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SAMSO TR-69-13 VOLUME II
4 "l
FINAL REPORT
ADVANCED PENETRATION PROBLEMS
WAKE STRUCTURE MEASUREMENTS
A. Demetriades
Space and Re-entry Systems
Division of Philco-Ford Corporation
October 196P
Advanced Research Projects Agency
Department of Defense
Washington, D. C.
This document may be further distributed by any holder only with specifi approval of SAMSO (SMSD). .Itowtan ftPIh Oalifom^a tüü A^ a^cuUJ, A4 S> (v^/ Qocfa The distribution of this report is/limited because it contain« requiring strict approval of all disclosures by SAMSO.
is technology
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SAMSO TR-69-13 VOLUME II
FINAL REPORT
ADVANCED PENETRATION PROBLEMS
WAKE STRUCTURE MEASUREMENTS
A. Demetriades
Space and Re-entry Systems
Division of Philco-rord Corporation
Getober 1968
Advanced Research Projects Agency
Department of Defense
Washington, D. C.
This document may be further distributed by any holder onl^ with specific acrproval of SAMSO (SMSD), Nni lull TB i fill iriii i ' n iMÜ
The distriböltion of this report i^ limited because it contains technology requiring strict approval of all disclosures by SAMSO.
FOREWORD
This document describes work ptrformed at Philc-Ford under Tatk 2, "U'ake Structure Measurements" of Advanced Penetration Problems, ARPA Order K88, monitored by SAMSO under contract FOA701-b8-C-0032, in the period 15 October 19b7 to 15 October 1968. Certain subtasks of this work have, upon completion, been issued under separate cover as SAMSO technical reports for the purpose of documenting Lnformmtlon in detail beyond that required contractually in monthly, semiannual, >>r final reports. These technical reports, already supplied to the appropriate SAMSO and ARPA personnel according to the pertinent distribution channels, are for brevity referred to frequently in the present document. They are :
(1) "Turbulent Front Structure of an Ax isvmmetric Compressible Wake", Philc-Ford Publication Number UG-4259, SAMSO TR h8-44, 15 November l1'^?.
(2) "Mean Flow Measurements in a Self-Preserving Turbulent Plasma Jet" SAMSO TK 68-166, February 1968,
(J) "Turbulent Mean-Flow Measurements Ln a Two- Dimensimal Compressible U'ake", Philco-Ford Publication Number tIG»443l, SAMSO TK 68-369, October 1968.
This technical report ha.- been r.■viewed and is approved.
R. W. i'cidt ield, l.L. , I'SAF Advanced Penetration Problems Proiect Officer
i i
ABSTRACT
This report summarizes exper imt'nta 1 work done in the period 15 October 11'<J7
to 15 October 1968 on the structure ol compressible turbulent wake« and turbulent plasmas. Detailed point measurements in the two dimensional wake, made very tar Lrom the body, have fully confirmed the predictions of the Dynamic Equilibrium Hypothesis regarding the asymptotic value« of the velocity and temperature iluctuation and the statistics of the Inter- face. For fltght at angle of incidence radical changes in the wake «truc- ture have been observed, while heat transferred from the naodel to the llov was found to delay greatly the onset of ' »nsltion to turbulence, tn tin plasma jet transition zone th- remnants oi the Laminar fluid create a turbulent fluid of highly heterogeneous electron density with hitherto unexpected statistics. The longitudinal scales of the electrons are larger than those of the temperaiure hut numerically not nu. h Kfferen' from Low-speed turbulence scale.-.. The electron densit> Elfwtuatlons al.a ■ predominate ihe temperature fluctuations .-specially at tin- highei fre- quencies. Spectral decay obtain« a (-5/3) range for tin tamperature but this behavior L« n>it observed fof tin- electrons«
Page iv Intent ion.illy Left Blanl
CONTENTS
SECTION PAGE
I SITMMARY OF MAJOR ACCOMPLISHMENTS AND CONCLUSIONS
1.1 Objectives 1 1.2 Guide to the Present Report 1 1.3 Major Accomplishments and Conclusions 2 1.4 Present Status 5
II TURBULENCE MEASUREMENTS IN A TWO-DIMENSIONAL COMPRESSIBLE WAKE
2.1 Introduction 7 2.2 Flow Facility and Model 7 2.3 Instrumentation 8 2.4 General Features of the Wake Flow Field 9 2.5 Experimental Technique and Procedure 11 2.6 Results 23 2.7 Scaling Laws and Similarity 51 2.8 Conclusions 64
III INTERMITTENCY OF THE TWO-DIMENSIONAL COMPRESSIBLE WAKE
3.1 Purpose ... 65 3.2 Technique and Procedure 65 3.J Results 66
IV TURBULENCE BEHAVIOR OF THE PLASMA JET
4.1 Critique of Current Turbulent Plasma Research .... 71 4.2 Intermittency In the Plasma Jet 72 4.3 Electron Density Fluctuations 81 4.4 The Gas Temperature Fluctuations 103 4.5 Comparison of Electron and Temperature Fluctuations . 117
V SUPERSONIC WAKES AT ANGLES OF ATTACK
5.1 Introduction 123 5.2 Model and Facilities 123 5.3 Experiment Design 125 5.4 Diagnostic Instrumentation 129 5.5 Procedure 129 5.6 Results of Measurements 129
VI SUPERSONIC WAKE WITH HEAT TRANSFER
6.1 Introduction 135 6.2 Model and Facilities 135
CONTENTS (Continued)
SECTION
6.3 Adjustment of Operating Conditions. . 6.-4 Procedures and Instrumentation
VII PROJECT LOGISTICS
APPENDICES
A THE JEA-1I COMPUTER PROGRAM,
B THE SPECTR COMPUTER PROGRAM,
REFERENCES
»AGL
I 36
US
1 J9 7.1 Personnel
7.2 Development of Facilities,'instrunents'nnd Technique
7.3 Information Exchange. 149
131
137
163
vi
FIGURE
3
12
ILLUSTRATIONS
PAGL
1 Schematic of MB Experiment Geometrv Showing Coordinate Nomenclature. Measurements Were Made Within the Re.tan- ^ gular Parallelepiped Shown
2 Electronic Circuit Used for the WED TurbuUnce Measurements 17
Typical Profiles of Mean Hot-Wire Voltage Across iwo-Dimen- sional Wake at Constant Distance Behind the Bodv. For Eact Curve the Wire current is Constant
Ivpical Profiles of RMS Wire Output Across Two-Dimensional
Wake
i
20
Tvpical Wire Output Spectrum. Vertical Lines Mark Scale
ment, of the Complete
:pical wire uutput ape.num. r«»»*«— -■ Changes
Frequencv Response of Each Component, 01 the Lompieue Electronic Equipment ("Instrument Transfer Function ) and of the Entire Svstem ("Overall Transfer Function ). . . .
7 Variation of Measured Hot-Wire Time Constant With \>Aa\ ^ (Above) and Lateral (Below) Distance
8 Variation of Error Ratio J Along Wake Axis. Dashed Line Alterrate Smoothing (For 1 - 7..01) Which Would Elminate Observed Anomalies Beyond X-Statton 17
Lateral Variation of .1 For Constant X . . . . • •
Variation of J With Heating Current For Two Lateral Positions 3U 9
10
M Effect of Computer-Aided Response Restoration on the Modally Unresolved Turbulence Spectra (WED Experiment)
Consistency Check Within The WEB-I1 Program: Axial Variation 13
13 Consistency Chec. Within The UTb-Il Program: Lateral ^ ^
Variation
U Effect of Heating Current (At A Fixed Point In the Wake) On Various Sensitivity Coefficients of the Hot lure
t5 Variation of the Mass-Flux and Total-Tempera.ure Cross- Correlation Coetficient Along the Wake Axis
VI i
ILLUSTRATIONS (Continued)
FIGURE PACE
16 Variation of the Mass-Flux and Total-Temperature Cross- Correlation Coefficient In the Lateral Direction (Fixed X) 40
17 Typical Variation of the RMS Mass-Flux Fluctuation (Normalized With Its Local Mean) In the Lateral Direction 41
18 Ty Leal Variation of the RMS Total Temperature Fluctuation (Normalized With Its Local Mean) In the Lateral Direction 42
19 Variation of the Normalized Mass-Flux and Total Tempera- ture Fluctuations Along the Wake Axis 43
20 Variation of the Normalized Velocity and Density (Temperature) Fluctuations Along the Wake Axis 45
21 Typical Lateral Variation of the Normalized Velocity Fluctuation 46
22 Typical Lateral Variation of the Normalized Density Fluctuation 48
23 Evolution of the Hot-Wire Mean-Square Voltage Output Spectrum Along the Wjkc Axis 49
24 Typical Lateral Evolution of the Hot-Wire Mean-Square Voltage Output Spectrum 50
23 Lateral Variation of the Axial Velocity Fluctuations Normalized With the LOCPI Wake Velocity Deficit. Above: Seif-Preserving Fluctuations ^Far W-ike) . Below: Near (Relaxing) Wake 53
26 Lateral Variation of the Density Fluctuations Normalized With the Local Wake Density Deficit. Above: Self- Presorving Fluctuations (Far u'ake) . Below: Near (Re'axing) Wake 54
27 Axial Variation of the Axis Velocity and Density Fluctua- tions Scaled to the Local Wake Deficits 55
28 Axial Development of the Maximum (At Each X) of the Velocity and Density Fluctuations Scaled to the Local Wake Deficits 57
VI 11
ILLUSTRATIONS (Continued)
FIGURE PAGE
29 Axial Variation of the Ratio of the Density to the Velocity Fluctuations Compared to Predictions of the Dynamic Equilibrium Hypothesis 58
30 Lateral Variations of the VeK city-Temperature Cross- Correlation Coefficient 5^
31 Test of the Strong Reynolds Analogy Alon^ the Wake Axil . 60
32 Test of the Strong Reynolds Analogy in the Lateral Direction at Constant X 61
33 Velocity, Shear, and Velocity Fluctuation Trofiles (Above) Compared K'ith Similar Properties of Low-Speed Wakes ^Below) 62
34 Axial Variations of the Turbulent Front Position and Its Standard Deviation N'ormalized With the WED Transverse Scale 67
35 Distribution of Intermittency Factor in WED Compared With Low-Speed Results 68
36 Distribution of the Intermittency Factor About the Front Position, in Units of the Standard Deviation 69
37 Lateral Distribution of the Front Location Probability (Above). Below, Points Denote the Most Probable Front Location 70
38 Typical Radial Distributions of Mean Electron Density, Mean Gas Temperature and Intemittency Factor in the Jet. 74
39 Most Probable Turbulent Front Position in the Jet .... 75
40 Axial Variation of the Turbulent From Position and its Standard Deviation in the Jet, Normalized With the Transverse Scale 76
41 Radial Distribution of Crossing Frequencies and Intermittency Factor in the Jet 77
42 Axial Distribution of Maximum Crossini; Frequt'iuv in the Jet 79
43 Front Wavelength for Jets and Wakes Normalized With the „„ Transverse ??ale for Each Flow
IX
ILLUSTRATIONS (Continued)
FIGURE PAGE
44 Comparison of Three Theoretical Predictions of the Sheath Radius Rs in Terms of the Probe Radius Rp and Debye Distance H 83
45 Axial Variation of the RMS Electron Density Fluctuations, Normalized With the Local Electron Density, on the Jet Axis 8^
46 Radial Variation of RMS Electron Density Fluctuation Normalized With the Axis Value 85
47 Oscilloscopic Study of Temperature and Electron Density Fluctuations 87
48 Schematic of Typical Instantaneous Electron Density Distribution Along the Jet Axis as Inferred From Probe Measurements 88
49 Typical Radial Variation of Normalized RMS Electron Density Fluctuations Also Showing the Suspected Contri- bution of Intermittency 91
50 Block Diagram of the Jet Turbulence Electronics 93
51 Transfer Function of Vacuum Thermocouple Used to Convert the Spectral Density Signal Into Dc Voltage 94
52 Normalized Spectral Density of Electron Fluctuations Along the Jet Axis 95
53 Axial Variation of Electron Spectral Density For Eddies Half the i-lacroscale Size, Showing the Decreasing Importance of Such Eddies Far From the Nozzle 96
54 Normalized Spectral Density of Electron Fluctuations At 18 Inches From the Nozzle q7
55 Normalized Spectral Density of Electron Fluctuations At 22 Inches From the Nozzle 98
56 Normalized Spectral Density of Electron Fluctuations at 26 Inches From the Nozzle 99
57 Normalized Spectral Density of Electron Fluctuations at 30 Inches From the Nozzle 100
ILLUSTRATIONS (Continued)
FIGURE PAGE
58 Nommlized Spectral Density of Flectron Fluctuations at 34 Inches From the Nozzle 10*
59 Axial Variations of Longitudinal Integral Scale of Electron Density Fluctuations Given Dimensionally CAbove) and Normalized With the Transverse Scale ''Below) 104
60 Axial Variation of Velocity and Gas Temperature Fluctuations Normalized With Their Corresponding Axis 'Deficits"
61 Typical Radial Variations of Gas Temperature Properties: Mean Temperature, Temperature Intermittency, and Tempera- ture Fluctuations
105
106
62 Normalized Spectral Density of tiic Gas Temperature Fluctuations Along the JeL Axis 109
63 Normalized Spectral Density of the Temperature Fluctuations at 26 Indies From the Nozzle 1 1()
64 Normalized Spectral Density of the Temperature Fluctuations at 30 Inches Fron the Nozzle i11
65 Normalized Spectral Density of the Temperature Fluctuations at J-'* Indies From the Nozzle H*
66 Comparison of Type i Temperature Spectra With High-Reynolds* Number Uotropl« Velocity Spectra and the Kanian Inter- polation Spectrum 11A
hi Comparison of Type n Temperature Spectra With Typical Low-Reynolds-Number Velocity Spectrum 115
h8 Axial Variations of Longitudinal Integral Scales of the Temperature Fluctuations in Dimensional Form (Above) and As Non-Dimension; 1ized With the Transverse Scale (Below) 110
69 Axial Variation of the Ratio of Total Normalized Electron Density Fluctuation to the Total Normalized Gas Temperature Fluctuation ^°
70 Radial Variation of the Ratio of Total Normalized Electron Density Fluctuation to the Total Normalized Gas Temperature Fluctuation 119
\ i
FIGURE
78
79
80
81
82
83
84
85
86
ILLUSTRATIONS (Continued)
73 Experimental Arrangement for Angle-OL-Attack Studies Showing the Protractor in the Test Section
74 Nomenclature and Flow Field for Angle-Of-Attnck Expcri ments (WEF)
LOW
Static-Pressure-Probe Traces In the K'nkc at JO-Deerec Incidence
Two-Wire Correlation Probe For Work In the Supersonic Wind-Tunnel. ...
87 The Nuseit Computer Program,
tAGE
71 Relative Importance of Electron and Temperature Spectral Densities in the "Heterogeneous" Portion of the Jet (Abscissa in Arbitrary) 1 ;n
72 Relative Importance of Electron and Temperature Spectral Densities in the "Homogeneous" Portion of the Jet
121
24
126
Characteristics Solution of the Two-Dimensional Flc. Behind A Plate Inclined 20 Degrees to a Mach 3 Flow. . 127
76 Predicted Flow Properties at S«1-cted Distances Behind the Model at 20-Degree Incidence i>s
II Comparison of Predicted and Measured Pi tot-Tube "Profile" at 20-Degree Incidence . . 130
Comparison of Measured Pitot Proiiles (at Fixed X) for Different Incidence Anglos 1j1
1 J3
1 37 Effect of Body Heating on Transition Distance (WEG).
Total-Enthalpy Probe Shown Prior to Assembly [Ao
Comparison of "Small" and "Large" Hot-Wire Probes. . . 142
Heat Transfer Characteristics of Typical 0.00002-Inch Wire of Same Aspect Ratio as 0.00005-Inch Wire .... 143
•43 Two-Wire Correlation Probe For Work in the Plasma Tunnel
The Linfit Computer Program i^g
147
xii
ILLUSTRATIONS (Continued)
PACE FICURE
A-l Procedural Diagram of the JEA Program 152
A-2 The JEA Program
A-3 Typical Output of the JEA Program
B-l Procedural Diagram of the Spectr Program 158
B-2 The Spectr Program
B-3 Typical Output of the Spectr Program
153
155
159
16 i
Ml 1 Page xiv Intentionally Left Blanl
SECTION I
SUMMARY OF MAJOR ACCOMPLISHMENTS AND CONCLUSIONS
1.1 OBJECTIVES
The objectives of this work can be summarized as followt]
(1) The general objective is to predict the turbulence structure ot the wake behind a vehicle moving in the atmosphere at hypersonic speeds.
(2) The specific objectives are (a) to measure experimentally the neutral g«a dynnmic.)] features of turbulent compressible wakes such as the mean, intermittent, turbulent, and eddy magni- tude distributions of velocity, density, and temperature «nd to map the statistical features of these var ables, inch as correlati m and spectral functiont; (b) to assess the importance, on these turbulence features, of real 1 istic re- entry phenomena such as angle ol attack and heat and mass transfer; (c) to measure the corresponding features of turbulent plasmas with the aim of establishing functional relationships between gasdynamical and electronic phenomena such as electron density, and gas velocity and temperature; and (d) to unity these results into laws not contradicting other available experimental results and to extend these scaling laws for hypersonic wake predictions through the hasu flight parameters Such as drag and altitude.
1.2 GUIDE TO THE PRESENT REPORT
This report covers work toward the cited objectives perlormed from 15 October 1%7 to 15 October 1968, and discusses five major experiments at various stages of completion. in Section I, the status of these exper- iments is given in tabular lorm and major conclusions drawn from them are discussed as affecting hypersonic wake calculations.
Section II deals with turbulence measurements in a two-dimensional com- pressible wake without heat transfer or incidence effects (designated WED), and Section III with the intcrmittency properties of the same wake. The WED mean flow was measured in the 19bb-19b7 period, analyzed in the current period and reported in a separate SAMSO technical report (Reference 1). Since the latter report has been printed and distributed to SAMSO, Aerospace, and ARPA, it is referred to herein only in abstract form (Paragraph 1.3) tor brevity.
Section IV discusses the turbulence and intermittency measurements in the plasma jet experiment (designated JEA). The JEA mean flow, measured in
-1-
the 1966-1967 period, was also analyzed in the current period and a SAMSO technical report (Reference 2) to this effect has been distributed as above. It is abstracted in Paragraph 1.3.
Section V discusses the wake at angle of attack (designated WEF) and Section VI the wake with heat transfer (WEG), and finally. Section VII presents recent developments in techniques and facilities devoted to this work and accounts for other such "logistics" of the project.
1.3 MAJOR ACCOMPLISHMENTS AND CONCLUSIONS
In the current period, the WED mean flow has well substantiated the earlier conclusions (Reference 3) that the mean axial velocity and the ambient wake temperatures are a Gaussian function of the wake radius. The abstract of Reference 1 states: "Excellent correlation of the lateral (radial) dis- tribution of axial velocity is obtained when the lateral distance is divided by the transverse wake scale which is formed from the measured velocity defect. The latter is found to decay as the inverse squc^e root of distance for the entire range of about 1850 virtual model thicknesses mapped; the trans.erse scale thus increases as the square root ol distance. In the latter half of this range, the lateral distribution of static tem- perature also appears to correlate in the same lateral coordinate, and the temperature defect also decays as the inverse square root of distance. It is demonstrated that these results are accurately predictable from a basic similarity analysis beginning with Townsend's measured velocity decay on the axis; the turbulent Reynolds number of 13.0 agrees closely with Townsend's 12.5. The corresponding Prandtl number found lies in the range from 0.65 to 0,70." Implications of these statements are that the com- pressible wake is predictable, in the mean, on the oasis of the local (inviscid) wake conditions and independently of the body shape (onlv the drag matters). The turbulent Reynolds number is now well settled, and for the axisymmetrlc wake the Prandtl number is, of course, higher than 0,70 (it is Ü.83, according to Reference 3).
The expected pronerties of the turbulent front (boundary) have been abstracted in Reference 4: "Intermittency measurements have been performed within the first one hundred virtual diameters of an axisymmei.. ic com- pressible wake. The primary measurements, performed with the hot-wire anemometer, concerned the intermittency factor and the frequency of zero occurrences. The intermittent flow covered most of the wake profile but for a narrow region abont the axis, and was found to be normally distributed around the average front position. The latter, along with the extent of the front standard deviation, was found to agree numerically with expecta- tions based on low speed wakes and to grow as the 1/3 power of axial distance. A week periodicity of the front was detected at a wavelength about nine times greater than the longitudinal scale of turbulent velocity fluctuations. This periodicity affects the turbulent spectra." In the two-dimensional wake experiments done in the current period, these con- clusions were soundly reinforced (Section III) regardless of the character- istic growth (as the 1/2 power of distance) of the front scales for two-dimensional geometries.
-2-
Extremely important conclusions afiectin^ the hypersonic wake turbulence were drawn in the current period from the WED turbulence studies detailed in Section II. The Dynamic Equilibrium Hypothesis had already been demonstrated to apply during the axisymmetric wake experiments (designated U'EB) done in 1966-196 7 (see References 5 and 6), and ttie same conclusion is now drawn from Section III. Specifically:
(1) The Strong Reynolds Analogy holds (i.e., given the velocity fluctuations one can computr the density or temperature fluctuations).
(2) The mass-flux and total temperature fluctuations are uncorrelated; the velocity and temperature are almost everywhere perfectly anti-correlated.
(3) On the axis, the velocity fluctuations IMCOM
asymptotically 38 percent of the axis mean velocity; the temperature fluctuations become 45 percent of the temperature "deticit" across the wake.
There '^ave also been phenomena observed differing substantially from previous expectations:
(1) The radial position of maximum velocity fluctuations (at a given distance behind the body) does not correspond to the maximum shear region (in contrast to WEB; see Reference 5).
(2) The radial distribution of the velocity fluctuation extends much farther out from the axis than the comparable low-speed fluctuations.
(3) It is possible to obtain fluctuation intensities which are larger in magnitude than the local velocity or density "deficits". The Utter, therefore, do'not indicate the absolute maximum attainable by the fluctuations as previously thought.
Although the angle-of-attack and heat-transter data are not fully reduced, three important conclusions are drawn from Sections V and VI:
(1) Even small angles of attack at moderate Mach numbers make the wake resemble a shear layer and create severe departures from the above conclusions.
(2) The boundary (front) structure, measured by the local wake thickness, is unaffected by heat transfer.
(3) Heating the body stabilizes the wake and greatly displaces (downstream) the transition region. This fully verifies stability predictions (Reference 7) which also predict des Lnbi 1 i z.it ion by cooling.
-3-
The conclusions drawn irom work done in tlie current period willi ihv turbulent plasma are now entering the phase oi practical appl it at i.m, Relerence 2 summarizes best the conclusions re^ardinK, iirst, the mean Clow of the reacting, highly heated ilow: "Measureu;ents oi the temperature, density, axial velocity and electron density show that the overall gasdynamical jet structure attains the so-called sell-preserving state within the region investigated. In the radial direction a similarity coordinate based on the Uowarth-Dorodnitzyn radius correlates the distributions oi temperature and axial velocity, and it is shown that the same coordinate should also corre- late the relative concentration of electrons though not the absolute electron density. The measurements show that the electron relative concentration does not in tact become similar, and it is conjectured that the axial decay ot electron density must be controlled by recombination react ions." There- Lore, it is demonstrated that dynamical self-equilibration eau occur independently of chemical relaxation U the ionization level is not too high. In Paragraph 4.2 it is turther shown that the front structure is independent of the chemistry and, very s ignil ic ant 1\ , the "electron inter- miltencv" is indistinguishable tt<M the regular intermit tenc y. This applies even to tho "weakly periodic" turbulent iront whose wavelength scales are the same as for the compressible wake.
From the host oi turbulent plasma phenomena observed and measured (Section IV), the following conclusions are drawn:
(1) Two distinct phases ol turbulence exist in the jet: A heterogeneous portion apparently associated with transition and a homogeneous portiot) resembling the familiar turbulence phenomenon.
(2) Nearer the heterogeneous region the ^as temperature spectra have a very clear -5/3 slope which change into a much faster spectral decay (with frequency) in the homogeneous region. The electrons never attain the -5/3 slope, and in the homogeneous region they decay about as the -4.D power ol irequeuey.
(3) In the homogeneous region the oil-axis maxima in the electron density lluctuations occur Where the flow gheer is a maximum.
(4) In the heterogeneous portion, abnormally high "spike" electron fluctuations make the rms electron density much higher (by a factor oi 5) than the mean. These spikes do not exist in the temperature and are unrelated to intermittencv, which also makes An/n very high near the jet edge.
(5) Agreement of the gas velocity and temperature lluctu- ations, scale magnitudes, etc., with values obtained with non-plasma jets in other laboratories is generally- very good. Specifically, the longitudinal Integral
-4-
scale A'i of the temperature seems to bear the same relation to the so-callet "transverse stale" (Arj = 0.75L) that it does in other jets and wakes,
(6) The longitudinal integral scale A ot electrons is related to rj as follows: '.e = 0.6 |.
(7) The frequency-integrated, normalized electron density fluctuation An/n is greater everywhere than the corr_sponding temperature fluctuation ArJ/T. At ea'h po^nt, it is also greater than A'l/T across the spectruiri.
1.4 PRESENT STATUS
The present status of the work is 'hown on Table 1.
-5-
FABLE I. ST.-nS dl" I.Xl'l KIMCNTAI. WORK IN SUPERSONIC WIM)-1V;NK1
Experiment Experineut
De s I pti Hardware
Construct i .'n Measurenent s Data D.it.T
Reduction Analysis Rep rt
S .s'.itM Mi an i low
i S Wake 1 nt > rtr.i i u m v
i S W iki- 1 urbu KtKi
■- Wikc v,-,in 1 low
.'- ' U' ik. Inl v r- i t tenc v
' - < W jki 1 urbu lenct
C
C
c
c
c
c
c
I
IP
c
c
c
c
c
c
(■
IF
c
r
c
IP
!nc ld«flce ( 10 Degrees I Mi in 'low
[m i lenc« ( 10 Qegt* et • hit if" i 11 ency
IP
I iK i .1. net (10 Oi iiri ■ •- > ': urbu K nee
IncLdence (20 Degrees) HI low
IP
I nc i 11 tu-1 ( JO Degrees) Intermitt encv
IP
!m i dunce (20 Degrees) Iurbu lence
IP
it r r ans t er an i low
a 1 r.ms i i r Inti r- i i t enc v
IP
II 11 i i ansi er i urbu 11 nc (.■
ir
I. t Mean Flov
t Int frml11 encv
I
i
■ t I urbu l.iu . i i. p. rature)
.■ t ■ urbu 11 iu c i l.ii rons i
■ i i .M'. Properti«
c
c IP
IP
IP
"M: i : i onpleted IP: in Progress
SECTION II
TURBULENCE MEASUREMENTS IN A TWO-DIMENSIONAL COMPRESSIBLE WAKE
2.1 INTRODUCTION
The ^plicity .f the two-dtaensional ->" «"-^^ J^^f«
years aso the bulk ot all knouleUKe on A nil„,bl.r „j Cith two-dmenaLonal models Mnmersed u, ;"' f/' ^',;|:\,.,1 lnü(.rs placed Lnvestl^ato. , reported detailed work *«»J«J ^ke ° ,-L
A- A. TSunsend normal to the stream; prominent among s"d
< ""fj^^ j'taiU,j c^,„„lbU (Reterenee »). In the present series o "^r^e^S
is^tt Lt wal< . turbulence inlormation has been *"^ -"h " V^Z] dcameters irom
(Reierence V^^^^^^^J^Z^ that the turbu- thc model. All evidence collecte.l in CM • distance, but the Unce .entities a. tac^dse-preservao with en ^ "^ ^et
signiLicance ot the results varrant therefore, was the measure- -ronr«»^ Ä^s^nur^i-«^. -u — such distances could be easily attained.
As with the mean-ilow results. ^t^^^^r.««lc I^T^. turbulence behavior in a two.aimens...al d . an ax s ^ ^^ ^ ^ example, the rms axis LluctuatLon level decrease^ jLn
X-l/2, whereas in the latter it decreases " * ' J^^ each L.onstant normalizi.. with the mean P-perties ^^^ ~ ^ aT^nsend and already (i.e.. independent ol 0 and, in tact as - - ^ k'0-di..ensional studies shown on Reference 5. are about ^^^.•^^^lU the Lundamental of turbulence, therefore, not only *reaL^ *C^ectls- to the needed practical knowledge on turbulent wakes, but cf"^J^^'^Tag^eerlng rules for predicting the m*i»ymmt*U behavior tvpical
appl ic at ions .
The turbulence measurements described -^h-s -ion were per.orm.0 with
the two-dimensional model ^^^^^ ^«tlon on the tunnel Reference 1. Reference 1 should be ^^/^ a bricl ^petition facilily and the characteristics of the nod. on > a vcr. du;cUSsion
9i this'iniormation will be ^\^ ^^^ [ ^l commentary on use will also be made of the results ol KeUrcncc I their method of acquisition.
2.2 FLOW FACILITY AND MODEL
XHe Work was done in the »ach 3.0 wind tunnel ^^^^^ o£
stannation pressure ol 730 ■"**"*"• *M6 inch wide stainless steel Moc. The model was a 0.004 inch thick. "• ■" ^ ^ft section. The ribbon stretched at zero -. e o a ta ^ Z^VZr^ -d the ».lll«g leading ed^e was beveled to a halt anM^
-7-
\
the model and flow, i..., the c-x.u.riment w.-.s ad inb., t U . Hw relevanl KeNTiolds numbers were as follows:
(1) The Reynolds number
= b'2 (I)
is based ofl conditions external to the wake (see Reference 1) and the equivalent ribbon "base height" CDh was -n reality the wake momentum thickness and was measured by inte^ratin« the measured momentum flux in the wake,
(2) The Reynolds number
Kew = *v: U - 138 (2)
is based on the velocity del u it Ucc -U(0) bctWMll the axis .?nd external velocities L',« and U(0), respectively, and aa the s.-cailed transverse scale L.
These and turther lindm^s oi the mean i 1 ov. iu Id will be diftCMMd later.
2.3 INSTRLT^IENTATION
nrobe^hiJh"" T^K^""'3
^ ^f0~<l "* * ****** ^-.^ anemometer probe which could be traversed continuously m the wake and could thus
thp8!: ^eS/n ÜW turbulente Properties over distances n.u h «IU, u.an the wake thickness. An elaborate description of the technique, ..,,..1, . • many respects classical, is provided m Reiere.ue 5; onlv a te^ point, of general importance will thereiore be mentioned here. The hot-w.re is oper- ated at a number ot predetermined electric heatin. currents (constant
o^n." r0P^ati0n and ttlUS Prtnid^. at ••* ?Oimtt a corresponding nur,ber of t uctuatmg voltage outputs. The latter are then inserted as lore in.
whichX5 lnt^.an.OV2r-de'e^in^ «>-tem of linear algebraic equations in uhich the coefficients of the unknowns are numericallv fixru bv the local mean flow properties (measured earlier and reported alreadv inRelerence 1)
nvokmg the constant-pressure assur,ption, the svstem is solved bv the east-squares method for the local iluctuation. U the flow veloc'itv
c^nt ' TM temperf UrC>' and *« temperature-velocity correlation c^elli- cient. This procedure is normally periormed lirst for a verv wiue trequencv band wi hin which the total (integrated) rms is obtained. Aiterwards a combined spectral-modal analysis is performed by which the contribution oi each fluctuation mode is obtained at each point in the spectrum.
det.ilpr^^T" ^ the hot-Wire' "- ^alibrat.ons periormed, and a detailed journal ot us usage are discussed m pages bl and 62 ot Reterence b.
-8-
2.4 GENERAL FEATURES OF THE WAKE FLOW FIELD
The two-dimensional wake of the ribbon grew in a regular manner behind the model for a distance of about 1850 virtual body diameters. It is worthwhile to summarize here some general features of this wake before the turbulence measurements are detailed:
(1) The uniformity of the wake along its span is quite satisfactory.
(2) No shock waves or other disturbances emanating from the model intersect or distort the wake. The bow shock system affects the wake only beyond (downstream of) the region studied.
(3) It was demonstrated conclusively that the angles of attack and twist were sufficiently close to zero.
(4) Measurements of transition, fluctuation intensity, spectral density, and intermittency demonstrated that the wake was indeed turbulent.
(5) Transition to turbulence occurred within the first few X-Stations along the wake (details will be furnished when the fluctuation measurements are described).
(6) Day-to-day reproducibility of the wake flow field was excellent.
A summary is given below of the mean-flow results for the turbulent wake at hand. These experimental results are shown correlated into simple algebraic formul.-.s which, at the same time, are the general scaling laws for two-dimensional compressible wakes. The nomenclature has the usual aerodynamic connotation.
(1) Proper axial coordinate: X-X
X - -ZZ" (x is virtual origin) (3) VCüh
(2) Velocity defect:
W "« -^/ = \/T7r= (RT = 13.0) (4) Uoo Vl0 x i
(3) Transverse scale:
L =^r-T- = 0.22 V^f 4W (5)
9-
(4) Lateral coordinate:
Y Jo Poo dY (The Howarth-Donodnitzyn radius) (6)
(5) Proper non-dimensional lateral variable:
n ■=■- Y/L
(b) Lateral variation of axial velocity:
(7)
U u« -u = e •0,697) 2
Uoo -u(0)
(7) Lateral variation of static temperature:
9
(«)
T T-T 00
T(0)-Tc = e •0.45T1 (9)
(8) Axial variation ot temperature defect:
(10)
These laws, which will be used frequently to understand the turbulence behavior at each point in the wake, arc applicable primarily in its self- preserving portion so that they are only approximate in the first 20 percent of the wake length studied, and exact thereafter.
The pertinent Reynolds numbers which are relevant to this wake are shown in Paragraph 2.2. The quality and behavior of turbulence can be prejudged on the basis of two more Reynolds numbers, added to those indicated above. First, consider the Reynolds number of turbulence:
Ren Au* A
(11)
w here Au is the rms velocity fluctuation, A the integral scale of turbulence, and v th« l.-'al kinematic viscosity of the gas. Now, asymptotically Au is about 0,4(; ,»U(0)) (on the axis) whereas A is of the order of the transverse stale L anu v is, far in the wake, of the order of the free-stream kinematic viscosity v«. Therefore, KeT is about 0.4 Kew where the latter is the wake Reynold« number, already noted in Paragraph 2,2, to be constant at about 160; thus, Kej ■ 64. Secondly, consider the dissipation time lor the verv small eddies which Kovasznay (Reference 9) has computed in typical wind tunnel situation;;. On the basis of his computation, a corresponding limit for the Reynolds number of the dissipating eddies has been derived in Reference 6; assuming that the smallest eddy is that which dlssipatefl over a convected distance equal to its size, then tliis Reynolds number (called ReO is 40.
-10-
These computations put bounds on ehe expected structure ol turbulence because they imply thc^t the macroscale and the microscalo are about equal. This wake is therefore coarse-grained in the sense that no eddies smaller than the integral scale are expected. Also, Reference 1 has already shown that the mean flow in this wake is in all respects almost exactly analogous to those obtained at a much higher Reynolds number. The Important additional conclusion is drawn that the arrangement of the mean (average) rroperties, and therefore the important mixing processes, result from the action of the larger eddies alone. It remains to see what the power spectrum of this coarse-grained wake is.
2.5 EXPERIMENTAL TECHNIQUE AND PROCEDURE
2.5.1 PURPOSE OF THE INSTRUMENTATION
The hot-wire anemometer was used to measure the following statistical properties of the turbulent wake: (1) the root-mean-square fluctuation of the axial component of fluid velocity (where "axial" will henceforth refer to a direction parallel to that of the tunnel stream) resulting from all active Fourier components, i.e., integrated across a very broad frequency band; (2) the root-mean-square fluctuations in the static temperature similarly integrated across the spectrum; (3) the spectral "density" of the above-mentioned velocity fluctuation; (4) the spectral density of the temperature fluctuation; (5) the integral scale (correlation length) of the velocity fluctuations in the axial direction; (6) the integral scale of temperature 1luctuations; (7) the "Taylor microscale" of velocity fluctuations; and (8) the same microscale of the temperature fluctuations. It was furthermore desired to map these quantities at each point in the turbulent flow.
Some points should be stressed regarding these objectives. First, certain combinations of the sought-after parameters (such as the mass-flux and total temperature fluctuation) are also directly obtainable by the hot-wire. Secondly, certain assumptions justified by earlier experiments are needed in reducing the data. For example, it is necessary to have no pressure fluctuations (sound waves) in order to extract the velocity fluctuations from the data. Third, there is no need to resort to questionable assump- tions (e.g., isotropy or homogeneity) in order to obtain these results.
2.5.2 CRITERIA FOR RESOLUTION AND STATISTICAL ACCURACY
A number of cr'teria must be satisfied so that the measurement will be valid. Some of these involve a precise knowledge of the measured quantities and thus, can be checked only a posteriori. However, with a precise knowledge of the electronic circuits and a fair estimate of the turbulence properties drawn from the mean measurements (Reference 1) and exploratory work, the criteria were also checked a priori.
-11-
a. Space Resolution. In the direction ot i'low (x direction), the 0.00ü05-inch diameter ot the wire assures excellent resolution.* Taking a typical wake width of 0.100 inch and estimating a typical small eddy size ot" 0.010 inch, one obtains a resolving power ol 1 to 200, applying equally to the x- and the y-direction (i.e., the lateral direction). However, in the z-direction the hot-wire length is 0.010 inch, that is equal to the estimated eddy size. Resolution in this direction is therefore not as good.
b. Time Resolution. Even If adequate space resolution in the x-direc- tion is assured, the question arises whether the hot-wire and its circuits are capable ol exploiting this resolution. The frequency, 1, corresponding to an eddy of size d = 0.01 inch = 0.025 cm and its convection velocity u = 60,000 cm/sec past the probe is f = u/d ■ 2,400,000 Hz. Formally, this is the estimated maximum frequency to which the turbulence spectrum extends. The hot-wire system must therefore operate properly at these frequencies. Now the hot-wire employed in this work has a time-constant of about 0.15 msec, that is, an intrinsic "cutoff" at 7000 llz; this is much lower than needed. To bridge the gap between the required and the available frequency limits, two supplementary techniques were used, one based on real-time electronic compensation of the high frequency response, and the other on computer corrections during the reduction of data. These two schemes have been described in Paragraph 2.b of Reference 5, so that only a brief review will be given here.
The constant-current amplifier used includes an adjustable RC network which has a gain of unity at low frequencies and amplifies pre f erent ia 11 \ the higher frequencies. The transfer function of this network is of the type
ftik^k* t-O)2) (12) in *
where 0) is the circular frequency and e,^ and e ^n are the rms voltage out of and into this network, respectively, in a narrow passband about CJQ. The circuit time constant tx is fully adjustable at the trout panel to an accuracy of 1 microsecond. The advantage of this transfer function is that, of course, it is algebraically inverse to that of the hot wire itseli where
^ . / 9 9\-L/2
-f±= (l + tV) (12) in *
with t being the time constant of the wire arising trom thermal lag. Just prior to each measurement, t is measured and tj is set equal to it. Then
v.- The wire is actually not stretched taut between the needle supports but with a curvature which is ot order 20 percent of its length, i.e., about 0.002 inch« Thus, for eddy sizes ot order 0.010 inch, one still obtains good resolution.
-12-
the compensator output eout is equal to the "tlow" input e'Ln into the hot wire (by multiplying Equation (12) with ') as would be expected of an
ideal system.
The upper frequency at which Equation (12) apples ai o marks the upper frequency limit where the comnen^ just indicated c, ";^s. This limit depends on tj.. To find th ti»*ct iorm of Equation (12), the a fier is calibrated before t h experiment. in the WED experiment the ea .brat ion was least-square i "ed by a trivariate lunction and used in the 'EB-11
program:
in /
The departure of Equation (12) irom Llie desired behavior (Equation (14)) is such that at tr = 0.1 msec the uppir coMpCtlMltlng Irequency is 800 kHz and at tT = 0.2 msec, it is 400 k\\z, Mhicb appears to greatly improve the 7 kHz intrinsic limit of the wire LtMlf«
Unfortunately, there are other trans ler Eunctlooa in the circuit to con- sider, and another limitation arises irom the "straight" amplitier itself. For the WED experiment, the transler Iuiu t ion ot the latter was Lalibrated and curve-fit ted into:
-AH = i + 6.144 x 10"4F - 7.718 x 10'bF2 ♦ 1.0H5 .< w'h e. (15) in
.12 4 -4.610 x 10 F
(with F in kHz) which indicates a roll-oil irequency begiUfling at about 80 kHz and an attenuation of eout/ein - 0.43 at 500 kHz. Thus, the straight amplifier response is generally inierior to that of a perfectly- matched (t = tj-) wire-compensator system. It is esti lated that the com- plete system begins degenerating severely around 300 kHz.
To extend this range further to the ? MHz c-stimated range ot turbulence, the "response restoratioi" technique described in pagei 13 to 29 of Reference 3 was used. This is based on the spectrum of a signal being obtained with a non-ideal system (i.e., a system with a non-llal response), then the correct spectrum can be reconstructed provided that tin irequency response of the entire system (i.e., its transler function) is known accurately. To do this, the irequency response of the chain oi experimental equipment' is obtained component-by-componcnt so that the so-called "overall transfer function" of the system is known at each point in the wake. Also, at each point, the spectrum of each admitted signal is measured, and a computer program is then used to restore the latter spectrum to lhe lorm it would have if detected by an ideal e1ectromechanital system.
The response-restoration technique is obviously linuled by the electronic- noise present. In this experiment, spectra were taken to 1.2 MHz so that slightly more than half the presumed range of turbulence activity is
-U-
covered. However, it should be considered that the majority o£ the turbu- lence signal at the hot-wire arises at the lower frequencies. The a priori conclusion was that with the present system, it should be possible to measure the rms velocity and temperature lluctuations integrated over the entire band oi turbulence activity, but that perhaps the details of the spectrum above 1 MHz are elusive. Further discussion of these points will be made during the presentation of experimental results.
c« Statistical Accuracy. A statistical measurement can become very inaccurate if the domain of measurement is not much larger than the size of eddies lying within it. Otherwise stated, the hot-wire must remain at the point of measurement for t time which is so long that a large number of eddies of ill tisef go bv it. In the course of earlier experiments (the WEB), it was seen that the integral scale, for example, was only 4 times smaller than the statistical wake diameter. Using the integral scale as a useful measure of the larger eddies, and a local wake velocity of order 6 x lO'4 cm/sec, the time of passage of such an eddy past a point is estimated typically as 2 microseconds. For proper statistics, the residence time of the probe at a point should be long enough to record the passage of, perhaps, 1000 such eddies; this time should then be 2 milliseconds. For the continuous-flow tunnel used here, this Lime is safely exceeded by orders of magnitude. Even with the method of traversing the probe continuously through the jet the residence-time requirement is fulfilled easily, SMice it takes several seconds lor the probe to traverse a lateral distance equal to one correlation length.
2.5.3 FULFILLMENT OF THE "FROZEN TURBULENCE" CRITERION
Another criterion to be fulfilled lag these measurementb to be vmlid is the so-called "frozen turbulence" criterion, i.e., the Taylor hypothesis. , This states that in a locally uniform convection, the time and space coordinates can be interchanged provided that the time needed to change the turbulence structure is not shorter than the averaging; time oi the signal. Otherwise stated, the eddies must remain unchangim; as thev are being counted by the probe. Estimates usually made of the validity of Taylor's hypothesis are limited to changes made m the line (s:ua 11-eddy) structure of turbulence by viscosity. Kovas/.nay (Reference 9) estimates the viscous decay time, tv, for small eddies to be of order (vk2)'1, where j V is the molecular kinematic viscosity and k is the eddy wake number, k = 27r/X (where X is the eddy diameter). Obviously, if the "lite distance" d = utv of such an eddy is much larger than its own size, the Tavlor hypothesis is valid; this criterion (see also Reference b, pa^e 12J) can be expressed by the following alternate lorms: *
ut »X. Re,, ^»40, X»^ v " v do)
-14-
Since the wake conditions will be cloM to ambient over most of the wake, the freestream unit Reynolds number iWVot, ■ 80,000 per cm (at the conditions used) can be substituted in the latter inequality. The result is that the « minimum eudy size which can be measured in the tramework of Taylor's hypothesis is 40/80,000 = 0.0005 cm in size. This rough estimate thus
) < • • • - J •
shows that the space-tin. trans for.at ion is ^-y roas.nable l.r the 0.025 en eddies estimated to make up the fine structure ol the wake at hand.
2.5.4 EXPERIMENTAL PROCEDURE
The hot-wire wa. positioned parallel to the ■ axis (Figure 1) at the
the wale LVthf Y directt.n and Us W versus pos U K,n was pitted on a
function plotter.
i- A .^ Rof^r^nre 5 For measurements OX spettrai amnmt.*.jt Appendix A ol Re erenc. i. ^or technical sweep drive;
a Moseley Model 7()0lA function plotter.
2.5.5 MEAN VOLTAGE MEASUREMENTS
Since aU data is hand.ed and uUUzed ^^^ ZSrtTZ'lo* (averaze) wire resistance variation across the wakt uas nccac . l^^^U^n diiferent secUn.s oi %* "^J^*^ T'
the wake, producing a voltage versus distance trace A ^ a ": cne wäre , . ,. in c, .ndq and produced a maximum deflection »I was completed in about 30 seconds and proauc ^fteen such traces is about 500 maiivolts dc . A representative set ol litt-*
shown in Figure 3.
2.5.b FLUCTUATING VOLTAGE MEASUREMENTS
eliminate stray sisals (suth as ehanee bO-oO. Ul l J^1 vlbr.tloM vibratu.ns) vhteh .i.ht arise at ^ "J-"1^*; /^^wi was a.au, had been eliminated in the prneess ol .al ibrat i.n.)
" ~" . ► , ^ fi. li<(.i.>v't>r the KOOd ciualitv
- r :;cw r.r:Tr: ia-o:5"a: ^rr//^^^ tests.
-15-
CM
E u
00
O O
< H
is '-1
Id >- s QC <
■
Q i: H c/5 • Z H g a Z Si
02 = a: ^: cAi
k 3 Q x '-D u:
^5 z: =-
u- u: J c pc: J
^) H =2 M < < H -J 0- < U «. Z. z: * LL: ^: < S £ ^ u c = v: z ^
3
-16-
HOT-WIRE
i HEATING CIRCUIT
DIGITAL VOLTMETER
i AMPLIFIER
I COMPENSATING AMPLIFIER
I
SO WAVE GENERATOR
PANORAMIC ANALYZER
r_ WAVE ANALYZER
1_ RMS VOLTMETER
i_ DETECTOR
i_ DETECTOR
SWEEP DRIVE
e X-Y
RECORDER
F09813U
FIGURE 2. ELECTRONIC CIRCUIT USED FOR THE WED TURBULENCE MEASUREMENTS
-17-
TABLE II. AXIS VALUES OF MEASURED TURBULENCE PROPERTIES
_ ^u o V» IIP ^gtatlon X Pu T u ^ r
mt r
ar
0 0.0477 0.0624 0.0117 0.0357 -1.23 -1.09
0.519 -- 0.0038 0.0469 -- -3.94
04 0.131 -- 0.0525 0.0962
251 0.152 0.0459 0.0436 0.1035 0.38
419 0.121 0.0307 0.0268 0.0957 -0.25
22 1760 0.045 0.013 0.0056^ 0.037 -0.32
''Uncorrected
■0.95
168 0.200 0.0758 0.0668 0.121 0.65 -0.88
•0.83
335 0.122 0.0338 0.031 0.0926 -0.05 -0.76
•0.80
7 503 0.119 0.0367 0.0214 0.0933 -0.Ü8 -0.84
8 587 0.113 0.0293 0.0057 0.0860 -0.09
9 670 0.103 0.035 0.0155 0.077b 0.14 -0.81
10 754 0.091 0.u281 0.0149 0.0702 0.03 -Ü.82
11 838 0.081 0.0241 0.0145 0.0626 0.01 -0.83
12 922 0.077 0.0219 0.017 0.0581 0.08 -0.77
U 1006 0.068 0.024 0.012 0.0522 0.13 -0.74
14 1089 0.068 0.020 0.014 0.052 0.09 -0.76
15 1173 0.064 0.019 0.015 0.048 0.18 -0.7b
16 1257 0.059 0.014 0.013 0.04b -0.08 -0.79
17 1341 0.056 0.016 0.013 0.044 -0.08 -0.71
18 1425 0.051 0.013 0.0066-.•.• 0.043 -0.41 -0.92
19 1508 0.051 0.013 0.0091* 0.041 -0.26 -0.80
20 1592 0.045 0.012 0.0056* 0.038 -0.46 -0.98
21 lb76 0.047 0.014 0.0049"- 0.038 -0.20 -1.09
-0.8b
-18-
5. 320
•4. .892
u. .292
1 .650
1 .17».
TABLi: III. HOT-WIRi: HKATINC CURRENTS ft» ITKBILI-Nn. MKASIRKMKNTS
Hi.h Ran^e (tna) M.^um Range (ma) Low RanKc ^
7.404 b-4i7
7.192 b.273
b.988 b-llti
b.795 5.825
h.bl4 5.562
IABLK IV. CH..\R.ACTERISTICS OF HOT-WIRES ISEU IN TM «8 EXPERIMENT
„.7 1 TurbuU.nc. n.V> ».MM U.OU 2M (all X-Staf ions)
0.001b2 0.011 220
37.43 0.00158 0.0105 210
b-7/1 Snectra >9.10 X-Stat ion
7-12/1 Spectra X-Station 3-9
7-19/1 Spectra X-Station 11-21
i/d
16.37 O.OOlbO 0.102 204
-19-
WIRK MEAN
VOLTAGE
KCI'Ki: )
WIRK CI'RRKNT IS CONSTANT ,K
-jo-
first positioned just outside the wake; its time constant was read and the compensator dial was set at that level. Typical time constants at each point varied from 150 to 110 microseconds, depending upon dc current. The reference (ambient) turbulence level and electronic noise level (independent of Y) were also recorded at this point. Then, for each Jurrent. the wire was traversed through the wake at a compensation setting equal to the free-stream value corresponding to that current. During tins traverse the ac signal is continuously converted to dc by the circuit o£
the rms meter proportional to the mean-square of the ac level. Finally this dc voltage is plotted versus position. Five of a typical set of fifteen such "turbulence" traces are shown in Figure 4.
2.5.7 MEASUREMENTS OF THE SPECTRA
in the previous paragraphs it was shown that a total of 15 + 15 = 30 traces were taken at each X-Stution; for the total of 24 stations involved this a-ds up to 720 traces. These, in principle, contain all the -formation necessary to deduce the turbulent fluctuations. As already noted, however, the insufficient frequency response of the system made it necessary to also measure the spectra of turbulence signals (at each wire currenr and point in the flow). Now. it w.U be recalled (Reference 5 W* f; •'• J^ the objective of the spectra, besides yielding the spectra density func tion. is to provide an "error ratio" J which is used to multiply the fluctuation intensity discussed in Paragraph 2 5.6; this ™ up h latter to the correct value if recorded by an ideal system. This would in turn, require that spectra are taken at closely spaced points for ea.h wire current. Since this is clearly impractical* the following was done: spectra were taken for each of 6 currents at each of 10 radial points at alternate X-Stations, beginning with X-Station I. for a total of ^0 spectra. Extensions of these J's so obtained to other currents and points could be later made bv interpolation. The electric currents used spanned the range if tho" used tor the "turbulence" measurements (see Table III), and were 3 174 4 891. 5.820, 6.432. 6.981. and 7.401 mil Iiampercs. Uire No. 6-7/i hli by this time, failed and other wires closely resembling it were used for the spectral measurements. Their characteristics are shown m
Table IV.
Each wire was Urst positioned outside the wake where its ti«»-^*"' was measured and compensated for. The wire was then lowered to the desired point in the wake, and with the compensation unchanged from ^e s rea value (for that particular current), the spectrum was taken. Amplifier gam wa 650. the passband was from I to 320 kHz. and the wave analyzer was set
at I volt range, normal mode at -10 dB input. A 3-kHz f^%b*f^/.ec was used and was swept across the spectrum at a speed -f about 7 to * *£/•" by means of the mechanical sweep drive. The signal in the 3 kHz bandwidth
,VFor example, if 20 radial points were chosen for the 24 x-stations and 15 currents, one would require 7200 spectra - the equivalent of about
1000 hours of testing.
-21-
(0)
y^.
riGURE '*. 1 FlllM U
YPICAL PROFILKS OF RMS WIRK OUTPUT ACROSS TWO-DIMENSIONAL WAKE
-22-
was converted into dc across a 1000 ohm resistor and fed L«tO th« Y axis Of the Moseley plotter. The sweep drive also produced tdc voltage pro- portional to Lrequency, which drove the other (x) axis ot the P^ter. A typical spectrum is shown Ln Figure 5. Since it is necessary to know the spectral distribution of electronic noise, that spectra of the noise were
also taken.
2.6 RESULTS
2.6.1 RESPONSE RESTORATION AND SYSTEM PERFORMANCE
Data reduction began with the restoration of the Lrequency response oi the system, accomplished by feeding the spectra Information (Paragraph Z.5.7J into the WEB-II program (SRS No. 0073). The main objective here was to extract the error ratio, J. at each point Ln the wake.
The irequemv response of the mam system components is sh.-wn, for a typical situation, m Figure 6. The ordinate of this plot denotes the Logarithm of 'Vain squared", that is. of the mean-square voltage com. out of each component divided by the mean-square voltage Input. The grapn shows results at a single point Ln the wake (X-Station 1, x - 0, Y
.,d for one particular current (7.401 ma). Note, first, the rapid deterioration oi the hot-wire itselt, the attenuation (in the squaiO being about a million at 600 kHz, The compensator has a time-constant setting not quite adequate because of mismatched t ime -. .ns t ant s. ^ l" ^ „ever exceeds 100.000, The amplifier* also deteriorates, and its frequenc> response together with that of the hot-wire and compensator, produce the curve labeled "overall transfer fuction" (OTF) which is seen to produce an attenuation oi about UK),000 at 1 MHz. The computer program is thus set up to multiply the wire output by L/OTF and thus bring it to th level
it would have ideally.
The hot-w.re response is. ot course, controlled by Lti time constant. Figure 7 shows the axial and lateral variation oi the hot-wire time con- stant at the two extremes ot current enpl »yedi 3.17 and 7.40 ma. For orientation, it should be recalled that th* .er.-.urrent time co^tant limit tor the type of wire employed is about 0.09 mil isecond w^ch is consistent with the data of Figure 7. More importantly, note that data aff displayed from three different wires. Except at the lowest ,nvrhea s (currents) it is evident that the time constant variation is small trom one wire to another. It is also evident that the variation of time con- stant with x and Y becomes quite small, as it should, at tar uista.ues although it depends strongly, of course, on the heating current value.
A crucial test of the effect of using different wires (unavoidable because of wire breakage) insofar as the error ratio J is concerned is shown Ln Figure 8. Here can be seen the very large "corrections" necessary to bring
*The zero-frequency «a in of the amplifier is not shown.
-23-
ft H U
H a. H O
< u M PL, P H
m
a«:
O
-24-
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<
-7
COMPENSATOR
IDEAL OVERAI.I. TRANSFER FUNCTION
f(MHz)
0.2 0.4 0.6 0.8 uo
INSTRUMENT TRANSFER FUNCTION
AMPLIFICATION
AMIM.IKIKH
ATTENUA1ION
1.2
L-uL-nnrvrv HKm'ONSF OF EACH COMPONENT, OF THK COW FI(U;RK ^ KQUIUFNT riN^IENT TRANSFER FUNCTION") AND Of
SYSTEM ("OVERALL TRANSFER FUHCTIOII") -25-
BUIOU COMPLETE ELECTRONIC
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(N
-27-
the data to the level produced by a hypothetical ideal system. The J is as high as 15 on the axis very near the body and at the higher currents. By X-Station 6, J has attained asymptotically a constant value bracketed between 4.7 (at high currents) and 2.8 at the lowest current. Tr.c curves marked "smoothed" are an empirical attempt to reduce the data scatter (in the WEB-IV and WEB-VII outputs) by reducing the scatter in the J. As will be seen later, the break in the high-current curve occuring around X-Station 16 is significant. Equally significant is the rather gross depar- ture, at the lowest current, between the actual and the smoothed J's past the same point. In the meantime, it is clear that there is no obvious break in the curves around X-Station It) where the change from wire 7-12/1 to 7-19/1 occured. As is seen from Table IV, these two wires are structurally similar; the conclusion is that, with this similarity, uniform J's are obtainable.
The lateral variation of J for I = 7.401 ma is shown in Figure 9 for various X-Stations. It is noteworthy that off-axis J reaches values even larger than the axis values. Finally, Figure 10 shows the variation of J with current for two lateral positions in the wake. In all these figures, the disconcerting fact is noted that J does not attain the low values (about 1.5) in the free-stream which it attained in the axisymmetric wake (WEB) experiment (see Reference 5, page 19). At this juncture, the most likely explanation is that there is much more high-frequency content in the freestream turbulence of this experiment than in the UTEB experiment.* However, no turbulence spectra were taken in the free-stream.
With the large J's shown on Figures 8 and 10 and the deteriorated frequency response of the system shown in Figure 6, it is clear that the output spectrum of the measuring system will be severely distorted at each current and flow point. The printed output of WEB-I1 lists both these actual (distorted) spectra and the "ideal" spectra; these are of course voltage output spectra, at this point still unresolved moda'ly (i.e., not indicatinn the velocity and density spectral densities separately;. A comparison of actual and ideal spectra are typically shown in Figure 11. They differ greatly, as they should. The differences lie not only at the hi^h ire- quencies where the actual spectra are greatly attenuated, but als* m shape. The latter very important point will be discussed further in Paragraph 2.6.4.
A final important point regarding the output of WEB-II concerns the two alternate methods of measuring the (integrated) flunctuations intensity. This is formally measured by the wide-band Ballantine voltmeter (sec- Paragraph 2.5.4), but is also independently available from the spectral measurements (Paragraph 2.5.7) since tlu total rms tflteaait) is, after all, the integral of the spectral density. The latter Integral is listed in WEB-II as VTVM2 (in units of volts squared) while a total rms measurement
The WEB experiment was done at P0 *• 5ü8 mm Hg wheiv the tunnel side-wall boundary-layer capable of radiating onto the wake was laminar. In l-.'ED (P0 ■ 730 mm Hg) the layer was turbulent, with possible enhancement ot the stream turbulence by radiation.
-28-
11
10 XSTATION
SYMBOL
11 13 15 17 14 21
+ ♦
I = 7 401 MA
AA
I ■ 4 0
♦i
IDEAL EI.ECTROMECHAMCAL SYSTEM
0
Y (INCH)
J I I I I I L 0.1 0.2 0.3 u.. 0.5 O.b 0.7 0.1
•14130
Fir.i'RE y. i \TI:K.M. VAKI.XTION OF J FOR CONSTAMT X
-29-
OFF AXIS
STATION SVMBOl
7 o
9 •
11 A
1 1 A
15 a
1. ■ 14 + Jl 1
H 1 (MA> BUUU
FIQ'RK 10. VARIATION OP .1 WITH MKATINO t l'KKKNT KOK TWO LATERAL POSITIONS
-JO-
10 T r 1—i i ' ' i 1 1 1—ri||
IU
f* -2 rr lo t
i1- 10 .
10 -4 WED
XSTA 3 Y ■ 0.003" I = 7.401
10 -5
10*
■ I ill» ' I '—»—»-
10
t (Hz.
10
B()8b5 T
PBOm 11. WfiCl Of COMPITKR-AIDKI) RKSPONSK RFSTORATION (M THt MDDALLY UNRESOLVED Tl'RBl'LENCE SPECTR-X vW:D EXPERIMENT)
-31-
made m conjunction with the spectra is labeled Eü2. Representative values tor the ratio E02/VTVM2 are shown in Figures 1? and 1J. This ratio should be unity tor pertect correspondence, but it is in tact almost everywhere constant near 1.5 (i.e.. a diturence ot about 20 percent in tlu root-me an-square) meaning that the directlv ntasured output is always kijmt than that reconstructed by integratin« the spectrum. Because ot the multitude ot operations necessary to the latter, the ?U percent ditterence is actually much better than expected and is in lact an endorsement of the accuracy ot the measurement.
2.6.2 THE WEB-III PROGRAM
The next step in the data reduction process combines the J values irom the WEB-II output and the turbulence data (Paragraph 2.5.6) into the WEB-III program (SRS frogram 008J) irom which the integrated rms wire voltage is obtained at each point ol the wake, and tor each heat.ng current, tree from J requeiuy-response limitations of the system.
Turbulence information was obtained from 22 equidistant points spaced 0.004 inch apart, beginning at the axis and extending laterally to Y = 0.084 inch The total points involved, therefore mw (22 T*s| x (15 currents) x (23 X-Stations) = 7540, since the J^th X-Station, that numbered .• >, was not used. At the WEB-11 output the number of J's available were (10 Y's) x (6 currents) x (12 X-Stations) = 720, llncc the sp.ctra m« taken sparsely to save time. The require.: J's were then obtained irom those available by interpolat i >n. In the latter pr>cess a certain amount ot smoothing of the data was :Hriormed m order to decrease experimental scatter in the tinal outcome. An indication ot this tvpe oi smoothing is already shown in Figure b. Certain parts ot this process are thought to have caused artilicial perturbations ot the : mal data, a point .-hich will be discussed lurther.
-32-
CM
to
O
QO
i i O K
II II
• <
CM
5 H
00
rsi tsi O ui rg
O in
§ M H < H
< >
8 Qi IX,
I
z
u H M W3 Z o Q
CM (—i
I N
33-
o IN vD
i—I
r—I oa
I
O W
es
in < 4
m o •
2 J " / i—( /
/
/ N / S / B / B
7.4
0
MA
•
<
*
O 41 4
o •
O •
O • < 4
o •
o«
O, • 4 4
•o
o • J .-^L 4.
o
-
o
IE Ü
s
|
P H en M
2 O u
-34-
2.6.3 EXPERIMENTAL RESULTS IN THE FLUCTUATION INTENSITY
The WEB-IV program gives the intensity of turbulent fluctuations at each of the 22 lateral positions and the 23 X-Stations (X-Station 0 through 22). This paragraph discusses the nomenclature, method of analyzing the data and the results themselves. The latter deal only with ehe so-called modal analysis, i.e., the fluctuation intensity; the spectra, as well as the scaling rules by which the results are applicable to high speeds, are discussed in subsequent paragraphs.
In the text and figures found below, the following nomenclature is used:
(1) Au/u is the local root-r.ean-square fluctuation in the axial velocity u, normalized by the local mean (average) axial velocity, and integrated over all frequencies,*
(2) AP/p is analogous to (1), above, for the local gas density.
(3) AT/T is analogous to (1) for the local static temper- ature. NoteAT/T = Af/p for constant pressure.
(4) APu/pu andAT /T0 are analogous to (1) for the local mass-flux pu arid total temperature T0.
(5) Upu/pu) (AT /T )
X" ■ o o mt (4pu/pu) (AT /T ) ^17) r 0 0
is the cross-correlation coefficient, at the same point, between pu and T0 fluctuation (the barred numerator obviously is the averaged product of the instantaneous counterparts of Aflu/pu and AT /T ).
^ r o o
,,. „ _CAu/u) SCT) K ' OT (Au/u) (AT/T) (18)
is the cross-correlation coefficient, at the same point, between u and T fluctuations. Note that although
^£ = AX (rms sense) P T (19)
ins tantaneously
\ P/INST. VT / INST. (20)
* In this work, and in Reference 5, Ais used as a root-mean-square operator
-35-
M ■ Af^u/pu
1 = Ät0/t0
RMT = r mt
0 = Sigma = Ap/p = AT/T
T - Tau = Au/u
RSTAU = rt 5T
so that the following relation exists between the velocity-density and the velocity-temperature correlations:
foVPXAuM _ (6T/T)(Au/u) (21) (ÄP/P)(^u/u) " ^T/T)(Au/u) ' 'raT
(7) In the WEB-IV output the following alternate desig- nations are used:
(22)
(23)
(24)
(25)
(26)
(27)
U PRIME = Au/^u«,- u(o)) (28)
RHO PRIME-AP/^- p(o)j (29)
where in the latter two cases, • and (0) refer to conditions outside of and on the axis of the wake, respectively, and where Au and APretain their rms meanings,
(8) Eta, or "H, is the normalized radial distance (see Equation (7)).
The equation relating the fluctuation intensities to the local rms voltage output e of the hot-wire can be written in the following alternate ways:
2 2 2 2 2 e=e M+e_T-2MTeer (30) m Tx mTmT % '
2 2 2 2 2 e=e T + e na + 2 ta ea e r (31)
with the symbols as given above and with e , eT and ea being the appropriate "sensitivity coefficient" to the various fluctuation modes. These coefficients are in principle functions only of the local mean flow properties, which were measured earlier (see Paragraph 2.4 and Reference 1) and of the wire character- istics, provided by the wire calibration and inputed into WEB-IV. Equation (30) is exact, but Equation (31) is approximate in that contributions to e2 due to
-36-
sound waves are assumed ni.* Either equation may be used, depending on which of the unknowns are to be obtained. Separate computations are pertormed in WEB-IV, one for each ol Equations (30) and (-U).
In the present program, Kovasrzay's original suggestion (ReLerencc y) is followed reducing these two formulas into convenient second-degree equations with unknown coefficients. For example, Equation (31) is written:
2 9 e 2 feP (32)
which is of the second degree in the known and controllable parameter i*rf*gr* Since at each heating current ser.ting a pair of number (eTA,,) and e^/a~a are measured, three suih settings result La a system of three Equations (31) in ehe three unknown r, o and r^y. The accuracy is much improved in the present system: fifteen settings are used and the computer least-squares fits a second-degree curve to the fifteen points.
a. Sensitivity Coefficients. Figure 14 shows typical variation of the hot-wire sensitivity coefficients at a point in thr wake. The true indication of wire sensiiivity is its so-called "overheat" A' which is roughly pro- portional to LIK percentage increase of wire resistance over its equilib- rium unheated value). A range of k* from perhaps 0.05 to 0.5 is desired usually in order to maintain measurement accuracy, the wire melts around A^ • 0.6, In Figure 14, A^ varies from 0.U2 to 0.40. In the example shown, note that A^ - O.i'35 (corresponding to 1 ■ 6.7 ma) the hot-wire sensitivity to velocU" fluctuations is nil, and the wire is therefore sensitive to density fluctuations onlv.
b. Mass-Flux-Total-Temperature Correlation. Figure 15 shows the axial (along Y = 0) and Figure 16 a typical lateral variation of rmt, the cross- correlation coefficient between pu and T0. No correlation was found in either direction, as also was noticed in the axisymmetric wake (Reference 5, page 51).
c. Mass-Flux and Total Temperature Fluxtuation. Typical lateral vari- ations of \pu/pu and \T0/T0 appear in Figures 17 and 18, and their axial variation (along Y = 0) in Figure 19. The \T0/T0 fluctuations are always much smaller than .\pu/pu by a factor varying from 3 to b.
The small size of ATQ/TQ is caused by the fact that the flow is adiabatic, and it should be zero if the effective Prandtl number of the wake was unity. As will be seen later, with very small .\T0 the so-called "Strong Rt ynolds Analogy" holds and enables one to predict the temperature (or density) fluctuations from known velocity fluctuations.
^Formally, inclusion of sound waves introduces three more terms in Equation (31) and three more unknowns: The pressure fluctuation and the pressure-velocity and pressure-density correlations. It should be also noted that both Equations (30) and (31) are linearized, that is, applicable for small magni- tudes of the unknowns, M, T, a and T.
-37-
I i
ft 2 ^•
M -
5 > ■s. >
H H
u ■^
■r. H ^ u c Eu *"* Si OC
5
S
-38-
o . ^
o • -
o
♦ J
• •
o • -
o
o
o
•
•
•
• -
0 • —
0
0
0
•
-
• -
o •
o • —
o
u 1
M
•
• -
• -
1 « 1 1 I 1 1 1
] I a
m
O z z o l-t
H < H
m
tn
E^
u
c c Z H C H H < H -J
a: a: < 5 > O
-39-
3 w a» >T
<r >; r. F^ ■ ■
CO
CROSS-
(FIXKI
u: z !■ a: B •■J ^ t-
cs P H a^ L: u: as — i-1
s: 2
c J ai
1 1
LUX
AND T(
IN THF L.
O CM i z
in u M H
MM o c z TT o z ^ o
VARIATIO
CORRKLAT
Q
o c
o
o o
INH o oo
o
o CN 5
•A0-
0.10
0.09 —
0.00 —
0.07
U ,06
0.05
0.04
0.03 —
0,02
0.00 0.40 0.80 1.20 1,60 ETA
2,00
FIGURE 17. TYPICAL VARIATION OF THE RMS MASS-FLUX FLUCTUATION (NORMALIZED WITH ITS LOCAL MEAN) IN THE LATERAL DIRECTION
2,40
BJ420U
•41
n
» 5 B
5 s 3 -
ac — Id - =
">$
H a: —
C. r-1 i—i
X
c
< [d > N
a. Q >■ 2
-^ Id ■ 9 Q M
c
<N
(01 X) 1
■42-
o A o
o e
o
0.3 o M (T - 0)
• T (T • 0)
0.1
o e o ApMio) o Pu(o)
o o
o
-
.01
003
o o
o o o 0 o
ATo(0)
-TTÖT
j I i I i I 16 20 24 0 8 12
XSTATION NUMBER B1422U
FIGURE 19, VARIATION OF THE NORMALIZED MASS-FLUX AND TOTAL TEMPERATURE FLUCTUATIONS ALONG THE WAKE AXIS
-43-
Laterally both types ot tluctuatijns »ham the- otf-a-.is laxinur t harac tcristits ot sytnnetric tree turbulent tlows; this will be discussed later.
<*• VeL)c Ll\ Flue tujl i Mia . The axial \ariatu)n .> t" vclocit} iluctuations \u/u is shown in Figure 20. As with the axial behavior OJ \To/T0 and Vu/pu, the iluctuations m veh- i^ .- initially increase until they reach a value ot about O.Ü<? at a distant« .>prox i.mately 200 diameters trorn tin body and thereatter decrease. In Ltie end oi the ran^f probed (beyond X-Station 17) the tluctuati'ns become quite anomalous. It is conjectured that this rather abrupt change is due to incorrect smoothing ot the J tactors, that is, to the artitically decreasing J shown beyond that distance on Figure Ö. To test this conjecture the loll owing test was pcriormed: the J values (tor each heating current) at X-Statiun 21, Y - 0 were taken as inputted into U'Kb-IV program but prior to the dUMfii noted around X-Station 17. Actually, the J values at X-Station 15, Y ^ 0 were used. The results were as lollows:
Using J trom X-Station 21:
T = \u/u ■ 0.0049
u = V//D = o.o JH
Using J trom X-Station 15:
T = 0.011J
O = 0.019
Two very important cinulusions are drawn trom this computition: (1) it the J's used in Lin.' "anomalous" region (X-Station 17 to 22) are made identical to those prior to that region, then the \u tluctuation levels come back on what seems to be the level properly expected; (2) the density f luctuat ion \/: are almost completely una.Uectcd In changing J. In changing J, \u changes by about 250 percent, whereas \p by about 3 percent only. The explanation of this behavior is ao tollows: In the computational nethod used (which) finds the fluctuations from the shape parameters of a curve fitting experi- mental points), the velocity fluctuations result from the slope of a curve (specifically, the e /e^ versus (e.T/ea) curve of Equation (32)), whereas the temperature fluctuations result from the intercept of this curve with the eT/ea axis. It turns out that the slope of the curve is very sensitive to J, whereas the intercept is not. At this juncture, the anomaly in J is studied so that its cause can be located.
Lateral distributions of the velocity fluctuations are typically shov/n on Figure 21. This lateral profile follows the general trend of the fluctua- tions in \pu/pu and \T0/T0: a region of relatively low turbulence on the axis, with a considerable increase off axis and the natural decline toward zero at the wake edge. Note that the maximum in the fluctuation intensity occurs at r) definitely higher than 1.0. This maximum is heretofore considered to mark the lateral location in the wake where turbulence production, shear,
-44-
.2
.1
o TAU (Y » 0)
• SIGMA (Y - 1)
• • •
9 P(o)
• •
.01
.001
o o Au(o) u(o)
o o
L_ o O
o
ANOMALY TRACED TO ANOMALY IN THE J
j I i I I I ■ l ■ I ■ 0 8 12 16 20
XSTATION NUMBER
24
B1423U
FIGURE 20. VARIATION OF THE NORMALIZED VELOCITY AND DENSITY (TEMPERATURE) FLUCTUATIONS ALONG THE WAKE AXIS
-45-
M
—
C — -
u H -
X
O c C o
c
(01 x) nvi
-46-
is also Liu1 greatesti However, the mean-flow experiments described in Refer- ence 1 indicate that the region oL maximum shear lies nearer Liu point Ji - 0.85. At this stage the conclusion is, therefore, that turbulence production alone cannot account for the maximum in \u/u.
c. Density (/IVinpcraturc) Fluctuations. The axis value oi the fluctuation AP/p in the density is shown in Figure 21, while Figure ^2 shows a typical lateral distribution. Because of the insensitivity oi this type oi fluctuation to J, there is no abnormal scatter in this data. It is significant that this fluctuation is higher everywhere than Au/u, and this differenct will later be explained on the basis oi the "Strong Reynolds Analogy" for an adiabatic body.
2,6.4 THE FLUCTUATION SPECTRA
In addition to the resolution oi the fluctuations into the different modes (e.^;,, velocity and temperature), it is necessary to carry out a spectral analysis for each mode separately. This analysis is clone by the WEB-VII com- puter program, which supplies additional information for each point in the wake such as the longitudinal integral scales of velocity and temperature. These computations are not completed as yet. In what follows, the analysis oi spectra is performed (from the- WKB-1V output) on the modally unresolved hot- wire output.
Figure 2J compares restored spectra of the signal at three different positions along the wake. The absolute Level of these spectra is irrelevant at thi;- point, but the other features shown are significant beyond the context of tin present experiment.
se. , , ipre- ont has a random spectrum (probably much like that of turbulence)
with a superimposed peak. This is called the "intermittency" spectrum. In reality the hot-wire responds to a superposition of this spectrum and the actual turbulence spectrum, and it is apparent that the peak persist:
s _ Im
-47-
0.16
0 ,08
0,00 0,40 0o8() 1.20 1 ,60 ETA
1,00 2.40 2.(;i
B1425Ü
FIGURE 22. TYPICAL LATERAL VARIATION OF THE NORMALIZED DENSITY FLUCTUATION
-48-
10 I I u J_J I I IM 1
10
FREQUENCY (KHz)
10
B0866 V
FIGURE 23. EVOLUTION OF THE HOT-WIRE MEAN ■SQUARE VOLTAGE OUTPUT Sl'ECTRUM
ALONG THE WAKE AXIS
-49-
SPECTRAL INTENSITY (ARB. UNITS)
f(KHz)
FIGURE 2'+. TYPICAL U TERAL EVOLUTION OF THE HOT-WIRE MEAN-SQUARE VOLTAGE OUTPUT SPECTRUM
-50-
Lt«, ml
h-
1
This Interpretation was first thought likely in the axlsyrametric wake work
(scv References 4 and 5) and was Ln fact used to compute the Eront waveleug ■V, in that experiment, ^ivin^ /\p*9L«2dj here L is the transverse scale a
d the approximate wake diameter. The interpretation can he LurLher Strengt ened ii a closely similar Ay is found tor the present experiment. Using a
peak frequency of 360 kHz and a stream velocity of 600 meters/sec, a wave- length Ap = 1/6 cm = 0.17 cm is computed. Furthermore, d, as defined ahove is twice the distance from the axis to the root-mean-square position of the turbulent front, represented by YKT and shown versus x on Figure 47, page 9
ol Reference 6. At X-Station 7, *| ■ 0.4 x lü-^inch)^ and Y^ - 2 x 10^. Therefore, d - 2Yn ■ 0.04 inch - 0.1 cm, so that ,\|.-/d ■ 0.17/0.1 - 1.7,
whereas the axisymmetric wake Ap/d ■ 2 as noted above. Although exact identity is not expected, it is clear that the ratio of the Iront wave- length to the wake diameter is nearly independent of geometry, as expected.
2.7 SCALING LAWS AND SIMILARITY
It remains to show how the present turbulence results car be used to derive or support scaling laws which are useful in predicting hypersonic wake properties. In the absence of a theory of turbulence, the present results can be used to test and support the most, if not the only, reasonable empirical
scaling laws grouped under the title "Dynamic Equilibrium Hypothesis" (DFH).
The DEH emerged from the original work of Townsend (Reference 8); its credentials include a satisfactory demonstration of its applicability to com- pressible flows by Morkovin (Reference 10) and equally satisfactory prediction of the results of the only detailed compressible wake experiment to date (Reference 5). In the absence of heat transfer or sound waves these scaling law detailed in the latter reference, give the following prediction for the self-
preserving compressible wake:
P(0) .\u(0) ■ fen) (23)
n 3 \ u / \ \?(0) / LU;
(34)
^ = a- i) M2 - T u
r = -1 a "i
(35)
(36)
W0) uoo-u(0)
\P (0) = Pflo-P(O)
;(0)
8(0)
oo 1/2
P(0) J
Poo J 1- w
(37)
(38)
-51-
^(0) uoo - u(Ü) _ (L-r) (1-w) p(0) Au(0) S 00 (39)
If the mean flow properties are know as a function of x, the above formulas can describe fully the fluctuation magnitudes and their variation from point co point in the compressible wake. Since the physical quantities represented by the above symbols are now known (for example r^ w. p. etc.. are known from the mean measurements of Reference 1 and the turbulence properties are presented in Paragraph 2.6) the objective of this paragraph will be to see if these formulas indeed hold. Note that S has been determined to be 0.84 for the present wake, while the DEH gives the value of g(0) as 0.14.
Program WEB-VII gives the measured turbulence properties in a form exactly as shown above. Since the WEB-VII output is not available yet, this compari- son will not be made as complete as desired. Thus, in Figur«! 25 and 26 the lateral distributions shown are in the form Au/(up-u(0)) and AP/(p-p(0)) rather than the form suggested by 'quations (33) and (34) which amount for o^wrPreSSLblllty; the rationali^tion here is that at these far distances hW/p« is very close to unity anyway. Note, first that the scaling with T] is poor until about X-Station 11. Beyond that station the data collapse on well-defined curves; lateral similarity is thus obviously attained both for the velocity and the density fluctuation, as predicted by Equations (33) and U-O. The shape of the correlating curves will be discussed later.
l^ llln^fc'^un^3^1 8(0) Can bc' CheCked by Pl^LingAu(0)/(uQc - u(0)) andap(0)/(poo -P(0)) versus x. In Figure 27 the asymptotic values of these normalized fluctuations, drawn in solid lines, are obtained from Equations (37; and (38) in the limit Poo = p(0) and 0)= 0, that is, in the far wake:
lim Au(0) X-»00 UoO u(0)
= Vs(o) =V0-14 = 0-38
1 im x-»oo
AP(0) . YäreT", 0.375 P(0) O.S'i
■ 0.45
(40)
(41)
The data show remarkably good agreement with the value of g(0) used above-, the slight deviation implying n g(0) a little greater tha 0.14. In this figure three distinct regions are distinguished: Up to about X-Station 3 the transition process is still continuing; from there to abou^ X-Station 8 for the velocity and X-Station 12 for the density the fluctuations deviate considerably from the DEH-predicted asymptotic value, which sets in bevond those stations. The disparity in the approach to equilibrium between the two fluctuation modes is, of course, predictable because of the generallv slower decay of temperature in high-speed wakes. What is interesting is that from work donc^ earlier the initial (relaxation) values of Atl(0)/(uai - u(0)) were predicted to be higher than the asymptotic value, as indeed verified in Figure- 25 but the density fluctuations, predicted to be small until they reach the asymptote, actually overshoot the latter, reaching a level of about'0.75 at about X-Stat ion 6.
-52-
0.5
□ Q ^
- A O O
A
O
A
XSTA 11
XSTA 9
XSTA 7
XS'IA 5
XS'IA 1
XS'IA 1
•
k • o
' o* 0
■
- Ar
1^-11(0)
-
1 |
n
A
□
i B1427U
FIGURE < LAtEiAI V.RIV1I0N OF THE AXlAi VELOCITY FLUCTUATIONS »ORMA"^ 1- illH TH.- LOJA[ W.KK VELOCITT DEFICIT M^ SELF-FJESEIVINC
FLUCTUATIONS (FAR WAKE). JEfegj- NEAR (RELAXINC AKE.
■53-
1.0
.5
XSTA 13-22
1.0
;
I
• u A
- A •O A
a 0
o o
AP Pio)
o XSTA 11
• XSTA 9
^ XSTA 7
1 A XSTA 5
A a XSTA 3 o ■ XSTA 1
o • AA
o
• a t
■
1
•
1
• o A A A
0.5 1.5 2.5 3 B1428U
FIGURE 2b. LATERAL VARIATION oh' THE DENSITY FLUCTUATIONS NORMALIZED WITH THE LOC/>L WAKE DENSITY DEFICIT. vBOVK: SELF-PRESERVING FLUCTUATIONS (FAR WAKE)« BELOW: NEAR (RELAXING) WAKE.
-54-
0 a.
0 3
a8 8 3
CL 3 <3 <
3
PQ
o f J
I
I"»
as
B X
•
•o
o •
• —
00 vD CN J.
'Si
t H
E I
H H
C H J M
H a .z
ss
OS 0
r i
S
-55-
From a dimensional standpoint, the velocity "scale11 at any distance behind the body is, of course, the local difference uu, - u(0); thai is why liquation (37) asymtotically connects Vi and u^ - u(0), The question arises whether Vi can ever exceed u^- u(ü). in Figure 2M, the maximum values ol the fluctu- ations Au/u« - u(0) and \p/(p«, - p (0)) are plotted as obtained from the off-axis maxima of Figures 25 and 2b. 4s.ymptotically these reach values oi i). 70 and 0,80, respectively. In the relaxing region, however, \u/(uoo- u(0)) reaehes a value equal to one, and near X-Station 6 the density fluctuations reach 125 percent ol the mean density difference across the wake, rhe precise physical rationale allowing such Large fluctuations is not clear.
Sine.' g(ü) controls both the velocity and the densit) fluctuations .lar from the body, a simple check of the DEH Is suggested by Equation (39), Figure 29 plots the Left-hand-side of this equation as measured directly, and Indepen- dently the right-hand-side (by a solid curve) with the w, r, and S supplied from the mean measurements. As expected, the agreement Is poor in the relax- ing portion oi the wake, but beyond 900 diameters the data are cl ise t • the expected behavior, In fact the data beyond L400 diameters, it corrected foi the difficulties met Ln computing J, continue in very good agreement with '"'■ the "theoretical" prediction,
The relative magnitude oi density (temperature) and velocity fluctuations wl:h respect to the stationary hot-wire, are given by Equation (39). Figure 10 shows '.hai the expectations are met (especially with data corrected for J as discussed above) Ln the self-preserving wake, Ln the latter, in fact, th< Strong Reynolds Analog) is closely followed by th» data in the Lateral coor- dinate except very near the wake edge. Her. the temperature fluctuations •'ri uncommonly large, as was also observed en the axisymmetric wake (Figure 35, pa e 7M, Reference 5). This is explained as occurriuj2 due to intermittency, implying that the temperature "jumps" across the turbulent front are much larger than th< corresponding velocity jumps.
thould be added that the Dynami« Equll lb Lbriian Hypothcais predicts that for ■': abati< ,.'ak. \T , > 0 and r(, ■ -1. Both >i those predictions, and espe- 1 lallj th. latter, are fully borne out Ln the present experiment, as shown by Figures 15 and JO. The result is that, one« the veloclt) fluctuation Ln .in adiabatlc wake is known, the temperature (density) fluctuations can be predicted. In fact, the ratio ol densltj to velocity fluctuations is a simpL function of the Mach number. This is well born« out Li Figures M and 32,
A final point concerns tlu rather high velocity fluctuations measured in the wake« Figur« 3J compares these measurements aith data taken by Townsend (Reference 8) at low speeds. It should be noted that Townsend's mean- velocity measurements are correlated Ln tin following empirical formula (Reference 8, page 162)S
Uoo - u u u(0)
-♦ ,-+a
^ rf
(42)
56-
o
—i CO
x:
H
x
H
^ •X
1** r- W
UN ' > i—i
r-1 U. LL
U, O — Üi
^ JL X ^j
•^
^ J ^• <f UJ U
— _J
•^ u S
^ -
C/5
X C/1 w- X.
s^ [_ H X s—.
s*
^■. s
r~ ~ _J - [>J r.
H Z
x
td
H
-57-
o
2:
tSl
33^ :—' .—J W U ba tt H 1 L_
2^ i -u -u — r: r
; X
-
>- cd H -
0 >
■r.
—1 -y. ■ '' x 1— C/3 v •_ #—, ■ '• » '.n ^^ *t
^ - — .-- CJ ^ X _:
-1
—
^J
[(o).i-00a](())cy7
■r5H-
{)
•0.2
■JT
-0.4
-0.6
.0.8
1.0 0.5 1.0 1.5 2.0
• •
•
•
• •
• •
•
•
• •
•
• • 1
• •
•
•
•1
•
•
2.5 r.
B1432U
FIGURE JO, LATERAL VARIATION'S OF THE VELOCITY-TEMPERATURE CROSS-CORRELATION COEFFICIENT
-59-
CO
X
i
<
X
6fl
-
< z <
-
I H
—
—
o c
M (I-O
pswtsnifT? [(ow/(owtn -60-
XSTATION 15 (X ■ 1173)
(/vr/'n/(Ai7V)
Cy-1) M2
O o
o O rt o • o
PREDIC1 ION FROM STRONG REYNOLDS ANALOGY
I B143AU
FIGURE 32. TEST OF THE STROHG KFVNOLl.S ANALOGY IN TüK UTERAl DIRECTIO«
AT CONSTANT X
-hi-
.0
1.0
0
2.0
1.0
PRESENT WORK (^3)
ÄtJ(O)
P l -ü<0) X,,
L ÖY
TOWNSEND (M=0)
*) - 0.76
FIGURE J3
3.0
Bl^SU
VELOCITY, SHEAR, AND VELOCITY PLUCIUATION I'ROFILKS (ABOVE) CGMPAIED WITH SIMILAR PROPKRTIKS OF LM-SfOB WAXES (lEUW)
-62-
wliL-re
(43)
and d is the cylinder diameter. This lateral coordinate a .an b« rc-laud to the- n used herein since for cylinder the urag coefflcleat CD 1 ami
since, in the present experiment
Y =s Y
L =
a: =
h I)
i.i |l/2 [(••-xo)/^^]
Since in Townsend's case i>ne ohtains
l^2-w1'2 nr
The result becomes / ' .[^A (44)
L =
and
4.r)b
Y ^.56
(45)
(-6)
With this Li-anslornation from a tOT), l.quation (42) becomes
^ -0.69» ( 1 ♦ 0.051^1' u = e
which L. in lOOd agreement with the nean-v.locUv dl.ttlbutlon found Hi
the "^esent work:
-o.ey^2
u - e
I„ Fiuru 3J tht u .urv.s UC Lhus identical, as arc lh> corrMpo«dt»i LI tb ion af slK.aräu/3Y. The slBni,icancc ot th. Utt« « ttat itt
In ^present wake. The net result is that the fluctuntten thukness of
-6J-
the present wake is considerably thicker than at low speeds. No explanation of this phenomenon can be offered at this time,
2.Ö CONCLUSIONS
The following conclusions can be drawn from the present work on two-dinu-nsional wake turbulence:
(1) General Conclusion: The data obtained support firmly the empirical body of predictions known as the Dynamic Kquilibrium Hypothesis.
(2) The axis values of temperature and longitudinal velocity fluctuations reach asymptotically the same percentage of the mean axis values as encountered in previous experiments, including those at low speeds.
(3) The wake tola! tenperature fluctuations are relatively insignificant when no heat is ex- changed between the flow and the bod v.
(-♦) The local velocity Ln the wake is Almost per« foctly Mti-COfTOlOfcod with the local tenpera- ture; Ebon is no correlation between total temperature and mass-flux fluctuations.
(5) For adiabatic wakes, the temperature (density) fluctuations can be obtained, bv the Strong Reynolds Analogy, iron a knowledge of the dis- tribution of mean Mach number and velocity fluctuations.
(6) Near the wake edge the Reynolds Analogy fails; it is conjectured that the front corrugations of the wake can be thought of as "iumps" in the mean properties, especially the tenperature,
(7) Similarity in the distribution of fluctuation occurs long after the n.an properties themselves become sei f-similar.
(8) By comparing almost all measured mean and turbulent properties with their low-speed counterparts, it is shown that the proper scaling length is not the body diameter but rather the appropriate momentum thickness of the wake.
(9) A notable exception shows in the lateral distribu- tion of velocity fluctuations; the maximum of these occurs farther from the axis Mid is higher than its counterpart at low speeds,
-64-
SECTION 111
1NTERM1TTENCY OF THE TWO-DIMENSIONAL COMPRESSIBLE WAKE
J.l PURPOSE
In addition to the mean-lK>w unest la^at ion of tlu- LW )-d urnns i »nal wake (Reureiue 1) and oi its turbuUntf Held (Section II), Us intermit U-iu v character ist us have also been measured and will be reported Ln this
Sec t ion.
The intermittent 11 ow plays an extremt-ls im( ortant role ui tlu characteris- tics ol the hviu-rsonic wake as viewed by a ground observer. In tlu v >rk with the ax 1 symmetric compressible weite (Riureiuc -) the Lnternittenc} measurements gave the rms location Y it tlM turbulent ir-nt aiu: its standard deviatim«. These quantities were lounu to bear nteRericell) the same relationship to the transverse icale L as in tlu tWO-diaenelooel wake oi Townsend's (sec Reureiue 3 , paee 42 ). This Lmportent finding, implying that neither the geometry ol the body nor compressibility effects VL and O/L, would so greatly sunpliiy hypersonu wake caKulatims that it merited additional study; hence the mt erm 11 tency measurements with tin
present two-uimens lonai wake were niadi-.
3,2 TECHNIQUE AND PROCEDURE
The technique necessary lor this type of measurement is described in greet detail in Reference 5. Brietly, the hot-wire anemometer is held at various lateral positions Y and at eac h X-Station. The heating current oi the element is increased to tHe maximum sensilivity possible and it', ac signal is Processed through the intermit teiu y meter built especially for such work at Aeronutronic. Through a series of rectifying and .lipping actions tin« instrument distinguishes between the time the wire is immersed in dc turbulence and the time it is not; its output in a fractioe ol one volt ac then gives the "intermittency lacLor" QCfCl which is the fraction ol turbulence immersion time to the total time. In a fully turbulent fluid -Y = 1, whereas whenever the sensor is so Lar trom the axis that it never encounters turbulence, 7= 0. I17(Y,x) is known then Y(x) end <f (x) can be calculated by statistical methods (Inference 11, pace IC) .
In addition to 7, the average wavelength of the front il important. A measurement oi the so-called null frequencies, N sec"1, can give this sort Of wavelength in the form of statistical scale of the front LI the latter is truly rand.mi. For the axisymmetric wake and aleo from work with the jet (Section IV), it appears that although the front is truly random m amplitude it may not be truly random in time and the existence, it any, of its wavelength (rather than the purely statistical scale) became
another objectives of this work.
Hot-wire No. 8-2/1 was used for measuring the two-dimensional wake mtermit- tency. Data were taken, beginning at Station 2, lor alIX-Stations used
during the mean and turbulence measurements.
-63-
3.J RESULTS
Figure 34 shows the Croat lateral radius Y and Us standard deviation »t
normalized with the t ransverst^sc ale L, plotted eloilg the wake. It is quite evident that the ratios Y/L and a/L are constant within the scatler Qlotfl that L increases by a tactor ot J in the rant« 200<I<1800)« For Y/L this constant value is about 1.96, whuh is only 7 percent lower than the value expected on the basis ot the known behavior oi wake tlows (see Table III, Refer-nce 4). The findings ot the HO experiment are therefore turther substantiated.
The value ot a/L however, shown ^n Figure 34 to be about O.JH, is con- siderably lower than expected, by a tactor ot 2 or more. This is shown in another manner on Figure 35, where the lateral distribution ot 7 is shown i>r all XSTATIONS. The data are scattered, so wmdk so that a distinction between "near-wake" and "far-wake" behavior is made. What is important, houe^er, is that the ragioa of intermittent activity is much shorter (and the extent ot fully turbulent fluid much greater) than Townsend found at low speeds; this means that a should be als,, much smaller, as Figure 35 already showed. _ln the mean-time, the distribution of intermittent activity around Y_is tairly symmetric; this is also illustrated on figur« 3ö. That Y ^rows as x1/- is also well illustrates in figure 37, where the Y corresponds to the maximum of the probabilitv distribution
To explain these findinus, two alternatives seem likely: (1) tlurt- is a substantial ditterence between this wake and Townseno; (2) there were inadequacies and errors m the experimental method. At this stage, the second alternative appears more likely. Since the corrections applied by computer to compensate tor the hot-wire trequemx response are applicable to the rms sense only, there is much ot the intermit tenc y behavior which the wire does not see. The turbulence caused by the truU its, m tact, proportional to 7(1-7) and thus is maximum at 7 - 1/2, where f is located. Near the wake axis (7= 1) and at the edge 0= 0) this turbulence is small and the wire does not sense that it is crossing into and out ot the Cront« Under these circumstances the Location ot | will be givan correctly but 0 will be greatly underestimated, as indeed tound.
The conclu.ion then, is as tollows: the position Yot the turbulent front is found with fair accuracy t..r WEU, hut the standard deviation is under- estimated due to inadequacies m the technique. Improvements m the hot- wire anerometer, presently under wax, will enable a nor« accurate repetitior of this measurement.
-bb-
o o o P vO 00
H C/3
m H M
o o
N
AN
D
AL
E
O U M V2 H M UJ m c/) o at CL, U
> H w Z i5
K H H Q SC a UJ !2 J
o o o
3 UJ CC X
<—1 3 H X
H W H
H Q
b b] 0 N
H Ol -J Z < 5 S M as H O < Z H ai Z < O ■■> M
H T .-< w •*
o < I-1
o H > iTS X UJ
< Q
•
r^
LJ s UJ U
o O
Psl
-67-
.8
.6
.•4
0 0
NEAR" WAKE 1.0 -;=■ —
TOWNSEND (LOW SPEED)
FAR" WAKE
B1436U
FIGURE 35, DISTRIBUTION OF INTERMITTENCY FACTOR IN WED COMPARED WITH LOW-SPEED RESULTS
-68-
H U (14
z >- c
s ,w' ^j
t— "S
z ^ >— p
^ ~ }—1
— (/)
M C
H H pi j^
5
-69-
>> •
x; c
u j a:
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;—1 ^ 2 2 "S
z 2 ?: — m i—t _^.' ^ H < H a y. 0 F- X z u
t/3 ir'
H ^ä
a:
-70-
SECTION LV
TURBULENCE BEHAVIOR OF THE PLASMA JET
4.1 CRITIQUE OF CURRENT TURBULENT PLASMA RESEARCH
The work dc^vihed so lar deals exclusively with perfect-g«! wakes devoid of ch-mical effecti, and from which geometric, niechanical, and to some extent thermal Leatures ol wake turbulence .an be extracted, A second area of effort, described in this Section, deaN with free turbulence In which the wake feature is discarded in favor of producing hyperthermal and electronic phenomena. The turbulent plasma jet, su.h as employed here, is a unique and inexpt ..s ive tool lor producing such phenomena.
It is lair to say that, m vieu oi the present shortage of and demand for Information on electron behavior Ln turbulent plasmas/'-- accurate and well- resolved data obtained from laboratory plasmas are significant regardless of their direct applicability ir the hypersonic wake problem. Ihns, the data alreadv obtained under the present contract (Reference 6) as well as those of Guthart (Reierence 12), Granatstem (Reference 13), and Johnson (Reterence 14) have tor the first time yielded information on the electron densitv fluctuation intensity and spectra, the correlation scales, etc. Phenomena peculiar to electron benavior (contrasted to ordinary turbulence) have also been observed and are reported in Paragraph 4.3 below.
For these data to be useful for the present purpose, they should bt com- piled into scaling laws. Preientl) these scaling laws appear very difficult to »btaln theoretically. Even in the case where they are obtalnabl« experimental lv in a jet, their simple transposition to the case oi th< wake it not straightforward, U the consensus >] References 6, 12, IJ, and m was tor example, that the turbulence scale ol electrons is a constant traction of the local jet radius, there is still no assurance that the same relation applies to the wake. Even lor totally inert chemistry, as another example, the laws of axial electron density decay assume different forms depending on compressibility (high or low speeds) geometry (two- dimensional or axisymmetru) and type ol flow (jet or wake;.
It appears that the major usefulness ol the |et experiments is to find an empirical connection between the electron turbulence behavior and the turbulence behavior of the overall gas. For instance, if a unique relation between the electron and the temperature integral scales is found, then the application to the wake would only require knowledge of the temperatun scales in the wake - knowledge which is now be ng accumulated under this contract (Sections 1 through III). It is therefore necessary to measure
*A substantial bod. of knowledge exists on the so-called 'plasma turbulence whuh, however, involves phenomena on the atomic scale with electric and magnetic fields and is of no consequence her« .
-71-
the tlu-.d-dyna^cal turbulence in the Jet, as well as the electron turbulence; hs has been done In the past year under th.s contract. The next crucU]
HTnT* nH T," '^ ^ 0r m0re variables 0" «»»ich thi. empirical connec-
for\tPZ / haS a!ready beün dinlL' (and' in f*ct« ^ ?*°K™ solved) for he two extremes Ln chemistry: equilibria flow (Reference« 15 and lb)
cont ou!n Z ^^^ }5)' Fo' the P«"nt. the choice of parameter ' unc e^ "' H' ^nneCtl0n betwetn ^sdynam.c and electron 11 uctuat ions is unclear, as the discussion of turbulence results will show.
There is one phenomenon which does not depend overtly on the chemlstrv: that is turbulence intermittency. Intermittency data in the plasma" jet were taken during the previous contract period (Reference b. pages 176-180) In he present contract period these data were reduced and interpreted and Will be discussed first prior to the turbulence results, in the following paragraphs.
4.2 INTERNITTENCY IN THE PLASMA JET
The intermittency properties of wake flows have already been obtained and discussed in Reference 4 for the axisymmetric wake and' in Section III of this report for the two-dimensional wake. Scaling laws have been given (Reference 4. page 47) by which the geometric structure of the hypersonic wake front can be predicted. The question now arises: will these .caling laws appear identical to a "temperature" anJ an "electron" observer? In other words, does the front surface, which is know,, to abruptly separate gases ot dissimilar temperature also separate the electron-rich fron, the electron-poor gas?
4.2.1 PROCEDURE
In the present experiment the front properties were measured with the hot' wire anemometer and the Langmuir probe. The signal iron, the hot-wire ampliner (or ehe ac amplitier connected across the load oi the Langmuir probe) was ted to an intermittency circuit; this circuit, described in Reference 4 is not unlike similar devices used by Bradbury (Reference 17) and others, and supplied the intermittency factor as a friction of one
volt dc The factor-* was recorded at each of about 20 radial positions \ at each x The rms front position V and its standard deviation a were then obtained from the usual formulas:
00
*/ dY d7dv « (4 7)
0° i dl , 1/2 (T-T)
2 g dor-nj (48)
In these formulas computational convenience requires that 7 is expressed
points'ithTh0' ^ r15 WaS ^ ^ '-'>■—l-L^ng the experimental points with the computer. !
-72-
In addition to Y and a the autocorrelation scali' >>l tt.i front Lfl oi some interest. It the front behaves like a staLimary random variable U is possible to i ind this scale trom a measuremeiu of Liie s.)--ailed null- crossings (or null frequencies) ol the front, tluit. is by the frequency N0 N(Y) at which a sensor, located at V ■ Y, enters tbe front. To this end the distribution ol null trequencies N(Y) with radiyn Wtie recorded by electronically counting the rectangular pulses at tlie Schmidt-trigger output oi the intermit tency circuit. These distributions, which of course peak at or nea*- Y, were also computer*fitted by polynomials. The ir.icroseale >f the front is given by
\
£2 uill
o (Ay)
(50)
where u(Y) is the jet velocity at Y. An alternate and possibly mire meaningful front "wavelength" is simply
A =^1 F N
o
4.2.2 RESULTS AND DISCUSSION
Figure J8 shows a typical comparison of the distributions, with radius, of the intermit tency factor, the temperature, ana tin. electron density. As expected, the fluid is stroogly intermittent at distancei from the axis at which the mean temperatures is very close to the ambient. Also from Figure J8, observe that the corresponding relation between electron density and the intermittency factor is analogous but highly inconsistent from one x to another: at a fixed value of 7 ■ 0.5, for example, rf varies considerably in the x-range investigated.
Important questions to be settled in analysing the in term i t ten», v data include the randomness of the interface, the coincidence between electron" and temperature-interface and the comnarison of the front geometrv and behavior to that of low-speed jets. The growth of tlu front "radius" Y is shown dimensionally in Figure 39 and non-dimensional1v as Y/L, together with the standard deviation (j/L, in Figure 40. There is Little doubt that these two quantities grow linearly and scale with L, and that they cer- tainly are independent ol the method of measurement. With Y and a SO computed it is possible to make a test of the randomness of the front such as is shown m Figure 41; we see that the Gaussian distributional the intermittency t actor about the front position, mat is with (Y-Y)/a, again obtains in the fashion characteristic of stationary random variables« In the :;ame figure further evidence ol randomness is supplied bv the distribu- tion of the normalized crossing frequencies N/Nniax about the radial Location ^max = ^(^max)• The scatter is appreciable, hue enough data points are available to illustrate the Gaussian behavior of fJ/N—-x characteristic ol randomness. As before, there is no systematic difference between data taken with the hot-wire and data taken with the Langmuir probe.
-7 3-
00 o SQ
E M AC H CM
^-^P" K DC
H OS p >-
— z ^s H P z c u ■ — H H U < w
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-74-
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g ^
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-75-
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O d d
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x B
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I—i
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5
m fi «M
-76-
1.0
0.8 -
0.6 _
0.*
DISTRIBUTION OF INTERMITTKNCY FACTOR
ABOUT THE FRONT POSITION
O LANGMl'IR TROBE
# HOT-WIRE
AlL JETS AND HAKES (GAUSSIAN)
J_
7 i
o
Y - 1
•e
1.2
l.o
0.8
"MAX
0.^
I .2 -
0 LANGKUIR PROBE
• HOT-WIRE
-r T
♦••i . V
DISTRIBUTION OF NBU rttQUElCUS
ABOUT THE FRONT POSITION
e - • • •••
••• *
o %
•o • o
o0 •
• /I. o
o o 0
* • •• o . • •
s ,i , %*•«t t— 0.. n.h o.H
.•••
^.. « " O o
o o * t
o, e
0 ( % •a_0o
to oo
'MAX B08h9 (
KKTRF W. RADIAL PISTRIB T10N OP CROSS FACTOR IN THF 1FT
VA ,., ,. ,-, i:> Ml WtEWXTTEN I
-77-
The null trequencies N0. deaned as th. CfmU* t*m*mmc$m* measured at
rL^81'1^ the intCrta-'' -••• &»■* tO be very . ! ,se L, Lhe maximum frequency Nmax measured (at each x) at Yniax; thus. N. s N(Ymax) - N (7) "JW* as expected. Figure 42 sh.ws the variation ol N0 wuh x; •gilJ
he trequencies measured wuh the h.t-wrr. and the Langmuir pr ,be are Ib.ut he same at each x The decrease of N0 sh.wn U. i. f^ure immediately uggests the lengthening of the fr.nt s.ale AF (.. AF) expected as th.
turbulent flow widens with distance. However, the imputation ,t these scales trom Equations (A9) and (50) cannot be perlormed with the veluity data shown so tar; these latter are mean velocities, whereas what U oi ' course needed is the velocity oi the ,ront itselt or at le^t the mean velocity within the front - the so-called eddy velocity.
Measurement ot eddy velocitles within "corrugations- in the jet bouncary were made with the double Langmuir probe (two-w. e correlation probe) mentioned previously and pictured on page 12b of Reierence b. Eddy velocities with such a probe can best be measured irom the cross-c orre lat ion liinct^n ot thv probv Sl>,nals. Ln tht> pri,Sl.nt w,rk tht. m(rt. imitlVi.
method was adopted ol obtaining a Unite number oi dual-trace ,sc 11 lograms. oi the turbulence pattern as it was convected by the wires. Fro,:, these samples a rudimentary statistical distributiv n the local eddv veluitv was constructed at each point Irom which the mean velocity (and' its rluctua- fclon) could be extracted. The (mean) -ddy velocity at T was then Med in place of u in Equations (A9) and (50).
Reierence 4 describes expen^nts done on the intermit tenc v lealures oi expressible wakes and advises the use ot the "iront wave length" AF (rather than AF) as a more significant measure ol the iront geometry In Soim so evidence is drawn rrom observations (Reference 5) oi the t.rbulence spectrl
but'L h6 tr™l^Siti™ Y> that *« *»«« itseli .ay not h. trulv tmdom, bu rather weakly periodic at a wave length AF. The asymptotic u'm •f/L = u.N L oi th-s wavelength for the axisymmetru wake is drawn ir. Fi.ure UJ to which the ;et front wavelengths, obtained per the prewous paragraph, .re also presented. The agreement between these two muependent experiment: is quite revealing. The wavelength oi the jet iront appears to bear the same relation to L (about AF/L » 9) that it does for the wake
It snould be noted that the physical dunensions oi the iront are .nen here in physical coordinates, and this should be- actuated lor ccLting the present results with other experiments. In the latter the radius is
e c ke r •.• t
„w..^» »■•?■• HBHUb«« in trie lacier trie r usually normalized with the so-called hall-rauius r^-'. Thus Be, (Reierence 18) gives \'/rl/2 - 1.7«. Bradburv (Reierence 19) {.72 and Corrsin and Kistler (Reference 11) values ran^in, irom l.b5 to 2.00. From the present experiment (see Figure .0) ._we obtain Y/L = 3.J5 on the u*Otm and in terms of the half-radius we get Y/r1/2 = 2.0. It thereiorc appears ' that quite a few jet experiments generally a^ree as to f/ri/2< It should be remembered, however, that heating the timid .enerallv increases the jet radius; the end result, shown on Figure 39. is that ourY blends iarther out, by about 30 percent, than Corrsin's Y lor example.
-78-
H
M
O Ö
Efa 5 z
H
H en H C
M
Ui
-79-
o o
oo o pa
D o o X
O
UJ ui _J 1 Z) M rs 00 on < 3 sr t— U c
M Li. o
M H U
C/2
H U U
o tu
1—3 5 2
T. O OC E
o
o
UJ
> <
P Q
^ ? E O D ^
en c/;
o o CO OQ | I a- a o Q
o
o
o
o
< o
g
^
o
o o rg <r
Ed
N Lu
O o O
-80-
The value of a/v obtained here is 0.23, not far from Bradbury's value of 0.22 or Corrsin's range of 0.23 to 0.29. However, iecke« et al obtained Q/Y = 0.16. This might be interpreted as a difference in intermittent properties between an inert contaminant and the temperature field, but it is more likely that Becker's method of measurement and perhaps differences in the turbulent Reynolds number are responsible. Becker and his co-workers have at any rate obtained a unique relation between the intermittenc> factor and the contaminant density distribution with radius. In the reacting jet employed here the electrons are distributed radially in an irregular manner because of reactions (see Figure 38) and this relation does not materialize.
4.2.3 CONCLUSIONS
The main question posed in this section has been answered: the front characteristics are identical for the electron-sensitive and the temperature' sensitive probe. The implication is that the intermittency characteristici of the hypersonic wake, as predicted from gasdynamical studies al also the intermittency characteristics relevant to the radar.
one. are
4.3 ELECTRON DENSITY FLUCTUATIONS
Data reduction has been completed on the magnitude of the electron density
fluctuations in the plasma jet, raw data on which were presented in last year's report (Reference 6). The final data reduction was accompanied by further experimental measurements needed to "till in" portions ol interesting electron behavior. In this section, the following is discussed: (1) Theore-
tical calculations on the validity of the Langmuir probe technique, (2) the final form of the rms electron density fluctuation magnitude as distributed axially and radially, (3) data-reduction of the electron density spectra, and (4) studies and interpretations of the very large fluctuation« observed in the transition region. Comparison with other measurements will also be
g i ve n.
4.3.1 LANGMUIR PROBE SHEATH CALCULAV10NS
The radius of the electrostatic sheath surrounding the Langmuir probe used
in this work is crucial to the validity of the data. Specifically, the
sheath ra'ius
a«Ae (51)
where \ , is the eleetron mean-free-path. The earliest computations of a, under this contract, were based on a combination ol the Lanmnuir-Mott-Smith and Langmuir-Blodgett theories (Reference 20). More recently tins computa- tion was replaced by one performed by Bettinger and Walker (Reference 21) whose attractiveness rests of its use of integral and conservation laws. Sutton (Reference 22) has proposed that the sheath is computed on tin basis
-81-
of work done by Laframboise which is basically an extension of original work by Langmuir. To compare these choices for computing a, the following formulas were plotted:
(1) Langmuir, Mott-Smith and Blodgett:
3/2
r 2-8\r ) ^ (52)
(2) Bettinger and Walker:
(3) Laframboise:
.a . . ... ik \0,6 .a/2 r (5) f = i-63 r n (54)
where r and h are the probe and Debye radius, respectively, and 7) the non- dim.nsional probe voltage T] = qv/kT. The former two equations are valid for h/r >1, whereas the latter presumably ur Ü.1-: h/rv2.
These relations have been plotted on Figure 44, Thev indicate that the Langmuir-Mott-Smith-Blodgett approach gives sheaths which are in agreement with the other theories for h/r = 1, but much higher than the latter for h/r»!. Because this theory is also the least sophisticated (and pre- sumably least accurate) of the others, it is concluded that the original estimates of a were unduly pessimistic; the results on electron fluctuations discussed in this report are thus more valid than originally thought.
4.3.2 MAGNITUDE OF ELECTRON DENSITY FLUCTUATIONS
Figures 45 and 4b summarize the final results of the electron fluctuation magnitude in the turbulent plasma. From these two figures, it is dear that the electron fluctuations undergo two phases: up to about 24 inches trom the nozzle the fluctuations are extremely large on the axis (about 5 times the mean) whereas beyond that distance they decrease to a small percentage of the^mean and develop off-axis peaks. The former will be called "transi- tional" or "heterogeneous" fluctuations whereas the latter will be called "asymptotic" or "homogeneous".
Perhaps the single most interesting phenomenon observed during the turbulence measurements was the very large magnitudes of the electron density fluctua- tion. It is statistically possible for the standard deviation of a stationary variable to exceed the mean value of the variable when the amplitude distri- bution of the latter is extremely skew. Such situations exist m the intermittent zones of ordinary turbulent jets lor any flow variable Q which fluctuates between nil in the ambient ("irrotational") environment and some mean level within the turbulent front. If the latter does not decrease
-82-
7 8 9 10
H R
Bl^SU
FIGURE 44. COMPARISON OF THREE THEORETICAL PREDICTIONS OF THE SHEATH RADIUS R IN TERMS OF THE PROBE RADIOS Rp AND DEBYE DISTANCE 11.
-83-
10.0
n(0)
0.04
}4 18
B1439U
FIGURE 45. AXIAL VARIATION OF THE RMS ELECTRON DENSITY I" LUC TU AT I ON S . NORMALIZED WITH THE LOCAL ELECTRON DENSITY, ON THE JET AXIS
-84-
ia
I
r.
it Of Z
•*
5
^ c
-85-
too last with increasing radius then it Li well known thai AQ/^ can diverge with radial uistance. In tact lecker, Botte] and Williams (Reference 18) have observed this divergence by utilizing an inert contaminant concentre« t ion for an ofeservab Le .
The possibility that the lar^e fluctuation! on tbc axis pictured on Figure 45 are caused by the intermit tenc y is excluded by the simple- tact that the llow on the axis is fully turbulent as already demonstrated. From the results thus tar shown m lact, it appears that we haw here a fully turbulent tluid with normal temperature fluctuation but with highly-skewed electron fluctuations. An oscllloscoplc study of the turbulent jet immediately showed Large "spikes" in the electron density time history at a point; these spikes are indeed what statistics would require to produce the Large An/n of Figure 45. Figure 47 showi a comparative oscilloscope study of the Langmuir probe and hot-wire output at various radial positions but at the same distance from the jet noszle, B\ properly adjusting the tcope gain it is possible to show conclusively, first, the differences between intermittent and tullv turbulent i 1 uv and, secondly, the differences between Langmulr-probe and hot-wire »utput in the full) turbulent region. Attention is drawn to the large spikes in i lu Langnulr proba traces which are clearly absent trom the hot-wire traces.
The appearance of the lar^e spikes persisted tor several inches in the upstream end of the turbulent sone studied, but decayed and eventuell) vanished as the probe was moved downstream; the fluctuation Level An/i; also decayed be 1 n-; unity as Figure ^5 shows. To complete the ptcture, an investigation of the laminar a'id transitional portions of the \et was nad< usiim a Langmuir probe thicker than described previously in this paper, so that it could withstand the much higher heat fluxes in the laminar jet. For obvious reasons the output of this probe was not quantitatively inter pre table, but it made possible to piece together a reasonable description »f the events leading to the' generation of the large fluctuations.
Figure 48 shows this picture« The Langmuir probe observation made is typiiied by an instantaneous "snapshot" of the electron density on the jet axis trom the nozzle exit well into the turbulent zone. In the laminar jet the mean electron density is h i ;h with an unsteady component consisting >f the' ree t it ier-dr iven 360 Hz modulation whose rms magnitude is about 10 percent of the mean. At the flow velocities prevalent here the wavelength >f this sinusoidal fluctuation is actually very much Larger than the Length >f the laminar *i.i. (au....' 10 feet compared to about 1 foot). In the transition region the breakdown r rocess mixes ambie-nt 1 1 u id with the ionized lluid; the formet is . Lectron-poor SO that larce "negative" pulcs (it one thinks of the electron current as producing a positive displacement of the scope beam) appear as shown on Figure UBi the signal is thus "negatiwK «ne- sided". The mean electron density thus decreases bei >w the maximum level, which also decreases because of recombinations. Farther downstream the spikes widen (but do not necessarily deepen), and still farther the signal begins reversing itself, i.e., becoming "positively ■me-sided". In this latter case the mean electron density drops eonsiderabl\ below the tops of the spikes, the lluctuati>n distribution is ver) skew and the rms fluctuation level is considerably higher than the mean Level, It is at this sta^e that the oscillograms shown on Figure 4 7 were taken.
-8h-
INTERFACE
NONTURBULENT FLUID
CAIN REDUCED BY 10
B0874 U
NONTURBULENT FLUID (n - 0)
SAME GAIN
GAIN REDUCED BY 10
B087 3 r
FIGURE 47. OSCILLOSCOPIC STUDY OF TEMPKRATTKK \M) ELECTRON DKNSITY FLUCTUATIONS
37-
LAMINAR TR/NSITIONAL - TURBULENT
/ MODULATION DUE TO RECTIFIER
MAXIMUM LEVEL
MEAN LEVEL
Mliin-r- X
/ \ 4£ s \J^ n
AB - 10% n / \
AT 360 Hz ^s \
^S \^
_^^
^^^~
An ^^^
^mm \ — —
FIGURE 48.
B0875U
SCHEMATIC OF TYPICAL INSTANTANEOUS KLKCTRON DENSITY DISTRIBITIO: ALONG THE JET AXIS AS INFERRED FROM PROBE MEASUREMENTS
-88-
It should a^aui be ■■ptllllUll that at thus .stai;i the I laid is lully turbu- lent fr.'m the standpoint >>t mt ermi t tenc y, a.id that turbuU:it tliKtual. MIS
m the electron density, of order 20 t.) 40 percent DI the -nean, exist in addition to the larm. electron density spikes. The latter are obviously tlK remnants ot the laminar tlow upstream >i the transition BOM, in which the electron density level is very high when e.nnpare'd to the- level in the turbulent fluid itself. Eventually these spikes als.) disappear and, as Figure 45 shows, the ratio Nn/n settles to values ot order 10 percent in the far jet.
In Figure 48 it is schematically shown that the maxinum of the normalized fluctuations is attained where the meai eleetron level is much be I >w the inaximum level r^, that is, the locus ol the spike maxima. It the spikes are truly the results of the process of eni;ulfment of the ambient, electron- poor fluid by the electron-rich lluid of the jet, and it the electron density of the tormer Li iic , then
v 2 (n /n - 1 1 2 (P/m - I) (^ U).-QLJ i (53) \n f fa /n - l)+ P/m "
^ m c '
where P/ra is the ratio of the total mass to the jet mass. Here it has been assumed that both fluid components are laminar so that the signal can Locally oscillate between nm and nL only, in the manner sunvested some time ago by Feldman and Proudian (Reference ?J) and Lin (RtfortacC 2-»). The type of fluctuations of Equation (55) are nil betöre entraiivnent begins (P/m = I) and also when P/m tends to infinity in the tar jet, and they peak in between with a magnitude depending on nra/nc. For equilibrium chemistry, wVn ri and nL, are directly obtainable fron the corresponding temperatures Tm and Tc,, it is shown by Reference 15 that An/n of »rd«S 10 or higher can obtain for practical values of Tm/Tc . For tinitc reaction rates the ratio An/n becomes extremely sensitive to the chemistry.
Nevertheless the simplicity of the jet llow brought about by gasdynamical self-preservation allows certain broad tests of Equation (55) to be made easily. For example the entrainment rate is given theoretically und has also been measured directly. For recombination reactions the n^ night als . be obtained as a tunction of x. The normalized electron density tluctuations of Equation (55) thus become dependent only on the ratio nmo (ol the maximum electron density in the laminar flow) to the "ambient" value nc. The farmer is actually obtainable from the experiment but the latter is not, since the electron density at the base of the spik.-s was detected to be turbulent and ol a mean value much higher than that outside the jet. Computations made with Equation (55) using estimated values of nt gave reasonable numerical agreement with the measured axial variation of An/n shown on Figure -45.
Equation (55) thus appears to be a reasonable descriptor of the physical mechanism giving rise to the large electron density fluctuations - on the strength of the mixing model it describes. It does not necessarily endorse the "laminar mixing" ideas of References (23) and (24) since the partici- pating lumps of fluid (whether electron-rich or electron-poor) are turbulent
-89-
in character. At this time it also appears to attt'ct tlu transitional zone more so than the turbulent activity in the lar jet; in the present experiment this zone is only a lew jet tli it kiusses l>n^.
Once beyond the region of very hi^h 1. ve 1, the electron density llmtuations decrease, according to Figure 45, to values more typical ot homogeneous mixing. The following points are s igm 1 u ant: iirst, the axis values ot \n/n do not appear to attain an asvmpt)te. This may be attributed either to the tact that the overall jet lluctuations themselves have n.)t relaxed to the self-preserving state; or, which is more likely, that no sell- preservation of tht electron fluctuations attains where all )ther types of fluctuations have become self-preserving (e.g., constant fractions of the mean values). Secondly, the oit-axts maxima of tlusi.- fluctuations (see Figure 4b) occur in the general vicinity of T) = \.i. By comparison, the region of ma-imum shear in the jet occurs at
f| .t| a - -) (5o)
which, using the sell-preserving velocity distribution
,2 u = e
-0.24T (57)
is seen to occur at 1/2
T] m 0.48
= 1.45 (58)
It thus seems that the maximum of electron density lluctuati.n «ccur,-. at or near the same radial position in the- t ucupud by the maximum slu ar region. This is an important finding with obvioui applicati>ns to the ..ypersonic v;ake problem.
At radial positions beyond T) = 1.-.5, the iluctuati.>n Kvel u>es n>H c:ecay as rapidly as expected. in tact it appears that iron the standp>int of fluctuations the jet is much wiuer than evidenced bv the mean-iln. measure- ments, There is presently no explanation oi this ptwniliMium available other than the effect of intermit tencv. As is already shown in Paragraph -4.2, the intermittent electron i I ow extends c ons icic-rab 1 \ lartlu r iro- the axis than the distribution of electron density. Pot example, at x = 30 inches, the llow is intermittent still at 7) = 5.5, v.lu reas the electron density has reached ambient (zero) value by T) = 4.5. Now in intermittent zones the "turbulent"' signal is made up ot a combination oi real turbulence and intermittency in a way given functionally by Corrsin and Kistler (Reierenc-1 11) In the example cited the intermittency contribution should be prevalent in the outer region, say in 4«^ T}- b. To test this. Figure 49 plot! the \n/n distribution at x = 30. Also plotted is the signal expected if it consisted of the intermittency contribution alone, as |iv*a bv the lomulas developed in Appendix B ot Reterence 4:
^-(M 1/2 (59)
-90-
0.«
0.3
0.2
n
B1441U
FIGURE 49 TYPICAL RADIAL VARIATION OF NORMALIZED RMS ELECTRON DENSITY FLUCTUATIONS ALSO SHOWING THE SUSPECTED CONTRIBUTION OF
INTERMITTENCY
-91-
where 7 is the intermittency factor. Near the axis, where 7= 1 the signal is obviously all due to turbulence, but the curves cross around *") = 2.3. This is-surprising since it says that r-ar the jet edge the signal is smaller than the minimum expected. The question is open at this juncture. A likely explanation is that Equation (59) is oversimplified because it assumes: (1) no electrons outside the jet, (2) an intermittency signal idealized by "flat top" distribution, and (3) a jump in electron density across the front which, at a point fixed near the jet edge, is constant in time,
4.3.3 SPECTRA OF ELECTRON DENSITY FLUCTUATIONS
Iri the previous reporting period, spectra of the electron density fluctua- tions were taken at ail x and Y positions with a wave analyzer whose minimum bandwidth was 200 Hz. These data, reduced during the current period, showed two deficiencies connected with the very-low frequency range. First, many of the spectra were recorded with an x-V r rorder «ain such that the low- frequency spectral density went off scale. Secondly, it was evident that the spectral density dropped off rapidly in the first few hundred cycles, so that measurements in that region were inaccurate due to the ^00 Hz bandwidth. Thus, the data could only be considered useful above a certain frequency, which was set at 2 kHz.
To fill the low-frequency gap in each spectrum, all spectra were re-taken in the 0-2 kHz rang« using the setup of Figure 50. A Hewlett-Packard Model No. 302A Wave Analyzer was used with a range of 50 kHz and bandwidth fixed at 7 Hz. This bandwidth could resolve the spectral der.sity at much lower irequencies than before, hut it. also introduced the classic output unsteadiness typical ol sharply filtered 1ow-frequency spectral analvsis. To damp this out, a vacyutn thermocouple was interposed between the wave analyzer dc output and the plotter. Figure 51 shows the transfer function of the thermocouple which was used in the computerized data reduction process to connect the dc appearing at the plotter input to the filtered output of the wave analyzer. With this equipment spectra were recorded from 0 to 2 kHz. Each of these spectra was then joined with its corresponding predecessor (taken with the previous arrangement) a!, the 2 klh. point. In the process, account was taken of the fact that the preceding spectra were in terms of the root-mean-square, while the most recent ones in terms of the mean-square spectra.
The data were reduced by the JEA-II (SRS 0024) computer program which is described m Appendix A. This program gives an independent check of the total rms fluctuation by integrating the area under each spectrum. After the data was first reduced it developed that this cross-check did not con- form with expectations. It was found that the Runge-Kutta integration scheme used was not accurate for functions changing rapidly between adjacent trequencies. The data were therefore processed again through the program using a Simpson-type integration.
The electron density fluctuation spectra are shown on Figures 52 through 58 The first two Ligures show the spectra on the axis; the remainder show
-92-
FLOW INPUT
HOT-WIRE
I 3 T
n
HEATING CIRCUIT
L
I AMPLIFIER
E^
D.C. VOLTMETER ER I
L_ VOLTMETER | |— LANCMUIR PROBE
1
COMPENSATING AMPLIFIER
I OSCILLOSCOPE
nz DISPLAY ANALYZER
nz WAVE ANALYZER
I
3 , RMS VOLTMETER
AC/DC CONVERTER 1 I
I AC/DC CONVERTER
VACUUM THERMOCOUPLE
DAMPING CAPACITOR
B1442U
FIGURE 50. BLOCK DIAGRAM Of THE JET Tl'RBULKNCI- ELECTRONICS
-93-
B1443U
FIGURE 51. TRANSFER FUNCTION OF VACUUM THERMOCOUPLE USED TO CONVERT THE SPECTRAL DENSITY SIGNAL INTO DC VOLTAGE
-94-
10s
10 -1
4 SLOPE
10
10
10
2x10 -5
SYMBOL
i
X (INCH)
18
20
22
24
32
34
li 0.01 o.i
A f/L
D 0
X » o
X D
0 e
+ o
FIGURE 52. NORMALIZED SPECTRAL DENSITY OF ELECTRON FLUCTUATIONS ALONG THE JET AXIS
-95-
10
An(f)\:
An(0)/
10 -2
10
10 -4
3 _
18 26
X (INCH)
30 J*4 38
B1443U
FIGURE 53. AXIAL VARIATION OF ELECTRON SPECTRAL DENSITY FOR EDDIES HALF THE MACROSCALE SIZE, SHOWING THE DECREASING IMPORTANCE OF SUCH EDDIES FAR FROM THE NOZZLE
-96-
- —
0.1
\An(0)j
0.U1
0.001
0.0001
0.01
X - 18"
oi
5 3
^ - SLOPE ^
SYMBOL Y (INCH)
e 0
• 0.74
A 1.48
A 2.22
J i a
V v
JA 0
A 8
ll J L
o.i
Aef D
10
B1446U
FIGURE 54. NORMALIZED SPECTRAL DENSITY OF ELECTRON FLUCTUATIONS AT 18 INCHES
FROM THE NOZZLE
-97-
0.1
\An(0)/
0.01
0.001
\ •
-\ 0 D
1
V A A
- \ A oa
\ <*
-
\ 0% \ ^~ " 3 SL0PE ^ o^S
■s ■ t
— O «A #A
a A
X = 22" 0 * *
■ \ a
SYMBOL Y (INCH) a
— o 0 —
• 0.74
A 1.48 — A 2.22
a 2.96
■■
0.0001 0.01
j i LJ i i U. J Ü 0.1
lef U
10
B1447U
FIGURE 55. NORMALIZED SPECTRAL DENSITY OF ELECTRON FLUCTl'ATIONS AT 22 INCHES FROM THE NOZZLE
-98-
{M •01
.001 ;
.01
^ SLOPE
X - 26"
•
A
- A
-
.0001 —1— -1—-
Y(IIICH)
0
1.47
2.96
4.43
A
I 0.1
o
• A0
• 0 ä,
• o A
• O A e
A • e
• A
OA
li ± J L
FIGURE bb. NORMALIZED SPECTRAL DENSI FROM THE NOZZLE
10
B1~8U
;SITY OF ELECTRON FLUCTV.VTIOKS AT 26 INCHES
u
-99-
10
10
10 _
10
10 .01
Y SLOPE
Y - 30'
SYWOL YdMCH)
0
1.47
2.96
4.43
j ■ I
e
A
O
• \
' ' J L
A.f 10
BU49U
PIGUtC 5/ '.«'RMALIZKD SPECTR.AL DKNSITY OF tUCIMM FLICTIATIONS AT W INCHES m* THJ wuu _100_
10
10 -i
(-AM2
10
10 -4
-
10 -5
.01 J L
X - 34"
o
e
a I
SYISOL XdNC)
• 0
• 1.47
A 2.96
A 4.43
a 5.90
xl .1
u
e
*J
*.*
il
*> *•
~>
A O • •
A.«
A«0
A«0
^4- 10
Bl-'iOU
FIGURE S8. NORMALIZED SPECTRAL DENSITY OF ELECTRON FLL'CTVATIONS AT )-. INCHES
FROM THE NOZZLE .l01_
representative spectra at ott-axis positions. The »rdmate in these graphs is in the square ot the electron fluctuation spectral density and is normalized to the asymptotic value at zero trequency. The abscissa ^N = f*e/u ^s t^e frequency made d imensionless with thf l>ial intt-cral scale of electrons Ac an^ t^6 loc^l velocity* u. For txampU, i^ = 0.1 reters to an eddy size ten times larger than the integtal scale.
The axis spectra evolve along a character ist it pattern. According to Figure 52, nearer the nozzle the dec'ine of spectral density with frequency is quite gradual, but becomes most prec irj: tous at the four XSTAT10NS. At the latter, the spectra appear to become "locked" to an invariant shape, for which
(An(0)) 2 -4.6
beyond -M -1. .t is further demonstrated by Figure 5J that the change in thv. spectral shapes occurs mainly between x = 24 inch and \ = 2b inch, that is, in the region where the transition from "heterogeneous" to "homogeneous" turbulence occurs.
In the radial direction the change in spectral shapes is generally gradual and small, especially at large X. In the "heterogeneous" portion, the spectral density tends to decrease at the higher rrequencies as on*1 moves away from the axis. At larger X a slight but repeatable reversal .ncurs, s> that the higher frequencies are more prominent on the axis and a^ain near the jet edge and less so in between.
It will be noted that in all graphs shown there is no portion of any spec- trun where the spectral density decavs with the (-5/J) power ot trequency as expected for an inert lal subrange. This matter will be discussed in detail in Paragraph 4*5«
The longituuinal scales (mac rose ales) ot electron tluctuations are derived in the JEA-II program trom the measured spectra by the usual formula:
. u »em1 (oo) e * 4 (\nr
2 Here u is the lo^al velocity and (\n)' is the total (trequeuev-integrated) mean-square tluctuation in units of cm" , Th« (\n(0))~ is the contribution to (\n)- which comes from a one-cps-wide passband at I = ('; it has the units (cm*6) x (cps) = (cm"b) (sec'1)" = (em" ) (sec), and has been obtained trom the spec, al density. Thus, 'e has the units of length, as it should. To doublc-chewk the validity ot (\n(0))-, the program performs the following integration from tne measured spectrum (\n(t))~ versus t at each point:
0D
EINT = f (WOT T1 (öl) y B
* Since .'.e is proportional to u also, this nond imens lonal trequency is independent of u.
-102-
u KMith du ■ 200 tt« and 7 US, respectively, ^ where IB is t»u .mer bandv.dth ( B 0 .Uy good agreement the two sets ol data obtained). Tl ^ tluetuation measured with a between EINT and the mean-square electro v ,Umeter and shown on Figure W.
The scales so measured are shown. - ^e.et^is, ^^J'*
tollowin^ observations are ^ J ^^^eneous re.ion. decreases (2) initially the scale • ^^f^J^L re.ion. Because ol the abruptly and increases slowly '"J^V ter the spectral measurements scat er a cross-check was Per tormed ^'^ '"^ w. The cross-check data l-re (\n)^ and ( n(0))^ — -corded ^M^ ^^ ^ (tilled-in s^bols on Figure 59) ^ave g«»e y ^ ^^ oi
ess-scattered, than the spectral ^ta. U turn ^^ XSTATL0NS
Lh measurements has still ower scatter.^ Taki^ ^ ^ ^ by
and the point (x - 0, A# - üj least squares:
. = 0«034 x
l the fll»^. P..—lU, -— .V ana tHe »ansv^ .C.l. L
oi the jet was lound: (6J)
. = 0.-47 L
v.prv dose to the scale magni- As „HI be seen below, these ^™]**^ Nevertheless the scatter tude tor jets in the absence o ^^^^^ (see Reierence 25) tvpi.al oi the technique "^^ ^^ Ut corre lat ion measurements . Li much worse than expected it<mt sas . c t
w. ■ alreadv shown in last year s „aaUl a1Stribations ^/^^/^iVl'eddv «laclt, «««r.-«t. are report (Reierence 6) are ueicrr
complete.
4.4 US GAS TEMPERATURE FLUCTUATIONS
4 4 I FLUCTUATION MAGNITUDES
t^cther wuh a ifa—lM »f*1^1 "'!!, data «t, taken to corroborate pa.e 181. 1" the P'"'"VT „ r^lT V ed and compared with earlier
.ncasurements in otnei
were made. hu-n Ml Figures 60 and 61. On the axis
The temperature fluctuations are *h^ ™[\\ ^ the Uecrease ot the mean Ihese decrease m a rate nearly ^^^^ the tamiliar off- temperature "dc licit «^-J^. /" ™ 1S n,ted. to a decree dependent axis increase in lluctuation mtensits is
-10 3-
* /^
/
/
><
O
tsi
00
o CM
X
vO
vO U< P-i B . vl u ä ^ 2 vi B
2§ M < «N H U
ä g Ou U W 1
(A X M
S S 6u U
(N
00
32
U.
u H
o
X
4 <H -104-
is..- -" ;^:
i
s - _ to
M UJ o 2 M
Sf u E H Q x H <
< z U H
a P z z c < 0-
>■ u H B K-l DC
o u '8
>
Q H
C H M M p 3
a M
X Q < z
o
u H
-105-
CO vO
O i o 8
H i
1-
8 8
\-
o O
P ■ * ^■
V5 ^ U U t-l 3- H Z ai U
E o p et >z o- <
ö>; < U a: F i ~
E cn z < H u
U
'^i x
> Ed
M « Cfl — ^ Z ^ EsJ H ii c_ ^
J ^ < < H •_) U H M zy
-106-
sttoHKly on the manner by which AT Is normal Ued.* There •"•«»""' similarities between these results and those ol Corrsrn -^ "hero especially In the ratlo \T/(T-T-) which attain a va ue of about 0 5 especially c „tacit» fluctuations measured with the double c^rUtronp^bear also shown on Pl.ure 60. These peaKsoriKlnaUy.
bureven ually seem to level out to a value proportional to the axi but eventually s correspondence between our data and the
Ta rr/cotL rnrUbeeroUOSHowever.Pit should ^^^^ ^ ' r r^^t-cin1« data with their own, Wy^nanski and tielder
diameters.
4.4.2 THE TEMPERATURE FLUCTUATION SPECTRA
During the current period, repeated measurements ol the temperature
-.t/;;sr;;u-rü;-^^:rr::u:er^:hr-;::rir; qdurp: rin
^ Lv dif icu t to detect and compensate for. i* practice the probe is \Zl ^^.^ the ^J.^-e -rma, U^me^red by ^ ».cU^cop^
compensation, deviations of the tme constant tto* ', ' '"^ ^e Is computed a -osterlorl and used to correct the readi, <*! !J^I*2.«. Identical to that used In the supersonic wind-tunnel, (see Paragraph ^ This c-putarion Is, In turn, made from Knowledge, of the variation ol wire resistance through the jet.
Additional data showed that the increase inside the tlow was not nigner
data are not discussed herein.
r^ rtfAA —Ero 2otoo r^rrÄ rn J.r the X-Y plotter. In the range trom 0 to 2 kHz, tne higi
^The difficulties arise in the problems of hea "^V^l ^ 0 001 at extremely small Mach and Reynolds numbers (typically) 0.01 and 0.001. respectiveiy). A technical report on this problem is contemplated.
-107-
outside the 7 H^ band ol a JOL'A U«Vf Analsv-er, whose restoreu output is channeled to a vacuum thermocouple and irom there to the plotter. Capaci- tor damping at the plottSC input was used lor stabilising the signal lurther. The circuit is sh.>wn in Figure 50.
As with the electron spectra, spectra were recorded every two inches ahmn the jet axi-s from x = 24 inches to \ = Jb inches. The lorward I unit, x = 24 inches, was chosen lot tear that «. 1 »ser to the nrttlv the h>t-wire would melt. At each XSTATION, spectra were recorded at radial distances spaced about 0.75 inch apart. The data were reduced with the aid oi the SPECTR program written tor the General Electric Time-Sharing System. An access terminal to this computer is available on an almost lull-time basis for this work. Details ol the program appear on Appendix B.
A summary ol the temperature spectral results appear on Figures 62 through b5. As with the electron spectra, the ordinate in these graphs is normalized with the spectral density at zero frequency. The irequency has been non-dimensionalized with the integral scale j (which will be discussed later) and the local axial velocity u. Figure b2 shows the evolution ot these spectra on the axis, while the other i Uures show their radial development at selected XSTAT10NS. The spectra are remarkably similar to each other and not t^o different ttom expectations. They seem to fall int.) three broad categories:
Type I; Nearer the nozzle and close to the axis the high-frequency content is intense. The spectrum t;oes as fw"5/3 where l^ = Ajf/u.
Type II; Over the rest of the entire jet but not too close to the edge the data collapse into a behavior showing a gradual decrease ot the spectral density without any distinct regions where it follows the (-j/J) slope. Typically at fg = ^> tlK' «P^tral con- tent is down a factor of 10 below the Type I spectra.
Type III; At the edge of the jet, the high-frequency content is still lower and the spectral decay some- what steeper.
The evolution of the spectra from one type into another is best illustrated on Figure 63. It is very clear that on and near the axis one obtains the (-5/3) slope. At Y = 1.47, the "break" away from this behavior (Type I) occurs at earlier frequencies. Also, the departure of the data at the jet edge (Y = 6.6^) from the Type II data is obvious. Tentatively, the following conclusion is reached that Type I spectra are associated with the "heterogeneous" jet, where the large electron density fluctuations also occur. Type II are apparently connected with the "homogeneous" jet, where the electron spectra alro assume a constant shape.
An attempt was made to compare these data with spectra taken in other jets. Of the latter there is only the data by Corrsin and Uberori (Reference 26).
-108-
\AT(0)/
.01
.001
.0001 .01
^l SLOPE
SYMBOL X(INCH)
o 24
• 26
A 28
A 30
a 32 ■ 34
+ 36
I 1 .1 V
a A ■
■
■ I L
U
10
B1454U
FIGURE 62. NORMALIZED SPECTRAL DENSITY OF THE GA3 TEMPERATURE FLUCTUATIONS ALONG THE JET AXIS
109-
(M-S \AT(C)/
.001 —
.0001 —
FIGURE 63. NORMALIZKD SPECTRAL DENSITY OF THE TEMPERATURE FLUCTUATIONS AT 26 INCHES FROM THE NOZZLE
-110-
.1
\AT(0);
.01
.001
.0001 .01
o
%
VL
X = 30' i
SYMBOL Y(INCH)
o 0
• 1.47
A 2.94
■ 4.42 5.88
.1 J L
V u
B
8
•1 A O
Ä
li J L 10
B1456U
FIGURE 64. NÜRMALIZLD SPECTRAL DENSITY OF THE TEMPERATURE FLUCTUATIONS
AT 30 INCHES FROM THE NOZZLE
-111-
ÜtfrV \AT(0)/
.01
.001
.0001
.01
o
I SLOPE
X - 34 ii
SYMBOL Y(INCH)
0
1.47
2.94
4.42
5.88
J Ll 1
0.
.1 AT£_ u
o + ^L
X
♦1
A
;*
ii 10
B1457U
FIGURE 65. NORMALIZED SPECTRAL DENSITY OF THE TEMPERATURE FLUCTUATIONS
AT 34 INCHES FROM THE NOZZLE
-112-
In KUures bo and 67. the data are instead I .mpareü with ■nore «envral
drawn. It tr. seen that the Type 1 spectra are c«-p«*U^Uh hljh
Reynolds number tl.ws where is.Hropy LS expected. At '""'^ ," ' t .^ „U t^ulence compares well with Type I spectra, ft. ' J " "^'^ lormula «ivin« a dependence t/2 does not correlate well c ether t>pe
data.
ThP lop.Uudmal integral scale of the temperature iluctaations is shown P re 68 As Cith the electron scales the Mtbod of n^asurement on Fiwure oö. äS witn cue ci.t^wa „,..<.,. The males
whuh utiUzes the spectra, results « rather l-^eS;^ ' J^/ t thy
are supposed to grow Unearly with distance, and ^^/^f^,^^ '^ V^ the straight line slown has been forced to go through the Mrtual origin öl" the jet (x - 12 inches). The linear growth is actually •«JPf^J» 'let by the near-proportionality oi h with the transverse scale L also
shown in Figure 68. The following relations emerge:
(6A) A a 0.079 x
(65) ht* 0.79 L
It should be noted that these two relations imply that L - **<>**• f^ is nTlar from the result found lor this jet in Reference 2. page 78.
(66) L ■ Ü.Ü79X
A comparison of this result with previous «1*^»" l! •["/^^ 03) Picn.rP 68 The excellent experiments ol Wygnanski and Fielder (Reference «| a Bo in!* hive been hosen or the purpose. These data are chosen because ll ^l^cirsuperiority in ^asuringtechni.ue and abundance o^poin.
rj ^ ^:z:r^^T^.u STJ^::^ by ^^ - Fielder is summarized as follows:
(67) L ■ 0.053 x
(68) A = 0.0385 x
in comparing the present scale growth. Equation (64) with ^^^«J"«^» ^r^S). itPshouIdbe stressed that thc P^sent jet .s .ghly^heated.
1= ^U^'viK ::it.!l,^e^^flf J. easily explain the apparent and contrast of Figure 68. First, the pre ,ent jet ^/htcktr because of the initially very high temperature, an efect predicted and ob erved by Corrsin and Uberoi (Reference 26) and analyzed by Laufer (Reference 27) and also immediately apparent from Equation (66) and (67).
f " o" ct d'« for the temperature effect the scale Au ^"^ * ^f* would move up by a factor of 0.079/0.053. from Equations (66) and (67).
A . 0,079 0.0385 x = 0.057 x (69)
0.053
-113-
.1
UT(O)/
.01
■
.001 __
.000 0.01
PRESENT DATA (TYPE I)
TYPICAL ISOTROPIC VELOCITY SPECTRA WITH -5/3 SLOPE (UUm'8 PIPE; Rep - 500,000) (SATO'S GRID; ReM 100,000)
A-r2'22
PRESENT DATA (TYPE II)
u
FtClIRE 66. CCWMIMM OF TYPE I TEMPERATURE SPECTRA WITH HIGH-REVNOLDS
SUM50™"' Vtt0Cm SPECT,W AND lm "^ "NiMPounoN
-114-
.1
UaJ
.01
.001
.0001
0.01
PRESENT DATA WITH -5/3 SLOPE (TYPE I)
PRESENT DATA (TYPE II)
u FAVRE GRID (ReM - 21,500) VELOCITY SPECTRA
j i a
FIGURE 67. COMPARISON OF TYPE II TEMPERATURE SPECTRA WITH TYPICML
LOW-REYNOLDS-NUMBER VELOCITY SPLCTRUM
•115-
pel u
OH O z w £ w H Z
H - t
Ü3
g 9
n2 w u > — w H ^3 X <
B 3
C a:
O C J 2: M < C V3 U -J 2: V2
M ^ S X" C M ^)
Z Z > - -J -^
H W3 S < 2 as i—" _ ;—
> < jr
< u t X J -^
-116-
<L
In the iecond place, however, it is known (Reference 26) that the tempera- ture scale Ls smaller than the velocity scale, so that value would a^ain decrease somewhat. In any way, the agreement with the Boeing results is good in view of the scatter in the present data and the possibility that the present Jet has not yet become self-preserving.
Two features of Figure 68 are important to the present problem: in both the Boeing and the present jet, A/L is about constant at 0.75; in other words, the longitudinal integral scale appears to be a constant traction of the jet width. Secondly, this ratio Ls apparently nearly the same in jets and wakes: note that about the same ratio A/L was obtained for the
WEB experiment (Reierence 4, page 42).
4.5 COMPARISON OF ELECTRON AND TEMPERATUR!: FLUCTUATIONS
As it was noted in the introduction to this section (Paragraph 4.1), the ultimate aim of this task is to establish a connection between electron and temperature fluctuations Ln a turbulent plasma. Certain results In this direction are now available and are summarized Ln Figures bcJ through 7?
On Figure 69, the ratio (.\n/n) / (\T/T) is shown on the jet axis beyond x = 2b inch, that is, in the region in which temperature fluctuation data are available. The electron density fluctuation here predominates, especially nearer the nozzle, where ratios as high as 5 are found. Note that at x ■ 26 inches, the jet flow is already beyond the so-called "heterogeneous" stage, implying that ratios much higher than 3 are probable in the range 18 inchv x< 26 inch. Toward the farthest point oi the axis (x ■ 36 inch), the ratio approaches unity. Near the jet edge, as Figure 70 shows, the ratio is as high as 10 or so.
Figures 71 and 72 plot the ratio oi electron-to-temperature iluctuations resolved according to wave number. Physically, these graphs indicate the desired ratio separately tor each eddy size. The two temperature spectral types, I and 11, are shown with their electron fluctuation counterparts as drawn from Figures such as 52, 62, etc. The abscissa has been adjusted to wave number units by essentially removing the scales '.e and *T from the abscissas of the cited figures. Note that or each eddy size the electron density fluctuation also predominates over the corresponding temperature fluctuation. The ratio of the two is plotted at the bottom of each Figure, The ratio of the relevant fluctuations \n/n and M'/T can then be obtained from the following formulas:
An(f)\2 _ /Vliilf (^i£l]2 (AllV (71) In/" VV0O/ V \n I Vn /
-117-
Mal VrM T(o)
X (INCH) B1461U
FIGURE 69. AXIAL VARIATION OF THE RATIO OF TOTAL NORMALIZED ELECTRON DENSITY FLUCTUATION TO THE TOTAL NORMALIZED GAS TEMPERATURE FLUCTUATION
-118-
16
U _
12
10
SYMBOL
O
A
X (INCH)
26
O
6 -_
(I 0 © # 0
» •
A A A
u 1 2 3 4 5 T)
B1462U
FIGURE 70. RADIAL VARIATION OF THE RATIO OF TOTAL NORMALIZED ELECTRON DENSITY FLUCTUATION TO THE TOTAL NORMALIZED GAS TEMPERATl'RF FLUCTUATION
•119-
1.0
.1
~
.01
.001
HETEROGENEOUS JET REGION
I I Mill H+m- Cln/An(o)r/ (AT/AT(o))
-I ' ' ' ' ' 'I1 ' I I I I | Ml1
1 10
B1463U
FIGURE 71. RELATIVE L1PORTANCE OF ELECTRON AND TEMPERATURF SPECTRA1 DENSITIES IN THE •'HETEROGENEOUS" PORTION O THE JFT (ABSCISSA IN ARBITRARY).
-120-
0.1
0.01
0.0Ü1
0.0001
Z. (Än/An(o))2/(Al/AT(o))2
0.01
HOMOGENEOUS JET REGION
I I I llllll 1 I I I MH|
■ i i » i
10
■ ■ ■ i t ml I—I llllll i
O.i
WAVENUMBER (ARABIC UNITS)
10
B1464U
FIGURE 72. RELATIVE IMPORTANCI- OF ELECTROM AND TEMPERATÜRE SPECTRAL DKNSITIKS IN THh "HOMOGKNEOUS" PORTION OK THE JKT
-121-
Here the nomeiuiature is as followaj
VQ(f) Spectral density of Q at frequency f
\Q(o) Spectral density of Q at zero frequency
AQ Frequency-integrated (total) fluctuation of Q
Q Mean value of Q.
From the definition of the integral scale
we obtain
(72)
(\n(f)/n)^ _ Ae A« (\T(f)/T)
\n(f)/\nfo) \T(f)/\T(o)
9
(73)
"tic A^T f,.' ". LPl-' 'y„8 !!n.ln "l«Ure M.0" "» J« «is. The ,/AT als„ varies Iröm eolnt V , u0" "" J" a!<is- ean be utven f, i-h„ H. — r-—• >- i~"u in cm jet, but on the
^-.tioSw)'^«?»",0' ,CCU"Cy WU" MhlCh E<'Uati- (") and e axis it
Ü _ 0.47L A- " 0.79L = 0.60
(74)
Although this ratio is smaller than iin<* , .u is considerably higher than uni ''i '*"**** ******* ln E^tion (73) iore, theelec^onl" trflTtJtr^^c^s'^^ ^w condition.. There- larger (occasionally very much «0^^ - < ^ctruB, «re numerically Details of these nuLricL v-rif^ tl«n the gas temperature fluctuation.,
the jet are n^yenvaUable "^ ^ ~b- ^ ^offl point in
-122-
SECTION V
SUPERSONIC WAKES AT ANGLE OF ATTACK
5.1 INTRODUCTION
Drastic changes art' introduced in the wake of a body flying at supersonic speeds when the body is inclined at some incidence (angle of attack) with respect to the flight vector; first, the increased total drag generates an intense inviscid wake, i.e., large gradients appear in the flow surround- ing the inner, or turbulent wake. Secondly, these gradients are generally asymmetric about the wake axis. Thirdly, changes in the viscous drag change the characteristics of the viscous wake. Finally, with the generation ol lifting forces vortical flows might also appear, causing added complexities to the flow field.
Although the new character of the turbulent wake is hard to assess in these circumstances, its role in the mixing process can be predicted along general lines. Its main complexity should be its growth in and interaction with the asymmetric inviscid wake. The flow thus consists of a "shear layer" contributed to by the inviscid wake, with a superposed wake flow. It is quite clear that the behavior of this composite flow cannot always follow simple wake rules of lateral growth, for example, or of velocity decay, since shear layers and wakes are generally governed by different rule's. Thus, a pure shear layer supplies a constant reference velocity scale In definition, while the corresponding velocity scale of the wake decreases with distance. In limiting cases, the competition between the shear-1 aver- like and wake-like behavior can be foreseen: for small angles of attack and large shear drag, the wake-like behavior should dominate early, while lor inclination angles large enough to cause very persistent inviscid asym- metries the flow is probably shear-1 aver-1 ike for Large distances.
The present experiment was designed mainly in a way so as to accentuate this competition between the inviscid and the viscous (turbulent) wake. Calculations of the supersonic inviscid flow behind a two-dimensional slender body at incidence, verified experimentally, showed a considerable persistence of asymmetries in a pattern approaching an ideal shear Layer« Thus, the problem is not only relevant, but was done in a way capable of fundamental conclusions on the basic behavior of fluids«
5.2 MODEL AiND FACILITIES
This work is performed in the supersonic wind-tunnel at a continuous air flow at Mach 3.Ü, a stagnation pressure of 730 ur. V, absolute and a total temperature of 390C. The model consisted of a 0 -inch thick, 0.1 16-inch wide stainless-steel ribbon stretched across tin ,nel test-section, identical to that used in the WED experiment (two-dimensional adiabatic wake at zero incidence). A major modification to the model support con- sisted of the addition of a fixed steel protractor and pointer by which incidence angle could be set and resolved to better than 0*25 degree. Twist- angle resolution is about 0.1 degree. The protractor is shown on Figure 73.
-123-
FIGURE 73. :XPERIMENTAL ARRANGEMENT KOK .WC ill: PROTRACTOR IX THE TEST SECTIO
LE-OF-ATTACK STUDIES SHOWING
-124-
i^nri' 74 shows the arrangement ui the low phenomena and coordinate axea«
loue and the nomenclature of the
5.3 EXPERIMENT DESIGN
5. 3.I INVISCID WAKE
Detailed calculations ot the inviscid wake Of Mio flat plate VJVW made uaing
the motiiod of t"\v'o-dimensional ciiaracteristics at an angle of attack ot" 20 degrees; lor different angles, the flow field should not alter qualita- tively from this calculation, provided that the incidence angle tor shock
detaci.uient at the leading edge (about JA degrees at this Much number) is
not exceeded. In this calculation the upstream boundary conditions on the windward side were the oblique shock at the Leading edge; for the leeward side, the trailing edge shock as modified by the Leading-edge expansion fan. Figure 75 shows graphically the result. Attention shuild be drawn
to the two nearly parallel streamlines showning on either side of the wake axis, it turns out that theae denark abruptly changing conditions in the sense of flow gradients (not in the sense of flow discontinuities). The
net result is that between each of these two itreamlines and the axis there
appears a uniform "plateau" in flow conditions; the two adjacent "plateau" constitute, then, a siuMr-l.iyer lituation which apparently does not decay
much, either lr extent or intensity, as one moves downstream. Typical such plateaus are seen in cross-sectiona1 views of Figure 75 shown in Figure 76.
The calculations outlined abov< demonstrate that, although quantitatively
different for the axisymmetric hyperaonlc wake, an eaaential feature of the wake-at*incidence problem could Indeed in obtained in our wind-tunnel. As
described in the following paragraphs, t lie shear-layer feature was clearly evident from the data ( 0 ected so far.
5.5. ciioici: OF 1 NU Dl NCE Si [NGS
To study the effect oi Lncidence, more than one Incidence angle should be chosen, it possible; a judicioua choice ot anglea is needed in order to illuminate the effect without undue labor. It is known on theoretical
grounds that beyond the detachment angle (J4 degrees) the inviscid wake "freezes" to a configuration not very sensitive to angle of incidence. Tests verified this effect, and in the detached case it was decided to work
only with a ■ 90° (plate normal to the stream) so that the blunt-body tur- bulent wake could at least be probed.
In the pre-detachment range of awake "pitot maps", such as shown for a= 0° on Figure JO of Reference 1, were taken at a - 10°, 15°, 20° and J0o. Such maps are easy to construct and are invaluable in giving an overall
picture of the flow field. Since the shear-layer-1 ike behavior was present in each case, the angles 0L - 10° and 2.0° were chosen for further study.
In designing the experiment, the farthest downstream distance where measure- ments can be made is important to know. In the wind-tunnel this distance
is shortened when the model is pitched because of the earlier reflection of the strengthened shocks from the tunnel wall. In the present set-up the farthest downstream distance for a ■ 0°, K'0, JO0 and 90° is 7.8 inches.
-125-
x O
f—
-126-
-127-
- - C
-
■
-128-
C) » 7 inches, 6.2 inches nnd 4,7 inches, respectively. Note that for Ot » 0
a distance of 7.8 inches implies a distance of about 1,800 virtual body
diameters.
5.4 DIAGNOSTIC INSTRUMENTATION
The diagnostic tools used for this experiment were Identical to those employed for the WED (see Reference 1). The 0,00005 inch diameter Pt 10 percent Rh hot-wire used for this work managed to stay intact through the
mean-flow and turbulence measurements and through most of the spectral measurements. This remarkable wire survived 45 calendar days ol use,
during which time it was operated for about 70 hours in supersonic tlow. Through frequent oven- and flow-calibrations small changes in its charac-
teristics could be monitored and accounted lor.
5.5 PROCEDURE
This experiment was designated WEF (Wake Experiment 1 ) and the a - 10°, 20°, and 90° sub-experiments were designated WEF-10, WEF-20, and WEF-90, respectively. As done with the WED experiment, the distance between the
model mid-chord and the end (farthest downstream) point was marked by X-
stations spaced by 0,300 inch increments. Continuous analog traverses were taken at each X-Station with the pilot and static probes and the hot-
wire anemometer, the latter operated either In the mean-flow or the turbu-
lent mode. From these data the mean and turbulent properties can be
extracted.
5.6 RESULTS OF MEASUREMENTS
As already mentioned, the actual viscous wake measurements were preceded by tracing the ir.viscid wake in order to observe the overall flow field and to examine the ex Stance of the "shear-lav! r" effect. Figure 77 compares a
typical pi tot traverse with the pi tot pressure expected from the character-
istics computation shown on Fipurea 75 and 76 for a - 20°. it is obvious from the measurement that two sho k . appear on each side ol the inviscid wake, instead ol one as given by the characteristics method. On the wind- ward side, ax> in addition to the bow shock at the leading edge, a second shock is thought tu originate In the recompression region oi the wake "neck",
as illustrated tentativel> on Figure 74, In the leeward side a shock
appears, of course, at the mode! leading edge in addition to the expansion fan,* Nevertheless the agreement shown on Figure 76 between the calculates and measured pitot pressures is adequate; both demonstrate, in fact, the
"plateaus" on either side of the turbulent wake.
A second preliminary measurement made before detailed studies wire attempted concerned the existence of turbulence. Qualitative traverses with the hoi- wire showed that angle of attack did not inhibit the appearance o! turbu-
lence in the inner wake. Proceeding to the bitter. Figure 7H shows pilot- pressure traces at typical X-Stattons for all three experiments, i.e.,
•Thotographv of the two-dimensional model Itseli is Impossible Because ot obstructions. The identification of the additional two shocks is left to
reasonable conjecture.
-129-
**
"l ' ' I ' ' i I I i i i r
''''''' lj' i I I
o
rsl O
3
• O '-' X
X o CO
90
OS
z
■_ ^•.
X
(N
tu a.
}0-
INCREASING PITOT PRESSURE
0.020 IN.
B0881U
FIGÜ1E 78. COMPARISON OF MEASURED PHOT PROFILES (AT INCIDENCE ANCLES
FIXED X) FOR DIFFERENT
-1 31-
WEF-10, tftr^ZO, and WKF- 40. A trace for WKI) (correspondlog to WKF-O) is also shown. The objecl ol tliis liguri' is to demons t r.i U' the wake svinmetrv which understandably obtains lor the symnetric body con 1 i «urat ions, natnelv for WED and WEF-90. Note, also, the expected change in " l"rrc-st ream" pi tot level for the WEF-10 and tfEP-20 traces, illustrating the "sliear-layer" effect.
Typical static pressure traverses are shown on Figttre 79. Although these traces appear reasonably smooth, it should be recalled that the static- probe resolution is quite poor, since the diameter of the probe was never smaller than five times or so the wake thickness. On the other hand there- is strong belief that the mixing in the far wake occurs at constant pressure, or else the whole flow system should shift progressively in the direction of decreasing pressure. In fact, this probe gave seemingly good resolution in n-gions of sensible pressure gradients, such as it or near shock waves.
Hot-wire measurements consist of the usual three sets: one set consists of five curves at each X-Station, necessary to complete the inputs tor the mean flow measurements. A second set, with 15 curves (each at different current) traces the variation of mean voltage across the wake; a companion set of 15 curves plots the mean-square of the wire ac (turbulent) component. Here one should note that the turbulent fluctuation! are highest on the side of the wake where the velocity gradients are the highest. Spectral measurements have not been taken as vet.
1 \2-
x X c
■-
1—
X
- I s
-
X H
x —
r.
A. i
_
v.
-
a«
ntent ionally L<. 11 B! auk
PFXCEDINS PiOS BLANK-NOT f TIMED
SECTIOM VI
SrFERSONIC WAKE WITH MAT TRANSFER
b.l INTkOÜl'CllÜN
TIKT.- drc several distinct reasons wliv the presence ot heat transur is
imponant to understanding the fluid mechanics of the hiyli-speed wakes. In the first place, it is well knouTi from stabilit\ arguments (Reference 7)
that the location of wake transition to turbulence is sensitive to heat exchanged between the bodv and the tlow. Secondly, the extent to which heat transfer changes the seif-prtservalion behavior is not well understood.
Third, the tluctuations in the wake are much more complex with heet-transfer; for example, the simple relationship between velocity and densit) thutua-
tions valid tor the Lsoenergetic wake doei not spply«
In the present series ot experiments, it is planned to itud) the mean, intermittent and turbulent tlow component behind an axi svmnc t r ic i.ooKd model and a two-d i • ens ional heated model. The latt<r experiment lias been initiated and most of the tests have sctuall) been computed. It will be
deacribed in this section.
b.: MODEL AMD FACILITIES
This experiment is performed in the same wind-tuniul, it the same conditions,
with the same model and concurrently as the anul e-oi-J t t ,ick experiment dis-
cussed in Section V. Proviaioai to the model support, additional t.i thoae described in the latter Section as necessary for t lu anele-of-attack measure- ment, were incorporated specifically for the heat-transfer measurement.
The steel ribbon is heated electrical 1\ bv | Harrison laboratories Model
No. 81-4A regulated dc power supplv. load regulation is held to hi low U. U5
percent, and piwer-lme ripple, already low, is msd« effectively Impercep« tihlc because of high thermal inertia ot the heated ribbon. The ribbon current can he adjusted from 0 to 25 amperes dc and is continuousl\ dU-
played on a SpaedOlliwW strip-chart recorder running at a speed of 1 inch of paper per minute. Aided by the chart resolution ind a lim variable
resistor added external1> to the circuit, the Operator can thus readjust
and control the ribbon current to about 0*015 percent ot the desired value, an error Iving much below the current change needed tor perceptible changei in the heated wake charac te'r ist ie s. The power settled upon for this
measurement will be give-n farther belotft
Expansion ot the mode'l bv thermal r- t 11 i on necessitated I scheme by which the ribbon tension could be adjusted automatica11\. This was done b\
spring*loading one end of the' ribbon so that the model could expand when heated and retract to a stretched position ..hen the' electrical power was
turne'd off.
-135-
6.3 ADJUSTMEMI OF OPERATING c:OM)rjic)NS
To brirm about easily observable lieae>transfer effects, it wmn de&ired to dissipate the highest possible amount ot power tn the ribbon. Severs] otbor conditions should be satisfied Bissiltaneous] ; the ribbon should not
weaken itmcturall) or deform, the tttrbnlence Bhould not be inhibited to the point where the woke- became- whell) Iminsr. and the ribbon tempersture non-umtormity because ot boat .onduc.ion into the supports should be kept
minimal. There was turthormorc some- feat that the Increased wske tempers- tures could restrict tin operating t c-mp.ra ture ot the hol-wir. or even
destrox it when both the model ,.nd the hot-wire operating temperatures were high. As it developed, all these criteria were iatisfied on., the ribbon maximum powat was set.
This was accomplished bv gradual 1« increasing the ribbon current until t lu mode! glowed taintIv in the supersonic flow. Ihe current was then reduce!
until the glow disappeared. At this point the ribbon current VSI Bet St ll*.^i raperes giving | voltage drop across it ot i.344 volts dc for a
totsl power dissipation ot U - 86.H watts. It is interesting to conpsre
tins power to the "Kinetic" power ot the flow P - (drag) x (flow velocit )
Utilising the viscous drsg coefficient of the ribbon fron the sero-incidenc« ••'D experiment (Section 11) I ratio of M/P - l.j la obtsined.
Al"t;,r ^ weessary testi for finding the trm cero-twist and sero-incident snglei (see Referenci I), the bot-wire wa mployed qualitative] I studying the transition to turbulence with end thi transver • (span- -.
uniformit) ot the besting process. Transition was detected '-. t ,! »ethod ol noting the point ot maximum turbulenci Intensit) along I • center line (Reference 28). Figure Ho shows tiu remarkable differences In transi- tion distsnee observed with besting« this distance, locsted about 100
virtual diaaetars (momentum thicknesses) behind tiu adiabati< hoch moved to ibOttt SOO diameters ..hen besting WSfl spplied. Tins phenomenon' is eon-
il tent with the predictions ot stsbility theory m which the tsminsi a i- itsbilised li t!ie mod.! or vehicle producing it La heated (Refer nee 7) (•tu result ot this transition delay wss that the svsilsbh rang( tn the
axial direction over which diagnostics could be nuuh was on!', shout bsU
the rangi available for wake studies v.ith the sdisbsti« body', in exchsng« however, one obtains a lonu transitional wake fro« which intornation Impor-
tant to the transition process could be extracted, lor this reason probin began again, as in UT:i), short IV downstrean of the bod) rather then at the transi tion distance.
Visual observation ot the ribbon following its overheating to the glowing point showed th/i :ts re.ir h.ilf (from shout nid-chord to the trailin- edge) had been discolored in the wav typical oJ ,netaN alter exposure to hi h temperatures. That the ribbon temperature Increasas slong its chord toward the trailing edge is fullv expected because ot Ue more efficient best
trankt er tor the thinner boundarv K.ver. The discolored region extended i.mtormly along the span, but it was observed to stop sbruptl) about one
Henceforth "heating" refers to the B6.8 watts settled upon as noted previously«
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ribbon chord before it reached the tunnel iidewalls. The ends of the nbbon were therefore cooler since, of course, heal conduction to the solid supports increased at those points.
The observations described above are crucial to the span-wise uniformity ot heat transfer from the ribbon to its wake, that is, the question of
true two-dimensionality of the experiment. This question was further exa- mined by taking hot-wire profile of the local total wake temperature at
fixed distances behind the model and difference spanwise stations. Within
an inch of the spanwise direction around the center-span position (covering about 35 percent of the total span), the wake axis temperature varied by
about 10 percent; at least part of this variation is attributable to slight flow non-uniformities. The two-dimensionality was thus judged to be adequate.
6.4 PROCEDURES AND INSTRUMENTATION
The instrumentation used for this work was identical to that used for the WED and WEE experiments. Although the ribbon itself was heated highly
turbulent diffusion reduced the local stagnation temperatures to the point where no question of damage to the probes bv high temperatures ever arose In tact the 0.00005 inch diameter wire was operated in the sam, full range'
ot heating currents (maximum of about 7.5 milliamperes) without ever fail- ing bv causes attributable to high wake temperatures.
The present experiment, done with the heated two-dimensional bodv at zero incidence, is designated WEG (Wake Experiment c). The measurements ..ere performed at each ot 23 axial positions along the wake. (X STATIONS 1
through 23) beginning at 0.658 inch from the ribbon mid-chord point. At each station one pitot-pressure transverse, one static-probe transverse
and live hot-wire traverses were performed to collect data sufficient to describe fully the mean flow field. Each wire traverse was of .ours, per- formed at different heating currents. lor the turbulence, 1r) traces ol
mean wire voltage and rms voltage were collected at each station. for the spectra, ten distinct radial locations were' chosen at v.hi 1, spectra were
recorded at each of six different heating currents. Since the acquisition and reduction ot the spectral data is extremely time-consuming, data were taken onlv at alternate X STATIONS (the- odd-numbered stations l ] 5 23). Thus a total of 10 x 6 x u . 720 spectra we're- recorded.
It is perhaps advisable to reiterate here the data reduction process through which the WEG data are now progressing. The mean-flow data have- been
digitized and put into the WEb-V and WEB-Vlll computer programs which have tor some time been prepared for the Philco-2000 digital computer The spectral data are first used into the WEB-I] program Irom which one extracts
the so-called error ratios, that is, a correction factor necessary to use in correcting the system frequency response. The output of this program and the turbulence data are then used into the WEB-I Jl and MEB-IV pr., , rr to deduce the turbulence properties and further into the WEB-VU program from which turbulence properties in scaled form are obtained.
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SECTION VII
PROJECT LOGISTICS
7.1 PERSONNET
This work is performed l"oi" the Space and Re-entry Systems Division under the general supervision of John Knudsen. The technical work is done at the Fluid Mechanics Department of the Aercnutronic Advanced Development Operation by A. Demetriades, Supervisor of tun Experimental Aerodynamics Section, assisted by Ernest L. Doughman, Research and Development Engineer and i.ee Von Seglern, Engineer. Computation services are rendered by the SRS Computation Department under N. Habibe, Supervisor.
7.2 DEVELOPMENT OF FACILITIES, INSTRUMENTS AND TECHNIQUE
7.2.1 FLOW FACILITIES
The work described in this report is performed Ln Che supersonic wind tunnel and plasma wind tunnel constructed and maintained by I'hi Ico-Ford. In the present period, improvements have been made by the Corporation to these facilities for the purpose of enhancing the efficiency of the work and the quality of data. An automatic current control has l-cen installed in the plasma wind tunnel for the purpose of avoiding excursions in the arc current of the plasma generator and the resulting changes in the turbulent jet characteristics. An improved plasma generator has also been purchased with which improvements in the precision and repeatability of the measurenents wi1 1 be sought.
7.2.2 INSTRUMENTATION
The following specialized instrumentation has been added by the comrany in the current period for the purpose of facilitating and improving current and projected work:
a. Heat-Flux Probe. A heat flux probe has been constructed for cross- checking mean-flow data acquired in the plasma jet by measuring the local heat flux. The sensor lias a flat circul " face 0.25-inch diameter and a calibrated range ol 500 Btu/ft^/sec. its output is 1 mv per 30 Btu/£t-/sec. This is shown in Figure 81.
b. I'ltra-Small Uot-Wirc Probes. The smallest hot-wire probes used in the supersonic wind tunnel to date have been 0.01-inch long and 0.00005-inch diameter, and have a limiting (zero-current) time constant of 0.100 msec. Although the frequency response of these wires is greatly augmented by electronic and computational methods, there is continuing need, in this work, for higher response instruments. Attempts were made ir the current period to mount wires ol 0.00002 and 0.00001 inch diameter (20 and 10 microinches. respectively) which -potentially have lime constants of 25 and 10 microseconds. Reportedly, such wires have been mounted elbewher« only rarely and have never been before used in supersonic flow. So far,
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'IGURE 81. TOTAL-ENTHALPY PROBE SHOWN PRIOR TO ASSEMBLY
-140-
0 00002-ltich diameter Pt 10 percent rh wires have been successfu ly mounted n lengths of 0.004 inch, annealed and calibrated in the controlled oven. xLy have also been immersed in the supersonic Clow without breakage and there heat-transfer characteristics in that flow have been measured. Ihcse
are pictured in Figures 82 and 83.
c Wire Conditioning Circuit. A hot-wire conditioning circuit for mounting, annealing and calibrating hot-wire jrobea has ^en designed and built by ?hilco-Ford personnel. It has greatly facilitated the hot-wire work reporved herein.
d VH.h-Freauencv Ampliiier. The need to cover the frequency range of turbulence oxtant il present and proiected experiments without overtaxing present techniques of electronic and computer compensation, ^ been frustrated by the lack of commercial^ available hot-wire amplifiers flat to 2 MHz. A new amplifier has therefore been designed and is now being built at the Company. Frequency response is designed to 2 MHz at a gam of 1,000. Compensation to 10 microseconds will be available as "«^ " innovations such as pushbutton wire current selection Two -f J.^1 ;C1S
are being built since two-point correlation measurccnts in the wake are
being planned.
e. Correlation Probes. For two-point correlation work, two novel probes arl being readied. For the supersonic wind tunnel a two-degree-oi- Leedom (five degree if the translation of the entire probe is included) two-wire probe will be used- for the plasma wind tunnel a six-deg ee-ol freedom, two-wire (or langmuir) probe is being adapted rom an ea 1 ei design. These probes pictured in Figures 84 and 85 will be actuated remotely so that the operator will be able to change the spacing of the two sensors rapidly and at will along any of two (or three) Cartesian axes.
f Processine Electronics. Other electronic circuits now planned include a constant-temperature anemometer amplifier and a circuit ^ performing one or more of the following operations on two sepainte signals. addmon, subtraction, multiplication, division, averaging, and integration.
7.2.3 ADDITIONS TO COMPUTATIONAL FACILITIES
In addition to the regular computing facilities available from the Aeronutronic Computing Services Center, Time-Si aring services arc now conveniently available for this work. A terminal to the I.os Angeles General Electric 235 System it available on full-tin« basis. The -ost common language is BASIC and FORTRAN II. Ln addition ^ the SPECTR
program shown in Appendix B, two BASIC language ^Y™ iVft^\ud hove been written for calibrating the hot-wire in the con rolled oxen and in the supersonic flow. These are shown in Figures 86 rnd o/.
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,-146-
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-U7-
7.2.4 THE NEW DATA ACQUISITION AND A/D CONVERSION SYSTEM
in the present period a review was made of needs to improve the flow of work from the data acquisition to the data analysis stage. Four major needs were delineated:
(1) Accelerate the analog-to-digital conversi process.
on
(2) Accelerate certain steps in data acquisition such as recording the spectra.
(3) Store the raw signals of a complete experiment
(4) Enable certain measurements such as two- point correlations.
The main criteria for the A/D conversion scheme were (1) continuous monitor-
P» i 'nnn^ 0g ? ^ dT8ital StaRe' and (2) compatibility with the Philco-2000 digital computer. Candidates for conversion were first dc bivanate signals fe.g., mean-square wire voltage versus probe position voltage) and secondly, the high-frequency time-dependent raw hot-wire signal containing frequencies up to 2 to 3 MHz. The conversion of each dc signal is accomplished by channeling the analog voltage through a digital TnlTT1: ,,,ewJett-p^k^d ^del Xo. 3440A) to a coupler and then to an IBM Model N0..6 card-Puncher which is continuously monitored by a digital recorder (Hewlett-Packard Model .o. 5030A). The output of the latter aJso gives 2* option of manual keypunch if desired. Finally, a Mosely Model MO. F-3B Line Follower System will be available for non-real-time A/D conversion of data already accumulated in analog form.
Spectra luwe been hitherto recorded in analog form at five-minute intervals In the supersonic tunnel as many as 1000 spectra per experimert are needed ' resulting in a .rent Jeal of effort. In Liu n.w syte«' th« .weep with frequency is done electronically in real time, so that an acceleration of the spectral measurements by a factor of 3 to 5 is thought possible.
A H.Mu^vii todel »a, 7o0() .even-chonnel mgnetU tope recorder has been acquired n.a.n 1 y in the purpose oi .torlng the rot lignola for future pro- cee.lng as the «eed arises and as tech, Lqutfl become availabK. A second important us. ot the playback »Ul be to "opltce-off« the tape eloctroolcoll. for measurement ol the .ddy proportle., A third Euoctlofl wUl be to bring ■
he si.na . uuh:. the uvquencv range ol processing eloctroolc. hovlng sta e-ol-tlu-art bandwidth 1 imitations. Pot example, the state-.i-the-art
bei w'the ^oon^nah'-dt'lay -—or-1'^'- c-rrentl, is 250 kH.:. much be n the 2.000 kH. rooje ot turbulerue. By recording the latter si.nal at 120 ips and playuu back at 15 Lps the s^nal conei within the 250 kH.: range .
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fr
7.3 INFORMATION EXCHANGE
Contact with other ARPA contractors has been maintained and accelerated in the current period through personal exchanges (visits, telephone conferences etc.) and technical reports issued by Philco-Ford and distributed via SAMSO channels. Especially useful have been the exchanges with the following:
(1) Cal Tech Hypersonic Group (Lees, Kubota, Behrens).
(2) University of Southern California (Lauier).
(3) Jet Propulsion Laboratory (Kendall).
(4) University of California, La Jolla (Lin, Gibson).
(5) University of Colorado (Scinborn) .
(6) Bell Telephone Laboratories (Granatstein).
(7) TRW Systems (Webb, Lewis).
(8) RCA Montreal (Jonnson).
(9) Stanford Research Institute (Guthart).
(10) Aerospace/El Segundo (Ross).
(11) Aerospace/SBO (Renau) .
The three Technical Reports issued in Lhe current period are:
(1) "Turbulent Front Structure of An Axisymmetric Compressible Wake", Philco-Ford Publication No. UG-4259, SAMSO TK 68-44, 15 November 1967.
(2) "Mean Flow Measurements In A Self-Preserving Turbulent Plasma let", SAMSO TR 68-166, February 1968.
(3) "Turbulent Mean-Flow Measurements In A Two- Dimensional Compressible Wake", SAMSO TR 68-369, July FSB.
Publication in the technical literature of selected portion of this work, as approved by SAMSO, has stimulated valuable feedback from the technical community. In the current period publication activity was as follows:
(1) "Mean Flow Measurements in An Axisymmetric Compressible Turbulent Wake", A1AA T., Vol. 6, No. 3, p. 432, March 1968.
-149.
(2) "Turbulence Measurements It An Axisymmetric Compressible Wake", Physics of Fluids, Vol. 11, No. 9, p. 1841, September 1968.
(3) "Turbulent Front Structure of An Axisymmetric Compressible Wake", to be published in the Journal of Fluid Mechanics, 1968.
(4) "The Mean and Intermittent Flow of A Self- Preserving Plasma Jet", accepted for publication in the AIAA Journal.
(5) "Turbulent Mean-Flow Measurements In A Two- Dimensional Supersonic Wake", accepted for publication in the Physics of Fluids.
(6) "Structure of Compressible Turbulent Wakes", Proceedings of the 25th AMRAC Meeting, Washington, D.C., 24-26 April 1968, p. 327.
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APPENDIX A
THE JEA-II COMPUTER PRf '.RAM
The purpose of the JEA-II program was to reduce the raw data of the electron density spectra measurements taken in the turbulent plasma jet. The program also calculates the total mean square values and the longitudinal integral scale. Inputs to this program wpre the wave analyzer center frequency, F, signal level, Vs, noise level Vn per 200 Hz bandwidth, the mean current E^an, directly from the Langmuir probe and the mean velocity U taken from the JEA-I computer program. Input consisted of data at zero Hz, 500 Hz, 1000 Hz, and then in steps of 1000 Hz up to frequencies where the signal and noise levels were the same. The highest frequency was 2b kHz. Therefore the input consisted of less than 30 input frequencies per spectrum.
moan The program output listed the following data: the probe position, x in inches from the jet nozzle, Y in volts (1 volt = 1/4 inch), the total m square value equal to the area under each spectrum curve E INT, the ratio of the mean square spectal density at zero frequency to the total mean square value under the spectra curve E(0)2/E2, and the longitudinal integral scale LAMDAF. Listed as a function of frequency are the following: rms signal value per 200 Hz passband E(F)S, rms noise value per 200 Hz passband E(F)N, mean square value per 200 Hz passband of the true signal (signal- noise) E(F)2, the ratio of the true rms per 200 Hz to the total mean value for all frequencies, Al, the ratio of the mean square per cycle to the total mean square for all frequencies A2, ratio of the mean square per cycle to the normalized mean square at zero irequency \3, and finally the normalized wave number, FN. The program computational procedure appears on Figure A-l, its listing on Figure A-l and a typical output page on Figure A-3.
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4
-155- Patf -15h- Intinl 1 -nal1\ Lilt Bl.mk
APPENDIX B
THE SPECTR COMPUTER PROGRAM
The SPECTR computer program was written for the CE Time Sharing computer to reduce the hot wire anemometer temperature spectra data taken in the turbulent plasma jet. Inputs to the program as a function of every 333.J Hz were signal, S, and noise, N, levols. The program was limited to 41 sets. FORTRAN II language was used. Other input tot each spectra consisted of mean velocity, u, from the JEA-1 program, and hot wire time constant, TK'. A number of other inputs were initially integrated into the program such as wave analyzer bandwidth, compensated time constant setting, amplifier gain, and the equations describing the hot wire response curve and the characteristic roll-off curve of the hot wire amplifier, as well as the conversion factor for changing inch readings of data measurements into millivolts.
The program listed the following outputs as a function of frequency: The signal Vi and noise D| levels; true signal H, (signal-noise); correction factor, OT, to adjust for drop-off of hot wire response and amplifier with frequency; corrected mean square of the true signal, E2; normalized corrected mean square of the true signal DN; and finally the r.ondimensionalized wave number FL. Also included is the total mean square value under the spectral curve before using the correction factor U, and after using the correction factor 12; the ratio of the two is given as J; and the longitudinal temperature integral scale is given as LT. The computational procedure of this program appears on Figure B-l, the program appears on Figure B-2, and a typical output (at a point in the jet) on Figure B-3.
-157-
3 c
3C
o.
e i s i N
Q
a
q
—
c
u
-158-
rl .» ~4_
SPECTR
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r CISC 0140
c'LOiU 0159 0160
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D^ 4 0r It",NP"v. 1 400 A^FA : A^^A + HtI )
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l:^rMFIil 690 AnFArAREA+ESCI ) l2sARCA«SSS#SSS599/6C/aQ ^IZ/ll LT:U*E2(l)/(4.*I2*Gr*ür) D0 700 1:1 NF Iflfl Fm3iFCl)»LT/U PFtr.T,*"*"lNPUT3" PRI1T,** v IN WILLIVtU-TS II pg?MT " ü l"! CÜ/SEC IS PRINT, * BANJJIDTH CONSTAWT C^ IN CP^ 12 PRINT* * WIRE TINE CTNSTANT T *' IN SECENJS 12 EBULI, " _ lUSTBUMENT TI.1E MMTAJUl IN SF-CÖNöS P^IST. " STRAIGHT A^PLIFI"^ GAIN 12
FIGURE B-2. THE SPECTR PROGRAM
-159-
9
H »
• F3
T',' TI U0
o'ssn PRINT;*Aä"0UTPUTS"
I 0500 PRINT Ä F(l).V(l)fD(l)#H(l),ßT(l) X- 0<510 DO 300 Ir2,NF CS20 J»fil?lT, F(l)rV(I),D(I) M(1J.flTcn 0'3^0 300 CÖNTINUR " 0*540 PTJT.--- F E2 DN Fl "
-0440 PiU::i * FCUt£2(llfDNCU.FLCn G^O Dl1 ^00 1 = 2 NF
■ 0570 PRINT, FC I),E2(I),DN(I).FL(I) üS7ä 500 CONTINUE ^30 PRINT *ST<!lJ.>!;iARY" ^?C PRINT," II -- ",11 C7C3 PRINT." 12 = ■" 12 OTin PRINT " J : "j C720 PK'IM," LT r "J ).;
jit* IF CNCÄSr-t.'U:'HFR) -»rn - ■ 7^ 3TCr
■ ^»i S»d ... - ne:00 IDATA
M* JFF f,T lit29 ELAPSE^ TER.'tlfiAl. Tl.lE : 5 »U.*
I '■'_
FIGURE B-2. (Continued)
-160-
1070 lIo6o,2.4l92E-3,-4.n3l2E-5,2.0l72E 4, s,?'*^- ->.
MM
_SMCIÄ 43122 L» SYSH «/28/68
UPUIS
N IN MILLIVCLTS IS T500*00
iämmUmmx FB IN CPS IS tm wo.oo SIRE TIPIE CONSTANT TW IN SECBNDS IS .004= IHSTRUMEiT TIHE CONSTANT IN SECONDS IS ^.0043 STRAIGHT AMPLIFIER GAIN 13 47.
OUTPUTS
F V
.00 1050.00 335.00 855.00 666.00 487.00
1000.00 590.00 1533.00 550.00 1665.00 230.00
2000.00 240.00 2533.00 210.00 2666.00 180.00 3000.00 160.00 5533.00 140.00 5666.00 125.00 4000.OC 110.00 4535.00 100.00 4666.00 90.00 9000.00 82.00 5555.00 78.00 56S6.00 71.00
6000.00 67.00 6333.00 64.00 6666.00 61.00 7000.00 60.00 7555,00 5«>.C0 7666.00 59.00 5000.00 58.00 8555.00 58.00 8666.00 59.00 9000.00 59.00 9355.00 59.00 9666.00 5^.00
45.00 56.6796 [•S® 50.00 29.177 .2023 15.00 17.0199 1.2355
Itrfltl l:r«? 9.7676 1.2329 8.5563 1.2307
26*00 7.2862 1.2554 MM 6.2057 1.2914 52 00 5.4814 1.3049 52-00 4.7572 1.5257
4.1955 1.5479 3.622 l.^77^ 5.2542 1.4124
^;ü J.«IJ [•uif 2.483 1.4933
13.00 19.00 22.00
55.00 55,00 57.00 58.00
41.00
»1,00 52.CO
1.5493 42.TG 2., . ... _ 43#00 1.9754 .MM 44 nr 1.7667 1.5585 MM »."58 [.mj 47 00 1.3595 1.8104 SiM 1.2537 1.8908 50.00 1.0951 l.?77i
.9553 2.0-'r)3 5933 2.17C3
55*00 '.3237 2.2769 11:11 Usn ^ 55.00 .7^56 2.51^ 56.00 S4Q4 2.54C7
'.5 325 2.7775 57.00
nCVKE B-3. TYPICAL OITPUT OF THE SPKCTR PROCRAM.
-161-
.00 353.00
—m.nn 1000.09 1333.00 l<U»Ofl 2000.00 2333.00
3000.00 3333.00
4000.00 4333.00 4&&&JU1 9000.00 5333.00 36M.Qfl sooc.oo S533.00 5SS6.CC 7000.00 7333.00 7SSS.00 8000.00 3353.00 S6SS.C0 9000.00 9333.00 9SS&.00
SUMMARY 11 • 1.9017 12 : 2.2S27 J :: 1.1898 LT = 2.5235
6.7269 1.00 .00 5.1199 1 if ft?
.7611 .112 •2241 .3365 I.t0l3 .1786
.8993 .1271 .4435 •tat .091 .5605
.4471 .066f .672-5
.5407 .0906 .735
.2487 .037 .097
.198 .0291 1.0094
.1498 .0223 1.1214
.118« .0176 1.2335
.0904 .0134 i.3459
.0739 .011 1.4579
.0577 .0086 1,5699
.0462 .0069 UC023
.0409 .0061 1,7944
.0313 .0047 1.9064
.026 .0039 B«0188
.021 .0031 2.13C£
.0167 .0025 2,242?
.015 .0022 2,3553
.0119 •00 li 2,4675
.0097 .0014 2.5793
.0038 • 0013 2.6917
.0077 .0311 2.8058
.0033 .0012 2.915=?
.007 .001 3.023Ä
,0056 8.27869E-04 I.I402 .0039 5.85509E-04 3.2523
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FIGURE B ). (t..nt .nurd)
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I,
REFERENCES
i. DeaetrUdef, A., "Turbulent Mean-Flow lte«aureraenti in 6 Two-Dlroen- sional Wake," Philco-Forci Fubl icat Ion No. UG-4431, SAMSO TR 68--3b9 (October 1968).
2. D.metriades, A. and Doughman, E., "Mean-Flow MeasuremeMCs in a Self- Preserving Turbulent Plasma Jet," SAMSO TK 68-166 February 1968).
\, Dcmctriades, A., "Mean-Flow Measurements in an A.\ isymme tr ic Compress- ible Turbulent Wake," Philco-Ford Corporation Report Ü-3978, Newport Beach, California (March 1967). Also, AIAA Journal. Vol. 6 No. 3 (March 1968), p. 432.
4. Demetriades, A. "Turbulent Front Structure of an A>c isymme trie Com- pressible Wake," Philco-Ford Publication No. ÜG-4259, SAMSO TR 68-44 (15 November 196 7) .
5. Demetriades. A., "Turbulence Measurements in an Axisymmetric Compress- ible Wake," Philco-Ford Report No. ÜG-41IS, Newport Beach, California (August 1967). Also, Physics of Fluids. Vol. 11, No. )) (September 1968), p. 1841.
6. "Advanced Penetration Problems, Wake Structure Measurements," Final Report, Contract AF 04(694)-994, Philco-Ford Publication No. t" 4201 (15 October 1967) .
7. Lees, L. and Gold, H., "Stability of Laminar Boundary Layers and (fakea at Hypersonic Speeds," Proceedings of International Symposium on Fundamental Phenoma in Hypersonic Flow, Cornell University Press (1966).
8. Townsend, A. A., "The Structure of Turbulent Shear Flow," Cambridge I'niversity Press (1956).
9. Kovasxnay, L. S. G., "Turbulence in Supersonic Flow," Jeurnal of Aeronautical Science. Vol. 20, No. 10 (October 1953), p.657.
10. Morkovin, M. V., "Effects of Compressibility on Turbulent Flows," Coll. International Du Centre Nationale de la Recherche Scientifique, No. 108: Mecanique de la Turbulence, Editions Du Centre Nationale de la Recherche Scientifique, 15 Quai Anatole, Paris, France (1962), p. 367.
U. Corrsin, S. and Kistler, A. L., "Free-Stream Boundaries of Turbulent Flows," NACA TR 1244, Washington, D.C. (1953).
12. Guthart, H. , Weissman, D. E. and Morita, T., "Measurements of the Charged Particles of an Equilibrium Turbulent Plasma," Physics of ElUidli Vo1- 9, No. 9 (September 1966), p. 176b.
REFERENCES (Continued)
13. Granatstein, V. L., "Structure of Wind-Driven Plasma Turbulence as Resolved by Continuum Ion Probes," Phy .jcs oi Fluids. Vol. 10 No. 6 (June 1967), p. 1236. '
14. Johnson,. T. (Private Communication, RCA, Montreal (1968).
15. Demetriades, A., "Electron Fluctuations in an Equilibrium Turbulent PlasmV AIAA Journal. Vol. 2, No. 7 (July 1964), p. 1347. Also Demetriades, A., "Reply by Author to F. Lane and S. L. Zeibera "' AIAA Journal (1965).
16. Guthart, H., "Spectrum of Neutral and Ion Density Fluctuations in an Equilibrium Turbulent Plasma," Physics of Fluids. Vol. 8, No. 5 (May 1965), p. 999.
17. Bradbury, L. J. S., "A Simple Circuit tor the Measurement of the Intermittency Factor in a Turbulent Flow," Aeronautical Quarterly Vol. 15 (1965), p. 281. ^ ^
18. Becker, H. A., Hottel, H. C. and Williams, G. C, "The No^le-Flu id Concentration Field of the Round Turbulent Free Jet," Journal of Fluid Mechanics. Vol. 30, Part 2 (1967), p. 285.
19. Bradbury, L. J. S., "The Structure of a Seit-Preserving Turbulent Plane Jet," Journal of Fluid Mechanics. Vol. 23, Part 1 (1965), p. 31.
20. Demetriades, A. and Doughman, E. L., "Langmulr Prob.. Diagnosis of Turbulent Plasmas," AIAA Journal. Vol. 4, No. 3 (March 1966), p. 451.
21. Bettinger, R. T. and Walker, E. 11., "Relat ionsln p lor Plasma Sheaths about Langmuir Probes," Physics oi Fluids. Vol. 8, No. 4 (April 1965), p• 748.
22. Sutton. G. W., "On the Feasibility of Using a Langmuir Probe to Measure Electron Densities in Turbulent Hypersonic Wakes " \vo- Everett, R. R., 276 (June 1967).
23. Proudi.n, A. P. and Feldman, S., "A New Model for Mixing and Fluctua- tions in a Turbulent Wake," AIAA Journal. Volume J, No. 4 (April I9b5) p. 602. vMiii lyojj,
24. Lin, S. C. and Hayes, J. E.. "A Quasi-One-Dimensional Treatment of Chemical Reactions in Turbulent Wakes of Hypersonic Objects," AIAA Journal. Vol. 2, No. 7 (July 1964), p. 1214.
25. Wygnanski, I. and Fiedler, H., "Some Measurements in the Self- Preserving Jet," Boeing Scientific Research Laboratory Report No. DI-82-0712 (April 1968). f
-164-
REFERENCES (Continued)
26. Corrsin, S. and Uberoi, M. S., "Further Experiments on the Flow and Heat Transfer in a Heated Turbulent Jet," NACA TR 998, '„'ashinuton D. C. (1950).
27. Laufer, J., "On Turbulent Shear Flows of Variable Density," AIAA Paper No. 68-41, 6th Aerospace Sciences Meeting, New York, New York (January 1968).
28. Demetriades, A., "Some Hot-Wire Anemometer Measurements in a Hyper- sonic Wake," Proceedings of the 1961 HTFMI, Stanford University Press, p.l.
165- Page -166- Intentionally Left Blank
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. o..G.N*T,NcACTl.l.yrco^ C5 1«. mSZmTZZZTi c W^^.C.T,^
Philco-Ford Corporation, Space and Re-entry Systems I Unclassified Division, Newport Beach, California
3 0 SHOuP
N/A 1 «POUT TITLt Advanced Penetration Problems, Wake Structure Measurements
4 DESCRIPTIVE NOT« fTyp« ol wport «nd mc/u«.^ d«»«») "" "—
Final Report, 15 October 19b7 Lo 15 October 1968 S AUTHOR'S) rZ.a*r name lint nam» Inlllml)
Demetriades, A.
« PEPO PT DATE
31 October 1968 7# T0T4LN0 O* PASFS
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12 SPONSONINC MILITAPV ACTIVITY
13 ABSTRACT
This report summarizes experimental work done in the period 15 October 1967 to 15 October 1968 on the structure of compressible turbulent wakes and turbulent plasmas. Detailed point measurements in the two dimensional wake, made very far from the body, have fully confirmed the predictions of the Dynamic Equilibrium Hypothesis regarding the asymptotic values of the velocity and temperature fluctua- tion and the statistics of the interface. For flight at angle of incidence radical changes in the wake structure have been observed, while heat transferred from the model to the flow was found to delay greatly the onset of transition to turbulence. In the plasma jet transition zone the remnants of the laminar fluid create a turbulent fluid of highly heterogeneous electron densitv with hitherto unexpected statistics. The longitudinal scales of the electrons'are larger than those of the temperature but numerically not much different from low-speed turbu- lence scales. The electron density fluctuations always predominate the temperature fluctuations especially at the higher frequencies. Spectral decay obtains a (-5/3) range for the temperature but this behavior is not observed for the 8lectrons .
DD FORM 1 JAN «4 1473
-167- Unclass itied
Security Classification
ünclassifled Secufity Classificatmn
14
Kf V WORDS
Compressible turbulent wakes
Compr«..ibl€ turbulent plas.nas riaaaa jet t ransition Elect ron dcnait y Spectral decay
Laminar £luid
LINK A
«OLE
LINK B
ROLE
LINK C
ROLt T
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