen" and "equilibrium" Mach waves are very closely clustered together. A "boundary layer technique", based on the fact that changes across the Mach waves are rapid compared to changes along Mach waves, is then applied to obtain a simplified version of the linearized equation that describes Mach waves inclined toward the downstream direction only. While the Mach wave structure is consistent with the exact treatment, the pressure coefficient takes on the much simpler form of decreasing exponentials. The transition is, again, from the "frozen" value at the leading edge towards the "equilibrium" value in the downstream direction insofar as the surface shape permits.
https://thesis.library.caltech.edu/id/eprint/4122Boundary current effects in magnetohydrodynamics with anisotropic conductivity
https://resolver.caltech.edu/CaltechETD:etd-01262004-143607
Authors: Smisek, Richard Franklin
Year: 1965
DOI: 10.7907/ANC6-1M76
A theoretical investigation is conducted to determine the effects of currents flowing through a boundary into the magnetohydrodynamic flow of an inviscid, incompressible fluid with anisotropic conductivity. The particular arrangement of an externally applied magnetic field parallel to the velocity field is investigated for two flow geometries; (i) semi-infinite flow over a conducting flat wall, and (ii) channel flow between a conducting lower wall and an insulating upper wall. In both cases the applied boundary currents are assumed to be sinusoidal in shape and flow into the fluid normal to the boundary.
A small perturbation analysis is used to linearize the macroscopic steady flow equations of a fully ionized gas. A Cartesian coordinate system is adopted in which the x-axis is in the flow direction and the y-axis is normal to the conducting wall. The problem is considered two dimensional from the standpoint that the perturbed quantities are independent of the z-coordinate although the z-components are, in general, non-zero. The general solution to the linearized equations is obtained for case (i). Because of the complexity of this solution, it is studied in detail only in the limits of small and large magnetic Reynold's number. Solutions for case (ii) are obtained in the limits of small and large magnetic Reynold's number by applying the limiting procedure to the linearized equations before solving them.
In the limit of small magnetic Reynold's number for both cases (i) and (ii), the magnetic and velocity field vectors are composed of an irrotational part and a rotational part. The irrotational portion always remains in the x-y plane. However, the rotational portion and, hence, the currents lie in a plane which is rotated about the x-axis; the angle between this plane and the x-y plane being strongly dependent upon the degree of anisotropy in the fluid's electrical conductivity. The currents in the fluid form symmetric loops closing at the conducting boundary. Anisotropic effects on the magnitude of the magnetic and velocity field components and the currents are generally moderate except near the conducting wall. At this wall the x and z current components can become quite large for strong anisotropic conductivity. Both the irrotational and rotational portions of the velocity field vector behave in a manner analogous to ordinary incompressible flow with the applied sinusoidal boundary current in the flat wall replaced by a solid sinusoidal wall.
In the limit of large magnetic Reynold's number for both cases (i) and (ii), anisotropic effects are absent to the order of the inverse square root of the magnetic Reynold's number. In addition, the currents and field perturbations are found to be confined to a thin magnetic boundary layer near the conducting wall. The currents lie entirely in the x-y plane and again form loops closing at the conducting boundary, but are steeply inclined toward the x-axis. The x-component of the current flowing in the fluid is found to be. larger than the applied boundary current by a factor of the square root of the magnetic Reynold's number.https://thesis.library.caltech.edu/id/eprint/354Atom-atom ionization mechanisms and cross sections in noble gases and noble gas mixtures
https://resolver.caltech.edu/CaltechETD:etd-04142003-122732
Authors: Kelly, Arnold James
Year: 1965
DOI: 10.7907/6CHH-Z732
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
An experimental investigation of the initial phase of shock produced ionization in argon, krypton, xenon, and argon-xenon mixtures has been conducted in order to elucidate the atom-atom ionization reaction and to determine the atom-atom ionization cross sections for the gases noted. A high-purity shock tube was employed to heat these gases to temperatures in the range 5000[degrees]K to 9000[degrees]K at neutral particle densities of 4.41x10[superscript 17] cm[superscript -3], 6.96x10[superscript 17] cm[superscript -3], and 13.76x10 [superscript 17] cm[superscript -3], and impurity levels of around 10[superscript -6]. A K-band (24 gcps) microwave system situated so that the microwave beam propagation direction was normal to the shock tube monitored the ionization relaxation process occurring immediately after the passage of the shock front. Electron density was calculated from the microwave data using a plane wave - plane plasma slab interaction theory corrected for near-field effects associated with the coupling of the microwave energy to the plasma. These data, adjusted to compensate for the effects of shock attenuation, verified that the dominant electron generation process involves a two-step, atom-atom ionization reaction, the first step (excitation to the first excited states) being rate determining. The quadratic dependence on neutral density associated with this reaction was experimentally demonstrated (with an uncertainty of [...] 15 per cent). The cross section, characterized as having a constant slope from threshold (first excited-energy level), represented as the cross-sectional slope constant C, was found to be equal to 1.2x10[superscript -19] [...] 15 per cent cm[superscript 2]/ev, 1.4x10 [superscript -19] [...] 15 per cent cm[superscript 2]/ev, 1.8x10 [superscript -20] [...] 15 per cent cm[superscript 2]/ev for argon, krypton, and xenon, respectively. The C factor for argon ionizing xenon was determined to be equal with an uncertainty of [...] 20 per cent to the xenon-xenon C factor, i.e., 1.8x10[superscript -20] cm[superscript 2]/ev. This would imply that, for atom-atom processes in the noble gases at about 1 atmosphere pressure and temperature of about 1 ev, the ionization cross section is independent of the electronic structure of the projectile atom. The electron-atom elastic momentum-exchange cross sections derived from the microwave data correlated quite well with Maxwell-averaged beam data, the agreement for the case of argon being [...] 20 per cent; krypton, [...] 30 per cent; and xenon, within a factor of 2.https://thesis.library.caltech.edu/id/eprint/1378Anisotropies and interactions in shear flow of macromolecular suspensions
https://resolver.caltech.edu/CaltechETD:etd-01102003-103458
Authors: Argyropoulos, George S.
Year: 1965
DOI: 10.7907/8KNM-5225
The problem of determining the orientation distribution function for rigid particles of arbitrary shape is formulated in a general stochastic approach to consider the influence of any acting orientation mechanism, stochastic or deterministic. The effect of the various orientation mechanisms on the partial differential equation of the problem, an equation of the Fokker-Planck type, is analyzed. The question of linearity or non-linearity of the superposition of the effects due to different orientation mechanisms is examined.
The orientation of rigid ellipsoidal particles in uniform shear flow is studied in detail, for different cases of acting orientation mechanisms. When only the viscous stresses act on the particles, the problem for the orientation distribution function becomes a deterministic first-order initial value problem, and its solution displays periodic behavior. In the case of macromolecules, when the Brownian influence is predominant, we examine the effect of a third orientation mechanism acting on the macromolecules in addition to the viscous stresses and the Brownian impulses. In Couette flow between concentric cylinders, the third orientation mechanism is considered to be a deterministic force field in the radial direction x, varying linearly with x. The steady state orientation distribution function is then determined to the third order, and the theory of streaming birefringence of a dilute suspension of rigid ellipsoidal macromolecules in Couette flow is generalized to include the effect of the additional influence. The direction of the isocline and the amount of birefringence are calculated to the second order.
When spherical macromolecules are added to the suspension in increasing concentration, the effect of hydrodynamic interactions between the two species on the orientation of the ellipsoidal particles is examined in Couette flow. It is shown that an effect of the presence of the spheres is to decrease the drift velocity of the ellipsoids--and thus decrease the amount of birefringence--and that the effect can be described as a decrease in the effective velocity gradient. The theoretical result for this decrease is in good agreement with experimental results for sphere concentrations comparable to the concentration of ellipsoids. On the other hand, as the concentration of spheres increases, the effect of their presence on the rotational diffusion constant of the asymmetrical particles can be large enough to reverse the trend and lead to a positive variation of the amount of birefringence with sphere concentration.
https://thesis.library.caltech.edu/id/eprint/97Equilibration of a liquid droplet-vapor-gas mixture downstream of a shock wave
https://resolver.caltech.edu/CaltechTHESIS:10212015-154326489
Authors: Rosen, Robert
Year: 1966
DOI: 10.7907/ZGM7-0E94
<p>The equations of motion for the flow of a mixture of liquid droplets, their vapor, and an inert gas through a normal shock wave are derived. A set of equations is obtained which is solved numerically for the equilibrium conditions far downstream of the shock. The equations describing the process of reaching equilibrium are also obtained. This is a set of first-order nonlinear differential equations and must also be solved numerically. The detailed equilibration process is obtained for several cases and the results are discussed.</p>https://thesis.library.caltech.edu/id/eprint/9235Rotating Flows in Acoustically Unstable Rocket Motors
https://resolver.caltech.edu/CaltechETD:etd-02272004-154250
Authors: Flandro, Gary Arnold
Year: 1967
DOI: 10.7907/BYWJ-5Q96
<p>One of the most interesting manifestations of acoustic combustion instability in solid propellant rocket motors is the formation of strong vortices in the combustion chamber. A single vortex filament stretching along the motor axis from the head-end has been observed in several experiments in association with gas oscillations in the frequently occurring traveling tangential mode of instability. These flows are sometimes accompanied by a quite noticeable axial torque on the motor itself, and this effect has given rise to flight performance difficulties in a number of instances. Previous theoretical studies of the vortex generation effect have been inadequate in several respects. The present work is an attempt to place the theory on a more firm base and to clarify the connection between traveling wave motions and the generation of vortices and torques.</p>
<p>It is readily shown that traveling waves transport momentum, and in the case of traveling tangential waves in a cylindrical combustion chamber this represents a steady axial component of angular momentum in the gas. This observation gives rise to a simple conceptual model of the vortex generation effect. Thus the presence of a steady mass flux about the axis implies the existence of a layer of vorticity at the chamber walls which may be represented by a vortex sheet composed of axially oriented bound vortex filaments. In the three-dimensional case these vortices are shed either at the end of propellant grain or at the periphery of the nozzle; the other ends of the filaments traverse the fore-end closure to the center and are combined and shed in an intense vortex filament along the symmetry axis of the motor.</p>
<p>Due to the production of gas at the chamber wall, tangential forces at the wall are produced by the interaction of this mean flow with the bound vortices. Angular momentum arguments must be used in this conceptual mechanism to estimate the strength of the axial vortex filament, and it is readily shown that the sense of the vortex must be opposite to the direction of travel of the waves. The direction and magnitude of the torque on the motor depend on the mean flow Mach number at the wall and must be established by calculation of the wall shear stresses.</p>
<p>The detailed calculations are guided by the mechanism just outlined. All physical features of the problem which appear to be significant are simulated mathematically. In particular, the effects of the three dimensional mean flow pattern in the chamber and the pressure-sensitive combustion region at the burning surface are represented. Also considered are the effects of freedom of motion of the rocket motor in the plane normal to the symmetry axis. Both inviscid and viscous theories are developed using multi-parameter asymptotic perturbation expansion techniques. It is proved that traveling tangential waves are subject to amplification under conditions existing in typical solid propellant rockets, and that a steady transport of gas about the chamber axis accompanies this motion as a second-order perturbation. The equations of motion admit of only a vortex-like steady second-order azimuthal solution. This must be superimposed on the acoustic wave motions in such a way that angular momentum is conserved (due consideration being given to body forces on the gas and tangential forces at the wall). Thus the net pattern of steady circumfer vential mass flux at a given motor cross-section consists of a drift of fluid in the direction of the wave adjacent to the wall with a rapid transition to an oppositely spinning vortex flow as the longitudinal axis is approached. Introduction of the viscous corrections gives rise to a boundary. condition which sets the vortex strength, and a formal connection with the classical acoustic streaming effect is established. Since momentum is dissipated in the shear region at the wall, a torque appears on the chamber itself. This roll moment is opposite in sense to the wave travel during amplification of the acoustic waves, and numerical calculations give torque magnitudes which are in agreement with experimental data from several sources.</p>
https://thesis.library.caltech.edu/id/eprint/779Low-density gas dynamic facility
https://resolver.caltech.edu/CaltechETD:etd-11152005-081030
Authors: McGill, James A.
Year: 1967
DOI: 10.7907/P04W-KX13
The question of optimizing nozzle contours for micro-thrust rockets led to the design, construction, and testing of a low-density gas dynamic facility. The primary objective was to investigate the mass flow rates of a gas through various profiles in the slip and transition flow regimes at high pressure ratios.
An initial test was conducted with an orifice as the test profile. The results showed that the facility can be used to investigate mass flow rates from the threshold of the free-molecule, through the transition and slip, to the continuum regimes. These results compare favorably with those of two previous investigators, and asymptotically approach the theoretical continuum and free-molecule limits. The ratio of mass flow rate to theoretical free-molecule mass flow rate is shown to transition smoothly from one theoretical limit to the other. A local maximum may occur in this ratio in the slip regime, and the attainment of the theoretical free-molecule limit appears to occur more slowly than expected.https://thesis.library.caltech.edu/id/eprint/4567I. The Attenuation and Dispersion of Sound in a Condensing Medium. II. The Flow of a Gas-Particle Mixture Downstream of a Normal Shock in a Nozzle
https://resolver.caltech.edu/CaltechTHESIS:11302015-130932926
Authors: Wooten, David Clark
Year: 1967
DOI: 10.7907/T68P-M138
<p>I. The attenuation of sound due to particles suspended in a gas was first calculated by Sewell and later by Epstein in their classical works on the propagation of sound in a two-phase medium. In their work, and in more recent works which include calculations of sound dispersion, the calculations were made for systems in which there was no mass transfer between the two phases. In the present work, mass transfer between phases is included in the calculations. </p>
<p>The attenuation and dispersion of sound in a two-phase condensing medium are calculated as functions of frequency. The medium in which the sound propagates consists of a gaseous phase, a mixture of inert gas and condensable vapor, which contains condensable liquid droplets. The droplets, which interact with the gaseous phase through the interchange of momentum, energy, and mass (through evaporation and condensation), are treated from the continuum viewpoint. Limiting cases, for flow either frozen or in equilibrium with respect to the various exchange processes, help demonstrate the effects of mass transfer between phases. Included in the calculation is the effect of thermal relaxation within droplets. Pressure relaxation between the two phases is examined, but is not included as a contributing factor because it is of interest only at much higher frequencies than the other relaxation processes. The results for a system typical of sodium droplets in sodium vapor are compared to calculations in which there is no mass exchange between phases. It is found that the maximum attenuation is about 25 per cent greater and occurs at about one-half the frequency for the case which includes mass transfer, and that the dispersion at low frequencies is about 35 per cent greater. Results for different values of latent heat are compared.</p>
<p>II. In the flow of a gas-particle mixture through a nozzle, a normal shock may exist in the diverging section of the nozzle. In Marble’s calculation for a shock in a constant area duct, the shock was described as a usual gas-dynamic shock followed by a relaxation zone in which the gas and particles return to equilibrium. The thickness of this zone, which is the total shock thickness in the gas-particle mixture, is of the order of the relaxation distance for a particle in the gas. In a nozzle, the area may change significantly over this relaxation zone so that the solution for a constant area duct is no longer adequate to describe the flow. In the present work, an asymptotic solution, which accounts for the area change, is obtained for the flow of a gas-particle mixture downstream of the shock in a nozzle, under the assumption of small slip between the particles and gas. This amounts to the assumption that the shock thickness is small compared with the length of the nozzle. The shock solution, valid in the region near the shock, is matched to the well known small-slip solution, which is valid in the flow downstream of the shock, to obtain a composite solution valid for the entire flow region. The solution is applied to a conical nozzle. A discussion of methods of finding the location of a shock in a nozzle is included. </p>https://thesis.library.caltech.edu/id/eprint/9296Particle fluid mechanics in shear flows, acoustic waves, and shock waves
https://resolver.caltech.edu/CaltechTHESIS:11302015-140521884
Authors: Zung, Laurence Bei-Yu
Year: 1967
DOI: 10.7907/4T4F-9359
<p>Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).</p>
<p><u>Part I</u></p>
<p>A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W<sub>p</sub>. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ<sub>v</sub>, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc. </p>
<p><u>Part II</u></p>
<p>The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ<sub>v</sub> and λ<sub>T</sub> approach zero and frozen flows in which λ<sub>v</sub> and λ<sub>T</sub> become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ<sub>v</sub> and λ<sub>T</sub>, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C<sub>D</sub> is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration. </p>
<p><u>Part III</u></p>
<p>Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ<sub>D</sub>. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ<sub>D</sub> within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.</p>
<p><u>Part IV</u></p>
<p>The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ<sub>D</sub>.</p>
<p>For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.</p>
<p>The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction. </p>
<p><u>Part V</u></p>
<p>For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible. </p>
https://thesis.library.caltech.edu/id/eprint/9297I. The effect of droplet solidification upon two-phase flow in a rocket nozzle. II. A kinetic theory investigation of some condensation-evaporation phenomena by a moment method
https://resolver.caltech.edu/CaltechTHESIS:12212015-140557422
Authors: Shankar, Pattamadai Narasimhan
Year: 1968
DOI: 10.7907/X1YG-2K03
<p>Part I:</p>
<p>The perturbation technique developed by Rannie and Marble is used to study the effect of droplet solidification upon two-phase flow in a rocket nozzle. It is shown that under certain conditions an equilibrium flow exists, where the gas and particle phases have the same velocity and temperature at each section of the nozzle. The flow is divided into three regions: the first region, where the particles are all in the form of liquid droplets; a second region, over which the droplets solidify at constant freezing temperature; and a third region, where the particles are all solid. By a perturbation about the equilibrium flow, a solution is obtained for small particle slip velocities using the Stokes drag law and the corresponding approximation for heat transfer between the particle and gas phases. Singular perturbation procedure is required to handle the problem at points where solidification first starts and where it is complete. The effects of solidification are noticeable.</p>
<p>Part II:</p>
<p>When a liquid surface, in contact with only its pure vapor, is not in the thermodynamic equilibrium with it, a net condensation or evaporation of fluid occurs. This phenomenon is studied from a kinetic theory viewpoint by means of moment method developed by Lees. The evaporation-condensation rate is calculated for a spherical droplet and for a liquid sheet, when the temperatures and pressures are not too far removed from their equilibrium values. The solutions are valid for the whole range of Knudsen numbers from the free molecule to the continuum limit. In the continuum limit, the mass flux rate is proportional to the pressure difference alone. </p>
https://thesis.library.caltech.edu/id/eprint/9341An experimental study of particle-wall collision relating to flow of solid particles in fluid
https://resolver.caltech.edu/CaltechETD:etd-09102004-144402
Authors: McLaughlin, Michael Herbert
Year: 1968
DOI: 10.7907/4FV5-JA03
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
A preliminary investigation was made into the momentum and energy losses resulting from particle collisions in a fluid with application to particle - fluid two-phase flows. In particular, the length scale over which these intereactions are important was investigated. The geometry chosen for the experiments was that of a sphere approaching an infinite wall, a geometry which tended to maximize the energy and momentum losses of the sphere.
The experiments were performed by dropping a steel sphere through a glycerin-water solution onto a steel surface. Flows for which the particle Reynolds number, [...] (based on terminal velocity and particle diameter), ranged from 0.05 to 7870 were investigated by taking high-speed motion pictures. Position-time curves were generated, and it was shown that above a moderate Reynolds number the important momentum and energy interactions occurred within a fraction of a ball radius of the wall. As the Reynolds number was increased from the Stokes flow regime, the decrease of this interaction length was shown. At higher [...] the viscous losses became an increasingly smaller percent of the particle kinetic energy.
A preliminary investigation was made of an alternate test procedure utilizing a thin liquid film rather than the continuum tank. The results showed that a critical film thickness existed, above which the energy loss did not significantly increase with increasing film thickness. The prospects of correlating the continuum loss effects with the thin-film loss effects appeared good and warrant further investigation.
Photographic materials on pages 5 and 14 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.
https://thesis.library.caltech.edu/id/eprint/3430Particle Kinetics of Gas-Solid Particle Mixtures
https://resolver.caltech.edu/CaltechTHESIS:03272017-145900980
Authors: Haas, Roger Allison
Year: 1969
DOI: 10.7907/BT3R-BW68
<p>In this thesis the interaction of a normal gas dynamic shock
wave with a gas containing a distribution of small solid spherical
particles of two distinct radii, σ<sub>1</sub> and σ<sub>2</sub>, is studied (1) to demonstrate
that the methods of kinetic theory can be extended to treat solid
particle collision phenomena in multidimensional gas-particle flows;
(2) to elucidate some of the essential physical characteristics associated
with particle-particle collision processes; and (3) to give some
indication regarding the importance of particle collisions in particle-laden
gas flows. It is assumed that upstream of the shock wave
particles σ<sub>1</sub> are uniformly distributed while particles σ<sub>2</sub> are non-uniformly
distributed parallel to the shock face and in much smaller
numbers than particles σ<sub>1</sub>. Under these conditions the gas-particle
σ<sub>1</sub> flow downstream of the shock wave is very nearly one-dimensional
and independent of the presence of particles σ<sub>2</sub>. The usual shock
relaxation zone is established by the interaction of particles σ and
the gas downstream of the shock wave. The collisional model pro-
posed by Marble<sup>3</sup> is then extended and used with a modified form
of the mean free path method of kinetic theory to calculate the macroscopic
distribution and velocity of particles σ<sub>2</sub> as determined by the
particle σ<sub>1</sub>- particle σ<sub>2</sub> and particle σ<sub>2</sub>-gas interactions. Within the
condition that the random velocity imparted to a particle σ<sub>2</sub> by a
collision is damped by its viscous interaction with the gas before it
suffers another collision, the kinetic theory method established here
may be extended to include more general particle-particle and particle-gas
interaction laws than those used by Marble. However, the
collisional model employed is particularly important because the
criteria for its application are easy to establish and because it
admits a wide class of physically interesting situations.</p>
<p>Within the restrictions of this collision model, it is possible
to analyze the macroscopic motion of particles σ<sub>2</sub> in three important
limiting cases: (σ<sub>2</sub>/σ<sub>1</sub>)<sup>2</sup> >> ⊥,(σ<sub>2</sub>/σ<sub>1</sub>)<sup>2</sup> << ⊥
and (σ<sub>2</sub>/σ<sub>1</sub>)<sup>2</sup> ~ ⊥. It is found that when
(σ<sub>2</sub>/σ<sub>1</sub>)<sup>2</sup> >> ⊥ there
is essentially no redistribution of particles σ<sub>2</sub> normal to the gas flow.
The only effect of particle σ<sub>1</sub> -particle σ<sub>2</sub> encounters is a drag force
acting to slow down particles σ<sub>2</sub>. When (σ<sub>2</sub>/σ<sub>1</sub>)<sup>2</sup> << ⊥ it is found
that particles σ<sub>2</sub>. may have many collisions during their passage
through the shock relaxation zone. As a consequence there may be
a substantial redistribution of particles σ<sub>2</sub> downstream of the shock
wave. The physical features of this process are studied in detail
together with the range of validity of this diffusion model. The case
(σ<sub>2</sub>/σ<sub>1</sub>)<sup>2</sup> ~ ⊥ is analyzed under the condition particles σ<sub>2</sub> have
at most one collision during their passage through the shock relaxation
zone. It is found that when the gas or particle σ<sub>1</sub> density is low,
the single collision effects may be important even when σ<sub>2</sub>/σ<sub>1</sub> differs
significantly from unity and the particles are not very small.</p>
<p>Under most conditions of practical significance, because there
is invariably a distribution of particles sizes present in a dusty gas,
the calculation of the particle distribution in the shock relaxation zone
should account for the effects of particle-particle encounters. It is
suggested that an experimental observation of particle size distribution
in a shock relaxation zone can yield significant information on particle-particle
and particle-gas interaction laws.</p>
https://thesis.library.caltech.edu/id/eprint/10109The effect of a spanwise blowing jet on the separation bubble length behind a rearward facing step
https://resolver.caltech.edu/CaltechTHESIS:08172010-162416535
Authors: Miyata, Gavien N.
Year: 1972
DOI: 10.7907/EFBF-0016
The problem of the effect of a spanwise blowing jet on the
flow past a rearward facing step is considered both theoretically and experimentally. The primary flow is considered to be a finite two dimensional jet blowing past a step and the spanwise jet is assumed to blow perpendicular to this primary flow. The equations predicting
the separation bubble length are de rived by assuming that the two dimensional jet is thin enough so that its radius of curvature can be determined by the pressure difference across the primary jet and the jet momentum. Then by doing a momentum balance at the reattachment point, the angle of reattachment is determined and the bubble geometry is fixed. The effect of the spanwise blowing jet is modeled by a two-dimensional sink with the sink strength given by the mass entrainment per unit length of a round jet in a semi-confined space.
The experimental work, which measured the bubble length
as a function of the two-dimensional jet thickness and the strength of the spanwise blowing jet, is matched with the theoretical predictions giving the spreading parameters of the shear layers on both sides of the primary jet.
https://thesis.library.caltech.edu/id/eprint/5994Transonic Wind Tunnel for Investigation of Turbomachinery Blades
https://resolver.caltech.edu/CaltechTHESIS:01062016-155803211
Authors: Dolait, Jean-Pierre
Year: 1972
DOI: 10.7907/4D2K-SR72
<p>The design of a two-stream wind tunnel was undertaken to allow
the simulation and study of certain features of the flow field around
the blades of high-speed axial-flow turbomachineries. The mixing of
the two parallel streams with designed Mach numbers respectively
equal to 1.4 and 0.7 will simulate the transonic Mach number distribution
generally obtained along the tips of the first stage blades in
large bypass-fan engines.</p>
<p>The GALCIT hypersonic compressor plant will be used as an
air supply for the wind tunnel, and consequently the calculations contained
in the first chapter are derived from the characteristics and
the performance of this plant.</p>
<p>The transonic part of the nozzle is computed by using a method
developed by K. O. Friedrichs. This method consists essentially of
expanding the coordinates and the characteristics of the flow in power
series. The development begins with prescribing, more or less arbitrarily,
a Mach number distribution along the centerline of the nozzle.
This method has been programmed for an IBM 360 computer to define
the wall contour of the nozzle.</p>
<p>A further computation is carried out to correct the contour for
boundary layer buildup. This boundary layer analysis included geometry,
pressure gradient, and Mach number effects. The subsonic nozzle
is calculated {including boundary layer buildup) by using the same
computer programs. Finally, the mixing zone downstream of the splitter
plate was investigated to prescribe the wall contour correction necessary
to ensure a constant-pressure test section.</p>https://thesis.library.caltech.edu/id/eprint/9360Analytical Studies of Some Acoustic Problems of Jet Engines
https://resolver.caltech.edu/CaltechETD:etd-10302003-153104
Authors: Candel, Sebastien M.
Year: 1972
DOI: 10.7907/E5DD-ZC41
<p>This thesis presents analytical studies of internal noise generation and transmission in jet engines and its radiation from the duct ends.</p>
<p>The propagation and generation of acoustic waves in a choked nozzle is considered first. Pressure and entropy fluctuations caused by gas stream non-uniformities like "hot spots," are incident on the nozzle entrance. A novel noise-generation mechanism is uncovered where acoustic waves are produced by a distribution of sources of strength proportional to the entrance entropy fluctuation and local gradient of the mean flow velocity.</p>
<p>The propagation of acoustic waves in a moving medium in the presence of semi-infinite or finite boundaries is then considered. A transformation is introduced which relates the solutions of such problems to the solutions of associated problems in a stationary medium. The method is described by discussing the Sommerfeld problem of diffraction of a plane wave by a half plane immersed in a subsonically moving medium. When the plane has a trailing edge, it is shown that both reflection and shadow regions expand; while the opposite occurs for a leading edge, in which circumstance an additional diffracted wave also appears.</p>
<p>In the supersonic case, all the diffraction problems are related to a single reference problem, solved by Fourier transform methods. A decomposition of the pressure field in a "geometrical optics" field and a diffracted field is given, showing some remarkable similarities with the subsonic case solution.</p>
<p>The radiation of acoustic modes from a duct immersed in a subsonically moving medium is treated by a similar transform method. The presence of the uniform flow has roughly the same effect as an increase in frequency of the incident wave, at constant mode number. The effect of acoustical lining on the radiation pattern is examined, and side radiation is shown to be greatly reduced for the lower order modes.</p>
<p>The transmission and reflection of acoustic waves incident on a blade row is analyzed by the transform method, and the transmission and reflection coefficients for the blade row immersed in a moving medium are expressed in terms of the basic acoustic characteristics of the blade row in a stationary medium.</p>https://thesis.library.caltech.edu/id/eprint/4322Behavior of spherical particles at low Reynolds numbers in a fluctuating translational flow
https://resolver.caltech.edu/CaltechTHESIS:11132015-144035933
Authors: Hill, Murray Keith
Year: 1973
DOI: 10.7907/22ME-5X65
<p>The behavior of spheres in non-steady translational flow
has been studied experimentally for values of Reynolds number
from 0.2 to 3000. The aim of the work was to improve our
qualitative understanding of particle transport in turbulent
gaseous media, a process of extreme importance in power
plants and energy transfer mechanisms.</p>
<p>Particles, subjected to sinusoidal oscillations parallel
to the direction of steady translation, were found to have changes
in average drag coefficient depending upon their translational
Reynolds number, the density ratio, and the dimensionless
frequency and amplitude of the oscillations. When the Reynolds
number based on sphere diameter was less than 200, the
oscillation had negligible effect on the average particle drag.</p>
<p>For Reynolds numbers exceeding 300, the coefficient of
the mean drag was increased significantly in a particular
frequency range. For example, at a Reynolds number of
3000, a 25 per cent increase in drag coefficient can be produced
with an amplitude of oscillation of only 2 per cent of the sphere
diameter, providing the frequency is near the frequency at which
vortices would be shed in a steady flow at the mean speed. Flow
visualization shows that over a wide range of frequencies, the
vortex shedding frequency locks in to the oscillation frequency.
Maximum effect at the natural frequency and lock-in show that a
non-linear interaction between wake vortex shedding and the
oscillation is responsible for the increase in drag.</p>https://thesis.library.caltech.edu/id/eprint/9280Noise produced by the interaction of acoustic waves and entropy waves with high-speed nozzle flows
https://resolver.caltech.edu/CaltechTHESIS:10152012-130328218
Authors: Bohn, Mark Stephen
Year: 1976
DOI: 10.7907/ZP95-5T73
<p>Some aspects of the noise generated internally by a turbojet
engine are considered analytically and experimentally. The emphasis
is placed on the interaction of pressure fluctuations and entropy fluctuations,
produced by the combustion process in the engine, with
gradients in the mean flow through the turbine blades or the exhaust
nozzle.</p>
<p>The one-dimensional interaction of pressure fluctuations and
entropy fluctuations with a subsonic nozzle is solved analytically. The
acoustic waves produced by each of three independent disturbances
are investigated. It is seen that results for a large number of physically
interesting nozzles may be presented in a concise manner.</p>
<p>Some of the second-order effects which result from the area
variations in a nozzle are investigated analytically. The interaction
of an entropy wave with a small area variation is investigated and the
two-dimensional duct modes, which propagate away from the nozzle,
are calculated.</p>
<p>An experiment is described in which one-dimensional acoustic
waves and entropy waves are made to interact with a subsonic nozzle.
The response of the nozzle to these disturbances is measured and
compared with the response as calculated by the analytical model.</p>
<p>The interaction of two-dimensional entropy waves with a subsonic
nozzle and with a supersonic nozzle is investigated experimentally.
The results are explained in terms of an analysis of the acoustic
waves and entropy waves produced by a region of arbitrary heat
addition in a duct with flow.</p>
https://thesis.library.caltech.edu/id/eprint/7236Analytical studies of steady and non-steady motions of a bubbly liquid
https://resolver.caltech.edu/CaltechETD:etd-08172005-082759
Authors: Symington, William Allan
Year: 1978
DOI: 10.7907/0ENX-DE36
A consistent set of continuum-like equations which describe, under certain limitations, the flow of bubbly gas-liquid mixtures is developed. These equations are then applied in the solution of a few problems that bear on technological issues of nuclear reactor safety. The solutions of these problems illustrate the importance of the ratio between the viscous relaxation time of the bubbles and the characteristic time of the flow, in scaling experimental results.
The choked flow of a bubbly mixture through a contraction in a one dimensional duct is treated. It is found that in many cases the ratio of the contraction residence time to the viscous relaxation time is small, indicating the motion of the bubbles will be dictated largely by the dynamic forces on them. The one-dimensional equations are solved approximately for small values of this ratio.
A rudimentary experiment on choked bubbly flow through a contraction was conducted using a contraction with gradual changes in area, making the experimental situation amenable to a one-dimensional analysis. Pressures and mass flow rates of liquid and gas were measured. The results compare favorably with theoretical calculations.
The rise through a liquid of a uniform cloud of bubbles is also analyzed. Self-preserving wave solutions of the non-linear equations are found to exist. They have the form of transitions between a region of high void fraction below and a region of lower void fraction above. These waves are unstable to small disturbances, so when they are created they will steepen, developing into clumps of bubbles above which are regions of low void fraction. The fact that the bubbles in these clumps may coalesce presents a mechanism for a change in flow regime from bubbly to some other, perhaps slug or annular flow. The effect of bubble-bubble interactions in impeding the formation of these clumps is speculated upon.
Finally, the flow of a bubbly mixture over a wavy wall is analyzed. The solution illustrates that the effect of interactions between bubbles and solid boundaries is lacking in our formalism. It is concluded that more work is required in the area of interactions, both of the bubble-bubble and bubble-boundary varieties.
https://thesis.library.caltech.edu/id/eprint/3154Non-steady behavior of a flame spreading from a point in a two-dimensional duct
https://resolver.caltech.edu/CaltechETD:etd-11012006-152708
Authors: Subbaiah, Malladi Venkata
Year: 1980
DOI: 10.7907/se8q-9c70
Non-steady behavior of a flame stabilized in a two-dimensional duct is studied in this thesis. The problem is formulated by an integral technique in which the governing equations are integrated across the duct to obtain integral relations for the mean flow variables. The flow fields on either side of the flame sheet are matched by appropriate matching conditions. Fluid flow through the flame surface causes the integral relations to explicitly involve the fluid velocities at the flame. An independent description of the flame shape and the irrotational flow field upstream of the flame is provided by a source distribution on the duct axis.
The integral relations are analyzed by a perturbation technique, in which the dominant order solution represents the steady flame development. The steady flame configuration is perturbed by an acoustic wave incident on the compact flame region. The time dependent counterpart of the integral relations describes the ensuing non-steady flow fields. The flame perturbation exhibits a travelling wave pattern with considerable amplification along the flame zone. A simple model to describe the growth of the flame perturbation is put forth, by considering the flame surface as an unstable shear layer.
Acoustic reflection and transmission coefficients of the flame region are obtained utilizing the time-dependent flame calculations. The response spectra exhibit active responses at certain well defined frequencies. The non-steady flame model is incorporated in a rudimentary afterburner configuration to investigate the low frequency behaviour of the afterburner. The results suggest a possible mechanism of low frequency instability in a combustion system.
https://thesis.library.caltech.edu/id/eprint/4362Structure and Stability of Buoyant Diffusion Flames
https://resolver.caltech.edu/CaltechETD:etd-09152006-121855
Authors: Fleming, Graham Christopher
Year: 1982
DOI: 10.7907/DVY5-MD93
<p>The structure and stability of the convecting fluid flow generated by a diffusion flame in gaseous reactants has been investigated. The flame extends vertically upwards from a solid horizontal boundary, and separates the fuel from the oxidizer which can be of a different density. Real fuels are modelled by choosing appropriate values for the density difference and stoichiometric ratio of the reaction.</p>
<p>A self-similar solution for the steady flow is obtained incorporating the Howarth transformation, which allows the large density variations inherent in the combustion of gases to be accommodated. The stoichiometric ratio and fuel/oxidizer density ratio are varied to examine their effects on the structure and flow properties of the flame.</p>
<p>An Orr-Sommerfeld equation governing the stability of buoyant flows is developed, incorporating all the variable density terms. Two different steady flows are studied, the symmetric flame (unit stoichiometry), and a flame with the stoichiometric ratio corresponding to methane burning in air. It was found that using the Boussinesq approximation which neglects density variations except for a buoyancy term is not applicable for the flame, and also introduced inaccuracy in the stability diagram for the buoyant plume. Although the flame bears a superficial similarity to the buoyant plume, the several differences cause a large difference in their stability. Empirically interpreting the stability diagrams to obtain an expected transition point gives Re<sub><i>T</i></sub> ≈ 250 for the flame compared to the less stable buoyant plume with Re<sub><i>T</i></sub> ≈ 140. A new unstable region consisting of waves with negative phase velocity but positive group velocity was found for both the buoyant flame and the buoyant plume.</p>
<p>The local analysis is inappropriate for disturbances with wavelengths long compared to the flame thickness, therefore an analysis treating the flame and associated plume as negligibly thin was undertaken. This showed that the primary cause of instability was centrifugal forces generated by the momentum flux following a curved path. Reasonably good agreement was obtained with the local analysis.</p>https://thesis.library.caltech.edu/id/eprint/3553An Analytical Study of Diffusion Flames in Vortex Structures
https://resolver.caltech.edu/CaltechETD:etd-09132005-133501
Authors: Karagozian, Ann Renee
Year: 1982
DOI: 10.7907/NE3D-T576
<p>The interaction of a laminar diffusion flame with two- and three-dimensional vortex structures is considered, in which the flame becomes severely distorted and is strained in its own plane. Fast chemical kinetics and unity stoichiometry are assumed. The resulting curved flame sheets are treated by applying the boundary layer approximation locally until neighboring flame sheets come sufficiently close to interact and consume the intervening reactant, thus creating a core of combustion products with external isolated flame sheets.</p>
<p>The simplest example is the deformation of a diffusion flame by a viscous vortex of circulation Γ. For large Γ the radius of the core of combustion products increases in proportion to Γ<sup>1/3</sup>D<sup>1/6</sup>t<sup>1/2</sup>, where D is the binary diffusivity, indicating the overall transport quantity to be Γ<sup>2/3</sup>D<sup>1/3</sup>. The augmentation of reactant consumption due to the presence of the vortex is time-independent and behaves as Γ<sup>2/3</sup>D<sup>1/3</sup>.</p>
<p>The interaction of a laminar flame with a viscous vortex undergoing constant axial straining also is examined. The growth of the core radius has the similarity relation ϒ · ~ Γ<sup>1/3</sup>D<sup>1/6</sup>[(1-e<sup>-εt</sup>)<sup>1/2</sup>]/ε<sup>1/2</sup> indicating that the core eventually reaches a steady state size. The core continues to store products and the outer flame arms continue to consume reactants independently of time, however, due to axial extension. Hence there exist two different time scales governing the development of the flame: one associated with the flame-vortex interaction and one associated with the external strain rate.</p>
<p>The effect of the release of heat (and subsequent density change) by the reaction on flame structure is examined by considering the interaction of a diffusion flame with a vortex undergoing a density change at the core. The decreased core density shifts the entire flowfleld radially outward, causing the burned core to be increased in size, while the radius of the unburned core decreases as [ρ<sub>1</sub>/ρ<sub>2</sub> + 1]<sup>-1/6</sup>, where ρ<sub>1</sub> is the reactant density and ρ<sub>2</sub> is the product density. The augmented consumption rate of the flame also is reduced, since the flame is being strained further from the viscous core and thus to a lesser extent.</p>https://thesis.library.caltech.edu/id/eprint/3516The Effects of a Vortex Field on Flames with Finite Reaction Rates
https://resolver.caltech.edu/CaltechETD:etd-09112006-111139
Authors: Norton, Olin Perry
Year: 1983
DOI: 10.7907/7vn8-4078
<p>A diffusion flame, supported by a one-step chemical reaction, is initiated along the horizontal axis between a fuel occupying the upper half-plane and an oxidizer below. Simultaneously, a vortex of circulation Γ is established at the origin. As time progresses the flame is extended and "wound up" by the vortex flow field. The effect of distortion of the flame is locally described by the time-dependent straining of a one-dimensional flame. The rate of chemical reaction is represented by the characteristic chemical reaction time, <i>t<sub>ch</sub></i>, of the system. The combustion field then consists of a totally reacted core region and an external flame region consisting of a pair of spiral arms extending off at large radii toward their original positions.</p>
<p>The presence of the vortex increases the rate of fuel consumption of the flame. For large values of Γ/D, the augmentation of fuel consumption due to the vortex is proportional to <i>ρ</i>Γ<sup>2/3</sup><i>D</i><sup>1/3</sup>, and is a function of <i>t</i>/<i>t<sub>ch</sub></i> which approaches a constant value as <i>t</i> → ∞. The growth of the fuel consumption rate from zero to its steady value for large times is governed by the time scale <i>t<sub>ch</sub></i>. If the products of combustion occupy more volume than the original reactants, then the spiral flame will appear as an unsteady volume dilitation for times on the order of the chemical time. An unsteady volume dilitation acts as an acoustic source, so the interaction of a vortex and a diffusion flame is shown to result in the generation of a pressure pulse; the peak pressure occurring after a delay proportional to the chemical time, and the strength of the pulse proportional to Γ<sup>2/3</sup><i>D</i><sup>1/3</sup> and inversely proportional to √<i>t<sub>ch</sub></i>.</p>
<p>These results are valid for hypergolic reaction systems in which the reactant temperature does not significantly effect the rates of the chemical reactions. For systems described as having "large activation energy", the rates are strongly temperature dependent and another description is appropriate. For these systems, a vortex established on an already ignited flame exhibits, in addition to the features described above, an extinct core of unburned reactants if the circulation of the vortex is large.</p>
<p>The results provide the fundamental structure for the mechanism of combustion instability proposed by Rogers and Marble in 1956.</p>https://thesis.library.caltech.edu/id/eprint/3457Two Mechanisms of Vorticity Generation in Combusting Flow Fields
https://resolver.caltech.edu/CaltechETD:etd-03192008-104812
Authors: Hendricks, Gavin Julian
Year: 1986
DOI: 10.7907/kj79-eq14
<p>In Part 1 of the thesis the behavior of a diffusion flame in an unbounded flow with an imposed pressure gradient is analysed. The problem is formulated using the compressible boundary layer equations, and the assumption of infinite reaction kinetics is employed. The equations are transformed to the equivalent incompressible equations by the application of the Howarth transformation. Solutions to these equations are obtained for a functional form of the pressure gradient which admits similarity solutions. Two stoichiometric fuel—air ratios are considered, φ = 1 which yields a symmetric flow field about the flame, and φ = 0.058 which corresponds to the combustion of methane in air and yields an unsymmetric flow field.</p>
<p>For favorable pressure gradients the fluid in the vicinity of the flame is accelerated more than the fluid in the free stream. The acceleration of the fluid as it is convected downstream causes an augmentation in the fuel mass consumption rate, the mechanism of which is similar to that of a strained diffusion flame in an unbounded counterflow. For adverse pressure gradients a reverse flow develops in the vicinity of the flame which severely affects the mass consumption rate of fuel. For a flame with unit stoichiometry, recirculation zones develop on either side of the flame which eventually lead to extinction. For the stoichiometric ratio corresponding to the combustion of methane in air, the recirculation zones are situated on the fuel side of the flame and no tendency toward extinction is shown.</p>
<p>In Part 2 a numerical study is done to investigate the formation of large vortex structures observed in the combustion chambers of air breathing engines under certain conditions. It has been proposed that these vortex structures are formed by a surging flow over the flameholding device which exists when longitudinal modes of the combustion system are excited. In the present study the surging flow is generated by passing a weak shock wave over a rearward facing step. The fluid entering the chamber is of high density (representing the cold fuel—air mixture) whereas the fluid in the chamber has a low density (the combustion products). The vortex formed by the surging flow induces a downward velocity in the high density fluid toward the lower wall. It is found that larger surge velocities result in the formation of stronger vortices (which induce higher downward velocities), whereas an increase in the mean velocity causes no significant change in the flow field. The time taken for the high density fluid to reach the lower wall is therefore decreased as the surge velocity is increased. By considering these results, a possible model for the sustenance of the vortex shedding mechanism is proposed.</p>https://thesis.library.caltech.edu/id/eprint/1017An Experimental and Numerical Investigation of Swirling Flows in a Rectangular Nozzle
https://resolver.caltech.edu/CaltechETD:etd-03052008-091015
Authors: Sobota, Thomas Henry
Year: 1987
DOI: 10.7907/dw4x-ex64
<p>The high thrust to weight ratios now possible for military aircraft have made thrust vector pitch control more attractive and versatile than aerodynamic surface pitch control. Use of a rectangular nozzle is a natural consequence because articulation and sealing problems are less formidable than for conventional circular nozzles. The rectangular nozzle offers the additional possibility that the exhaust may mix rapidly with the ambient air and thereby reduce the radiative signature of the exhaust. Some previous investigations have suggested that a series of axial vortices may form in the nozzle, as a result of residual swirl from the gas turbine exhaust, and further enhance the mixing rate.</p>
<p>A detailed experimental investigation is described in this thesis which demonstrates that the formation of axial vortices in the nozzle is dependant on the vorticity distribution at the turbine exhaust. Further, three mechanisms which provide for the formation of axial vortices are identified.</p>
<p>A parallel computational investigation was carried out which not only confirmed the relationship between the turbine exhaust vorticity and the vortex patterns formed in the nozzle but also provided details of the flow field between the turbine discharge and the nozzle exit. On the basis of this more detailed understanding, it is now possible to "tailor" the vortex distribution at the nozzle exit by design of the turbine discharge and the intervening passage.</p>
https://thesis.library.caltech.edu/id/eprint/881An Investigation of Contoured Wall Injectors for Hypervelocity Mixing Augmentation
https://resolver.caltech.edu/CaltechETD:etd-07172007-083103
Authors: Waitz, Ian Anton
Year: 1991
DOI: 10.7907/MPJS-1Q71
<p>A parametric study of a class of contoured wall fuel injectors is presented. The injectors were aimed at enabling shock-enhanced mixing for the supersonic combustion ramjet engines currently envisioned for applications on hypersonic vehicles. Short combustor residence time, a requirement for fuel injection parallel to the freestream, and strong sensitivity of overall vehicle performance to combustion efficiency motivated the investigation. Several salient parametric dependencies were investigated. Injector performance was evaluated in terms of mixing, losses, jet penetration and heating considerations.</p>
<p>A large portion of the research involved a series of tests conducted at the NASA Langley High - Reynolds Number Mach 6 Wind-Tunnel. Helium was used as an injectant gas to simulate hydrogen fuel. The parameters investigated include injector spacing, boundary layer height, and injectant to freestream pressure and velocity ratios. Conclusions concerning injector performance and parameter dependencies are supported by extensive three-dimensional flow field surveys as well as data from a variety of flow visualization techniques including Rayleigh scattering, Schlieren, spark-shadowgraph, and surface oil flow.</p>
<p>As an adjunct to these experiments, a three-dimensional Navier-Stokes solver was used to conduct a parametric study which closely tracked the experimental effort. The results of these investigations strongly complemented the experimental work. Use of the code also allowed research beyond the fairly rigid bounds of the experimental test matrix. These studies included both basic investigations of shock-enhanced mixing on generic injectors, and applied efforts such as combining film-cooling with the contoured wall injectors.</p>
<p>Location of an oblique shock at the base of the injection plane was found to be a loss-effective method for enhancing hypervelocity mixing through baroclinic generation of vorticity and subsequent convection and diffusion. Injector performance was strongly dependent on the displacement effect of the hypersonic boundary layer which acted to modify the effective wall geometry. Strong dependence on injectant to freestream pressure ratio was also displayed. Mixing enhancement related to interaction of the unsteady component of the boundary layer with both steady and unsteady components of the flow field was found to be secondary, as were effects due to variation in mean shear between the injectant and the freestream in the exit plane.</p>https://thesis.library.caltech.edu/id/eprint/2909