(PHD, 2007)

Abstract:

Vortex-induced vibrations have been studied experimentally with emphasis on damping and Reynolds number effects. Our system was an elastically-mounted rigid circular cylinder, free to oscillate only transverse to the flow direction, with very low inherent damping. We were able to prescribe the mass, damping, and elasticity of the system over a wide range of values, with the damping controlled by a custom-made variable magnetic eddy-current damping system.

Special emphasis is put on a nontraditional parameter formulation. The advantages of this formulation are explained, and an important new parameter, effective stiffness, is introduced. Using this new formulation, the amplitude and frequency responses are only a function of damping, Reynolds number, and effective stiffness. We show the effects that damping and Reynolds number each have on the amplitude and frequency response profiles and make the interesting observation that changes in damping or Reynolds number have similar effects.

The maximum amplitudes of our systems are studied in detail. We theoretically show that they should be functions of both damping and Reynolds number. This allows us to create constant-Reynolds-number curves of maximum amplitude over a large range of damping values, which we call a “generalized” Griffin plot. We also define maximum amplitudes in the case of zero damping as limiting amplitudes, and show that they are only a function of Reynolds number. We experimentally determine our limiting amplitude dependence on Reynolds number over the range 200 < Reynolds number < 5050.

Discontinuities in the amplitude response profile are also investigated. The discontinuity between the initial branch and the large-amplitude, upper branch is studied in two ways. First, the time-averaged behavior is examined to understand what controls the discontinuity and look for damping and Reynolds number effects. Second, we track the cycle-by-cycle transient response through this discontinuous amplitude change, induced either by changes in the tunnel velocity or system damping. Finally, we also find a new discontinuity hysteresis region between the lower branch and the desynchronized region, which appears to be a low Reynolds number effect and is only seen in systems with Reynolds number < 1000.

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(PHD, 1997)

Abstract:

NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.

We present some exact expressions for the evaluation of time-dependent forces on a body in an incompressible and viscous cross-flow which only require the knowledge of the velocity field (and its derivatives) in a finite and arbitrarily chosen region enclosing the body.

Given a control volume V with external surface S which encloses an arbitrary body, the fluid-dynamic force F on the body can be evaluated from one of the following three expressions (in abbreviated form):

F = […] + body motion terms,

F = […] + body motion terms,

F = no volume integral terms + […] + body motion terms,

where N is the space dimension, u is the flow velocity, […] is the vorticity, x is the position vector, and the tensors […], […], […] depend only on the velocity field u and its (spatial and temporal) derivatives.

The first equation is already known for either simply connected domains or inviscid flows. We re-derive it here for viscous flows in doubly connected domains (i.e. domains which include a body). We then obtain the second and third equation through a simple algebraic manipulation of the first equation.

These expressions are particularly useful for experimental techniques like Digital particle Image Velocimetry (DPIV) which provide time sequences of 2D velocity fields but not pressure fields.

They are tested experimentally with DPIV on two-dimensional, low Reynolds number circular cylinder flows. Both steady and unsteady motions are studied.

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(PHD, 1996)

Abstract:

An experimental study is performed in a water tunnel (Re = 40,000 to Re = 60,000) to study the interaction between the wake of a circular disk and the free surface. The deformation of the free surface is correlated with the behavior of the wake by utilizing surface pictures, wake flow visualization, drag measurement and Digital Particle Image Velocimetry techniques. It is observed that the wake can exist in two modes with different stabilities. The flow can switch between these two modes and the switching process exhibits hysteresis. The topological differences between these modes and their relation to the observed surface patterns are discussed. The changes in the wake are reflected by an increase in Cd which reaches a maximum value when the upper edge of the disk is 0.125 diameters from the surface. Comparison is also made with a disk approaching a solid boundary.

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(PHD, 1996)

Abstract:

An experimental study of the effects of exit Mach number and density ratio on the development of axisymmetric jets is described in this thesis. Jet exit Mach numbers of 1.41, 2.0, and 3.0, were studied for jets of helium, argon, and nitrogen. The jets exit into a gas at rest (velocity ratio = 0), in order to better isolate the effects of compressibility and density ratio. Density ratios vary from 0.23 to 5.5.

In order to generate shock free-jets, unique nozzles were designed and constructed for each gas and Mach number combination. A plating method for the construction of the nozzles was developed to ensure high-accuracy and a good surface finish at a cost significantly less than direct-machining techniques.

The spreading rate of the jet for several downstream locations is measured with a pitot probe. Centerline data are used to characterise the length of the potential core of the jet, which correlates well with the relative spreading rates. Limited frequency data is obtained through the use of piezo-resistive pressure probes. This method is promising for flows that are not conducive to hot-wire probes.

Spark shadography is used to visualize both the mean and instantaneous flow, with the minimum spark time being 20 nanoseconds. The convection velocity of large-scale disturbances is estimated from the visible Mach-type acoustic waves emanating from the jet.

For a wide range of jet Mach and Reynolds numbers, the convection velocity of the large scale disturbances in the potential core region of the jet is approximately 0.8 times the jet velocity, the approximate velocity of the first helical instability mode of the jet.

The main objectives of the present work were to investigate the effects of compressibility and density on the initial development of the axisymmetric jet. Although the data are not sufficient to determine if the convective Mach number concept used in 2-d shear layer research will work in the case of an axisymmetric jet, it is clear that the axisymmetric data do not collapse onto the 2-d curve. However, the density ratio scaling used for the 2-d shear layer appears to work well for the axisymmetric jet, based on the available data.

The data appear to indicate that the initial development of the jet is dominated by instability modes of the jet as a whole, rather than the shear layers.

One anomaly noted was that there were long period variations in the centerline total pressure, with times on the order of 3000 jet time scales. The fluctuations did not appear to be experimental artifacts.
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(PHD, 1993)

Abstract:

NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.

Measurements in the near wake region of a circular cylinder in a uniform flow in the Reynolds number range […] with permeable splitter plates spanning the wake center plane are presented. Permeability is defined by the pressure drop across the plates, and the relationship between permeability and plate solidity is determined for a set of plates constructed from woven wire mesh, permitting unambiguous characterization of the splitter plates by the solidity. The effects of different solidities on the flow in the near wake are investigated using smoke wire flow visualization, hot-wire anemometry, and measurements of the mean pressure at the cylinder surface, and the results are related to cylinder flow without a splitter plate.

Flow visualization results demonstrate that the introduction of low solidity splitter plates does not change the basic near wake structure, and that sufficiently high solidity uncouples the large-scale wake instability from the body, with the primary vortex formation occurring downstream of the separation bubble due to instability of the wake profile. Hotwire and surface pressure measurements confirm and quantify the flow visualization results, showing that the permeable splitter plates reduce the drag and modify the primary wake frequency. When the solidity is high enough that the wake is convectively unstable, the base pressure is independent of the Reynolds number and solidity. For a wide range of solidities, the same asymptotic value of the Strouhal number is reached at high Reynolds numbers. The relationship between the Strouhal number and the base pressure is discussed.

Detailed measurements in the separating shear layers with splitter plates moderating the primary vortex formation show that in the mean the development of the separating shear layers is similar to that of the plane mixing layer. The presence of the splitter plates enhances shear layer development, and it is found that for all solidities the instability amplifies a broad frequency band without discrete spectral features. Turbulent transition in the shear layer and its role in the pronounced Reynolds number dependency of the flow in this Reynolds number range is discussed. Acoustic excitation of the separated shear layers confirms the broad band frequency response of the shear layer instability, and the effect of the driven shear layers on the near wake is investigated.
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(PHD, 1993)

Abstract:

NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.

Experiments were conducted on lifted, turbulent jet diffusion flames. An automated technique using a linear photodiode array was implemented to measure the temporal history of the liftoff height h. The measurements enabled accurate determination of the mean liftoff height […] under a wide range of flow conditions, including several fuels, nozzle diameters, and exit velocities […]. The results showed an approximately linear relationship between […] and […], with a slight dependence on Reynolds number. A strain-rate model for liftoff, based on far-field scaling of turbulent jets, provides an explanation for the linear dependence of […] on […]. Measurements were also made in which the nozzle fluid contained varying amounts of air, where it was found that the slope of the […] vs. […] line increases faster than predicted by far-field scaling of turbulent jets. The discrepancy is attributed to near-field effects.

The amplitudes of the fluctuations in h were found to be of the order of the local large scale of the jet. There is a slight increase in normalized fluctuation level […] with […], and there is some variation of […] with fuel type. The time scales of the fluctuations of h were found to be considerably longer than the local large-scale time of the turbulence […]. By using fuels of different chemical times to vary […], the measured correlation time […] normalized by […] was found to collapse with Richardson number […]. Experiments in which the nozzles were oriented horizontally showed no change in […], however. Additional experiments were conducted to investigate alternative explanations for the variation of […] with […]. These experiments included measuring the flame length L simultaneously with h, and measuring the visible radiation I simultaneously with h. L(t) was found to be nearly uncorrelated with h(t), dismissing the possibility that a feedback mechanism from L to h controls the fluctuations of h. Although I(t) is highly correlated with h(t) for the most sooting fuel, acetylene, it is not deemed responsible for the longer correlation times of that fuel. This was deduced from experiments using mixtures of hydrogen with other fuels, which produce very little radiation, but which have values of […] comparable to those of acetylene flames.

Another experiment was conducted in which two-dimensional images of fuel concentration (CH4) and reaction zones (indicated by CH) were obtained. The images showed a wide variety of structure types, indicating that there is no universal description of the flow field at the flame base. The flame stabilization position showed large fluctuations in both the axial and radial directions. The shot to shot variation in methane number density at the flame base was also large.
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(PHD, 1993)

Abstract:

Towing tank and water channel experiments and a two-dimensional vortex element numerical model were used to study the forces experienced by a bluff flat plate set normal to a nominally two-dimensional flow. Intrinsic (small scale) and extrinsic (large scale) three-dimensional motions in the experimental flow were isolated and their separate and combined effects on forces and overall wake development were studied. Transient flow development starting from rest, as well as steady flow conditions, were investigated.

A force balance was used to measure the unsteady lift and drag of vertically oriented models projecting through a free surface with various lower end conditions; simultaneous LIF flow visualizations imaged the structure of the vortices in the wake. Plate aspect ratio, lower end condition and angle of attack were varied to effect changes in large scale three-dimensional motions, while changes in Reynolds number and Richardson number (flow stratification) modified the small scale three dimensionality intrinsic to the flow.

Towing tank experiments indicated that normal plates required sixty to one hundred chord lengths of travel to establish steady vortex shedding. An initial drag peak during acceleration was followed by a drag minimum of […] reached while the wake was confined to a symmetric vortex bubble. Subsequent to the breakdown of this bubble, a region of symmetric flow with […] and no vortex shedding was apparent for twenty to thirty chord lengths, followed by the final onset of vortex shedding which occurred exponentially. During this onset forces overshot their final steady-state values […]. Flows with less large scale extrinsic three dimensionality (higher aspect ratio, “more two-dimensional” end conditions, and stratified flow) had longer development times and higher subsequent overshoot levels.

Small geometric asymmetries (angle of attack variations) increased the minimum drag level seen after the acceleration and resulted in an earlier breakdown of the closed wake, followed by an immediate transition to steady shedding. The breakdown of the initial bubble in this case was more coherent spanwise and did not result in a long-lasting symmetric nonshedding flow.

During “steady-state” shedding, modulation in the vortex shedding amplitude at a time scale of five to ten Strouhal periods resulted in a twenty percent fluctuation in mean drag level, with a corresponding increase in rms lift. This modulation accompanied a slow oscillation in the formation distance of the shed vorticity, the period of which was Reynolds number independent but decreased with increasing aspect ratio, reaching a minimum value of six Strouhal periods for aspect ratios greater than ten.

Agreement between three-dimensional experimental and two-dimensional numerical-model results was good at early times, indicating the experiments were two-dimensional until the breakdown of the closed wake bubble following the initial acceleration. Prior to this breakdown the numerical model of a normal plate gave a drag coefficient […], similar to that given by the Kirchhoff-Rayleigh free-streamline prediction but lower than experiments. Small asymmetries of the 2d model resulted in an increase in the minimum drag level to […] . Subsequent to the closed wake breakdown, drag levels of […] are 65% higher than steady-state experimental values.

Although no region corresponding to the post-acceleration non-vortex-shedding seen experimentally was found in the basic numerical results, the addition of circulation decay to the numerical-model resulted in a region which appeared qualitatively similar. This circulation decay also decreased mean drag levels […] and gave an exponential shedding onset with subsequent long period shedding modulation.

Stabilizing spanwise stratification of the experimental flow had little effect for Richardson numbers […] (based on chord). For […] and […] a longer lasting post-acceleration closed wake was followed by strong initial shedding and a large drag overshoot, with a subsequent decrease in shedding amplitude and increase in formation distance to the levels seen in the unstratified […] case, which exhibited considerable Reynolds number dependence. For plates at […] angle of attack the symmetric nonvortex shedding region was reduced in duration and subsequent “steady-state” drag levels were increased ten to fifteen percent […] from the unstratified case.

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(PHD, 1992)

Abstract:

Light transmission through incompressible gaseous turbulent mixing layers is investigated with the objective of understanding the effects of large-scale coherent structures and mixing transition on the optical quality of the mixing layer. Experiments are done in a vertically flowing mixing layer which is enclosed inside a pressure tank and fed by two banks of high-pressure gas bottles. The study considers both the unequal density (high-speed […] and low-speed […]) and equal density (high-speed […] and low-speed […]) cases; the mixing of dissimilar gases is the source of the optical aberrations. Large-scale Reynolds numbers range between 3500 and 80000 over pressures from 2 to 6 bar. Light transmission characteristics are first studied qualitatively using a network of thin sheets of short-exposure ([…]) white light which are aberrated by the mixing layer and then image directly onto photographic film. Light transmission characteristics are then studied quantitatively using a lateral effect detector to dynamically track a thin He-Ne laser beam as it wanders under the influence of the passing coherent structures.

The study finds that the spanwise coherent structures generate systematic deflections of the light beam in the streamwise direction; the greatest deflections occur near the trailing edges of the structures at a formation called the cusp, where the high-speed fluid and low-speed fluid are entrained into the vortex core. The streamwise coherent structures, which form later in the mixing layer’s development than the spanwise structures, generate substantial beam deflections in the span-wise direction which are closely associated with the streamwise streaks in plan-view shadowgraphs. The rms fluctuations of the streamwise and spanwise deflection angles increase rapidly during mixing transition, peaking at 380 high-speed-side momentum thicknesses downstream from the splitter plate, then decrease far down-stream to asymptotic values of 0.6 to 0.8 as scaled by the static pressure and the Gladstone-Dale constant shift across the mixing layer. The data suggest that a possible mechanism for the deflections is the interaction of the beam with the thin interfaces which bound relatively uniform bodies of fluid inside the structures.
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(PHD, 1990)

Abstract:

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.

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.

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.

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.

Possible implications for mixing are briefly discussed.

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(PHD, 1987)

Abstract:

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.

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.

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.

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.

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^{5}, 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.

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(PHD, 1986)

Abstract:

An unsteady and three-dimensional large-scale structure is proposed for the reattachment region of a separation bubble, based on a visualization study of the flow over a plate with a square leading edge and its axisymmetric counterpart, a flat-faced circular cylinder aligned coaxially with the free-stream. The initial free shear layer structures are primarily two-dimensional but evolve into boundary layer type structures as they near reattachment and interact with the wall. Some segments form “loops” which convect away from the wall and downstream, while spanwise adjacent parts convect toward the wall and upstream. The loops are sometimes clearly arranged in a staggered pattern. Their legs form a series of counter-rotating streamwise vortex pairs which bridge the reattachment zone. These observations reconcile apparently contradictory propositions concerning the fate of the structures as they encounter reattachment. The interaction between successive vortices at alternating spanwise locations is fundamental to several flows. The structure of turbulent wakes is also discussed.

An experimental study was made of the effect of a periodic velocity perturbation on the separation bubble downstream of the sharp- edged blunt face of a circular cylinder aligned coaxially with the free stream. Velocity fluctuations were produced with an acoustic driver located within the cylinder and a small circumferential gap located immediately downstream of the fixed separation line to allow communication with the external flow. The flow could be considerably modified when forced at frequencies lower than the initial Kelvin-Helmholtz frequencies of the free shear layer, and with associated vortex wavelengths comparable to the bubble height. Reattachment length, bubble height, pressure at separation, and average pressure on the face were all reduced. The effects on the large-scale structures were studied on flow photographs obtained by the smoke-wire technique. The forcing increased the entrainment near the leading edge.

In both forced and unforced cases it was concluded that the final vortex of the shear layer before reattachment is an important element of the flow structure. There are two different instabilities involved, the Kelvin-Helmholtz instability of the free shear layer and the “shedding” type instability of the entire bubble. The latter results from an interaction with the image vortices due to the presence of the wall. A method of frequency scaling is proposed that correlates data for a variety of bubbles and supports an analogy with Karman vortex shedding.

New methods for approximating axisymmetric flows are presented. Transition of shear-layers and separation bubbles is also discussed.

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(PHD, 1985)

Abstract:

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.

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.

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.

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(PHD, 1984)

Abstract:

Smoke-wire flow visualization and hot-wire anemometry have been used to study near and far wakes of two-dimensional bluff bodies. For the case of a circular cylinder at 70 < Re < 2000, a very rapid (exponential) decay of velocity fluctuations at the Karman vortex street frequency is observed. Beyond this region of decay, larger-scale (lower wave-number) structure can be seen. In the far wake (beyond one hundred diameters) a broad band of frequencies is selectively amplified and then damped, the center of the band shifting to lower frequencies as downstream distance is increased.

The far-wake structure does not depend directly on the scale or frequency of the original Karman vortices; the growth of this structure is due to hydro-dynamic instability of the developing mean wake profile; it is not caused by amalgamation of the Karman vortices. Under certain conditions amalgamation can take place, but is purely incidental, and is not the driving mechanism responsible for the growth of larger-scale structure. Similar large structure is observed downstream of porous flat plates (Re ≈ 6000), which do not initially shed Karman-type vortices into the wake.

Hot-wire measurements show that two-dimensional locally-parallel inviscid linear stability theory is adequate to explain the growth of downstream structure. Namely, measured prominent frequencies in the cylinder wake are in close agreement with those predicted by the theory, when streamwise growth of wake width is taken into account.

Finally, three-dimensionality in the far wake of a circular cylinder is briefly discussed.

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(PHD, 1983)

Abstract:

The phenomenon of cavity flow oscillation is investigated to determine the conditions for onset of periodic oscillations and to understand the relationship between the state of the shear layer and the cavity drag. Experiments have been performed in a water tunnel using a 4" axisymmetric cavity model instrumented with a strip heater on the nose cone and pressure taps in and around the cavity. A complete set of measurements of oscillation phase, amplitude amplification along the flow direction, distribution of shear stress and other momentum flux is obtained by means of a laser Doppler velocimeter. Drag measurements were made by integrating the mean pressure over the solid surfaces of the cavity. Results indicated exponential cavity drag dependence on the length of the cavity. A jump in the cavity drag coefrcient is observed as the cavity flow shows a bluff body wake type behavior. An independent estimate of the drag, which is obtained by integration of shear and mean momentum transfer terms over the peripheral area of the cavity, confirms the exponential dependence of drag on the length of the cavity. Results, also reveal that the drag of the cavity in the non-oscillating mode is less than the case if the cavity were replaced by a solid surface. Natural and forced oscillations of the cavity shear layer spanning the gap are studied. The forced oscillations are introduced by a sinusoidally heated thin-film strip which excites the Tollmein-Schlichting waves in the boundary layer upstream of the gap, For a sufficiently large gap, self-sustained periodic oscillations are observed while for smaller gaps, which do not oscillate naturally, periodic oscillations can be obtained by external forcing through the strip-heater. In the latter case resonance is observed whenever the forcing frequency satisfies the phase criterion φ/(2π) = N, and its amplitude exceeds certain threshold levels, but the phenomenon is non-self-supporting. The drag of the cavity can be increased by one order of magnitude in the non-oscillating case through external forcing. For naturally occurring oscillations, it is possible for two waves to co-exist in the shear layer (natural and forced). Also, it is possible to completely eliminate mode switching by applying external forcing. For the first time a test is performed to cancel or dampen the amplitude of Kelvin-Helmholtz wave in the cavity shear layer. This is done through introducing an external perturbation with the same frequency of the natural component but having a different phase. Reduction by a factor of 2 is obtained in the amplitude of the oscillation.

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(PHD, 1981)

Abstract:

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.

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.

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.

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(PHD, 1979)

Abstract:

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.

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(PHD, 1978)

Abstract:

The objective of this study is to obtain better understanding of the flow over two tandemly positioned bluff bodies in close enough proximity to strongly interact with each other. This interaction is often beneficial in that the drag of the overall system is reduced. Prototypes for this problem come from tractor-trailer and cab-van combinations and from various add-on devices designed to reduce their drag.

The object of the present investigation is an axisymmetric configuration which seems to have first been studied by Saunders (1966). A disc of diameter d1 is coaxially placed in front of a flat faced cylinder of diameter d2. For a given ratio d1/d2, there is a value of gap ratio, g*/d2 for which the drag of the system is a minimum. In the most optimum configuration, d1/d2 = 0.75, g*/d2 = 0.375, and the corresponding drag coefficient is 0.01, a remarkable reduction from the value of 0.72 for the cylinder alone. For each value of d1/d2, the minimum drag configuration g*/d2 appears to correspond to a condition in which the separation streamsurface just matches (joins tangentially onto) the rearbody. Support for this idea is furnished by comparison with results derived from free-streamline theory and from flow visualization experiments. However, when g*/d2 exceeds a critical value of about 0.5, the value of CD, while still optimum, is almost an order of magnitude higher than for subcritical optimum gap ratios. The increase seems to be connected with the onset of cavity oscillations.

Measurements of the velocity field in the vicinity of the forebody have been made using a frequency-shifted laser-Doppler velocimeter. These measurements indicate an order of magnitude difference in the shear stress along the separation surface between optimum subcritical and supercritical geometries.

The drag characteristics of the axisymmetric forebody system are altered by modifying the shape of the component bodies. Modifications that change the conditions at separation from the frontbody, interfere with the cavity flow or effect the flow on the rearbody face can produce significant changes in the forebody drag.

For non-axisymmetric geometry (square cross-sections) the separation surface cannot exactly match the rear body and the subcritical minimum values of drag are higher than for circular cross-sections.

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(PHD, 1977)

Abstract:

The extent of molecular mixing in several two-dimensional free turbulent shear flows was measured using a concentration probe with a frequency response of 100 kHz and a spatial resolution of 0.1 mm. The flows investigated were (i) a shear layer in which the gases on either side of the layer are of unequal density, (ii) a shear layer in which the gases on either side of the layer are of equal density, and (iii) a wake in which the gases on either side of the wake are of unequal densities. The extent of mixing was measured as a function of Reynolds number for the first case.

It was found that at a critical Reynolds number the extent of molecular mixing sharply increased (25%). Power spectral density curves of the concentration time histories also indicated a marked increase in the high frequency fluctuations above this Reynolds number. A shadowgraph investigation of this phenomenon revealed that three-dimensional Taylor-type vortices whose axes of rotation are basically in the flow direction exist in the flow in addition to the two-dimensional large structures previously observed. These Taylor vortices were found to be unstable above the critical Reynolds number and were producing the increase in molecular mixing. The growth and development of the two-dimensional large structures were found to be basically unaffected by this instability. It is proposed that the fully developed turbulence of shear flows is maintained by a combination of the development of the large structures and of the coupling between the large structures and these unstable Taylor vortices.

These data were also used to predict results for shear flows in which diffusion-limited chemical reactions have been incorporated.

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(PHD, 1975)

Abstract:

In this study, an analytical and experimental approach has been used to investigate the phenomenon of flow induced oscillations in cavities. Laminar axisymmetric flows over shallow cavities at low subsonic speeds were experimentally investigated using constant temperature hot-wire anemometry. This study comprised the following: study of the effect of the freestream and cavity configuration on onset of cavity oscillations; measurements of cavity shear layer under a wide range of cavity and flow configurations, and the distribution of the phase of the propagating disturbances during both first and second mode of cavity oscillation for a fixed Reynolds number at the upstream corner. Both motion and instant pictures of cavity shear flow, visualized by smoke injection, were obtained. Experiments were also done to investigate the effect of artificial excitation and of mass injection on the onset of cavity oscillations.

The present study indicates that the cavity depth has little effect on oscillations in shallow cavities, except when the depth is of the order of the thickness of the cavity shear flow. For such cavity configurations, measurements indicate a strong stabilizing effect of depth on laminar cavity shear layer. Results of motion pictures and hot-wire surveys of the cavity shear layer show that, close to the downstream cavity corner, large lateral motion of the shear layer occurs, which results in a periodic shedding of vortices at a frequency of cavity oscillations. Mean velocity measurements show growth rates as high as […] 0.022 where […] is the shear layer momentum thickness and x is the streamwise coordinate. These are attributed to strong imposed velocity fluctuations on the flow, by the oscillating cavity system.

Phase measurements indicate that the disturbances propagate at a constant phase speed through the cavity shear layer. The wave length of the propagating disturbance bears an approximate integral relation to cavity width, in each mode of cavity oscillation given by […] where b is the cavity width, […] the wave length of the propagating disturbance and N is an integer, which takes values 0, 1, 2, … etc. depending upon the mode of oscillation.

Stability calculations of the measured mean velocity profile were made by numerically integrating the governing equation of motion. These numerical results were used to compute the phase and the integrated amplification of the growing disturbances, through the cavity shear layer. Finally, the mode of cavity oscillation can be predicted for a given cavity flow by studying simultaneously the phase and integrated amplification of various disturbance frequencies through the shear layer and applying the mode relation.

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(PHD, 1973)

Abstract:

An analytical and experimental study has been made of the turbulent mixing layer in a pressure gradient. Theory predicts the possible existence of equilibrium flows, and this was confirmed experimentally for turbulent shear layers between streams of helium and nitrogen. The only case for which similarity is possible is for P2 U_2^2 = P1 U_1^2 since then P_2 (x) = P_1 (x). These equilibrium flows are of the form U_1 ~x^ α and δ~X, where α=x/U_1 dU_1/dx is non –dimensional pressure gradient parameter. The experimental investigation was conducted in the facility designed by Brown to produce turbulent flows at pressures up to 10 atmospheres. The adjustable walls of the test section of the apparatus were modified in order to set the pressure gradient. Shadowgraphs of the mixing zone for α = 0 and α = - 0.18, at different Reynolds numbers, revealed a large scale structure noticeably different for each α. The similarity properties of the shear layer were established from mean profiles of total head and density. In addition, the rms density fluctuations were found to be self-preserving. From the mean profiles, the spreading rate, turbulent mass diffusion, Reynolds stress and Schmidt number distributions were calculated from the equations of motion. The experimental results show that the spreading rate for the adverse pressure gradient is 60% A greater than for the α = 0 case. The maximum shearing stress is 70% larger and the maximum value of the turbulent mass diffusion is 20% larger than their α = 0 counterparts. The maximum rms density fluctuations are approximately 0.2 in both flows. Surprisingly low values of turbulent Schmidt numbers were found; e. g., at the dividing streamline Sc_t = 0.16 for α = 0 and Sc_t = 0. 33 for α = - 0. 18.

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(PHD, 1973)

Abstract:

An experimental investigation of the strengthening of a shock wave propagating through an isobaric region of increasing density is presented. A new experimental configuration consisting of a pressure-driven shock tube mounted vertically with the test section partially immersed in a cryogenic bath is used. The resulting test gas density distribution consists of a uniform region of low density near the shock tube diaphragm, then a strong local gradient followed by another uniform region of high density. The Mach number of the shock initiated at the diaphragm is determined as the shock emerges from the gradient from velocity and temperature measurements for various initial conditions. The experimental data are compared with predictions from approximate theoretical models and a numerical integration of the exact flow equations for the shock-gradient interaction. The measured Mach numbers are considerably higher than these predictions indicating that the models are not adequate to represent the experimental configuration. Calculations show that the additional strengthening of the shock results from multiple interactions between waves generated within the gradient and flow nonuniformities due to the shock formation mechanism.

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(Engineer, 1973)

Abstract:

By use of various lengths of shroud an experimental study was made of a partially confined jet to examine the transition between the flow configuration for a free jet to that of a confined jet. An examination of the reattachment pressure distributions and the parameters at the entrance of the abrupt channel expansion was made. A smooth transition of mean flow quantities was found to occur in the transition from a free jet to a partially confined jet and then to a fully confined jet. The distance to reattachment was measured for various shroud lengths and shown to exhibit an asymptotic value which was Reynolds number dependent. Associated with this maximum reattachment length was a maximum pressure recovery factor. The range of Reynolds numbers - based upon the jet diameter - for the present study was 80,000 to 280,000.

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(Engineer, 1972)

Abstract:

A numerical integration of the Navier-Stokes equations is given for the steady, symmetric flow around a circular cylinder. The problem is formulated in terms of a streamfunction and the vorticity. The method used is the semi-analytical one of series truncation, in which the streamfunction and the vorticity are expanded in a finite Fourier sine series with argument β, the polar angle. Substitution of the truncated series into the Navier- Stokes equations yields a system of non linear, coupled, ordinary differential equations for the Fourier coefficients which is subjected to boundary conditions on the cylinder and at infinity. In order to be able to do a numerical calculation the free stream conditions at infinity are replaced by the asymptotic Oseen conditions at a finite distance from the cylinder. The resulting two point boundary value problem for the system of differential equations is solved numerically by a finite difference method. This method gives rise to a non linear system of algebraic difference equations. Four different iteration methods are discussed to solve this algebraic system. The most efficient iteration method seems to be Newton’s method, which needs only about three iterations to converge to a solution of the difference equations. The approximation of the solution of the finite difference equations to the exact solution of the differential equations is improved by performing a Richardson extrapolation.

It can be concluded that a very efficient scheme has been obtained to solve the system of ordinary differential equations which follow from the application of the method of series truncation. It has been found however that the number of terms in the Fourier series needed to describe the flow adequately and correspondingly the computation time increase considerably with the Reynolds number. Nevertheless, it is believed that the method developed here is much more efficient than previous ones. Calculations have been done for R = 0.5, 2.0, 3.5 and 5.0 where R = Ua/ γ (a is the radius of the cylinder). The results compare reasonably well with previous numerical calculations of Keller-Takami and Dennis-Chang.
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(PHD, 1971)

Abstract:

Measurements of mass flow rate and mean density have been made in separated laminar boundary layers having large transverse density gradients. A 3/8 in. by 1 1/2 in. rectangular half-jet was used to generate a two-dimensional shear layer and the density heterogeneity was produced in an incompressible flow by exhausting one gas into a reservoir of another gas having a different molecular weight. Two Freons were used having a density ratio of 1.98 and unique properties which permitted the measurement of the mass flow rate in all mixtures of the gases with a single hot wire.

Mean density and mass flow rate profiles were compared to the Holmboe model used in theoretical hydrodynamic stability analyses. Fluctuations in the mass flow rate were analyzed and the frequency, wave number and amplification rate of the most unstable oscillation were measured and compared to theoretically predicted values. The oscillations were found to have a higher amplification rate, lower wave number and lower frequency than homogeneous flow when the lighter gas flowed into the heavier one, in agreement with the theoretical predictions. Opposite trends were observed with the heavy gas flowing.

The development of harmonic frequency oscillations in the non-linear region is discussed briefly.

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(PHD, 1969)

Abstract:

An experimental investigation of the steady, laminar nearwake flow field of a two-dimensional, adiabatic, circular cylinder with surface mass transfer has been made at a free-stream Mach number of 6. 0, and free-stream Reynolds numbers Re_{∞,d}=0.9 and 3.0x10^{4}.

A flush-mounted porous section was used to transfer argon, nitrogen or helium into the near wake of the circular cylinder to determine the flow field associated with the addition of a passive scalar. Two cases were studied: mass transfer from the forward stagnation region, and mass transfer from the base. The pressure field was mapped by standard Pitot- and static-pressure measurements. The mass-concentration field was monitored by a continuous sampling mass-spectrometer system which utilized the output of a single mass peak to determine the relative mass-concentration levels.

For mass addition from the base, a recirculating vortex remains in the near-wake flow and the characteristic near-wake pressure is the pressure at the stagnation point created by the interaction of the reversed flow with the injected fluid. This pressure, and the entire near-wake flow field, correlates with the ratio of the momentum flux of the injected fluid to the momentum flux in the cylinder boundary layer upstream of separation, and not the mass flow of the injected fluid as predicted by Chapman.

For mass addition from the base, the axial mass concentration decays rapidly away from the base as a consequence of the countercurrent diffusion of mass into the oncoming recirculating flow. In addition, strong transverse mass-concentration gradients exist in the region between the two stagnation points and a local maximum occurs in the vicinity of the u = 0 locus for those cases in which ReSc > 0(1) for the reversed flow.

With moderate mass addition from the forward stagnation region, the near-wake pressure field is unperturbed. In addition, because there is no source in the base region, the near-wake mass-concentration field is nearly uniform in the region of reversed flow. Bounding the uniform region, in the vicinity of the viscous shear layers, narrow diffusion layers govern the transport of mass into the outer flow.

In the intermediate-wake region, immediately downstream of the neck, the mass-concentration fields for both forward and base injection are explained by a single model which incorporates the influence both of the accelerating axial velocity and of an assumed Gaussian distribution for the mass-concentration of argon. This model predicts the axial decay of mass concentration in the intermediate wake, and establishes the location of the virtual origin of the asymptotic far wake in terms of the mass-concentration profile parameters at the neck.

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(PHD, 1969)

Abstract:

This report is concerned primarily with the effect of surface injection on viscous two-dimensional flows. More precisely, the investigation centers on surface injection rates where the wall shear has been considerably reduced below the no-injection value, but where the momentum of the injectant is still negligible compared to that in the free stream. Three separate problems are investigated to try to obtain an understanding of the physical mechanisms which control the flow.

For the case of laminar boundary-layer flow, asymptotic solutions are obtained for large injection and heat transfer. It is found in this case that the boundary layer may be divided into two regions: (1) an inner region adjacent to the surface where viscous mixing plays a minor role; (2) a viscous layer where the transition occurs from the inner solution to the inviscid flow outside the boundary layer. In the case of the insulated wall the viscous layer contributes only small corrections to the boundary-layer properties. For the highly-cooled wall the boundary layer is strongly influenced by the viscous mixing between the inviscid outer flow and the high density low-speed gas adjacent to the wall.

For turbulent flow, experiments with constant distributed surface injection at M_{∞}=2.6 have been performed. These show that large injection leads to a constant pressure self-similar flow with linear growth. The experimental results are shown to be in good agreement with low Mach number experiments when the normal coordinate is stretched by using a Howarth-Dorodnitsyn transformation at the same value of the ratio of wall mass flow per unit area to that in the free stream.

Finally, the third part considers the upstream effect of the termination of injection on the flow in the “blown” layer. An analysis, using an integral approach is presented which agrees with the experimentally observed effects. In particular, as injection rates approaching the maximum value which can be entrained by a constant pressure mixing layer are approached, the analysis predicts that virtually the entire porous region experiences a falling pressure. It is postulated that this effect provides for a smooth transition from a boundary-layer flow to one where mixing is negligible, except in a thin layer near the streamline which divides the injected and freestream gas. Therefore, the analysis provides the step which gives a quantitative estimate for the range of injection rates in turbulent flow where the effect of mixing can be neglected and inviscid flow models utilized.

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(PHD, 1969)

Abstract:

Velocity profiles have been measured in subsonic, inhomogeneous, axisymmetric turbulent jets, using a new velocity measuring probe. This probe creates a train of heat pulses at one point in the flow and measures the time interval between the time a pulse is created and the time at which it is convected by the flow past a sensing wire a short distance downstream. In a turbulent flow the detected pulses are highly disturbed, but reconstruction of a mean pulse, by a digital computer, from several hundred pulses enabled calculation of a mean velocity and a velocity fluctuation level.

Measurements were made with this probe from near the nozzle to 48 diameters downstream in several combinations of jet gas and ambient gas (air-air, air-He, He-air, and He-SF[subfield 6]) having a range of jet/ambient density ratios from 0.03 to 7.25. Axial profiles of the variation with the density ratio of the jet width, mean velocity, and turbulence level were obtained from these measurements, showing the entrainment and approach to homogeneity of the inhomogeneous jet. A jet which is less dense than the ambient fluid is seen to entrain the ambient fluid more vigorously than the denser jet, as is demonstrated by its higher turbulence levels, more rapid growth, and more rapid axial decay of the mean velocity.

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(Engineer, 1968)

Abstract:

Base pressure measurements of circular cylinders at Reynolds numbers from 100 to 3 x […] were obtained in a low speed wind tunnel. Pressure distributions from […] to […] were also obtained.

In the Reynolds number region from the first appearance of an unsteady wake to the critical Reynolds number the base pressure coefficient shows two maximums and two minimums. The first maximum (Rd […] 50) coincides with the first appearance, of the Karman vortex street. The succeeding minimum (Rd […] 300) probably corresponds to the movement of the onset of transition from the end of the vortex-formation region into the free shear layers. The following maximum (Rd […] 2200) is accompanied by a small discontinuity in the base pressure curve and a decrease in the Strouhal number. The final minimum corresponds to the end of the Schiller-Linke region, at which point transition to turbulence occurs in the free shear layers very near to the shoulder of the cylinder.

A comparison of the blockage correction theories of Maskell and Allen and Vincenti was made at […] = 6 x […]. The value of the base pressure coefficient in an unlimited stream at this Reynolds number was found to be […] = -1.215 for cylinders of one particular roughness, though this value depends on other unit Reynolds number effects. These effects can also result in a significant Reynolds number shift of the base pressure coefficients.
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(PHD, 1967)

Abstract:

The results of an experimental investigation of the reflection of strong shocks in xenon from the end wall of the GALCIT 6" shock tube are presented. The reflection of the incident shock structure, consisting of a frozen shock front, a region of relatively uniform frozen flow, and an ionization front, was observed with a fast-rise (0.3 [mu] sec) pressure gauge mounted in the shock tube end wall. The interaction between the reflecting shock and the ionizing gas in the incident shock structure was of particular interest. This interaction produces a complicated series of shock and rarefaction waves; those waves that propagate back to the end wall were observed with the pressure gauge. The incident shock Mach number was varied from 11 to 20, and the initial pressure was varied from 0.1 to 1.5 mm Hg.

A simple model which includes the gross features of the shock reflection process is used to calculate end wall pressures. The calculated pressures agree well with the experimental observations. In addition, ionization relaxation times for xenon behind the incident and reflected shocks are determined from this simple model and the measured pressure histories. The relaxation time data yield a better understanding of the ionization relaxation process in monatomic gases and provide an estimate for the electron-atom, inelastic excitation cross section for xenon.
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(Engineer, 1965)

Abstract:

An experimental study was made of the problem of separated flow with reattachment at subsonic speeds in various geometrical configurations. It was found that when the boundary layer thickness at separation was small, the values of the reattachment pressure rise coefficient agreed with those from the Korst-Chapman theory. The importance of the relative positions of the transition and reattachment was investigated. In the free shear layer, transition occurred at Reynolds numbers as low as 3 x 10[superscript 3], based on distance from the separation point.

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(Engineer, 1963)

Abstract:

Preliminary results of measurements of thermal shock structure are presented. Cold wire probes, of the type developed by W. H. Christiansen (Ref. 2), were constructed utilizing wires of .00001" and .00005" diameters. Heat transfer measurements were obtained at […] and 7.5 in the GALCIT 17-inch shock tube over a range of initial pressures from 25 to 200 […], producing thicknesses on the order of one centimeter.

The heat transfer data obtained are compared with predictions based on the Navier-Stokes theory and the recent Liepmann-Narasimha-Chahine theory (Ref. 3) for shock profiles and the free molecule heat-transfer theory of Stalder, et al. (Ref. 1).

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(Engineer, 1961)

Abstract:

The equilibrium interface technique has been suggested as a possible shock tunnel driver method. If this technique is workable, reservoir enthalpy levels can be increased substantially over those obtainable with the tailored interface technique without any physical modification of the shock tube. In order to determine the feasibility of the equilibrium interface technique as a shock tunnel driver method, experiments were performed in a shock tube, utilizing a cold helium driver, over the shock Mach number range 3.29 to 7.26.

Pressure histories were measured at the end of the driven tube; this pressure was found to reach an equilibrium condition for the complete shock Mach number range investigated. From the pressure histories the equilibrium pressure, time to reach equilibrium, and test time were determined. Measured equilibrium pressures were compared with an exact theory and two approximate theories. From the measured equilibrium pressure, the equilibrium enthalpy level was computed. The maximum equilibrium enthalpy was more than six times the reservoir enthalpy produced using the tailored interface technique.
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(PHD, 1961)

Abstract:

The use of a fine unheated wire for making shock tube flow measurements is investigated. The operation of the instrument depends on the transient nature of the shock tube flow. The wire is referred to here as a cold wire; it operates in a non-steady manner which is completely different from the usual hot wire operation. This report describes the construction and calibration of the cold wire.

The experimental law for the rate of gain of heat to the wire in air is determined over a range of Mach numbers from 0.4 to 1.9 and a range of Reynolds numbers from 0.035 to 3,500 based on the wire diameter and the conditions in the hot flow following the initial shock wave. Similar measurements are reported for argon. The heat transfer measurements cover the continuum region, the slip and transitional regions, and extend into the free-molecule flow region. The dimensionless results are compared with hot wire measurements obtained in wind tunnels and are found to differ slightly. A difference exists because the cold wire gains heat from the fluid while the hot wire loses heat to the fluid. The measurements are very repeatable and self-consistent, and they indicate that the wire can be used to give an accurate flow measurement in the shock tube.

Some potential applications of the wire for the study of shocktube flows are presented. It is concluded that the fine unheated wire is a versatile tool that can be used to great advantage in the shock tube.

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(PHD, 1961)

Abstract:

The following paper is divided into three more or less separate sections. The first section (Chapters II - VI) deals with an analysis of the transport properties of a partially ionized gas subject to the constraint that the average random energy of all constituent particles is exactly equal (equipartition of energy). This constraint is necessary so that the formal Chapman-Enskog solution of Boltzman’s equation can be used to evaluate the various transport coefficients. Subject to this constraint, a set of tractable equations describing the mass and energy diffusion in a partially ionized gas is obtained that includes all terms correct to the order of the square root of the ratio of the electron to atom mass compared to one. The transport coefficients are evaluated for helium and argon over the complete range of partial ionization assuming that the species particle densities are quite close to their equilibrium values.

The analysis indicates that the electron and ion diffusion velocities are more closely coupled than the equations of Chapman and Cowling show. The added coupling implicitly applies the constraint of zero mass velocity to the gas locally. Because of this constraint a current in the direction of (E x B) x B occurs in addition to the direct and Hall currents.

It is shown that the only part of the thermal conductivity that can be influenced by a magnetic field is that part of the energy carried by the diffusion of the charged particles. For this reason, magnetic fields, in general, cannot be nearly as effective in reducing heat transfer rates as was previously thought, e. g., a magnetic field will have no influence on the thermal conductivity in a fully ionized gas, except through its influence on the current density and the thermal diffusion.

Chapters VII - IX comprise the second section of this paper and deal with the development of a similarity solution for axially symmetric electric discharges. A number of parameters are obtained and discussed. The solution is evaluated for a discharge in argon gas at one atmosphere pressure in which the temperature on the axis of the discharge varies from 6,000°K to 19,000°K. The current-voltage characteristic obtained from this solution is compared with an experimentally determined curve of H. Maecker.

The third section of this paper (Chapters X - XIII) is concerned with the mechanisms of energy transfer in arc jet devices. Use is made of the previous sections of the paper to determine the relative magnitude of the amount of energy that is transferred to the gas in the various parts of the electric discharge. The various possible electrode configurations are discussed in detail and compared. The design and performance of an annular electrode arc heater with a rotating arc is next described and discussed. Because of a number of undesirable performance characteristics of this type of electrode configuration, a modified heater was constructed with the cathode emission occurring along the axis of the applied magnetic field. Details of the unexpectedly good performance of this configuration are given. It is shown that the arc potential drop depends primarily on the strength of the applied magnetic field and the gas enthalpy downstream of the arc. The dependence of the arc potential drop on the arc current and the ambient pressure is shown to be weak over the ranges tested, e. g., 50 to 300 amperes for the current and 1 to 4 atmospheres for the pressure. Some heat transfer measurements taken with this equipment are presented.

Appendix I is concerned with the evaluation of the transport coefficients in a partially ionized gas. Formulae are developed for determining the viscosity, thermal conductivity, and electric conductivity of the plasma. These coefficients are computed for argon and helium at one atmosphere pressure and over the temperature range of partial ionization.

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(Engineer, 1961)

Abstract:

Measurements of aerodynamic noise, in the form of pressure fluctuations in a turbulent boundary layer, were made on a smooth flat plate in the 12- and 20-in. supersonic wind tunnels at the Jet Propulsion Laboratory. The noise was measured with small piezoelectric pressure transducers (0.015-0.03 in. diameter) constructed of barium titanate crystals which were flush-mounted in the flat plate.

Spectral-energy distributions of the pressure fluctuations are obtained up to a frequency of 0.5 mc at freestream Mach numbers from 2.0 to 5.0, and Reynolds numbers based an bound layer-displacement thickness from 5 x 10(3) to 5 x 10(4). By grouping the test variables into the proper nondimensional forms and correcting for the finite transducer size, the energy spectra are found to be similar and uniquely related to both Mach number and Reynolds number. The total, or integrated, level of noise at the plate surface, in terms of root-mean-square values of the pressure fluctuations, is a constant equal to about 10 times the shear stress […] the wall. The intensity, […], is directly proportional to the fourth power of the freestream Mach number.

Correlation measurements in time and in the streamwise direction in space show that the noise at the plate surface to convected downstream with a characteristic velocity equal to 75% of the freestream velocity. The correlation dies off rapidly with spacing between pickup points, and the convection velocity shows no dependence on either Mach number or Reynolds number.
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(PHD, 1961)

Abstract:

Three problems concerned with the motion of a shock wave are discussed. The first is an analytical and experimental study of the performance of a shock tube with area change near the diaphragm. Interesting results of this section are the development of a simple shock-speed control through the use of area change, and the fact that a spread-out dissipation region was shown to exist for a configuration where a non-stationary secondary shock wave was originally expected. A general discussion of the use of this type of area change is also included.

The second problem is a study of the effects of boundary-layer growth on the motion of a shock wave. A simple theory for predicting the attenuation of a shock wave on entering an upstream-facing tube is developed from the analysis of Spence and Woods. When simple laminar boundary-layer approximations are applied, the theory shows good agreement with measurements.

The final problem is an experimental study of the motion of a shock wave downstream of a finite-length area contraction. Normalized results are presented which show that the shock wave emerges from the area change at a speed close to the “linearized” theory value, and is then attenuated by second-order disturbances until it reaches the speed predicted for the steady-state configuration. The results are presented in a form which is shown to be insensitive to both the incident shock Mach number and the amount of the area reduction.
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(Engineer, 1959)

Abstract:

An investigation of a family of two-dimensional airfoils was conducted in the Merrill Wind Tunnel at California Institute of Technology, to determine experimentally the effect of camber on an airfoil that stalls at the nose, and to compare the results with a simplified thin airfoil theory, which requires that flow conditions at the nose be similar.

The nine percent thick models had cambers of zero, three, and six percent, and a fourth model with six percent camber had a rear slot at about 70 percent chord.

Tests conducted at Reynolds Numbers of 640,000 and 840,000 showed that the addition of camber to a nose-stalling airfoil tended to make it a trailing-edge staller or partially so, but that by use of the slot, the stall was shifted back to the nose.

Good agreement was obtained in the theoretical and experimental determination of maximum lift for the slotted airfoil, but not for the angle at which this occurred.
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(Engineer, 1959)

Abstract:

A shock wave propagating in air in a shock tube was reflected from an orifice plate, and the strength or Mach number of the transmitted wave was measured for a range of incident shock Mach numbers from 3 to 9 for several types of orifices. Also schlieren photographs of the starting flow pattern were made for some of the orifices investigated.

The measured values of transmitted shock strength are compared with predicted values based on a theoretical one-dimensional flow model for both an ideal gas and a real gas. The agreement between the measured values of transmitted wave Mach number and the theoretically predicted values is extremely good in the Mach number range investigated for a wedge type orifice at an ambient shock tube pressure of 5.0 mm Hg, and also for a conical type orifice at an ambient shock tube pressure of 2.5 mm Hg. For both orifices the ratio of outlet area to inlet area is 7.67.

The data also indicate that for a wedge type orifice of area ratio of 23.0 and for a plate (free expansion) type orifice of area ratio 23.0 possible boundary layer and shock wave interactions downstream of the orifice result in measured values of transmitted wave Mach number somewhat greater than that predicted by the one-dimensional flow model.

Investigation of the conical orifice with an area ratio 7.67 at a low ambient pressure in the shock tube (0.4 mm Hg) also yields measured values of transmitted wave Mach number greater than that predicted by the one-dimensional flow model, indicating the probable development of a thick boundary layer behind the transmitted wave downstream of the orifice.
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(Engineer, 1959)

Abstract: Vortex formation and shedding from the trailing edge of a two-dimensional, thin, flat plate parallel to the free stream is studied experimentally for the case of incompressible flow. Consideration of the classical boundary layer theory, the Karman vortex-street theory, the formation of the vortex centers, and some annihilation of vorticity in the free shear layers leads to an estimate of Strouhal number. This estimate is in reasonable agreement with experiment. The flow phenomena of a splitter plate mounted aft of the main plate and of a NACA 0012 airfoil are also observed experimentally and are found to be in essential agreement with applicable portions of the theory.

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(PHD, 1958)

Abstract:

A directionally-sensitive hot-wire anemometer was developed for measuring the three-dimensional boundary-layer flow on a spinning, axisymmetric body in a low-speed wind tunnel. Boundary-layer velocity profiles at numerous positions around the body are presented for several spin rates at incidence angles of zero and 3 degrees. Displacement thickness distributions, based on integration of the velocity profiles, are also included.

The asymmetries in the azimuthal distribution of the boundary layer around the spinning body at a small angle of incidence (3°) are examined by means of a Fourier analysis of the experimental data. The experimental results are compared with the results of certain theoretical analyses (BRL 870 (Revised), NAVORD 5036) which provide a method for determining Magnus force (and also normal force) due to the displacement effect of the boundary layer.
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(PHD, 1956)

Abstract:

In an experimental investigation of subsonic and supersonic flows of air past rectangular cavities cut into a flat surface it was discovered that the cavities emit a strong acoustic radiation.

The frequency of the sound-producing oscillations measured by a hot wire in the cavity was found to be inversely proportional to the breadth for fixed depth. For fixed breadth the frequency was found to increase, though not systematically, with a decrease in depth.

A non-dimensional frequency S is defined in terms of the frequency of emission, the gap breadth, and the free stream velocity. The dependence of S on the various parameters in the problem, such as Mach number, Reynolds number and ratio of the boundary layer thickness to a dimension of the cavity, is discussed in light of appropriate experiments.

An estimate of the intensity of the radiation was obtained by means of an optical interferometer of the Mach-Zehnder type. For points located at 3 to 4 cavity breadths from the cavity, intensities of the order of 100 - 150 decibels were found for sound fields from cavities 0.1" deep and 0.1 to 0.2 inch broad at Mach numbers 0.7 to 0.85.

Possible mechanisms for the sound production by the cavities are discussed.
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(Engineer, 1955)

Abstract:

Two simplified theories for the corrections to be applied to the measured pressure in order to determine the pressure distribution on a rotating body are presented. One is based on continuous sampling, and the other is based upon pulse sampling. The problems associated with and the design features of systems using different pressure sensing elements are reviewed. From these considerations, the system offering the simplest solution is selected. The design features and compromises of a model designed and constructed utilizing pulse sampling are discussed.

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(Engineer, 1955)

Abstract:

This report covers an experimental investigation of boundary layer transition on a body of revolution at low subsonic speeds, with emphasis placed on the effects of spin and yaw on transition.

The methods tried for detecting boundary layer transition for this particular investigation are reviewed and the technique finally adopted, the use of a hot wire anemometer, is described in detail.

It was found that at angles of yaw, the transition from laminar to turbulent flow in the boundary layer occurs at a higher Reynolds number over most of the body than at zero yaw, and that spin has a negligible effect on the transition Reynolds number. It was observed however that the effect of spin varies from the front to the rear of the body, although it was not ascertained whether this effect was a result of the influence of the nose section, the tripping device which was used to obtain transition, or a combination of both.

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(Engineer, 1955)

Abstract:

A two-dimensional investigation was carried out in the Merril Wind Tunnel at the California Institute of Technology to determine the effect on low speed lift of retracting the leading edge of a thin, circular-arc airfoil.

Several configurations were tried, some with a spanwise slot milled into the upper surface so that the leading edge recess formed by retraction could be utilized as an air intake to improve the flow. A comparison was made between the configurations with the leading edge retracted to various positions and the basic airfoil.

The investigation showed that leading edge retraction caused a linear loss of maximum lift proportional to the percent reduction in chord up to a critical position where lift and the stalling angle of attack increased abruptly. Thereafter, maximum lift was reduced at a rate higher than the chord reduction. The effect of the slot was negligible.

The critical position phenomenon warrants further study.
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