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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 01:08:19 +0000A chemically reacting, turbulent shear layer
https://resolver.caltech.edu/CaltechETD:etd-10272006-111937
Authors: {'items': [{'id': 'Breidenthal-R-E', 'name': {'family': 'Breidenthal', 'given': 'Robert Edward'}, 'show_email': 'NO'}]}
Year: 1979
DOI: 10.7907/hj67-9h91
A chemically reacting turbulent shear layer was investigated in a new, blow-down water tunnel. In a diffusion-limited reaction, a pH indicator, phenolphthalein, in one stream mixed and reacted with a base, sodium hydroxide, in the other stream to form a visible reaction product. Using optical densitometry techniques, the amount of product was measured as a function of Reynolds number, at a relatively high Schmidt number of approximately 600. The results were compared with both the previous mixing measurements of Konrad in a gaseous shear layer (Sc = 0.7) and the simple mixing model of Broadwell.
The product was found to be distributed, as expected, in concentrated lumps associated with the large, spanwise-coherent structures of the turbulence. The time averaged amount of product in the layer exhibited a rapid transition at a large-structure Reynolds number of about 5 x 10(3) for a velocity ratio of 0.38. Above the transition, the amount of product within the layer was independent of Reynolds number.
This transition is related to the introduction of small scale, three-dimensional motions into the layer. In the initial region, where the flow was already unsteady and contained large structures but was strictly two-dimensional, very little mixing was observed. Downstream the flow became unstable to three-dimensional perturbations and small scale, three-dimensional motions were introduced into the layer. Across this transition, the aqueous mixing increased by an order of magnitude, indicating the sensitivity of mixing to small scales of the turbulence in a high Schmidt number fluid. At high Reynolds numbers, changing the Schmidt number by three orders of magnitude only altered the molecular mixing by about a factor of two or less. The mixing model of Broadwell, which addresses the effect of Schmidt number, is in satisfactory qualitative agreement with the observations.
The unique flow visualization of the visible reaction product in water permitted a study of the three-dimensional instability and evolution of small scale motions in the layer. Streamwise streaks which had been previously observed in the Brown-Roshko gas apparatus were found to originate from a spanwise-sinuous wiggle which appeared at a large-structure Reynolds number which varied with velocity ratio, indicating an influence of initial conditions on the instability.
https://thesis.library.caltech.edu/id/eprint/4277Theoretical Studies of the Nonlinear Infrared Properties of p-Type Semiconductors
https://resolver.caltech.edu/CaltechETD:etd-10102006-093346
Authors: {'items': [{'id': 'James-Ralph-Boyd', 'name': {'family': 'James', 'given': 'Ralph Boyd'}, 'show_email': 'NO'}]}
Year: 1981
DOI: 10.7907/e2ha-tt71
<p>This thesis presents theoretical studies of the nonlinear optical properties of p-type semiconductors. Chapter 2 is concerned with the intensity dependence of the complex dielectric constant of p-type germanium for light with a wavelength in the 9-11 µm region. The nonlinear absorption is described by the imaginary part of the complex dielectric constant, and the nonlinear dispersive properties are described by the intensity dependence of the real part of the dielectric constant. Chapter 3 deals with the saturation characteristics of practically all Groups IV and III-V p-type semiconductors and includes a discussion of the systematic dependence of the saturation intensity on the material parameters. Chapters 4 and 5 are concerned with several "pump-and-probe" experiments. Here, the transmission of a low-intensity light beam (probe) can be altered by the presence of a high-intensity laser (pump). In these chapters the modulation of the probe transmission is analyzed as a function of the intensity of the pump laser. Chapter 6 treats the intensity dependence of the conductivity of p-Ge for light with a wavelength of 10.6 µm.</p>
<p>In Chapter 2, we present a theory of the saturation of heavy- to light-hole band transitions in p-type germanium by high-intensity light with a wavelength near 10 µm. The free-hole distribution function is modified by the high-intensity light, which leads to an intensity dependence in the absorption coefficient and the index of refraction. The absorption coefficient is found to decrease with intensity in a manner closely approximated by an inhomogeneously broadened two-level model. For temperatures and hole concentrations where hole-phonon dominates hole-impurity and hole-hole scattering, the saturation intensity is independent of the hole concentration. For larger hole densities, the saturation intensity is found to increase monotonically with increasing hole concentration. We calculate the saturation intensity as a function of excitation wavelength and temperature for p-Ge. The saturation intensity is found to increase with increasing photon energy and temperature. The calculated results for the absorption saturation are compared with the available experimental data and good agreement is found. In addition to the nonlinear absorption, there exist laser-induced changes in the index of refraction resulting from the saturation of the intervalence-band transitions. Calculations of the intensity dependence of the real part of the dielectric constant are performed for room temperature and for light with a wavelength of 10.6 µm. The index of refraction is found to increase monotonically with increasing intensity.</p>
<p>In Chapter 3, we present the results of the theory describing the saturation behavior of most p-type semiconductors with the diamond or zincblende crystal structure by high-intensity CO<sub>2</sub> light. For materials with large spin-orbit splittings as compared to the excitation wavelength (as for Ge), the dominant absorption mechanism is direct intervalence-band transitions where a free hole in the heavy-hole band absorbs a photon and makes a transition to the light-hole band. For materials with small spin-orbit splittings as compared to the excitation wavelength (as for Si), direct intervalence-band transitions are allowed between the heavy-hole and light-hole, heavy-hole and split-off, and light-hole and split-off hole bands. In each material, values of the saturation intensity are reported as a function of the photon energy and temperature.</p>
<p>In Chapter 4, we present a theory to describe the enhanced transmission of a weak tunable probe laser with a wavelength near 3 µm in the presence of a high-intensity saturating beam with a wavelength near 10 µm in p-Ge. The mechanism responsible for the increasing transmission of the probe laser is the depletion of holes in the heavy-hole band by the saturating beam. Room temperature values of the absorption coefficient of the probe are predicted as a function of the intensity of the pump beam.</p>
<p>In Chapter 5, we present a theory of the absorption lineshape of a low-intensity probe laser which is tuned in the vicinity of a high-intensity pump laser with a wavelength of 10.6 µm. Values for the absorption coefficient of the probe are calculated at room temperature as a function of the intensity of the pump laser. We find the probe absorption can be divided into two contributions: one being due to the depletion of holes in the resonant region of the heavy-hole band by the saturable pump, and the other being due to a coupling of the pump and probe beams which allow the pump photons to be scattered into the probe and vice versa. The calculated results for the composite lineshape of the probe are compared with the experimental data and good agreement is found.</p>
<p>In Chapter 6, we show how the modification of the free hole distribution function by the saturating beam leads to a change in the conductivity of p-Ge. The photoconductive response is calculated as a function of the doping level, temperature and light intensity.</p>https://thesis.library.caltech.edu/id/eprint/4009The Coherent Structure of Turbulent Mixing Layers. I. Similarity of the Primary Vortex Structure. II. Secondary Streamwise Vortex Structure
https://resolver.caltech.edu/CaltechETD:etd-08262005-154143
Authors: {'items': [{'id': 'Bernal-Luis-Paulino', 'name': {'family': 'Bernal', 'given': 'Luis Paulino'}, 'show_email': 'NO'}]}
Year: 1981
DOI: 10.7907/Z52D-SA34
<p>The primary spanwise organized vortex structure and the secondary streamwise vortex structure of turbulent mixing layers have been investigated. Flow visualization motion pictures of a constant density mixing layer were used to measure the properties of the large scale vortices. It was found that after an initial transition region mean properties of the large scale vortices reach the expected linear growth with downstream distance required by similarity. In the self-similar region, the vortex core area and visual thickness increase continuously during its life-span.</p>
<p>A theoretical model of probability distribution function for the large-scale vortex circulation was developed. This distribution is found to be lognormal and to have a standard deviation, normalized with the mean of 0.28. From this model the mean life-span of the vortices could also be obtained and was found to be 0.67 times the mean life-span position.</p>
<p>The streamwise streak pattern observed by Konrad (1976) and Breidenthal (1978) in plan-view pictures of the mixing layer was investigated, using flow visualization and spanwise concentration measurements. It was confirmed that this pattern is the result of a secondary vortex structure dominated by streamwise, counterrotating vortices. A detailed description of its spatial relation to the primary, spanwise vortex structure is presented. From time average flow pictures, the onset position and initial scale of the secondary structures were determined. From concentration measurements, spanwise variations in mean properties, resulting from the secondary structure, were found. This also showed an increase of the spanwise scale with downstream distance and the existence of the streamwise vortices in the fully developed turbulent region. In this region the mean spacing is found approximately equal to the vorticity thickness.</p>https://thesis.library.caltech.edu/id/eprint/3228Experiments on Mixing and Combustion with Low Heat Release in a Turbulent Shear Flow
https://resolver.caltech.edu/CaltechETD:etd-09142006-144655
Authors: {'items': [{'email': 'mungal@stanford.edu', 'id': 'Mungal-Mark-Godfrey', 'name': {'family': 'Mungal', 'given': 'Mark Godfrey'}, 'show_email': 'NO'}]}
Year: 1983
DOI: 10.7907/QZ4F-V692
<p>A new blowdown facility to study mixing and combustion in a turbulent shear layer has been built. The system is capable of 100 m/s for three seconds in a 5 x 20 cm exit area on the high speed side, and 50 m/s in a 10 x 20 cm exit area on the low speed side. Dilute concentrations of hydrogen and fluorine, carried in an inert gas, react when both fluid streams meet at the tip of a splitter plate. The reaction is spontaneous, rapid, and highly exothermic. The resulting temperature field has been studied using a rake of eight fast response thermometers placed across the width of the layer. Runs have been performed for low heat release over a wide range of equivalence (concentration) ratios, at a Reynolds number of 30,800 based on velocity difference and vorticity thickness. The heat release is sufficiently low so that the overall properties of the mixing layer are not significantly changed from the cold case.</p>
<p>The results show the presence of large, hot structures within the flow together with cool, irrotational tongues of freestream fluid that penetrate deep into the layer. Thus, it is possible for the entire width of the layer to be quite hot, owing to the passage of a large structure, or for the layer to be quite cool, owing to the presence of the cool fluid tongues. The mean temperature results from a duty cycle whereby a given point in the flow sees alternating hot and cool fluid which averages into the local mean. The mean temperature profiles do not achieve the adiabatic flame temperature at any location across the layer, with the maximum mean temperature, depending upon the equivalence ratio, varying from 54% to 67% of the adiabatic flame temperature. The location of the maximum mean temperature shifts by about 25% of the visual thickness of the layer for a change of equivalence ratio by a factor of 64. The amount of product formed in the layer is compared to earlier measurements in water, and, it is found that at a speed ratio of 0.40, there exists 20 to 25% more product in gaseous flows, implying that molecular diffusion, or in nondimensional form the Schmidt number, plays a role in mixing at large Reynolds number. The present results compare favorably with the recent theoretical model of Broadwell and Breidenthal for mixing and chemical reaction in a turbulent shear layer. With this model it is possible to bring the results for gases and liquids into quantitative agreement.</p>https://thesis.library.caltech.edu/id/eprint/3541Experiments on Entrainment, Mixing and Chemical Reactions in Turbulent Jets at Large Schmidt Number
https://resolver.caltech.edu/CaltechETD:etd-12062006-104125
Authors: {'items': [{'id': 'Dahm-Werner-Johann-Anton', 'name': {'family': 'Dahm', 'given': 'Werner Johann Anton'}, 'show_email': 'NO'}]}
Year: 1985
DOI: 10.7907/k93g-jh12
<p>Entrainment, mixing and chemical reactions are investigated in the far field of steady, axisymmetric, momentum-driven, turbulent jets issuing into an unconfined, quiescent medium in the large Schmidt number (liquid-phase) regime. Visualization experiments using both passive and chemically sensitive planar laser induced fluorescence (LIF) techniques show the importance of large scale transport in the jet far field, and suggest that entrainment, mixing and chemical reactions in the far field are dominated by a large scale organization of the flow. Successive instantaneous profiles of the jet fluid concentration along the axial and radial directions in the jet far field are measured by combining these LIF techniques with direct, high-resolution, linear photodiode array imaging and high-speed digital data acquisition. These imaging measurements have revealed an axial similarity concentration variable for which probability density functions (PDFs) in the jet far field are self-similar along rays. A chemical reaction method is presented which allows the self-similar form of these PDFs to be measured with full resolution at all scales of transport and mixing. Furthermore, these imaging measurements have shown that instantaneous radial profiles of the jet fluid concentration do not resemble the mean concentration profile. Specifically, unmixed ambient fluid is found deep within the jet and the composition of molecularly mixed fluid within large regions in the jet is approximately uniform. The results from these experiments are interpreted in the context of a simple conceptual model for large scale organization of entrainment, mixing and chemical reactions in the far field of turbulent jets.</p>https://thesis.library.caltech.edu/id/eprint/4815Effects of a Periodic Disturbance on Structure and Mixing in Turbulent Shear Layers and Wakes
https://resolver.caltech.edu/CaltechETD:etd-03252008-144801
Authors: {'items': [{'id': 'Roberts-Fredrick-Allen', 'name': {'family': 'Roberts', 'given': 'Fredrick Allen'}, 'show_email': 'NO'}]}
Year: 1985
DOI: 10.7907/syy5-a334
<p>Large scale structure and mixing processes are investigated in chemically reacting wakes and shear layers to which a periodic disturbance is applied. The experiments employ a diffusion-limited acid-base reaction to directly measure the extent of mixing. Optical diagnostics used include laser absorption and laser induced fluorescence. Absorption of laser light by reacted product provides a measure of cross-stream average product. Fluorescence was measured by a self-scanning linear photodiode array using high speed computer data acquisition to obtain the product distribution across the layer.</p>
<p>Previous results showing that forcing alters the structure and growth rate of shear layers are confirmed. Forcing artificially extends the lifetime of vortices whose size is consistent with the disturbance wavelength. Amalgamation of smaller vortices is enhanced over that in the natural layer until the frequency locked scale is achieved. At high Reynolds number product measurements show reduction of product with forcing. At moderate Reynolds numbers, on the other hand, there is an increase in product when forced. In one case a five fold increase in product was observed. The differences are related to the different effects of forcing on entrainment, composition ratio and secondary structure.</p>
<p>A dramatic, order of magnitude increase in mixing was discovered for certain forced wake flows. This effect is strongly associated with an interaction between the spanwise organized wake vortices and the test-section side walls.</p>
https://thesis.library.caltech.edu/id/eprint/1123Laser Doppler Velocity and Vorticity Measurements in Turbulent Shear Layers
https://resolver.caltech.edu/CaltechETD:etd-08312005-112325
Authors: {'items': [{'email': 'dbl@tyrvos.caltech.edu', 'id': 'Lang-Daniel-Bernard', 'name': {'family': 'Lang', 'given': 'Daniel Bernard'}, 'show_email': 'NO'}]}
Year: 1985
DOI: 10.7907/YFR4-VE59
<p>A Laser Doppler Velocimeter (LDV) system was developed to measure the instantaneous spanwise vorticity, -w<sub>z</sub>, in a turbulent shear layer. It was necessary to design and fabricate the LDV optics and processing electronics, as no commercially available LDV systems met the specifications of measuring the velocity at four closely spaced points to the requisite accuracy. Measurements were also made of the instantaneous u, v, u', v', and -u'v'. The instantaneous vorticity was processed to obtain an estimate of its probability density function, from which the mean and rms values were estimated. It was also possible to separate the irrotational fraction of the flow (-w<sub>z</sub> ≈ 0) from the rotational (intermittent) fraction of the flow (-w<sub>z</sub> ≠ 0). The development of the intermittency profiles, based on vorticity, as a function of the downstream distance from the splitter plate was studied. A notable feature is that the vorticity is found to have values opposite the mean sense of rotation, i.e., -w<sub>z</sub>(t) < 0, a significant fraction of the time. Additionally, a detailed study was performed to evaluate the approximation of -∂v/∂x, in terms of various local temporal derivatives ∂v/u(y)∂t. The optimum choice for u(y) can be found and is influenced by the relative local convection velocities of the small and large scale structures.</p>
https://thesis.library.caltech.edu/id/eprint/3291Heat Release Effects in a Turbulent, Reacting Shear Layer
https://resolver.caltech.edu/CaltechETD:etd-06132007-075717
Authors: {'items': [{'email': 'jherm@aa.washington.edu', 'id': 'Hermanson-James-Carl', 'name': {'family': 'Hermanson', 'given': 'James Carl'}, 'show_email': 'NO'}]}
Year: 1985
DOI: 10.7907/y722-za34
<p>The effects of heat release were studied in a planar, gaseous reacting mixing layer formed between free streams containing hydrogen and fluorine in inert diluents. Sufficiently high concentrations of reactants were employed to produce adiabatic flame temperature rises of up to 940 K (1240 K absolute). The Reynolds number at the measuring station, based on velocity difference, 1% temperature thickness and cold kinematic viscosity was approximately 6x10<sup>4</sup>. The temperature field was measured with cold wire resistance thermometers and thermocouples. Flow visualization was accomplished by schlieren spark and motion picture photography. Mean velocity information was extracted from mean pitot probe dynamic pressure measurements.</p>
<p>Though the displacement thickness of the layer, for zero streamwise pressure gradient, increased with increasing heat release, the actual growth rate of the layer did not increase, but instead decreased slightly. The overall entrainment into the layer was seen to be substantially reduced as a consequence of heat release. Calculations showed that the decrease in layer growth rate can be accounted for by a corresponding reduction in turbulent shear stress.</p>
<p>The mean temperature rise profiles, normalized by the adiabatic flame temperature rise, were not greatly changed in shape by heat release. A small decrease in normalized mean temperature rise with heat release was observed. Large scale coherent structures were observed to persist at all levels of heat release in this investigation. The mean structure spacing decreased with increasing temperature. This decrease exceeded the rate of layer growth rate reduction, and suggests that the mechanisms of vortex amalgamation were, to some extent, inhibited by heat release.</p>
<p>Imposition of a favorable pressure gradient resulted in additional thinning of the layer, and caused a slight increase in the mixing and amount of chemical product formation. The change in layer growth rate can be shown to be related to a change in free stream velocity ratio induced by pressure gradient.</p>https://thesis.library.caltech.edu/id/eprint/2574Experimental Investigation of Heterogeneous Compressible Shear Layers
https://resolver.caltech.edu/CaltechETD:etd-12192007-085328
Authors: {'items': [{'id': 'Papamoschou-Dimitri', 'name': {'family': 'Papamoschou', 'given': 'Dimitri'}, 'show_email': 'NO'}]}
Year: 1987
DOI: 10.7907/M7PQ-Y494
<p>The compressible, two-dimensional shear layer is investigated experimentally in a novel facility. In this facility, it is possible to flow similar or, dissimilar gases of different densities and to select different Mach numbers for each stream over a wide range of Reynolds numbers. In the current experiments, ten combinations of gases and Mach numbers are studied in which the freestream Mach numbers range from 0.2 to 4, the density ratio varies from 0.2 to 9.2, and the velocity ratio varies from 0.13 to 1. The growth of the turbulent region of the layer is measured by means of pitot pressure profiles obtained at several streamwise locations. The resulting growth rate is estimated to be about 80% of the visual growth rate. The transition from laminar to turbulent flow, as well as the structure of the turbulent layer, are observed with Schlieren photographs of 20 nanosecond duration. Streamwise pressure distribution and total pressures are measured by means of a Scanivalve-pressure transducer system.</p>
<p>An underlying objective of this investigation was the definition of a compressibility-effect parameter that correlates and consolidates the experimental results, especially the turbulent growth rates. A brief analytical investigation of the vortex sheet suggests that such a parameter is the Mach number in a frame of reference moving with the phase speed of the disturbance, called here the convective Mach number. In a similar manner, the convective Mach number of a turbulent shear layer is defined as the one seen by an observer moving with the convective velocity of the dominant waves and structures. It happens to have about the same value for each stream. In the current experiments, it ranges from 0 to 1.9.</p>
<p>The correlations of the growth rate with convective Mach number fall approximately onto one curve when the growth rate is normalized by its incompressible value at the same velocity and density ratios. The normalized growth rate, which is unity for incompressible flow, decreases gradually with increasing convective Mach number, reaching an asymptotic value of about 0.25 for supersonic convective Mach numbers. The above behavior is in qualitative agreement with results of linear stability theory as well as with those of previous, one-stream experiments.</p>
<p>Large-scale structures, resembling those observed in subsonic shear layers, are evident in the Schlieren photographs. It is estimated that the mean structure spacing, normalized by the local thickness, is reduced to about half its incompressible value as the convective Mach number becomes supersonic.</p>
<p>An estimate of the transition Reynolds number has been obtained from the photographs of two shear layers having quite different convective Mach numbers, one low subsonic and the other sonic. In both cases, it is about 2 x 10<sup>5</sup>, based on distance to transition and properties of the high unit Reynolds number stream, thus suggesting that, in this experiment, transition is dominated by instabilities of the wake, rather than of the shear layer.</p>
https://thesis.library.caltech.edu/id/eprint/5067Structure Measurements in a Synthetic Turbulent Boundary Layer
https://resolver.caltech.edu/CaltechETD:etd-03192008-085206
Authors: {'items': [{'email': 'jaywant@mecheng.iisc.ernet.in', 'id': 'Arakeri-Jaywant-H', 'name': {'family': 'Arakeri', 'given': 'Jaywant H.'}, 'show_email': 'NO'}]}
Year: 1987
DOI: 10.7907/FABW-YZ77
<p>Extensive hot-wire measurements have been made to determine the structure of the large eddy in a synthejc turbulent boundary layer on a flat-plate model. The experiments were carried out in a wind tunnel at a nominal free-stream velocity of 12 m/s. The synthetic turbulent boundary layer had a hexagonal pattern of eddies and a ratio of streamwise scale to spanwise scale of 3.2:1. The measured celerity of the large eddy was 84.2 percent of the free-stream velocity. There was some loss of coherence, but very little distortion, as the eddies moved downstream. Several mean properties of the synthetic boundary layer were found to agree quite well with the mean properties of a natural turbulent boundary layer at the same Reynolds number.</p>
<p>The large eddy is composed of a pair of primary counter-rotating vortices about five δ long in the streamwise direction and about one δ apart in the spanwise direction, where δ is the mean boundary-layer thickness. The sense of the primary pair is such as to pump fluid away from the wall in the region between the vortices. A secondary pair of counter-rotating streamwise vortices, having a sense opposite to that of the primary pair, is observed outside of and slightly downstream from the primary vortices. Both pairs of vortices extend across the full thickness of the boundary layer and are inclined at a shallow angle to the surface of the flat plate. The data show that the mean vorticity vectors are not tangential to the large-eddy vortices. In fact, the streamwise and normal vorticity components that signal the presence of the eddy are of the same order of magnitude. Definite signatures are obtained in terms of the mean skin-friction coefficient and the mean wake parameter averaged at constant phase. Velocities induced by the vortices are partly responsible for entrainment of irrotational fluid, for transport of momentum, for generation of Reynolds stresses, and for maintenance of streamwise and normal vorticity in the outer flow. A stretching mechanism is important in matching spanwise vorticity close to the wall to variations in turbulent shearing stress. Regions where the stretching term is large coincide with regions of large wall shearing stress and large turbulence production.</p>https://thesis.library.caltech.edu/id/eprint/1012New Solutions of an Amplitude Equation Describing Transition in a Laminar Shear Flow
https://resolver.caltech.edu/CaltechETD:etd-03032008-130724
Authors: {'items': [{'email': 'mlandman@giantpond.com', 'id': 'Landman-Michael-J', 'name': {'family': 'Landman', 'given': 'Michael J.'}, 'show_email': 'NO'}]}
Year: 1987
DOI: 10.7907/CYPP-D856
<p>In order to better understand the process of laminar-turbulent transition in parallel shear flows, the study of the stability of viscous flow between parallel plates, known as plane Poiseuille flow, is found to be a good prototype. For Reynolds number near the critical value at which a linear instability first appears, Stewartson and Stuart (1971) developed a weakly nonlinear theory for which an amplitude equation is derived describing the evolution of a disturbance in plane Poiseuille flow in two space dimensions. This nonlinear partial differential equation is now commonly known in the literature as the Ginzburg-Landau equation, and is of the form</p>
<p>(∂A)/(∂t) = (a<sub>r</sub> + ia<sub>i</sub>)[(∂<sup>2</sup>A)/(∂x<sup>2</sup>)] + (Re - Re<sub>c</sub>)A + (d<sub>r</sub> + id<sub>i</sub>)A|A|<sup>2</sup>.</p>
<p>This dissertation concentrates on analyzing quasi-steady solutions of the Ginzburg-Landau equation, where</p>
<p>A = e<sup>-iΩt</sup>Φ(x - ct).</p>
<p>These solutions describe modulations to the wave of primary instability, with amplitude which is steady in an appropriate moving coordinate system. The ordinary differential equation describing the spatial structure of quasi-steady solutions is viewed as a low-dimensional dynamical system. Using numerical continuation and perturbation techniques, new spatially periodic and quasi-periodic solutions are found which bifurcate from the laminar state and undergo a complex series of bifurcations. Moreover, solitary waves and other solutions suggestive of laminar transition are found numerically for Reynolds number on either side of Re<sub>c</sub>, connecting the laminar state to finite amplitude states, some of the latter corresponding to known solutions of the full fluid equations. The existence of these new spatially quasi-periodic and transition solutions suggests the existence of a similar class of solutions in the Navier Stokes equations, describing pulses and fronts of instability, as observed experimentally in parallel shear flows.</p>https://thesis.library.caltech.edu/id/eprint/853Mixing in Gas Phase Turbulent Jets
https://resolver.caltech.edu/CaltechETD:etd-06132005-160404
Authors: {'items': [{'id': 'Dowling-David-Russell', 'name': {'family': 'Dowling', 'given': 'David Russell'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/9233-5476
<p>This work is an experimental investigation of the mixing of the nozzle fluid of a round, turbulent jet with the entrained reservoir fluid, using laser-Rayleigh scattering methods. The measurements, at Reynolds numbers of 5,000 and 16,000, cover the axial range from 20 to 90 jet exit diameters and resolve the full range of temporal and spatial concentration scales. The measured mean and rms values of the concentration, and the mean scalar dissipation rate, when estimated from the time derivative of concentration, are consistent with jet similarity laws. Concentration fluctuation power spectra are found to be self-similar along rays emanating from the virtual origin of the jet, and are consistent with the universal form of scalar spectra proposed by Gibson (1968 II). The probability density functions for the concentration, the time derivative of concentration, and the square of the time derivative of concentration, are compiled and are also found to be self-similar along rays. Features of the measured distributions and spectra are consistent with the existence of large-scale structures within the flow that span the local diameter of the jet's turbulent cone. On the centerline of the jet, the scaled probability density function of jet gas concentration is found to be almost independent of the Reynolds number while the local mixing rate in the inner part of jet is not. The usual assumptions concerning isotropy and correlation of derivatives are found to lead to erroneous results for the probablility density function of the scalar dissipation rate.</p>https://thesis.library.caltech.edu/id/eprint/2571On the Interaction of Shock Waves with Contact Surfaces Between Gases of Different Densities
https://resolver.caltech.edu/CaltechETD:etd-10302003-102505
Authors: {'items': [{'email': 'martin.brouillette@usherbrooke.ca', 'id': 'Brouillette-Martin', 'name': {'family': 'Brouillette', 'given': 'Martin'}, 'show_email': 'YES'}]}
Year: 1989
DOI: 10.7907/9JGS-ZX78
<p>The interaction of shock waves with a contact surface between gases of different densities has been studied experimentally and theoretically. The basic mechanism for the instability of perturbations at the interface is baroclinic vorticity generation resulting from the misalignment of the pressure gradient of the shock and the density gradient of the interface. In the present study, the effects of interface density contrast and initial thickness, and incident wave strength on the development of the instability at the interface are investigated. The experiments were performed in a new vertical shock tube facility where the interaction of a shock wave with either a discontinuous interface, formed by a thin (0.5 µm) plastic membrane, or a continuous interface, created by retracting a metal plate initially separating the two gases, was studied. Air was used on one side of the interface and either helium, carbon dioxide, refrigerant-22 or sulphur hexafluoride was used on the other side as the test gas.</p>
<p>Experiments to study the time evolution of quasi-sinusoidal perturbations on a continuous interface have shown that the growth rates are reduced as the interface thickness is increased. It has been observed that growth rates of perturbations of wavelength λ ~ 25 mm on interfaces of thickness δ ~ 10 mm are about three times smaller than those predicted by the linear theory for the impulsive acceleration of discontinuous interfaces. A new model that accounts for the growth rate reduction caused by the presence of a finite density gradient on the interface has been proposed, and good agreement was obtained with the present experimental results.</p>
<p>Experiments were also performed to observe the schlieren visual thickness of plane discontinuous or continuous interfaces with random small-scale perturbations after interaction with the incident shock wave and its reverberations. The interface was initially located near the end wall of the shock tube to permit the observation of the development of the interface phenomena after the arrival of the incident shock and its reverberations. It is found that the interaction of a shock wave with a discontinuous interface causes the appearance of a turbulent mixing zone between the two gases, whose growth rate slows down as time increases, owing to a decrease in turbulence intensity and the action of viscosity. Because of the large uncertainty associated with the measurements a short time after the interaction with the incident shock, the accurate determination of a possible universal power law governing the thickening of the interface is not feasible. Results for the interaction of the first reverberation of the primary wave with the already turbulent interface have demonstrated that this growth is sensitive to the initial pre-growth state of the interface. It also appears that the thickening of the turbulent mixing zone is accomplished by the merging of large structures within the interface. However, since the energy available for the turbulent motions at the impulsively accelerated interface remains constant after the interaction with the shock and also depends on the wavelength of the initial perturbation, it is not certain whether the development of mixing at the interface achieves an asymptotic stage of self-similar turbulence independent of initial conditions, as has been observed for the gravity-driven interfaces. Also, it has been found that the growth rates measured in the present experiments with discontinuous interfaces are nearly an order of magnitude lower than those reported by previous investigators. The continuous interfaces formed by the retracting plate are smoothed by molecular diffusion, and thus the combination of low density gradient and small initial perturbations is such that they exhibit growth only after being perturbed by acoustic noise introduced by the reverberation of waves between the interface, the side walls and the end of the shock tube.</p>
<p>The development of viscous boundary layers on the side walls of the test section can cause the bifurcation of waves reflected from the end wall of the shock tube, and, thereafter, the formation of wall bubbles and interface contaminating jets. Moreover, the generation of vortical structures by the baroclinic instability excited by the interaction of reflected waves with the distorted interface within the boundary layer has been demonstrated. Significant contamination of the test gas can by achieved by these structures, even if reflected-wave bifurcation is absent. Moreover, the strain induced by the vorticity in these wall structures tends to thin the interface; the magnitude of this effect on the growth rates in the present plane interface experiments is estimated to be of order 10% for discontinuous interfaces and 50% for continuous interfaces.</p>
https://thesis.library.caltech.edu/id/eprint/4315Observations of Stochastic Ion Heating by Low Frequency Drift Waves
https://resolver.caltech.edu/CaltechETD:etd-02092007-143250
Authors: {'items': [{'id': 'McChesney-Jon-Mearns', 'name': {'family': 'McChesney', 'given': 'Jon Mearns'}, 'show_email': 'NO'}]}
Year: 1989
DOI: 10.7907/vyaq-ye14
<p>Several laser induced fluorescence (LIF) experiments were performed on the Encore tokamak device. These experiments represent the first application of this technique to the majority ions of a tokamak. The main laser system selected consisted of a copper vapor laser (CVL), which pumped a narrowband, tunable dye laser. This system allowed the Doppler-broadened, ion distribution function to be scanned with high resolution, giving accurate ion temperature measurements. As a preliminary test, the diagnostic was used to observe ion heating in the presence of lower hybrid RF power. Ion temperatures were found to increase dramatically with increasing RF power.</p>
<p>By using a second dye laser, actual ion trajectories were determined using the technique of "optical tagging." Tagging involves the use of a so-called "pump" laser to alter the fraction of ions in a particular quantum state. As a preliminary test, this technique was used to demonstrate ion gyro-motion in Encore.</p>
<p>Using the ion distribution functions determined by means of LIF, it was possible to make detailed measurements of ion heating during an ohmically heated tokamak discharge. It was found that the observed rate of ion heating was nearly two orders of magnitude faster than expected from collisional energy exchange with the hot electrons. The high ion temperatures inferred from the LIF measurements were later verified by measuring the Landau damping of ion acoustic waves. The observed damping lengths were roughly in accord with those calculated using measured values of T<sub>e</sub> and T<sub>i</sub>.</p>
<p>This enhanced ion heating was correlated with the presence of large amplitude, low frequency (ω < ω<sub>ci</sub>), drift-Alfvén waves. Using numerical calculations, it was shown that in the presence of electrostatic modes (such as drift waves) of sufficient amplitude, ion motion becomes stochastic or chaotic. In physical terms, stochasticity occurs when the ion displacement that is due to the polarization drift becomes comparable to the perpendicular wavelength, i.e., when α = m<sub>i</sub>k<sup>2</sup><sub>⊥</sub>φ<sub>0</sub>/qB<sup>2</sup><sub>0</sub> ~ 1. A combination of numerical calculations and experiments was used to demonstrate that stochasticity was indeed responsible for the observed rapid heating.</p>
<p>Finally, we concluded by speculating that stochastic heating may also be the cause of the anomalously high ion temperatures observed in reversed field pinches (RFP's) and in field reversed configurations (FRC's). Intrinsic stochasticity is also important in the field of auxiliary plasma heating. As is now well known, a large amplitude RF electric field can heat particles despite a large mismatch between the wave frequency and the gyrofrequency.</p>https://thesis.library.caltech.edu/id/eprint/575An investigation of the inviscid spatial instability of compressible mixing layers
https://resolver.caltech.edu/CaltechETD:etd-11132007-094001
Authors: {'items': [{'id': 'Zhuang-M', 'name': {'family': 'Zhuang', 'given': 'Mei'}, 'show_email': 'NO'}]}
Year: 1990
DOI: 10.7907/650s-9t96
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The behavior of both unbounded and bounded compressible plane mixing layers with respect to two- and three-dimensional, spatially growing wave disturbances is investigated using linear stability analysis. The mixing layer is formed by two parallel streams with different gases and the flow is assumed to be inviscid and non-reacting.
For unbounded mixing layers, the effects of the free stream Mach number, velocity ratio, temperature ratio, gas constant (molecular weight) ratio and the ratios of specific heats on the linear spatial instability characteristics of a mixing layer are determined. A nearly universal dependence of the normalized maximum amplification rate on the convective Mach number is found for two-dimensional spatially growing disturbances. The effects of the mean flow profiles on the instability behavior of the mixing layers are also studied. It is shown that decreasing the thickness of the total temperature profile relative to the mean velocity profile, or adding a wake component in the mean velocity profile can make the normalized amplification rate decrease slower as the convective Mach number increases for both subsonic and supersonic convective Mach numbers.
For an unbounded mixing layer with subsonic convective Mach numbers, there is only one unstable mode propagating with a phase velocity [...] approximately equal to the isentropically estimated convective velocity of the large scale structures [...]. As the convective Mach number approaches or exceeds unity, there are always two unstable spatial modes. One is with a phase velocity [...] (slow mode and the other is with a phase velocity [...] (fast mode). For the low supersonic convective Mach numbers, the fast mode is more unstable than the slow mode when the heavy gas is on the low speed side and the slow mode is dominant when the heavy gas is on the high speed side.
The effect of parallel flow guide walls on a spatially growing mixing layer is also investigated. It is shown that, in this case, if the convective Mach number exceeds a critical value of approximately unity, there are many supersonic unstable modes. The maximum amplification rates of mixing layers approach an asymptotic value and this maximum amplification rate increases to a maximum value and decreases again as the distance between the walls decreases. For a mixing layer inside parallel flow guide walls, the growth rate of three-dimensional modes is larger than the corresponding two-dimensional mode at high convective Mach numbers. But the growth rate of two-dimensional supersonic instability waves has a larger value than their three-dimensional counterparts for a mixing layer inside a rectangular duct (Tam & Hu [1988], [1989]). Contour plots of the pressure perturbation fields for both unbounded and bounded mixing layers indicate that there are waves propagating outward from the mixing layer along the Mach angle, and that the walls provide a feedback mechanism between the growing mixing layer and this compression/expansion wave system. The bounded mixing layers are more unstable than the corresponding free mixing layers for supersonic convective Mach numbers. The streaklines of the flow confirm that the spreading rate of the mixing layer is unusually small for supersonic disturbances.
https://thesis.library.caltech.edu/id/eprint/4540Vortex Simulation of Separated Flows in Two and Three Dimensions
https://resolver.caltech.edu/CaltechETD:etd-08092005-142847
Authors: {'items': [{'email': 'bsgh@tm.net.my', 'id': 'Chua-Kiat', 'name': {'family': 'Chua', 'given': 'Kiat'}, 'show_email': 'YES'}]}
Year: 1990
DOI: 10.7907/9ENS-EP36
<p>This thesis is concerned with the applications of vortex methods to the problem of unsteady, separated flows in two and three dimensions, and can be divided into three parts. In the first part, an improved method for satisfying the boundary conditions on a flat plate is developed and applied to the two-dimensional separated flow problem. In this method, boundary layers on both side of the plate are represented by stacks of multiple vortex panels, the strength of which are determined by enforcing both the no-through flow and no-slip boundary conditions at the plate. Vortex shedding at the sharp edge of the plate is represented as the separation of the boundary vortex elements. Both forced and unforced flows are studied and comparisons to experiments are carried out. For the case without forcing, large discrepancy between calculations and experiments, which is also reported by other workers using a different vortex method or Navier-Stokes calculations, is observed. In the case with forcing, the discrepancy is reduced with lateral forcing at low amplitude; and eliminated, regardless of amplitude, with streamwise forcing (acceleration). In the second part, an improved three-dimensional vortex particle method is developed. In this method, vortex elements of vorticity that move with the local velocity and are stretched and rotated according to the local strain field, are used. To mimic the effects of vorticity cancellations, close pairs of opposite sign vortex elements are replaced by high order dipoles. The method is designed to handle complex high Reynolds number vortical flows and a non-linear viscosity model is included to treat small-scale effects in such flows. Applications to two problems involving strong interactions of vortex tubes are carried out and core deformation with complex internal strucures and induced axial flow within vortex tubes are observed. Qualitative comparison to experiments are encouraging. In the third part, the two-dimensional method developed in the first part is modified and extended to three dimensions. Here, solenoidal condition for vorticity is considered and closed vortex loops are used to represent the boundary layer vorticity and the vorticity at shedding. For the evolution of the vortex wake, the vortex particle method developed in the second part is used. Applications to the flow past a normal square plate is carried out and the early stages of the flow are studied.</p>https://thesis.library.caltech.edu/id/eprint/3064Structure in the Near Field of the Transverse Jet
https://resolver.caltech.edu/CaltechETD:etd-02232007-075829
Authors: {'items': [{'id': 'Fric-Thomas-Frank', 'name': {'family': 'Fric', 'given': 'Thomas Frank'}, 'show_email': 'NO'}]}
Year: 1990
DOI: 10.7907/JVHG-E582
<p>Photographs of an axisymmetric turbulent jet issuing from a wall into a crossflow display the four types of vortical structures which exist in the near field: the jet shear layer vortices, the nascent far field vortex pair, the near wall horseshoe vortices, and a system of vortices in the wake of the jet.</p>
<p>Additionally, results of hot-wire measurements in the wake of the transverse jet are presented. Among these results are characteristic wake Strouhal frequencies, which vary with the jet to crossflow velocity ratio, and wake velocity profiles.</p>
<p>It is found that the wake vorticity is not "shed" from the jet but is formed from vorticity which originated in the wall boundary layer. Therefore, analogies between the wakes of transverse jets and the wakes of solid cylinders are incorrect. Since the jet is not a solid obstacle to the crossflow, as a cylinder is, new vorticity is not generated at the interface between the jet and the crossflow. Instead, the boundary layer on the wall from which the jet issues separates near the downstream side of the jet because it cannot negotiate the adverse pressure gradient imposed on it by the flow around the jet, which is not "separated" as it is for a cylinder. The wake vortices subsequently formed are found to be most coherent near a jet to crossflow velocity ratio of four.</p>
<p>The near field development of the counterrotating vortex pair, which is the dominant structure of the far field jet, is also addressed. It is argued that the source of vorticity for the vortex pair is the vorticity from the boundary layer within the jet nozzle. Estimates for the strength of these vortices are obtained by considering the flux of vorticity emanating from the nozzle.</p>
<p>Possible implications for mixing are briefly discussed.</p>https://thesis.library.caltech.edu/id/eprint/719Active control of the flow past a cylinder executing rotary motions
https://resolver.caltech.edu/CaltechETD:etd-04132004-141454
Authors: {'items': [{'id': 'Tokumaru-P-T', 'name': {'family': 'Tokumaru', 'given': 'Phillip Takeo'}, 'show_email': 'NO'}]}
Year: 1991
DOI: 10.7907/v7p7-d977
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Exploratory experiments have been performed on circular cylinders executing forced rotary motions in a steady uniform flow. These motions include harmonic oscillations, steady rotation, and combinations of the two. Flow visualization and laser-Doppler velocimetry measurements were used to characterize the wake structure, and to estimate the convection speed, spacing, and strength of the vortical structures. Laser-Doppler velocimetry measurements were also made to estimate the cylinder drag coefficient and wake displacement thickness. In addition, the periodic flow close the cylinder and in the near wake region was mapped for a particular forced case. The data show that a considerable amount of control can be exerted over the flow by such means. In particular, a large increase, or decrease, in the resulting displacement thickness, estimated cylinder drag, and associated mixing with the free stream can be achieved, depending on the frequency and amplitude of oscillation. In order to assess the effects of oscillatory forcing on a cylinder with a net (mean) rotation rate, a novel method for estimating the steady lift forces was employed. Using this method, it was also found that the addition of forced rotary oscillations to the steady rotation of the cylinder helped to increase [...] in the cases where the wake would normally be separated in the steadily rotating case, and decrease it otherwise. Results obtained for a steadily rotating cylinder (no forced oscillations) compare favorably with similar data published in the literature.https://thesis.library.caltech.edu/id/eprint/1368An experimental investigation of chemically-reacting, gas-phase turbulent jets
https://resolver.caltech.edu/CaltechETD:etd-06272007-091419
Authors: {'items': [{'id': 'Gilbrech-R-J', 'name': {'family': 'Gilbrech', 'given': 'Richard Joseph'}, 'show_email': 'NO'}]}
Year: 1991
DOI: 10.7907/p80s-h321
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
A new high pressure combustion facility was built to investigate mixing in axisymmetric, turbulent jets exiting into quiescent reservoirs. The facility uses fluorine and nitric oxide, diluted with nitrogen, for chemical product formation that is accompanied by heat release. The average temperature was measured by a set of long, thin, resistance wire thermometers stretched across the jet centerline at 16 downstream locations from x/d[subscript 0] = 30 to 240. Runs at several stoichiometric mixture ratios [phi], for Reynolds numbers ranging from 10,000 [...] Re [...] 150,000, were performed to determine any dependence of flame length on Reynolds number. The Reynolds number was varied through density, i.e., pressure, while the jet exit velocity and exit diameter were held constant. The time-averaged line integral of temperature, measured along the transverse axis of the jet by the wires, displays a logarithmic dependence on x/d* within the flame zone, and asymptotes to a constant value beyond the flame tip, as predicted from scaling and similarity arguments for a momentum-dominated, turbulent jet. The main result of the work is that the flame length, as estimated from the temperature measurements, varies with changes in Reynolds number, suggesting that the mixing process is not Reynolds number independent up to Re = 150,000. Specifically, the normalized flame length Lf/d* displays a linear dependence on [phi], with a slope that decreases from Re = 10,000 to 20,000, and then remains constant for Re > 20,000. Additionally, the measurements revealed a "mixing virtual origin," defined as the far-field flame length extrapolated to [phi] = 0, that increases with increasing Re for Re [...]20,000 and then decreases with increasing Re for Re > 20, 000. A separate set of experiments indicated that the runs described above were momentum dominated to the farthest measuring station and that the kinetics of the chemical reactions were fast compared to the characteristic mixing time. The transition of the jet flow from a momentum- dominated to a buoyancy-dominated regime was identified in another set of experiments.https://thesis.library.caltech.edu/id/eprint/2742Studies of mixing and combustion in hypervelocity flows with hot hydrogen injection
https://resolver.caltech.edu/CaltechETD:etd-08222007-092852
Authors: {'items': [{'email': 'jacquesbelanger@comcast.net', 'id': 'Belanger-Jacques', 'name': {'family': 'Belanger', 'given': 'Jacques'}, 'show_email': 'YES'}]}
Year: 1993
DOI: 10.7907/012K-GE91
<p>The ability to build an air-breathing single-stage-to-orbit propulsion system requires examination of key elements such as turbulent mixing rates, especially at the "zero shear" fuel-air mixing condition, and combustion efficiency. The required data can only be obtained in experiments which simultaneously match the flight total pressure and total enthalpy as well as the fuel conditions. GALCIT, with its new free piston shock tunnel T5, has the capability to do some of these combustion experiments. But prior to these tests, it was felt that there was a need to simulate the gas dynamical processes in the free piston shock tunnel and also in a new combustion driven shock tunnel built for these experiments so that both systems could be used as efficiently as possible. The numerical code helped explain the piston motion in the free piston shock tunnel. The code was also very useful for the design of the combustion driven shock tunnel.</p>
<p>Because hydrogen has to be injected into the combustion chamber of the propulsion system after being used as a cooling fluid, a combustion driven shock tunnel was built to reproduce this "hot" hydrogen fuel. The system has been used successfully to supply hydrogen at up to 1500 K for the experiments. To reduce the complexity of the problem, a very basic configuration for the hydrogen injection system was tested. This was first done with an injection system mounted flush with the surface of a flat plate in the test section of T5. Different test conditions as well as Mach 2 and 5 nozzle injectors at angles of 15° or 30° were tested to determine criteria for significant combustion. Lower limits in pressure and enthalpy were found where hydrogen combustion becomes very limited using this "hot" hydrogen fuel. The second set of experiments still used an injection system mounted flush with the surface but involved a small combustor model previously tested in the hypervelocity HYPULSE facility. Low pressure experiments were performed to reproduce some of the HYPULSE tests and excellent agreement was found. Experiments at high pressure were also performed to better match the real flight total pressure and some hydrogen combustion was detected in these tests.</p>https://thesis.library.caltech.edu/id/eprint/3197An adaptive Lagrangian method for computing 1-D reacting flows, and, The theory of Riemann invariant manifolds for the compressible Euler equations
https://resolver.caltech.edu/CaltechETD:etd-09192007-130342
Authors: {'items': [{'id': 'Lappas-T', 'name': {'family': 'Lappas', 'given': 'Tasso'}, 'show_email': 'NO'}]}
Year: 1993
DOI: 10.7907/bw0e-2789
In the first part of this thesis, a method for computing one-dimensional, unsteady compressible flows, with and without chemical reactions, is presented. This work has focused on accurate computation of the discontinuous waves that arise in such flows. The main feature of the method is the use of an adaptive Lagrangian grid. This allows the computation of discontinuous waves and their interactions with the accuracy of front-tracking algorithms. This is done without the use of additional grid points representing shocks, in contrast to conventional, front-tracking schemes. The Lagrangian character of the present scheme also allows contact discontinuities to be captured easily. The algorithm avoids interpolation across discontinuities in a natural and efficient way. The method has been used on a variety of reacting and non-reacting flows in order to test its ability to compute complicated wave interactions accurately and in a robust way.
In the second part of this thesis, a new approach is presented for computing multidimensional flows of an inviscid gas. The goal is to use the knowledge of the one-dimensional, characteristic problem for gas dynamics to compute genuinely multidimensional flows in a mathematically consistent way. A family of spacetime manifolds is found on which an equivalent 1-D problem holds. These manifolds are referred to as Riemann Invariant Manifolds. Their geometry depends on the local, spatial gradients of the flow, and they provide locally a convenient system of coordinate surfaces for spacetime. In the case of zero entropy gradients, functions analogous to the Riemann invariants of 1-D gas dynamics can be introduced. These generalized Riemann Invariants are constant on the Riemann Invariant Manifolds. The equations of motion are integrable on these manifolds, and the problem of computing the solution becomes that of determining the geometry of these manifolds locally in spacetime.
The geometry of these manifolds is examined, and in particular, their relation to the characteristic surfaces. It turns out that they can be space-like or time-like, depending on the flow gradients. An important parameter is introduced, which plays the role of a Mach number for the wave fronts that these manifolds represent. Finally, the issue of determining the solution at points in spacetime, using information that propagates along space-like surfaces is discussed. The question of whether it is possible to use information outside the domain of dependence of a point in spacetime to determine the solution is discussed in relation to the existence and uniqueness theorems, which introduce the concept of domain of dependence.
This theory can be viewed as an extension of the method of characteristics to multidimensional, unsteady flows. There are many ways of using the theory to develop practical, numerical schemes. It is shown how it is possible to correct a conventional, second-order Godunov scheme for multidimensional effects, using this theory. A family of second-order, conservative Godunov schemes is derived, using the theory of Riemann Invariant Manifolds, for the case of two-dimensional flow. The extension to three dimensions is straightforward. One of these schemes is used to compute two standard test cases and a two-dimensional, inviscid, shear layer.
https://thesis.library.caltech.edu/id/eprint/3644Theoretical and computational studies of isotropic homogeneous turbulence
https://resolver.caltech.edu/CaltechETD:etd-06222005-133921
Authors: {'items': [{'email': 'mjhuang@ntu.edu.tw', 'id': 'Huang-M', 'name': {'family': 'Huang', 'given': 'Mei-Jiau'}, 'show_email': 'YES'}]}
Year: 1994
DOI: 10.7907/CQ2T-Z242
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Numerical simulations are presented for viscous incompressible homogeneous turbulent flows with periodic boundary conditions. Our numerical method is based on the spectral Fourier method. Rogallo's code is modified and extended to trace fluid particles and simulate the evolution of material line elements.
The first part of the thesis is about modifying and applying the code to simulate a passive vector field convected and stretched by the so-called ABC flows in the presence of viscosity. The correlation of the geometry of the physical structures of the passive vector with the external straining is investigated. It is observed that most amplifications either occur in the neighborhoods of local unstable manifolds of the stagnation points of the ABC flows, if they exist, especially those with only one positive eigenvalue, or they are confined within the chaotic regions of the ABC flows if there is no stagnation point. Tube-like structures in all simulations are observed.
The second part of the thesis is an investigation of the power-law energy decay of turbulence. Two decay exponents, 1.24 and 1.54, are measured from simulations. A new similarity form for the double and triple velocity autocorrelation functions using the Taylor microscale as the scaling, consistent with the Karman-Howarth equation and a power-law, energy decay, is proposed and compared with numerical results. The proposed similarity form seems applicable at small to intermediate Reynolds number. For flows with very large Reynolds number, an expansion form of energy spectrum is proposed instead. Two lengthscales are used to express the energy spectrum in the energy-containing range and in the dissipation range of wave numbers. The uniform expansion is obtained by matching spectra in the inertial subrange to the famous Kolmogorov's [...] spectrum.
The third part of the thesis is a presentation of the Lagrangian data collected by tracking fluid particles in decaying turbulent flows. The mean growth rates of the magnitudes of material line elements, that of the vorticity due to nonlinear forces, and the mean principal rates of strain tensors are found to be proportional to the square root of the mean enstrophy. The proportional coefficients remain constant during the decay. The mean angles between material line elements and the principal directions of the strain tensors corresponding to the most stretching and the intermediate principal rates are about the same which is probably caused by the averaging process and by the possible switch of principal directions. The evolution of these angles under the action of one Burger's vortex is examined and the results support the conjecture. Following fluid particles which suffer substantial stretching in their history, we, through use of flow visualization tools, observe the evolution of nearby vorticity structures. It is observed that vortex sheets are created first by the nonlinear stretching which gradually become tubes at later times by diffusion.
https://thesis.library.caltech.edu/id/eprint/2685Laser-Induced Thermal Ccoustics
https://resolver.caltech.edu/CaltechETD:etd-09182007-085047
Authors: {'items': [{'id': 'Cummings-Eric-Bryant', 'name': {'family': 'Cummings', 'given': 'Eric Bryant'}, 'show_email': 'NO'}]}
Year: 1995
DOI: 10.7907/p7mb-d967
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Laser-induced thermal acoustics (LITA) is a new technique for remote nonintrusive measurement of thermophysical gas properties. LITA involves forming, via opto-acoustic effects, grating-shaped perturbations of gas properties using intersecting beams from a short-pulse laser. A third beam scatters coherently into a signal beam off the perturbation grating via acousto-optical effects. The evolution of the gas perturbations modulates the scattered signal beam. Accurate values of the sound speed, transport properties, and composition of the gas can be extracted by analyzing the signal beam.
An analytical expression for the spectrum, absolute magnitude, and time history of the LITA signal is derived. The optoacoustic effects of thermalization and electrostriction are treated. Finite beam-diameter, beam-duration, and thermalization-rate effects are included in the analysis. The expression accurately models experimental signals over a wide range of gas conditions.
Experimental tests using LITA have been conducted on pure and [...]-seeded air and helium at pressures ranging from ~0.1 kPa-14 MPa. Carbon dioxide has been explored near its liquid-vapor critical point. Accuracies of 0.1% in sound speed measurements have been achieved in these tests. Accuracies of ~1% have been achieved in measurements of thermal diffusivity, although beam misalignment effects have typically degraded this accuracy by a factor of ~10-20. Using LITA, susceptibility spectra have been taken of approximately a femtogram of [...]. The effects of fluid motion and turbulence have been explored. LITA velocimetry has been demonstrated, in which the Doppler shift of light scattered from a flowing fluid is measured. LITA velocimetry requires no particle seeding, has a coherent signal beam, and can be applied to pulsed flows. LITA has also been applied to measure single-shot [...] or "Rayleigh scattering" spectra of a gas using a technique of wavelength-division multiplexing, called multiplex LITA. The LITA apparatus used in these tests costs about one-tenth that of many conventional laser diagnostics. Narrowband LITA measurements of the sound speed and transport properties and multiplex LITA measurements of the spectral properties of gases may be taken in a single laser shot.
https://thesis.library.caltech.edu/id/eprint/3627Transport, stirring and mixing in two-dimensional vortex flows
https://resolver.caltech.edu/CaltechETD:etd-10182007-132306
Authors: {'items': [{'id': 'Min-I-A', 'name': {'family': 'Min', 'given': 'Inki A.'}, 'show_email': 'NO'}]}
Year: 1995
DOI: 10.7907/8y2c-8203
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
To understand the basic contribution of vortex motion in the transport and mixing of passive fluid, we study a system of N discrete vortices. With variation of N and [...] (a vorticity distribution parameter), we are able to experiment with a range of vortex dynamics sufficient to capture many of the features of two-dimensional turbulence in their elementary form - such as vortex merging (inverse cascade of energy), filamentation (enstrophy cascade), etc. With this model the mixing of the fluid is numerically studied via stretch statistics and the spatial distribution of a non-diffusive scalar interface. The spectrum of spatial distribution of scalars as a result of the stirring motion of the N vortices is particularly important in view of the recent (as well as historical) interest in the characterization of the scalar distribution in turbulence. We also examine the velocity field statistics and the Lagrangian motion of fluid particles. It is also instructive to look at the kinematic causes behind the types of statistics that are obtained for the velocity structure functions. A 'building block' approach to understanding these effects in turbulence may lie in building up from a collection of discrete vortices, as done in this thesis, to adding vortices of different scales and the three-dimensional effects. It is in the context of these wider issues that we study the N-vortex problem.
In the final part of this thesis we investigate the two-dimensional mixing produced by large scale vortical structures during the evolution of a spatially developing mixing layer. Although the advent of three-dimensionality and fully developed turbulence are essential features of mixing layers, it is still dominated by the large scale two-dimensional structures and its effect on the mixing is illustrated here.
https://thesis.library.caltech.edu/id/eprint/4169Unsplit Numerical Schemes for Hyperbolic Systems of Conservation Laws with Source Terms
https://resolver.caltech.edu/CaltechETD:etd-06032005-161139
Authors: {'items': [{'email': 'miltos@term.ucl.ac.be', 'id': 'Papalexandris-Miltiadis-Vassilios', 'name': {'family': 'Papalexandris', 'given': 'Miltiadis Vassilios'}, 'show_email': 'YES'}]}
Year: 1997
DOI: 10.7907/HW7S-AR36
In this thesis, a new method for the design of unsplit numerical schemes for hyperbolic systems of conservation laws with source terms is developed. Appropriate curves in space-time are introduced, along which the conservation equations decouple to the characteristic equations of the corresponding one-dimensional homogeneous system. The local geometry of these curves depends on the source terms and the spatial derivatives of the solution vector. Numerical integration of the characteristic equations is performed on these curves.
In the first chapter, a scalar conservation law with a stiff, nonlinear source term is studied using the proposed unsplit scheme. Various tests are made, and the results are compared with the ones obtained by conventional schemes. The effect of the stiffness of the source term is also examined.
In the second chapter, the scheme is extended to the one-dimensional, unsteady Euler equations for compressible, chemically-reacting flows. A numerical study of unstable detonations is performed. Detonations in the regime of low overdrive factors are also studied. The numerical simulations verify that the dynamics of the flow-field exhibit chaotic behavior in this regime.
The third chapter deals with the development and implementation of the unsplit scheme, for the two-dimensional, reactive Euler equations. In systems with more than two independent variables there are one-parameter families of curves, forming manifolds in space-time, along which the one-dimensional characteristic equations hold. The local geometry of these manifolds and their position relative to the classical characteristic rays are studied. These manifolds might be space-like or time-like, depending on the local flow gradients and the source terms.
In the fourth chapter a numerical study of two-dimensional detonations in performed. These flows are intrinsically unstable and produce very complicated patterns, such as cellular structures and vortex sheets. The proposed scheme appears to be capable of capturing many of the the important details of the flow-fields. Unlike traditional schemes, no explicit artificial-viscosity mechanisms need to be used with the proposed scheme.https://thesis.library.caltech.edu/id/eprint/2427Mixing and Isosurface Geometry in Turbulent Transverse Jets
https://resolver.caltech.edu/CaltechETD:etd-01082002-152648
Authors: {'items': [{'email': 'jshan@its.caltech.edu', 'id': 'Shan-Wei-Jen-Jerry', 'name': {'family': 'Shan', 'given': 'Wei-Jen Jerry'}, 'show_email': 'YES'}]}
Year: 2001
DOI: 10.7907/0R6S-DY34
Mixing and the geometry of jet-fluid-concentration level sets in turbulent transverse jets were experimentally studied. Jet-fluid concentration fields were measured with laser-induced fluorescence and digital imaging techniques for Reynolds numbers between 1000 and 20000. The scalar field is assessed in terms of classical measures, such as two-dimensional power spectra, as well as probability-density functions (PDFs). Enhanced scalar mixing with increasing Reynolds number is found in the evolution of PDFs of jet-fluid concentration. In the far field of the transverse jet, the scalar PDF is seen to evolve from a monotonically-decreasing function to a strongly-peaked distribution with increasing Reynolds number. Turbulent mixing is found to be flow dependent, based on differences between PDFs of scalar fields in transverse jets and axisymmetric, turbulent jets. The distribution of scalar increments is also studied for separations of varying distance and direction. A novel technique for whole-field measurement of scalar increments is introduced. Probability-density functions of scalar increments are found to trend toward exponential-tailed distributions with decreasing separation distances. The scalar field is anisotropic with decreasing scale, as seen in the two-dimensional power spectra, directional scalar microscales, and in directional PDFs of scalar increments.
The geometric complexity of level-sets (iso-concentration contours) in turbulent mixing is assessed within the framework of fractal geometry.
Generalized coverage statistics are introduced for anisotropic, non-self-similar geometries. This generalized coverage counting involves covering with parallelepipeds of varying size and aspect ratio. A scale-dependent measure of the anisotropy of a set is also introduced. It is shown that this scale-dependent measure transforms the generalized coverage count to isotropy through a scale-dependent normalization of the coordinates. Level sets of jet-fluid concentration in the transverse jet are found to be anisotropic at both large and small scales. The small-scale anisotropy is explained by vertically-oriented extensional strain caused by a counter-rotating vortex pair, while the large-scale anisotropy is associated with the horizontally-elongated shape of the cross-section of the transverse jet. For the special case of isotropic box-counting, the scale-dependent coverage dimension is found to vary from unity, at the smallest length scales, to 2, at the largest length scales, indicating that the isosurfaces produced by turbulent mixing are more complex than can be described by power-law fractalshttps://thesis.library.caltech.edu/id/eprint/61Theory and Simulation of Passive Scalar Mixing in the Presence of a Mean Scalar Gradient
https://resolver.caltech.edu/CaltechETD:etd-05272004-150652
Authors: {'items': [{'email': 'pog@mit.edu', 'id': "O'Gorman-Paul-Ambrose", 'name': {'family': "O'Gorman", 'given': 'Paul Ambrose'}, 'show_email': 'NO'}]}
Year: 2004
DOI: 10.7907/K02H-HK48
<p>The turbulent mixing of a passive scalar in the presence of a mean scalar gradient was investigated using theory and simulation. The velocity-scalar cospectrum measures the distribution of the mean scalar flux across scales. An inequality is shown to bound the magnitude of the cospectrum in terms of the shell-summed energy and scalar spectra. At high Schmidt number this bound limits the possible contribution of the sub-Kolmogorov scales to the scalar flux. At low Schmidt number we use an argument of Batchelor, Howells, and Townsend (1959) to derive a new asymptotic result for the cospectrum in the inertial-diffusive range, with a -11/3 power law wavenumber dependence. A comparison is made with results from large-eddy simulation at low Schmidt number.</p>
<p>The sparse direct-interaction perturbation (SDIP) was used to calculate the cospectrum for a range of Schmidt numbers. The Kolmogorov type scaling result is recovered in the inertial-convective range, and the constant of proportionality was calculated. At high Schmidt numbers, the cospectrum is found to decay exponentially in the viscous-convective range, and at low Schmidt numbers the -11/3 power law is observed in the inertial-diffusive range. The stretched-spiral vortex model was used to calculate the cospectrum, and asymptotic expressions were found for the contribution to the cospectrum from the axial velocity in the vortex structures. Results are reported for the cospectrum from a direct numerical simulation at a Taylor Reynolds number of 265, and a comparison is made of results for the cospectrum from the SDIP, the stretched-spiral vortex model, simulation, and experiment.</p>
<p>The stretched-spiral vortex model was also used to derive expressions for the modal time correlation functions of the velocity and scalar fields. These expressions were evaluated numerically and asymptotically. Winding by the vortex core is shown to lead to an inertial timescale, and movement of the vortex structures by the large scale flow leads to a sweeping timescale. The velocity and scalar modal time correlation functions were calculated in the direct numerical simulation. They coincide for large enough wavenumber, and are found to collapse to universal forms when a sweeping timescale is used.</p>https://thesis.library.caltech.edu/id/eprint/2136Aerodynamic Control and Mixing with Ramp Injection
https://resolver.caltech.edu/CaltechETD:etd-05262005-112117
Authors: {'items': [{'email': 'johns3c@uwindsor.ca', 'id': 'Johnson-Michael-Bernard', 'name': {'family': 'Johnson', 'given': 'Michael Bernard'}, 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/8EVK-FK75
<p>Experiments have been conducted in the GALCIT Supersonic Shear Layer Facility (S3L) to investigate the behaviour of a flow and geometry with many features that are potentially useful for a Supersonic Combustion Ramjet (SCRAMJET) engine - a recirculation zone for flameholding, enhanced mixing between fuel and air, and low total-pressure losses. In a subsonic diffuser configuration with no mass injection, the exit velocity and guidewall static-pressure profiles collapse over a large range of inlet Reynolds numbers. Significant control of exit velocity and guidewall pressure profiles is possible via injection through a perforated ramp into the freestream. The control authority on the overall pressure coefficient increases with increasing inlet Reynolds number. Simple control volume models put bounds on the overall pressure coefficient for the device.</p>
<p>In low-supersonic flow, the area ratio calculated from measured pressures agrees well with the visual shear-layer thickness, illustrating the low total-pressure losses present.</p>
<p>Further control is possible through variable heat release from a fast-chemical reaction between reactants carried in the two streams. At the highest heat release studied, mass injection requirements are lowered by, roughly, a factor of two. Measurements of mixing inferred from the temperature rise from such a reaction indicate a high level of mixing vs. classical free shear layers. As in free shear layers, however, the level of mixing begins to decrease with increasing heat release.</p>https://thesis.library.caltech.edu/id/eprint/2091Experiments and Modeling of Impinging Jets and Premixed Hydrocarbon Stagnation Flames
https://resolver.caltech.edu/CaltechETD:etd-05242005-165713
Authors: {'items': [{'email': 'jeffrey.bergthorson@mcgill.ca', 'id': 'Bergthorson-Jeffrey-Myles', 'name': {'family': 'Bergthorson', 'given': 'Jeffrey Myles'}, 'orcid': '0000-0003-2924-7317', 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/7FQZ-EY88
<p>To model the combustion of long-chain hydrocarbon fuels, an accurate kinetics mechanism must first be developed for the oxidation of small hydrocarbons, such as methane, ethane, and ethylene. Even for methane, a generally accepted mechanism is still elusive due to a lack of kinetically independent experimental data. In this work, a combined experimental and modeling technique is developed to validate and further optimize these mechanisms. This technique relies on detailed measurements of strained flames in a jet-wall stagnation flow using simultaneous Particle Streak Velocimetry (PSV) and CH Planar Laser Induced Fluorescence (PLIF). Stagnation flames are simulated using an axisymmetric, one-dimensional model with accurate specification of the requisite boundary conditions. Direct comparisons between experiment and simulation allow for an assessment of the various models employed, with an emphasis on the chemistry model performance.</p>
<p>The flow field for a cold impinging laminar jet is found to be independent of the nozzle-to-plate separation distance if velocities are scaled by the Bernoulli velocity. The one-dimensional formulation is found to accurately model the stagnation flow if the velocity boundary conditions are appropriately specified. The boundary-layer-displacement-thickness corrected diameter is found to be an appropriate scale for axial distances and allows the identification of an empirical, analytical expression for the flow field of the impinging laminar jet.</p>
<p>Strained methane-air flame experiments confirm that the reacting flow is also independent of the nozzle-to-plate separation distance. Methane, ethane, and ethylene flames are studied as functions of the applied strain rate, mixture dilution, and mixture fraction. Mechanism performance is found to be relatively insensitive to both the mixture dilution and the imposed strain rate, while exhibiting a stronger dependence on the fuel type and flame stoichiometry. The approach and diagnostics presented here permit an assessment of the predictions of strained-hydrocarbon flames for several combustion chemistry mechanisms. The data presented in this thesis are made available to kineticists looking for optimization targets, with the goal of developing a predictive kinetics model for hydrocarbon fuels. The methodology described here can allow new optimization targets to be rapidly measured, reducing the experimental burden required to fully constrain the chemistry models.</p>https://thesis.library.caltech.edu/id/eprint/2004Modeling and Simulation of Axisymmetric Stagnation Flames
https://resolver.caltech.edu/CaltechETD:etd-04252007-170838
Authors: {'items': [{'id': 'Sone-Kazuo', 'name': {'family': 'Sone', 'given': 'Kazuo'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/DYGA-YJ20
<p>Laminar flame modeling is an important element in turbulent combustion research. The accuracy of a turbulent combustion model is highly dependent upon our understanding of laminar flames and their behavior in many situations. How much we understand combustion can only be measured by how well the model describes and predicts combustion phenomena. One of the most commonly used methane combustion models is GRI-Mech 3.0. However, how well the model describes the reacting flow phenomena is still uncertain even after many attempts to validate the model or quantify uncertainties.</p>
<p>In the present study, the behavior of laminar flames under different aerodynamic and thermodynamic conditions is studied numerically in a stagnation-flow configuration. In order to make such a numerical study possible, the spectral element method is reformulated to accommodate the large density variations in methane reacting flows. In addition, a new axisymmetric basis function set for the spectral element method that satisfies the correct behavior near the axis is developed, and efficient integration techniques are developed to accurately model axisymmetric reacting flow within a reasonable amount of computational time. The numerical method is implemented using an object-oriented programming technique, and the resulting computer program is verified with several different verification methods.</p>
<p>The present study then shows variances with the commonly used GRI-Mech 3.0 chemical kinetics model through a direct simulation of laboratory flames that allows direct comparison to experimental data. It is shown that the methane combustion model based on GRI-Mech 3.0 works well for methane-air mixtures near stoichiometry. However, GRI-Mech 3.0 leads to an overprediction of laminar flame speed for lean mixtures and an underprediction for rich mixtures. This result is slightly different from conclusion drawn in previous work, in which experimental data are compared with a one-dimensional numerical solutions. Detailed analysis reveals that flame speed is sensitive to even slight flame front curvature as well as its finite extension in the radial direction. Neither of these can be incorporated in one-dimensional flow modeling.</p>https://thesis.library.caltech.edu/id/eprint/1500Transition Between Regular Reflection and Mach Reflection in the Dual-Solution Domain
https://resolver.caltech.edu/CaltechETD:etd-01052007-125557
Authors: {'items': [{'email': 'cm@k-a-p.com', 'id': 'Mouton-Christopher-Andre', 'name': {'family': 'Mouton', 'given': 'Christopher Andre'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/TEA0-Q468
<p>A study of the shock-reflection domain for steady flow is presented. Conditions defining boundaries between different possible shock-reflection solutions are given, and where possible, simple analytic expressions for these conditions are presented. A new, more accurate estimate of the steady-state Mach stem height is derived based on geometric considerations of the flow. In particular, the location of the sonic throat through which the subsonic convergent flow behind the Mach stem is accelerated to divergent supersonic flow is considered. Comparisons with previous computational and experimental work show that the theory presented in this thesis more accurately predicts the Mach stem height than previous theories. The Mach stem height theory is generalized to allow for a moving triple point. Based on this moving triple point theory, a Mach stem growth rate theory is developed. This theory agrees well with computational and experimental results. Numerical computations of the effects of water vapor disturbances are also presented. These disturbances are shown to be sufficient to cause transition from regular reflection to Mach reflection in the dual-solution domain. These disturbances are also modeled as a simple energy deposition on one of the wedges, and an estimate for the minimum energy required to cause transition is derived.</p>
<p>Experimental results using an asymmetric wedge configuration in the Ludwieg tube facility at the California institute of Technology are presented. A Mach 4.0 nozzle was designed and built for the Ludwieg tube facility. This Mach number is sufficient to provide a large dual-solution domain, while being small enough not to require preheating of the test gas. The test time of the facility is 100ms, which requires the use of high-speed cinematography and a fast motor to rotate one of the two wedges. Hysteresis in the transition between regular to Mach reflection was successfully demonstrated in the Ludwieg tube facility. The experiments show that regular reflection could be maintained up to a shock angle approximately halfway between the von Neumann condition and the detachment condition.</p>
<p>Energy deposition studies were performed using an Nd:YAG laser. Triggering transition in this manner is found to depend on the location of the energy deposition. This finding is consistent with the numerical work presented in this thesis. Experiments were also performed to measure the Mach stem height and its growth rate. These results are compared with the theoretical estimates presented in this thesis. Excellent agreement between the steady-state Mach stem height and the theoretical estimates is seen. Comparisons of Mach stem growth rate with theoretical estimates show significant differences, but do show good agreement regarding the time required to reach the steady-state height.</p>https://thesis.library.caltech.edu/id/eprint/36Large-Eddy Simulations of Molecular Mixing in a Recirculating Shear Flow
https://resolver.caltech.edu/CaltechETD:etd-05262008-152803
Authors: {'items': [{'email': 'georgios.matheou@uconn.edu', 'id': 'Matheou-Georgios', 'name': {'family': 'Matheou', 'given': 'Georgios'}, 'orcid': '0000-0003-4024-4571', 'show_email': 'YES'}]}
Year: 2008
DOI: 10.7907/VFKF-SC30
<p>The flow field and mixing in an expansion-ramp geometry is studied using large-eddy simulation (LES) with subgrid scale (SGS) modeling based on the stretched-vortex model. The expansionramp geometry was developed to provide enhanced mixing and flameholding characteristics while maintaining low total-pressure losses, elements that are important in the design and performance of combustors for hypersonic air-breathing propulsion applications. The mixing was studied by tracking a passive scalar without taking into account the effects of chemical reactions and heat release.</p>
<p>In order to verify the solver and the boundary closure implementation, a method utilizing results from linear stability analysis (LSA) theory is developed. LSA can be used to compute unstable perturbations to a flow, subject to certain approximations. The perturbations computed from LSA are used as an inflow condition to the flow computed by the solver been assessed. A projection based metric is constructed that only assumes the shape of the solution and not the growth rate of the perturbations, thus also allowing the latter to be determined as part of the verification. The growth rate of the perturbations for an unbounded (effectively) incompressible shear layer and a confined compressible shear layer is found to be in agreement with the prediction of the LSA.</p>
<p>The flow and mixing predictions of the LES are in good agreement with experimental measurements. Total (resolved and subgrid) probability density functions (PDFs) of the passive scalar are estimated using an assumed beta-distribution model for the subgrid scalar field. The improved mixing characteristics of the expansion-ramp geometry compared to free shear layers are illustrated by the shapes of the PDFs. Moreover, the temperature rise and the probability of mixed fluid profiles are in good agreement with the experimental measurements, indicating that the mixing on a molecular scale is correctly predicted by the LES–SGS model. Finally, the predictions of the LES are shown to be resolution-independent. The mean fields and passive scalar PDFs have essentially converged at the two finer grid-resolutions used.</p>https://thesis.library.caltech.edu/id/eprint/2117Premixed Hydrocarbon Stagnation Flames: Experiments and Simulations to Validate Combustion Chemical-Kinetic Models
https://resolver.caltech.edu/CaltechETD:etd-05302008-113043
Authors: {'items': [{'email': 'benezech.laurent@gmail.com', 'id': 'Benezech-Laurent-Jean-Michel', 'name': {'family': 'Benezech', 'given': 'Laurent Jean-Michel'}, 'show_email': 'YES'}]}
Year: 2008
DOI: 10.7907/TVB9-4266
<p>A methodology based on the comparison of flame simulations relying on reacting flow models with experiment is applied to C<sub>1</sub>–C<sub>3</sub> stagnation flames. The work reported targets the assessment and validation of the modeled reactions and reaction rates relevant to (C<sub>1</sub>–C<sub>3</sub>)-flame propagation in several detailed combustion kinetic models. A concensus does not, as yet, exist on the modeling of the reasonably well-understood oxidation of C<sub>1</sub>–C<sub>2</sub> flames, and a better knowledge of C<sub>3</sub> hydrocarbon combustion chemistry is required before attempting to bridge the gap between the oxidation of C<sub>1</sub>–C<sub>2</sub> hydrocarbons and the more complex chemistry of heavier hydrocarbons in a single kinetic model.</p>
<p>Simultaneous measurements of velocity and CH-radical profiles were performed in atmospheric propane(C<sub>3</sub>H<sub>8</sub>)- and propylene(C<sub>3</sub>H<sub>6</sub>)-air laminar premixed stagnation flames stabilized in a jet-wall configuration. These nearly-flat flames can be modeled by one-dimensional simulations, providing a means to validate kinetic models. Experimental data for these C<sub>3</sub> flames and similar experimental data for atmospheric methane(CH<sub>4</sub>)-, ethane(C<sub>2</sub>H<sub>6</sub>)-, and ethylene(C<sub>2</sub>H<sub>4</sub>)-air flames are compared to numerical simulations performed with a one-dimensional hydrodynamic model, a multi-component transport formulation including thermal diffusion, and different detailed-chemistry models, in order to assess the adequacy of the models employed. A novel continuation technique between kinetic models was developed and applied successfully to obtain solutions with the less-robust models. The 2005/12 and 2005/10 releases of the San Diego mechanism are found to have the best overall performance in C<sub>3</sub>H<sub>8</sub> and C<sub>3</sub>H<sub>6</sub> flames, and in CH<sub>4</sub>, C<sub>2</sub>H<sub>6</sub>, and C<sub>2</sub>H<sub>4</sub> flames, respectively.</p>
<p>Flame position provides a good surrogate for flame speed in stagnation-flow stabilized flames. The logarithmic sensitivities of the simulated flame locations to variations in the kinetic rates are calculated via the "brute-force" method for fifteen representative flames covering the five fuels under study and the very lean, stoichiometric, and very rich burning regimes, in order to identify the most-important reactions for each flame investigated. The rates of reactions identified in this manner are compared between the different kinetic models. Several reaction-rate differences are thus identified that are likely responsible for the variance in flame-position (or flame-speed) predictions in C<sub>1</sub>–C<sub>2</sub> flames.</p>https://thesis.library.caltech.edu/id/eprint/2316Mixing, Chemical Reactions, and Combustion in Supersonic Flows
https://resolver.caltech.edu/CaltechTHESIS:05242016-143905617
Authors: {'items': [{'email': 'niccolo.cymbalist@gmail.com', 'id': 'Cymbalist-Niccolo', 'name': {'family': 'Cymbalist', 'given': 'Niccolo'}, 'show_email': 'YES'}]}
Year: 2016
DOI: 10.7907/Z9G73BNR
<p>Experiments were conducted at the GALCIT supersonic shear-layer facility to investigate
aspects of reacting transverse jets in supersonic crossflow using chemiluminescence and schlieren
image-correlation velocimetry. In particular, experiments were designed to examine mixing-delay
length dependencies on jet-fluid molar mass, jet diameter, and jet inclination.</p>
<p>The experimental results show that mixing-delay length depends on jet Reynolds number, when
appropriately normalized, up to a jet Reynolds number of 500,000. Jet inclination increases the
mixing-delay length, but causes less disturbance to the crossflow when compared to normal jet
injection. This can be explained, in part, in terms of a control-volume analysis that relates jet
inclination to flow conditions downstream of injection.</p>
<p>In the second part of this thesis, a combustion-modeling framework is proposed and developed
that is tailored to large-eddy simulations of turbulent combustion in high-speed flows. Scaling arguments place supersonic hydrocarbon combustion in a regime of autoignition-dominated distributed
reaction zones (DRZ). The proposed evolution-variable manifold (EVM) framework incorporates an
ignition-delay data-driven induction model with a post-ignition manifold that uses a Lagrangian
convected 'balloon' reactor model for chemistry tabulation. A large-eddy simulation incorporating
the EVM framework captures several important reacting-flow features of a transverse hydrogen jet
in heated-air crossflow experiment.</p>https://thesis.library.caltech.edu/id/eprint/9742Investigations of Incompressible Variable-Density Turbulence in an External Acceleration Field
https://resolver.caltech.edu/CaltechTHESIS:12052017-154614667
Authors: {'items': [{'email': 'ilana.gat@gmail.com', 'id': 'Gat-Ilana-Batya', 'name': {'family': 'Gat', 'given': 'Ilana Batya'}, 'orcid': '0000-0003-0223-0507', 'show_email': 'NO'}]}
Year: 2018
DOI: 10.7907/Z9JM27V7
<p>Of interest to turbulence modeling is the behavior of variable-density flow at high Reynolds numbers - a flow difficult to model. This thesis provides insight into variable-density flow behavior by examining the dynamics and mixing of variable-density turbulence subject to an externally imposed acceleration field. The flow is studied in the zero-Mach-number limit with a series of direct numerical simulations. The flow configuration consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of 1.005 to 10 are investigated. The flow produces temporally evolving shear layers.</p>
<p>A perpendicular mean density–pressure gradient is maintained as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime.</p>
<p>An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate with the square-root of time followed by a turbulence-dominated regime with a cubic growth rate in time. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted ('non-marching') hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.</p>
<p>The mixed-fluid orientations of vorticity, baroclinic torques, density gradients, and pressure gradients are presented. Baroclinic torques, the cross product of the density and pressure gradients, tend to be aligned with positive or negative vorticity direction, with vorticity preferentially aligning with the intermediate eigenvector of the local strain-rate tensor, with some variance.</p>https://thesis.library.caltech.edu/id/eprint/10586