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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:35:50 +0000On the Influence of Wall Boundary Layers in Closed Transonic Test Sections
https://resolver.caltech.edu/CaltechETD:etd-12052003-143311
Authors: Berndt, Sune Bertil
Year: 1955
DOI: 10.7907/T014-DR86
The boundary layers at the test section walls of a transonic wind tunnel are known to reduce the wall interference. In the present paper this effect is studied by means of small perturbation theory, assuming viscosity to be negligible when perturbing a turbulent boundary layer. An approximation for thin boundary layers leads to a modified boundary condition at the wall of the test section, expressing the normal streamline slope induced by changes in mass flow density and crossflow within the boundary layer. This boundary condition is applied to the linearized equations of subsonic flow and to the non-linear transonic equations at choking, the cases of plane and circular test sections only being treated in detail.
The results of linear theory show that all corrections except the three-dimensional angle-of-attack correction are considerably reduced by the presence of the boundary layers at Mach numbers greater than 0.9, the essential part of their influence being due to the change of mass flow density with pressure. In the case of choking the analysis indicates that the presence of boundary layers will increase the maximum model size for which the flow can be interpreted as corresponding to Mach number one in free flight. Finally, the technique of using artificial thickening of the wall boundary layers for reduction of wall interference is considered, though without reaching a definite conclusion as to its value compared to other techniques.https://thesis.library.caltech.edu/id/eprint/4790Viscous Effects on Static Pressure Distribution for a Slender Cone at a Nominal Mach Number of 5.8
https://resolver.caltech.edu/CaltechETD:etd-11242003-104401
Authors: Baldwin, Lawrence Cloyd
Year: 1955
DOI: 10.7907/XNB2-P865
An experimental investigation was conducted in the GALCIT Hypersonic Wind Tunnel, Leg No. 1, to determine the static pressure distribution on a cone with 5[degrees] semivertex angle at a nominal Mach number of 5.8.
This investigation was concerned with the effect of hypersonic boundary layer-shock wave interaction on the pressure at the cone surface. Pressure distributions were measured for three values of Reynolds numbers per inch and a comparison was made with theoretically calculated pressure distributions.
The influence of viscosity in hypersonic flow was demonstrated by an induced pressure rise of approximately 45% above theoretical inviscid pressure for the lowest Reynolds number tested.https://thesis.library.caltech.edu/id/eprint/4648Rayleigh's Problem at Lo\w Mach Number According to the Kinetic Theory of Gases
https://resolver.caltech.edu/CaltechETD:etd-01142004-105335
Authors: Yang, Hsun-Tiao
Year: 1955
DOI: 10.7907/2VK2-FC14
Rayleigh's problem of an infinite flat plate set into uniform motion impulsively in its own plane is studied by using Grad's equations and boundary conditions developed from the kinetic theory of gases. For a heat insulated plate and a small impulsive velocity (low Mach number), only tangential shear stress and velocity and energy (heat) flow parallel to the plate are generated, while the pressure, density, and temperature of the gas remain unchanged. Moreover, no normal velocity, normal stress, or normal energy flow is developed. Near the start of the motion the flow behaves like a "free-molecule flow", and all physical quantities are analytic functions of the flow parameters and time. The results obtained for "large time", however, add to the growing lack of confidence in the Burnett-type series expansions in powers of mean free path. Although such expansions are obtained here, they are poorly convergent and inappropriate to the problem. To replace these unsatisfactory solutions, approximate closed-form solutions valid for all values of the time are developed, which agree with the free-molecule values for small time and the classical Rayleigh solution for large time. This technique may be useful in studying more general flow problems within the framework of the kinetic theory of gases.https://thesis.library.caltech.edu/id/eprint/161A Preliminary Experimental Investigation of the Flow over Simple Bodies of Revolution at M = 18.4 in Helium
https://resolver.caltech.edu/CaltechETD:etd-06162004-141355
Authors: Munson, Albert Gallatin
Year: 1956
DOI: 10.7907/X3HZ-BN39
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
An experimental investigation was conducted in the GALCIT hypersonic blow-down tunnel to determine surface pressure distributions and shock wave shapes for a series of "sharp" nosed and slightly blunted bodies of revolution at a nominal Mach number of 18.5 and a free stream Reynolds number of 4.75 x 10[superscript 5] per inch. The four bodies investigated were as follows: (1) 15[degree] half-angle "sharp" cone; (2) 15[degree] half-angle spherically-blunt cone (bluntness ratio = .24); (3) 20[degree] half-angle "sharp" cone; and (4) 2/3 power body.
The pressure distributions on the "sharp" cones agreed well with the Taylor Maccoll theory. The pressure near the nose of the blunt cone was much higher than that predicted by the theory, as is expected, but decreases monotonically to a value lower than the theoretical value, indicating that the flow has over expanded. The measured shock wave shape for the 2/3 power body was found to be proportional to x[...], and the shock wave ordinates agree very closely with those predicted by Cole.https://thesis.library.caltech.edu/id/eprint/2619An Experimental Investigation of Hypersonic Flow over Blunt Nosed Cones at a Mach Number of 5.8
https://resolver.caltech.edu/CaltechETD:etd-06182004-111807
Authors: O'Bryant, William Theral
Year: 1956
DOI: 10.7907/923A-XB12
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Shock shapes were observed and static pressures were measured on spherically-blunted cones at a nominal Mach number of 5.8 over a range of Reynolds numbers per inch from 97,000 to 238,000 for angles of yaw from 0[degrees] to 8[degrees]. Six combinations of the bluntness ratios 0.4, 0.8, and 1.064 with the cone half angles 10[degrees], 20[degrees], and 40[degrees] were used in determining the significant parameters governing pressure distribution.
The pressure distribution on the spherical nose for both yawed and unyawed bodies is predicted quite accurately by the modified Newtonian theory given by [...], where [...] is the angle between the normal to a surface element and the flow direction ahead of the bow shock. On the nose-cone junction and the conical afterbody, cone half angle was found to be the significant parameter in determining the length of the transition zone. For a cone half-angle of 40[degrees], a pressure minimum exists on the skirt immediately downstream of the nose-cone junction, but this pressure minimum is located far downstream when the half-angle is 20[degrees]. The tangent cone concept at angles of yaw is useful in predicting the downstream movement of the pressure minimum. Shock detachment distance between bow shock and body surface on the axis varies linearly with nose radius. Drag coefficients for bodies at zero yaw compare very closely with those obtained by integrating the modified Newtonian approximation, except at large half-angles and low bluntnesses where drag approaches that given by the Taylor-Maccoll theory for sharp cones.https://thesis.library.caltech.edu/id/eprint/2636An Experimental Investigation of Leading Edge Shock Wave-Boundary Layer Interaction at Hypersonic Speeds
https://resolver.caltech.edu/CaltechETD:etd-03252004-153340
Authors: Kendall, James Madison
Year: 1956
DOI: 10.7907/6XVK-B331
<p>The boundary layer on a slender body tends to be very thick at hypersonic speeds. It interacts with the external flow by producing larger flow deflections near the leading edge than those due to the body alone. The increased shock strength affects the boundary layer growth. The flow around the boundary layer gives rise to an induced pressure with a negative gradient which thins the boundary layer and increases the skin friction with respect to the zero pressure gradient value.</p>
<p>Experiments on a flat plate with a sharp leading edge (Reₜ < 100) have been performed in the GALCIT 5 x 5 inch Mach 5.8 hypersonic wind tunnel. The induced pressure was measured by means of orifices in the plate surface. Profiles of Mach number, velocity, mass flow, pressure, and momentum deficiency were calculated from impact pressure surveys normal to the plate surface made at various distances from the leading edge.</p>
<p>The results are as follows: (1) The induced pressures are 25 per cent higher than the weak interaction theory. (2) The boundary layer and the external flow are distinctly separate for Reₓ as low as 6000. (3) The shock wave location is in good agreement with that predicted by the Friedrichs theory for a body shape equivalent to the observed boundary layer displacement thickness. (4) Expansion waves reflected from the shock are weak. (5) The average skin friction coefficient tends toward and nearly matches the zero pressure gradient value downstream, but increases to approximately twice that value as the leading edge is approached.</p>https://thesis.library.caltech.edu/id/eprint/1112An Experimental Investigation of Hypersonic Flow over Blunt Nosed Cones at a Mach Number of 5.8
https://resolver.caltech.edu/CaltechETD:etd-03262004-145512
Authors: Machell, Reginald Montague
Year: 1956
DOI: 10.7907/SJ75-6W93
Six spherical nosed cone static pressure models with cone semivertex angles of 10°, 20°, and 40° were tested in the GALCIT 5 x 5 inch hypersonic wind tunnel at a Mach number of 5.8. The static pressure distributions obtained at yaw angles of 0°, 4°, and 8° agreed very closely with the modified Newtonian approximation, C<sub>p</sub> = C<sub>p<sub>max</sub></sub> cos<sup>2</sup>η on the spherical portions of the models, where η is the angle between the normal to the body surface and the free stream direction. On the conical portions of the models the pressure distributions agreed reasonably well with the theoretical results for inviscid supersonic flow over cones as tabulated by Kopal. The significant parameter which influenced the deviations from the Newtonian and the Kopal predictions was the cone semivertex angle. The flow over the 40° spherical nosed cone models overexpanded with respect to the Kopal pressure in the region of the spherical-conical juncture, after which the pressure returned rapidly to the Kopal value. For models with smaller cone angles the region of minimum pressure occurred farther back on the conical portion of the model, and the Kopal pressure was approached more gradually. The shape of the pressure distributions as described in nondimensional coordinates was independent of the radius of the spherical nose and of the Reynolds number over the range of Reynolds number per inch between . 97 x 10<sup>5</sup> and 2.38 x 10<sup>5</sup>. Integrated results for the pressure foredrag of the models at zero yaw compared very closely with the predictions of the modified Newtonian approximation, except for models with large cone angles and small nose radii.https://thesis.library.caltech.edu/id/eprint/1135Development and Application of a Technique for Steady State Aerodynamic Heat Transfer Measurements
https://resolver.caltech.edu/CaltechETD:etd-07132004-161800
Authors: Hartwig, Frederic William
Year: 1957
DOI: 10.7907/Y2JY-A341
<p>A technique was developed for measuring steady state heat transfer on a hemisphere cylinder and the results are compared with theory. The instrumentation consisted of a miniaturized thermopile of silver-constantan thermocouples approximately 1/8" x 1/16" x 1/100". The repeatability of readings with this device was found to be excellent. These heat measuring devices, or heat meters, were installed in both a ceramic hemisphere cylinder and in a similar metal one. There were obtained three different heat flow rates at each of six different combinations of tunnel pressure and temperature.</p>
<p>The results compared very well with a theory developed by Lester Lees based upon the assumption of local similarity.</p>
https://thesis.library.caltech.edu/id/eprint/2873Investigation of Flow Around Simple Bodies in Hypersonic Flow
https://resolver.caltech.edu/CaltechETD:etd-07142004-143403
Authors: Kubota, Toshi
Year: 1957
DOI: 10.7907/ZVPP-FK96
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
A theoretical analysis of the flow around slender blunt-nosed bodies was made by applying the flow similarity concept to the hypersonic small-disturbance equations. The flow field around a class of bodies of the form [...] exhibits a certain similarity in the sense that the pressure, density and transverse velocity are described by relations of the form Q(x,r)/Q(R) = f(r/R), where R is the distance from the axis to the shock wave. This similarity holds when the Mach number is infinitely large, and when the exponent in the equation defining the body shape lies in the range [...] for axially-symmetric bodies and in the range [...] for two-dimensional bodies. For large but finite Mach numbers a second approximation was obtained by expanding solutions in series of powers of [...].
An experimental investigation of the flow around "similar-flow" bodies of revolution was conducted at Mach number 7.7 in the GALCIT hypersonic wind tunnel. The surface pressure distributions agreed closely with the theoretical predictions, after a simplified correction was made for the boundary-layer displacement effect. The results indicated that the boundary layer interaction effect needs a further investigation.https://thesis.library.caltech.edu/id/eprint/2880Aerodynamic Studies in the Shock Tube
https://resolver.caltech.edu/CaltechETD:etd-09152004-142813
Authors: Rabinowicz, Josef
Year: 1957
DOI: 10.7907/MXH9-5H80
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
In order to utilize the shock tube for quantitative investigations of some aerodynamic problems a thin platinum film resistance thermometer was developed for heat transfer rate measurements. The present report describes the construction and calibration of the heat transfer gage. Since the experimental technique presents a major problem this investigation has been carried out in the straight section of the shock tube where the flow conditions are well defined and readily measured. These flow conditions were calculated utilizing the most recent NBS data on air properties at high temperatures. The flow conditions were also measured utilizing the heat transfer gage and, several independent experimental techniques, and good agreement was found with the equilibrium flow calculations after an initial period of 30 - 50 [...]sec. Measurements of the heat transfer rate at the forward stagnation point and on the circumference of a circular cylinder are reported and compared with the theoretical calculations of L. Lees. A method for deduction of surface pressure distribution from the laminar boundary-layer heat transfer data is also presented.https://thesis.library.caltech.edu/id/eprint/3546An Experimental Investigation of Flow over Simple Blunt Bodies at Mach Number of 5.8
https://resolver.caltech.edu/CaltechETD:etd-08062004-154112
Authors: Wisenbaker, Eugene Morgan
Year: 1957
DOI: 10.7907/0KC4-4827
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Shock stand-off distances and shock shapes were measured and/or observed for a series of 14 blunt-nosed bodies at a Mach number of 5. 8 and Reynolds number per inch of [...]. Nine of these bodies had hemisphere-segment noses designed to include the entire range of possible nose radii of curvature from flat-faced to hemispherical. Two models characterized by sharp shoulders and concave hemisphere-segment noses were also tested. Three additional models representing the round-shouldered, flat-faced type completed the set of 14. All models had cylindrical afterbodies 1.50 inches in diameter, and were yawed at angles of 0, 4, and 8 degrees.
Stand-off distances are compared to the theoretical predictions of Hayes, Frobstein, and Heybey where applicable, and shock shape is compared to that given by Hayes for the body with infinite nose radius of curvature. Results of the stand-off distance comparisons varied from under prediction by a factor of two to over prediction by the same amount. Hayes' shock shape approximated that actually observed very closely. It was generally found that body shape in the sonic region greatly influenced the shock shape and stand-off distance.
Static pressure distributions were measured on three representative bodies selected as follows: (1) a hemisphere-segment body having a ratio of nose radius to base diameter of 1.30 and falling in the middle of the range from hemisphere to flat-nosed; (2) a flat-faced body with sharp shoulder; and (3) a flat-faced body with a rounded shoulder of 5/16 inch radius. Pressures very close to stagnation values generally were found to be present over a large area of the nose in the case of the flat-faced body. Rounding of the shoulder tended to reduce values of [...] below those observed at corresponding points on the completely flat-faced body, except in the region near the body axis The pressure distributions are compared where applicable with the modified Newtonian approximation and with Probstein's approximation to [...] for zero angle of yaw. Agreement with the modified Newtonian values was generally good near the axis, but deteriorated rapidly in the shoulder regions, except in the case of the rounded shoulder body.https://thesis.library.caltech.edu/id/eprint/3024An Experimental Investigation of Hypersonic Flow over Blunt-Nosed Bodies at a Mach Number 5.8
https://resolver.caltech.edu/CaltechETD:etd-07082004-144120
Authors: Fraasa, Donald Gordon
Year: 1957
DOI: 10.7907/G6D1-N841
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
An experimental investigation to obtain schlieren photographs of the flow over several blunt-nosed bodies and to determine the surface static pressure distribution on certain of these models was conducted in the GALCIT hypersonic wind tunnel, leg no. 1, at a nominal Mach number of 5.8 and a free stream Reynolds number per inch of 2.22 x 10[...].
Schlieren photographs were made of the following blunt-nosed models, all with cylindrical afterbodies, at angles of yaw of 0, 4, and 8 degrees: a family of nine round-nosed bodies with nose radii of curvature varying from the radius of the afterbody cylinder (hemispherical nose) to infinity (flat nose), two concave-nosed bodies having nose radii of curvature equal to 0.8 and 1.6 times the afterbody diameter, and three flat-nosed cylinders with rounded shoulders whose radii of curvature were .083, .125, and .208 times the afterbody diameter.
Static pressure distributions at angles of yaw of 0, 4, and 8 degrees were determined for three of the blunt bodies: (1) the flatnosed cylinder with infinite nose radius of curvature, (2) the flatnosed cylinder with a rounded shoulder of radius equal to .208 of the afterbody diameter, and (3) a round-nosed cylinder with nose radius of curvature equal to 1.3 times the afterbody diameter.
The schlieren photographs were analyzed on a contour projector to measure shock standoff distances, to determine the sonic point on the shock, and to observe shock shape. Data derived from these studies and the pressure distributions are presented in graphical form. Comparisons are made between the experimental results and appropriate theoretical approximations for hypersonic flow.https://thesis.library.caltech.edu/id/eprint/2833An Experimental Investigation of Heat Transfer Rates on a Blunt Body in Hypersonic Flow
https://resolver.caltech.edu/CaltechETD:etd-08172004-095231
Authors: Richards, Homer Keener
Year: 1957
DOI: 10.7907/C7F5-2G95
An experimental investigation was made in the GALCIT hypersonic wind tunnel, leg number 1, at a nominal Mach number of 5.8 to determine the heat transfer rate and temperature distributions on a water-cooled, ellipsoid-cone at angles of yaw of 0, 4 and 8 degrees, respectively. The Reynolds number per inch based on free stream conditions was [...].
The experimental means employed was a steady-state technique developed by Mr. F. W. Hartwig at GALCIT during the past several years. This technique utilizes a heat transducer or heat meter of very small size. The primary advantage of this method is that it obviates the necessity of correcting for axial temperature gradients in the model.
Surface pressure distributions were also studied on a model of identical geometry for angles of yaw of 0, 4, 8 and 12 degrees, respectively. The primary interest here was to obtain data necessary for the theoretical calculation of the heat transfer rate distributions using laminar flow theory.
The investigation showed that the heat meters were very reliable. The data obtained from independent wind tunnel runs were repeatable within [plus or minus] 1.5 per cent. It was found that the local heat transfer rate and the local pressure coefficient vary linearly with angle of yaw. The agreement of the experimentally determined stagnation heat transfer rate and the theoretically calculated one was good. Further refinement of the calibration technique appears to be the logical direction of effort for subsequent investigators.https://thesis.library.caltech.edu/id/eprint/3150The Effects of Blunt Leading Edges on Delta Wings at Mach 5.8
https://resolver.caltech.edu/CaltechETD:etd-01242006-094259
Authors: Nicholson, Kenneth F.
Year: 1958
DOI: 10.7907/ZSFZ-MN41
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Pressure distributions were measured on a series of four delta wings with subsonic and supersonic leading edges, both sharp and blunt. The blunt leading edge radius was about 0.5 per cent of root chord. Schlieren studies were also made to determine top and side view shock locations. The tests were conducted at a nominal Mach number of 5.8, and at Reynolds numbers between 0.335 x 10(6) and 0.901 x 10(6) based on root chord. Angular settings covered a range [...] in pitch at zero yaw (about [...]), and a range of v/V = +/- 0.125 (about +/- 7.2°) at a fixed angle of pitch of 11.5°.
The effects of bluntness were found to be small. Also, the pressures produced by shock wave interactions with the boundary layer, and the inviscid pressures generated by the blunt leading edges, were found to be small compared with the inviscid pressures producing lift on the basic wing. Spanwise pressure distributions show no similarity to those obtained by linearized theory. Centerline lower surface pressure in pitch at zero yaw is bracketed between the Newtonian value [...] and the two-dimensional exact value.https://thesis.library.caltech.edu/id/eprint/317An Experimental Investigation of the Stability of the Hypersonic Laminar Boundary Layer
https://resolver.caltech.edu/CaltechETD:etd-09232004-093013
Authors: Demetriades, Anthony
Year: 1958
DOI: 10.7907/7SR9-9M59
NOTE: text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
An experimental investigation of the stability of the hypersonic laminar boundary layer was carried out for the case of a flat insulated surface at zero angle of attack. The stream-wise amplitude variation of both "natural" disturbances (i.e., flow fluctuations existing naturally in the boundary layer) and of disturbances artificially excited with a "siren" mechanism was studied with the aid of a hot-wire anemometer. In both cases it was found that such small fluctuations amplify for certain ranges of the fluctuation frequency and the Reynolds number [...], and damp for others. The demarcation boundaries for the amplification (instability) zone were found to resemble the corresponding boundaries of boundary layer instability at lower speeds. A "line of maximum amplification" of disturbances was also found. The amplification rates and hence the degree of "selectivity" of the hypersonic layer were found, however, to be considerably lower than those at the lower speeds. The disturbances selected by the layer for maximum amplification have a wavelength estimated at about twenty times the boundary-layer thickness [...], which is appreciably longer than the corresponding wave-lengths for low-speed boundary-layer flow.https://thesis.library.caltech.edu/id/eprint/3719An Experimental Study of the Effect of Mass Injection at the Stagnation Point of a Blunt Body
https://resolver.caltech.edu/CaltechETD:etd-01262006-142812
Authors: McMahon, Howard Martin
Year: 1958
DOI: 10.7907/PWSC-6787
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
An experimental study of the effect of the injection of nitrogen and helium coolant gases at the stagnation point of a blunt body was carried out in the GALCIT Hypersonic Wind Tunnel at a Mach number of 5.8. The gases were injected straight out of the stagnation point and also tangential to the body surface. The model was also fitted with flow separation spikes.
The injection of the coolant gas resulted in a marked reduction in the model equilibrium temperature, and this cooling effect persisted over the entire length of the model. For the same mass flow, helium was a better coolant than nitrogen.
The average heat transfer near the nose of the body was reduced almost to zero by injecting a mass of helium as small as 1/2 per cent of the mass flow of free-stream air contained in the "capture" area [...] of the spherical nose.
Separation near the spike tip was observed up to a ratio of spike length to spherical nose diameter of 1.78 and a free-stream Reynolds number based on nose diameter of 2.84 x 10(5), resulting in a value of the foredrag coefficient which was one-third the value with no spike attached.https://thesis.library.caltech.edu/id/eprint/357An Experimental Investigation of Viscous Effects on Static and Impact Pressure Probes in Hypersonic Flow
https://resolver.caltech.edu/CaltechETD:etd-01112006-091955
Authors: Matthews, Malcolm LeRoy
Year: 1958
DOI: 10.7907/MQPD-A933
<p>An experimental investigation of viscous effects on static and impact pressure probes was conducted in the GALCIT Leg 1 hypersonic wind tunnel.</p>
<p>This investigation of the impact probes showed viscous effects to be important for free stream Reynolds numbers less than 6000 based on the probe diameter, in the Mach number range 5.4 to 5.7. For 80 < Re < 6000, the results showed the measured impact pressure to be less than the inviscid value. The maximum deviation from the inviscid impact pressure was 2.3 per cent at a Reynolds number of 200. For Re < 80 the measured impact pressure was greater than the inviscid value.</p>
<p>The investigation of the static pressure probes for a Mach number 5.8 and a free stream Reynolds number of 16,000 based on the probe diameter showed a very thick and rapidly growing boundary layer over the probe surface. This boundary layer was sufficient to cause the static pressure measured by a 10 degree cone-nosed probe with its orifice 45 diameters aft of the probe tip to be 7.5 per cent greater than the free stream static pressure. The boundary layer thickness on the 10 degree cone-nosed probe was several times that of the probe radius. The boundary layer was surveyed on a hemispherical-nosed and a flat-nosed probe and showed the boundary layer thickness to be several times that of the 10 degree cone-nosed probe.</p>https://thesis.library.caltech.edu/id/eprint/124An Experimental Investigation of Hypersonic Stagnation Temperature Probes
https://resolver.caltech.edu/CaltechETD:etd-02082006-130736
Authors: Wood, Richard Donald
Year: 1959
DOI: 10.7907/KXK1-JQ18
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
An experimental investigation of single-shielded hypersonic stagnation temperature probes was conducted in the GALCIT Leg No.1 hypersonic wind tunnel and in the Jet Propulsion Laboratory 12-inch supersonic wind tunnel.
By the combined use of both shield and base heating, a probe recovery factor of r = 1.0 was obtained over a range of Reynolds numbers at M [...] = 5.75. By using the experimental data and simple heat balance equations, the probe losses, for the conditions investigated, were found to be in the proportion: shield conduction loss - 15; base conduction loss - 3; thermocouple conduction loss - 1; thermocouple radiation loss - 3/100. The typical decrease in probe recovery factor observed for decreasing Reynolds number appears to be related to a decrease in the base temperature and not to the wire conduction loss as commonly assumed.
An optimum probe vent to entrance area ratio of [...] was found and is shown to be a function of the number of vent holes used in the shield.
No single calibration parameter was found that could relate the experimental recovery factors under all conditions.https://thesis.library.caltech.edu/id/eprint/549Hypersonic Flow Over an Elliptic Cone: Theory and Experiment
https://resolver.caltech.edu/CaltechETD:etd-01032006-130909
Authors: Chapkis, Robert Lynn
Year: 1959
DOI: 10.7907/35S5-3H33
By applying hypersonic approximations to Ferri's linearized characteristics method simple results were obtained for the shock shape and surface pressure distribution for an unyawed conical body of arbitrary cross-section. Calculations were carried out for an elliptic cone having a ratio of major to minor axis of 2:1, and a semi-vertex angle of about 12° in the meridian plane containing the major axis. An experimental investigation of the flow over this body conducted at a Mach number of 5.8 in the GALCIT hypersonic wind tunnel showed that the surface pressure distribution at zero angle of attack agreed quite closely with the theoretical prediction. On the other hand the simple Newtonian approximation predicts pressures that are too low.
Surface pressure distributions and schlieren photographs of the shock shape were also obtained at angles of attack up to 14° at zero yaw, and at angles of yaw up to 10°, at zero pitch. At the higher angles of attack the Newtonian approximation for the surface pressures is quite accurate.https://thesis.library.caltech.edu/id/eprint/11Investigation of the Transmission of a Shock Wave Through an Orifice
https://resolver.caltech.edu/CaltechETD:etd-08122005-134039
Authors: Monroe, Louis L.
Year: 1959
DOI: 10.7907/Y42Q-9F44
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.https://thesis.library.caltech.edu/id/eprint/3102Stability of the Compressible Laminar Boundary Layer
https://resolver.caltech.edu/CaltechETD:etd-01042006-141741
Authors: Reshotko, Eli
Year: 1960
DOI: 10.7907/M6HG-WW29
In previous theoretical treatments of the stability of the compressible laminar boundary layer the effect of the temperature fluctuations on the "viscous" (rapidly varying) disturbances is either ignored (Lees-Lin), or is accounted for incompletely (Dunn-Lin). A thorough reexamination of this problem shows that temperature fluctuations have a profound influence on both the "inviscid" (slowly varying) and viscous disturbances above a Mach number of about 2.0. The present analysis includes the effect of temperature fluctuations on the viscosity and thermal conductivity, and also introduces the viscous dissipation term that was dropped in the earlier theoretical treatments.
Some important results of the present study are: (1), the rate of conversion of energy from the mean flow to the disturbance flow through the action of viscosity in the vicinity of the wall increases with Mach number; (2), instead of being nearly constant across the boundary layer, the amplitude of inviscid pressure fluctuations for Mach numbers greater than 3 decreases markedly with distance outward from the plate surface. This behavior means that the jump in magnitude of the Reynolds stress in the neighborhood of the critical layer is greatly reduced; (3), at Mach numbers less than about 2 dissipation effects are minor, but they become extremely important at higher Mach numbers since for neutral disturbances they must compensate for the generally destabilizing effects of items (1) and (2).
Numerical examples illustrating the effects of compressibility (including neutral stability characteristics) are obtained and are compared with the experimental results of Laufer and Vrebalovich at M = 2.2, and of Demetriades at M = 5.8.https://thesis.library.caltech.edu/id/eprint/23Experimental Study of Helium Diffusion in the Wake of a Circular Cylinder at M=5.8
https://resolver.caltech.edu/CaltechETD:etd-12092005-131025
Authors: Mohlenhoff, William
Year: 1960
DOI: 10.7907/QH2Z-TC50
An experimental study of the diffusion of helium in the wake of a circular cylinder was conducted in the GALCIT hypersonic wind tunnel at a Mach number of 5.8. The cylinder was constructed of material having random porosity and was mounted with its axis perpendicular to the stream. The light gas was injected in small amounts and the thermal conductivity method was utilized to detect the concentration of helium in the air at points downstream. Problems in the utilization of the thermal conductivity method for low sample densities were overcome by suitable calibration.
Flow in the wake of the cylinder was found to display characteristically similar behavior at a few diameters downstream, with respect to decay and spread of the concentration. Reynolds number similarity was established in the laminar case, but turbulent Reynolds number similarity may require reference to momentum thickness, which was not possible with the present data.
Profile data was somewhat marred by a tunnel pressure perturbation, but many of the important conclusions were not affected. The profiles appear to follow the theoretical Gaussian distribution in the similar region.
The thermal conductivity method is quite promising as a means of tracing the diffusion of one binary gas constituent in another, as applied to hypersonic wind tunnel experiment. It will also serve in the analysis of transition and turbulence, and of the lateral spreading of the turbulent fluid into the rest of the wake region behind the bow shock.https://thesis.library.caltech.edu/id/eprint/4903Modified Crocco-Lees Mixing Theory for Supersonic Separated and Reattaching Flows
https://resolver.caltech.edu/CaltechETD:etd-12082005-132722
Authors: Glick, Herbert Seymour
Year: 1960
DOI: 10.7907/0V7K-QS61
Re-examination of the Crocco-Lees method has shown that the previous quantitative disagreement between theory and experiment in the region of flow up to separation was caused primarily by the improper C(K) relation assumed. A new C(K) correlation, based on low-speed theoretical and experimental data and on supersonic experimental results, has been developed and found to be satisfactory for accurate calculation of two-dimensional laminar supersonic flows up to separation.
A study of separated and reattaching regions of flow has led to a physical model which incorporates the concept of the "dividing" streamline and the results of experiment. According to this physical model, viscous momentum transport is the essential mechanism in the zone between separation and the beginning of reattachment, while the reattachment process is, on the contrary, an essentially inviscid process. This physical model has been translated into Crocco-Lees language using a semi-empirical approach, and approximate C(K) and F(K) relations have been determined for the separated and reattaching regions. The results of this analysis have been applied to the problem of shock wave-laminar boundary layer interaction, and satisfactory quantitative agreement with experiment has been achieved.https://thesis.library.caltech.edu/id/eprint/4861Investigation of Ablation of Ice Bodies in Hypersonic Flows
https://resolver.caltech.edu/CaltechETD:etd-12082005-140201
Authors: Anderson, David Ellsworth
Year: 1960
DOI: 10.7907/CD24-6081
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The physical characteristics of the ablation process are described. A theoretical approach to calculate the heat transfer to the wall of an ablating body under flow conditions encountered in the GALCIT hypersonic tunnels is outlined. Simplification is achieved by assuming the vapor pressure next to the subliming body is at its equilibrium value. The GALCIT hypersonic test facilities are described briefly. Methods of manufacture are given for [...], [...], and [...] models. Techniques and special test equipment used in obtaining experiments results with [...] and [...] (camphor) are described. An illustration of the computational technique used to determine the heat transfer rates to the wall and the wall temperature distributions is included. Figures to show the agreement between theory and experiment are presented and reasonable results are obtained for temperature distribution, but heat-transfer rates (ablation rates) are greater for theory than for experiment.https://thesis.library.caltech.edu/id/eprint/4864Experimental Study of Helium and Argon Diffusion in the Wake of a Circular Cylinder at M = 5.8
https://resolver.caltech.edu/CaltechETD:etd-12092005-081550
Authors: Kingsland, Louis
Year: 1961
DOI: 10.7907/1FDZ-JX04
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Experimental measurements of the diffusion of helium and argon in the wake of a porous cylinder were made in the GALCIT hypersonic wind tunnel at Mach number 5.8. The cylinder was mounted perpendicular to the flow and small quantities of tracer gas were pumped through the model walls into the flow. The thermal conductivity method of gas analysis was used to determine the concentration of sample gases extracted from points in the wake.
The transverse and axial distribution of concentration appeared to follow theoretical estimates of "similarity behavior". Injection of tracer gas was found to have a measurable effect on stagnation pressure and this effect was taken into account during computations. Numerical values of diffusion coefficients along the wake centerline were computed from the experimental data and then compared with theoretical values for laminar flow. Close agreement between experimental and theoretical values at [...] = 18,000 verified that the inner wake was laminar as far downstream as measurements could be made (15 diameters). At [...] = 72,000, the data showed that mixing processes were 3 times more rapid for helium, and 10 times more rapid for argon, than those expected in laminar flow. This result confirmed the presence of turbulence at this flow condition.https://thesis.library.caltech.edu/id/eprint/4901Part I. Cylindrical Couette Flow in a Rarefied Gas According to Grad's Equation. Part II. Small Perturbations in the Unsteady Flow of a Rarefied Gas Based on Grad's Thirteen Moment Approximation
https://resolver.caltech.edu/CaltechETD:etd-12092005-131707
Authors: Ai, Daniel Kwoh-i
Year: 1961
DOI: 10.7907/9P2N-HF23
<p>Part I</p>
<p>Grad's thirteen moment method is applied to the problem of the shear flow and heat conduction between two concentric, rotating cylinders of infinite length. In order to concentrate on the effects of curvature the problem is linearized by requiring that the Mach number is small compared with unity, and that the temperature difference between the two cylinders is small compared with the mean temperature. The solutions of the linearized Grad equations show a qualitatively correct transition of the cylinder drag from free-molecule flow to the classical Navier-Stokes regime. However the magnitude of the curvature effect on the drag in rarefied flow is not given correctly, because Grad's distribution function ignores the wedge-like domains of influence of the two cylinders.</p>
<p>The solution obtained for the heat transfer rate is physically unrealistic in the free-molecule flow limit, and this result is produced by a cross-coupling between the normal stresses and the radial heat flux imposed by Grad's distribution function. In this simple problem the difficulty can be eliminated by taking the normal stresses to be identically zero and employing a truncated moment method. However, in general this device cannot be utilized in problems involving curved solid boundaries, or when dissipation is considered. One concludes that the choice of the distribution function to be employed in Maxwell's moment equations is dictated by the requirements imposed in the limiting case of highly rarefied gas flows, as well as in the Navier-Stokes regime.</p>
<p>Part II</p>
<p>In this paper, the unsteady one-dimensional flow of a compressible, viscous and heat conducting fluid is treated, based on linearized Grad's thirteen moment equations. The fluid, initially at rest, is set into motion by some small external disturbances. Our interest is to examine the nature of all the responses. The fluid field extends to infinity in both directions; thus no length is involved, and also there is no solid wall boundary existing in the problem. The nature of the external disturbances is restricted to having a unit impulse in the momentum equation and a unit heat addition in the energy equation. The disturbances are located on an infinite plane normal to the flow direction; and the responses induced correspond to fundamental solutions of the problem. The method of Laplace transforms is applied, and the inverse transforms of all quantities are obtained in integral form. Because of the complicated expressions of the integrands involved, we consider only certain limiting cases which correspond to small and large times from the start of the motion, compared to the average time between molecular collisions. In order to study these limiting cases, it is essential to understand the behavior of the integrand in the complex plane; hence all singularities and branch points are obtained.</p>
<p>When t is small, the integrand is expanded in powers of t to obtain a wave front approximation. All discontinuities are propagated along the characteristics of the linearized system, and a damping term also appears.</p>
<p>At large values of time, the integrand gets its main contribution around the branch points, and these solutions are identical to those obtained from the Navier-Stokes equation. The fundamental solution of the one-dimensional unsteady flow, idealized as it seems to be, offers itself as a tool to understand other related problems. The piston problem, as well as the normal quantities in Rayleigh's problem (e.g., normal velocity, normal stress, and thermodynamical quantities), are governed by the same set of equations. Hence, certain parts of the fundamental solutions can be applied directly to these problems. The limiting forms of the normal quantities in Rayleigh's problem are expected to be worked out in another paper in the near future.</p>https://thesis.library.caltech.edu/id/eprint/4904An Experimental Investigation of the Effect of a Transverse Hypersonic Flow Velocity upon a Low-Density D.C. Electrical Discharge in Air
https://resolver.caltech.edu/CaltechETD:etd-12132005-105051
Authors: Marlotte, Gary Lynn
Year: 1962
DOI: 10.7907/3BR3-ZT02
The low-density D.C. electrical discharge in a uniform gas stationary with respect to the electrodes has been studied extensively. However, when the gas moves at a hypersonic speed transverse to the electrodes, several completely new effects are introduced. Experiments were carried out with air in the GALCIT 5-inch by 5-inch hypersonic wind tunnel with a nominal Mach number of 5.8. D.C. breakdown voltages and steady-state sub-normal glow voltages were measured across a channel formed by two sharp-edged insulating flat plates in which flat-plate "Rogowski" electrodes were embedded. Segmented electrodes were then used in the normal glow regime to measure current distributions at each electrode for various electrode segment combinations, total currents, and densities.
Some important results of the present study are the following. For the characteristic dimensions and speeds involved, the explicit dependence of electrical breakdown upon the velocity of the stream is small compared to the effect of boundary layer density defects. A theoretical treatment of breakdown is given and qualitative agreement with experiments is obtained. In the normal glow regime using segmented electrodes, an unmistakable explicit flow velocity effect was observed, with the discharge current paths being displaced downstream compared to static bell-jar tests at equivalent densities.https://thesis.library.caltech.edu/id/eprint/4980Hypersonic Wakes
https://resolver.caltech.edu/CaltechETD:etd-03302009-092458
Authors: McCarthy, John Francis
Year: 1962
DOI: 10.7907/63NK-AG38
An experimental investigation was made of the flow field behind a two-dimensional circular cylinder at a nominal Mach number of 5.7. The free-stream Reynolds number based on the cylinder diameter was varied over a range from 4300 to 66, 500 by changing both the diameter of the cylinder and the stagnation pressure of the wind tunnel. Pitot-pressure, static-pressure, and total-temperature measurements were made at various distances behind the cylindrical rod in order to determine the state properties in the wake. Base-pressure measurements were also taken at various Reynolds numbers.
From these measurements, the transition from laminar to turbulent flow in the wake was determined and successfully correlated with other data. A transition Reynolds number based on local conditions and the length of laminar run was determined. Extensive comparison of the experimental data with Kubota's theory for laminar flow was then made. A satisfactory comparison was made between theory and experiment. Because of the nature of the tests conducted, only a qualitative comparison was made with the theory of Lees and Hromas for turbulent flow.https://thesis.library.caltech.edu/id/eprint/1219Part I. Kinetic Theory Description of Plane, Compressible Couette Flow. Part II. Kinetic Theory Description of Conductive Heat Transfer from a Fine Wire
https://resolver.caltech.edu/CaltechETD:etd-12092005-133941
Authors: Liu, Chung-Yen
Year: 1962
DOI: 10.7907/Q16R-JR92
PART I:
By utilizing the two-stream Maxwellian in Maxwell's integral equations of transfer we are able to find a closed-form solution of the problem of compressible plane Couette flow over the whole range of gas density from free molecule flow to atmospheric. The ratio of shear stress to the product of ordinary viscosity and velocity gradient, which is unity for a Newtonian fluid, here depends also on the gas density, the plate temperatures and the plate spacing. For example, this ratio decreases rapidly with increasing plate Mach number when the plate temperatures are fixed. On the other hand, at a fixed Mach number based on the temperature of one plate, this ratio approaches unity as the temperature of the other plate increases. Similar remarks can be made for the ratio of heat flux to the product of ordinary heat conduction coefficient and temperature gradient.
The effect of gas density on the skin friction and heat transfer coefficients is described in terms of a single rarefaction parameter, which amounts to evaluating gas properties at a certain "kinetic temperature" defined in terms of plate Mach number and plate temperature ratio. One interesting result is the effect of plate temperature on velocity "slip". In the Navier-Stokes regime most of the gas follows the hot plate, because the gas viscosity is larger there. As the gas density decreases the situation is reversed, because the velocity slip is larger at the hot plate than at the cold plate. In the limiting case of a highly rarefied gas most of the gas follows the cold plate.
Limitations of the present six-moment approximation at high plate Mach numbers are discussed and it is concluded that an eight-moment approximation would eliminate these difficulties. The results obtained in this simple geometry suggest certain conclusions about hypersonic flow over solid bodies when the surface temperature is much lower than the kinetic temperature.
PART II:
The Maxwell moment method utilizing the two-sided Maxwellian distribution function is applied to the problem of conductive heat transfer between two concentric clylinders at rest. Analytical solutions are obtained for small temperature differences between the cylinders. The predicted heat transfer agrees very well with experiments performed by Bomelburg, Schafer-Rating and Eucken. Comparison with results given by the Grad's thirteen moment equations, and with those given by Fourier's "law" plus Maxwell-Smoluchowski temperature-jump boundary condition shows that the two-sided character in the distribution function is a crucial factor in problems involving surface curvature.https://thesis.library.caltech.edu/id/eprint/4906The effect of heat transfer on separation of laminar compressible boundary layers
https://resolver.caltech.edu/CaltechETD:etd-12072005-143749
Authors: Savage, Stuart B.
Year: 1962
DOI: 10.7907/XCR8-Y474
Tani's integral method is extended to treat laminar two-dimensional compressible boundary layers with heat transfer and arbitrary pressure gradient for both attached and separated flows. A carefully chosen one-parameter family for the velocity profiles and a "universal" stagnation enthalpy profile are assumed for attached flows. The accuracy of the method is examined by comparing the results with several "exact" numerical solutions and satisfactory agreement is obtained. For separated flows one-parameter families are assumed for both the velocity and stagnation enthalpy profiles. In this case the accuracy of the method is poor; however, suggestions are made as to how it might be improved within the present framework.
https://thesis.library.caltech.edu/id/eprint/4837The gray gas in hypersonic flow
https://resolver.caltech.edu/CaltechETD:etd-10182005-082033
Authors: Thompson, Thomas R.
Year: 1963
DOI: 10.7907/9865-C310
The assumption that the spectral absorption coefficient is independent of frequency in problems involving radiant energy transfer in hot gases is examined. A particular case, that of the hypersonic wake, is treated in some detail, and a non-gray transfer equation involving two mean coefficients is developed. One mean absorption coefficient is related to emission, and the other to absorption.
The problems arising from lack of chemical equilibrium are discussed, and a modification of the equations used for prediction of the spectral absorption coefficient (for diatomic species) is suggested, wherein two distinct temperatures are utilized. Sample calculations for one nitrogen band have been made and the results presented graphically.https://thesis.library.caltech.edu/id/eprint/4154Stability of laminar wakes
https://resolver.caltech.edu/CaltechETD:etd-12212005-152513
Authors: Gold, Harris
Year: 1963
DOI: 10.7907/X1TJ-MG72
This investigation deals with the effects of compressibility on the hydrodynamic stability of wake flows. It is found that the effect of temperature is two-fold: (1), as the wake core temperature increases, the range of Mach numbers over which neutral and self-excited subsonic disturbances can exist also increases; (2) as long as the relative Mach number is below the critical Mach number the neutral inviscid wave number will decrease with increasing core temperature, implying that a hot wake will be more stable than a cool one.
The analysis of Batchelor and Gill for the inviscid stability of axi-symmetric incompressible jets has been extended to the more general problem of compressible wakes and jets. It is shown that the results are directly analogous to those obtained for the two-dimensional problem. The sinuous (n = 1) mode is the most unstable allowable mode. This unstable mode is observed in a hypersonic wake.
https://thesis.library.caltech.edu/id/eprint/5104Flow Generated by Suddenly Heated Flat Plate
https://resolver.caltech.edu/CaltechETD:etd-10052004-163535
Authors: Wu, Ying-Chu Lin Susan
Year: 1963
DOI: 10.7907/CPQD-RQ29
<p>By employing the two-sided Maxwellian in Maxwell's moment method a kinetic theory description is obtained of the flow generated by a step-function increase in the temperature of an infinite flat plate. Four moments are employed in order to satisfy the three conservation equations, plus one additional equation involving the heat flux in the direction normal to the plate. For a small temperature rise the equations are linearized, and closed-form solutions are obtained for small and large time in terms of the average collision time.</p>
<p>Initially the disturbances propagate along two distinct characteristics, but the discontinuities across these waves damp out as time increases. At large time the main disturbance propagates with the isentropic sound speed. Solutions for mean normal velocity and temperature show the transition from the nearly collision-free regime to the Navier-Stokes-Fourier regime, which is characterized by a boundary layer near the plate surface merging into a diffuse "wave". The classical continuum equations, plus a temperature jump boundary condition, seem to be perfectly adequate to describe the flow beyond a few collision times, provided one accounts properly for the interaction between the inner thermal layer and the outer diffuse wave.</p>https://thesis.library.caltech.edu/id/eprint/3925Measurements in highly dissipative regions of hypersonic flows. Part I. Hot-wire measurements in low Reynolds number hypersonic flows. Part II. The near wake of a blunt body at hypersonic speeds
https://resolver.caltech.edu/CaltechETD:etd-12212005-083759
Authors: Dewey, Clarence Forbes
Year: 1963
DOI: 10.7907/XG0Q-ZA42
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Part I:
Measurements were made of the heat loss and recovery temperature of a fine hot-wire at a nominal Mach number of 5.8. Data were obtained over an eight-fold range of Reynolds numbers in the transitional regime between continuum and free-molecule flow. At high Reynolds numbers, the heat transfer data agree well with the results of Laufer and McClellan, which were obtained at lower Mach numbers. At lower Reynolds numbers, the results indicate a monotonic transition between continuum and free molecule heat transfer laws. The slope of the heat transfer correlation also appears to vary monotonically, with Nu [...] at high Reynolds numbers and Nu ~ Re for Re< < 1.
Data on the wire recovery temperature (corresponding to zero net heat transfer) were obtained for free-stream Knudsen numbers between 0.4 and 3.0. Comparison with previous supersonic data suggests that for Mach numbers greater than about two the normalized variation of recovery temperature in the transitional regime is a unique function of the free-stream Knudsen number. The recent data of Vrebalovich (33) suggests that the relation between the normalized recovery temperature and Knudsen number found in this investigation also applies to subsonic and transonic flow.
The steady-state hot-wire may be used to obtain two thermodynamic measurements: the rate of heat transfer from the wire and the wire recovery temperature. An illustrative experiment was performed in the wake of a transverse cylinder, using both hot-wire and pressure instruments in a redundant system of measurements. It was shown that good accuracy may be obtained with a hot-wire even when the Reynolds number based on wire diameter is small.
Part II:
A theoretical model of the near wake is derived following the ideas of Chapman. This model is based on the postulates of mass conservation in the base flow region, thin viscous shear layers, and a recompression process which is independent of Reynolds number. The analysis, which includes the effects of initial shear layer thickness and base flow temperature, shows that the characteristics of the near wake (base pressure, shear layer angle, etc.) are independent of Reynolds number, and that the shear layer and initial wake thicknesses are proportional to Re[...].
A series of experiments are presented which show that the postulate of thin shear layers is invalid for Reynolds numbers less than about [...]. At higher Reynolds numbers, the theory is qualitatively incorrect if the Mach number [...] external to the shear layer is large. Detailed measurements with a steady-state hot-wire in the near wake of a two-dimensional circular cylinder indicate that the compression process at the neck is not isentropic, and that the maximum pressure rise occurs downstream of the stagnation point formed by the merging shear layers. Comparison between the experimental and theoretical results points out the importance of the base flow temperature and the initial shear layer profile in determining the observable characteristics of the near wake.https://thesis.library.caltech.edu/id/eprint/5097Flow Field and Stability of the Far Wake Behind Cylinders at Hypersonic Speeds
https://resolver.caltech.edu/CaltechTHESIS:08172010-151639253
Authors: Behrens, Hermann Wilhelm
Year: 1966
DOI: 10.7907/K0KH-9W58
<p>An experimental study of the mean wake flow field and its stability has been carried out in the far wake of circular cylinders at a Mach number of 6. The Reynolds numbers ranged from 200 to 4000 with a few measurements at higher Reynolds number. Pitot pressure, static pressure and mean flow hot wire measurements were done at many axial stations behind cylinders up to (x/d) = 2400. </p>
<p>The inner wake formed from the cylinder boundary layers is laminar and loses its identity within the first 60 diameters or less depending on the Reynolds numbers so that only the outer wake, caused by the bow shock, has to be considered. Within a certain region the experimental results compare well with linear laminar theory, but the wake profiles are not similar up to the farthest downstream station (x/d = 2400). At four Reynolds numbers strong deviations from steady laminar behavior were observed far behind the cylinder, indicating breakdown of the flow because of non-linear instability effects. </p>
<p>In the instability study hot wire fluctuation measurements were made over the whole frequency range (f = 1 - 320 KC) and also at particular frequencies in a band width of 1 KC up to x/d = 12000 at the lowest Reynolds number. Two instability regions were found and investigated: the linear growth region and the non-linear region. In the linear region there is quite a close correspondence with linear stability theory. The onset of non-linearity is characterized by the simultaneous strong deviation of the mean flow from laminar steady behavior, the increase of the fundamental frequency fluctuation component on the wake axis and the sudden rise of the first harmonic frequency component. The non-linear region is compared with the non-linear wake region at low speeds behind a flat plate. On the basis of these measurements a tentative picture is given of the onset of non-linearity and/or transition in the inner and outer wake behind blunt bodies at hypersonic speeds.</p>
https://thesis.library.caltech.edu/id/eprint/5992Laminar boundary layer separation and near wake flow for a smooth blunt body at supersonic and hypersonic speeds
https://resolver.caltech.edu/CaltechETD:etd-11112005-152028
Authors: Grange, Jean-Marie
Year: 1966
DOI: 10.7907/3ZN7-BC18
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
At supersonic and hypersonic speeds the location of the boundary layer separation point on the surface of a smooth, blunt body is not fixed a priori, but is determined by the pressure rise communicated upstream through the subcritical base flow. By utilizing the integral or moment method of Reeves and Lees the separation-interaction region is joined smoothly to the near-wake interaction region passing through a "throat" downstream of the rear stagnation point. One interesting feature of this problem is that the viscous flow over the blunt body "overexpands" and goes supercritical. This flow is joined to the near-wake by means of a supercritical-subcritical "jump" upstream of separation, and the jump location is determined by the matching conditions.
Downstream of the jump the viscous flow separates in response to the pressure rise, and forms a constant pressure mixing region leading into the near wake. As an illustrative example the method is applied to an adiabatic circular cylinder at [...] = 6, and the results are compared with the experimental measurements of Dewey and McCarthy. This method can be extended to non-adiabatic bodies, and to slender bodies with smooth bases, provided that the radius of curvature is large compared to the boundary layer thickness.
https://thesis.library.caltech.edu/id/eprint/4509Integral Theory for Turbulent Base Flows at Subsonic and Supersonic Speeds
https://resolver.caltech.edu/CaltechETD:etd-10302003-141417
Authors: Alber, Irwin Emanuel
Year: 1967
DOI: 10.7907/0YEZ-H062
<p>The integral near wake analysis of Reeves and Lees developed for supersonic laminar base flows is extended to the case of fully turbulent separated adiabatic flow behind a rearward facing step at both subsonic and supersonic speeds. A turbulent eddy viscosity model is formulated for the shear stress scaling of the dissipation integral in the mechanical energy equation. It is shown that the eddy viscosity can be described simply by one incompressible constant (valid for both shear layers and wakes) and one reference density ρ<sub>r</sub>. Using a compressibility transformation, theoretical solutions for the spreading rates of free shear layers are found to agree with experiment when the reference density is chosen to be the centerline density for the wake flow.</p>
<p>Two alternate methods are presented for joining the wake flow solution to the body first, through a turbulent free shear layer mixing solution, and then through the use of a two parameter family of velocity profiles valid near the body. A simple conservation model is presented to relate the viscous sublayer after expansion to the initial boundary layer ahead of the step.</p>
<p>For free stream Mach numbers M<sub>1</sub> ≤ 2.3, the integral theory is found to give good estimates for the length scales and centerline pressure variations measured experimentally for both wake flows and step flows (where reattachment is to a solid surface).</p>
<p>An iterative method of solution for the incompressible wake flow problem is presented as an extension of the work of Green. The calculation proposes the proper criteria for obtaining a convergent solution. The base pressure coefficient is found to be equal to the difference between the momentum thicknesses in the far wake and at the base.</p>
https://thesis.library.caltech.edu/id/eprint/4317Experimental investigation of supersonic laminar, two-dimensional boundary layer separation in a compression corner with and without cooling
https://resolver.caltech.edu/CaltechETD:etd-11162005-102455
Authors: Lewis, John Eldon
Year: 1967
DOI: 10.7907/R0FB-DD20
An experimental investigation of the boundary layer separation associated with a compression corner was conducted in the GALCIT Mach 6 wind tunnel, and a supplementary study was performed in the JPL supersonic wind tunnel. Special emphasis was placed on the development of a wind tunnel model which approximated true two-dimensional flow, and which could be run in either a highly cooled or an adiabatic configuration. The basic measurements consist of the model surface pressure and temperature, and Pitot surveys of the boundary layer. The surface pressure distributions for the adiabatic wall configurations are compared with the theory of Lees and Reeves (modified by Klineberg and Lees). The surface pressure distribution for the cold wall was compared with the adiabatic configuration for a laminar interaction, and the dependence on Reynolds number for both laminar and transitional interactions are observed. The "free interaction" similarity suggested by Chapman is empirically tested and found to be a good approximation for the adiabatic configuration, but it fails to correlate the cooled with the adiabatic case. The scaling suggested by Curle was tested and found to eliminate this deficiency.https://thesis.library.caltech.edu/id/eprint/4587Experimental investigation of wakes behind two-dimensional slender bodies at Mach number six
https://resolver.caltech.edu/CaltechETD:etd-12292005-132450
Authors: Batt, Richard George
Year: 1967
DOI: 10.7907/3WW3-B746
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
An experimental investigation has been conducted to determine mean flow properties for both near and far wakes behind several two-dimensional slender bodies at M[...] = 6. Three adiabatic wall models consisting of a flat plate model and two 20 [degree] included angle wedge models (H = .15", H = .3") were tested. The effect of wall temperature on wake properties was examined by cooling the larger of these two wedge models with the internal flow of liquid nitrogen ([...] = .19). Free stream Reynolds numbers were varied from [...] to [...] for each of these four configurations. In the far wake, measurements of total temperature, as determined with hot wire probes, and Pitot and static pressures were used to derive all other mean flow properties. The effect of transition on these far wake data was determined. Near wake flows were laminar for all adiabatic wall tests and at least for the two lowest test Reynolds numbers of the cold wall wedge. Base region flow field mappings and shear layer profiles were obtained for the .3"H wedge model by combining Pitot pressure data with hot wire measurements of total temperature and mass flux. These results illustrated that for slender bodies with flat bases, the basic structure for laminar near wakes is appreciably more complex for hypersonic than for supersonic flow primarily because, in hypersonic flow, the corner expansion fan extends into the separated shear layers and base region shocks now become imbedded within the viscous portion of the shear layers.
https://thesis.library.caltech.edu/id/eprint/5163Theory of laminar viscous-inviscid interactions in supersonic flow
https://resolver.caltech.edu/CaltechETD:etd-09252002-110303
Authors: Klineberg, John Michael
Year: 1968
DOI: 10.7907/P246-JJ81
This investigation is concerned with those fluid-mechanical problems in which the pressure distribution is determined by the interaction between an external, supersonic inviscid flow and an inner, laminar viscous layer. The boundary-layer approximations are assumed to remain valid throughout the viscous region, and the integral or moment method of Lees and Reeves, extended to include flows with heat transfer; is used in the analysis.
The general features of interacting flows are established, including the important distinctions between subcritical and supercritical viscous layers. The eigensolution representing self-induced boundary-layer flow along a semi-infinite flat plate is determined, and a consistent set of departure conditions is derived for determining solutions to interactions caused by external disturbances. Complete viscous-inviscid interactions are discussed in detail, with emphasis on methods of solution for both subcritical and supercritical flows. The method is also shown to be capable of predicting the laminar flow field in the near wake of blunt bodies.
Results of the present theory are shown to be in good agreement with the measurements of Lewis for boundary-layer separation in adiabatic and non-adiabatic compression corners, and with the near-wake experiments of Dewey and McCarthy for adiabatic flow over a circular cylinder. Extensions of the method to flows with mass injection at the surface and to subsonic interactions are indicated.
https://thesis.library.caltech.edu/id/eprint/3749Constant-pressure laminar mixing of a shear layer with a quiescent fluid
https://resolver.caltech.edu/CaltechETD:etd-11112005-153627
Authors: Chao, Chia-Chun
Year: 1968
DOI: 10.7907/8FYR-SB25
The constant-pressure laminar mixing of an initial shear layer with a quiescent fluid is studied theoretically. The line of singularities at the starting point is removed by abandoning the conventional restriction that the dividing streamline must coincide with the x-axis. Instead, the shape of this streamline in the "near-field" is determined by properly matching inner and outer flow regions so as to cancel any additional induced normal velocity and pressure disturbances in the outer flow. The "far-field" is obtained by applying the momentum integral technique beginning with the profiles determined by the near-field solution some distance downstream of the start of mixing. Universal functions are obtained that enable the progress of the mixing process to be followed both for a Blasius initial profile and an initial profile with a finite slip.https://thesis.library.caltech.edu/id/eprint/4511A kinetic theory description for external spherical flows with arbitrary Knudsen number by a moment method
https://resolver.caltech.edu/CaltechTHESIS:01112016-132852787
Authors: Brinker, Gary Duane
Year: 1969
DOI: 10.7907/B115-B274
<p>The Maxwell integral equations of transfer are applied to a series of problems involving flows of arbitrary density gases about spheres. As suggested by Lees a two sided Maxwellian-like weighting function containing a number of free parameters is utilized and a sufficient number of partial differential moment equations is used to determine these parameters. Maxwell's inverse fifth-power force law is used to simplify the evaluation of the collision integrals appearing in the moment equations. All flow quantities are then determined by integration of the weighting function which results from the solution of the differential moment system. Three problems are treated: the heat-flux from a slightly heated sphere at rest in an infinite gas; the velocity field and drag of a slowly moving sphere in an unbounded space; the velocity field and drag torque on a slowly rotating sphere. Solutions to the third problem are found to both first and second-order in surface Mach number with the secondary centrifugal fan motion being of particular interest. Singular aspects of the moment method are encountered in the last two problems and an asymptotic study of these difficulties leads to a formal criterion for a "well posed" moment system. The previously unanswered question of just how many moments must be used in a specific problem is now clarified to a great extent. </p>https://thesis.library.caltech.edu/id/eprint/9368Superorbital entry heat transfer including atomic line radiation and massive blowing
https://resolver.caltech.edu/CaltechETD:etd-11112005-161727
Authors: Dirling, Raymond B.
Year: 1969
DOI: 10.7907/C3KT-S738
At superorbital reentry velocities radiative heating is the dominant mode of heat transfer to the stagnation region of blunt reentry vehicles. The radiative heat transfer rate at the wall is determined by the temperature profile through the shock layer which depends on the net radiative transport through both the viscous inner region adjacent to the wall and the outer region where convection and radiative transport processes dominate the energy transfer. When atomic line transitions are included a very small scale length for radiant energy transport is introduced which results in characteristic changes in the shock layer flow. The inclusion of atomic line transitions necessitates consideration of self-absorption of radiant energy and results in the coupling of radiant energy transport and convection and conduction transport processes even for relatively small vehicle nose radii.
In the formulation of this problem no restrictions are placed on the variation of the absorption coefficient of the medium with wavelength. As an illustrative example the effects of nose radius, wall reflectivity, and massive blowing have been computed for the shock layer flow field of a spherically blunted vehicle at 50,000 feet per second and 200,000 foot altitude in air.https://thesis.library.caltech.edu/id/eprint/4513The Hypersonic Laminar Boundary Layer Near a Sharp Expansion Corner
https://resolver.caltech.edu/CaltechETD:etd-06172009-151827
Authors: Victoria, Keith Jordis
Year: 1969
DOI: 10.7907/EZX3-M918
<p>The integral moment method for treating interactions between a laminar boundary layer and an external supersonic flow is applied to the problem of the hypersonic laminar boundary layer near sharp and slightly rounded convex (expansion) corners. The general features of this type of interacting flow are established by an analytical solution of the integral equations using the method of matched asymptotic expansions for the case of small interaction parameter. Numerical solutions are obtained for flows for which the interaction parameter can no longer be considered small.</p>
<p>An experimental study is carried out in the GALCIT Mach 8 hypersonic wind tunnel in order to study the two-dimensional laminar boundary layer expansion. Major emphasis is placed on the acquisition of detailed data near the corner region. The basic measurements consist of the model surface pressure distribution and pitot pressure surveys of the boundary layer and inviscid flow field between the boundary layer and the leading edge shock wave both upstream and downstream of the corner region. The surface pressure measurements illustrate the striking departure of the flow field at hypersonic speeds from the classical Prandtl-Meyer description.</p>
<p>These data with appropriate assumptions made regarding the static pressure and temperature fields at points away from the model surface allow calculation of the distributions of profile functions defined in the integral moment method formulation. These distributions along with the surface pressure distribution are compared directly with solutions of the moment equations.</p>
https://thesis.library.caltech.edu/id/eprint/2633Two-Dimensional Viscous Flows with Large Distributed Surface Injection. Part I. Boundary Layer Flows with Large Injection and Heat Transfer. Part II. Experiments in Supersonic Turbulent Flow with Large Distributed Surface Injection. Part III. The Effect of Finite Plate Length
https://resolver.caltech.edu/CaltechETD:etd-10302003-155216
Authors: Fernandez, Fernando Lawrence
Year: 1969
DOI: 10.7907/TCCK-HT69
<p>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.</p>
<p>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.</p>
<p>For turbulent flow, experiments with constant distributed surface injection at M<sub>∞</sub>=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.</p>
<p>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.</p>https://thesis.library.caltech.edu/id/eprint/4324The Near Wake of a Two-Dimensional Hypersonic Blunt Body with Mass Addition
https://resolver.caltech.edu/CaltechETD:etd-10072002-144356
Authors: Collins, Donald James
Year: 1969
DOI: 10.7907/ZHBC-A772
<p>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<sub>∞,d</sub>=0.9 and 3.0x10<sup>4</sup>.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
https://thesis.library.caltech.edu/id/eprint/3957Experimental study of satellite wakes in a simulated ionospheric plasma
https://resolver.caltech.edu/CaltechTHESIS:07092010-100552106
Authors: Blumenthal, Donald Lawrence
Year: 1970
DOI: 10.7907/PYM3-H107
Wakes of simple bodies (discs, strips) were investigated using an electrostatically accelerated stream of argon
ions and electrons. Typical conditions are: beam ion energy is 80 eV, ion density is 10^7-10^8 cm^(-3), electron
temperature 1-3 eV, ion thermal speed very small compared to mean ion velocity. The dimensionless parameters
closely approximate satellite flight conditions, with the exception of the electron-ion temperature ratio, which
is near unity in flight and large in these experiments.
The dependence of principal near wake features (such as the large ion current peak on the centerline behind the
body) on the shape of the body was investigated systematically. All trends can be explained qualitatively by
recognizing the dominant role of those portions of the sheath where the free stream ion velocity is tangential to
the body.
The far wake of a strip (downstream of the ion current peak) displays a decaying radial distribution on the scale
of the body size, somewhat similar to what is expected from a neutral gas. For axial symmetric models, the far
wake displays a small structure on the scale of the ion current peak. The evolution of these disturbances
is qualitatively explained by a simple, linearized two fluid theory. These features are initiated by the
interaction of the inwardly deflected ion streams behind the body. At least in certain regions of the flow field,
this interaction involves two-humped ion distribution functions, which may play a role in the further development
of the far wake.
The effects on the simulation of varying the vacuum chamber background pressure was also examined in detail.
https://thesis.library.caltech.edu/id/eprint/5969An investigation of non-equilibrium effects in an argon free-jet plasma
https://resolver.caltech.edu/CaltechTHESIS:10012010-092851271
Authors: Cassady, Phillip Earl
Year: 1970
DOI: 10.7907/WHYP-RZ81
The non-equilibrium effects present in the formation of a strong normal shock wave in a low density, slightly ionized argon flow field, particularly as evidenced by the appearance of a dark region upstream of the shock wave, have been analyzed both theoretically and experimentally. A model for the flow through the shock wave was formulated which incorporates a quantum mechanical theory to explain the existence of the dark region, and the problem was solved numerically to yield flow field property distributions. A precursor region of high electron temperature was found to exist upstream of the main body of the heavy-particle shock wave.
An experimental investigation of the phenomenon was carried out in an arc heated free jet flow field. A test facility was constructed in which the goal has been to attain operation at low enough enthalpies to allow precise and extensive diagnostic testing while still high enough to exhibit the interesting non-equilibrium effects. Extensive study was carried out on the effect of electrode design and gas flow phenomena on the stability of the arc discharge. The completed unit was instrumented fully for measurement of the operating parameters and a computer program was developed to monitor its operation as a supply of slightly ionized argon for free-jet experiments.
The non-equilibrium aspects of the free-jet were analyzed both theoretically and experimentally. A theoretical model was developed and numerically solved for the free-jet expansion of slightly ionized argon. Pitot pressure measurements were completed and compared favorably with predictions calculated from this theoretical model.
Electron temperature and ion density profiles were measured both along the axis of the empty free-jet and through the normal shock wave in front of a cooled blunt body using a new type of cooled Langmuir probe, the operation of which was theoretically analyzed. The existence of a region of electron temperature in front of a strong normal shock wave coincident with the observed dark region was experimentally verified.https://thesis.library.caltech.edu/id/eprint/6083Theory of Particle Deposition by Inertial Forces at Bifurcations in the Human Respiratory Tract
https://resolver.caltech.edu/CaltechTHESIS:05172018-084339801
Authors: Bell, Karl Ammon
Year: 1970
DOI: 10.7907/XVNX-TN65
<p>The prediction of lung disease development in man from
aerosol particles and the medical justification for subsequent
control of particulate atmospheric pollutants requires specific
knowledge of the rate and location of the aerosol deposition
in the lungs. A theoretical development is presented to
numerically predict the rate and location of aerosol deposition
by impaction at the wedge walls in a model of a lung bifurcation.
Two limiting flow cases, steady potential flow and steady
laminar boundary layer flow, are analyzed and found to
represent upper and lower bounds of limited experimental deposition
data for one-micron particle obtained from a lung apparatus
simulating normal inhalations.</p>
<p>Numerical deposition results for 20, 10, 5, 4, 3, 2,
and 1 micron particles in steady potential flow show
deposition fluxes to be functions of Stokes number and also
the local air velocity distribution along the wedge. Boundary
layer deposition results for the same particle are found to
correspond to the first few data points of the steady potential
case, however no boundary layer deposition occurs beyond a
few particle diameters along the wedge.</p>https://thesis.library.caltech.edu/id/eprint/10907An experimental investigation of the turbulent boundary layer over a wavy wall
https://resolver.caltech.edu/CaltechTHESIS:09232010-101022816
Authors: Sigal, Asher
Year: 1971
DOI: 10.7907/VK9A-XA44
An experimental investigation of turbulent boundary layer flow over wavy surfaces was conducted at low speed.
Two models with the ratio of the amplitude to the wave length a/λ = 0.03 and wave lengths λ = 6" and 12" were tested in an open-circuit wind tunnel. The free stream velocity was 15.4 m/sec, giving Reynolds number Re = 2.54 X 10^4 per inch. Boundary-layer thickness varied from δ = 1.5" to δ = 4. 1" by means of boundary-layer trips of various height, in order to change the ratio λ/6.
The following measurements were taken:
* Wall pressure distribution
* Average velocity and turbulence level, using a single element hot-wire probe
* Wall stress distribution, using Preston's tube
* Static and total pressures
* Turbulence intensities and shear stress using X-array hot-wire probe.
An appreciable modulation of all the flow quantities, imposed by the wavy boundary, is observed throughout the investigation. Wall pressure is much lower than predicted by uniform, inviscid theory and is slightly non-symmetric. Wall stress distribution has a peak with C_f/C_fo = 1.2 upstream of the crest and a dip of C_f/C_fo = 0. 6 upstream of the trough. Static pressure decays exponentially in the outer layer while its gradient is decreased toward the surface in the wall layer.
The turbulence intensities and shear stress distributions near the wall show oscillatory modulation superimposed on the reference flat plate profiles. The amplitude of the oscillations decay exponentially toward the edge of the layer, so that in the outer part of the layer the turbulence quantities are practically independent of the longitudinal position.
It was found that Coles' Law of the Wall does not apply in the present situation because of the modulation of the slope of the semi-logarithmic portion of the velocity profiles. A presentation of velocity profiles is suggested through the use of total velocity defined by U^t = (U^2 + 2(p–p_∞)/p)^(1/2). This quantity obeys the Law of the Wake. Mixing length and eddy viscosity profiles based on the derivative ∂U^t/∂y are reduced into one curve which is the reference flat plate distribution.
https://thesis.library.caltech.edu/id/eprint/6041An investigation of a two-dimensional propulsive lifting system
https://resolver.caltech.edu/CaltechTHESIS:08312010-081235652
Authors: Shollenberger, Carl Alvin
Year: 1971
DOI: 10.7907/GZNT-1X61
Several aspects of the nonhomogeneous flow associated with a system combining lifting and propulsive requirements of an aircraft are considered in detail by analytical and experimental methods. The basic geometry of the problem is that of two lifting surfaces with an actuator disk located between them. The resulting flow consists of two regions of different total energies.
Propulsive lift systems are prototypes of many similar multi-energy flow problems. The principles governing flow with energy addition are examined. Basic equations and boundary conditions are developed for the complete inviscid and incompressible analysis for the two-dimensional case. The corresponding flow singularities are discussed and the integral equations which completely specify the system are derived.
The two special cases of small and large energy addition are considered in detail including solutions.
A numerical procedure is developed to solve the full problem including allowance for the wake deflection. Appropriate vorticity forms are used to represent the entire system. Wake vorticity is provided the freedom to move in the plane. An iterative scheme is presented which rapidly converges to a solution for the magnitude and location of the system vorticity distributions. Forces and moments are evaluated on the propulsive lift system.
Analytical results are given from the numerical solution for various values of the geometric and energy parameters. Comparison of the numerical result with the solutions for extreme values of energizing is given.
Results from a wind tunnel study of the two-dimensional propulsive-lift system provide a check on the importance of real effects. Comparison of the analytical and experimental results is given in detail. The experimentally determined wake development is observed to be similar to the predicted shape. In addition, the lift augmentation is similar for the theoretical and experimental cases. Further, the airfoil pressure distributions and resulting pitching moments are seen to exhibit the behavior expected from the calculations.
https://thesis.library.caltech.edu/id/eprint/6018Experimental investigation of the effect of cooling on near wake of circular cylinder at mach number six
https://resolver.caltech.edu/CaltechTHESIS:04152011-112031398
Authors: Ramaswamy, Mathagondapally A.
Year: 1971
DOI: 10.7907/8ZZ8-PC49
<p>An experimental investigation has been conducted to study the near wake of a two-dimensional circular cylinder of 0.2 in. diameter at M_∞ = 6. Mean flow properties were determined from Pitot pressure, static pressure, and hot-wire recovery temperature measurements at free stream Reynolds number of 0.905 X 10^4 and 2.95 X 10^4 for both adiabatic and cooled models, the latter at 0.19 T_o.</p>
<p>The near-wake was laminar for the adiabatic model at both
the Reynolds numbers tested. For the cold model, the near-wake was laminar for the lower Reynolds number and transition occurred in the near wake at the higher Reynolds number. The wake shocks, the shear layer edge and the thermal layer edge moved closer to the wake centerline with cooling and with increase in Reynolds number. The base pressure decreased with cooling and the sonic point moved closer to the model on cooling. In the recirculating region, the total temperature distributions exhibited a minimum close to the dividing stream line for all the cases, and the total temperature on the centerline was nearly constant and equal to the value at the rear stagnation point (0.5 T_o for the cold models) indicating that the heat transfer in this region was mainly by convection. The existence of a thin thermal layer on the base was evident for the cold models.</p>
<p>Preliminary experiments on the two-dimensionality of the
flow and an emperical formulation for the viscous corrections to the measured Pitot pressure have been included in the Appendices.</p>
https://thesis.library.caltech.edu/id/eprint/6335Hypersonic viscous-inviscid flow interactions including boundary layer separation on a flat plate at angle of attack
https://resolver.caltech.edu/CaltechTHESIS:09032010-111033039
Authors: Hulcher, Gregory D.
Year: 1972
DOI: 10.7907/PZCP-FT88
Experimental measurements of mean flow properties over the leeward surface and in the near wake of an adiabatic thin flat plate at an angle of attack of α = 15° were obtained at Mach 6 and Reynolds number based on the chord length of 186,000. The leading edge thickness is the predominant variable which affects the pre-separation interaction region. The effects of the large windward pressure, which separates the boundary layer at ℓ/L ≃ .7 are felt at points considerably forward of the separation point. The pressure rise in the separation region is similar to the rise on a flat plate-ramp model, and the data correlate according to Chapman's parameters. Also, the leeward side flow of the thin flat plate is found to be very similar to the flow over a wedge whose leeward side is inclined to the same angle. The wake centerline quantities behave similar to those behind a flat plate at zero angle of attack, but the streamwise gradients are less than those behind an inclined wedge. The flow appears to remain laminar throughout the entire field of measurement.https://thesis.library.caltech.edu/id/eprint/6021An economic air pollution control model-application : photochemical smog in Los Angeles County in 1975
https://resolver.caltech.edu/CaltechTHESIS:06262014-113258422
Authors: Trijonis, John Charles
Year: 1972
DOI: 10.7907/hxbp-pc89
<p>An economic air pollution control model, which determines the least cost of reaching various air quality levels, is formulated. The model takes the form of a general, nonlinear, mathematical programming problem. Primary contaminant emission levels are the independent variables. The objective function is the cost of attaining various emission levels and is to be minimized subject to constraints that given air quality levels be attained.</p>
<p>The model is applied to a simplified statement of the photochemical smog problem in Los Angeles County in 1975 with emissions specified by a two-dimensional vector, total reactive hydrocarbon, (RHC), and nitrogen oxide, (NO<sub>x</sub>), emissions. Air quality, also two-dimensional, is measured by the expected number of days per year that nitrogen dioxide, (NO<sub>2</sub>), and mid-day ozone, (O<sub>3</sub>), exceed standards in Central Los Angeles.</p>
<p>The minimum cost of reaching various emission levels is found by a linear programming model. The base or "uncontrolled" emission levels are those that will exist in 1975 with the present new car control program and with the degree of stationary source control existing in 1971. Controls, basically "add-on devices", are considered here for used cars, aircraft, and existing stationary sources. It is found that with these added controls, Los Angeles County emission levels [(1300
tons/day RHC, 1000 tons /day NO<sub>x</sub>) in 1969] and [(670 tons/day RHC, 790 tons/day NO<sub>x</sub>) at the base 1975 level], can be reduced to 260 tons/day RHC (minimum RHC program) and 460 tons/day NO<sub>x</sub> (minimum NO<sub>x</sub> program).</p>
<p>"Phenomenological" or statistical air quality models provide the relationship between air quality and emissions. These models estimate the relationship by using atmospheric monitoring data taken at one (yearly) emission level and by using certain simple physical assumptions, (e. g., that emissions are reduced proportionately at all points in space and time). For NO<sub>2</sub>, (concentrations assumed proportional to NO<sub>x</sub> emissions), it is found that standard violations in
Central Los Angeles, (55 in 1969), can be reduced to 25, 5, and 0 days per year by controlling emissions to 800, 550, and 300 tons /day, respectively. A probabilistic model reveals that RHC control is much more effective than NO<sub>x</sub> control in reducing Central Los Angeles ozone. The 150 days per year ozone violations in 1969 can be reduced to 75, 30, 10, and 0 days per year by abating RHC emissions to 700, 450, 300, and 150 tons/day, respectively, (at the 1969 NO<sub>x</sub> emission level).</p>
<p>The control cost-emission level and air quality-emission level relationships are combined in a graphical solution of the complete model to find the cost of various air quality levels. Best possible air quality levels with the controls considered here are 8 O<sub>3</sub> and 10 NO<sub>2</sub> violations per year (minimum ozone program) or 25 O<sub>3</sub> and 3 NO<sub>2</sub> violations per year (minimum NO<sub>2</sub> program) with an annualized cost of $230,000,000 (above the estimated $150,000,000 per year for the new car control program for Los Angeles County motor vehicles in 1975).</p>
https://thesis.library.caltech.edu/id/eprint/8527Viscous-Inviscid Flow Interaction in Stratified Flow Over a Barrier
https://resolver.caltech.edu/CaltechTHESIS:08182010-154704323
Authors: Su, Tsung-chow Joe
Year: 1973
DOI: 10.7907/XNJM-ES87
<p>The gross effect of boundary layer separation on the flow field of stratified flow over a barrier was studied by means of the integral method of Lees and Reeves.</p>
<p>The complete integral formulation of both inner and outer flow field of stratified flow over a barrier was obtained.</p>
<p>Furthermore, an iteration scheme of computation is proposed for the simple case of incompressible homogeneous flow over a barrier with viscous-inviscid interaction included.</p>
<p>However, in viewing the increasing importance, a considerable amount of work remains to be done on this problem.</p>https://thesis.library.caltech.edu/id/eprint/5998Methods for sulfate air quality management with applications to Los Angeles
https://resolver.caltech.edu/CaltechETD:etd-06172004-111601
Authors: Cass, Glen Rowan
Year: 1978
DOI: 10.7907/WWJR-PJ15
Particulate sulfate air pollutants contribute to visibility deterioration and are of current public health concern. This study develops the technical understanding needed for sulfate air quality control strategy design. Methods which link sulfate air quality and air quality impacts on visibility to the cost of controlling sulfur oxides air pollutant emissions are presented. These techniques are tested by application to the Los Angeles Basin over the years 1972 through 1974.
An air quality simulation model is developed which directly calculates long-term average sulfate concentrations under unsteady meteorological conditions. Pollutant concentrations are estimated from Lagrangian marked-particle statistics based on the time sequence of historical measured wind speed, wind direction and inversion base height motion. First order chemical reactions and ground level pollutant dry deposition are incorporated within a computational scheme which conserves pollutant mass.
Techniques are demonstrated for performing both mass balance and energy balance calculations on flows of energy resources containing sulfur throughout the economy of an air quality control region. The energy and sulfur balance approach is used to check the consistency of a spatially and temporally resolved air quality modeling emission inventory for the South Coast Air Basin.
Next the air quality model is validated against sulfur oxides emissions and sulfate air quality patterns observed in the Los Angeles Basin over each month of the years 1972 through 1974. A seasonal variation in the rate of SO2 oxidation to form sulfates is inferred. Overall average SO2 oxidation rates of about 6% per hour prevail during late spring, summer and early fall, while mean SO2 oxidation rates of between 0.5% per hour and 3% per hour prevail from October through February of our test years. From the model results, it is concluded that three to five major SO2 source classes plus background sulfates must be considered simultaneously at most monitoring sites in order to come close to explaining observed sulfate levels. The implication is that a mixed strategy aimed simultaneously at a number of specified source types will be needed if substantial sulfate air quality improvements are to be achieved within this particular airshed.
Techniques are developed for analysis of the long-run impact of pollutant concentrations on visibility. Existing statistical models for light scattering by aerosols which use particle chemical composition as a key to particle size and solubility are modified so that the relative humidity dependence of light-scattering by hygroscopic aerosols could be represented in a more physically realistic manner. Coefficients are fitted to the model based on ten years of air pollution control agency routine air monitoring data taken at downtown Los Angeles. Sulfates are found to be the most effective light scatterers in the Los Angeles atmosphere. It is estimated that the visibility impact of reducing sulfates to a half or to a quarter of their measured historic values on each past day of record would be manifested most clearly in a reduction in the number of days per year of less than three-mile visibility. The number of days of average visibility less than ten miles would be little affected.
Two retrospective examples are worked to show how the results of the air quality simulation models may be used to define a variety of sulfate air quality control strategy options. It is suggested that a package of technological emissions control measures and institutional changes (including natural gas price deregulation) may provide greater improvements in both sulfate air quality and visibility at less cost than can be obtained from a purely technological solution to the Los Angeles sulfate problem.
https://thesis.library.caltech.edu/id/eprint/2629