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Helium concentration measurements utilizing laser induced Raman scattering

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Helium concentration measurements utilizing laser induced Raman scattering

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Content HELIUM CONCENTRATION MEASUREMENTS UTILIZING LASER INDUCED RAMAN SCATTERING by Morton Meyer Glick A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Aerospace Engineering) September 1972 INFORMATION TO USERS This dissertation was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1. The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity. 2. When an image on the film is obliterated w ith a large round black mark, it is an indication that the photographer suspected that the copy may have moved during exposure and thus cause a blurred image. You will find a good image of the page in the adjacent frame. 3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the material. It is customary to begin photoing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again — beginning below the first row and continuing on until complete. 4. The m ajority of users indicate that the textual content is of greatest value, however, a somewhat higher quality reproduction could be made from "photographs" if essential to the understanding of the dissertation. Silver prints of "photographs" may be ordered at additional charge by writing the Order Departm ent, giving the catalog number, title, author and specific pages you wish reproduced. University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 A Xerox Education Company 73-737 GLICK, Morton Meyer, 1941- HELIUM CONCENTRATION MEASUREMENTS UTILIZING LASER INDUCED RAMAN SCATTERING. University of Southern California, Ph.D., 1972 Aerospace Studies University Microfilms, A XERO\Company , Ann Arbor, Michigan © Copyright by MORTON MEYER G-LICK 1972 THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED U N IV E R S IT Y O F S O U T H E R N C A L IF O R N IA T H E G R A D U A TE S C H O O L U N IV E R S IT Y PARK LO S A N G E LE S . C A L IF O R N IA 9 0 0 0 7 This dissertation, written by ............Wo? to?.. Meyer..Glick under the direction of his.... Dissertation C om mittee, and approved by a ll its members, has been presented to and accepted by The Graduate School, in p artial fulfillm ent of requirements of the degree of D O C T O R O F P H I L O S O P H Y Septem ber 1972 D a te............. DISSERTATION COMMITTEE Chairman PLEASE NOTE: Some pages may have i n d is ti n c t p r in t . Fi imed as received. U n ive rs ity M icrofilm s, A X ero x Education Company ABSTRACT HELIUM CONCENTRATION MEASUREMENTS UTILIZING LASER INDUCED RAMAN SCATTERING A technique which requires the monitoring of laser induced Raman scattered light from gas molecules has been developed for measuring density in a mass diffusing jet. The validity of this method, which does not disturb the flow field, is demonstrated by applying it to an air-helium turbulent jet to measure the mean density profiles and by showing that, based upon the empirical data, the mass balance of the helium specie can be computed to within £ 5% at several stations. In addition, the corresponding pres sure and velocity profiles in the jet are presented along with estimates of the laser power necessary to make time resolved measurements in the above flow field. ACKNOWLEDGEMENTS First, I would like to thank my wife, Virginia, and my son, David, for their extreme patience. I would also like to thank the many, many people at USC who have helped me in this work. In particular, I offer thanks to Drs. Muntz, Laufer, Porto, Kellam and Kaplan; to Elizabeth Harris and Gail Wamsley; to D. C. Kingsbury, C. C. DeVries and A. Bleeker. I would also thank Ellen Jones for typing the manuscript, Gene Messenger for doing the illustrations and graphs, and the Office of Naval Research who sponsored this work under contract N0014-67-A-0269-0015. TABLE OF CONTENTS Page ABSTRACT...................................................ii ACKNOWLEDGEMENTS.........................................iii LIST OF FIGURES.......................................... v LIST OF TABLES...........................................vii LIST OF SYMBOLS................... ................. . .viii I. INTRODUCTION ...................................... 1 II. EXPERIMENTAL METHOD............................. 9 III. EXPERIMENTAL EQUIPMENT ......................... 23 IV. EXPERIMENTAL PROCEDURE ........................ 30 V. RESULTS..............................................60 VI. CONCLUSIONS..........................................72 REFERENCES.................................................74 FIGURES.....................................................77 APPENDIX I ................................................109 iv 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 LIST OF FIGURES The Raman and Rayleigh Scattering Processes. Schematic Diagram of Typical O^ and N^ Raman Spectrum ..................................... Optical System ............................... Helium-Air Jet and Traversing Mechanism. . . Test Facility Excluding Laser............... Helium Nozzle and Coflowing Air Cylinder . . Perkin-Elmer Argon-Ion Laser ............... Air Filtering System ........................ Schematic Drawing of Test Facility ......... Laser Beam Passing Through Mixing Region . . Stokes Raman Spectrum of Air . . . ......... Voltage Attenuation and Integrator Circuit . Helium-Air Jet ............................... Typical Absolute Spectral Response of S-20 Photocathode ................................. Valve System for Pressure Measurements . . . Pressure Survey Pattern in Coflowing Air Stream ....................................... Pitot Probe Used To Survey Helium Jet. . . . v 94 95 96 97 98 99 100 101 102 103 104 105 106 107 Velocity Profile at X/D = 0................. Velocity Profile at X/D = 0................. Axial Pressure Decay ........................ Pressure Profile at X/D =15.2 ............. Halfwidth of Pressure and Density Versus X . Least Squares Curve Fit to Pressure Data . . Transverse Pressure Profile................. Density Profile at X/D = 9 ................. Density Profile at X/D = 11................ Density Profile at X/D = 14. ........ Density Profile at X/D =18................ Similarity Density Profile ................. Least Squares Curve Fit to Density Data. . . Centerline Velocity and Density............. Transverse Velocity Profile................. vi LIST OF TABLES Table Page 1 Results of Helium Mass Balance ............... 67 2 Results of Momentum Balance...................... 69 3 Results of Increasing Total Pressure upon Momentum and Mass Balance........................ 71 vii LIST OF SYMBOLS Lower Case English c = speed of light = 3 X 10^ cm/sec d =s diameter--cm f = focal length— cm fLS = frequency of large scale turbulent motion— sec ^ fgg = frequency of small scale turbulent motion--sec-' * ' 2 g = gravitational acceleration = 981 cm/sec -27 h = Planck's Constant = 6.625 X 10 erg-sec k = Boltzmann Constant = 1.38 X 10” "^ erg/deg 1 = length of laser beam examined by PMT--cm O pstatic=s" ta" t^c Pressure — dyne/cm p = dynamic pressure--dyne/cm 2 p^ =dynamic pressure at the jet centerline--dyne/cm u* =root mean square value of the axial component of the instantaneous velocity fluctuation— cm/sec Capital English O A =angstrom = 1.0 X 10~ cm A. =area of the image of the scattering volume on the monochromator slit--cm 2 A =illuminated area of the slit--cm s viii C ^specific heat at constant pressure--cal/gram °K I • , =magnitude of the locally measured Raman signal from * the jet I& =magnitude of the measured Raman signal from the air ’ in the coflowing air stream IN =magnitude of the recorded noise of the system I0(^-) = rr -polarized laser intensity K =thermal conductivity--cal/cm-sec-°K L =transmission factor of all of the optics passing collected Raman light N =effective number of molecules per cubic centimeter illuminated by laser beam =effective number of molecules illuminated by laser beam P^ =power level of incident laser beam— watts =collected Raman power level--watts Ra =gas constant of air RHe =gas constant of helium T =absolute temperature--°K V =average local velocity--cm/sec V^. =average velocity of helium at X/D = 0— cm/sec VQ =average velocity of coflowing air stream— cm/sec V(^ =average velocity at a point on the centerline of the jet— cm/sec Lower Case Greek >ab= the derivative of the component of the polari- zability tensor with respect to the normal vibra tional coordinate at the equilibrium position t' =root mean square of the instantaneous specie con centration fluctuation ix v9' = root mean square of the instantaneous temperature fluctuation--°K r- = reduced mass; micron t= 1.0 X 10”6 meters U ab = ■ laser frequency--sec” 1 U R = frequency of Raman scattered light--sec” 1 e = density— gm/cm ea 3 = local density of air--gm/cm ^ a ,co 3 = density of air in coflowing air stream--gm/cm ^ He 3 = local density of helium--gm/cm es 3 = local specie density— gm/cm ^ T = total density at a point— gm/cm ^ R 2 =effective Raman scattering cross-section--cm / s t eradia n-molec Upper Case Greek V =mean specie concentration T1 He =local helium concentration TS = . local specie concentration © =difference between mean absolute temperature of a point in the flow and the receiving medium— K XL = solid angle— steradian; electrical resistance--ohms X CHAPTER I INTRODUCTION The problem of a turbulent jet with heat or mass transfer has been studied by many investigators (1 - 9) during the past several decades. It has been established by some of these researchers (1-5) that the measured temper ature or concentration profiles always extend to larger lateral dimensions than do the corresponding velocity pro files, even for Prandtl or Schmidt numbers close to unity. Furthermore, schlieren techniques have shown that a distinct temperature (concentration) interface exists between the region into which heat has spread and the ambient field surrounding the jet. This interface is similar to the vorticity interface which exists between the turbulent region of a constant density jet and the external fluid. Based upon the preceding evidence, it could be concluded that within the heat (or mass) diffusing jet two regions exist, a core in which both vorticity and temperature (or concentration) fluctuations are found and an outer zone containing only temperature (or concentration) fluctuations. On the other hand, such a conclusion would be inconsistent with the concept of Prandtl (or Schmidt) number equal to one. Concerning this apparent contradiction, it was suggested that the difficulty lies in the technique of measuring mean quantities in a highly intermittent region of a shear flow. In addition, a method of making a stochastic ensemble average was proposed that would give a better picture of the true conditions near an interface. However, in order to be able to effect this stochastic ensemble averaging technique at either the temperature (or concentration) or velocity interface, a suitable detector, sensitive to the appropriate fluctuation, is required. The hot-wire anemometer is the instrument most often used to measure fluctuating quantities in a turbulent flow of the type described above. However, while the single hot-wire involves a rather simple experimental procedure when used in a constant density flow to measure velocity, its facility is greatly diminished when moni toring temperature or concentration perturbations in vari able density flows. In the case of simultaneous heat and momentum transfer in air (and other gases), in which the dependence upon temperature of p, Cp and K is known and in which the mean absolute temperature can be measured, a single hot-wire measurement is sufficient to determine the i mean velocity, U . To obtain the turbulent intensity, 3 and the temperature fluctuation l ev el ,, with a single hot-wire set perpendicular to the fluid stream requires that three measurements at each point in the flow be taken. These measurements are made with the same probe at three different wire currents (1 0 ). In the flow of an isothermal gas with mass and momentum diffusion, two hot-wire measurements are necessary in order to determine 0 and J* . However, unlike the flow in vh ich heat transfer occurs, it is not possible to use the same hot-wire for both measurements. Corrsin (10) has shown that two hot-wires having different diameters are necessary. The turbulent intensity and the concentration fluctuation level, , can be obtained from a single reading from each of three separate hot-wires placed successively at the same point. Again, the wire diameters of any two of these probes must be different. The necessity for making multiple measurements in either of the above cases has two major disadvantages: first, the final numerical results will have substantially larger errors -than results stemming from single hot-wire measurements; and second, the experimental procedure will be very lengthy. In the mass diffusing flow, the necessity to change probes will greatly compound these two effects. Tombach (11) has reported another serious disadvantage of using hot-wires to measure concentration. His instruments 4 suffered a history effect when subjected to high concen trations of helium in an air-helium mixture. There are a number of other techniques available for measuring mean or instantaneous temperature or concen tration. These techniques include: the use of probes which monitor temperature or remove fluid for composition analysis; photographic methods such as the schlieren (1 2 , 13), shadow (12, 13), or interference (12 - 14) techniques; and scattering methods utilizing an electron beam (15, 16), Thompson (17), or Rayleigh (18) scattering. The probe and photographic methods are not well- suited for measuring instantaneous fluctuations due to their large inertia, insensitivity to small perturbations, or inability to repeat measurements at a rapid enough rate. The use of any probe (or hot-wire) also implies that a physical object is being placed in the gas stream at the point of measurement. It is inevitable that the instrument will create some disturbance within the flow field and thereby change the flow conditions, or that the measurement being made will in some way be affected by the presence of the probe itself. The electron beam fluorescence technique, although capable of measuring instantaneous specie concentration, is currently limited to an upper-operating pressure of a few Torr. As pointed out by Widhopf and Lederman (19), the Thompson scattering method requires a high density "hot1 5 plasma since the radiation scattered from free electrons is used. Finally, Rayleigh scattering is, in most situations, so encumbered by the presence of dust that an accurate determination of specie concentration is impossible. In view of the difficulties encountered in using the above techniques for measuring temperature and concen tration fluctuations, it would seem appropriate and indeed necessary to develop a new method. The development of the laser and associated optical equipment has made possible a new technique for measuring both the time-averaged and instantaneous values of specie concentration in flows of mixed gases. This method requires the monitoring of the intensity of inelastically scattered light resulting from the collision of laser photons and diatomic (polyatomic) gas molecules. The inelastic scattering process is known as the Raman effect. Raman scattered light is characterized by a change in both frequency and direction from that of the incident radiation. The increase or decrease in the energies of the scattered photons corresponds to the energy differences between rotational and vibrational states of the molecule. Light scattered with a decreased frequency (increased wavelength) forms the (Raman) Stokes spectrum while light scattered with increased frequencies forms the anti-Stokes lines. The Raman spectrum is so completely characteristic 6 of the vibrational and rotational states of the molecule involved in the process that it can be used as a means of specie identification. Raman scattering was first predicted by Smeakl (20) in 1923, and it was first demonstrated by C. V. Raman (21) in 1928. Since then many theoretical and experimental investigations ( 2 2 - 26) of this effect have been made. Most of these studies were undertaken in an effort to better understand the process itself or to determine properties of the molecules involved. The application of Raman scattering is well-suited to the measurement of specie concentration (density); in addition, it offers several advantages over other tech niques. Some of the features of this technique are: (1) This method, which simply requires the passing of a beam of laser light through the mixing fluid, does not, in the fluid mechanical sense, disturb the flow. The energy of the incident photons is used to excite the vibrational or rotational states of the gas molecules but not those of translation. No probe or other device needs to be placed within the flow. (2) The measurement of concentration can be obtained from a single reading. (3) The measurement of a particular specie con centration will not be affected by the presence of other 7 gases. The frequency shifts of the Raman light from that of the exciting line is discreet and corresponds to a given specie. (4) Through the use of lenses, the characteristic length of the test volume can be made less than the micro scale of the turbulence. This condition is necessary to insure a uniform density throughout the sample region. (5) Unlike hot-wires and other probes in which compensation must be made for inertia effects, the signal strength will vary instantaneously with concentration fluc tuations. The limiting response of the detection system is that of a photomultiplier tube which is on the order of a few nanoseconds. (6 ) The sensitivity of the system to small fluc tuations will be excellent, limited only by the rate of scattered photons for which meaningful statistics exist. (7) The technique will not be affected by dust or other particles which scatter incident laser radiation without a frequency change. (8 ) The system is stable so that mean calibrations are accurately known over the period of a given test. Widhopf and Lederman (19) have reported making density and specie concentration measurements in gases using the Raman scattering technique. Their tests were static calibrations, performed under highly controlled conditions, and utilized a Q-switched Ruby laser. The 8 laser had a pulse duration of ten nanoseconds and a peak output of approximately 100 megawatts. In these investi gations they have shown that the Raman intensity from pure O2 and N2 varies linearly over a density range of nearly two and one-half orders of magnitude for gas pressures that range between a few Torr and one atmosphere. They were also able to accurately measure specie concentration of a trace gas in a high density mixture although the former represented only 0.4% of the total mixture. The objectives of this paper are to show that Raman scattering can be used to obtain specie concentration in dynamic (flow) situations, and to ascertain the experi mental conditions necessary for applying this method to investigate the concentration interface in a mass diffusing jet. To accomplish the above the mean density profiles in an air-helium turbulent j*et have been measured using the Raman scattering technique. This study was made with a low-power, Argon-ion, gas laser as the source of incident radiation. CHAPTER II EXPERIMENTAL METHOD Raman Scattering When a photon is incident upon a diatomic or polyatomic molecule, it can be scattered either elastically or inelastically. If the scattering is elastic, the scat tered photon will have the same energy as the incident quantum and the state of the molecule will remain unchanged. This process is known as Rayleigh scattering. The molecule, on the other hand, can take from or give to the incident photon an amount of energy, AE, corresponding to the energy difference between two states of the molecule. If the incident quantum has energy h 1/ , then the scattered photon must have an energy of h ]) . A E. This process is known as Raman scattering. Along with the aforementioned Rayleigh scattering, this latter process is shown schematically in Figure 1. In this figure the initial and final states of the molecule are marked I and F respectively. The arrow marked h U represents 9 10 the energy of the incident photon relative to the initial energy state of the molecule, and the double arrow shows the energy of the scattered photon. As shown, a Stokes photon corresponds to a molecule making a transition from a lower to a higher energy level, while an anti-Stokes photon indicates a decrease in molecular energy. A typical Raman spectrum for 02 or is illustrated in Figure 2. On either side of the exciting (Rayleigh) line, and within 1 0 0 cm-' * " of it, is found a series of lines which are closely spaced and equidistant from one another. Also to be found is a single peak which is substantially removed from the Rayleigh line. The occurrence of the samll Raman displacements is successfully predicted from the quantum mechanical theory for the rigid rotator (2 2 ), while the large Raman displacement can be predicted from harmonic oscillator theory. In Raman scattering, then, the interaction of the incident photon with the gas molecule causes changes in the rotational and vibrational states of the molecule; the translational states are left essentially unaffected. From a macroscopic, fluid mechanical viewpoint the fluid is not disturbed by the incident radiation. The Raman scattering process differs from that of fluorescence. In fluorescence, the molecule will be trans formed to an excited energy state by completely absorbing the incident photon. Subsequently, the molecule will relax by emitting another photon known as fluorescent light. 11 _7 This process requires a mean time on the order of 10 seconds for allowed transitions (16), and is only possible with incident radiation having a frequency (energy) that can be absorbed by the molecule. Raman scattering, on the — 14 other hand, occurs in approximately 10 seconds (27), and it is possible with incident light of any frequency. The intensity of a Stokes-shifted Raman line, polarized in a direction ^ , excited by a laser polarized in a direction tr is (28) 3 Tr- j(f.°- __________ <<ve ' 4 ^c4 Uab Ll. (-hi/ab/kT)} (Equation 1) The intensity that will actually be measured, however, will be somewhat less than that given above due to attenuation factors introduced by the experimental apparatus. The measured intensity will be: As Jab^ f )meas- = Iab^ f ) x ^ x L x A7 (Equation 2) From these equations it should be noted that the measured intensity is directly proportional to the number of scat tering centers, and in the case when two measured inten sities are ratioed, for the same experimental set-up and I , the ratio of the measurements will be such that: *1 - N2. o T M 12 Concentration Measurements When a jet of gas issues from an orifice into an ambient field, a mixing of the jet fluid with that of the surrounding medium takes place. If the two fluids involved are dissimilar, then the concentration of the jet gas will decrease with increasing distance from the orifice. The concentration of a given specie, at a point within the flow, is defined as: (Equation 3) where P and Q are the density of the specie gas w O and total density of the gas in grams per cubic centimeter respectively. The concentration of the jet gas equals one, (1.0), at the helium orifice, ( /D - 0). Equation 1 shows that the Raman light scattered by a particular specie varies directly with the number of specie molecules per unit volume. But, the number of these molecules per unit volume multiplied by their molecular weight simply defines the specie density, P s* Hence, the local specie concentration, Equation 3, is directly propor tional to the intensity of the Raman light scattered by the molecules. In the experiments described herein, a jet of helium mixes with a coflowing stream of air; the mixing is isothermal at room temperature and atmospheric pressure. 13 A direct measurement of the local helium density is not possible, however, since helium is monatomic and does not have an associated Raman spectrum. The helium density is obtained indirectly by monitoring the Raman-scattered light from the oxygen and nitrogen molecules also within the sample region. The lower limit of the expected Raman signal is zero and corresponds to 100% helium at the test point. The degree to which this limit can be measured is determined by the "noise” within the detection system. The principal sources of this noise are photomultiplier dark current, amplifier noise and stray light. The upper limit of the Raman intensity corresponds to 100% air within the scat tering region. The magnitude of this signal is determined experimentally, and it will depend upon the pressure and temperature of the gas. Between these two bounds the signal intensity varies linearly with the local air density. If the density of the ambient air (coflowing stream) is known, the local air density within the mixing region can be computed from: Ia.l ~ 1N (Equation 4) The local helium density can then be obtained from the equation for the sum of the partial pressures of a gas, i.e., f rom: 14 Pstatic = gT (Ra ^ a + RHe ^ He^ (Equation 5) The local helium specie concentration follows from: "P - ^ He ~ eHe + ea (Equation 6) In the above procedure for calculating TlH e» it is assumed that the presence of gases other than oxygen, nitrogen, and helium is negligible. It is further assumed that re-scattering or absorption of the Raman scattered light by the gas molecules themselves can be ignored. Test Facility In order to apply the Raman scattering technique to measure the mean helium concentration profiles in an air-helium turbulent get, an experimental facility as shown in Figures 3 through 8 was set up. This facility consisted of four major parts: a laser; an air-helium jet assembly; an optical system; and a signal monitoring and recording system. The source of the incident radiation in the Raman process was a continuous-wave, argon-ion laser having a nominal power of 250 mw at 4880 A outside of the cavity. A more complete description of this laser is given in Chapter III, Experimental Equipment. As illustrated in Figures 9 and 10, the laser beam was passed above the jet assembly, 15 but through the mixing region of the turbulent fluid. With reference to the established coordinate system, the beam propagated parallel to the floor in the Y-direction, perpendicular to the axis (X-direction) of the vertical jet. The electric vector of the polarized light was also parallel to the floor in the i Z-direction. A simple lens, , was used to focus the laser beam to a "point" within the jet. By focusing the beam, very high optical energy density was obtained in a very small sample volume. This method of sample illumination p increases the brightness (watts/cm /steradian) of the Raman scattered light, to a point where only a single pass of the beam through the jet is sufficient for the measurement of density. The focusing lens also served to define the effective spatial extent of the scattering region. Barrett and Adams (29), using confocal resonator theory, have defined a "source cylinder" within the focused laser beam from which nearly all of the Raman light is scattered. Their calculations show, that for a 40 mm focal length lens and a laser beam having a diameter of 3 mm, the size of the source cylinder, to within an order of magnitude, will be 8.6 J±- in diameter by 0.48 mm in length. In the experi ments described herein, the laser beam diameter and the focal length of the lens, L^, were 3 mm and 40 mm respec tively. The length of the sampling volume was estimated to be 4 or 5 mm. 16 The lens, L2, was used to collect light scattered from the sample volume. In order to obtain as much light as possible, and be able to place the lens well away from the scattering point, this lens must be as large as possi ble in both solid angle of collection and in diameter. The lens used in this investigation was an f/1.2 with a diam eter of 50 mm. The intensity of the Rayleigh light scat tered from the sampling volume is at least three orders of magnitude greater than that of the scattered Raman light. However, since the depolarization ratio of the Rayleigh light is but a few percent, it is possible to minimize the intensity of this light as seen by the collecting lens, L2 (28, 29). This lens must be placed at 90° with respect to the laser beam so that it "looks into" the electric vector of the incident radiation, as shown in Figure 9. The light leaving the collecting lens was passed through a dove prism. Using the prism, the horizontal image of the scattering region was rotated toward the vertical until it was parallel to the entrance slit of the spectrometer. An imaging lens, L^, focused the collected light into the entrance slit. This lens was an f/3.0 with a 72 mm diameter and was selected so as to illuminate as much of the acceptance cone of the spectrometer as possible. The magnification of the test volume at the slit was about 6: 1. 17 In order to determine the gas density at a given point in the jet, the intensities of the Stokes-shifted J — 4 and J “ 6 lines of the rotational Raman spectrum of and N2, respectively, were continuously monitored. Both lines are displaced by 60 cm"'1 from the Rayleigh line and were passed simultaneously through the monochromator. In terms of the Raman spectrum of air, these lines form an unresolved single peak of large amplitude as shown in Figure 11. To accomplish the density measurements, the monochromator1s wavelength drive was not scanned but set at the wavelength corresponding to the maximum of this peak. This maximum occurred at approximately 9780 A when the grating was used in second order. Slit widths of 30 or 35 jx. were used depending on the particular test. The signal intensity was photoelectrically moni tored using an ITT FW-130 photomultiplier tube. This tube was thermoelectrically cooled to -30° C and biased at 2250 volts. At these operating conditions the PMT had a dark —12 6 current of 5‘ x 10 amperes and a gain of 7.5 x 10 . A DC picoammeter was used to measure the current output of this tube. The maximum PMT output, corresponding to 100% air at the scattering point, ranged between 5 x 10" ^ and 8 x 10"11 amperes. This value varied from test to test and was primarily a function of the optical alignment between the scattering volume, the lenses L and L~, and 18 the spectrometer. The signal to noise ratio was approxi mately 5.5:1. In practice, a much larger power signal could be obtained by opening the monochromator slits beyond 35 However, widening the slits invariably caused a decrease in the signal to noise ratio. Opening the slits as much as 100 J* would cause the Stokes spectrum of air to be superimposed on the exponentially-decaying tail of the Rayleigh line. This problem stems from the fact that the monochromator employed in these tests was not specifi cally designed for Raman spectroscopy. The stray light level in this instrument is about one part in 10 , whereas 12 in Raman (double) spectrometers it is about one part in 10 . The voltage output of the picoammeter corresponding to its meter deflection was divided, time integrated, divided again, and then recorded. The circuit for these operations is shown in Figure 12. The two-step voltage attenuation was necessary for impedance matching purposes. The first division reduced the 3V-maximum picoammeter out put to 91 mv. This was accomplished by using a divider net work consisting of a five percent, 33,000 XL resistor in series with a five percent, 1,000 XL resistor. In order to time integrate the signal, a simple RC circuit con taining a 100 megohm one percent resistor in parallel with a variable decade capacitor was built. Concentration measurements were made with both three and five second time constants. The input impedance to the second voltage 19 12 divider network was made very large at 10 XL by incor porating an operational amplifier into the circuit as shown. This second attenuation further reduced the maximum voltage signal to 10 mv . The voltage signal was then recorded on a ten millivolt, strip chart, ink pen recorder. Figures 5 and 6 are pictures of the coflowing helium-air jet assembly used in these experiments. The jet consists of two concentric parts: an inner nozzle, with an orifice diameter of 6.35 mm, through which helium flows; and an outer cylinder, 152.4 mm in diameter, from which the secondary air issues. The helium is supplied to the nozzle from commercially available bottles of the com pressed gas, while the air is obtained from an air supply that is common to all laboratories in the building. The average helium orifice velocity and coflowing air velocity are 14.1 and 0.488 meters per second, respectively. Initially, the jet assembly consisted of the helium nozzle only; the gas which issued from this nozzle mixed with the ambient air in the laboratory. However, with this arrangement, the signals from both dynamic head pressure measurements and laser concentration measurements contained large amplitude, low frequency fluctuations. The fluctu ations had an average frequency between one-half and one cycle per minute. On the basis of this data it was sus pected that the jet flow was unstable and slowly wavering about its axis. Since the sample volume for either the 20 pressure or concentration measurement was fixed in space, a wavering of the flow meant that the data was being obtained from a succession of different points, with vastly different signals levels, rather than from one point within the jet. With the addition of the coflowing air stream the jet was apparently stabilized; the fluctuations described above disappeared from the data signals. The jet was mounted on the vertical arm of the three-way traversing system shown in Figure 6. Measure ments at different points within the flow were accomplished by moving the jet relative to the fixed laser and optical system. The traversing mechanism was positioned beneath the table on which the focusing and collecting optics were placed, the X-direction traverse and jet projecting upward through a large hole in the top of this table. The jet could be raised, by the X-traverse, a maximum height of 40.7 cm above the table, an elevation at which the helium orifice intersected the laser beam. A large drum, 58.5 cm in diameter and 76.2 cm in height with both ends completely removed, was placed on the optics table so that it was concentric with the jet. The purpose of this drum was to help prevent convection currents created by the room air conditioning system and other such disturbances from influencing the jet flow. Holes were cut into the wall of the drum to permit the 21 passage of light, the placement of lenses, and the align ment of equipment. As mentioned before, the rejection ratio of the monochromator was relatively poor for Raman spectroscopy. Consequently, every effort had to be made to eliminate all sources of stray light. One of the principle sources of this radiation was laser light scattered without a frequency shift from dust particles suspended in the jet. These particles were induced into the helium flow along with the coflowing air. This Tyndall scattered light appeared as spikes of varying amplitude and random frequency in the recorded data. These spikes were always positive signals and hence biased the data such that its mean value increased. It was impossible to separate the true Raman signal from that of the dust. In order to eliminate this problem almost completely, a series of filters (described in Chapter III) were installed on the line carrying the air to the jet. Dust particles two microns, 2 , in size and greater were removed from the air by these filters. The intensity of stray light scattered from the inside wall of the drum from lens holders and the jet was significantly reduced by spraying them with ultra-flat black paint. A light trap was used to absorb the laser beam diverging from the scattering point. This trap con sisted of a cardboard tube, 45.7 cm in length and 10.1 cm in diameter, and a glass cone that was 15.2 cm in height 22 and 15.2 cm in diameter at its base. Both the tube and cone were blackened before assembly, the tube by spraying its interior and exterior surfaces with paint and the cone by dipping it into a solution of aquadag. The cone was then inserted, as far as it would go, into the back end of the tube with its apex along the centerline of the latter. The light trap was rigidly held in position, coaxial with the incident laser beam, by pushing it through a 10 cm diameter hole cut into the wall of the drum. The trap projected a distance of 7.5 cm into the interior of the drum. Laser light entering this tube was either absorbed by its walls directly or it was reflected by the cone toward the wall and then absorbed. This type of trap is very effective and has been used by several other researchers (11, 17). Finally, the incident laser light backscattered from the focusing lens, L^, was also con fined to a tube. This second tube, 1.27 cm in diameter by 40.6 cm in length, was placed concentrically with the inci dent beam such that this light could pass through it. The tube protruded through the wall of the drum and butted against the first (with respect to the beam) surface of the focusing lens. Light backscattered from this lens reentered the tube and was either absorbed in its walls or reflected back through it. CHAPTER III EXPERIMENTAL EQUIPMENT Helium-Air Coflowing Jet System A sketch of the helium-air coflowing jet used in these experiments is shown in Figure 13. The helium jet, itself, was constructed from a piece of stainless steel tubing, 15.2 cm in length with an inside diameter of 2.86 cm, and three copper pipe reducing sections. The orifice of the jet was formed by consecutively soldering two of the reducers to one end of the stainless tubing. The first reducer was used to decrease the inside diameter from 2.86 cm to 1.27 cm, while the second reducer caused a further decrease from 1.27 cm to 0.635 cm. The remaining reducer was ultimately attached to the upstream end (helium inlet) side of the nozzle. A 90° elbow fitting was soldered to this latter reducer in order to accommodate the line connecting the helium supply to the jet. Also, as shown in the figure, a 1.91 cm thick piece of aluminum honeycomb was placed inside of the upstream reducer to act 23 24 as a flow straightener. The forty mesh screen on top of the honeycomb helped to uniformly spread the helium flow-as it entered the plenum. Precaution was taken when assembling the get to insure that the axis of the stainless tubing and the axes of the downstream reducers were colinear. Alignment was achieved by fitting these pieces over a lathe-turned wooden mandrel just prior to soldering them together. The small pipe-stopping collars inside the reducer sections and excess solder were removed so that the inside walls were continuously smooth throughout the contractions. The helium jet was held in position inside the 15.2 cm diameter, cardboard coflow cylinder by three support rods. The rods were threaded, and after being passed through the walls of the outer cylinder, were screwed into nuts soldered on the outside of the plenum chamber. These rods were located in a plane approximately 11.4 cm beneath the jet orifice, two of the rods at an angle of 90° with respect to the third. Two nuts, one on either side of the cardboard wall, were used to prevent each support rod (jet) from moving once the jet was positioned. The coflowing air entered the space around the helium jet through a large funnel attached to the end of the cardboard cylinder. The funnel was filled with a highly porous, fibrous material in which the plastic fibers 25 were randomly oriented in order to diffuse the flow throughout the cylinder. A uniform flow of air from the cylinder was obtained by passing the air through a second, 5.08 cm thick section of this same material and then through two consecutive forty mesh wire screens. The second layer of fibrous material was rested on the support rods with the first screen on top of it. The second and final screen was stretched over the top of the cardboard cylinder, Figures 6 and 13. This arrangement left 3.81 cm or 150 screen wire diameters between the two screens and allowed some time for disturbances to the air from the first screen to dampen before the air reached the second screen. In order to allow time for disturbances created at the final screen to dampen before the air was entrained into the get, the get orifice was located 2.54 cm or 100 screen wire diameters above the downstream end of the coflow cylinder. The temperature of the helium gas was measured with the use of a copper-constantan thermocouple located in the plenum chamber of the jet. This thermocouple was approximately 11.4 cm from the orifice or 4.45 cm upstream of the double contraction. This thermocouple was inserted through the wall of the jet and projected approximately 1.27 cm into the chamber. The hole through which the thermocouple was inserted was filled with epoxy to prevent helium leakage. A second, copper-constantan thermocouple was used to measure the temperature of the coflowing air. This thermocouple was placed approximately halfway between the jet and the wall of cylinder and 3.8 cm below one of the support rods. The helium flow rate from the nozzle was controlled by a two-stage pressure regulator on the helium supply bottle and by a micrometer-driven precision needle valve installed on the helium supply line. The coflowing air, on the other hand, was controlled by two pressure regu lators. The first of these was located upstream of the air filtering system and controlled the flow into the latter, while the second regulator was downstream of the filters. The mechanical air filtering system shown in Figure 8 consisted of two separate stages. The initial stage removed larger solid particles, water, oil and other such substances from the air; the second stage was used to remove any remaining liquid and smaller particles such as dust. In order to make the system as effective as possi ble, the air was passed through two second-stage filters, placed! in series, on the air supply line. According to the manufacturer of this equipment, a single second-stage filter is capable of removing all particles two microns, 2 jut , in size and larger. The maximum volumetric flow rate of the second stage, filter was only 15 cfs, therefore, it was necessary to place three sets of these filters in parallel in order to obtain a suitable coflowing stream. 27 Monochromator The monochromator available for use in these exper iments was a Perkin-Elmer Model E-l Monochromator. This instrument has a focal length of 580 mm and an aperture ratio of f/8. It utilizes a pair of curved, bilateral slits which have a radius of curvature of 6.45 cm and are 12 mm in height. These slits are continuously adjustable from a width of 10 jx to 10 mm with a setting repeatabil ity of t 2 jj- over the full range of the width. The monochromator has a dispersion of 5.3 A/mm at 5000 A which is achieved by sending the radiation through the instrument twice in a double pass optical system. The monochromator is equipped with an Ebert-mounted, single, plane replicated diffraction grating having a ruled area of 84 mm x 84 mm with 576 lines/mm. The grating is used in second order to resolve radiation with wavelengths between 4000 A and 1.0 JX with a resolution of 0.1 A at a second order wave length of 1.0 JX . Wavelength is scanned by rotating the diffraction grating about a vertical axis. The wavelength drive mechanism is linear in wavelength with a stated accuracy of one part in 10,000 at all wavelengths and a stated repeatability of one part in 50,000 at all wave lengths . Photomultiplier Tube An ITT FW-130 multiplier phototube was used to monitor the radiation exiting from the monochromator. This high gain tube is constructed with a 16 stage box and grid dynode chain and a 2.54 mm diameter, end-window type photo cathode having an S-20 spectral response, Figure 14. The tube was kept in a light sealed Products For Research, Model TS-104, Photomultiplier Tube Housing, which was attached to the monochromator and thermoelectrically cooled to -30 £ 5g° C. At an overall operating voltage of 2250 V, the tube was found to have a dark current signal of -12 6 approximately 5 x 10 amperes and a gain of 7.5 x 10 . Laser A prototype, continuous-wave, argon-ion laser, designed and manufactured by the Perkin-Elmer Corporation, was used as the source of incident radiation in the density measurement experiments, Figure 7. This laser employs a flow through gas system rather than the more conventional sealed plasma tube. During operation, argon gas is con tinuously removed from it by a vacuum pump. In addition, the laser utilizes a cold tungstun cathode instead of one which is preheated electrically. A magnetic field is used to help confine the electric discharge within the quartz bore tube. This instrument is capable of producing light at five different wavelengths and has an all-lines power 29 output of 800 mw. Maximum gain is achieved when operating at 4880 A (450 mw maximum) or 5145 A (300 mw maximum). As can be seen in Figure 7, the mirrors which form the optical cavity are separate from the main body of the laser. Wave length selection is achieved through the use of a prism as the totally reflecting dielectric mirror. In the present case, the mirrors had a radius of curvature of three meters. The laser is water-cooled to prevent overheating and is one meter in length (not including the mirrors). CHAPTER IV EXPERIMENTAL PROCEDURE Helium-Air Jet Alignment Because of the manner in which the jet assembly was mounted to the traversing system, an inclination of the axis of the jet away from the vertical direction existed initially. By using the two support brackets, Figure 4, to connect the jet to the X-traverse, the weight of the jet created a clockwise moment about an axis in the Y direction. The result was that the jet leaned, in the -Z direction, toward the monochromator. In addition, since the two brackets were each fastened to the slave of the Unislide with a single bolt, the brackets (as a unit) and hence the ; jet, were also found to be tilted from the vertical in the -Y direction. The first step in the testing procedure was to align the jet assembly in the vertical direction. The jet alignment was accomplished with the help of a Gaertner, Model M-911, cathetometer. The cathetometer is an instrument for the accurate measurement of vertical distances and displacements and consists of a tripod stand, 30 31 a vertical guide bar and a telescope, horizontally mounted on a carriage. The telescope can be displaced vertically by sliding the carriage along the guide bar, or it can be rotated in a horizontal plane about the guide bar through 360°. The cathetometer is also equipped with leveling screws and bubble levels on its tripod stand and telescope. With the cathetometer in a level position, a pair of cross hairs within the telescope are in the true vertical and horizontal directions. To begin the alignment procedure, the cathetometer was placed in a position from which the jet could be viewed and then leveled with respect to the floor. This position was such that the axis of the telescope was in the Y direction and the jet could be seen in the X-Z plane. Following this, a check on the direction of the vertical cross hair was made. To facilitate this check, a plumb bob was suspended from the ceiling by a string. Then, without moving the tripod base, the telescope was rotated toward the plumb bob and optically adjusted until the string was in focus. If the vertical cross hair could be made to completely coincide with the string, then it was considered to be properly oriented; if not, level adjustments were made until the string and cross hair were coincident. Next, the telescope was focused on the helium nozzle such that the vertical cross hair was tangent to a small white spot on the surface of the jet. This spot was located near the 32 orifice and was painted on the jet before the alignment process began. The jet was then traversed in the -X direction a distance of 20.3 cm (32 helium orifice diam eters) while the position of the spot was continuously monitored. If the spot remained tangent to the cross hair, then the jet was traversing in a vertical direction as viewed from this one position. Initially, however, it was necessary to add shims between the jet and one of the mounting brackets in order to correct the original mis alignment. The horizontal motion of the jet in the -Z direc tion was examined once the vertical adjustment, described above, was completed. The telescope was moved along the guide bar until the horizontal cross hair was tangent to the white spot. Then as the jet was traversed horizon tally, the position of the spot relative to the cross hair was monitored. No alignment corrections were necessary, however, as the jet moved parallel to the floor. This whole alignment procedure, as described above, was repeated with the cathetometer placed at an angle of 90° with respect to the first viewing position, the axis of the telescope parallel to the Z direction. In order to align the jet with the X axis, when viewing from this latter direction, the two screws holding the support brackets to the Unislide were loosened and the brackets 33 rotated as necessary. Again, as before, no corrections were made to the horizontal, *Y, motion of the jet. Pressure Measurements Before any concentration measurements were attempted, dynamic head pressure surveys of both the helium jet and the coflowing, secondary air stream were made. The primary objectives of these tests were to deter mine the uniformity of the coflowing air and whether or not the helium jet was axisymmetric. The same pressure data was also used in the computation of the coflowing air velocity and the helium-air jet velocity profiles. All pressure measurements were made with a pitot probe suspended above the jet. An MKS Baratron, Electronic Pressure Meter was used to sense the pressure and indicate its magnitude. This instrument is capable of measuring -4 any pressure differential between three mm and 1.0 x 10 mm of mercury. Two methods of pressure readout are avail able with the MKS Baratron. First, the pressure can be read directly from the indicator meter. Eight meter scales, corresponding to full scale meter readings of 3, 1.0, 0.3, 0.1, 0.03, 0.01, 0.003 and 0.001 mm of mercury can be selected. Depending on the scale used, the meter can be read accurately to within one to three percent of the full scale reading. The second method of pressure readout involves balancing an AC bridge circuit located in 34 the Baratron Pressure Sensing Head. The bridge circuit is nulled by a voltage from a voltage divider network, which, in turn, is adjusted by three decade switches and an inter polating potentiometer decade. The pressure is read directly from the Pressure Readout dials (divider network controls) with five place readability. The stated accuracy of this second method of pressure readout is 0.15% of the dial reading plus 0.005% (or better) of the full range. The Baratron also provides a DC voltage output of zero to £ 100 mv for recording purposes. This voltage output is linear with pressure and proportional to the (£) meter deflection. During each pressure test, the voltage signals from the Baratron were time integrated for two seconds, divided by a factor of ten, and then recorded on a strip chart recorder. The displacement of the ink pen was calibrated with the Baratron output as follows: After the proper meter scale was selected, the Indicator Meter was zeroed and the corresponding position of the ink pen was recorded; then, the null switches were used to unbalance the AC bridge circuit such that the needle of the Indicator Meter deflected a desired amount; the new position of the ink pen was recorded. The displacement of the ink pen from its original position was then measured from the strip chart and compared with the "dialed in" pressure obtained from the Pressure Readout dials. 35 The test pressure port of the Baratron sensing head was connected directly to the pitot probe being used, while the reference port was vented to atmospheric pressure. In this manner the Baratron made a direct reading of the dynamic head. Instead of opening the reference pressure port directly to the laboratory, it was connected to the quiescent air inside of a hollow cylinder. This cylinder was completely sealed from the laboratory except for a small hole in its side, and it prevented small pressure fluctuations, caused by stray air currents and other dis turbances in the laboratory, from affecting the value of the reference pressure. Before each pressure survey was begun, the Indi cator Meter was set to zero. Following the manufacturer's recommendation, this adjustment was done with the test pressure and the reference pressure ports connected directly to each other. The Baratron was found to be extremely stable, requiring only a single zero adjustment each day. As a precaution, however, the meter drift was checked three times during each coflow survey and at least once during each test within the helium jet. The zero was also checked at the conclusion of every test. To facili tate these checks, the valve system shown in Figure 15 was set up. With valves A and B closed, and valve C open, the two pressure ports of the sensing head were connected to each other. This configuration permitted an adjustment or check of the meter zero. With valves A and B open and C closed, the system was set to measure dynamic pressure. This valving arrangement allowed for a quick check of the meter drift without having to move the pitot probe or dis connect any lines. Coflow Pressure Measurements The pressure measurements of the coflowing air were made in the absence of any helium flow. The pitot probe used in these tests was a straight piece of thin-walled aluminum tubing, 12.7 cm in length and having an inside diameter of 5.55 mm. In order to mount this probe above the jet, two small holes, diametrically opposite to each other, were cut into the wall of the large cardboard drum surrounding the jet assembly. An aluminum rod, 107 cm in length and 1.27 cm in diameter, was supported in a horizon tal position across the drum by inserting one end through each of these openings. The pitot probe was then clamped to this rod. The axes of the probe were perpendicular to the axis of the rod and parallel to that of the jet. The tip of the probe was 12.7 cm below the horizontal rod. The cathetometer was used to align the cylindrical pitot probe in the vertical direction. As was done when aligning the jet assembly, the probe was viewed from two different locations, each perpendicular to the other. The probe was viewed from an axis parallel to the Y direction 37 and from an axis parallel to that of the aluminum support rod. The probe was considered to be properly oriented when, from each viewing position, either of its outermost trace elements (as seen through the telescope) was tangent at every point to the vertical cross hair. Adjustments in the probe alignment in the X-Y plane were made by rotating the support rod, while corrections in the X-Z plane were accomplished by raising or lowering one end of this same rod. The set of coflow pressure measurements was made over a period of one week. Two complete pressure surveys were conducted with the pitot probe 5.08 cm above the forty mesh screen covering the surface of the coflowing jet. This distance equalled two hundred screen wire diameters and was chosen so as to allow time for disturbances in the air, created by the screen, to decay before measurements were made. One complete survey was also made further down stream at a distance of 17.8 cm from the screen. In addi tion, partial surveys at both stations were conducted. At the beginning of each test, the jet had to be positioned with respect to the stationary pitot probe. The positioning was accomplished by maneuvering the jet assembly until the tip of the probe just started to enter the helium orifice. This was possible since the outer diameter of the pitot probe was just a few thousandths of a centimeter smaller than the inner diameter of the orifice. The jet was then traversed in the -X direction, away from the probe, until the proper distance between the probe and the screen was achieved. In order to sample the pressure at different points within the secondary air stream, the jet was moved relative to the probe since, as noted above, the probe was stationary. Figure 16 shows the locations relative to the face of the jet at which measurements were made. These points form a grid pattern centered about the helium orifice; the distance between the centers of succes sive measurements was 1.27 cm. The pressure at a given location was sampled for a period of approximately one min ute with one minute of elapsed time between measurements. As noted, the flow of air through the jet was con trolled by the two pressure regulators on the air inlet line. The upstream regulator was always set at 1.73 x 10^ o dyne/cm while the downstream regulator was adjusted to 6 2 0.69 x 10 dyne/cm . During some of the tests, small 4 2 pressure fluctuations of approximately 6.9 x 10 dyne/cm were noticed at the upstream regulator. However, no per turbations ever occurred at the downstream regulator. Helium Orifice Pressure Measurements The pitot probe used to measure the pressure pro files in the mixing region of the turbulent jet is shown in Figure 17. This probe was constructed from 4.76 mm - O.D., thin-walled, stainless steel tubing, except for a 39 4.45 cm section near the tip. This latter section was also stainless steel, but its outer diameter was only 1.27 mm while its inside diameter was 0.888 mm. The probe was approximately L-shaped; the longer leg was 52 cm in length. The tip of the probe was 19.7 cm from the centerline of the long leg. Unlike the probe used in the coflow pressure sur vey, this second probe was not suspended above the jet from the horizontal support rod. The longer leg of this probe was passed through the wall of the cardboard drum and attached to the slave of a micrometer-driven, three-way positioner. This micropositioner was located atop an aluminum frame, as shown in Figure 3, with its three mutually perpendicular axes oriented in the X, Y and Z directions established earlier. The centerline of the longer side of the pitot probe was parallel to the - Z axis. The procedure used to align this probe in the vertical direction was the same as the one used to align the pitot probe employed in the coflow pressure tests. The first measurements made in the helium-air jet were at the helium orifice, i.e., at X/D — 0. These tests required that the location of the centerline of the jet be found, and that the pitot probe be placed along this line with its tip in the plane of the orifice. In order to do this, the jet was raised to almost its maximum height above the optical table. Then the micorpositioner was adjusted 40 until the tip of the probe entered the helium orifice. The position of the probe was further adjusted until it was possible to start with the probe just touching the wall of the nozzle; then the probe was traversed across the jet orifice in the Z direction, a distance of 3.81 nun before making contact with the wall again. This distance equalled the diameter of the helium orifice minus twice the probe diameter. By recording the micrometer reading when the probe was touching the wall and then adding (or subtracting) 1.91 mm, the probe could be placed at the centerline of the jet. A check on the centerline position, as found above, was made by moving the probe in the plus or minus Y direction a distance of 1.91 mm to see if the probe would contact the wall. Once the probe was placed at the center- line, it was no longer moved; relative motion between the jet and the probe was accomplished by moving the jet. The end of the pitot probe was set at X/D = 0 using a 0.175 mm thick, feeler gauge. With the gauge laid across the orifice, the jet was moved in the vertical direction until contact between the feeler gauge and the tip of the probe was made. The thickness of the gauge represented sixteen counts on the X direction traverse counter, and so, after removing the gauge the jet was raised by this number of counts. In the experiments reported herein, the value of the dynamic pressure head of the helium gas flow at the 41' center of the nozzle orifice and at X/D = 0 was always set to 0.1477 mm of mercury. Calculations have shown that at an absolute helium temperature of 288.8°K this value of the dynamic pressure head corresponds to a gas velocity of 15.24 meters per second. The MKS Baratron Electronic Pressure Meter was used to set this value of the pressure head in each of these tests. After the pitot probe was positioned as mentioned above, the Pressure Readout Dials on the Baratron were set to read 0.1477 mm of mercury. This adjustment of the dials unbalanced the AC bridge cir cuit in the pressure sensing head, which, in turn, caused a negative deflection of the Indicator Meter needle. This bridge circuit was then balanced by allowing helium to flow through the nozzle with a dynamic pressure head at the orifice of 0.1477 mm Hg. The flow of gas through the orifice, and hence the value of the dynamic pressure, was regulated by the micrometer-driven needle valve on the helium supply line. This valve was adjusted as necessary until the needle of the Indicator Meter showed a value of zero dynamic pressure head, i.e., until the bridge circuit was nulled. By returning the pressure dials to zero, the needle deflected positively and the ink pen of the recorder was displaced by an amount corresponding to the dynamic pressure. Measurements of the dynamic pressure at X/D = 0 were always started at the center of the orifice. Following 42 this initial measurement, the jet was traversed in the +Z direction a distance of 0.625 mm and then the next measure ment was made. This process was repeated again and again until the probe was at the wall of the nozzle. The jet was then returned to its original location, and the procedure repeated in the -Z direction. Upon conclusion of these tests, the orifice was surveyed along its diameter in the Y direction. The pressure was sampled at each point for a time period of between fifteen and twenty seconds with approximately a one minute time interval between measure ments. The orifice was surveyed five times in the space of one month. At the beginning of each test, the procedures for aligning the pitot probe in the vertical direction; for locating the center of the orifice; for setting the end of the probe at X/D = 0; and for adjusting the flow rate were repeated as previously described. The results of these tests are shown in Figures 18 and 19. Pressure Measurements at Downstream Stations Transverse pressure profiles in the turbulent mixing region of the jet were obtained at eight stations downstream of the helium orifice. This data was collected during two separate tests in which four stations were surveyed each time. In the first test, the stations were located 9.20, 12.20, 15.20 and 18.20 helium orifice diam eters from the orifice itself; whereas, in the second test, the stations corresponded to X/D's of 9, 12, 15, and 18. Each of these sets of pressure measurements was begun in the same manner as were the helium orifice pressure surveys. The centerline of the helium nozzle was located and the pitot probe placed colinear with it. The helium flow rate was then established with the end of the pitot probe at X/D s= o. Following these initial steps, the jet was tra versed in the -X direction until the desired distance between the orifice and the pitot probe was achieved. Rather than measure this distance with a scale or some other such device, the reading on the digital counter was simply increased at the rate of 1312 counts per centimeter of get travel by the appropriate number of counts. At each station the jet was extensively surveyed in the Y direction. Measurements were made at least every 2.54 mm on either side of the jet centerline until the probe was outside of the mixing region. The jet was always sampled in a semi random fashion. For example, if the first measurement was made along the +Y axis at a displacement (+ AY) of 1.02 cm from the centerline, then the second measurement would have been taken at an equal displacement of 1 . 0 2 cm along the -Y axis. The third and fourth samples might have been taken at - AY = 1.78 cm while the fifth and sixth at -&Y - 0.254 cm, etc. This form of sampling allowed for a very quick and graphic comparison between the signal levels of paired measurements; the symmetry of the profile about the 44 centerline could easily be seen. A given point within the jet was sampled for approximately thirty seconds. Pressure profiles determined from preliminary sur veys at several downstream stations were asymmetric with respect to the centerline position established with the pitot probe at X/D = 0. These profiles showed that the degree to which the profiles were not symmetric increased directly with the distance from the orifice, and that the point of maximum pressure in each profile occurred away from this centerline rather than on it. On the other hand, by assuming that the point of maximum pressure occurred on the axis of the jet and replotting the data accordingly, several of the profiles became very nearly symmetrical. It was concluded from these tests that the axis of the jet was not aligned in the vertical direction despite the alignment procedure described earlier. Calculations based on this preliminary data showed the angle of inclination in the X-Y plane to be slightly more than one degree. This amounts to the position of the centerline shifting laterally in the Y direction one pitot probe diameter (1.27 mm) with every seven orifice diameters the jet is moved away from the probe. Rather than attempt to correct the small angular deviation of the jet from the vertical, a method was developed for locating the centerline at each station, thereby accounting for the inclination. This procedure was 45 based upon the assumptions that the pressure distribution at a given station was symmetrical about the axis of the jet and that the point of maximum pressure occurred on the centerline. The first step in the procedure followed at each station was to locate the approximate position of the centerline. This was accomplished by traversing the jet, first along the Y axis and then along the Z axis, until in each case the recorded pressure data signal appeared to have reached a maximum value. The position of the jet at this approximate centerline was denoted by the readings on the verniers and scales of the Y and Z direction Unislides. The problem with using this technique to locate the exact position of the axis was that within one pitot probe diam~ eter of the true centerline, the pressure reached a magni tude of 95% or more of its peak value; consequently, a near centerline position was often indistinguishable from that of the true centerline upon a qualitative examination of the data signals, Figure 21. The exact position of the centerline was found by searching for symmetry in the pressure profile. Advantage was taken of the fact that near the half-peak amplitude (halfwidth) of each profile, the slope of the curve was very steep due to the rapid decay of the pressure head with distance from the centerline. A misjudgement of the true centerline location by even a very small amount resulted in a distinct asymmetry in the profile between two corresponding points (± a y or ±AZ) in the nearly linear regions* of the curve. For example, consider the pressure profile at X/D = 15.20 shown in Figure 21. This profile is symmetrical about the line, Y — 0.0 cm, or the axis of the jet. On the other hand, suppose that initially the probe was placed along the +Y axis at Y = 0.254 mm or one- fifth of a probe diameter from the true centerline. Then at +Y sk 0.788 cm and -Y = 0.736 cm, two corresponding points with respect to the position of the probe, the measured relative pressure, P/P ^ , would be approximately 0.47 and 0.53 respectively. A distinct asymmetry exists; the -Y measurement is about 13% larger than the +Y measure ment. In order to find the axis of symmetry, the jet was traversed in the +Y direction in increments of 0.254 cm away from the approximate centerline until the value of the pressure head was between 40% and 50% of its previously recorded peak. The pressure signal at this point and the distance the jet was traversed were then recorded. Next, the jet was displaced along the -Y axis by the same amount as above, and the pressure signal was again recorded. If the two recorded signals were of equal magnitude, then the approximate centerline was, in fact, the true axis of the jet. On the other hand, if the magnitudes were dif ferent, a new position for the centerline was chosen based on the data just obtained and the symmetry test repeated. Once the centerline of the jet along the Y axis was found, 47 a symmetry check in the Z direction was begun. Finally, a check was also made to be sure that the jet was axisym- metric. The requirement for axisymmetry was that the mag nitude of the pressure signal at a given distance from the centerline along the Y axis equalled the magnitude of the signal at a corresponding point along the Z axis. In addition to the orifice pressure surveys and the transverse surveys at the eight downstream stations, a sur vey along the centerline of the jet was also made. Measurements were taken at fifteen stations between the orifice and X/D =• 18. The results of this test were com pared with the centerline pressures obtained during the transverse surveys and are shown in Figure 2 0. Concentration Measurements: Optical Alignment As previously explained, the optical system used when making concentration measurements consisted of a prism and the focusing, collecting and imaging lenses, L^, L2, and Lg, respectively. The support systems for these optical components can be seen in Figures 3, 5, and 6 . The focusing lens was held in position by a lens holder attached to a two-way, mechanical microscope stage. This stage and hence the lens was, in turn, fixed to the same aluminum rod as had been the pitot probe used to measure the pressure of the coflowing air stream. In this case, the aluminum rod was not positioned across a diameter of a 48 horizontal section of the drum as before, but rather along a chord of the section. Again, the rod was parallel to the Z axis. The rod was clamped to the framework supporting the three-way micropositioner in order to prevent it from moving. The lens could be traversed by the stage for positioning purposes in the vertical direction and along the axis of the laser beam. The lens L2 was attached to the micropositioner by the aluminum bar and lens holder shown in Figure 3. This arrangement allowed the lens to be inside of the drum, while its position was controlled from the outside. The lens L3 and the prism were mounted on an optical railing which was located on the table in front of the monochrom ator. The railing was placed lengthwise and parallel to the Z direction between the jet and the monochromator. Alignment of the optical system was accomplished with the aid of a small helium-neon laser. This second laser was mounted on a camera tripod and positioned at the opposite end of the optical table from the monochromator. The tripod was adjusted so that the laser beam would be parallel to the floor, pass directly above and along the optical bench, and be incident upon the center of the entrance slit to the spectrometer. By design, the beam then also passed diametrically across the cardboard drum. During this laser adjustment procedure, all of the lenses and the prism were removed from the path of the beam. 49 The imaging lens was the first component to be positioned. This lens was placed on the optical railing 300 mm from the entrance slit. The plane of this lens was perpendicular to the direction of propagation of the helium-neon laser beam, but parallel to the plane of the entrance slit of the monochromator. The height of this lens above the optical table was adjusted so that the laser beam passed through its center. Next, the dove prism was attached to the optical railing. It was positioned so that the laser beam entered at the center of its front face and exited at the center of its rear surface. In order to properly locate the lenses and L2, both the helium-neon laser beam and the argon-ion laser beam were necessary. The requirements for positioning the collecting lens were the same as for the lens L3 except, in the present case, the lens was placed 50 mm from the argon-ion laser beam. The lens was adjusted so that it would be perpendicular to the argon-ion beam with the beam passing through its midpoint. Using the mechanical microscope stage, the focusing lens was traversed in the Y direction until the distance between this lens and the center of the helium-neon beam equalled the focal length of the lens. At this point, the necessary fine adjustments to the optical alignment were made. The first step was to focus the collected radiation on the entrance slit of the 50 monochromator. This was done by traversing the collecting lens in the Y and Z directions until the photomultiplier tube output, as registered on the picoammeter, was maxi mized. However, this often proved to be rather tedious. A simpler method was to begin by allowing liquid nitrogen vapors to pass through the scattering region. The resul ting scattered light from water condensed from the air was of sufficient intensity so that the image of the sampling region could be seen superimposed on the entrance slit. Slight adjustments in the position of the lens L2 resulted in the image being properly focused on the monochromator inlet. The second step was to move the dove prism along the optical railing until all of the light collected by the lens L2 was incident upon the dove prism. This was done in order to reduce the amount of collected light that was lost in the optical system. Here again, in order to see the collected light, liquid nitrogen vapor was passed through the focal point of the lens L^. Helium density profiles were obtained at four stations in the helium-air turbulent jet. These stations were located 9, 11, 14 and 18 orifice diameters downstream of the nozzle. At the conclusion of the optical alignment procedure, the jet was moved in the -X direction until the distance between the orifice and the scattering region equalled one of the above number of orifice diameters. This distance was accurately measured using a six-inch 51 steel scale and a piece of masking tape. The scale, which was divided into one hundred divisions per inch, was epoxyed into a slot cut into the end of a cylindrical aluminum plug. This plug was 6.22 mm in diameter by 1.27 cm in length. Since the width of the scale was greater than that of the helium orifice, the end of the scale rested on the lip of the nozzle when the plug was inserted into the latter. The piece of masking tape was placed on the scale such that one of its edges was the prescribed dis tance (number of orifice diameters) from the end of the scale. With the plug inserted into the orifice, the jet was moved to place the masking tape at the focal point of the lens L.^ and then it was traversed vertically away from the beam. As the tape passed in front of the beam, an extremely thin line was burned into it. The vertical motion of the jet was stopped when this line reached the end of the tape. Tests in which the jet was repeatedly positioned at X/D = 9 showed that the reading of the mechanical counter on the X direction traverse varied by only an average of plus or minus 30 counts from the nominal reading at this jet location; the maximum counter deviation was 70 counts. Since an X/D ss g corresponds to the jet being 5.72 cm or 7500 counts upstream of the scattering point, an average deviation of * 30 counts represents an average uncertainty of - 0.023 cm in the position of the jet. Raman Spectrum of Air A Stokes-shifted rotational Raman spectrum of air was taken just prior to the beginn5,ng of, and at the con clusion of, each helium concentration test. Figure 11 is an example of one of these spectra. The main purpose of the initial test taken each day was to check the alignment of the optical system. This check consisted of making sure that the signal to noise ratio between the peak of the Jt=4, oxygen, and J = 6 , nitrogen, lines and the noise level was at least five to one. If the signal to noise ratio was less than this, an optical realignment was made. This piece of data was also used to determine whether or not the indi vidual lines of the spectrum were being fully resolved. Because of the spectrometer used for these tests, a small amount of stray light was always contributing to the recorded data signal. The effect of the stray light mani fested itself as a displacement of the entire Raman spectrum in the positive direction along the intensity axis (ordinate) of the strip chart recording. Unless the indi vidual lines of the Raman spectrum could be completely resolved, it was impossible to determine the effect of this unwanted light upon the magnitude of the various peaks. In a fully resolved Raman spectrum, the stray light signal corresponded to the distance between the recorded PMT dark current signal level and a line connecting the valleys between the Raman peaks. In this connection, the final 53 Raman air spectrum obtained each day was used as a second piece of data from which to determine the noise signal, Ijj. The argon-ion laser was turned on at least forty minutes before measuring the first Raman spectrum of air. This was done in order to stabilize the power output of the laser by allowing it to reach thermal equilibrium. The power output of the laser was always set to 250 mw and measured by passing the beam through a calibrated, 2 0% transmitting, neutral density filter and then allowing it to be incident upon the sensing head of a Spectra-Physics, Model 4018, Power Meter. This laser output was also con tinuously monitored during each scattering experiment. A beam splitter was used to reflect a small fraction (about 2%) of the incident light into the sensing head of the power meter as illustrated in Figure 9. For convenience, the voltage output of the power meter, corresponding to its meter reading, was fed to a digital voltmeter and displayed digitally. This voltage output was recorded manually on the strip chart beside each piece of data to be able to normalize the latter to the initial laser power. If and when the power output changed by more than three percent, the laser was readjusted to again provide the initial 250 mw. The Raman spectrum of air was always taken at a point within the coflowing air stream. Generally, the entire rotational Stokes spectrum was not obtained; only 54 that portion of it near the combined peak, mentioned earlier, was recorded. Usually the first peak on the recording corresponded to the J = 1 oxygen line, while the last recorded peak was either the J = 5 oxygen or the J = 8 nitrogen line, Figure 11. The spectrometer scanning rate was two angstroms per minute in all of these tests. Helium Concentration Measurements Helium concentration measurements were begun almost immediately upon completion of a satisfactory Raman spectrum. The only two things that remained to do at this point before starting the helium surveys were, first, to set the spectrometer to pass the proper wavelength of light, and second, to establish the helium flow rate from the orifice. Using the Raman spectrum of air as a guide, the wavelength drive of the monochromator was manually set to within two angstroms of the wavelength at which the maxi mum of the combined peak occurred. The spectro meter was then scanned at the rate of one angstrom per minute until the ink pen of the recorder indicated that the maximum of the above peak was reached. At this point, the scanning drive of the spectrometer was turned off. The helium flow rate was set by establishing a dynamic pressure head of 0.1477 mm Hg at the orifice. The procedure for doing this was the same as the one described in the section on helium orifice pressure measurements. For these tests, 55 the pitot probe was clamped to a vertical aluminum rod mounted on an optical bench outside of the cardboard drum. By moving the optical rail foot that held the rod along the bench the pitot probe could be inserted through a thin vertical slot cut into the wall of the drum and positioned above the jet. The tip of the probe was always placed less than one orifice diameter above the exit plane of the nozzle and approximately at its center. This probe was removed from the drum after setting the dynamic pressure head. The method used to find the centerline of the jet and to obtain the concentration data was almost exactly the same as the technique employed to measure the transverse pressure profile signals. The approximate centerline was determined by finding the position of the jet at which the minimum Raman signal was recorded. This minimum signal represented the fact that the largest concentration of helium (smallest concentrations of 0 2 and N2) occurred along the axis of the jet. Again, as before, the symmetry property of each profile was used to locate the exact posi tion of the centerline. Axisymmetry was checked by com paring the Raman signal obtained at the halfwidth of the jet along the Y axis with the corresponding signal from along the Z axis. Except for one difference, each station was exten sively surveyed in the i Y direction using the paired, random sampling technique described earlier. The only difference was that after each pair of measurements in the jet, a reference measurement was made in the coflowing air stream outside of the turbulent mixing zone. These samp lings in the secondary stream were used to detect what might be described as an optical alignment drift of the system and they were used to normalize each piece of data to the maximum scattering signal. The optical alignment drift was probably the result of either minute vibrations of the focusing and collecting lenses due to the secondary air flowing past them or accidental and unnoticed bumpings of the optical table when changing the position of the jet between measurements or both. From time to time it was necessary to refocus the image of the scattering region on the entrance slit of the monochromator. This adjustment was made by moving the collecting lens until the reference signal from the coflowing air was returned to its initial value, i.e., maximized. As noted, the jet was surveyed at 9, 11, 14 and 18 orifice diameters downstream of the nozzle. The station at X/D = 11 was surveyed twice while the stations at X/D = 9 and 14 were monitored three times each and the remaining station at X/D = 18 was surveyed four times. Out of the twelve tests that were conducted, six were run individually. That is, the tests were made on six different days. Two of the tests, one at X/D = 11 and the other at X/D =■ 14, were made consecutively on the same day without any interruption 57 between them. And finally, to conclude these experiments, four surveys, one at each station, were made during the same test run. Measurements were made at least every 2.54 mm on either side of the centerline and they were extended until the scattering volume was outside of the jet. In each test, the position corresponding to the axis of the jet was sampled at least three times. In addition, one or more repeat measurements were made at 45% of the total number of points sampled. Points within the jet were surveyed for an average time period of two and one-half minutes each. Periodically throughout each data run, the tempera tures of the coflowing air stream, the helium gas, and the air in the laboratory were recorded. The measured dif ference between any two of these readings was never more than 256.5° K. Also, at the conclusion of each survey the dynamic pressure head at the nozzle orifice was checked in order to be sure that no changes in the orifice velocity had occurred. Procedure for Estimating the Experimental Error in the Quantity According to Doebelin (30), the absolute error, Ej^, in any quantity, X » which depends upon the measured values of the variables P 1 » ^ 2 > P 3. . .and is related to them by X = f( p 2, p 3« . .), can be computed from: 58 9 f 9^1 9 f Now the quantity He ^H€ 9^3 ~ 3 (Equation 7) can be related to the measured parameters I ,, I , and I through the equation cl^ J. cl j JL cl j O O ? He = (^,1 - IN) - ^a.oo - IN) _ Ia,l - Ia,c ^ ^a,!^ " IN^ ~ ^a,oo N Ia>1<t~ Ia» f He CO OO (Equation 8 ) hence: P He / P He i A Xa.l i , - i a.,.l a, co , *i I - I a, x a, oo i "a,®* a’H I , - I ■ ia I ____ -.a .l - - - - o A 1 (i _ - i 7 ' *s 1 Jfc a /V-k / a,oo As in Equation 4, I I . ^ 7 a,l* a,l| a,co a,l<£ a,<t> (Equation 9) and I_ represent the locally measured Raman signal at any point in the jet, along the jet centerline or in the coflowing air surrounding the jet, respectively. These values can be expressed in any convenient units such as amperes, number of photons per second or even in terms of the length of a trace on recording paper. In order to numerically evaluate Equation 9, the values of AI , , A I . and AI ^ must be computed. olji & y JL vL a ^ w The first step in obtaining these quantities is to calculate the number of photons per unit time that are incident on the PMT photocathode and which correspond to the values of 59 I , « 1 , and I . If I is the photomultiplier tube a,I7 a,l(g. a, co r c output in amperes, then the number of these photons per second is: N= Qfe = 0-555-T I X 1013 (Equation 10) where: T = total integration time of the signal I (seconds) -19 q ss charge on one electron = 1.6 X 10 coulombs QE — quantum efficiency of photocathods s 0.15 electrons photon G r: gain of photomultiplier tube = 7.5 X 106 For a typical integration time of 120 seconds and a PMT output of 5 X 10“ ^ amperes, N equals 333 photons per second. Next, if Poisson statistics are assumed for the rate at which photons impinge on the photocathode then an approximate value for AI is given by: ± A I i-vfiT I N (Equation 11) The absolute error E p^e// p^e as computed from these equations is shown by the error bars in Figures 25 through 28. As can be seen, the estimates of the absolute error correspond well with the scatter in the data. CHAPTER V RESULTS Helium Orifice Pressure Measurements Figures 18 and 19 show the results of the helium orifice dynamic head pressure measurements in terms of the corresponding velocity profiles at X/D = 0. The data points in these figures have been computed from the equation for o dynamic pressure: P= h ^HeVj • In both figures, the data obtained at the center of the jet exit plane and at probe displacements of - 0.0635 cm and - 0.127 cm indicate a flat profile with an average velocity of 15.24 meters/sec. The scatter in the data within this region is i 1 .0% of the average velocity and indicates the repeatability with which the same helium mass flow rate from the orifice can be established in successive tests. The data obtained at probe positions further from the jet axis than those men tioned above indicate that at least part of the pitot probe was within the wall boundary layer. This is evidenced by the fact that the velocity at these probe positions is less than 15.24 meters / second. Since the velocity gradient 60 61 (total pressure gradient) within the boundary layer is large, the average value of the total pressure that is measured is very sensitive to the position and size of the probe within this region. Hence, the increase in the scatter above I1 1 .0% of the average velocity among these latter data points is most likely the result of errors in probe placement and size. The average value of the orifice helium velocity as determined from these profiles is 14.1 meters/sec. . Transverse Pressure Measurements The results of the transverse, dynamic head pressure measurements which were made at eight stations downstream of the helium orifice are shown in Figure 24. At each station the measurements were normalized with respect to the value of the corresponding centerline pressure and Y plotted versus the nondimensional coordxnate, . As can be seen when plotted in this manner, the data collapse to a similar profile which is symmetrical about the jet center- line: Y = 0.0. The line which has been drawn through the data points in the figure represents the results of a least squares polynomial curve fit to the data. The least squares curve fits used in this paper were done by a computer. Polynomials of ever-increasing order were applied successively to each set of data until the minimum standard deviation of the data about the curve 62 fit was achieved. Whereas the pressure measurements shown in Figure 24 are best fit by a ninth order polynomial, the density data was generally fit with a sixth or seventh order polynomial. In order to determine the virtual origin, X0, the pressure data were grouped into four sets. The data taken at X/D = 9 and at X/D =9.2 formed one of the sets, the data at X/D = 12 and 12.2 another, etc. Each set of data points was then curve fit with the use of a least squares approximation. From these curves, the halfwidth of each pressure profile was determined and plotted versus X, the corresponding average distance1 from the orifice at which the profile was obtained. Figure 22 shows that all four halfwidth points lie on a straight line which has an inter cept along the X axis (ordinate) at -3.18.cm. This inter cept is five orifice diameters from the exit plane of the jet and corresponds to the virtual origin for the pressure profiles. At the same time as the above procedure was applied to the pressure data, the same thing was being done with the density data. Figure 22 shows that the halfwidth points of the density profiles at X/D = 9, 11 and 14 all lie along a straight line which also intercepts the X axis 1The average distances from the orifice correspond to X/D =s 9.1, 12.1, 15.1 and 18.1 and equal 5.34 cm, 6.51 cm, 8.25 cm, and 10.6 cm, respectively. 63 at -3.18. cm. The point denoting the halfwidth at X/D — 18 does not fall on this line, indicating that the jet is no longer spreading linearly at this station. Figure 23 shows some of the results of the least squares curve fits to the pressure data in which the virtual origin was assumed to equal -3.18 cm. This figure shows that the curves representing the pressure data at X/D = 12, 15 and 18 nearly collapse to a single curve except for values of P/P^ less than 0.35; the curve representing X/D = 9 departs slightly from the rest. This latter curve, however, is within two standard deviations of the data scatter about the curves at the other stations up to a point where P/P^_ = 0.35. The fact that the maximum value of the dynamic pressure ratio is shown to be less than one (1.0) in this figure is the result of the least squares curve fit. The axial decay of the centerline dynamic pressure is shown in Figure 20. From this figure the length of the potential core within the jet has been determined as 4.3 orifice diameters. This was obtained using the criterion that the length of the potential core equals the distance from the orifice to the point where the velocity in the jet equals 0.99 or equivalent to the point where the pres sure equals 0.98 porifice* A length of 4.3 orifice diam eters for the potential core is consistent with the findings of other investigators (4, 6). However, an 64 exact comparison is difficult since the length of the potential core depends upon the jet velocity, the velocity of the coflowing stream, the density ratio between the jet and the external fluid, and the initial boundary layer on the wall of the nozzle at X/D = 0. Results of the Density Measurements The results of the helium density measurements are shown in Figures 25 through 28. As was done with the trans verse pressure data, the density data have also been nor malized with respect to the value of the corresponding centerline density and plotted versus the nondimensional coordinate, Y/(x - XQ). As mentioned earlier, the curves which have been faired through the data points represent the results of least squares curve fits. As can be seen, with the exception of the data at X/D = 11, the least squares curve fits yield profiles which are nearly symmet rical about the jet centerline. The vertical error bars shown in these figures give the results of calculations of the most probable error as described on pages 57 - 59. These error bars show that the scatter in the data is pre dictable. It must be noted that a predictable scatter in the data occurred at the density ratio P He = 1 .0 , however, this scatter is not shown in these figures due to the normalization procedure. 65 Figure 29 is a similarity profile showing the data at X/D =9, 11 and 14. This figure does not include the density data taken at X/D = 18 since the profile at this station has been found not to be similar. Figure 30 shows the least squares curves (positive values of Y only) for the density data at each station. The curves representing the best fit to the data at X/D = 9, 11 and 14 tend to follow a single line whereas the curve at X/D = 18 substan tially departs from the others. In terms of standard deviations about a least squares curve fit to the combined data of stations 9, 11 and 14, the curve at X/D = 18 varies by two standard deviations at its halfwidth and by three standard deviations at a value of ^He/ ^He^ = 0.368. Velocity Profiles The velocity profiles in the turbulent jet are shown in Figure 32. The points shown in this figure are based upon the least squares curve fit values to the pres sure and density data at each station and have been computed from the equation for dynamic pressure. The computed veloc ity curves at X/D = 9, 11, and 14 form a similarity profile, consistent with the fact that the corresponding pressure and density profiles also form similar profiles, respecti\«Qy. The nondimensional velocities at X/D — 18 follow the trend of the density data at this station and show a departure from similarity. In terms of a least squares curve fit to the data at X/D =9, 11 and 14, the velocities at X/D = 18 show departures from similarity which equal two standard deviations at Y/(X - XQ)= 0.44 and three standard deviations at Y/(X - X q ) = 1.33. It is interesting to note that based upon the empirical data, similarity in the velocity profile seems to require similarity in both the pressure and density profiles, respectively. Figure 31 shows the decay in the centerline velocity between X/D = 9 and X/D = 18 along with the axial decay in density. In the region of the jet where both mass and momentum are spreading linearly, the ratio of the density profile halfwidth to the velocity profile halfwidth equals 1.11. This result is consistent with that obtained by the investigators in references 1 - 5 who have also found that mass (temperature) spreads more rapidly than momentum in subsonic inhomogeneous (non-isothermal) jets. In particular, Peters, Chriss and Paulk ( 4) find that in the coaxial free mixing of hydrogen and air the ratio of the concentration profile halfwidth to the velocity profile halfwidth equals 1.13; Corrsin and Uberoi find the ratio between the halfwidths of the temperature and velocity profiles for their high temperature jet to equal 1.29 and for their low temperature jet to equal 1.19. 67 Specie Continuity and Momentum Balance As a check on the accuracy with which the density profiles have been measured utilizing the laser induced Raman scattering technique, the mass flow rate of helium was computed at each station and compared with the flow rate from the orifice. The helium specie continuity equation is: (°° P .V D 2 \ PHeVydy r — 2. -- (Equation 12) o The left hand side of this equation was determined by graphical integration while the right side was computed numerically. The rt ults of the specie continuity check are shown in Table 1. TABLE I Results of Helium Mass Balance X/D ^ eHeVydy Pu .V.D.^ rH. eJ. J . . ? . . . 8 % Difference 9 1.225 X lO-2 gm sec 1.185 X 10"2 gm sec 3.4% 11 1.121 X 10“2 gm sec 1.185 X 10“2 sec - 5.4% 14 1.123 X 10"2 2SL sec 1.185 X 10”2 gm sec - 5.1% 18 1.077 X 10"2 gm s'etr 1.185 X 10“2 gm s'etr 9.1% This table shows that the mass flow rates at X/D = 9, 11, and 14 were measured to within ± 5.4% of the orifice value. This is gratifying since it gives one confidence in the 68 Raman scattering technique. The mass flow rate at X/D = 18 was found to be approximately 10% smaller than that of the orifice. This is not surprising, however, because of the small signal to noise ratio at this station, the maximum of which was 2.5:1.0. Indeed, the result of having a poor signal to noise ratio at X/D = 18 might be the departure of the density profile from similarity. A second check on the accuracy of the measurements was performed by doing a momentum balance at each station. The momentum equation as given by Keagy and Weller (3) is: f00 ( K f 00 P .D2 .V .(V . - V ) ) ev(v-vo)ydy - g J j (po -e)ydydx+ ^ --2-Z-J---- 2_ o o o (Equation 13) The integrals in this equation were graphically integrated while the last term was computed numerically. The double integral on the right hand side repre sents the effect of buoyancy and its magnitude at any station was evaluated with the aid of an approximation. Between the axial positions of X/D = 0 and X/D — 9 a. linear iCO increase (from zero) in the value of J ( p0 -p)ydy was o assumed since no density measurements were made in this region. The buoyancy force at X/D s: 9 was found to equal I.0% of the momentum force at the orifice and at stations II, 14 and 18 it equalled 3%, 6.5% and 9.1% of the orifice value, respectively. Upon considering the magnitude of each buoyancy term and the accuracy with which it could be 69 determined, it was assumed to be negligible at each station. Table 2, which is shown below, gives a comparison between the momentum force at the orifice and the force due to the momentum flux at the stations of interest. TABLE 2 Results of Momentum Balance X/D A: J°°e V(V-V0)ydy o B: eHeiDiVj(Vr Vo) 8 (A-B) B X 100 9 16.08 16.24 dyne - 1.0% 11 13.25 16.24 dyne -17.5% 14 12.23 16.24 dyne -25 % 18 ........ 1Q,. .9 6._..... .... 16.24 ..dyne. .. _______r3£L As can be seen, a very good balance is obtained at X/D = 9 where the percentage difference between the two terms is approximately 1.0%. However, as is also evident, the momentum balance is not nearly as good at the other stations. Undoubtedly, the very poor balance at X/D = 18 is again due, in part, to the low signal to noise ratio in the density measurements. In view of the satisfactory results of the helium continuity check, it is suspected that the largest source of error in the momentum balance is in the total pressure (i.e., velocity) measurements. The centerline and near centerline pressure measurements are probably well known; the signal to noise ratios are large enough for accurate measurements. The error, then, appears to be in the measurements in the "tail" (P/Pq. < 0.3) of the pressure profile; Figure 24 shows a large scatter among the data points along this portion of the curve. Additionally, this same figure shows that pressure measurements should have been taken at larger values of * V( X - XQ) in order to define more accurately this low signal region and the jet (pressure) width. As a means of determining the effect of the pres sure measurements upon the momentum balance, one standard deviation of pressure (as determined by the least squares curve fit) was added to all values of the pressure less than P/P<£ < 0.3. This addition to the pressure values increased the calculated velocity at corresponding points in the jet, extended the velocity profile to a larger lateral dimension, and increased the force due to the momentum flux at each station. Table 3 shows the effect of this pressure increase upon both the momentum and helium specie continuity integrals. The numbers in the column labeled %MOM (%CONT) represent the value of the momentum (continuity) integral minus the orifice value, the quantity divided by the latter and multiplied by 100 (see Table 2). 71 TABLE 3 Results of Increasing Total Pressure Upon Momentum and Mass Balances X/D %MOM %CONT 9 8 8.9 11 -10 -0.4 14 -15 -1.1 Whereas the momentum balance at X/D — 9 has become worse when compared with the results shown in Table 2, the balances at X/D = 11 and 14 have improved. These calcu lations strongly suggest that the error in the momentum balance is due to inadequate information in the outer edge of the jet. CHAPTER VI CONCLUSIONS The laser induced Raman scattering technique (when used as described in this paper and applied to free, turbu lent air-helium jets) is suitable for studying the mean concentration (density) distribution within these flows. This conclusion is based upon several facts: First, a helium mass balance was obtained at each station using the empirical data; second, the measured density profiles were found to be broader than the measured velocity profiles by an amount consistent with the findings of other investi gators; and finally, similarity profiles in both density and velocity were obtained. The results of these experiments confirm the con clusions of Widhopf and Lederman (19) as to the capacity of the technique to measure the concentration of a particular specie in a gas mixture, to measure local values of concen tration without the influence of disturbing probes, and to make measurements not affected by the presence of dust particles in the gas. In addition, these experiments show 72 73 conclusively that the technique can be applied to flowing gas problems in order to make meaningful concentration measurements. It is to be expected that the technique can be extended to measure concentration fluctuations. Appendix I shows the steps for computing the necessary laser power to make such measurements. In particular, the calculations shown are applicable to the experiments discussed in this dissertation and give an estimate of the laser power needed to investigate both the large scale and small scale turbu lent structure. These calculations show that the minimum laser power required in order to study the large scale tur bulent motion is 2.5 watts and that 50 watts is needed to investigate the small scale structure. 74 REFERENCES 1. W. Forstall, Jr. and A. H. Shapiro, "Momentum and Mass Transfer in Coaxial Jets," J. Appl. Mech. , 17_, 399- 408, (1950). 2. S. Corrsin and M. S. Uberoi, "Further Experiments on the Flow and Heat Transfer in a Heated Turbulent Air Jet," NACA TR 998, (1950). 3. W. R. Keagy and A. E. Weller, "A Study of Freely Expanding Inhomogeneous Jets," Heat Transfer and Fluid Mech. Inst., 89-99, (1949). 4. C. E. Peters, D. E. Chriss and R. A. Paulk, "Turbulent Transport Properties in Subsonic Coaxial Free Mixing Systems," AIAA 2nd Fluid and Plasma Dynamics Conference, June (1969). 5. L. G. Alexander, A. Kivnick, E. Coming and E. D. Henze, "Experimental Study of a Non-Isothermal Jet of Air Discharging into a Duct," AIChE J. , 1_, 55-61, March (1955). 6. P. T. Harsha, "Free Turbulent Mixing: A Critical Evaluation of Theory and Experiment," AEDC-TR-71-36, Feb. (1971). 7. J. Laufer, "Turbulent Shear Flows of Variable Density," AIAA Journal, 7_, 706-713, April (1969). 8. V. Zakky, E. Krause and S. D. L. Woo, "Turbulent Trans port Properties for Axisymmetric Hetrogeneous Mixing," AIAA Journal, 2, 1939-1947, Nov. (1964). 9. T. S. Zawacki and H. Weinstein, "Experimental Investi gation of Turbulence in the Mixing Region between Coaxial Streams," NASA CR-959, Feb. (1968). 10. S. Corrsin, "Extended Applications of the Hot-Wire Anemometer," NACA TN 1864, (1949). 11. I. H. Tombach, "Velocity Measurements with a New Probe in Inhomogeneous Turbulent Jets," Ph.D. thesis, California Institute of Technology, (1969). 12. H. W. Liepman and A. Roshko, Elements of Gas Dynamics, Wiley, 153-170, (1957). 75 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. N. F. Barnes, "Optical Techniques for Fluid Flow," J. SMPTE, 6_1, 487-511, Oct. (1953). P. B. Gooderum, G. P. Wood and M. J. Brevoot, "Investi gation with an Interferometer of the Turbulent Mixing of a Free Supersonic Jet," NACA Kept. 963, (1950). E. P. Muntz, "Measurement of Rotational Temperature, Vibrational Temperature, and Molecule Concentration in Non-Radiating Flow of Low-Density Nitrogen," UTIA Rept. No. 71, (1961). E. P. Muntz and D. J. Marsden, "Electron Excitation Applied to the Experimental Investigation of Rarefied Gas Flows," Rarefied Gas Dynamics, Ed. by J. A. Laurmann, 11, Academic (1963). E. T. Gerry and D. J. Rose, "Plasma Diagnostics by Thompson Scattering of a Laser Beam," J. Appl. Phys., 37. 2715-2724, June (1966). C. M. Sadowsky and J. E. H. Vanoverschelde, "The Measurement of Mass Density in a Turbulent Wake by Means of Rayleigh Scattering from a Laser Beam," Canadian Armament Research and Development Establish ment, TN 1764/67. G. F. Widhopf and S. Lederman, "Specie Concentration Measurements Utilizing Raman Scattering of a Laser Beam," PIBAL Report No. 69-46, Nov. (1969). A. Smekal, "Zur Quantentheorie der Dispersion," Die Naturwissenschaften, 1_1, 873, (1923). C. V. Raman, "A New Radiation," Indian J. Phys., 2, 387-898, March (1928). G. Herzberg, Infrared and Raman Spectra of Diatomic Molecules, D. Van Nostrand, New York, (1945). B. P. Stoicheff, "High Resolution Raman Spectroscopy," Advances in Spectroscopy, JL, Interscience, (1959). E. B. Wilson, Jr., J. C. Decius and P. C. Cross, Molecular Vibrations. McGraw-Hill, (1955). J. H. Hibben, The Raman Effect and Its Chemical Applications, Reinhold, (1939). 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 76 ! S. Bhagavantam, Scattering of Light and the Raman Effect, Chemical Publishing Co.,(1942). G. F. J. Garlick, "Luminescence," Handbuch Per Physik, XXVI, Light and Matter II, Springer-Verlag, (1958). S. P. S. Porto, "Angular Dependence and Depolarization Ratio of the Raman Effect," J. Opt. Soc. of Am., 56, 1585-1589, Nov. (1966). J. J. Barrett and N. I. Adams, III, "Laser-Excited Rotation-Vibration Raman Scattering in Ultra Small Gas Samples," (paper presented at the October, 1966, meeting of Optical Society of America). E. O. Doebelin, Measurement Systems; Application and Design, McGraw-Hill, (1966). J. G. Skinner and W. G. Nilsen, "Absolute Raman ^ Scattering Cross-Section Measurements of the 992 cm" Line of Benzene," J. Opt. Soc. Am., 58, 113-119, Jan. (1968). J. M. Kellam and M. M. Glick, "Gas Density Measurements in a Jet Using Raman Scattering," (to be published AIAA Journal, 1972). C. E. Shannon, "Communication in the Presence of Noise," Proc. I.R.E., 10-21, Jan. (1949). J. J. Stiffler, "Telecommunications," Space Communi cations V, NASA SP-69, 1-4, (1966). "Cary 82 Laser Raman Spectrophotometer," Cary Instru ments Bulletin 182, Aug. (1971). (a) (b) h l / 0 h* o+AE RAMAN STOKES RAYLEIGH RAMAN ANTI-STOKES FIGURE I THE RAMAN AND RAYLEIGH SCATTERING PROCESSES RAYLE10H (INCIDENT) LINE ~i - ioo cm"1 ROTATIONAL LINES — 1000 cm“! VIBRATIONAL BANDS FIGURE 2 SCHEMATIC DIAGRAM OF TYPICAL 0 OR N RAMAN SPECTRUM 2 2 79 FIGURE 3 OPTICAL SYSTEM 80 FIGURE 4 HELIUM-AIR JET AND TRAVERSING MECHANISM I FIGURE 5 TEST FACILITY EXCLUDING LASER FIGURE 6 HELIUM NOZZLE AND COFLOWING AIR CYLINDER 83 FIGURE 7 PERKIN-ELMER ARGON-ION LASER FIGURE 8 AIR FILTERING SYSTEM OPTICS TABLE ^BEAM SPLITTER ! r LASER fh POWER l —J METER OPTICAL BENCH COFLOW TUBE ELECTRIC VECTOR OF LASER BEAM X ® DRUM DOVE PRI8M MONO CHROMATOR P M T LIGHT TRAP / Z 3 PICOAMMETER VOLTAGE*-A INTEGRATOR FIGURE 9 SCHEMATIC DRAWING OF TEST FACILITY 85 ;>0 MIXING REGION LASER BEAM '//////// / / i n /111 n ) t n NT7 LIGHT TRAP COFLOWING AIR HELIUM ORIFICE COFLOW CYLINDER FIGURE 10 LASER BEAM PASSING THROUGH MIXING REGION 86 Og: J s4 N2 :J = 6 X FIGURE 1 1 STOKES-RAMAN SPECTRUM OF AIR 0 :J=I 00 iOOmtg S I AAAA- RECORDER FIGURE 12 VOLTAGE ATTENUATION AND INTEGRATOR CIRCUIT 00 00 89 40 mesh screen support & positioning rods (3 ) flow straight eners thermocouples /KXXXXXXXX)^ xxxxxxxxxx XXXXXXXXX supply j(^Q _ ^ ,„ to helium screen (40 mesh) precision needle valve to air supply FIGURE 1 3 HELIUM - AIR JET 90 100 - - sa- •a- EFFICIENCXt!^ K)% QUANTUM 8 0 - 2 0 lO- Il8'" b e - LINE EFFICII tC 4 1% QUAN 2- - ^.8 - I .6 - LINE QUANTUM 0. 1% > . 4 - 700 300 400 500 800 800 WAVELENGTH - NANOMETERS FIGURE 14 TYPICAL ABSOLUTE SPECTRAL RESPONSE OF S-20 PHOTOCATHODE BARATRON SENSING HEAD TEST L PRESSURE PORT REFERENCE PRESSURE PORT B TO PITOT PROBE TO CYLINDER FIGURE 15 VALVE SYSTEM FOR PRESSURE MEASUREMENT 16 PRESSURE SURVEY PATTERN C0FL0WIN6 AIR STREAM FIGURE 17 PITOT PROBE USED TO SURVEY HELIUM JET o 16 9 9 is 14 13 12 I I V (m/sec) io 9 8 7- 6 6 4 3 2 WALL - 0.3 - 0.2 - 0.1 o □ V o RUN#^ I RUN# 2 RUN# 3 RUN# 4 RUN# 5 94 $ § 0 Y(cm) o.i O o □ V///A 0.2 0.3 FIGURE 18 VELOCITY PROFILE AT X /D * 0 16 V 14 13 12 I I . 1 0 . V(m/sec) 9 8. 7. 6 5 4. 3. 2 I . WALL /////-\— - 0.3 - 0.2 - 0. 1 O RUN # I q RUN it 2 □ RUN n 3 V RUN 4 o RUN# 5 95 O o □ V 4-///// o Z(cm) o.i 0.2 0.3 FIGURE 19 VELOCITY PROFILE AT X/D=0 0 RUN # 1 - 5 O RUN # 1 —5 Q RUN # 6 0.9 - 0.8- 0 . 7 - 0.6 0 . 5 - 0.1- 0.0 0 I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 1 7 18 x/o FIGURE 20 AXIAL PRESSURE DECAY FIGURE 21 PRESSURE PROFILE AT X/D = 15.2 0.9 0.8 0 .7 0.6 0.5 0.4 0.3 0.2 0 . 1 Y (cm) vO 98 X(cm) 12 II-. 10-. 9- PRESBURE 8 - 7 6 - 5- 4 3 2-- ORIFiCE WALL Xcm 1 I I l Os\\\ - 1 . 2 5 - 1 .0 0-. 75- 5 0- -4 FIGURE 22 HALFWIDTHS OF PRESSURE AND DENSITY VERSUS X 99 A X/D = 9 X/D o X/D 1.0 X/D 0 . 9 - 0.8- 0.7 - 0.6- 0 .5 - 0 .4 - 0.2 - 0.1 - 0 . 1 0 0.15 0.20 0.05 0.0 Y X— Xo FIGURE 23 LEAST SQUARES FIT TO PRESSURE DATA FIGURE 24 TRANSVERSE PRESSURE PROFILE O X/D = 9 A X/D = 9.2 O X /D * 12 o X /D * 12.2 X X /D * 15 O X/D* 15.2 0 X/D* 18 (\ X/D* 18.2 0.15 0.20 100 FIGURE 25 DENSITY PROFILE AT Q X/D * 9 A 0 5 0 .3 - -0 .0 5 X-X o -0 .2 0 -0.15 V RUN # 15 — 1---------- 1---------- | -----0 ----b- 0.05 0.10 0.15 0.20 101 RUN 0.9- FIGURE 26 DENSITY PROFILE AT RUN # 24 0.8- 0.7 0.4 0.3- 0.2- 0.20 0 . 1 0 0.05 0.0 0.05 0 . 1 0 0.15 0.20 X-Xo 102 RUN 20 FIGURE27 DENSITY PROFILE 0.9 - AT X/D = 14 o RUN 25 0.8 0.7- 0.6 0.5- 0 .4 - 0.3- 0.2 - 0.1 - - 0.20 0 . 1 0 0.05 0.0 -0 .0 5 0,20 - 0 . 1 0 0.15 “0.15 Y X-Xo 103 FIGURE 28 DENSITY PROFILE AT X/D = 18 h RUN #17 6 RUN #18 A RUN #19 O RUN #26 0.20 104 X/D FIGURE 29 SIMILARITY X/D 0.9 - X/D 0.8- PROFILE 0.7 0.4 0.3 - 0.2 - 0 .1 0.15 0.20 0 . 1 0 0.0 0.05 -0 .0 5 -0.15 - 0 . 1 0 - 0.20 Y/(X-Xo) 105 106 A X/D = O X/D = 0.9 0.8 0.7 pHe 0.6 0.5 0.4- 0.3 0.2 o; 0.0 0.05 0 . 1 0 0.15 0.20 Y/(X— Xo) FIGURE 30 LEAST SQUARES CURVE FIT TO DENSITY DATA 9 h«./ P h« VELOCITY > X >C I 7 6 5 4 3 2 0 20 40 60 80 100 120 140 160 180 X-Xo FIGURE 3 1 CENTERLINE VELOCITY AND DENSITY DENSITY X = -5 D 107 ! X/D © X/D 0 .9 - X/D FIGURE 32 TRANSVERSE 0.8 - X/D VELOCITY 0.7 PROFILE V-Vb 0.6 - V^-Vo 0 .5 - o 0.4 - 0.3 - 0.2- o 0 . 1 - o o -0.15 - 0.20 -0 . 1 0 0.0 0.20 -0.05 0.05 0 . 1 0 0.15 Y/(X— Xo) 108 APPENDIX I CALCULATION OF LASER POWER NECESSARY FOR TIME RESOLVED MEASUREMENTS The laser power necessary in order to make time resolved measurements in the air helium jet used in these experiments can be calculated from (31): N1o^rR (Equation 14) The value of the effective Raman scattering cross section -30 2 will be taken as = 9.0 X 10 cm /steradian-molec as determined from the experiments of Kellam and Glick (32), and the length of the sample region will be assumed to be 0 . 1 cm, a value which is consistent with the scale of the turbulence and with hot wire technique. Furthermore, in order to obtain the most reasonable estimate of the required; laser power, it will be assumed that a Raman double spectrometer is available. An example of such an instru ment is the Spex Model 1401 Spectrometer which has an f/d . - 6 .8 . It will also be assumed for calculation mirror purposes that at any point within the jet, the ratio of the 109 110 number of N2 molecules to the number of 0 2 molecules is the same as in the composition of ordinary air; sufficient power to measure a minimum air density of 1 / 1 0 atmosphere •J Q Q (N = 2.7 X 10 molec/cm ) is necessary. The number of measurements per second that are needed to determine the turbulent structure in the jet depends upon the maximum frequency of the turbulent fluc tuations involved. As shown by Shannon and Stiffler (33, 34), the number of these measurements per second will equal twice this maximum frequency. The maximum frequency of the large scale turbulent motion can be estimated as: f^g = jet velocity/jet diameter — 50 1/50 = 2500 —i— sec and the maximum frequency of the small scale motion for low Reynolds numbers (< 50,000) as: fee = f.c x 20 = 5 X 104 —i— SS LS sec In high Reynolds number situations the maximum small scale frequency is approximately an order of magnitude larger 5 1 than that above, i.e., fQ- = 5 X 10 . Assumxng that oo sec the large scale motion is to be investigated, then 5,000 measurements per second will be necessary. If 1.0% accuracy in each measurement is desired, then based upon the statistics of the number of photons Ill incident upon the PMT, 10,000 photons per measurement are required. The error, in this case, is computed from — - j —- . 4 7 At 5,000 samples/sec and 10 photons/sample, 5 X 10 photons/sec need to be incident on the PMT per second. Assuming 30% transmittance of light through the optical system, which includes the collecting lens, spectrometer, etc., the number of photons per second, n , which need to be collected is n = 5 X 107/0.3 = 17 X 107 photons/sec The Raman power, PR, to be collected is PR = hl»Rn =2.04 X 10“12 watts a -J Equation 14 yields: P^ = 49.4 watts 50 watts The amount of power required can be reduced by a factor of approximately 20 if a multiple scattering technique is employed. Reference (35) shows a schematic drawing of one possible system which can be set up for the multiple scattering. The power required to investigate the larger scale turbulent motion when multiple scattering is used is 2.5 watts. From the above calculations it can be seen that the power needed to investigate the small scale motion for low Reynolds number is 50 watts and for large Reynolds number is 500 watts.

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Creator Glick, Morton Meyer (author)

Core Title Helium concentration measurements utilizing laser induced Raman scattering

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Philosophy

Degree Program Aerospace Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, aerospace,OAI-PMH Harvest

Language English

Advisor Muntz, Eric Phillip (committee chair), Kaplan, Robert E. (committee member), Laufer, John (committee member), Porto, Sergio P.S. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-768936

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