The work herein generally applies to the problem of combustion instability. Combustion instabilities first arose in engineering practice in the 1940s when they were experienced during the development of solid and liquid propellant rocket engines. Later, similar problems arose in gas turbine combustors and afterburners. However, the earliest technical case of the phenomenon dates back to Rijke in 1859 with his “singing” tube.

The presented work focuses on the study of a simple, stagnation plane stabilized, laminar, flat-flame burner. In particular the dynamic response of the burner is examined under excitation by a driven acoustic field. After characterization of the burner’s operational range, the response of the system is measured from 20 Hz to nearly 2000 Hz over the span of operating parameters using an optically filtered PMT and lens combination. A library of the collected and reduced data is generated.

A deeper investigation of the burner dynamics at a given reference operating condition is performed using phase-resolved PLIF. Fluctuations in the spatial distributions of the LIF signals for several target species (OH, CH, CH_{2}O) under acoustic forcing are measured. In addition, visualization of the unsteady reactant flow using precision acetone seeding and PLIF at 277 nm is performed. Subsequent cinematographic sequences are produced along with spatially resolved plots of the combustion response function and the forced Rayleigh index for numerous drive frequencies. A library of the collected and reduced data is assembled.

Analysis of the collected data reveals two principal mechanisms contributing to the unsteady response of the flame. Structure development in (and subsequent convention along) the unsteady shear layer of the laminar jet dominates the response at the outer reaches of the flame. The inner region of the flame is driven largely by the Helmholtz response of the burner nozzle cavity. These two operations mutually contribute to produce the general shape of the combustion response curve. Ultimately, the data is used to construct a simplified model for the combustion response function. The model is enhanced with two additional revisions guided by the improved understanding of the mechanisms involved.

The document ends with numerous appendices describing, in detail, the equipment used, much of which was fabricated specifically for this work. These appendices, in combination with information presented in the chapters, provide substantial detail regarding the experimental configuration and operating conditions. Great effort was made to provide the necessary information to allow replication of the experiments as well as to support future modeling endeavors as a validation dataset.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/3TWK-W923, author = {Ciucci, Francesco}, title = {Continuum Modeling of Mixed Conductors: A Study of Ceria}, school = {California Institute of Technology}, year = {2009}, doi = {10.7907/3TWK-W923}, url = {https://resolver.caltech.edu/CaltechETD:etd-07212009-142144}, abstract = {

In this thesis we have derived a new way to analyze the impedance response of mixed conducting materials for use in solid oxide fuel cells (SOFCs), with the main focus on anodic materials, in particular cerium oxides.

First we have analyzed the impact of mixed conductivity coupled to electrocatalytic behavior in the linear time-independent domain for a thick ceria sample. We have derived that, for a promising fuel cell material, Samarium Doped Ceria, chemical reactions are the determining component of the polarization resistance.

As a second step we have extended the previous model to the time-dependent case, where we focused on single harmonic excitation, the impedance spectroscopy conditions. We extended the model to the case where some input diffusivities are spatially nonuniform. For instance we considered the case where diffusivities change significantly in the vicinity of the electrocatalytic region.

As a third and final step we use to model to capture the two dimensional behavior of mixed conducting thin films, where the electronic motion from one side of the sample to the other is impeded. Such conditions are similar to those encountered in fuel cells where an electrolyte conducting exclusively oxygen ions is placed between the anode and the cathode. The framework developed was also extended to study a popular cathodic material, Lanthanum Manganite.

The model is used to give unprecedented insight in SOFC polarization resistance analysis of mixed conductors. It helps elucidate rigorously rate determining steps and to address the interplay of diffusion with diffusion losses. Electrochemical surface losses dominate for most experimental conditions of Samarium Doped Ceria and they are shown to be strongly dependent on geometry.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Goodwin, David G.}, } @phdthesis{10.7907/XWSV-1E98, author = {Kolasinski, Robert David}, title = {Fundamental Ion-Surface Interactions in Plasma Thrusters}, school = {California Institute of Technology}, year = {2007}, doi = {10.7907/XWSV-1E98}, url = {https://resolver.caltech.edu/CaltechETD:etd-11222006-105854}, abstract = {Ion thrusters offer the potential to enable many future interplanetary robotic missions presently under consideration by NASA. To realize the benefits offered by these low thrust devices, the sputtering mechanisms that are responsible for the degradation of thruster components over time must be well understood. Predictions of thruster life depend directly on the material removal rates from thruster electrodes such as the ion optics and hollow cathodes. To better understand the conditions encountered at these surfaces, this study includes an investigation of low energy sputtering at glancing incidence. Relevant ion–target combinations that were considered included Xe⁺ incident on Mo, C, and Cu, as well as Ar⁺ incident on W, C, and Cu. To characterize the sputtering yield angular dependence experimentally, an ion beam was used to etch a coated quartz crystal microbalance. This required the development of techniques to accurately measure the incident low energy ion flux to the target and the use of surface diagnostics to investigate the properties of target materials. Measurements of C and Mo sputtering yields were obtained for Xe⁺ incidence angles up to 80° from the surface normal and for energies ranging from 80 eV–1 keV. In addition, existing transport theory models were used to examine projectile scattering within the different target media. The models also indicate that the sputtering behavior as a function of angle of incidence is not a strong function of energy, a conclusion that is supported by the experimental results. The surface roughness of the targets was investigated using atomic force microscopy to obtain local incidence angle distributions. A surface layer activation technique served as an alternate method of evaluating the sputtering rates of thruster components for situations where the ion bombardment conditions are not well known. In this study, a radioactive tracer was produced in the surfaces of a number of laboratory model ion thruster cathode assemblies by high energy proton bombardment. The cathodes were tested in a 30 cm diameter xenon ion thruster to provide insight into the relevant wear mechanisms at different thruster operating points. Methods for combating cathode degradation are proposed based on the experimental results.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/6F5N-9G88, author = {Kang, Dal Mo}, title = {Measurements of Combustion Dynamics with Laser-Based Diagnostic Techniques}, school = {California Institute of Technology}, year = {2006}, doi = {10.7907/6F5N-9G88}, url = {https://resolver.caltech.edu/CaltechETD:etd-12182005-164746}, abstract = {

Since the early days of gas turbine engines, combustion/flow instability inside the combustor has been an issue in many engines, but little has been understood as to how the dynamics of the system involved contribute to the instability. The primary objective of this work is to provide general experimental procedures and to validate methods for examining the dynamic behaviors of combustion systems, and to provide accurate measurements of the combustion dynamics for use as a foundation for further theoretical and numerical research. Knowledge of the fundamental dynamics of combustion systems is crucial in understanding and modeling the flame behavior and enabling the use of insights in design process and for creating robust active control of combustors.

Since mixing plays significant roles in combustion processes, the dynamics of fuel/air mixing were studied. A non-premixed burner was examined with acoustic excitations at 22~55 Hz to assess the mixing and its relation to the thermo-acoustic coupling. Phase-resolved acetone-PLIF was used to image the mixing, and from this the unmixedness was calculated, which quantifies the degree of mixing. The results show that (1) the acoustic waves induce periodicity in the degree of mixing; (2) the way the unmixedness behaves coincides well with the behavior of the Rayleigh index, implying the degree of mixing is a major factor in determining the stability of the combustion system; (3) the two-dimensional measurements of temporal unmixedness effectively visualize the shear mixing zone.

A second low-swirl premixed burner was studied to examine the impact of acoustic waves on the combustion dynamics. Measurements were performed with OH-PLIF, with acoustic forcing up to 400 Hz. Swirl burners at higher pressure are industry standard, and this study examined the dynamics at elevated combustor pressure. The results show that (1) the thermo-acoustic coupling seems to be closely coupled to the vortices generated at the flame boundary; (2) high magnitude of flame response coincides with the high absolute value of Rayleigh index; (3) the way the thermo-acoustic coupling is distributed over the space is highly dependent on the excitation frequencies; (4) high pressure suppresses the sensitivity of combustions system to outside disturbances.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/T337-T709, author = {Parkin, Kevin L.G.}, title = {The Microwave Thermal Thruster and Its Application to the Launch Problem}, school = {California Institute of Technology}, year = {2006}, doi = {10.7907/T337-T709}, url = {https://resolver.caltech.edu/CaltechETD:etd-06022006-160023}, abstract = {Nuclear thermal thrusters long ago bypassed the 50-year-old specific impulse (Isp) limitation of conventional thrusters, using nuclear powered heat exchangers in place of conventional combustion to heat a hydrogen propellant. These heat exchanger thrusters experimentally achieved an Isp of 825 seconds, but with a thrust-to-weight ratio (T/W) of less than ten they have thus far been too heavy to propel rockets into orbit.

This thesis proposes a new idea to achieve both high Isp and high T/W: The Microwave Thermal Thruster. This thruster covers the underside of a rocket aeroshell with a lightweight microwave absorbent heat exchange layer that may double as a re-entry heat shield. By illuminating the layer with microwaves directed from a ground-based phased array, an Isp of 700–900 seconds and T/W of 50–150 is possible using a hydrogen propellant. The single propellant simplifies vehicle design, and the high Isp increases payload fraction and structural margins. These factors combined could have a profound effect on the economics of building and reusing rockets.

A laboratory-scale microwave thermal heat exchanger is constructed using a single channel in a cylindrical microwave resonant cavity, and new type of coupled electromagnetic-conduction-convection model is developed to simulate it. The resonant cavity approach to small-scale testing reveals several drawbacks, including an unexpected oscillatory behavior. Stable operation of the laboratory-scale thruster is nevertheless successful, and the simulations are consistent with the experimental results.

In addition to proposing a new type of propulsion and demonstrating it, this thesis provides three other principal contributions: The first is a new perspective on the launch problem, placing it in a wider economic context. The second is a new type of ascent trajectory that significantly reduces the diameter, and hence cost, of the ground-based phased array. The third is an eclectic collection of data, techniques, and ideas that constitute a Microwave Thermal Rocket as it is presently conceived, in turn selecting and motivating the particular experimental and computational analyses undertaken.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/VKKE-PC20, author = {Wirz, Richard Edward}, title = {Discharge Plasma Processes of Ring-Cusp Ion Thrusters}, school = {California Institute of Technology}, year = {2005}, doi = {10.7907/VKKE-PC20}, url = {https://resolver.caltech.edu/CaltechETD:etd-05232005-162628}, abstract = {This study has increased the viability of miniature ion thruster technology, advanced state-of-the-art discharge modeling, and revealed important aspects of discharge plasma processes. These extensions of existing ion thruster technology and understanding are necessary to fulfill the needs of future space missions. Experimental comparisons of the discharge performance of an array of miniature (3cm diameter) ion thruster discharge configurations were conducted and showed that a 3-ring configuration with length-to-diameter of 1.0 exhibited the best performance. A compact and lightweight version of this configuration, using small accelerator grid holes, exhibited discharge losses of 250-550eV/ion and propellant efficiency of as much as 87%. This performance represents a significant advancement in miniature (less than 5cm diameter) ion thruster technology and demonstrates that a miniature ion thruster of low magnet and thruster weight can yield desirable performance.

A multi-component hybrid 2-D computational Discharge Model was developed to help identify important ion thruster discharge processes and investigate miniaturization issues. Combining experimental and computational results reveals that magnetic field optimization for a miniature ion thruster is bracketed by considerations of primary electron utilization and discharge stability. Discharge Model analysis of the larger (30cm diameter) NSTAR thruster revealed that the peak observed in the NSTAR beam profile is due to double ions that are created by over-confinement of primary electrons on the thruster axis. Design sensitivity results show that, at the NSTAR thruster scale, efficient confinement of primary electrons is relatively easy to achieve; therefore, efforts to improve thruster performance should focus on effectively utilizing the primary electrons to minimize double ion production and maximize the number of single ions extracted to the beam.

The observations from this study have furthered the understanding of discharge processes and should improve future ion thruster design and modeling efforts. The Discharge Model advances state-of-the-art ion thruster modeling and provides a framework for a complete thruster model that can be used for long-life performance assessment and life validation.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/0FX2-AM50, author = {Thunnissen, Daniel Pierre}, title = {Propagating and Mitigating Uncertainty in the Design of Complex Multidisciplinary Systems}, school = {California Institute of Technology}, year = {2005}, doi = {10.7907/0FX2-AM50}, url = {https://resolver.caltech.edu/CaltechETD:etd-01072005-162147}, abstract = {As humanity has developed increasingly ingenious and complicated systems, it has not been able to accurately predict the performance, development time, reliability, or cost of such systems. This inability to accurately predict parameters of interest in the design of complex multidisciplinary systems such as automobiles, aircraft, or spacecraft is due in great part to uncertainty. Uncertainty in complex multidisciplinary system design is currently mitigated through the use of heuristic margins. The use of these heuristic margins can result in a system being overdesigned during development or failing during operation.

This thesis proposes a formal method to propagate and mitigate uncertainty in the design of complex multidisciplinary systems. Specifically, applying the proposed method produces a rigorous foundation for determining design margins. The method comprises five distinct steps: identifying tradable parameters; generating analysis models; classifying and addressing uncertainties; quantifying interaction uncertainty; and determining margins, analyzing the design, and trading parameters. The five steps of the proposed method are defined in detail. Margins are now a function of risk tolerance and are measured relative to mean expected system performance, not variations in design parameters measured relative to heuristic values.

As an example, the proposed method is applied to the preliminary design of a spacecraft attitude determination and control system. In particular, the design of the attitude control system on the Mars Exploration Rover spacecraft cruise stage is used. Use of the proposed method for the example presented yields significant differences between the calculated design margins and the values assumed by the Mars Exploration Rover project.

In addition to providing a formal and rigorous method for determining design margins, this thesis provides three other principal contributions. The first is an uncertainty taxonomy for use in the design of complex multidisciplinary systems with detailed definitions for each uncertainty type. The second is the modification of two simulation techniques, the mean value method and subset simulation, that can significantly reduce the computational burden in applying the proposed method. The third is a set of diverse application examples and various simulation techniques that demonstrate the generality and benefit of the proposed method.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/V1WS-S833, author = {Malhotra, Sanjeev}, title = {On Combustion Instability in Solid Rocket Motors}, school = {California Institute of Technology}, year = {2004}, doi = {10.7907/V1WS-S833}, url = {https://resolver.caltech.edu/CaltechETD:etd-05062004-130913}, abstract = {An investigation of combustion instability in solid rocket motors was conducted using perturbation techniques, with particular emphasis placed upon understanding the fluid dynamics of the chamber environment. It was shown that although the phenomena generally manifests itself as oscillations of pressure, with the frequencies measured in tests well predicted by classical acoustic formulas, important aspects of the behavior cannot be explained without due recognition of the two basic processes of fluid dynamics—i.e., the compressing/expanding process and the shearing process.

Thus, a new framework for studying these instabilities that accommodated both linear and nonlinear behavior was developed. The approach differed from previous work in its use of linear stability eigenfunctions—that satisfy the no-slip boundary condition—as a basis for the expansion, with adjoints used to effect a spatial averaging. Among other things, this allowed for the self-consistent inclusion of vortical flow effects.

With respect to the linear behavior, two dominant vorticity-related pathways were shown to exist: one because of sound creating vorticity, and the other, because of that vorticity, in turn, creating more sound. These effects cancel however and thus to leading order no net contribution exists. Though this finding had been reported in an earlier study, restrictive assumptions were introduced. In contrast, we establish that the result is independent of grain geometry and holds for any fluid motion, turbulent or otherwise.

A nonlinear coupling to the flame zone owing to vorticity creation was also identified. The term was left unevaluated however, since no satisfactory model of the flame response presently exists. To help circumvent this difficulty, i.e., that much remains to be done on modeling nonlinear processes, the amplitude equations were studied in a general way using perturbation techniques based on ideas of resonance. The advantage of such an approach is that the nonlinear coefficients need not be specified a priori—only conditions on the linear behavior of the system need to be placed. Closed form results were derived for the limiting periodic behavior when the first mode is unstable and compared against results from numerical integration. Striking agreement was shown.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/3X6A-6D11, author = {Matveev, Konstantin Ivanovich}, title = {Thermoacoustic Instabilities in the Rijke Tube: Experiments and Modeling}, school = {California Institute of Technology}, year = {2003}, doi = {10.7907/3X6A-6D11}, url = {https://resolver.caltech.edu/CaltechETD:etd-03042003-102221}, abstract = {Thermoacoustic instability can appear in thermal devices when unsteady heat release is coupled with pressure perturbations. This effect results in excitation of eigen acoustic modes of the system. These instabilities are important in various technical applications, for instance, in rocket motors and thermoacoustic engines.

A Rijke tube, representing a resonator with a mean flow and a concentrated heat source, is a convenient system for studying the fundamental physics of thermoacoustic instabilities. At certain values of the main system parameters, a loud sound is generated through a process similar to that in real-world devices prone to thermoacoustic instability. Rijke devices have been extensively employed for research purposes. The current work is intended to overcome the serious deficiencies of previous investigations with regard to estimating experimental errors and the influence of parameter variation on the results. Also, part of the objective here is to account for temperature field non-uniformity and to interpret nonlinear phenomena. The major goals of this study are to deliver accurate experimental results for the transition to instability and the scope and nature of the excited regimes, and to develop a theory that explains and predicts the effects observed.

An electrically heated, horizontally oriented, Rijke tube is used for the experimental study of transition to instability. The stability boundary is quantified as a function of major system parameters with measured uncertainties for the data collected. Hysteresis in the stability boundary is observed for certain operating regimes of the Rijke tube.

An innovative theory is developed for modeling the Rijke oscillations. First, linear theory, incorporating thermal analysis that accurately determines the properties of the modes responsible for the transition to instability, is used to predict the stability boundary. Then, a nonlinear extension of the theory is derived by introducing a hypothesis for a special form of the nonlinear heat transfer function. This nonlinear modeling is shown to predict the hysteresis phenomenon and the limit cycles observed during the tests.

A new, reduced-order modeling approach for combustion instabilities in systems with vortex shedding is derived using the developed analytical framework. A hypothesis for the vortex detachment criterion is introduced, and a kicked oscillator model is applied to produce nonlinear results characteristic for unstable combustion systems.

The experimental system and the mathematical model, developed in this work for the Rijke tube, are recommended for preliminary design and analysis of real-world thermal devices, where thermoacoustic instability is a concern.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/K408-J123, author = {Duchemin, Olivier Bernard}, title = {An investigation of ion engine erosion by low energy sputtering}, school = {California Institute of Technology}, year = {2001}, doi = {10.7907/K408-J123}, url = {https://resolver.caltech.edu/CaltechETD:etd-02242002-122344}, abstract = {Unlike chemical propulsion systems, which are fundamentally limited in performance by propellant energy density, electric propulsion devices, such as ion engines, are limited in iotal deliverable impulse by maximum propellant throughput due to engine wear. In order to perform realistic modeling of engine lifetime, the erosion mechanisms involved must be understood. In particular, the damage—or sputtering—caused by slow ions on solid surfaces is extremely difficult to quantify. We first review the engine failure modes in which sputtering of molybdenum by slow xenon ions plays a critical role. We then present the relevant physical mechanisms, and describe a model for estimating the minimum kinetic energy necessary to dislodge a surface atom. Over seventeen analytical approaches to the energy dependence of sputtering have been published in the literature. We implement the four that are most relevant to ion engine erosion processes. In addition, we use the Monte-Carlo simulation program TRIM to calculate sputtering yields. We find, in particular, that the relative sensitivity of sputtering yield to surface binding energy increases dramatically near the sputtering threshold energy. Although the surface binding energy is a (weak) function of temperature, we show that the sputtering yield should not increase significantly at temperatures typical of ion engine operation. An experimental approach to the measurement of low energy sputtering yields is implemented and validated. Based on the Quartz Crystal Microbalance (QCM) technique, this method takes advantage of the differential mass sensitivity exhibited by the piezoelectric quartz resonator used in this study. Because of the importance of surface contamination in low energy sputtering, a surface kinetics model is presented to describe a surface under the simultaneous cleaning effect of ion bombardment, and background gas flow contamination. A special case of simultaneous surface contamination and erosion occurs during engine ground testing, where carbon is backsputtered on the accelerator grid from the facility. We describe experiments to measure ion-induced desorption cross-sections for carbon on molybdenum, before concluding that the protective effect of the carbon contamination is unlikely to significantly affect engine erosion, so that ground testing results are applicable to space operations}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/JKFD-7W43, author = {Seywert, Claude N. L.}, title = {Combustion instabilities : issues in modeling and control}, school = {California Institute of Technology}, year = {2001}, doi = {10.7907/JKFD-7W43}, url = {https://resolver.caltech.edu/CaltechETD:etd-01252007-135242}, abstract = {This study deals with various aspects in the development of active control of combustion instabilities. A low-order model is developed, reconciling along the way two different approaches taken by researchers to attack the description of combustion instabilities. The model is demonstrated with application to a Rijke tube and compared to experiments. The Rijke burner experiments suggest two major discrepancies with the model: the presence of a hysteresis loop is unaccounted for and the model does not describe the seemingly random fluctuations in the amplitude of the pressure oscillations in the ‘unstable’ regime. So far no explanation for the hysteresis can be given; however, this phenomenon is successfully exploited by using a novel nonlinear control technique to expand the stable operating range of the burner. The origin of the ‘noise’ in the pressure trace is explained by considering entropy and vorticity waves in the combustor. Their presence leads to a slight modification of the original model, introducing stochastic source terms into the oscillator equations. The consequences of the presence of these terms is analyzed by means of simulations. One interesting result is that they allow for the identification of model parameters from a single experimental run of a stable combustion system. Finally, a unified approach to controlling combustion instabilities is presented. The formulation and analysis account for truncation to a few modes; uncertainties in the description of the system (including uncertain sensing and actuating); external disturbances; and intrinsic noise sources. An explicit expression is derived against which any controller can be checked for stability.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/SPSR-VD18, author = {Pun, Winston}, title = {Measurements of thermo-acoustic coupling}, school = {California Institute of Technology}, year = {2001}, doi = {10.7907/SPSR-VD18}, url = {https://resolver.caltech.edu/CaltechETD:etd-08222001-170336}, abstract = {The problem of combustion instabilities has existed since the early 1940s, when they were observed during the development of solid and liquid rocket engines. While various engineering solutions have served well in these fields, the problem is revisited in modern gas-turbine engines. The purpose of this work is to provide experimental measurements of laboratory devices that exhibit thermo-acoustic coupling, similar to the interaction observed during combustion instabilities, which will aid in the design and development of stable systems. Possibly the simplest device which exhibits these characteristics is a Rijke tube. An electrical, horizontally mounted, 1 m long version of the original Rijke tube is presented, with measurements taken during unstable and stable operation. An accurate stability boundary with uncertainty is determined for a heater position of x/L = ?, as a function of mass flow rate and heater power. Hysteresis, not previously reported, is observed at flow rates above 3 g/s. A one-dimensional model of the stability boundary with linear acoustics is shown to have qualitative agreement with experimental data. A novel technique has also been devised which can provide insight into the local dynamic response of a flame to an acoustic field. In the experiments, a test chamber is acoustically excited by a pair of low-frequency drivers. The response of the flame is visualized by two techniques; chemiluminescence and planar laser-induced fluorescence (PLIF) of the hydroxyl (OH) radical, both of which are well-known indicators for heat release in flames. The resulting images are phase-resolved and averaged to yield a qualitative picture of the fluctuation of the heat release. The images are correlated with a pressure transducer near the flame, which allows stability to be evaluated using Rayleigh?s criterion and a combustion response function. This is the first known measurement of the combustion dynamics of a flame over a range of frequencies. Results indicate that the drive frequency and burner configuration have a pronounced effect on the response of the flame. Drive frequencies ranging from 22 Hz to 55 Hz are applied to the jet mixed burner, supplied with a premixed 50/50 mixture of methane and carbon dioxide at a Reynolds number of 20,000. The burner is operated in two configurations; with an aerodynamically stabilized flame and with a flame stabilized by two protruding bluff-bodies. Results indicate that in general the bluff-body stabilized flame is less sensitive to chamber acoustic excitation.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/k1rf-a525, author = {Isella, Giorgio Carlo}, title = {Modeling and Simulation of Combustion Chamber and Propellant Dynamics and Issues in Active Control of Combustion Instabilities}, school = {California Institute of Technology}, year = {2001}, doi = {10.7907/k1rf-a525}, url = {https://resolver.caltech.edu/CaltechETD:etd-03012006-093758}, abstract = {A method for a comprehensive approach to analysis of the dynamics of an actively controlled combustion chamber, with detailed analysis of the combustion models for the case of a solid rocket propellant, is presented here. The objective is to model the system as interconnected blocks describing the dynamics of the chamber, combustion and control (including sensors and actuators).

The analytical framework for the analysis of the dynamics of a combustion chamber is based on spatial averaging, as introduced by Culick. This method results in the determination of a set of coupled oscillator equations that are then integrated with the appropriate forcing terms deriving from combustion and control.

Combustion dynamics are analyzed for the case of a solid propellant. Considerable data exists suggesting that the response functions for many solid propellants tend to have higher values, in some ranges of frequencies, than predicted by the conventional quasi-steady theory. Hence, quasi-steady theory is extended to include the dynamics of the gas-phase and also of a surface layer interposed between the gaseous flame zone and the heated solid phase of the propellant. The models are constructed so that they produce a combustion response function for the solid propellant that can be immediately introduced in the our analytical framework. The principal objective of this analysis is to determine which characteristics of the solid propellant are responsible for the large sensitivity, observed experimentally, of propellant burning response to small variations in the conditions. We show that velocity coupling, and not pressure coupling, has the potential to be the mechanism responsible for that high sensitivity. Some issues related to the modeling of solid propellant are also discussed, namely the importance of particulate modeling and its effect on the global dynamics of the chamber and a revisited interpretation of the intrinsic stability limit for burning of solid propellants.

Active control is also considered in the analysis. A critical discussion about the most commonly used control strategies used in combustion allows us to define which are the most promising algorithms to use on future experiments. Particular attention is devoted to the effect of time delay (between sensing and actuation) on the control strategy; several methods to compensate for it are presented and discussed, with numerical examples based on the approximate analysis produced by our framework.

Experimental results are presented for the case of a Dump Combustor. The combustor exhibits an unstable burning mode, defined through the measurement of the pressure trace and shadowgraph imaging. The transition between stable and unstable modes of operation is characterized by the presence of hysteresis, also observed in other experimental works, and hence not a special characteristic of this combustor. Control is introduced in the form of pulsed secondary fuel. We show the capability of forcing the transition from unstable to stable burning, hence extending the stable operating regime of the combustor. The transition, characterized by the use of a shadowgraph movie sequence, is attributed to a combined fluid-mechanic and combustion mechanism.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/3QG6-JN34, author = {Swenson, Grant Douglas}, title = {Numerical simulations of combustion instabilities in gas turbine combustors, with applications}, school = {California Institute of Technology}, year = {2000}, doi = {10.7907/3QG6-JN34}, url = {https://resolver.caltech.edu/CaltechETD:etd-01162008-140810}, abstract = {Recent advances in technology have opened up a potential market for small gas turbine power systems in the 50-100 MW range. In an effort to improve their systems, the gas-turbine industry is interested in understanding and controlling combustion instabilities as well as reducing pollutant production. To understand the dynamics inherent in a combustion system, information about the flow field behavior is required. Because of a scarcity of available experimental or numerical results for full-scale gas-turbine combustors, we decided to use numerical simulations to provide the required information about the flow field dynamics. The ability of the numerical simulations to reproduce unstable behavior in combustion environments will be presented. The investigation of the flow field dynamics has been conducted for three test cases; a planar heat source in a tube, premixed flow in a dump combustor, and premixed and diffusion flames in a full-scale gas turbine combustor. The numerically determined unsteady acoustic modes will be shown to compare well with theory and experiments. An investigation of the local heat release response to an unsteady flow field is conducted for incorporation into an approximate analysis method. The results of including a Helmholtz resonator in a dump combustor as a passive control mechanism will be presented. The production of NOx and CO will be compared between stable and unstable flow configurations. The pollutant results indicate that for the planar flame in a tube and the dump combustor, the NOx levels at the exit plane are reduced when the system is unstable.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/013z-q287, author = {Burnley, Victor Scott}, title = {Nonlinear Combustion Instabilities and Stochastic Sources}, school = {California Institute of Technology}, year = {1996}, doi = {10.7907/013z-q287}, url = {https://resolver.caltech.edu/CaltechETD:etd-04012005-140017}, abstract = {An investigation of combustion instabilities was conducted using an approximate analysis which allows any relevant physical processes to be included. The resulting system of coupled nonlinear oscillator equations was studied using the methods of dynamical systems theory. Previous investigations have further simplified the system using the method of time-averaging and truncation to a small number of modes. We have investigated the consequences of using these additional approximations, a case which had not been addressed completely in the literature. It was determined that application of the method of time-averaging introduces a stability boundary which limits the range in which the averaged equations are valid.

Transverse oscillations in a cylindrical chamber were also treated. It was established that in addition to its role in energy transfer between modes, nonlinear gasdynamics also provides a means of shifting the frequencies of oscillations to integral multiples of the fundamental. This additional role can reduce the efficiency of energy transfer, thus increasing the acoustic amplitudes. An example of a low amplitude transverse oscillation was produced suggesting a means by which the amplitudes of transverse modes, as well as nonintegral longitudinal modes, may be reduced.

The coupling between combustion processes and acoustic oscillations was studied as a possible explanation of the phenomenon known as triggering. Using several ad hoc models, the effects of nonlinear pressure coupling and velocity coupling on the behavior of the system were investigated. Substantial regions of possible triggering were produced when using a model of velocity coupling with a threshold, but only if nonlinear gas dynamics was also included.

The interaction between combustion noise and acoustic instabilities has received relatively little attention. The sources of noise in a combustion chamber are associated with vorticity and entropy waves. By including these contributions in the approximate analysis, the general forms of the stochastic excitations were obtained. Subsequently, the efects of these excitations on the amplitudes of acoustic modes were studied. When only nonlinear gasdynamics was included, no cases of bimodal probability density functions, characteristic of triggering, were found. However, when the model of velocity coupling with a threshold is added, bimodal probability densities can occur.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/PDWR-J354, author = {Sercel, Joel Christopher}, title = {An experimental and theoretical study of the ECR plasma engine}, school = {California Institute of Technology}, year = {1993}, doi = {10.7907/PDWR-J354}, url = {https://resolver.caltech.edu/CaltechETD:etd-10192005-142203}, abstract = {NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.

The process of Electron-Cyclotron-Resonance (ECR) plasma acceleration has several potential applications including use as a new type of electric space propulsion device designated the ECR plasma engine. The ECR plasma engine is interesting due to its theoretical promise to deliver a combination of improved efficiency, specific impulse, power-handling capability, length of life, or operational flexibility relative to other electric propulsion devices now being developed. Besides its possible application in electric propulsion, the ECR plasma engine might be useful for beamed-energy propulsion or fusion propulsion. Related devices are used in the semiconductors field for plasma etching.

This study includes theoretical modeling and a series of experimental measurements. The theoretical work was focused in two areas. The first area involved the development of a collisionless, steady-state, axisymmetric model of a cold flowing plasma separating from a diverging magnetic field. This model suggests that beam divergence can be an important loss mechanism for plasma propulsion devices that use magnetic nozzles, but that the use of optimized field geometries can reduce divergence losses to acceptable levels. We suggest that future research be directed at confirming theoretical predictions made using the axisymmetric model of beam separation.

The second area of theoretical investigation involved the development of a steady-state, quasi-one-dimensional model that provides theoretical predictions of plasma density, electron temperature, plasma potential, ion energy, engine specific impulse, efficiency, and thrust. The quasi-one-dimensional model consists of a system of five first-order, nonlinear, ordinary differential equations. The boundary conditions required to solve the system of equations are relationships between the ambient neutral gas density, the plasma density, the two components of the electron temperature, and the position at which the plasma passes through the ion-acoustic Mach number 1. The model was used to solve two classes of problems that are thought to bound the conditions under which the ECR plasma accelerator operates. The first class of problem is based on the assumption of negligible conductive heat flow within the plasma. The second class of problem is based on the assumption that electron thermal transport along magnetic field lines is so large that the component of the electron temperature along magnetic field lines is isothermal. The model can be used to simulate accelerator operation in space or in the presence of a vacuum system with finite tank pressure. Measurements of plasma conditions in a working research device confirm the general features of the quasi-one-dimensional theory.

The experimental apparatus constructed to study ECR plasma acceleration consists of a vacuum facility, a 20-kW microwave power supply, and an ECR plasma accelerator. In tests of the facility we have measured microwave input power, reflected power, propellant flow rate, and vacuum-tank static pressure. The working ECR plasma research device uses argon propellant gas with 2.12-GHz microwave radiation at power levels of up to a few kilowatts. Among the plasma diagnostics employed in this research are a gridded energy analyzer, a Faraday cup beam-density analyzer, Langmuir probes, emissive probes, and a diamagnetic loop. With these diagnostics, we have measured plasma potentials of up to 70 eV and electron temperatures of up to 35 eV. Measurements of accelerated-ion kinetic energy show a direct relationship between ion energy and peak plasma potential, as predicted by theory. Indirect measurements indicate that the plasma density in the existing accelerator is on the order of […].

We now understand previously unexplained losses in converting microwave power to jet power by ECR plasma acceleration as the result of diffusion of energized plasma to the metallic walls of the accelerator. Our theory suggests that future researchers should attempt to reduce the influence of these diffusion losses by increasing the cross-sectional area of the accelerator. It may be possible to reduce line radiation losses due to electron-ion and electron-atom inelastic collisions below levels estimated by past researchers through careful accelerator design. Minimizing inelastic collision losses will place a limit on the maximum thrust density that can be achieved using argon and other non-hydrogenic propellant materials. High thrust density may be achievable using propellants that are isotopes of hydrogen because once ionized, these species exhibit negligible inelastic collision effects. Deuterium is arguably the best candidate for achieving both high efficiency and high thrust, but will only be effective at specific impulses of over about 10,000 lbf s/lbm.

We expect that efficient ECR plasma engines can be designed for use in high specific impulse spacecraft propulsion at power levels ranging from a few kilowatts to tens of megawatts. The maximum theoretical efficiency of converting applied microwave power to directed jet power in this device can be more than 60 percent. The achievable total efficiency of converting direct-current electric power to jet power in a propulsion system based on the ECR plasma engine will probably be considerably less.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/j09c-vb03, author = {Iinoya, Fujio}, title = {Pulsed expansion of plasma in a magnetic thruster}, school = {California Institute of Technology}, year = {1993}, doi = {10.7907/j09c-vb03}, url = {https://resolver.caltech.edu/CaltechTHESIS:10012010-143404379}, abstract = {The inertial confinement fusion (ICF) pulse rocket is an advanced space propulsion system, which, through intermittent nuclear fusion energy production isolated from the vehicle structure, is capable of both extremely high specific impulses and high thrust-to-weight ratios. Such rockets, if realized, should revolutionize space travel by making possible very robust interplanetary missions as well as interstellar flight. The thruster of the rocket, which converts an initially isotropically expanding ICF debris plasma into a directed pulse jet exhaust, is to be fabricated out of magnetic fields created by current coils attached to the vehicle. The proper operation of such a thruster therefore rests upon the successful redirection of an initially spherical plasma of high conductivity by a suitably configured vacuum magnetic field against which the plasma expands. But to date, there have been no detailed analyses to guarantee that the concept in the present form will function satisfactorily as envisioned to yield reasonable propulsive efficiencies. Because of the highly dynamic behavior of the flow, which is bounded by an interface whose motion is unknown a priori, the first problem which must be investigated is that of the bulk flow under idealized conditions. In the work contained in this thesis, the plasma was assumed to be impermeable to the external fields, and the fields entered the debris dynamics only by way of applying a magnetic pressure force at the plasma-vacuum interface. The interface motion, bulk fluid profiles (when applicable), and resultant efficiencies were investigated for various parameter ratios and geometries. Such idealized bulk flow analyses are intended to serve as a basis for more detailed studies of how the flow will behave with a real plasma. Numerical simulations of the bulk flow process were conducted under both the thin-shell and the classical hydrodynamic approximations. The thin-shell calculation has been pioneered by other authors, but the present work is more complete, and as for the hydrodynamical calculations, application to the type of flows to be found in the magnetic thrusters of proposed ICF pulse rockets may be unique to this work, despite earlier claims. In the former approach, all of the plasma is assumed to be collected into an azimuthally symmetric perfectly conducting shell at the interface by virtue of the finite applied pressure at the interface. No fluid dynamics is considered under this approximation. These simulations showed that promising propulsive efficiencies could be obtained for a range of field-to-plasma energy ratios and thruster geometries, and the efficiencies reached a well-defined maximum for particular values of these parameters. However, because of the approximations used in this model, the efficiencies obtained do overestimate the real efficiencies. The thin-shell code is simpler to implement, and allows faster calculations and requires far less memory, than the more realistic hydrodynamic code, but the approximation made is not entirely accurate nor physical. In the second approach, the plasma is approximated by an unmagnetized perfectly conducting fluid obeying the laws of classical hydrodynamics. Here, we have a novel problem of a fluid expanding against a region of zero density, which nevertheless exerts a finite pressure on the fluid interface. In both the two-dimensional thin-shell and hydrodynamic calculations, the vacuum magnetic pressure applying at the plasma-vacuum interface was calculated from the quasi-static Maxwell Equations. By assuming the plasma and field coil structures to be perfectly conducting, the magnetic field in the vacuum region, from which the magnetic pressure at the interface was computed, was calculated by prescribing the initial flux through the field coils to remain trapped between the expanding plasma surface and the surfaces of the field coil structures. Such a prescription, which can be explained through the presence of surface currents, is valid as long as we have ideal perfect conductors. The hydrodynamic codes (both 1-D and 2-D) employed an advanced Classical Particle-In-Cell (PIC) scheme, and were successful at capturing the interface motion self-consistently (with pressure matching across the interface), and without iterations, via appropriate application of boundary conditions. The shock arising from the interface deceleration was also captured correctly. The formation of a shell-like structure originating close to the interface was observed in simulations of flows with large expansion ratios that were carried out in two dimensions employing realistic thruster fields. But depending upon the pressure history at the interface, these “shells” did not necessarily stay at the interfacial region. When tested on such processes as free expansion into a vacuum or shock-tube problems, for which well-known theoretical solutions exist, the one-dimensional planar-geometry simulations gave results that matched well with the analytical calculations. The qualitative features of the interface and its motion as found by the hydrodynamic simulations were similar to those obtained by the thin-shell simulations. Nevertheless, the physics of the internal flow was found to affect the performance of the thruster in ways not accountable by the thin-shell model. There were also implications that not all of the debris plasma may leave the thruster in one reflection. The substantial shock heating observed in the interfacial regions downstream of the inward-facing shock would help contribute towards maintaining high temperatures there for (possibly) achieving sufficient conductivities, provided the plasma stayed highly ionized. But because of the large expansion ratio experienced, the bulk temperature of an ICF debris plasma will fall below the ionization temperature from relatively early stages of expansion in the magnetic thrusters of currently proposed ICF pulse rockets, and the design parameters of these thrusters do not appear that promising. Because of memory limitations imposed by computers, the maximum expansion ratio treatable by the two-dimensional hydrodynamic codes was limited, and initial plasma states rather far removed from those typical of situations in proposed thrusters had to be employed. This also lowered the efficiency values quite notably. The ignorance of real plasma properties such as finite conductivities further rendered the results of this work very optimistic. However, the primary goal of this work, which was to acquire intuition for the bulk flow and performance under idealized conditions, was accomplished. Furthermore, techniques for handling this type of problem were developed. Future work should concentrate on treating more realistic parameters and on incorporating more precise plasma physics into the analysis, based on bulk flow results heretofore obtained.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/47t1-2f31, author = {Ruoff, Carl F.}, title = {Robotic hand-eye motor learning}, school = {California Institute of Technology}, year = {1993}, doi = {10.7907/47t1-2f31}, url = {https://resolver.caltech.edu/CaltechETD:etd-12052007-130729}, abstract = {This thesis investigates the use of neural networks and nonlinear estimation in robotic motor learning. It presents a detailed experimental investigation of the performance and parametric sensitivity of resource-allocating neural networks along with a new learning algorithm that offers rapid adaptation and excellent accuracy. It also includes an appendix that relates feed-forward neural networks to familiar mathematical ideas. In addition, it presents two learning hand-eye calibration systems, one based on neural networks and the other on nonlinear estimation. The network-based system learns to correct robot positioning errors arising from the use of nominal system kinematics, while the estimation-based system identifies the robot’s kinematic parameters. Both systems employ the same two-link robot with stereo vision, and include noise and various other error sources. The network-based system is robust to all error sources considered, though noise naturally limits performance. The estimation-based system has significantly better performance when the robot and vision systems are well modeled, but is extremely sensitive to unmodeled error sources and noise. Finally, it presents a robot control system based on neural networks that learns to catch balls perfectly without requiring explicit programming or conventional controllers. It uses only feed-forward pursuit motions learned through practice, and is initially incapable of even moving its arm in response to external stimuli. It learns to identify and control its pursuit movements, to identify and predict ball behavior, and, with the aid of advice from a critic, to modify its movement commands to improve catching success. The system, which incorporates information from visual, arm state, and drive force sensors, characterizes control situations using input/response pairs. This allows it to learn and respond to plant variations without requiring parametric models or parameter identification. It achieves robust execution by comparing predicted and observed behavior, using inconsistencies to trigger learning and behavioral change. The architectural approach, which involves both declarative and analog knowledge as well as short- and long-term memory, can be extended to learning other sensor-motor skills like mechanical assembly and synchronizing motor actions with external processes.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/ks5z-8e20, author = {Lee, Ho-Hoon}, title = {Robust adaptive control of manipulators with application to joint flexibility}, school = {California Institute of Technology}, year = {1992}, doi = {10.7907/ks5z-8e20}, url = {https://resolver.caltech.edu/CaltechETD:etd-08072007-073507}, abstract = {This thesis discusses the model-based adaptive trajectory control of commercial manipulators whose dynamics are well known with uncertainties confined to parameters. This thesis emphasizes the importance of the transient behavior as well as robust stability of a system and takes it into account in the design of adaptive control laws. The basic idea is to search for compensators in the direction of minimizing a quadratic performance index, and then analyze the stability and robustness of the selected compensators in the presence of bounded disturbances, sensor noises, and unmodelled dynamics. With this idea, centralized and decentralized adaptive control schemes are proposed for rigid-joint manipulators. Stability bounds for disturbances, control and adaptation gains, and desired trajectories and their time-derivatives are derived for the proposed schemes. These bounds are sufficient conditions for robust stability of the proposed schemes in the presence of unmodelled dynamics such as feedback delays in the digital control systems and the coupled dynamics in the decentralized scheme. A flexibility compensator is designed to treat the problem of joint flexibility. With the flexibility compensator, a manipulator having flexible joints is transformed to that having rigid joints with high-frequency dynamics of joint couplings representing unmodelled dynamics. In this way, control of flexible-joint manipulators is converted to that of the corresponding rigid-joint manipulators. Accordingly, the robust adaptive control schemes proposed for rigid-joint manipulators are applied. Then, through stability analysis, stability bounds for disturbances, control and adaptation gains, and desired trajectories and their time-derivatives are derived for the scheme with the flexibility compensator, in the presence of the unmodelled dynamics. Under the constraint of these bounds, the proposed adaptive scheme is not only almost independent of the gear-reduction ratios, flexibilities of joint couplings, and characteristics of actuators, but also free from the requirements of measuring angular accelerations and jerks of links.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/9KZS-XC46, author = {Jahnke, Craig C.}, title = {Application of dynamical systems theory to nonlinear aircraft dynamics}, school = {California Institute of Technology}, year = {1990}, doi = {10.7907/9KZS-XC46}, url = {https://resolver.caltech.edu/CaltechETD:etd-05092007-134504}, abstract = {A continuation method has been used to determine the steady states of three nonlinear aircraft models: a general aviation aircraft with a canard configuration, a generic jet fighter, and the F-14. The continuation method calculated the steady states of the aircraft as functions of the control surface deflections. Bifurcations of these steady states were determined and shown to cause instabilities which resulted in qualitative changes in the state of the aircraft. A longitudinal instability which resulted in a deep stall was determined for the general aviation aircraft. Roll-coupling and high angle of attack instabilities were determined for the generic jet fighter, and wing rock, directional divergence and high angle of attack instabilities were determined for the F-14.

Knowledge of the control surface deflections at which bifurcations occurred was used to either put limits on the control surface deflections or to program the control surface deflections such that a combination of control surface deflections at which bifurcations occur could not be attained. Simple control systems were included in the aircraft models to determine the effects of control systems on the instabilities of each aircraft. Steady spin modes were determined for each aircraft. A successful recovery technique was determined for the general aviation aircraft, but no successful recovery technique could be found for the F-14.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/chyb-nk54, author = {Beran, Philip Stewart}, title = {An Investigation of the Bursting of Trailing Vortices Using Numerical Simulation}, school = {California Institute of Technology}, year = {1989}, doi = {10.7907/chyb-nk54}, url = {https://resolver.caltech.edu/CaltechETD:etd-02012007-105641}, abstract = {Solutions of the Navier-Stokes equations are obtained for the flow of an isolated, trailing vortex, and for the swirling flow through a frictionless pipe. In both cases, the flow is assumed to be steady, incompressible and rotationally symmetric. Solutions are computed using Newton’s method and Gaussian elimination for a wide range of values of two parameters: Reynolds number, Re, and vortex strength, V. Pseudo-arclength continuation is employed to facilitate the computation of solution points in the parameter space. The numerical procedure is validated through comparison of solutions with solutions obtained in previous investigations for the case of a trailing vortex. Solutions are also compared with results reported by Brown and Lopez (1988) for the case of flow through a pipe.

Solutions of the quasi-cylindrical equations are obtained for the flow of a trailing vortex. Solutions are computed using an explicit, space-marching scheme, and are compared with solutions of the Navier-Stokes equations.

Provided that Re is about 200, or larger, four vortex states are observed.

- When V is sufficiently small, the flow is entirely supercritical.
- As V is increased, the flow at an axial station becomes critical and a transition point forms. At the point, the flow departs from an upstream state that is supercritical to a downstream state that is marked by large-amplitude, spatial oscillations of core radius. When Re is large, the downstream state is nearly periodic. The general features of transition are well described by the conjugate-flow theory of Benjamin 1967). Failure of the quasi-cylindrical equations is found to be a necessary and sufficient condition for the existence of a transition point. As V is further increased, the transition point moves upstream. Reversed flow is not observed.
- Over a narrow range of vortex strengths, a small bubble of reversed flow is observed downstream of the transition point.

- As V is increased, the flow at an axial station becomes critical and a transition point forms. At the point, the flow departs from an upstream state that is supercritical to a downstream state that is marked by large-amplitude, spatial oscillations of core radius. When Re is large, the downstream state is nearly periodic. The general features of transition are well described by the conjugate-flow theory of Benjamin 1967). Failure of the quasi-cylindrical equations is found to be a necessary and sufficient condition for the existence of a transition point. As V is further increased, the transition point moves upstream. Reversed flow is not observed.

4. When V is large, the entire flow is marked by large-amplitude, spatial oscillations of core radius. A transition point is not evident within the computational domain. Typically, large regions of reversed flow are observed.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/ZXQ4-SA60, author = {Humphrey, Joseph William, III}, title = {Linear and Nonlinear Acoustics with Nonuniform Entropy in Combustion Chambers}, school = {California Institute of Technology}, year = {1987}, doi = {10.7907/ZXQ4-SA60}, url = {https://resolver.caltech.edu/CaltechETD:etd-03032008-105855}, abstract = {A one-dimensional analytical model is presented for calculating the longitudinal acoustic modes of idealized “dump-type” ramjet engines. The geometry considered is the coaxial flow type with the inlet flow opening to the combustor at a simple dump plane. Since the frequencies are very low, the dominant modes are the one-dimensional longitudinal modes and allow the predictions to be extended to more complicated geometries (such as side dump combustors) with good success. A plane flame has been studied and incorporated into the combustor model where the flame is allowed to move or oscillate in the combustor. This provides three mechanisms of interaction at the flame sheet: change in mean temperature in the combustor, energy conversion at the sheet due to upstream fluctuations, and fluctuating heat release. A supersonic inlet upstream contains a shock wave in its diffuser section while the downstream exit is terminated by a choked nozzle. The linear coupling of the acoustic and entropy waves at the inlet shock, flame sheet, and exit nozzle along with acoustic admittances at the inlet and exit are combined to determine the stability of the system as well as the acoustic modes. Since the acoustic and entropy waves travel at different velocities, the geometry is a critical factor in determining stability. Typical values of the admittances will produce damped solutions when the entropy is neglected, but, as the ratio of the entropy to acoustic fluctuations is increased, the coupling can either feed acoustic energy into or out of different modes independently. This transfer of energy has a destabilizing or stabilizing effect on the acoustic modes of the system depending on the relative phases between the acoustic and entropy waves.

In the linear case, the entropy and acoustics are decoupled in the flow field. All linear coupling occurs at the boundary conditions. For cases where the entropy fluctuations are of the same order of magnitude as the pressure oscillations and the coupling is of comparable order, the linear stability of the acoustic field is strongly dependent upon the entropy fluctuations. The linear acoustics are predominantly governed by the boundary conditions; thus it is imperative that the entire system of inlet, combustor, and exit be considered together to determine the characteristic eigenvalues (resonant frequencies) and eigenfunctions (mode shapes). In addition, there are two modes of acoustic pressure oscillations: the classical acoustic mode and the entropy-induced mode of pressure oscillation. The nonlinear case treats the quadratic nonlinear fluid mechanic interactions in the coupling of two acoustic modes. The result is that the nonlinear acoustic-entropy interactions are much smaller than the acoustic-acoustic interactions for this case. Hence, the nonlinear acoustic field is influenced by the nonuniform entropy only by its dependence upon the linear solution which can be strongly dependent upon the entropy.

The energy in the acoustics of this model is controlled by the energy loss (gain) at the boundaries balanced with the energy gain (loss) at the flame front. Acoustic energy is typically lost at both the inlet and exit, but fluctuating entropy waves convecting with the mean flow velocity that impinge upon a choked nozzle generate acoustic waves that can, under the proper conditions, feed acoustic energy into the system. In addition, the Rayleigh condition for driving the system with a fluctuating heat release can also contribute to the stability of the system. The plane flame mechanism also contributes to the acoustic energy from the interaction of entropy and acoustic waves at a flame sheet. This allows a systematic study of the influence of entropy-acoustic wave interactions on the linear stability and modes of this combustor system.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/bfy8-1995, author = {Aaron, Kim Maynard}, title = {Edgetones and Acoustic Resonances in a Duct}, school = {California Institute of Technology}, year = {1985}, doi = {10.7907/bfy8-1995}, url = {https://resolver.caltech.edu/CaltechETD:etd-01222007-092606}, abstract = {

Undesirable sound generation in the combustion chamber of segmented solid propellant rocket motors has been attributed to vortex shedding from obstructions that are uncovered as the propellant burns back. This phenomenon has been investigated experimentally and the mechanism explained.

A pair of aluminum baffles within a lucite duct through which air is drawn models the important aspects which enable the sound generation mechanism to operate. The baffles form an edgetone system which interacts with the longitudinal acoustic modes of the chamber. Acoustic tones occur spontaneously, at frequencies determined by the acoustic resonances, when the spacing between the baffles satisfies certain criteria.

Flow visualization using smoke and a strobe light triggered by the pressure oscillations indicate that vortex shedding occurs at the first baffle in phase with the acoustic velocity oscillations there. The interaction of these vortices with the downstream baffle drives the acoustic resonance which, in turn, triggers the formation of new vortices at the upstream separation point.

The phase relations for this feedback to operate require that there be close to an integral number of wavelengths, or vortices, from the separation point to the impingement point.

A model has been developed which predicts the experimentally observed behaviour well. Pressure amplitudes are predicted within an order of magnitude. Mean flow rates and baffle spacings yielding maximum response are determined correctly by the model.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/rfpg-es59, author = {Yang, Vigor}, title = {Pressure Oscillations in Liquid-Fueled Ramjet Engines}, school = {California Institute of Technology}, year = {1984}, doi = {10.7907/rfpg-es59}, url = {https://resolver.caltech.edu/CaltechETD:etd-09052006-153951}, abstract = {Pressure oscillations in liquid-fueled ramjet engines have been studied both analytically and numerically within the low frequency range. We examine first the linear unsteady motions in coaxial-dump configurations. The flowfield in the dump combustor is approximated by division into three parts: a flow of reactants, a region containing combustion products, and a recirculation zone, separated by two infinitesimally thin sheets: the flame and the vortex sheets. The three zones are matched at these sheets by taking into account kinematic and conservation relations. The oscillatory field in the inlet is coupled to the field in the combustor at the dump plane to determine the complex frequencies characterizing the linear stability of the engine. Favorable comparison with the experimental data obtained at the California Institute of Technology has been obtained.

Numerical analysis has been applied to investigate the nonlinear behavior of the shock wave in the inlet diffuser. Both viscous effects and the influences of injecting fuel/air mixture are accounted for. The response of a shock wave to various disturbances, including finite and large amplitude oscillations, has been studied in detail. The results obtained serve as a basis for analyzing the stability characteristics of the inlet flow.

Numerical calculations have also been conducted for the pressure oscillations in side-dump ramjet engines. The flowfields have been constructed in two regions: the inlet section, including a region of fuel injection, and a dump combustor. Each region is treated separately and matched with the other at the dump plane. Following the calculation of the mean flowfield, the oscillatory characteristics of the engine are determined by its response to a disturbance imposed on the mean flow. Results for the frequencies and mode shapes have shown good agreement with the experimental data reported by the Naval Weapons Center, China Lake.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/h9sr-tq76, author = {Awad, Elias A.}, title = {Nonlinear Acoustics Instabilities in Combustion Chambers}, school = {California Institute of Technology}, year = {1983}, doi = {10.7907/h9sr-tq76}, url = {https://resolver.caltech.edu/CaltechETD:etd-12182006-131617}, abstract = {

In this report, we show, following a second order expansion in the pressure amplitude, analytical expressions for the amplitude, and the conditions for existence and stability of limit cycles for pressure oscillations in combustion chambers. Two techniques are used. The first technique is an asymptotic-perturbation technique where the asymptotic oscillatory behavior is sought by expanding the asymptotic solution in a measure of the amplitude of the wave, mainly the amplitude of the fundamental. The second technique is a perturbation-averaging technique where an approximate solution is sought by applying a perturbation method followed by an expansion of the solution in the normal modes of the acoustic field in the chamber. It is shown, to third order in the amplitude of the wave, that both techniques yield the same results regarding the amplitude and the conditions for existence and stability of the limit cycle. However, while the first technique can be extended to higher orders in the pressure amplitude, the second technique suffers serious difficulties. The advantage of the second technique is in its ability to handle easily a large number of modes.

A stable limit cycle seems to be unique. The conditions for existence and stability are found to be dependent only on the linear parameters. The nonlinear parameter affects only the wave amplitude. In very special cases, the initial conditions can change the stability of the limit cycle. The imaginary parts of the linear responses, to pressure oscillations, of the different processes in the chamber play an important role in the stability of the limit cycle. They also affect the direction of flow of energy among modes. In the absence of the imaginary parts, in order for an infinitesimal perturbation in the flow to reach a finite amplitude, the lowest mode must be unstable while the highest must be stable; thus energy flows from the lowest mode to the highest one. The same case exists when the imaginary parts are non-zero, but in addition, the contrary situation is possible. There are conditions under which an infinitesimal perturbation may reach a finite amplitude if the lowest mode is stable while the highest is unstable. Thus energy can flow “backward” from the highest mode to the lowest one. It is also shown that the imaginary parts increase the final wave amplitude.

Second, the triggering of pressure oscillations in solid propellant rockets is discussed. In order to explain the triggering of the oscillations to a non-trivial stable limit cycle, the treatment of two modes and the inclusion in the combustion response of either a second order nonlinear velocity coupling or a third order nonlinear pressure coupling seem to be sufficient. Moreover, some mechanisms which are likely to be responsible for triggering are identified.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/CAPG-QQ92, author = {Grossman, William Mark}, title = {Combustion of CS₂/O₂ in a laminar mixing layer and processes in the CO chemical laser}, school = {California Institute of Technology}, year = {1979}, doi = {10.7907/CAPG-QQ92}, url = {https://resolver.caltech.edu/CaltechTHESIS:07172014-104557879}, abstract = {

The combustion of CS₂ and O₂ in a free burning laminar mixing layer at low pressure was investigated using emission spectroscopy. The temperature fields, CO vibrational distributions, and CO concentrations were measured. The data indicate that vibration ally excited CO was produced in the mixing layer flames, but that there were no vibrational population inversions. In comparison with the CS₂/O₂ premixed flames, the mixing layer flames favored greater production of COS and CO₂. Computer modeling was used to study the mechanisms responsible for the production of COS and CO₂, and to study how the branching chain mechanism responsible for production of CO affects the behavior of the mixing layer flame. The influences of the gas additives, N₂O, COS, and CNBr, were also investigated.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/a9bz-sw68, author = {Kushner, Mark Jay}, title = {Electronic and kinetic processes in the Cu/CuCl double pulse laser}, school = {California Institute of Technology}, year = {1979}, doi = {10.7907/a9bz-sw68}, url = {https://resolver.caltech.edu/CaltechTHESIS:07172014-092719903}, abstract = {Kinetic and electronic processes in a Cu/CuCl double pulsed laser were investigated by measuring discharge and laser pulse characteristics, and by computer modeling. There are two time scales inherent to the operation of the Cu/CuCl laser. The first is during the interpulse afterglow (tens to hundreds of microseconds). The second is during the pumping pulse (tens of nanoseconds). It was found that the character of the pumping pulse is largely determined by the initial conditions provided by the interpulse afterglow. By tailoring the dissociation pulse to be long and low energy, and by conditioning the afterglow, one may select the desired initial conditions and thereby significantly improve laser performance. With a low energy dissociation pulse, the fraction of metastable copper obtained from a CuCl dissociation is low. By maintaining the afterglow, contributions to the metastable state from ion recombinations are prevented, and the plasma impedance remains low thereby increasing the rate of current rise during the pumping pulse. Computer models for the dissociation pulse, afterglow, pumping pulse and laser pulse reproduced experimentally observed behavior of laser pulse energy and power as a function of time delay, pumping pulse characteristics, and buffer gas pressure. The sensitivity of laser pulse properties on collisional processes (e.g., CuCl reassociation rates) was investigated.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/TR93-1793, author = {Magiawala, Kiran Ramanlal}, title = {Measurements of energy exchange between acoustic fields and non-uniform steady flow fields}, school = {California Institute of Technology}, year = {1978}, doi = {10.7907/TR93-1793}, url = {https://resolver.caltech.edu/CaltechETD:etd-10302006-154249}, abstract = {Study of the unsteady burning of solid propellants can be best carried out under widely varying conditions and at relatively inexpensive cost in a simple test device known as the T-burner. This simple configuration is used to observe the spontaneous growth and decay of oscillations. Knowing the losses involved in the system, one can infer the frequency response of the burning surface within the approximations of linearity. A significant undertainty in the interpretation of data taken with T-burners arises because very little has been known about some of the acoustics, in particular the influence of the exhaust vent. The present investigation is a study of the influence of a subsonic exhaust vent. The primary apparatus is a resonance tube operated at room temperature with different resonance frequencies of the first longitudinal mode of oscillation. Experiments have been done over ranges of the average Mach number of the flow in the resonance tube, and with vent having different sizes and shapes. According to the one-dimensional linear stability analysis, the attenuation constant associated with the influence of the exhaust vent is given by the product of four times the resonance frequency of oscillation times the average Mach number of the flow in the resonance tube. The following major conclusions were predicted and verified: (i) the vent produces a gain of acoustic energy proportional to the average Mach number of the flow in main resonance tube (ii) the gain is proportional to the frequency of the fundamental longitudinal mode (iii) the gain is independent of the shape and size of the vent. The influence of the exhaust vent, hence, cannot be neglected in the interpretation of T-burner data.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/8EH0-TH11, author = {Sovero, Emilio}, title = {Application of microwave diagnostics to copper chloride and carbon dioxide lasers}, school = {California Institute of Technology}, year = {1977}, doi = {10.7907/8EH0-TH11}, url = {https://resolver.caltech.edu/CaltechTHESIS:02182014-152349321}, abstract = {Part A

A problem restricting the development of the CuCl laser has been the decrease in output power with increases of tube temperature above 400°C. At that temperature the CuCl vapor pressure is about .1 torr. This is a small fraction of the buffer gas pressure (He at 10 torr).

The aim of the project was to measure the peak radiation temperature (assumed related to the mean energy of electrons) in the laser discharge as a function of the tube temperature. A 24 gHz gated microwave radiometer was used.

It was found that at the tube temperatures at which the output power began to deteriorate, the electron radiation temperature showed a sharp increase (compared with radiation temperature in pure buffer).

Using the above result, we have postulated that this sudden increase is a result of Penning ionization of the Cu atoms. As a consequence of this process the number of Cu atoms available for lasing decrease.

PART B

The aim of the project was to study the dissociation of CO_{2} in
the glow discharge of flowing CO_{2} lasers.

A TM_{011} microwave (3 gHz) cavity was used to measure the radially
averaged electron density n_{e} and the electron-neutral collision frequency
in the laser discharge. An estimate of the electric field is made
from these two measurements. A gas chromatograph was used to measure
the chemical composition of the gases after going through the discharge.
This instrument was checked against a mass spectrometer for
accuracy and sensitivity.

Several typical laser mixtures were .used: CO_{2}-N_{2}-He (1,3,16),
(1,3,0), (1,0,16), (1,2,10), (1,2,0), (1,0,10), (2,3,15), (2,3,0),
(2,0,15), (1,3,16)+ H_{2}O and pure CO_{2}. Results show that for the conditions
studied the dissociation as a function of the electron density
is uniquely determined by the STP partial flow rate of CO_{2}, regardless
of the amount of N_{2} and/or He present. The presence of water vapor in
the discharge decreased the degree of dissociation.

A simple theoretical model was developed using thermodynamic equilibrium. The electrons were replaced in the calculations by a distributed heat source.

The results are analyzed with a simple kinetic model.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/D6QA-YZ15, author = {Vetter, Alan August}, title = {Kinetics and Structure of the CS₂/O₂ Flame Laser}, school = {California Institute of Technology}, year = {1975}, doi = {10.7907/D6QA-YZ15}, url = {https://resolver.caltech.edu/CaltechETD:etd-01102007-131039}, abstract = {This thesis is a study of the interactions of chemical kinetics, relaxation processes, and low-speed fluid mechanics for the deflagration of gaseous carbon disulfide and oxygen under conditions for which laser action has been demonstrated. A four-reaction branching chain reaction mechanism is deduced from experimental evidence and reaction rates to represent the chemical kinetics of CS2/O2 combustion. This chain mechanism is used to explain some explosion phenomena and to obtain the initial conditions and initial chemical kinetics expected for the different types of CS2/O2 chemical lasers. The dynamics of chemical population and relaxation, including selective depopulation, of the vibrational levels of CO are discussed. Three analytical methods are employed to solve the premixed laminar flame problem for the CS2/O2 flame. The von Karman approximations and the thermal theory approximation are two of these methods; the third, which considers diffusion of only the chain carrier, is termed the single-species diffusion approximation. The flame speed, which is the eigenvalue of laminar flame propagation theories, was experimentally determined for the low-pressure CS2/O2 flame and compared to the magnitude and dependencies calculated by the analytic methods. Some qualitative measures of flame structure are compared to the calculated structure. Details are given for a multi-slit injector whose design allows complete control over mixing. Results for this burner and premixed configuration burners are discussed. CO emission spectra were taken from CS2/O2 flames and the relative vibrational populations determined. The rates of population of the upper vibrational levels are calculated from these experimental spectra.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, } @phdthesis{10.7907/J91E-7262, author = {Perry, Edward Harris}, title = {Investigations of the T-burner and its role in combustion instability studies}, school = {California Institute of Technology}, year = {1970}, doi = {10.7907/J91E-7262}, url = {https://resolver.caltech.edu/CaltechETD:etd-03312008-132130}, abstract = {

Of several devices introduced to study combustion instability in solid rocket propellants, one, known as the “T-burner,” has become the most widely used. With this device the response of a burning propellant to a small pressure disturbance can be measured. Such information is vital both to the understanding of unsteady combustion processes as well as to the assessment of the stability characteristics of solid rocket motors.

Although the T-burner has been used for several years, several questions concerning the device have arisen and, for the most part, have remained unanswered. Moreover, little effort has been given toward showing the relevance of T-burner data to predictions of instability in rocket motors.

The present investigations, comprising over 400 test firings in T-burners of various lengths and diameters, were undertaken with the major objective of gaining a better understanding of the T-burner itself in order to answer some of these unresolved questions. Another objective was to compare T-burner predictions of rocket motor instability with actual observations made in a previous study.

Among the investigations was a comparison of several ignition procedures which showed clearly that a poor, uneven ignition can seriously affect the test results. Included among the ignition studies were tests conducted in transparent chambers to permit high-speed motion photography of the firings. These tests confirmed the common assumption that the T-burner is basically a one-dimensional device.

Tests using burners of different diameters showed that although the acoustic losses of the T-burner are nearly independent of diameter, the limiting amplitude of the oscillations is strongly dependent on the latter. The dilemma raised by these observations was resolved by measurements which indicate that the heat transfer from the combustion gases to the burner wall is strongly dependent on the amplitude of the waves. From these measurements emerged a nonlinear description of the damping in the T-burner which accounts for both the behavior of the losses as well as that of the limiting amplitude.

When two independent T-burner methods were compared, the results obtained were initially in very poor agreement. However, when the T-burner losses were assumed to be non-linear as mentioned earlier, excellent agreement was observed.

Finally, the T-burner predictions of instability in rocket motors were in rather poor agreement with direct observations made in a previous study. Although this lack of agreement is not understood, it is doubtful in the light of the present investigations that the major error lies in the T-burner measurements, for these should be relatively accurate. Moreover, these results indicate the need for more comparisons of this type in order to determine the usefulness of the T-burner in predicting combustion instability in solid propellant rockets.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Culick, Fred E. C.}, }