[ { "id": "authors:zkd8s-x7v20", "collection": "authors", "collection_id": "zkd8s-x7v20", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121018-103119474", "type": "article", "title": "Spatial averaging combined with a perturbation/iteration procedure", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "A matter of increasing interest is finding the best way to integrate the use of powerful computational facilities with the traditional practices of analysis and related disciplines. This is largely a problem in research and development, rather than fabrication of machines, or even development of codes. There is little question that modern manufacturing, for example, cannot be accomplished competitively without computing machinery - in fact, the more the merrier. However, there is a fairly widespread sense that in areas depending on the development and applications of new ideas, and perhaps especially in education, the general emphasis has been skewed too much to rely excessively on computers.\nThis paper has been prepared partly to make the point with examples taken from the author's experiences with unsteady combustion. My claim here is that in many cases, analytical methods (necessarily approximate) offer a path often initially preferable to that presented by numerical methods, which in the cases at hand, mean computational fluid mechanics. The first simple example treated here is the Rijke tube, well known primarily for two reasons: The physical behavior is easy to produce, and for which data may be relatively easily collected; and the necessary analysis seems quite simple, at first glance. Some recently published experimental results will be cited, with an approximate theory based on the known differential equations for one-dimensional motions.\nThe next section is a brief historical summary of Galerkin's method, followed by several sections summarizing the manner in which it may be combined with a perturbation/iteration method to give an effective approximate method. The general approach has been widely used to analyze practical problems of combustion instabilities arising in development of operational systems. Thus a large part of the paper is a review of previously published material, but with considerable clarifications of points that have caused some confusion.\n\nThe paper ends with a brief discussion answering a serious criticism, of the method, nearly fifteen years old. The basis for the criticism, arising from solution to a relatively simple problem, is shown to be a result of an omission of a term that arises when the average density in a flow changes abruptly. Presently, there is no known problem of combustion instability for which the kind of analysis discussed here is not applicable. The formalism is general; much effort is generally required to apply the analysis to a particular problem.\nA particularly significant point, not elaborated here, is the inextricable dependence on expansion of the equations and their boundary conditions, in two small parameters, measures of the steady and unsteady flows. Whether or not those Mach numbers are actually 'small' in fact, is really beside the point. Work out applications of the method as if they were! Then maybe to get more accurate results, resort to some form of CFD. It is a huge practical point that the approach taken and advocated here cannot be expected to give precise results, but however accurate they may be, they will be obtained with relative ease and will always be instructive. In any case, the expansions must be carried out carefully with faithful attention to the rules of systematic procedures. Otherwise, inadvertent errors may arise from inclusion or exclusion of contributions.\nI state without proof or further examples that the general method discussed here has been quite well and widely tested for practical systems much more complex than those normally studied in the laboratory. Every case has shown encouraging results. Thus the lifetimes of approximate analyses developed before computing resources became commonplace seem to be very long indeed.", "doi": "10.1260/1756-8277.4.3.185", "issn": "1756-8277", "publisher": "Multi-Science Publishing", "publication": "International Journal of Spray and Combustion Dynamics", "publication_date": "2012-09", "series_number": "3", "volume": "4", "issue": "3", "pages": "185-216" }, { "id": "authors:qvmpv-6b830", "collection": "authors", "collection_id": "qvmpv-6b830", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KANcf09", "type": "article", "title": "Measurements of fuel mixture fraction oscillations of a turbulent jet non-premixed flame", "author": [ { "family_name": "Kang", "given_name": "D. M.", "clpid": "Kang-D-M" }, { "family_name": "Fernandez", "given_name": "V.", "clpid": "Fernandez-V" }, { "family_name": "Ratner", "given_name": "A.", "clpid": "Ratner-A" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "This work describes new type of combustion instability for which the 3-way coupling between mixing, flame heat release, and acoustics is modified by local buoyancy effects. Measurements of fuel mixture fraction are made for a non-premixed jet flame in a combustion chamber to assess the dynamics of mixing under imposed acoustic oscillations (22\u201355 Hz). Infrared laser absorption and phase resolved\nacetone-planar laser induced fluorescence are used to measure the fuel mixture fraction and then the\ndegree of fuel/air mixing is calculated by determining the unmixedness. Results show acoustic excitation causes oscillations in the degree of fuel/air mixing at the driving frequency, which results in oscillatory\nflame behavior. This oscillatory flame behavior couples to the buoyancy and this in turn affects the mixing. Results also show that the mixing becomes less effective when the excitation frequency is increased or when the flame is present, compared to the non-reacting case. This work describes a key coupling mechanism that occurs when buoyancy is a significant factor in the flow field.", "doi": "10.1016/j.combustflame.2008.07.008", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2009-01", "series_number": "1", "volume": "156", "issue": "1", "pages": "214-220" }, { "id": "authors:6v44v-qpf37", "collection": "authors", "collection_id": "6v44v-qpf37", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:SHUctm08", "type": "article", "title": "Limitation of the ZN approach for calculating the response function of homogeneous propellants", "author": [ { "family_name": "Shusser", "given_name": "M.", "clpid": "Shusser-M" }, { "family_name": "Cohen", "given_name": "N.", "clpid": "Cohen-N-S" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "This note compares the QSHOD (quasi-steady homogeneous one-dimensional) approach and the Zeldovich-Novozhilov (ZN) method for calculating the combustion response of solid propellants. The goal is to draw attention to a certain limitation on the applicability of the ZN method which appears to have been overlooked. It is shown that under certain conditions the ZN and QSHOD approaches produce different expressions for the combustion response function of homogeneous propellants, and the reason for this discrepancy is explained.", "doi": "10.1080/13647830802203846", "issn": "1364-7830", "publisher": "Taylor & Francis", "publication": "Combustion Theory and Modelling", "publication_date": "2008-12", "series_number": "6", "volume": "12", "issue": "6", "pages": "1049-1054" }, { "id": "authors:qrqne-mhn76", "collection": "authors", "collection_id": "qrqne-mhn76", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:SHUjpp08", "type": "article", "title": "Analytical Solution for Pressure-Coupled Combustion Response Functions of Composite Solid Propellants", "author": [ { "family_name": "Shusser", "given_name": "Michael", "clpid": "Shusser-M" }, { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Cohen", "given_name": "Norman S.", "clpid": "Cohen-N-S" } ], "abstract": "This paper extends the classical analytical solution for small perturbation analysis of the pressure-coupled response of a homogeneous propellant to any two-component composite propellant. The solution obtained is general and can be used with any particular model for propellant combustion. As an example, the Cohen and Strand ammonium perchlorate propellant model for a single ammonium perchlorate particle size was used in this work. The results and their mechanistic significance are presented and discussed. It is shown that, for a two-component composite propellant, two forms of pressure exponents arise from the analysis. The significance of the second exponent is that it enables the composite propellant to be viewed as a homogeneous propellant with a frequency-dependent exponent via the coupling coefficients. It is found that the ammonium perchlorate is the main source of instability because of its condensed phase exothermicity and monopropellant flame kinetics. This will be a problem with energetic materials in general. The inert binder provides a stabilizing influence because of its endothermicity and the diffusion flame formed with the ammonium perchlorate. Effects of ammonium perchlorate particle size and pressure stem from the changing flame structure and its effect on burning rate.", "doi": "10.2514/1.21502", "issn": "0748-4658", "publisher": "AIAA", "publication": "Journal of Propulsion and Power", "publication_date": "2008-09", "series_number": "5", "volume": "24", "issue": "5", "pages": "1058-1067" }, { "id": "authors:hef87-kjb93", "collection": "authors", "collection_id": "hef87-kjb93", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110207-072124993", "type": "article", "title": "Reduced-order modeling and dynamics of nonlinear acoustic waves in a combustion chamber", "author": [ { "family_name": "Ananthkrishnan", "given_name": "N.", "clpid": "Ananthkrishnan-N" }, { "family_name": "Deo", "given_name": "Shardul", "clpid": "Deo-S" }, { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "For understanding the fundamental properties of unsteady motions in combustion chambers, and for applications of active feedback control, reduced-order models occupy a uniquely important position. A framework exists for transforming the representation of general behavior by a set of infinite-dimensional partial differential equations to a finite set of nonlinear second-order ordinary\ndifferential equations in time. The procedure rests on an expansion of the pressure and velocity fields in modal or basis functions, followed by spatial averaging to give the set of second-order equations in time. Nonlinear gasdynamics\nis accounted for explicitly, but all other contributing processes require modeling. Reduced-order models of the global behavior of the chamber dynamics, most importantly of the pressure, are obtained simply by truncating the\nmodal expansion to the desired number of terms. Central to the procedures is a criterion for deciding how many modes must be retained to give accurate results. Addressing that problem is the principal purpose of this paper. Our\nanalysis shows that, in case of longitudinal modes, a first mode instability problem requires a minimum of four modes in the modal truncation whereas, for a second mode instability, one needs to retain at least the first eight modes. A second important problem concerns the conditions under which a linearly stable system becomes unstable to sufficiently large disturbances. Previous work has given a partial answer, suggesting that nonlinear gasdynamics alone cannot produce pulsed or 'triggered' true nonlinear instabilities; that suggestion is now theoretically established. Also, a certain form of the nonlinear energy\naddition by combustion processes is known to lead to stable limit cycles in a linearly stable system. A second form of nonlinear combustion dynamics with a new velocity coupling function that naturally displays a threshold character\nis shown here also to produce triggered limit cycle behavior.", "doi": "10.1080/00102200590900219", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "2005-02", "series_number": "2", "volume": "177", "issue": "2", "pages": "221-247" }, { "id": "authors:yx2m5-b8f06", "collection": "authors", "collection_id": "yx2m5-b8f06", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101130-144132487", "type": "article", "title": "Limit-Cycle Properties of a Rijke Tube", "author": [ { "family_name": "Matveev", "given_name": "K. I.", "clpid": "Matveev-K-I" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Thermoacoustic instability appears when unsteady heat release is favourably coupled with acoustic pressure perturbations. The important technical applications involving thermoacoustics are combustion instability in rocket motors and low-pollutant lean flames; noisy industrial burners; pulsed combustors; and thermoacoustic engines. The simplest device for studying thermoacoustic instability is a Rijke tube. In this work, a series of experiments is carried out to determine the nonlinear behavior of the transition to instability and the excited regimes for an electrically driven Rijke tube. A hysteresis effect in the stability boundary is observed. A mathematical theory involving heat transfer, acoustics, and thermoacoustic interactions is developed to predict the transition to instability and limit-cycle properties.", "issn": "1819-2408", "publisher": "East-European Acoustical Association (EEAA)", "publication": "Electronic Journal Technical Acoustics", "publication_date": "2003-12-06", "series_number": "12", "volume": "12", "issue": "12", "pages": "1-13" }, { "id": "authors:pzx59-1nh73", "collection": "authors", "collection_id": "pzx59-1nh73", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101118-102239874", "type": "article", "title": "A study of the transition to instability in a Rijke tube\n with axial temperature gradient", "author": [ { "family_name": "Matveev", "given_name": "K. I.", "clpid": "Matveev-K-I" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "A horizontal Rijke tube with an electric heat source is a system convenient for studying the fundamental\nprinciples of thermoacoustic instabilities both experimentally and theoretically. Given the long history of\nthe device, there is a surprising lack of accurate data defining its behavior. In this work, the main system\nparameters are varied in a quasi-steady fashion in order to find stability boundaries accurately. The chief\npurposes of this study are to obtain precise values of the system parameters at the transition to instability\nwith specified uncertainties and to determine how well the experimental results can be explained with\nexisting theory. Measurement errors are reported, and the influence of experimental procedures on the\nresults is discussed. A form of hysteresis effect at stability boundaries has been observed. Mathematical\nmodelling is based on a thermal analysis determining the temperature of the heater and the temperature\nfield in the air inside the tube, which, consequently, affects acoustical mode shapes. Solutions of the\nlinearized wave equation for a non-uniform medium, including losses and a heat source term, determine\nthe stability properties of the eigen modes. Calculated results are compared with experimental data and\nwith results of the modelling based on the common assumption of a constant temperature in the tube. The\nmathematical model developed here can be applied to designing thermal devices with low Mach number\nflows, where thermoacoustic issue is a concern.", "doi": "10.1016/S0022-460X(02)01217-8", "issn": "0022-460X", "publisher": "Elsevier", "publication": "Journal of Sound and Vibration", "publication_date": "2003-07-10", "series_number": "3", "volume": "264", "issue": "3", "pages": "689-706" }, { "id": "authors:mjnjq-4a740", "collection": "authors", "collection_id": "mjnjq-4a740", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CULaiaaj03", "type": "article", "title": "The Wright Brothers: First Aeronautical Engineers and Test Pilots", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Sir George Cayley invented the conventional configuration of the airplane at the turn of the 19th century. Otto Lilienthal realized that building a successful aircraft meant learning how to fly; he became the first hang glider pilot and also the first flight fatality in 1896. Beginning in the late 1890s, the Wright Brothers absorbed all that was known in aeronautics before them, then added their own discoveries and developed the first successful airplane. Technically, their greatest fundamental achievement was their invention of three-axis aerodynamic control. Less obviously, their success was a consequence of style, their manner of working out their ideas and of progressing systematically to their stunning achievements. They were indeed the first aeronautical engineers, understanding as best they could all aspects of their aircraft and flying. They were thinkers, designers, constructors, analysts, and especially flight-testpilots. Their powers of observation and interpretation of the behavior of their aircraft in flight were remarkable and essential to their development of the airplane. Their work in the period 1899\u20131905 constitutes the first true research and development program carried out in the style of the 20th century. As the centenary of their first powered flights approaches, the Wright Brothers' magnificent achievements excite growing admiration and respect for their achievements. The broad features of their accomplishments have long been well known. Only in the past two decades has serious attention been directed to the scientific and technical content of their work, to explain the nature of the problems they faced and how they solved them. After a century's progress in aeronautics, the principles, understanding,and methods not available to the Wrights provide the basis for interpreting in modern terms the experiences that the Wrights themselves documented so meticulously in their diaries, papers, and correspondence. It is a unique opportunity in the history of technology.", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "2003-06", "series_number": "6", "volume": "41", "issue": "6", "pages": "985-1006" }, { "id": "authors:ds7zq-f1520", "collection": "authors", "collection_id": "ds7zq-f1520", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101117-101453870", "type": "article", "title": "A model for combustion instability involving vortex shedding", "author": [ { "family_name": "Matveev", "given_name": "Konstantin I.", "clpid": "Matveev-K-I" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Vigorous burning of vortices, formed behind flame stabilizers, can drive significant pressure oscillations inside premixed-type combustors. The goal of this work is to derive a reduced-order model for interaction among vortex shedding, chamber acoustics, and combustion process. A dump combustor is considered a general system configuration. Formation of vortices at the sudden expansion in a chamber is affected by the oscillatory flow. A new quasi-steady model is proposed for determining the moment of vortex separation. Vortex burning is assumed to be localized in space and time. A \"kicked\" oscillator model is utilized for deriving the appropriate dynamical system. The moment of burning and the corresponding vortex location are dependent on the chamber geometry, velocity field, and characteristic chemical and hydrodynamic times. If Rayleigh's criterion is satisfied, acoustic waves can develop in the chamber. Model and experimental results are compared for a chosen configuration. A study of model performance for a realistic system is carried out by variation of parameters where the mean flow velocity and the number of modes are treated as variables.", "doi": "10.1080/00102200390201622", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "2003-06", "series_number": "6", "volume": "175", "issue": "6", "pages": "1059-1083" }, { "id": "authors:ghagg-sym58", "collection": "authors", "collection_id": "ghagg-sym58", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:SHUaiaaj02", "type": "article", "title": "Combustion Response of Ammonium Perchlorate", "author": [ { "family_name": "Shusser", "given_name": "Michael", "clpid": "Shusser-M" }, { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Cohen", "given_name": "Norman S.", "clpid": "Cohen-N-S" } ], "abstract": "A modified Price\u2013Boggs\u2013Derr model is applied to compute the linear and nonlinear combustion response properties of monopropellant ammonium perchlorate (AP). The kinetics constants were changed to achieve good agreement with response function data as well as with steady-state data.The numerical method was first validated with the classical theory. Computations using the Levine and Culick boundary condition in the limit of small perturbations were compared with the exact mathematical solution for linear response, and the effect of perturbation amplitude was explored. Then, using the AP model for the boundary condition, various linear and nonlinear computations were performed. Supplemental mathematical analyses relate the AP model to the basic two parameters of the classical theory and show the key factors determining the nature of the combustion response.", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "2002-04", "series_number": "4", "volume": "40", "issue": "4", "pages": "722-730" }, { "id": "authors:bgq8z-b0w37", "collection": "authors", "collection_id": "bgq8z-b0w37", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101118-082923771", "type": "article", "title": "Phase-Resolved NO Planar Laser-Induced Fluorescence of a Jet Flame in an Acoustic Chamber with Excitation at Frequencies <60Hz", "author": [ { "family_name": "Ratner", "given_name": "Albert", "clpid": "Ratner-A" }, { "family_name": "Pun", "given_name": "Winston", "clpid": "Pun-W" }, { "family_name": "Palm", "given_name": "Steven L.", "clpid": "Palm-S-L" }, { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The California Institute of Technology's Combustion Acoustics Facility is used to measure the changes in\nthe creation of NO in a partially premixed jet flame due to acoustic forcing at frequencies ranging from 22\nto 55 Hz. The facility generates bulk acoustic modes that simulate unstable combustor conditions in the\nabsence of velocity fluctuations. This facility and a similar burner have been previously used to measure\nthe phase-resolved response of the OH field. In this experiment, phase-resolved NO planar laser-induced\nfluorescence (PLIF) measurements are recorded. The location and phase coupling of the NO field are\nanalyzed, and the production and transport of NO are compared with previously reported OH field\nmeasurements. The NO levels increase for frequencies that exhibit stronger acoustic coupling to the flame.\nThe NO concentration variations with the phase of the chamber pressure lead the OH field variations. This\nis probably a result of the greater NO sensitivity to temperature.", "doi": "10.1016/S1540-7489(02)80015-3", "issn": "1540-7489", "publisher": "Elsevier", "publication": "Proceedings of the Combustion Institute", "publication_date": "2002", "series_number": "1", "volume": "29", "issue": "1", "pages": "85-90" }, { "id": "authors:b463z-x4c95", "collection": "authors", "collection_id": "b463z-x4c95", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:BURaiaaj00", "type": "article", "title": "Influence of Random Excitations on Acoustic Instabilities in Combustion Chambers", "author": [ { "family_name": "Burnley", "given_name": "V. S.", "clpid": "Burnley-V-S" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Although flows in combustors contain considerable noise, arising from several kinds of sources, there is a sound basis for treating organized oscillations as distinct motions. That has been an essential assumption incorporated in virtually all treatments of combustion instabilities. However, certain characteristics of the organized or deterministic motions seem to have the nature of stochastic processes. For example, the amplitudes in limit cycles always exhibit a random character, and even the occurrence of instabilities seems occasionally to possess some statistical features. Analysis of nonlinear coherent motions in the presence of stochastic sources is, therefore, an important part of the theory. We report a few results for organized oscillations in the presence of noise. The most significant deficiency is that, because of the low level of current understanding, the stochastic sources of noise are modeled in ad hoc fashion and are not founded on a solid physical basis appropriate to combustion chambers.", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "2000-08", "series_number": "8", "volume": "38", "issue": "8", "pages": "1403-1410" }, { "id": "authors:zemgy-3p820", "collection": "authors", "collection_id": "zemgy-3p820", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:BURjpp00", "type": "article", "title": "Comment on \"Triggering of Longitudinal Combustion Instabilities in Rocket Motors: Nonlinear Combustion Response\"", "author": [ { "family_name": "Burnley", "given_name": "V. S.", "clpid": "Burnley-V-S" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Triggering of oscillations in rocket motors is the subject of an ongoing investigation at the California Institute of Technology. Some issues that have been previously addressed in several recent publications by the authors [1-3] have more recently been examined by Wicker et al.[4] Whereas the latter paper provides a thorough investigation of the equations as derived, it apparently overlooks the possible effects of two key approximations that were used in the derivation of these equations. Some of the possible effects of these assumptions have been addressed previously, [3] and the authors suggest that the work by Wicker et al. might have benefited from our earlier and accessible conclusions.", "issn": "0748-4658", "publisher": "AIAA", "publication": "Journal of Propulsion and Power", "publication_date": "2000-01", "series_number": "1", "volume": "16", "issue": "1", "pages": "164-165" }, { "id": "authors:499eh-ewy57", "collection": "authors", "collection_id": "499eh-ewy57", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101118-135546896", "type": "article", "title": "On the Energy Transfer between Transverse Acoustic Modes in a Cylindrical Combustion Chamber", "author": [ { "family_name": "Burnley", "given_name": "Victor S.", "clpid": "Burnley-V-S" }, { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Most of the previous work on periodic limit cycles in linearly unstable combustors has been carried out for the case of purely longitudinal classical modes whose natural frequencies are integral multiples of the fundamental. The contrary situation of transverse modes in a cylindrical chamber has led to unexpectedly high amplitudes in the periodic limit cycles, the reasons for which have not been thoroughly understood. Some results reported here serve to clarify the two chief consequences of nonlinear coupling between modes: the first is obvious, for the nonlinear coupling causes excitation of higher modes, and hence energy transfer, when, say, the first mode is unstable; the second has long been known, namely that the coupling must also cause shifts of the frequencies from their linear non-integral values to the integral values required for a periodic limit cycle, but part of the significance of this property has been unclear. In particular, the necessity for the frequency shifts reduces the efficiency at which energy is transfered between modes and leads to higher amplitude oscillations. Our analysis shows that the larger are the differences of the linear frequencies from perfect integral values, the larger are the amplitudes in the limit cycle. These conclusions suggest a way to reduce the amplitudes of transverse oscillations, and examples are presented showing this possibility.", "doi": "10.1080/00102209908924195", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1999-09", "series_number": "1-6", "volume": "144", "issue": "1-6", "pages": "1-19" }, { "id": "authors:gxgb9-t6432", "collection": "authors", "collection_id": "gxgb9-t6432", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101118-151443293", "type": "article", "title": "A further Note on Active Control of Combustion instabilities Based on Hysteresis", "author": [ { "family_name": "Isella", "given_name": "G.", "clpid": "Isella-G" }, { "family_name": "Seywert", "given_name": "C.", "clpid": "Seywert-C" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Zukoski", "given_name": "E. E.", "clpid": "Zukoski-E-E" } ], "abstract": "Hysteretic behaviour, as found in the dump combustor facility at GALCIT, allows nonlinear\nactive control of the instability, demonstrated recently by Knoop et al. (1996). As in that work,\npulses of secondary fuel, based on a simple on/off control law, have been successfully used to\ndrive the transition between the two modes present in the hysteretic region, thereby reducing\nthe amplitude of the pressure oscillations with minimal use of fuel. In order to clarify the origin\nof the phenomenon, high speed shadowgraph images of the flowfield during the transition\nbetween 'unstable' and stable burning have been taken, showing distinctive features that may\nhelp in modeling the observed behaviour. A preliminary parametric study (type of injector,\nduration of pulses, type of secondary flow) has also been conducted, showing that the transition\ncan be obtained over a broad range of conditions.", "doi": "10.1080/00102209708935682", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1997-07", "series_number": "1-6", "volume": "126", "issue": "1-6", "pages": "381-388" }, { "id": "authors:fnhh3-r9t44", "collection": "authors", "collection_id": "fnhh3-r9t44", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140527-081613688", "type": "article", "title": "Flight on the Horizon: The Pivotal Year of 1896", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "In the stunning rush of inventions at the end of the 19th century, the year 1896 held events remarkably significant for the development of the airplane and aeronautics in the early part of the 20th century. The three major figures responsible for those pioneering aeronautical events were the German mechanical engineer Otto Lilienthal (1848-1896) and two Americans: Samuel P. Langley (1834-1906), a self-educated physicist and Secretary of the Smithsonian Institution, and Octave Chanute (1832-1910) an eminent\ncivil engineer best known for his participation in development of the railway system in the midwest United States but in 1896 devoting his energies almost totally to invention of the flying machine.", "doi": "10.2514/2.88", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1997-02", "series_number": "2", "volume": "35", "issue": "2", "pages": "217-218" }, { "id": "authors:rpzx7-99j64", "collection": "authors", "collection_id": "rpzx7-99j64", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101119-151322582", "type": "article", "title": "Some dynamics of acoustic oscillations with nonlinear combustion and noise", "author": [ { "family_name": "Burnley", "given_name": "V. S.", "clpid": "Burnley-V-S" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The results given in this paper constitute a continuation of progress with nonlinear analysis of coherent oscillations in combustion chambers. We are currently focusing attention on two general problems of nonlinear behavior important to practical applications: the conditions under which a linearly unstable system will execute stable periodic limit cycles; and the conditions under which a linearly stable system is unstable to a sufficiently large disturbance. The first of these is often called 'soft' excitation, or supercritical bifurcation; the second is called 'hard' excitation, 'triggering,' or subcritical bifurcation and is the focus of this paper. Previous works extending over more than a decade have established beyond serious doubt (although no formal proof exists) that nonlinear gasdynamics alone does not contain subcritical bifurcations. The present work has shown that nonlinear combustion alone also does not contain subcritical bifurcations, but the combination of nonlinear gasdynamics and combustion does. Some examples are given for simple models of nonlinear combustion of a solid propellant but the broad conclusion just mentioned is valid for any combustion system.\nAlthough flows in combustors contain considerable noise, arising from several kinds of sources, there is sound basis for treating organized oscillations as distinct motions. That has been an essential assumption incorporated in virtually all treatments of combustion instabilities. However, certain characteristics of the organized or deterministic motions seem to have the nature of stochastic processes. For example, the amplitudes in limit cycles always exhibit a random character and even the occurrence of instabilities seems occasionally to possess some statistical features. Analysis of nonlinear coherent motions in the presence of stochastic sources is therefore an important part of the theory. We report here a few results of power spectral densities of acoustic amplitudes in the presence of a subcritical bifurcation associated with nonlinear combustion and gasdynamics.", "issn": "2150-766X", "publisher": "Begell House", "publication": "International Journal of Energetic Materials and Chemical Propulsion", "publication_date": "1997", "series_number": "1+6", "volume": "4", "issue": "1+6", "pages": "998-1013" }, { "id": "authors:zkhrm-0cq30", "collection": "authors", "collection_id": "zkhrm-0cq30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101119-150022314", "type": "article", "title": "Extension of the Stability of Motions in a Combustion Chamber by Nonlinear Active Control Based on Hysteresis", "author": [ { "family_name": "Knoop", "given_name": "P.", "clpid": "Knoop-P" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Zukoski", "given_name": "E. E.", "clpid": "Zukoski-E-E" } ], "abstract": "Experimental results for instabilities in dump combustors have long shown the presence of some sort\nof hysteresis, in the vicinity of the stability boundary defined by flow speed and mixture ratio. This\nnote reports measurements of the precise character of hysteresis loops found when the mixture ratio\nis varied with flow speed held constant. The upper branch represents relatively high amplitude limit\ncycles and the lower branch contains low level oscillations possibly driven by stochastic sources\nwithin the chamber. Existence of the hysteresis loops suggests the possibility of causing a transition\nfrom the upper unstable branch to the lower stable branch. This has been accomplished by injecting\nshort pulses of secondary fuel either in the boundary layer upstream of the dump plane or in the\nrecirculation zone. Only a single pulse is required if its flow rate and width are suitably chosen. These\nresults demonstrate the feasibility of a novel method of active control of combustion instabilities if\nhysteresis is present, apparently the first example of true nonlinear control of combustor dynamics.\nThe main advantage is the small amount of secondary fuel required. More generally, this work\nillustrates the value, for active control, of understanding the dynamics of the uncontrolled system.", "doi": "10.1080/00102209708935635", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1997", "series_number": "1-6", "volume": "123", "issue": "1-6", "pages": "363-376" }, { "id": "authors:f9t7d-6re26", "collection": "authors", "collection_id": "f9t7d-6re26", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101118-150130234", "type": "article", "title": "A Note on Ordering Perturbations and the Insignificance of Linear Coupling in Combustion Instabilities", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Formal analysis of combustion instabilities has been based on expansion of the equations of motion in two small parameters, March numbers characterizing the average and fluctuating flows. The procedure is reviewed and extended in this note explain how new terms involving nonlinear mean flow/acoustic interactions may be incorporated. As a further example of the ordering procedure, the reasoning is given to show why coupling of modes, linear in the average March number, cannot legitimately be retained when the equations have been expanded only to first order in Mach number.", "doi": "10.1080/00102209708935681", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1997", "series_number": "1", "volume": "126", "issue": "1", "pages": "359-377" }, { "id": "authors:anqwm-vpa16", "collection": "authors", "collection_id": "anqwm-vpa16", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101122-080359296", "type": "article", "title": "A robust decoupled adaptive control of robots", "author": [ { "family_name": "Lee", "given_name": "Ho-Hoon", "clpid": "Lee-H-H" }, { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "A decoupled adaptive scheme is proposed for the trajectory control of robots.\nUnder moderate constraints, the scheme is stable and robust in the presence of\nfeedback delay and signal hold due to digital computation in the control loop.\nThe design procedure involves a search for compensators with the aim of\nminimizing a quadratic performance index in order to minimize the maximum\ntracking error. Stability analysis of the proposed control law (the selected\ncompensators) then provides stability bounds of disturbances, control and\nadaptation gains, and desired trajectories and their time-derivatives. The region\nof attraction is local due to unmodelled dynamics.", "doi": "10.1080/00207179508921905", "issn": "0020-7179", "publisher": "Taylor & Francis", "publication": "International Journal of Control", "publication_date": "1995-02", "series_number": "2", "volume": "61", "issue": "2", "pages": "309-331" }, { "id": "authors:0yk6p-xeq68", "collection": "authors", "collection_id": "0yk6p-xeq68", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101124-101555564", "type": "article", "title": "Application of dynamical systems theory to nonlinear combustion instabilities", "author": [ { "family_name": "Jahnke", "given_name": "Craig C.", "clpid": "Jahnke-C-C" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Two important approximations have been incorporated in much or the work with approximate analysis or\nunsteady motions in combustion chambers: 1) truncation of the series expansion to a finite number or modes,\nand 2) time-averaging. A major purpose or the present analysis is to investigate the limitations or those approximations.\nA continuation method Is used to determine the limit cycle behavior or the time-dependent\namplitudes or the longitudinal acoustic modes in a combustion chamber. The results show that time-averaging\nworks well only when the system Is slightly unstable. In addition, the stability boundaries predicted by the twomode\napproximation are shown to be artifacts of the truncation of the system. Systems of two, four. and six\nmodes are analyzed and show that more modes are needed to analyze more unstable systems. For the six-mode\napproximation with an unstable second-mode, two birurcations are found to exist: 1) a pitchfork bifurcation\nleading to a new branch of limit cycles, and 2) a torus bifurcation leading to quasiperiodic motions.", "issn": "0748-4658", "publisher": "American Institute of Aeronautics and Astronautics", "publication": "Journal of Propulsion and Power", "publication_date": "1994-07", "series_number": "4", "volume": "10", "issue": "4", "pages": "508-517" }, { "id": "authors:wxe51-w8b40", "collection": "authors", "collection_id": "wxe51-w8b40", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101123-102858346", "type": "article", "title": "Application of Bifurcation Theory to the High-Angle-of-Attack Dynamics of the F-14", "author": [ { "family_name": "Jahnke", "given_name": "C. C.", "clpid": "Jahnke-C-C" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Bifurcation theory has been used to study Ihe nonlinear dynamics of the F-14. An 8 degree-of-freedom model\nthat does not include the control system present in operational F-14's has been analyzed. The aerodynamic\nmodel, supplied by NASA, includes nonlinearlties as functions of the angles of attack and sideslip, the rotation\nrate about the velocity vector, and the elevator deflection. A continuation method has been used to calculate\nthe steady states of the F -14 as continuous functions of the elevator deflection. Bifurcations of these steady states\nhave been used to predict the onset of wing rock, spiral divergence, and jump phenomena that cause the aircraft\nto enter a spin. A simple feedback control system was designed to eliminate the wing rock and spiral divergence\ninstabilities. The predictions were verified with numerical simulations.", "issn": "0021-8669", "publisher": "American Institute of Aeronautics and Astronautics", "publication": "Journal of Aircraft", "publication_date": "1994-01", "series_number": "1", "volume": "31", "issue": "1", "pages": "26-34" }, { "id": "authors:baerr-sen06", "collection": "authors", "collection_id": "baerr-sen06", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101123-094949189", "type": "article", "title": "Some Recent Results for Nonlinear Acoustics in Combustion Chambers", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "N/A", "doi": "10.2514/3.11962", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1994-01", "series_number": "1", "volume": "32", "issue": "1", "pages": "146-169" }, { "id": "authors:skxde-6xn90", "collection": "authors", "collection_id": "skxde-6xn90", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101123-141347474", "type": "article", "title": "Design of robust adaptive control law for robotic manipulators", "author": [ { "family_name": "Lee", "given_name": "Ho-Hoon", "clpid": "Lee-H-H" }, { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "In this article, a robust adaptive control scheme for robotic manipulators is designed based on the concept of performance index and Lyapunov's second method. Compensators are selected for a given feedback system by using a quadratic performance index. Then the stability of the system is proven based on Lyapunov's method, where a Lyapunov function and its time-derivative are derived from the selected compensators. In the process of stabilization, stability bounds are obtained for disturbances, control gains, adaptation gains, and desired trajectories, in the presence of feedback delay due to digital computation and first-order hold in the control loop.", "doi": "10.1002/rob.4620110402", "issn": "0741-2223", "publisher": "Wiley", "publication": "Journal of Robotic Systems", "publication_date": "1994", "series_number": "4", "volume": "11", "issue": "4", "pages": "241-255" }, { "id": "authors:h3dcj-91x40", "collection": "authors", "collection_id": "h3dcj-91x40", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101129-102843529", "type": "article", "title": "The role of non-uniqueness in the development of vortex breakdown in tubes", "author": [ { "family_name": "Beran", "given_name": "Philip S.", "clpid": "Beran-P-S" }, { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Numerical solutions of viscous, swirling flows through circular pipes of constant radius and circular pipes with throats have been obtained. Solutions were computed for several values of vortex circulation, Reynolds number and throat/inlet area ratio, under the assumptions of steady flow, rotational symmetry and frictionless flow at the pipe wall. When the Reynolds number is sufficiently large, vortex breakdown occurs abruptly with increased circulation as a result of the existence of non-unique solutions. Solution paths for Reynolds numbers exceeding approximately 1000 are characterized by an ensemble of three inviscid flow types: columnar (for pipes of constant radius), soliton and wavetrain. Flows that are quasi-cylindrical and which do not exhibit vortex breakdown exist below a critical circulation, dependent on the Reynolds number and the throat/inlet area ratio. Wavetrain solutions are observed over a small range of circulation below the critical circulation, while above the critical value, wave solutions with large regions of reversed flow are found that are primarily solitary in nature. The quasi-cylindrical (QC) equations first fail near the critical value, in support of Hall's theory of vortex breakdown (1967). However, the QC equations are not found to be effective in predicting the spatial position of the breakdown structure.", "doi": "10.1017/S0022112092002477", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "1992-09", "volume": "242", "pages": "491-527" }, { "id": "authors:9smk2-sxz94", "collection": "authors", "collection_id": "9smk2-sxz94", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101130-073713187", "type": "article", "title": "Triggering of Longitudinal Pressure Oscillations in\n Combustion Chambers. I: Nonlinear Gasdynamics", "author": [ { "family_name": "Yang", "given_name": "V.", "clpid": "Yang-V" }, { "family_name": "Kim", "given_name": "S. I.", "clpid": "Kim-S-I" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Based on spatial and temporal averaging of the conservation equations, an approximate analysis\nprovides a convenient vehicle for analyzing the nonlinear behavior of unsteady motions in combustion\nchambers. Recent work has been concerned with the conditions for existence and stability of limit cycles,\nand in particular their dependence on the order of nonlinear terms contained in the equations of motion.\nIt seems to be generally true that if only nonlinear gasdynamic terms to second order are accounted for,\na stable nontrivial limit cycle is unique. This implies that no initial disturbance will cause a linearly stable\nsystem to execute a limit cycle, a result contrary to prior experience with, for example, solid propellant\nrocket motors. In this paper, we study some conditions under which true nonlinear instabilities may be\nfound, with special attention focused on the effect of nonlinear gasdynamics. Our results indicate that\nthird-order terms in the acoustic motions do not lead to triggering to either a stable or an unstable limit\ncycle; they only modify the stability domain of the system. However, the interactions between mean flow\nand nonlinear acoustic waves may trigger a linearly stable system to an unstable limit cycle. The influence\nof nonlinear combustion response may have quite different consequences and will be discussed in Part II\nof this work.", "doi": "10.1080/00102209008951647", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1990", "series_number": "4-6", "volume": "72", "issue": "4-6", "pages": "183-214" }, { "id": "authors:mz0vn-rkr22", "collection": "authors", "collection_id": "mz0vn-rkr22", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101129-110317027", "type": "article", "title": "On the Existence and Stability of Limit Cycles for Transverse Acoustic Oscillations in a Cylindrical Combustion Chamber. 1: Standing Modes", "author": [ { "family_name": "Yang", "given_name": "Vigor", "clpid": "Yang-V" }, { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Nonlinear pressure oscillations in combustion chambers have been studied using an approximate analysis which treats the unsteady motions as a collection of coupled nonlinear oscillators, each corresponding to an acoustic mode of the chamber. Based on spatial and temporal averaging of the\nconservation equations, the formulation provides a convenient means for analyzing the nonlinear behavior\nof acoustic wave motions. The work addresses the linear and nonlinear characteristics of transverse acoustic waves in a cylindrical chamber, with attention focused on the conditions for the existence and stability of limit cycles. As a result of the special structure of the equations, both general and precise conclusions can be reached. Explicit results are given for the special cases of two and three standing modes.\nSpinning wave motions will be treated in a subsequent paper.", "doi": "10.1080/00102209008951639", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1990", "series_number": "1-3", "volume": "72", "issue": "1-3", "pages": "37-65" }, { "id": "authors:ysjdz-81515", "collection": "authors", "collection_id": "ysjdz-81515", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101203-081753345", "type": "article", "title": "The Two-Mode Approximation to Nonlinear Acoustics in Combustion Chambers. I. Exact Solution for Second Order Acoustics", "author": [ { "family_name": "Paparizos", "given_name": "Leonidas G.", "clpid": "Paparizos-Leonidas-G" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The behavior of unsteady pressure fluctuations in combustion chambers is examined. An approximate method used in the derivation of the amplitude equations is based on the spatial and time domain averaging of the conservation equations, and follows the analytical framework introduced by Culick (1976a,b). The first order perturbation terms retained in the analysis correspond to linear contributions\nfrom the combustion processes, gas/particle interactions, mean flow and boundary conditions, as well as second order nonlinear gas dynamics terms. Further simplification of these equations is obtained by an appropriate change of variables. Following this step, the analysis based on two longitudinal modes is reduced to the solution of a three-dimensional system of nonlinear equations. This enables derivation of exact results for the existence, stability and the amplitude of the limit cycle, in the general case of frequency shifted periodic oscillations. Consideration is also given to the transfer of energy within the spectrum of the acoustic modes. In agreement with experimental observations, it is shown analytically that the preferred\ndirection of energy transfer is from the lower to the higher acoustic modes. Validation of the results is\naccomplished by comparison with numerical results obtained when higher numbers of modes are treated. Finally, it is shown that combustion instabilities can be treated analytically using the center manifold theory.", "doi": "10.1080/00102208908924041", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1989-05", "series_number": "1-3", "volume": "65", "issue": "1-3", "pages": "39-65" }, { "id": "authors:bswjy-65617", "collection": "authors", "collection_id": "bswjy-65617", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101202-151716445", "type": "article", "title": "A Note on Rayleigh's Criterion", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "N/A", "doi": "10.1080/00102208708947087", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1987", "series_number": "4-6", "volume": "56", "issue": "4-6", "pages": "159-166" }, { "id": "authors:wem0g-sqw98", "collection": "authors", "collection_id": "wem0g-sqw98", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101201-085332901", "type": "article", "title": "Longitudinal Combustion Instabilities in Ramjet Engines:\n Identification of Acoustic Modes", "author": [ { "family_name": "Crump", "given_name": "James E.", "clpid": "Crump-J-E" }, { "family_name": "Schadow", "given_name": "Klaus C.", "clpid": "Schadow-K-C" }, { "family_name": "Yang", "given_name": "Vigor", "clpid": "Yang-V" }, { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Longitudinal combustion instabilities in liquid-fueled ramjet engines have been investigated with attention\nfocused on determination of the acoustic mode structures. Detailed pressure measurements, including both amplitude and phase, were made at ten positions spanning the length of the engine. The experimental data have been analyzed using two linear acoustic models. Four distinct modes were observed for various inlet/combustor combinations. These results help identify the mechanisms exciting low-frequency pressure oscillations in ramjet engines.", "issn": "0748-4658", "publisher": "AIAA", "publication": "Journal of Propulsion and Power", "publication_date": "1986-03", "series_number": "2", "volume": "2", "issue": "2", "pages": "105-109" }, { "id": "authors:x8qsk-hk764", "collection": "authors", "collection_id": "x8qsk-hk764", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101201-083223351", "type": "article", "title": "On the Existence and Stability of Limit Cycles for\n Longitudinal Acoustic Modes in a Combustion Chamber", "author": [ { "family_name": "Awad", "given_name": "E.", "clpid": "Awad-E" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Unsteady motions in combustion chambers have previously been treated with an approximate analysis in which an acoustic field is represented as a collection of coupled nonlinear oscillators constructed in one-to-one correspondence to the acoustic modes. Two parameters\ncharacterize the linear behavior of each oscillator; a single parameter arises from the nonlinear acoustics carried out to second order in small fluctuations. The formal results are used here as the basis for studying the existence and stability of limit cycles for longitudinal modes. Owing to the special structure of the equations, explicit and precise conclusions can be reached. Existence\nand stability depend only on the parameters defining the linear motions. The nonlinear gasdynamics influence the amplitudes of motion in the limit cycle. At least one of the acoustic modes must be linearly unstable to produce a nontrivial limit cycle. Generally, energy flows both up and down among the modes, but there are exceptional cases when limit cycles exist only if the fundamental mode is unstable. Explicit results are given for the special cases of two and three modes; the analysis is extendible to any number of modes.", "doi": "10.1080/00102208608959800", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1986", "series_number": "3-6", "volume": "46", "issue": "3-6", "pages": "195-222" }, { "id": "authors:hg7kr-3zy11", "collection": "authors", "collection_id": "hg7kr-3zy11", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110125-143851324", "type": "article", "title": "Analysis of unsteady inviscid diffuser flow with a shock wave", "author": [ { "family_name": "Yang", "given_name": "V.", "clpid": "Yang-V" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "A finite difference scheme with a shock-fitting algorithm has been used to investigate unsteady inviscid now\nwith a shock in an inlet diffuser. The flowfield consists of three different regions: the supersonic and the subsonic\nregions, and a region containing both air and liquid fuel droplets, separated by a normal shock wave and a\nfuel injection system. The analysis is based on a two-phase, quasi-one-dimensional model. The response of a\nshock wave to various disturbances has been studied, including large-amplitude periodic oscillations and pulse\nperturbations.", "issn": "0748-4658", "publisher": "American Institute of Aeronautics and Astronautics", "publication": "Journal of Propulsion and Power", "publication_date": "1985", "series_number": "3", "volume": "1", "issue": "3", "pages": "222-228" }, { "id": "authors:xyxx9-h6n68", "collection": "authors", "collection_id": "xyxx9-h6n68", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101208-111845159", "type": "article", "title": "The Response of Normal Shocks in Diffusers", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Rogers", "given_name": "T.", "clpid": "Rogers-T" } ], "abstract": "The frequency response of a normal shock in a diverging channel is calculated for application to problems of\npressure oscillations in ramjet engines. Two limits of a linearized analysis arc discussed: one represents isentropic\nflow on both sides of a shock wave; the other may be a crude appr'l'I;imation to the influence of flow separation\ninduced hy the wave. Numerical results arc given, and the influences of the shock wave on oscillations in the\nengine are discus,ed.", "doi": "10.2514/3.60147", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1983-10", "series_number": "10", "volume": "21", "issue": "10", "pages": "1382-1390" }, { "id": "authors:vp90y-a2g80", "collection": "authors", "collection_id": "vp90y-a2g80", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101209-093924977", "type": "article", "title": "An experimental investigation of pure tone generation by vortex shedding in a duct", "author": [ { "family_name": "Nomoto", "given_name": "H.", "clpid": "Nomoto-H" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "An experimental investigation has been carried out for acoustic oscillations sustained by flow through a duct containing two baffles. Pure acoustic tones corresponding to longitudinal resonant modes of the duct are produced when certain flow and geometrical conditions are satisfied. The conditions are such as to ensure close coincidence between the frequency of vortex shedding from the forward baffle, and a natural frequency of the duct. Flow visualization has shown that under these conditions a stable vortex structure exists between the baffles, containing at all times an integral number of vortices.", "doi": "10.1016/S0022-460X(82)80007-2", "issn": "0022-460X", "publisher": "Elsevier", "publication": "Journal of Sound and Vibration", "publication_date": "1982-09-22", "series_number": "2", "volume": "84", "issue": "2", "pages": "247-252" }, { "id": "authors:4ejc4-xxa73", "collection": "authors", "collection_id": "4ejc4-xxa73", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KUSjap81", "type": "article", "title": "Electron collision quenching of CO(v) chemiluminescence in CS2/O2 and CS2/O2/N2O flames", "author": [ { "family_name": "Kushner", "given_name": "M. J.", "clpid": "Kushner-M-J" }, { "family_name": "Grossman", "given_name": "W. M.", "clpid": "Grossman-W-M" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Chemiluminescence from vibrationally excited carbon monoxide formed by the reaction CS+O-->CO(v)+S was observed in CS2/O2 and CS2/O2/N2O flames to which an electric discharge was applied. Although the total amount of chemiluminescence increased with increasing discharge current probably due to enhanced reaction rates as a result of radical formation, the vibrational distribution was quenched, becoming thermal in character. The thermalization is attributed to superelastic electron collisions [e+CO(v)-->e+CO(v\u22121)]. The technique demonstrates a sensitive method for detecting collisional transfers between excited states by separating the perturbation (electron collisions) from the initial excitation mechanism (chemical reactions).", "doi": "10.1063/1.329215", "issn": "0021-8979", "publisher": "Journal of Applied Physics", "publication": "Journal of Applied Physics", "publication_date": "1981-06-01", "series_number": "6", "volume": "52", "issue": "6", "pages": "3776-3779" }, { "id": "authors:k616g-5d484", "collection": "authors", "collection_id": "k616g-5d484", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101209-102019799", "type": "article", "title": "Measurements of energy exchange between acoustic fields and non-uniform steady flow fields", "author": [ { "family_name": "Magiawala", "given_name": "K. R.", "clpid": "Magiawala-K-R" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "This paper describes an experimental investigation of interactions between acoustic\nwaves and a non-uniform steady flow field. Data have been obtained for a resonance tube\nhaving a vent at the center in the lateral boundary, an average flow being introduced at the\nends. Experiments have been done for both circular and slot vents, over ranges of both\nfrequency and Mach number. According to the one-dimensional linear stability analysis,\nthe interactions between the longitudinal acoustic field and the mean flow in the vicinity of\nthe vent cause a net transfer of acoustic energy from the average flow to the acoustic field.\nThis result has been verified by the experiments reported here. The gain of energy\nmeasured is less than that deduced from a one-dimensional analysis.", "doi": "10.1016/0022-460X(81)90438-7", "issn": "0022-460X", "publisher": "Elsevier", "publication": "Journal of Sound and Vibration", "publication_date": "1981-04-22", "series_number": "4", "volume": "75", "issue": "4", "pages": "503-517" }, { "id": "authors:bqqcw-yzs49", "collection": "authors", "collection_id": "bqqcw-yzs49", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KUSjap80", "type": "article", "title": "A model for the dissociation pulse, afterglow, and laser pulse in the Cu/CuCl double pulse laser", "author": [ { "family_name": "Kushner", "given_name": "M. J.", "clpid": "Kushner-M-J" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "A model which completely describes the Cu/CuCl double pulse laser is presented. The dissociation discharge pulse and afterglow are simulated and the results are used as initial conditions for an analysis of the pumping discharge pulse and laser pulse. Experimental behavior including the minimum, optimum, and maximum delays between pulses, and the dependence of laser pulse energy on dissociation energy are satisfactorily reproduced. An optimum tube temperature is calculated, and the dependence of laser pulse energy on tube temperature (i.e., CuCl vapor pressure) is explained for the first time.", "doi": "10.1063/1.328088", "issn": "0021-8979", "publisher": "Journal of Applied Physics", "publication": "Journal of Applied Physics", "publication_date": "1980-06-01", "series_number": "6", "volume": "51", "issue": "6", "pages": "3020-3032" }, { "id": "authors:8mche-bq346", "collection": "authors", "collection_id": "8mche-bq346", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KUSieeejqe80", "type": "article", "title": "Characteristics of the pumping pulse and the output laser pulse for a Cu/CuCl double pulse laser", "author": [ { "family_name": "Kushner", "given_name": "M. J.", "clpid": "Kushner-M-J" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Characteristics of the pumping discharge pulse and laser pulse in a Cu/CuCl double pulse laser have been measured as a function of time delay, buffer gas pressure, and tube temperature. We have found that for otherwise fixed discharge conditions, pumping rates decrease as these quantities are increased. The shape of the laser pulse as a function of time delay is shown to be dependent on the rate of current rise of the pumping pulse. The length of time required by the pumping pulse to achieve threshold is found to be a function of time delay, buffer gas pressure, and tube temperature. The implications of this behavior for the role of metastable copper and its mode of relaxation are discussed.", "issn": "0018-9197", "publisher": "IEEE Journal of Quantum Electronics", "publication": "IEEE Journal of Quantum Electronics", "publication_date": "1980-06-01", "series_number": "6", "volume": "16", "issue": "6", "pages": "677-682" }, { "id": "authors:j1j4z-6hv06", "collection": "authors", "collection_id": "j1j4z-6hv06", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101208-101900961", "type": "article", "title": "A model for the dissociation pulse, afterglow, and laser pulse in the Cu/CuCI double pulse laser", "author": [ { "family_name": "Kushner", "given_name": "M. J.", "clpid": "Kushner-M-J" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "A model which completely describes the Cu/CuCI double pulse laser is presented. The dissociation discharge pulse and afterglow are simulated and the results are used as initial\nconditions for an analysis of the pumping discharge pulse and laser pulse. Experimental behavior including the minimum, optimum, and maximum delays between pulses, and the dependence of laser pulse energy on dissociation energy are satisfactorily reproduced. An optimum tube temperature is calculated, and the dependence of laser pulse energy on tube temperature (i.e., CuCI vapor pressure) is explained for the first time.", "doi": "10.1063/1.328088", "issn": "0021-8979", "publisher": "American Institute of Physics", "publication": "Journal of Applied Physics", "publication_date": "1980-06-01", "series_number": "6", "volume": "51", "issue": "6", "pages": "3020-3032" }, { "id": "authors:xx761-2fp28", "collection": "authors", "collection_id": "xx761-2fp28", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KUSieeejqe79", "type": "article", "title": "A continuous discharge improves the performance of the Cu/CuCl double pulse laser", "author": [ { "family_name": "Kushner", "given_name": "M. J.", "clpid": "Kushner-M-J" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "A continuous glow discharge was applied to a Cu/CuCl double pulse laser. Maximum laser pulse energy was observed to increase as much as 35 percent at low buffer gas pressure and 3.5 percent at optimum buffer gas pressure. Minimum and optimum time delays decreased with increasing glow discharge current. The greater pulse energy may be due to increased rate of current rise of the pumping discharge pulse, and decreased contribution to the population of metastable copper from ion recombination.", "issn": "0018-9197", "publisher": "IEEE Journal of Quantum Electronics", "publication": "IEEE Journal of Quantum Electronics", "publication_date": "1979-09-01", "series_number": "9", "volume": "15", "issue": "9", "pages": "835-837" }, { "id": "authors:15066-zwv15", "collection": "authors", "collection_id": "15066-zwv15", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101213-084217131", "type": "article", "title": "Excitation of acoustic modes in a chamber by vortex shedding", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Magiawala", "given_name": "K.", "clpid": "Magiawala-K" } ], "abstract": "Large solid propellant rocket motors are conveniently assembled with segmented grains.\nThe interfaces of the grains are coated with inert, slow-burning material. As the propellant\nburns radially during a firing, the inert material is exposed in the form of annular rings\noriented normal to the axis of the chamber. The flow through a ring will produce periodic\nshedding of vortices over a broad range of conditions.", "doi": "10.1016/0022-460X(79)90591-1", "issn": "0022-460X", "publisher": "Elsevier", "publication": "Journal of Sound and Vibration", "publication_date": "1979-06-08", "series_number": "3", "volume": "64", "issue": "3", "pages": "455-457" }, { "id": "authors:kvgjh-eka52", "collection": "authors", "collection_id": "kvgjh-eka52", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101213-074304929", "type": "article", "title": "The Origins of the First Powered, Man-carrying Airplane", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The Wright brothers' \"Flyer\" of 1903 was not just a lucky effort by two bicycle mechanics from Dayton but the outcome of an intensive program of research, engineering and testing", "doi": "10.1038/scientificamerican0779-86", "issn": "0036-8733", "publisher": "Scientific American", "publication": "Scientific American", "publication_date": "1979", "series_number": "1", "volume": "241", "issue": "1", "pages": "86-100" }, { "id": "authors:9kj87-2kc67", "collection": "authors", "collection_id": "9kj87-2kc67", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KUSapl78", "type": "article", "title": "Extrema of electron density and output pulse energy in a CuCl/Ne discharge and a Cu/CuCl double-pulsed laser", "author": [ { "family_name": "Kushner", "given_name": "M. J.", "clpid": "Kushner-M-J" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Electron-density measurements have been made in a CuCl/Ne discharge using a CO2 laser interferometer. A local maximum followed by a local minimum in electron density have been found to move a higher tube temperature with higher buffer pressure. Extrema in Cu/CuCl double-pulsed laser energy may be correlated with the extrema in electron density. An analysis based on rate equations yields qualitative agreement with measured laser-pulse energies. The results support the idea that ionization of copper is primarily responsible for the decrease of laser output as the tube temperature is increased.", "doi": "10.1063/1.90518", "issn": "0003-6951", "publisher": "American Institute of Physics", "publication": "Applied Physics Letters", "publication_date": "1978-10-15", "series_number": "8", "volume": "33", "issue": "8", "pages": "728-731" }, { "id": "authors:tap91-xnz70", "collection": "authors", "collection_id": "tap91-xnz70", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101210-120127838", "type": "article", "title": "Thermal Theory Approximation to a Low-Pressure CS_2/O_2 Flame", "author": [ { "family_name": "Vetter", "given_name": "A. A.", "clpid": "Vetter-A-A" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "A one-dimensional thermal theory is applied to a low-pressure, laminar, premixed, CS_2/O_2 flame. The\nspatial distribution of the species concentrations and rate of production of carbon monoxide are calculated.\nThe flame speed is calculated as a function of the initial O_2/CS_2 ratio at a pressure of 1 kPa.", "doi": "10.1016/0010-2180(78)90058-5", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "1978", "series_number": "2", "volume": "33", "issue": "2", "pages": "169-177" }, { "id": "authors:dyknv-4j546", "collection": "authors", "collection_id": "dyknv-4j546", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:VETjcp77", "type": "article", "title": "Rate of population of CO(v) in a CS2/O2 flame", "author": [ { "family_name": "Vetter", "given_name": "A. A.", "clpid": "Vetter-A-A" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The rate of vibrational population of carbon monoxide in a steady CS2/O2 flame has been determined from CO overtone emission. A steady-state analysis indicates that, for a flame, the fifteenth vibrational level has the largest rate of population.", "doi": "10.1063/1.435065", "issn": "0021-9606", "publisher": "Journal of Chemical Physics", "publication": "Journal of Chemical Physics", "publication_date": "1977-09-01", "series_number": "5", "volume": "67", "issue": "5", "pages": "2304-2308" }, { "id": "authors:shqd2-5md72", "collection": "authors", "collection_id": "shqd2-5md72", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101213-112042239", "type": "article", "title": "Rate of population of CO(v) in a CS_2/O_2 flame", "author": [ { "family_name": "Vetter", "given_name": "A. A.", "clpid": "Vetter-A-A" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The rate of vibrational population of carbon monoxide in a steady CS_2/O_2 flame has been determined\nfrom CO overtone emission. A steady-state analysis indicates that, for a flame, the fifteenth vibrational\nlevel has the largest rate of population.", "doi": "10.1063/1.435065", "issn": "0021-9606", "publisher": "American Institute of Physics", "publication": "Journal of Chemical Physics", "publication_date": "1977-09-01", "series_number": "5", "volume": "67", "issue": "5", "pages": "2304-2308" }, { "id": "authors:1yvnh-ysx22", "collection": "authors", "collection_id": "1yvnh-ysx22", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101213-105529799", "type": "article", "title": "Role of Condensed Phase Details in the Oscillatory Combustion of Composite Propellants", "author": [ { "family_name": "Kumar", "given_name": "R. N.", "clpid": "Kumar-R-N" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The response functions of composite propellants are theoretically derived, including explicitly the pressure-dependent degradation term in the condensed phase, hypothesizing that the overall rate-limiting reactions are in the relatively low temperature condensed phase. The method of \"inner\" and \"outer\" expansions with the reduced activation energy as the singular perturbation parameter has been employed. The results cover subsurface reactions with and without surface reactions, adiabatic and uniform-combustion models for the quasisteady gas phase processes. The response functions display several experimentally observed features like dependence on mean pressure and the instability behavior of some \"zero-n\" propellants.", "doi": "10.1080/00102207708946783", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1977", "series_number": "5", "volume": "15", "issue": "5", "pages": "179-199" }, { "id": "authors:5nt82-g1y85", "collection": "authors", "collection_id": "5nt82-g1y85", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101210-102405671", "type": "article", "title": "Flame Speed of a Low Pressure CS_2/O_2 Flame", "author": [ { "family_name": "Vetter", "given_name": "A. A.", "clpid": "Vetter-A-A" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The flame speed for a low speed premixed CS_2/O_2 flame has been experimentally determined as a function of O_2/CS_2 ratio. The data, which are given in Fig. 1, were taken for lean flames at 1 kPa, under conditions which are similar to those found in flame lasers.", "doi": "10.1016/0010-2180(77)90055-4", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "1977", "series_number": "1", "volume": "30", "issue": "1", "pages": "107-109" }, { "id": "authors:c37ym-e0t82", "collection": "authors", "collection_id": "c37ym-e0t82", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101214-075406344", "type": "article", "title": "Remarks on Entropy Production in the One-Dimensional Approximation to Unsteady Flow in Combustion Chambers", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "N/A", "doi": "10.1080/00102207708946774", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1977", "series_number": "3", "volume": "15", "issue": "3", "pages": "93-97" }, { "id": "authors:tbjnj-f7w02", "collection": "authors", "collection_id": "tbjnj-f7w02", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:SOVjap76", "type": "article", "title": "Electron temperature measurements in a copper chloride laser utilizing a microwave radiometer", "author": [ { "family_name": "Sovero", "given_name": "Emilio", "clpid": "Sovero-E" }, { "family_name": "Chen", "given_name": "Che Jen", "clpid": "Chen-C-J" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The electron temperature as a function of laser tube temperature of a copper vapor laser utilizing copper chloride as a lasant has been obtained by measuring the microwave incoherent radiation from the plasma in the laser tube. An unexpected increase of electron temperature at higher laser tube temperature may be due mainly to Penning ionization of the Cu atom by the metastable state of He or Ne buffer gases. The results obtained in this work provide part of the basis for understanding the behavior of the laser output as a function of tube temperature.", "doi": "10.1063/1.322426", "issn": "0021-8979", "publisher": "Journal of Applied Physics", "publication": "Journal of Applied Physics", "publication_date": "1976-10-10", "series_number": "10", "volume": "47", "issue": "10", "pages": "4538-4542" }, { "id": "authors:5ac3z-2m661", "collection": "authors", "collection_id": "5ac3z-2m661", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CULieeejqe76", "type": "article", "title": "Acoustic waves and heating due to molecular energy transfer in an electric discharge CO laser", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Shen", "given_name": "P. I.", "clpid": "Shen-P-I" }, { "family_name": "Griffin", "given_name": "W. S.", "clpid": "Griffin-W-S" } ], "abstract": "This paper summarizes analytical studies and the interpretation of experimental results for the compression and rarefaction waves generated in the cavity of a pulsed CO electric discharge laser. A one-dimensional analysis of acoustic waves is applied to a transversely excited laser. The influences of heating in the cathode fall, heat transfer to the cathode, flow through both the anode and cathode, and bulk heating of the plasma are included. The analysis is used to relate the bulk heating rate to observable features of the pressure and density waves. Data obtained from interferograms and reported elsewhere are used to infer the bulk heating rates in a pulsed CO laser. Results are presented for CO/Ar, CO/N2, and N2 plasmas. Comparison of the data with recent theoretical results for the heating due to electron/ neutral collisions and the anharmonic defect associated with V-V energy transfer shows substantial differences at lower values of total energy deposition. The change of heating with E/N is in fairly good agreement with predicted values.", "issn": "0018-9197", "publisher": "IEEE Journal of Quantum Electronics", "publication": "IEEE Journal of Quantum Electronics", "publication_date": "1976-10", "series_number": "10", "volume": "12", "issue": "10", "pages": "566-574" }, { "id": "authors:j19ye-0xt38", "collection": "authors", "collection_id": "j19ye-0xt38", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101217-103254887", "type": "article", "title": "Nonlinear behavior of acoustic waves in combustion chambers\u2014II", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The approximate analysis developed in Part I of Ihis work is apllied to severa1 specific problems. One purpose is to illustrate the use of the formalism, and second is to demostrate the validity of the method by comparing results with numerical solutions, obtained elsewhere, for the\n\"exact\" equations. A simple problem is treated first, the decay of a standing wave in a box containing a mixture of gas and suspended particles; one example of the steepening of an initially sinusoidal wave in pure gas is included. Viscous losses on an inert surface are treated essentially according to classical linear theory; recent experimental results are used as the basis for incorporating approximately the influence of nonlinear heat transfer in unsteady flow. All of the preceding results are combined in\ncalculations of two examples of unstable motions in a solid propellant rocket motor and in a T-burner.", "doi": "10.1016/0094-5765(76)90108-9", "issn": "0094-5765", "publisher": "Elsevier", "publication": "Acta Astronautica", "publication_date": "1976-09", "series_number": "9-10", "volume": "3", "issue": "9-10", "pages": "735-757" }, { "id": "authors:7gm2f-ary87", "collection": "authors", "collection_id": "7gm2f-ary87", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101217-100432116", "type": "article", "title": "Nonlinear behavior of acoustic waves in combustion chambers\u2014I", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "This paper is concerned with the general problem of the nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber. The analysis is intended to provide a formal framework within which practical problems can be treated with a minimum of effort and expense. There are broadly three parts. First, the general conservation equations are expanded in two small parameters, one characterizing the mean flow field and one measuring the amplitude of oscillations, and then combined to yield a nonlinear inhomogeneous wave equation. Second, the unsteady pressure and velocity fields are expressed as syntheses of the normal modes of the chamber, but with unknown time-varying amplitudes. This procedure yields a representation of a general unsteady field as a system of coupled nonlinear oscillators. Finally, the system of nonlinear equations is treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. These must be solved numerically, but results can be obtained quite inexpensively.\n\nSubject to the approximations used, the analysis is applicable to any combustion chamber. The most interesting applications are probably to solid rockets, liquid rockets, or thrust augmentors on jet engines. The discussion of this report is oriented towards solid propellant rockets.", "doi": "10.1016/0094-5765(76)90107-7", "issn": "0094-5765", "publisher": "Elsevier", "publication": "Acta Astronautica", "publication_date": "1976", "series_number": "9", "volume": "3", "issue": "9", "pages": "715-734" }, { "id": "authors:hcfva-nfy18", "collection": "authors", "collection_id": "hcfva-nfy18", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101216-154702705", "type": "article", "title": "Stability of Three-Dimensional Motions in a Combustion Chamber", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The problem oflinearized three-dimensional motions in a non-uniform flowfield is re-examined. Several modifications of the general analysis are effected: The influence of particulate matter is acounted for, to zeroth order,\nand certain boundary processes treated in earher one-dimensional computations are incorporated in an analysis\napplicable to any geometry. All processes occurring in combustion chambers are accommodated. As a specific\nexample, the results are applied to a problem of linear stability in solid propellant rocket motors.", "doi": "10.1080/00102207508946663", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1975-03", "series_number": "3", "volume": "10", "issue": "3", "pages": "109-124" }, { "id": "authors:0bw5s-ycx61", "collection": "authors", "collection_id": "0bw5s-ycx61", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101216-110120321", "type": "article", "title": "Measurements of Wall Heat Transfer in the Presence of Large-Amplitude Combustion-Driven Oscillations", "author": [ { "family_name": "Perry", "given_name": "E. H.", "clpid": "Perry-E-H" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Two independent methods were used to measure the rate of heat transfer from a hot gas to the walls of\na cylindrical combustion chamber in which large-amplitude combustion-driven oscillations accompanied a mean\nflow. The results obtained from the two methods were in good agreement and indicated a definite increase in the heat\ntransfer in the presence of oscillations. The increase was found to vary approximately as the square root of the\noscillation amplitude and as the fourth root of the frequency. A correlation in terms of dimensionless variables\nwas obtained using the thickness of the acoustic boundary layer as the appropriate length scale.", "doi": "10.1080/00102207408960336", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1974", "series_number": "1/2", "volume": "9", "issue": "1/2", "pages": "49-53" }, { "id": "authors:0kxt9-z8s13", "collection": "authors", "collection_id": "0kxt9-z8s13", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101216-101742743", "type": "article", "title": "Influence of Mechanical Properties on the Combustion of Propellants", "author": [ { "family_name": "Kumar", "given_name": "R. N.", "clpid": "Kumar-R-N" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "This work is aimed at experimentally exploring the effects of minor compositional variables upon the combustion behavior of composite solid propellants. More specifically, it is intended to determine the influence, if any, of ingredients that improve the mechanical properties upon the oscillatory combustion characteristics. Tests are carried out in the familiar Crawford bomb, a low-pressure L^* burner, and a high-pressure T-burner. Two families of propellants are investigated; each family consists of two propellants with a minor compositional variation between them. In the family that shows a decreasing (steady state) pressure index (n) with increasing pressures, all of the combustion characteristics are found to be very similar although the mechanical properties are widely different. In the other family, which shows an increasing n with increasing pressures, unmistakable differences\nare found between the two propellants in the low-pressure L ^* instability behavior (along with the differences in the\nmechanical properties), while the other combustion characteristics are almost identical. The results are interpreted to be consistent with a theory that highlights the importance of condensed phase heat-transfer effects.", "doi": "10.1080/00102207308946638", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1973-12", "series_number": "4", "volume": "8", "issue": "4", "pages": "149-158" }, { "id": "authors:5qehg-b4c15", "collection": "authors", "collection_id": "5qehg-b4c15", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101214-143437599", "type": "article", "title": "The Stability of One-Dimensional Motions in a Rocket Motor", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The problem of linearized one-dimensional motions in a non-uniform flow field is re-examined. Earlier\nwork is clarified, and some assumptions previously used are relaxed. The formalism accommodates all processes\noccurring in combustion chambers, including sources of mass, momentum, and energy at the lateral boundary.\nThe work is intended partly to provide some results required for subsequent analyses of linear and nonlinear\nthree-dimensional unsteady motions.", "doi": "10.1080/00102207308952355", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1973-06", "series_number": "4", "volume": "7", "issue": "4", "pages": "165-175" }, { "id": "authors:fwwyx-y4q07", "collection": "authors", "collection_id": "fwwyx-y4q07", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101214-084430395", "type": "article", "title": "Non-Linear Growth and Limiting Amplitude of Acoustic Oscillations in Combustion Chambers", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Due to non-linear loss or gain of energy, unstable oscillations in combustion chambers cannot grow\nindefinitely. Very often the limiting amplitudes are sufficiently low that the wave motions appear to be sinusoidal without discontinuities. The analysis presented here is based on the idea that the gasdynamics throughout most of the volume can be handled in a linear fashion. Non-linear behavior is associated with localized energy losses,\nsuch as wall losses and particle attenuation, or with the interaction between the oscillations and the combustion\nprocesses which sustain the motions. The formal procedure describes the non-linear growth and decay of an\nacoustic mode whose spatial structure does not change with time. Integration of the conservation equations over\nthe volume of the chamber produces a single non-linear ordinary differential equation for the time-dependent\namplitude of the mode. The equation can be solved easily by standard techniques, producing very simple results\nfor the non-linear growth rate, decay rate, and limiting amplitude. Most of the treatment is developed for unstable\nmotions in solid propellant rocket chambers. Other combustion chambers can be represented as special cases\nof the general description.", "doi": "10.1080/00102207108952266", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1971-04", "series_number": "1", "volume": "3", "issue": "1", "pages": "1-16" }, { "id": "authors:v4y3v-phc49", "collection": "authors", "collection_id": "v4y3v-phc49", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101220-152647813", "type": "article", "title": "Stability of Longitudinal Oscillations with Pressure and Velocity Coupling in a Solid Propellant Rocket", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Of the various unstable motions observed in solid propellant rocket chambers, the most troublesome\ncurrently are those involving oscillatory motions parallel to the axis. Such instabilities are found to arise particularly\nin larger rockets using propellants which contain aluminum. The problem is formulated here in one-dimensional\nform and solved for the case of small amplitude standing waves. Both pressure and velocity coupling\nmay be accommodated, although the proper description of the response function for velocity coupling is not yet\nknown. In addition to several special cases, the stability boundary is discussed for a straight chamber having\nvariable cross section. The influences of the mean flow field, the nozzle, particulate matter, and motions of the solid propellant grain are taken into account.", "doi": "10.1080/00102207008952247", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1970-12", "series_number": "4", "volume": "2", "issue": "4", "pages": "179-201" }, { "id": "authors:w6nfz-5kq31", "collection": "authors", "collection_id": "w6nfz-5kq31", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101221-134757282", "type": "article", "title": "An Elementary Calculation for the Burning Rate of Composite Solid Propellants", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Dehority", "given_name": "G. L.", "clpid": "Dehority-G-L" } ], "abstract": "A calculation of the burning rate for a composite solid propellant is based on a model in which the distribution of combustion in the gas phase is specified. The formulation of the problem can accommodate an arbitrary distribution, but only the simplest case of uniform combustion is treated here. An inverse numerical computation is carried out, as the magnitude of the reaction rate, and its dependence on pressure, are calculated for several specified burning rates. Simultaneously, flame stand-off distances and thicknesses are determined as part of the solution. The numerical results for those characteristics of the flame appear to be comparable to observed values. However, the principal value of this treatment of the problem is due to the ease with which one can study and understand the influence of the various physical properties and combustion characteristics.", "doi": "10.1080/00102206908952200", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1969-11", "series_number": "3", "volume": "1", "issue": "3", "pages": "193-204" }, { "id": "authors:h44mt-3ed44", "collection": "authors", "collection_id": "h44mt-3ed44", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101221-094400998", "type": "article", "title": "Remarks on Extinguishment and the Response Function for a Burning Solid Propellant", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1969-07", "series_number": "7", "volume": "7", "issue": "7", "pages": "1403-1404" }, { "id": "authors:smap0-srt32", "collection": "authors", "collection_id": "smap0-srt32", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101221-083201081", "type": "article", "title": "T-Burner Data and Combustion Instability in Solid Propellant Rockets", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Perry", "given_name": "E. H.", "clpid": "Perry-E-H" } ], "abstract": "It has long been a cherished hope of some people that\nmeasurements of unsteady burning in the laboratory\nshould be applicable to the very important practical problem\nof instabilities in a rocket chamber. In this Note, we wish\nto describe what appears to be the first experimental verification\nof this idea.", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1969-06", "series_number": "6", "volume": "7", "issue": "6", "pages": "1204-1205" }, { "id": "authors:rs2xp-5rv69", "collection": "authors", "collection_id": "rs2xp-5rv69", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101221-114030246", "type": "article", "title": "Combustion instability of solid propellants", "author": [ { "family_name": "Beckstead", "given_name": "M. W.", "clpid": "Beckstead-M-W" }, { "family_name": "Mathes", "given_name": "H. B.", "clpid": "Mathes-H-B" }, { "family_name": "Price", "given_name": "E. W.", "clpid": "Price-E-W" }, { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Experimental data has been obtained from two T-burners and an L^* burner over a range of frequencies from 10 cps to 8000 cps and from 25 psia to 1000 psia. From these data the\nresponse of the propellants to a pressure perturbation has been calculated and has been found to be consistent between burners. The results have been interpreted as a response function surface with burning rate and frequencies as independent variables. The data indicates that for a given pressure level the response function has a peak value at a frequency that increases as pressure increases. The magnitude of this peak height varies with pressure so that there is a localized peak in the response function surface for a given propellant. The results are in qualitative\nagreement with theoretical studies in that the models also predict a maximum value in the response function. However, they also predict that this magnitude should be approximately a constant and not dependent on the pressure and frequency to the extent observed in the present study. The results obtained for an aluminized propellant indicate that presence of metal in the combustion zone greatly influences both the magnitude of the response function\npeak as well as its location.", "doi": "10.1016/S0082-0784(69)80404-2", "issn": "0082-0784", "publisher": "Elsevier", "publication": "Symposium (International) on Combustion", "publication_date": "1969", "series_number": "1", "volume": "12", "issue": "1", "pages": "203-211" }, { "id": "authors:zkn1r-8sg04", "collection": "authors", "collection_id": "zkn1r-8sg04", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101221-102902637", "type": "article", "title": "An Elementary Calculation of the Combustion of Solid Propellants", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "An Elementary Calculation of the Combustion of Solid Propellants. The problem of the burning\nof a solid propellant is treated in an approximate manner by prescribing the spatial distribution of energy\nrdease in the gas phase. Adoption of this inverse approach converts the usual non-linear problem to a\nlinear eigenvalue problem which is easily solvable. Results for concentrated combustion (a flame front)\nand special cases of distributed energy release are given. Qualitative aspects such as flame stand-off distance,\nflame thickness, and various components of heat transfer within the combustion region are clearly shown.\nExamination of the influence of energy loss by radiation from the solid-gas interface gives satisfactory\nagreement with previous computations based on the non-linear formulation. An application to the problem\nof unsteady burning, and the response to pressure fluctuations is discussed briefly. The ease with which\nuseful results can be obtained seems to justify the imperfect nature of the analysis.", "issn": "0004-6205", "publisher": "Pergamon Press", "publication": "Astronautica Acta", "publication_date": "1969", "series_number": "2", "volume": "14", "issue": "2", "pages": "171-181" }, { "id": "authors:c5464-1fy88", "collection": "authors", "collection_id": "c5464-1fy88", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101223-101546101", "type": "article", "title": "A review of calculations for unsteady burning of a solid propellant", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1968-12", "series_number": "12", "volume": "6", "issue": "12", "pages": "2241-2255" }, { "id": "authors:d60yj-m4n73", "collection": "authors", "collection_id": "d60yj-m4n73", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101222-075221402", "type": "article", "title": "Calculation of the Admittance Function for a Burning Surface", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Calculation of the Admittance Function for a Burning Surface. A thorough analysis of pressure\noscillations in a solid propellant rocket requires specification of the response of the burning solid. Indeed,\nfor the case of small amplitude waves, this is the most crucial aspect of the problem; unfortunately, it is also\npoorly understood. The admittance function is merely a convenient expression of the response which\ncontains the primary mechanism for driving waves. In the work reported here, the usual one-dimensional\napproximation is made, and three main regions are distinguished: the solid phase being heated, the solid\nphase involving decomposition (a thin region near the surface), and the gas phase. The problem reduces\nsimply to the solution of appropriate ordinary differential equations and satisfaction of boundary conditions,\nwhich include matching at interfaces.\nThe most significant differences from previous work are incorporation of a decomposition region and the\ntreatment of the gas phase. A greatly simplified analysis of the latter leads essentially to the same results\nfound elsewhere, but with substantially less labor. Only a quasistatic analysis, valid for frequencies less than\na few thousand cycles per second, is covered, but it can be extended to higher frequencies.\nLaboratory measurements have shown that the response consists generally of a single peak in the range\nof frequency for which the quasi static approximation appears to be accurate. The qualitative aspects of\nsuch peaks, and their connection with 'self-excited' oscillations, are discussed. In particular, the influence\nof decomposition and pressure sensitivity of the various chemical reactions is examined. Limited numerical\nresults are included.\nEventually, the aim of calculations is principally to gain some understanding of the unsteady combustion\nprocess and to aid in classifying propellants. The regions involved in the burning are separately characterized\nby a small number of dimensionless groups. It appears that the effects represented by these parameters\nmay be distinguished in the response function; one may therefore be able, by use of experimental results,\nto determine at least qualitative connections between the response to pressure oscillations and changes\nof composition. In this regard, observations made in both T -burners and L * burners should prove useful.", "issn": "0004-6205", "publisher": "Pergamon Press", "publication": "Astronautica Acta", "publication_date": "1967", "series_number": "3", "volume": "13", "issue": "3", "pages": "221-237" }, { "id": "authors:zsdrv-33c07", "collection": "authors", "collection_id": "zsdrv-33c07", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110103-101232276", "type": "article", "title": "Acoustic oscillations in solid propellant rocket chambers", "author": [ { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Acoustic Oscillations in Solid Propellant Rocket\nChambers. Among the various kinds of periodic motions\nobserved in rocket combustion chambers, the most\ncommon and simplest to analyze are those related to\nclassical acoustic modes. If the amplitudes are small,\nthe main perturbations of the familiar standing or\ntravelling waves in a closed chamber are proportional\nto the Mach number of the mean flow. The correct\nequations describing the problem are here obtained from\nthe general equations of motion by a limit process which\nwill also provide equations for studying waves of finite\namplitude. Subsequently, a single non-homogeneous\nwave equation is deduced, and solved by an iteration\u00b7\nperturbation procedure. The principal result is a simple\nformula for the complex frequency showing explicitly\nthe effects of burning, suspended particles in the gases,\nthe exhaust nozzle, and viscous wall forces as well as\nthe mean flow itself. The last is particularly interesting\nsince, owing primarily to the flow inward from the\nburning surface, the mean flow, if it is irrotational,\nnever acts to damp modes which do not involve axial\noscillations. As a particular application, the extensive\ndata taken by BROWNLEE and MARBLE are interpreted\nto the extent that the linear analysis permits. A stability\nboundary was obtained from 250 firings of small cylindrical\nrockets, the principal variables being initial port\ndiameter and length. The propellant did not contain\nmetal particles, and it appears that the observations\ncannot be explained by the supposition that viscous\ndamping associated with particles in the product gases\nwas the main source of energy loss. Apparently dissipation\nat the head end, such as that associated with tangential\nwall shear forces, was an important loss. On the other\nhand, there is little doubt that if the combustion produces\nparticles, the consequent dissipation is adequate\nto damp small amplitude waves.", "issn": "0004-6205", "publisher": "Springer-Verlag", "publication": "Astronautica Acta", "publication_date": "1966", "series_number": "2", "volume": "12", "issue": "2", "pages": "113-126" }, { "id": "authors:5t4ef-jp130", "collection": "authors", "collection_id": "5t4ef-jp130", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110103-102744600", "type": "article", "title": "Rotational axisymmetric mean flow and damping of acoustic waves in a solid propellant rocket", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1966", "series_number": "8", "volume": "4", "issue": "8", "pages": "1462-1464" }, { "id": "authors:1n2qc-2pb97", "collection": "authors", "collection_id": "1n2qc-2pb97", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110103-100121099", "type": "article", "title": "Remarks on acoustic oscillations in a solid propellant rocket", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1966", "series_number": "6", "volume": "4", "issue": "6", "pages": "1120-1121" }, { "id": "authors:vjq4a-1j348", "collection": "authors", "collection_id": "vjq4a-1j348", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CULpof64", "type": "article", "title": "Boltzmann equation applied to a problem of two-phase flow", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "A limiting case of the interaction between particles in a viscous fluid is described by a linear form of Boltzmann's equation. The distribution function, f(v), is found for small particles falling under the action of gravity and viscous drag, and colliding with large particles. Several approximate procedures for computing f(v) and the connection with flows of gases containing solid particles are examined.", "doi": "10.1063/1.1711098", "issn": "0031-9171", "publisher": "Physics of Fluids", "publication": "Physics of Fluids", "publication_date": "1964-12-01", "series_number": "12", "volume": "7", "issue": "12", "pages": "1898-1904" }, { "id": "authors:e82m7-v8p22", "collection": "authors", "collection_id": "e82m7-v8p22", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110104-142506543", "type": "article", "title": "Compressible magnetogasdynamic channel flow", "author": [ { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "N/A", "doi": "10.1007/BF01602655", "issn": "0044-2275", "publisher": "Springer", "publication": "Zeitschrift f\u00fcr Angewandte Mathematick und Physik", "publication_date": "1964-03", "series_number": "2", "volume": "15", "issue": "2", "pages": "126-143" }, { "id": "authors:aamnp-s1k45", "collection": "authors", "collection_id": "aamnp-s1k45", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110104-112109595", "type": "article", "title": "A boundary-layer problem associated with magnetogasdynamic channel flow", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1963-11", "series_number": "11", "volume": "1", "issue": "11", "pages": "2666-2667" }, { "id": "authors:qg7w2-amm72", "collection": "authors", "collection_id": "qg7w2-amm72", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110104-082306038", "type": "article", "title": "Stability of high-frequency pressure oscillations in rocket combustion chambers", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "The problem of determining the stability of high-frequency pressure oscillations in rocket combustion chambers is treated explicitly as a perturbation of the classical acoustics problem. On the basis of previous experimental results, the energy addition hy combustion is emphasized,\nand an analysis is developed for tbe stability of stationary pressure waves in chammers using either liquid or gaseous propellants. The formulation is for the three-dimensional case; computations are carried out in detail for a cylindrical chamber in which the mean velocity is parallel to the axis and varies only with axial position. The principal result is a formula for the imaginary part of the complex frequency associated with each of the natural\nmodes of the chamber. This yields a single dimensionless group as a measure of the stability of individual chamber modes. Because of the present lack of sufficiently detailed experimental evidence, quantitative interpretation seems impossible, but qualitative agreement with observations can be demonstrated.", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1963-05", "series_number": "5", "volume": "1", "issue": "5", "pages": "1097-1104" }, { "id": "authors:nsp8s-tt415", "collection": "authors", "collection_id": "nsp8s-tt415", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110104-093958992", "type": "article", "title": "Comments on a hanging soap film", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1963", "series_number": "6", "volume": "1", "issue": "6", "pages": "1462-1463" }, { "id": "authors:frtzk-83q98", "collection": "authors", "collection_id": "frtzk-83q98", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CULjap60", "type": "article", "title": "Comments on a Ruptured Soap Film", "author": [ { "family_name": "Culick", "given_name": "F. E. C.", "clpid": "Culick-F-E-C" } ], "abstract": "Subsequent to puncturing at a point, a horizontal soap film develops a hole whose edge, owing to surface tension, propagates outward from the point of puncture at apparently constant velocity. Measurements by Ranz [1] yielded results roughly 10% lower than those calculated on the basis of a simple energy conservation suggested by Rayleigh [2]. The discrepancy was attributed to an additional retarding viscous stress not included in the analysis. It appears, however, that the energy balance quoted [1] neglects an important contribution, indeed related to th viscous effect noted by Ranz, but which reduces the calculated values to 20% below those measured. A more detailed analysis of the motion of the edge gives this result; the neglected contribution arises from inelastic acceleration of the undisturbed fluid up to the velocity of the edge. The concomitant loss in mechanical energy may be identified with viscous dissipation which is estimated to be confined to a relatively thin region. Lack of agreement between calculated and measured values of the edge velocity seems to be causes by a second-order effect in the method used [1] to determine the thickness of the film.", "doi": "10.1063/1.1735765", "issn": "0021-8979", "publisher": "Journal of Applied Physics", "publication": "Journal of Applied Physics", "publication_date": "1960-06-01", "series_number": "6", "volume": "31", "issue": "6", "pages": "1128-1129" } ]