AFOSR-76-3006 C.oA Memo. 7706
GLANCING INTERACTION WITH A TURBULENT
BOUNDARY LAYER
Clifford C. Dickman
^
^
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July 1977 TECHNISCHE HOGESCHOOL DELFT LUCHTVAART- EN RUIMTEVAARTTECHNIEK
BIBLIOTHEEK Kluyverweg 1 - DELFT
Cranfield
College of Aeronautics
Report for the period : 1 Oct. 1976 - 30 June 1977
Approved for public release ; distribution unlimited
PREPARED FOR AIR FORCE WRIGHT AERONAUTICAL LABORATORIES , UNITED STATES Alf? FORCE AND
REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM
1. Report Number 2. Govt Accession No, 3. Recipient's Catalog Number
4. Title (and Subtitle)
GLANCING INTERACTION WITH TURBULENT BOUNDARY LAYER
5. Type of Report & Period Covered Interim Report.
1st October 1976 - 50th June 1977,
6. Performing Org. Report Number
Author(s)
Clifford C. DICKMAN
8. Contract or Grant Number AFOSR 76-5006
9. Performing Organization Name and Address Cranfield Institute of Technology, College of Aeronauticst
Aerodynamics Department,
Craiifield, Bedford MK45 OAL, U.K.
10. Program Element, Project, Task Area & Work Unit Numbers
61102P
1929-04
11. Controlling Office Name and Address
Air Force Fli^^t Dynamics Laboratory ( F X G ) Wri^t-Patterson AFB, Ohio 45455
12. Report Date
July 1977
13. Number of Pages106
14. Monitoring Agency Name and AddressBOARD (BOX 14) FPO N.Y, 09510
15.
16. & 17. Distribution Statement
Approved for public release; distribution unlimited. 18. Supplementary Notes
19. Key Words
GLANCING INTERACTIOl, TURBULENT BOUNDARY LAYER
20. Abstract
An investigation intc a glancing interaction with a turbulent boimdary layer has been conducted. Schlieren and oil flow visTialisation techniques were used and the test wall was extensively pressure tapped to record the pressure vsiriation throughout the whole of the interaction region. For a particular shock strength the boundary layer downstream of tne glancing interaction was esamlned in some detail. Results of these
experiments are dlscxissed and reasons for the flow behaviour are put fozrward.
11 TABLE OF CONTENTS SECTION 1. INTRODUCTION 2. EXPERIMENTAL PROGRAMME 2.1 General Objectives 2.2 Specific Test Plans
2.2.1 Geometrical Arrangement 2.2.2 Wind Tunnel 2.2.2.1 Mach Number 2.2.2.2 Reynolds Number 2.2.2.5 Summary of Experimental Conditions 2.2.5 Test Sections 2.2.4 Experimental Measurements 2.5 Typical Data and Techniques
2.5.1 Oil Flow and Schlieren Studies 2.5.2 Static Pressure Distributions
2.5.2.1 Scanning Valve and Data Reduction
2.5.5 Probe Traverse Instrumentation 2.5.4 Pitot Surveys
2.5.5 Static Pressure Siirveys 2.5.6 Pitch Surveys
2.5.7 Total TeDiperature Svirveys 5. ANALYSIS OF RESULTS AND DISCUSSION
5.1 Static Pressure Distributions 5.2 Static Pressure Surveys
5,5 Pitch Surveys
5.4 Mach Number Boxmdary Layer Profile 5.5 Total Temperature Surveys
5.6 Velocity Profiles 4. CONCLUDING REMARKS 5. LIST OF SYMBOLS
SECTION 6. APPENDICES A Appendix Ax Appendix B: Appendix C: Appendix D: Appendix E: Appendix P:
TA.3Lt OF CONTENTS (contd)
through P 29
Schlieren Results of Wind Tunnel 50 Calibration
Schlieren and Oil Flow Visualisation of 55 the Glancing Interaction
Pressure Tapped Sldewall Relative to 47 Model
Determination of Working Section ' 5 1 Reynolds Niunber
Graphs of Sldewall Pressure 54 Distributions
Graphs of Boundary Layer Probing 85
iv
LIST OF ILLUSTRATIONS
Figure No. Title Page
1 Region of Investigation 4
2 Schematic of working section with model 8
5 Coordinate System 10
4 Relative position of pressure tappings to 15 leading edge of shock generator
5 Schematic of pressure scanning valve 15
6 Black diagram of scanning valve logic system 16
7 Location of botindary layer probes 17
APPENDIX A
Plow past a wedge. 0 = 5.5°» \J = 50.0°, 51 M » 2.58
5 - 7.8°. 0 - 52.5°, '52
M = 2.56
A5 Flow past a wedge. 5 =15.0° 0 » 57.0°, 35 M = 2.56
A4 Plow past a cone. 0 «11,5°, 0 = 27.0°, 54 M = 2.40
APPENDIX B
B1 and B2 Model installation in working section of wind 56 tunnel
fi5 Schlieren photograph of working section 0 =>
B4 Oil flow pattern on side wall produced by the model at 5^ Incidence (shock and expansion waves superimposed from Figure B5)
A1
A2 Flow past a wedge.
B5 Schlieren photograph of working section
5.
B6 Oil flow pattern on side wall produced by themodel at 7° incidence (shock and expansion wave superimposed from Figure B5)
5°
7°
57
58
59
40
Figure No. Title Page B7 Schlieren photograph of working section 0 = 9 41
B8 Oil flow pattern on side wall produced by 1;he 42 model at 9^ incidence (shock suid expansion
waves superimposed from Figure B7)
B9 Schlieren photograph of working section Q = 10 45 (incipient separation noticed at this
deflection angle)
BIO Oil flow pattern on side wall produced by the 44 model at 10^ .incidence (shock and expansion
waves superimposed from Figure B9)
B11 Schlieren photograph of working section 0 = 11 45 (Tvinnel "chokisd" due to shock induced
separation of boiindary layers)
B12 Oil flow pattern on side wall produced by the 46 model at 11° incidence (Tunnel "choked")
APPENDIX C
CI Relative position of pressure tappings to 48 model at 5*^ and calculated shock waves and
expansion fan
C2 Relative position of pressure tappings to 49 model at 7° aj:
expansion fan
model at 7° suid calculated shock waves and
C5 Relative position of pressure tappings to 50 model at 9° a.'^ calculated shock waves and
expansion fan
APPENDIX E
El Pressure distribution along side wall 55 Y = 0,5) inches
E2 Pressure distribution along side wall 59 Y = 0.8) inches
E5 Pressure distribution along side wall 65 Y = 1.03 inches
E4 Preasxire distribution along side wall 67 Y = 1.5) inches
vi
Fi£ure_No. Title Page E5 Pressure distribution along aide wall 71
Y = 1.55 inches
&6 Pressure distribution along side wall 75 Y = 1.80 Inches
E7 Pressure distribution along side wall 79 Y = 2.05 Inches
APPENDIX F
PI Transverse pressure variations 84 P2 Variation in .riow direction throu^ boundary 86
layer
P5 Mach number profile 88 P4 Total temperature variation through boundary 89
layer
P5 Velocity profile 90 F 6 Velocity profile of boxmdary layer 94
LIST OF TABLES
Table No. Title Page APPENDIX A
A1 Calibrated Maoh number in working section 50
APPENDIX E
El Pressure distribution for deflection angle 56 of 5° at station Y = 0.55 inches
E2 Pressure distribution for deflection angle 57 of 7° at station Y = 0.55 inches
E5 Pressure distribution for deflection angle 58 of 9° at station Y = 0.55 Inches
E4 Pressure dis-':ribution for deflection angle 60 of 5° at station Y = 0.80 inches
E5 Pressure distribution for deflection angle 61 of 7° at station Y = 0.60 inches
E 6 Pressure distribution for deflection angle 62 of 9° at stal ion Y = 0.80 Inches
E7 Pressure distribution for deflection angle 64 of 50 at station Y = 1.05 inches
E8 Pressure distribution for deflection angle 65 of 7° at station Y = 1.05 Inches
E9 Pressure distribution for deflection angle 66 of 9° at station Y = 1.05 inches
E10 Pressure distribution for deflection angle 68 of 50 at station Y = I.50 inches
Ell Pressure distribution for deflection angle 69 of 7° at station Y = 1,50 inches
El2 Pressxire distribution for deflection angle 70 of 9° at station Y = I.50 inches
El5 PresstLre distribution for deflection angle 72 of 5° at station Y = 1.55 inches
EI4 Press\ire distribution for deflection angle 75 of 70 at station Y = 1.55 inches
vlli
Table E15
£16
El 7
No, Title Page
Pressure distribution for deflection angle 74 of 9° at station Y » 1,55 Inches
Pressure distribution for deflection angle 76 of 5° at station Y «= 1.80 inches
Pressure distribution for deflection amgle 77 of 70 at station Y = 1.80 inches
B18 Pressure distribution for deflection angle 78 of 90 at station Y = 1.80 inches
El 9 Pressure distribution for deflection angle 80 of 5° at station Y = 2.05 inches
E20 Pressxxre distribution for deflection angle 81 of 7° at station Y = 2.05 inches
E21 Pressure distribution for deflection angle 82 of 90 at station Y = 2.05 inches
APPENDIX F
F1 Transverse pressure variations 85
F2 Variation in flow deflection through boundary 87 layer behind Incident shock wave
F5 Pitot and static pressure variation through 91 boundary layer
F4 Temperature variation through boimdary layer 92 F5 Velocity distribution throu^ boundary layer 95
P 6 Velocity profile 95 F7 and F8 Least sqviares fit to V7th power law 96
r
lx
SUMMARY
An investigation into a glancing interaction with a turbulent boundary layer has been conducted. Schlieren and oil flow visualisation techniques were used and the test wall was extensively pressure tapped to record the pressure variation throughout the >diole of the Interaction region. For a particular shock strength the boundary layer downstream of the glancing interaction was examined in some detail. Results of these experiments are discussed and reasons for the flow behaviour are put forward.
1
1. IMTRODUCTION
The glancing interaction of a shock wave with a turbulent boundary layer has been the subject of contintiing major Investigations. In particular, the shock strength, or pressure rise across the shock, necessary to induce separation and the heat transfer rates associated with the interaction axe of key interest to 'designers of h l ^ speed vehicles. Air Intakes, wing/body Junctions and control surfaces are all prone to shock induced separations and the consequential loss of power or control may greatly affect the perfozrmance of the vehicle*
McCabe (Reference 1) made the reasonable assumption that incipient sei>£Lratlon occurs when the surface flow becomes aligned with the shock wave. From this assumption, Korkegl (Reference 2) derived the simple relation that for incipient separation, the free stream Mach number, Mco and the flow deflection angle, Q were related byi
Moo 5 «= 0.50 (1)
This shows that the Mach number normal to the shock wave, M|^ = 1.20 and that the pressure ratio across the shock = 1.50. Good agreement with experiment was found for free stream Hach numbers up to 5*5.
Stanbrook (Reference 5) vas in agreement with Korkegl that the necessary shock pressure ratio to Induce separation was 1.5 and that this
o o corresponded to an inviscld flow deflection of between 7.5 and 8 •
Neiuuann and Hayes (Reference 4) investigated the magnitude of peak pressure and heat transfer encountered in a shock wave/boundary layer Interaction and showed that the data were correlated by the empirical relationships:
^ =
[MLSin 0 ] " ' = (2)
and rZH = IM, S i n 0 - 1 In- * 0-75 (5)
te obtained data, where Hp and n^^ are functions of non-dimensional distance /R and M L is the local Maoh number.
Further investigations by Peake (Reference 5) revealed that the development of the viscous flow in the swept Interaction region (leading eventually to three-dimensional separation with increasing deflection angle of the shock generator), was a gradual, progressive amd relatively steady process in which the flow leaves the three-dimensional separation line as a free shear layer to roll-up into a flattened vortex rou^ly within the depth of the original iindisturbed boundary layer. He also found that the precise shock generator angle at which incipient separation occurred was particvdarly elusive xuiless he applied McCabe's criterion
(Reference 1) of parallelism of the limiting streamlines with the calculated shock wave.
Oskam, Vas and Bogdonoff (Reference 6) found that McCabe's
criterion for incipient separation was not a stifficient condition to define flow 8epsu::ation. ;t^om surface pressure measurements and oil flow i>attems, as well as heat transfer data, they deduced that the interaction region was quasi-two-dimensional in an area well a%ray from the end-regions. This means that data presented in a coordinate system baised upon the shock location will be similar for all positions along t;he shock direction. They also showed that the downstream extent of the interaction in the free stream direction was at least four times as large as the corresponding upstream extent.
The study presented herein follows the general pattern of previous investigations but examines a wider region surrounding the interaction. The chosen geometry generates an oblique shock wave/
turbulent bovindary layer interaction at a free stream Maoh nximber of 2.4. The planar oblique shock is well-defined and normal to the test surface. The main objective was the study of the glancing interaction with one relatively thick (5mm) turbulent boundary layer.
3
2. EXPERIMENTAL PROGBAMME
2.1 General Objectives
In an attempt to provide a detailed mapping of the flow field of a three-dimensional shock wave/boundary layer interaction the test section of an Intermittent supersonic wind txinziel was arranged as follows. The oblique shock wave was generated by a variable incidence plate \diioh spanned the tunnel between the two side walls. Flow visualisation
techniques (Schlieren and surface oil flow) were used to Investigate the two-dimensional and three-dimensional interaction regions. A large region of the tvinnel side wall was pressure tapped to provide static pressure reaulings which began upstream of the interaction and continued throu^ the interaction and downstream of the expansion and reflected shock of the shock generator. To further describe the flow field, detailed measurements o:r total temperature, pitot pressure and static pressure were made in the boundary layer downstream of the three-dimensional interaction.
2.2 Specific Test Plans
2.2.1 Geometrical Airrangement
A schematic of the experimental configuration showing the region of detailed measurement is shown in Figure 1. The region of stvidy extends upstream of the shock to establish initial conditions. The region extends to the shock generator surface and is not limited in extent by the
expansion from the trailing edge of the shock generator or by the reflected shock from the bottom wall. These regions were inclxided in the survey in order to give additional information about the extent of disturbances travelling upstream through the subsonic region of the bovindary layer.
Because the shock strength (or pressure ratio across the shock) is of primary importance with regard to boundary layer separation, the shock generator or flow deflection angle was variable.
wave
Model
Measurements taken
within this area
Reflected shock
wave
5
2.2.2 Wind Tunnel
The experimental study was carried out in the Cranfield Izistltute of Technology intermittent supersonic wind tunnel. This tunnel has a cross-section of 6.55 cm by 6.55 cm (2^ inch by 2^ inch) and is driven by air at atmospheric pressuzre into an evacuated tank. Stagnation conditions were therefore nearly atmospheric but were sll^tly lower after passing throu^ a silica gel drying system. Because atmospheric conditions varied from day to day with the changing weather, the stagnation pressure and
temperature also fluctuated. The low pressure tank has a volume of 46 cubic metres (approximately 1600 cubic feet) and is continually evacuated by a 25 kilowatt (55.5 horsepower) electrically driven pump. For the present tests a Mach 2.5 two-dimensional nozzle section was used. Subsequent calibration of the wind tunnel did, however, reveal that the Ilach number obtained was sli^tly lower.
The above constraints resulted In a maximum running time of approximately 25 seconds and necessitated the use of several standard intermittent tunnel techniques to obtain steady state data. These techniques are described in the relevant experiments.
2.2.2.1 Mach Number
The working section Mach number was determined by several means. Existing cone and wedge models were moiinted on a sting and the Schlieren system was used to show the resulting shock wave angles. From the shock wave angles and known flow deflection auigles, the working section Mach number was evalviated using standard tables, (Reference 7 ) . Photographs of the Schlieren pictures are shown in Appendix A, Figures A1, A2, A5f A4. From these photographs the working section Hach number was shown to be approximately 2.4± 0.02, As an additional check, a pressure tapping was drilled thiou^ the top liner and was situated upstream of the shock generator. By measuring the stagnation pressure the free stream Mach number was calciilated using the isentroplc flow relations for each
experiment conducted and was found to be consistantly constauit and in good af^reement witn the Schlieren results. The resultant working section Mach number was established as 2.40.
2.2.2.2 Reynolds Number
The working section Reynolds number. Re was w/s
determined as follows:
The working section Mach momber was obtained as deHcribed in section 2.2.2.1. Isentroplc relations then gave the free stream static temperature for a given stagnation temperature. Stagnation 1;emperature had to be taken as atmospheric initially since the wind tunnel facility does not at present incorporate stagnation temperature measurement. Southerland's Law of viscosity was used to determine the working section viscosity aind density was obtained from the equation of state for the air
in the working section. Working section velocity was derived using the local speed of sound (from temperature considerations) and Mach nvunber.
The Reynolds number in the working section was shown to be 5
approximately 10 million per metre or 2.5 x 10 per inch. Details of tl
workinf'; may be found in Appendix D.
2.2.2.5 Sximmary of Experimental Conditions
Althouj-^h the flow conditions varied slightly from day to day, the followinfr values were typical:
Staf?iation Conditions
Sta^^nation pressvire, R = 720 - 7.5 mm, mercury Stagnation temperatui-e, T Q = 287°K i 10°K
Working section Mach number, M,„/ = 2.40
w/s _ Working section Reynolds nximber. Re = 10 /m. Working section Prandtl number, R- = 0.71
7
2,2.5 Test Sections
The boundary layer growing on the side wall was used as the test layer in all of the present experiments. To generate shock waves of varying strenfrths a plate tapered in thickness was mounted on a quadrant whicn was suspended from the specially made top liner of the tiuinel. The quadrant was adjTistable so that prescribed deflection angles co\ild be set. With the model brouf^t into contact with the top liner, the deflection an/rle was 5 • The model was 8.89 CM (5i inches) in length which
permitted the reflected shock wave from the bottom liner to pass well downstreeun of the trailing edge. The model spanned the tunnel between the two side walls and sealing grooves were cut in the model to prevent leakage between the model and the walls. The pivot point of the model was
desif^ied to exactly coincide with the leaiding edge. This featvire increased the maximum deflection angle possible and reduced lesikage around the leading edge.
Fiit'ure 2 shows a drawing of the model mounted in the test section and Fif:ures B1 and B2 are photographs of the test section revealin/T the model installation in the tvmnel.
Because of symmetry, both the side walls could be used as the test boundary layer. In the present experiments, after the Schlieren ima^:e8 haui been photographed, one of the glass side walls was removed and was replaced with a steel side wall. All the experiments were then
conducted on that side and the remaining glass sldewall served as an
observation window. •^
Only one static pressure tapping was drilled in the top li-^er and was situated near to and upstream of the leading edge of the model. All otner pressure tappings and probe moxmtings were located on the steel side wall.
Sealing grooves
Model (at 5" incidence
deflection surface 10')
Tunnel bottom liner
9
The coordinate system used in obtaining and presenting the data in the following sections is shown in Figure 5* Specific data were
obtained along stations parallel to the free stream at diffetrent
transverse distances from the leading edge of the plate. The coordinate system uses the calculated shock location to provide the framework for the measurements in the flow direction. The coordinate, Z » Is normal to the test wall and extends from the wall Into the free stream (through the boundary layer or interaction region).
Due to the low static pressure in the working section (0.065 atmospheres) great care was taken to ensure that the side walls were properly sealed to avoid leakage.
2.2.4 Experimental Measva-ements
Under the given test conditions, the boundary layer on the side wall had been able to grow along some 20 metres measured from the
atnospheric inlet before reaching the test section. Prom the Schlieren photographs. Figures B5, B5, B7, B9, the optical boundary layer thickness was estimated to be approximately 5 mm. The boundazy layer entering the interaction region has to be characterised along the swept line of the oblique shock. Therefore the initial conditions along this interaction are not exactly constant, as the boundary layer at some distance from the shock generator has travelled a longer distance than that entering near the tip of the shock generator. The difference in thickness however was assumed to be small due to the small percentage Increase In
compared wi1:h the length of inlet.
Four techniques were used to obtain information over the surface area of interest. The standard technique to obtain an indication of the fli}w direction on the surface is the use of an oil film which, due to the shearing action of the flow, forms a pattern of oil streak lines. A Schlieren flow visualisation technique was used in conjunction with the oil flow patterns.
^ r <^ <' t' ^ r^
Calculated shock, x^s 0
Model deflection surface
^ ^ ^ >' ^ -^ ^ ^ f
11
TWO hundred and ten static pressure orifices were arranged in seven rows of 50 tappings along the side wall to examine the pressure field on the wall for varying shock strengths. A micrometer drive was mounted on the side walls so that probes for measuring total temperature, pitot pressure and static pressure could be used for boundary layer
probing. A calibrated scale for pitch was used in conjunction with the micrometer drive so that a combined pitch-pltot survey wsta possible. 2.5 Typical Data emd Techniques
2.5.1 Oil Flow and Schlieren Studies
A technique developed for the specific test conditions and geometry used a mixtiire of titanium dioxide suspended in motor oil. A drop of oleic acid was added to the mixture to prevent coagulation of the titanium dioxide. A steel side wall was prepared with a polished black finish to provide the greatest contrast with the white oil mixttire. In order to photograph the flow pattern, it was found necessary to remove the side wall because the glass side wall opposite created reflections which could not be avoided. For this reason, preliminary experiments were conducted so that a titanium dioxide mixture could be determined which wculd reveal the surface flow pattern when the tunnel was running and would not change (due to gravity or surface tension) when the tunnel was shut down aivi during the time necessary to remove and photograph the side wall. Subsequent experiments were then conducted by applying the mixture with a paint brush so that the brxish strokes were perpendicular to the free stream direction upstream of the interaction. In this way, the ensuing flow pattern could be attributed entirely to the surface shear stresses.
With the shock generator at a fixed angle, oil flow visualisation photographs were taken and without altering the flow
deflection angle, both glass side walls were fitted to the working section and photographs of the Schlieren image were recorded. This enabled a more accurate estimate of the true shock location to be made so that it could be superimposed on the oil flow pattern for that i>articulaLr shock
generator angle. Typical flow patterns and Schlieren Images may be found in Appendix B.
2.5.2. Static Pressure Distributions
The pressure orifices of O.5O8 MM (0.020 Inches) diameter were azrranged as shown in Figure 4. Figures C1, C2, C5 are photographs of the installation and show the variation in calcxilated shook location for the tnree deflection angles tested.
During a test, a fixed generator position was held while the pressure measurements took place. The pressures were measured with a pressure transducer axid scanning valve eiasembly (see section 2.5.2.1). Experimental procedure was as follows: The pressure in the lines was allowed to fall as much as possible during the run. A pneumatically operated guillotine clamp was used to trap the pressures in the lines when the tunnel was closed down. When the low pressure tank in the wind turinel system had been sufficiently evacuated, the operating valve was thrown open and after several seconds when steady state conditions had been reaohed in the working section, the clamp was opened to allow the pressures to equalise. This procedure was repeated several times until the pressures in the lines had reached an equilibrium. With the clamp closed, the lines were sequentially connected to the transducer and
pressxire readings were taken. The volumes of the lines between the cleuap and the scanner in which the pressures were trapped were large compared with the scanner valve and transducer volume (more than 100 times) so that the volume when vented to the transducer was not materially affected.
Results were taken along rows of pressure tappings for three flow deflection angles, 0 = 5 * * » 0 = 7 ° and 0 = 9 ° .
2.5.2.1 Scanning Valve auid Data Reduction
In using the scanner valve, side wall or probe pressures were allowed to stablise in the lines leading from the guillotine clamp throu^ the stator of the scanner valve. The rotor was then turned, connecting each pressiire tube in turn to a pressure transducer through a slot (see
Model leading edge
\ . . / '
Model
(All dimensions in inches)
VJJ
Figure A. Relative position of pressure tappings to leading
edge of shock generator.
Figure 5 ) . Seals between the individual pressures at the scanner valve were commonly maintained by the very close contact of the hairdened steel surfaces of the stator and rotor which are lapped together. The force holding the two surfaces in close contact was provided by a low pressure vacuum pump (0.05 mm. mercury). The pressxire transducer responded linearly
to changes in pressure and was calibrated for each Individual run. The transducer was calibrated by obtaining two readings at known pressures. A "T-junction" from the vacuum pump connected to a port provided a low pressure reading and a port left open to atmosphere provided the second reading. All fiirther readings were then converted to absolute pressures from the known slope and intercept of the calibration curve.
All data reduction was made with the aid of the departmental Di{^ico Micro 16 microprocessor which accepted data from the punch in the
sctinner circuit.
2.5.5 Probe Traverse Instrumentation
To carry out detailed flow field measiirements in the Interaction region, a probe drive system was designed, built and attached to the steel side wall. The drive system was movinted so that the probes would be
located in the middle of the working section behind the interaction region. The drive assembly moved the probes normal to the wall and also pitched them so that the probes cotild be aligned with the local direction of the flow. Determination of distance from the wall was made by a micrometer. The pitch anple of the probe was determined with a needle connected directly to the portion of the probe extended from the side wall and poj.nted to a calibrated scale. Tlie ajxgles were measured relative to the
X - direction. Figure 7 shows the probe location relative to the snooks and expansions produced by the shock generator.
Care was taken to ensure that there were no leaks in the side wall where the probe passed through from the micrometer drive system to
Model pressure
tube connector
'O'-ring seal
Section on A-A
(Stator)
Balance pressure
vent
Pressure transducer
Stator
Section on B-B
(Rotor)
Rotor shaft driven by
solenoid or motor
Vent to model pressure
Vent to pressure transducer
Hardened steel surfaces
lapped together
VJ1
i- Slot for sequentially
connecting model pressure
vents to pressure
trans-— trans-— ducer vent.
Vacuum
0 IÜHRIIIINU 1 1IIN 8 HII li 1 1Scanner
^90 I - *»-Scanner
Control
1 1 rSignal
Conditioner
(amp.)
Data
Logger
Control
^Manual
Entry
Digital
Voltmeter
ITerminal
Panel
Punch
Drive
. • 1Punch
i fVisual
Display
l n f » r f n r »Visual
Display
Unit
OSModel
Expansion fan
^ c f' /'
Incident shock
wave
Reflected shock
wave
The shook generator wais fixed at a deflection angle of ^ for all the pressure and temperature probing.
2.5.4 Pitot Surveys
Since the determination of the pitot pressure req\iires that the flow direction be known, this measvirement was combined with the pitch surveys. The probe used was a flattened open ended piece of hypodermic tube vthich was bent through a right angle to permit it to pass through the tunnel side wall. The pitot pressvire was measured by connecting the probe to the scanning valve via the guillotine clamp in the same manner as the side wall pressures were measured. Two guides to the direction of flow In the boundary layer were already known: at the wall, the flow was known to be almost parallel to the shock wave produced by the shock generator while in the free stream outside the boundary layer, the flow was parallel to the deflection angle of the shock generator from izr^iscld considerations.
The experiments were conducted by initially estimating the flow angle and running the wind tunnel as many times as necessary until the pressure reading became sensibly constant. The exeict flow angle azid correct pitot pressure were then obtained by running the tunnel and
varying the pitch angle slowly tmtll a maximum reading from the transducer was obtained, which Indicated that the probe was pointing directly into the
local flow. Some nineteen points throTi^ the boundary layer were measured in this way. Because the Maoh number rises quickly with displacement throu^ the boundary layer to become greater than unity, Raylel^'s supersonic pitot formula was used in the data reduction when isentroplc relations could no longer be used. The local Mach number was also confirmed with tables (Reference 7 ) .
19
2.5.5 static Pressure Surveys
The static pressure probe used in this series of experiments was made of hypodermic tube. The nose of the probe was a cone of 56 Included angle and had four static orifices evenly spaced around xhe circumference located 6 diameters downstream of the shoulder. Pope's "Hij^ speed wing tunnel testing" (Reference 8) quotes that
Heasured Static Pressure
- 0.99 Stream Static Presstire
for this configuration.The probe was connected to the scanner valve in the same May as the pitot probe and the experiments were conducted in a
similar manner to those using the pitot probe except that alignment with the local flow direction was Indicated by a minimum pressiire reading. Pitch angles of the static probe were found to be in good agreeaient (- 1 ) with those obtained with the pitot probe.
Because the pitot probe had a flattened inlet, the centre lines of the probes did not coincide for the same readings on the micrometer drive assembly. In order to obtain pitot and static readings at the same centre line displacement from the wall, the micrometer was adjusted
accordingly. The static probing was conducted through the boundary layer and well out into the free stream.
2.5.6 Fitch Surveys
The pitch surveys were conducted in conjunction with the pitot and static probing through the boundary layer. In the oase of the pitot probe, the pitch angle was adjusted until the pressure reading was a
ma-ri imim and the statlc probe was varied in pitch until a alnimum pressure reading was obtained. Good agreement in pitch angles at a given
2.5.7 Total Temperature Surveys
The total temperatitre probe tised in these experiments vas made of the same hypodermic tube as the pitot and static probes. A chrome/ alumel thermocouple was embedded in the tip of the probe and was
insiilated from it to avoid errors due to conduction. At a given
displacement, the pitch angle was set to the corresponding angle obtained from the pltot/static experiments and the micrometer was adjtisted so that the centre lines of the probes coincided. A recovery factor of 0.95 was used in 1;he data reduction. The variation in total temperature through the botuidary layer is presented in Figure F4.
21
5. ANALYSIS OF RESULTS AMD DISCÜSSIOM
5.1 static Pressure Distributions
The variations in static pressure with free stream direction for varying shock strengths are graphically represented in Appendix £, Figures £1 throu^ E7. By using the cooz^lnate Xs for distance
measured from the shock location, the upstream Influence ( Xs '*^ 0 ) is easily checked. The first Mach line in the Prandtl-Meyer expansion
around the trailing edge of the shock generator was calculated and the points at \riiich this and the theoretically calc\ilated reflected shock cross the row of pressure tappings are indicated on the graphs. There axe
essentially three features of prime Interest to be noted from these curves. Firstly, the static pressure is slow to rise across the initial shock. Theoretically of course, the inviscld solution is a step function with
d(P/R) '
= CX> at Xs » 0 and _ L _ rising
d (Xyg ) P,
to a fixed strength for that shock generator position. Instead, the step has become "smeared" by the action of viscosity. The pressure requires approximately ten boundary layer thicknesses to reach its maximum value and this maximum value is still lower than the inviscld prediction by anything up to 10^ (when the influence of the reflected shock is not present).
Secondly, the upstream Influences due to signals travelling throu£^ the subsonic region of the boundary layer are felt as much as six bovindary layer thicknesses ahead of the initial shock wave.
Thirdly, the effects of the expansion fan and reflected shock wave are seen to greatly influence the pressure distributions when they are encountered and their presence is also detected upstream of their theoretical location. The influence of pressure due to the shock is again felt at approximately six boxuidary layer thicknesses upstream of the
theoretical location but the isentroplc expansion begins to modify the pressure distributions only one boundary layer thickness ahead of its location (see Figures £1 and E2) when the reflected shock influence is not felt).
One of the outstanding features of these curves which must be explained is that the shock strengths do not jreach the inviscld values. For this reason, a static pressure profile from the test wall throu^ the boundary layer and out into the free stream was necessary in order to discover whether or not there was a transverse pressure gradient which would account for the low values of the wall pressure rise and also to discover if indeed the inviscld shock strength was present outside the boundary layer.
5.2 static Pressure Stirveys
The result of the static pressure probing through the boundary layer is shown in Figure F1. The static pressure remains sensibly constant in the Z direction from the tunnel wall to the edge of the boundary layer. With Increasing distance into the Inviscld stream, the pressure appe£u:s to assymptote to a hl^er value than that obtained at the wall. This transverse pressure gradient shows that the values obtained at the side wall are significantly lower than those in the inviscld stream. Recalling that the static pressure probing behind the initial shock was conducted with a shock generator angle of 7 > the theoretical shock strength at a Mach number of 2.40 is 1.53. Figure F1 shows that the inviscld shock strength experimentally measvired is I.56 which is in good agreement.
5.5 Pitch Surveys
The results of the pitch survey are shown in Figure P2. The pitch angle remained constant with distance throu^ the boundary layer up to a value of Z/c> 'ï^ 0.8. The pitch then decreased almost linearly
23
assymptoting to the inviscld flow deflection angle of 7° at a displacement of 10 mm. or a value of Z/-. = 1.82.
0
The most striking feature of this curve is the fact that the flow continued to change direction outside the optical boundary layer for some considerable distance.
The flow upstream but near to the shock wave is nearly parallel to the shock (approximately 50 ) but the flow direction measured with the pitot probe behind the shock was found to be at an angle of 57*^ to the
X - axis; that is the flow behind the shock has been turned through a further 7°.
5.4 Mach Number Boimdary Layer Profile
The Mach number profile through the boundary layer althou^ of little importance is plotted in Figure F5. As in the case of the velocity profile, the curve must pass through the origin due to the no-slip
condition applied at the side wall.
One point worth mentioning is that the correct free stream Mach number of 2.4 Is reached at the edge of the boundary layer which further substantiates the results of the pitot / static probing.
5.5 Total Temperattire Surveys
This survey was conducted primarily to discover whether or not ti'ie total temperature throu^ the botindary layer coxild be assumed aa constant. The results are plotted in Figure F4. Although the equipment used to measure the stagnation temperature was not very sophisticated
(see section 2.5*7) the results are acceptable and in order to deduce the velocity profile from the Mach ntunber profile, an average sta^aation temperature of 297.5 K was assiimed.
5.6 Velooity rroflles
The velocity profile is plotted in Figure P5. Very little difference %ras noticed when compared with the Mach number profile. The velocity profile was then non-dimensionallsed with respect to free stream conditions and boundary layer thickness. This curve is shown in
Figure F 6 . There is very good agreement with the /7th power law normally fitted to a turbulent boundary layer. Althou^ the probe was aligned with the flow in the X-Y plane by varying the pitch angle it was not possible to align it in the X — Z plane (i.e. the plane
containing the model). There may well be considerable changes of the direction of the flow in this plane through the boundary layer and so the profiles presented here cannot be said to be truly representative of the actual flow. Moreover the agreement with a '/7th (or any other) power law is fortuitous since the boundary layer here is very skewed.
25
4. CONCLUDING REMARKS
Boundaxy layer separation due to the glancing interaction was found to occur at 11 , It was Indicated by a build-up of oil in the surface flow photographs along a line which was perpendicular to the free stream direction of the flow. At 10 incidence, the point of incipient separation was located. At this shock generator angle, the surface streamlines were parallel to the superimposed shock wave taken from a Schlieren photograph. This is in agreement with the criterion of three-dimensional separation put forward by McCabe. It differs from Korkegl*s
o theoretical prediction of 8
Pressure measurements along the side wall throu^ the interaction r(!glon have shown that the Influence of shook waves are felt approximately six boundary layer thicknesses upstream of the theoretical shook location. The pressure rise along the side wall requires more than ten boundary layer thicknesses to xreach the inviscld shock strength. A transverse P2*essure gradient (i.e. from the inviscld stream throu^ the boundary layer to the test wall) has been located and is to a large degree
responsible for obtaining shock strengths on the test wall vrtiich are lower than inviscld predictions.
Detailed jneasurements of bo\mdary layer parameters downstream of the incident shock have been made.
Heat transfer measurements with the Princeton developed heat gauge will commence shortly.
ACKNOWLSDGIMESTS
I would like to thank Professor J.L. Stollery for his continuous help and guidance in the experimental research and
preparation of this report. Also Mr. S. Clarke and the members of his workshop for their prompt and efficient work which was always done with a smile.
27
5. LIST OF SYMBOLS
speed of soxind
specific heat of air at constant pressure
specific heat of air at constant volume
Coefficient of conductivity for air
Mach number = )L
a
power index
pressure
heat transfer rate
Prandtl number m Reynolds number > Stanton number s absolute temperature velocity
MCp
k
PVx
Clw
PVCp(T^-T,)
UnitsVs
J/Kg deg.K J/Kg deg.K J / M s deg.K -MM Eg j/sec -m, Deg.K M/sec.coordinate parallel to tunnel axis measTured from leading ecLge of shook generator
coordinate parallel to X-axis measured
from calcvilated shock position
M
coordinate normal to X-axis in the plane of the test surface meas\ired from
leading edge of shock generator
Coordinate normal to X- and Ï- axis meaaarsd from test surface
ratio of specific heatS = T T -Lv
boundary layer thickness
shock wave angle measured from X-axis
coefficient of viscosity
density
pitch angle measured from X-«xis
suiiabatic wall conditions
local conditions
normal to shock wave
related to pressure
peak value
measured from shock location
related to Stanton ntimber
wall conditions
working section conditions
stagnation conditions
value upstream of shock wave
value downstream of shock wave
29
APPENDIX A
SCHLIEREN RESULTS OF WIND TUNNEL GALIBBATION
The Mach number in the working section was evaluated with the aid of three wedges of known included angle and a cone. The models were sting mounted and aligned in the free stream direction. The resulting Schlieren Images were photographed, (Figures A1, A2, A5f A4) and the free stream Mach number was deduced from the shock wave angles. The results are tabulated in Table A1 from which the average free stream Mach number was 2.575.
W E D G £ S C 0 N E Deflection angle (degs.) 5.5 7.8 15.0 11.5 Wave angle (degs.) 50.0 32.5 37.0 27.0 Average Mach number Maoh Number M 2.38 2.36 2.36 2.40 = 2.375
VM
ro
VM
V>J
55
APPENDK B; SCHLIEREN AND OIL PLOW VISUALISATION t OP GLANCING INTERACTION
>
'
I
Model mounted
on quadrant to
top liner
Figure B.I.
Figure B.2
Sealing
grooves - r ^ ^
,é
Figures B.I. and B.2. Model installation in working section
of wind tunnel. 6 = 5°
V>4 - J
Figure B.A. Oil flow pattern on sidewall produced by the model at 5
VN VO
Figure B.6. Oil flow pattern on sidewall produced by the model at 7
•
^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^^^^H|
^^^^Q
^^BÜJl
^^BS
^^^^^^^^^^^^^^^^^^^^^^^Kf^""" ^^^^^^^^^^^^^^^^KÊf^^^ * ^^^^^^^^^^^^^^^^^^^ZIHHV^'''- - ^ ^ i ü i M ^
^ - First Mach line
i in expansion fan
/— Reflected shock _^^^
r wave ^ ^ ^ F <
É^H
Figure B.7 Schlieren photograph
y
Figure B.8. Oil flow pattern on sidewall produced by the model at 9'
incidence. (Shock and expansion waves superimposed from figure B.7.)
VM
Figure B.9. Schlieren photograph of working section. 6 = 10
è
Figure B.10. Oil flow pattern on sidewall produced by the model at 10'
Figure B.11. Schlieren photograph of working section. 6 = 11"
m
ON
Figure B.12. Oil flow pattern on sidewall produced by the model at 11
47
APPENDK Ct PRESSURE TAPPED SIDE WALL RELATIVE TQ MODEL
APPENDIX Cl PRESSURE TAPPED SIDE WALL RELATIVE TQ MODEL
51
AJ^PEHDIX D
DETERMINATION OF WORKING SECTION REYNOLDS NUMBffi
Reynolds number is defined as n p VooX Moo where p = air density
V = velocity
X = characteristic length scale |J = viscosity
00 = free stream conditions
Now Mach number, M « V 0
where Q = local speed of soirnd
and in the working^ section of the wind tunnel, M ^ . has been shown to w/s
be 2.4.
Isentropic flow relations show that the static temperatvtre in the working section is given by
-^
= [1 +(JM) M^ ] (Bi)
For a stagnation temperature near atmospheric,
Tg = 15 C » 288 K
From equation ( B 1 ) ,
= 288 [l + 0.2 (2.4)^ ] "''
assuming that the ratio of specific heats, '^ is constant and equal to 1.4,
Therefore the working section static temperature, T is found to be 153.8°K,
Using Southerland's Law of v i s c o s i t y ,
Ref
T
T
Ref 3 A TRef * KT * K
(B2)
where p
Ref TRefK
» 17.89 X 10 Kg/ma
= 288,15°K
= 110
Hence, p^^^ = 1 7 . 8 9 x 1 0 " ^ [ I g ^ j
3/2 268.15 + 110133.8 + 110
U = 17.89 X 10"° X 0.5165 X 598.15 ^ W / S 243.83Mw/s = 9.246 X 10"* Kg/ms
The l o c a l speed of sound, a i s given by
a = TTRT
(B3)
where y s ratio of specific heats s 1.4
R = gas constant for air » 287 J/Kg.deg.I,
Hence, from eqxiation ( B 3 ) ,
a = 1 . 4 x 2 8 7 x 1 3 3 . 8 = 53760.84
a = 231.86 m/sec.
53
Since Mach number, M
V
V
V
= _V_ , the working section velocity is
a
«
M
a
= 2.4 X 231.86 =* 556.47 m/sec.
Adiabatic flow conditions show that
T
1
y-1
(B4)
Atmospheric air density is approximately 1.18 kg/m^ and so from equation ( B 4 ) , the density is found to be
w/s
Po
'To
1
. Tw/s
1.18 0.1756
* K y-1 288133.8
«/»5
-2.5Therefore, the Reynolds niunber per u n i t l e n g t h i s
Ri PWAV w/s wA »w/s w/s Mw/s 0.1756 X 556.47 9.246 X 10"^ t h e r e f o r e ' ^ V s -: 10.45 X 10^ /M.
54
*{
Theoretical location of
1*' Mach line in trailing
edge expansion
^ ^Theoretical location of
reflected shock wave
U 1
VJ1
Figure E.I. Pressure distribution along side wall
( y = 0 . 5 5 inches )
Deflection angle (degs.) : 5 Atmospheric pressure (mm. Hg): 761 Atmospheric temperature (degs. c ) : 15.5 Vacuum reference (mm. Hg): 0.05
Scanning valve calibration factor s 10.40/mm.' Hg Intercept on calibration curve at a reading of 915 Free stream Maoh number » 2.40
Theoretical shock wave angle (degrees): 28.5 Maoh number downstream of initial shock: 1«474 Theoretical reflected shock wave angle (degrees): 49 Optical boundary layer thickness (mm): 6 > 0.236 inches station Y » 13.97 mn. » 0.55 inches
Reflected shock at Xs/delta <r 22.379
First Mach line inP/M expansion fan at Xs/delta | 11.415
|:!: f: ;« it - I ; « : * * + + *:•: k + * * * * * * * * + * + + + * * * * j ) < * i e * * * * * * - . | t : 1 e ) c + 4 : + *ic;(! + 1; I: ij-)c +
* TAPPIMG ^J'^. •>! P:i?-.JS'J:1K CM-'I. HG> * P R E S S . C G E F F . * ] P / P l * • ^ S / n i ' L T I •:•: jet; 'fi^ (; f: f. ****i:*i: * * * * * * * * * * * * * * * * * * * * :^**** ** J<: t - ¥ * * * * * * * * * * * * * * * * * * * * * * * * *t
* 1 + P. ••<' 3 * /4 •= 5 «c r, tc 7 + >? * 9 • 10 * 1 1 * 1 2 + 1 3 * 1 4 * 1 5 * 16 * 1 7 + IP! * 19 * 2 0 * 2 1 * 2 2 * 2 3 * 2 4 * 2 5 X 2 6 * 2 7 * 2 8 * 2 9 * 3 0 :»: * * * * •: * * * * K * + * * * * * * * * * * * * * * * * * 5 3 . 1 / » 5 5 . 2 5 5 7 . 1 8 5 5 . 5 2 ••. 5 9 . 2 9 5 9 . = ? 7 6 0 . 0 6 6 0 . 5 4 6 0 . 7 3 6 0 . 9 2 6 1 . 1 2 6 1 . 2 1 6 1 . 6 0 6 1 . 8 8 6 8 . 0 8 6 2 . 0 8 6 2 . 2 7 6 2 . 6 5 6 2 . 8 4 6 2 . 9 4 6 3 . 1 3 6 1 . 2 1 5 6 . 0 2 5 2 . 4 7 5 0 . 8 3 4 9 . 7 8 4 9 . 5 8 4 9 . 78 5 0 . 0 6 5 0 . 5 4 * * * * * * * * * * * * * * * * * * * * * * • 4e * * * * * * 0 . 0 1 3 6 0 . 0 2 4 0 0 . 0 3 3 4 0 . 0 4 0 0 n . n / i 3 7 0 . 0 4 6 6 0 . 0 4 7 5 0 . 0 4 9 8 0 . 0 5 0 8 0 . 0 5 1 7 0 . 0 5 2 7 0 . 0 5 3 1 0 . 0 5 5 0 0 . 0 5 6 4 0 . 0 5 7 4 0 . 0 5 7 4 0 . 0 58 3 0 . 0 6 0 2 0 . 0 6 1 1 0 . 0 6 1 6 0 . 0 6 2 6 0 . 0 5 3 1 0 . 0 2 7 7 0 . 0 1 0 3 0 . 0 0 2 3 - 0 . 0 0 2 8 - 0 . 0 0 3 7 - 0 . 0 0 2 8 - 0 . 0 0 1 4 0 . 0 0 0 9 * * + * * * * * * * * * * * * * * * * * * * * * * * * * * * •^***^^***:t:**^c**********************************ie***y 1 . n 5 s ••^ 1 . 0 9 7 * 1 . 1 3 5 * 1 . 1 6 2 + 1 . 1 7 7 + 1 . 18<-M: 1 . 1 9 2 * 1 . 2 0 2 * 1 . 2 0 6 * 1 . 2 0 9 * 1 . 2 1 3 * 1 . 2 1 5 * 1 . 2 2 3 * 1 . 2 2 8 + 1 . 2 3 2 * 1 . 2 3 2 * 1 . 2 3 6 * 1 . 2 4 4 * 1 . 2 4 8 * 1 . 2 4 9 * 1 . 2 5 3 * 1 . 2 1 5 * 1 . 1 1 2 * 1 . 0 4 1 * 1 . 0 0 9 * [ 1 . 9 8 8 * [1.98 4 * n . 9 8 8 * 0 . 9 9 4 * 1 . n 0 3 * )c*Hc**** - ^ . 3 3 2 * - 1 . 6 9 7 * - 1 . 0 6 2 * - 0 . 4 0 7 •-: 0 . 2 0 7 + n.'"5 4T * 1 . 4 7 7 + 2 . 1 1 2 * 2 . 7 4 7 * 3 . 3 8 2 * 4 . 0 1 7 * 4 . 6 5 2 + 5 . P 8 7 * 5 . 0 2 2 + 6 . 5 5 7 + 7 . 1 9 2 * 7 . 8 2 7 * 8 . 4 6 P * 9 . 09 7 * 9 . 7 3 2 * 1 0 . 3 6 7 * 11 . o n s A 1 1 . 6 3 7 * • 1 2 . 2 7 2 * 1 2 . 9 0 7 * 1 3 . 5 4 2 * 1 4 . 1 7 7 * 1 4 . 8 1 2 * 1 5 . 4 4 7 * 1 6 . 0 8 2 * • • • • ^ e * * * * *
WIRKI^JG SECTIOM REYMGLDS MU!«IBER = 10.26 X 1 0 T 6 / M = 2.60 X 10t5 / IMCH
TABLE El Press\are distribution for deflection angle of 5° at Station Y B 0*55 inches
57
Deflection angle (degs.) : 7
Atmospheric press\ire (mm. Hg): 758.6 Atmospheric temperature (degs.C): 16.6 Vaoutim reference (mm. Hg): 0.05
Scanning valve calibration factor > 10.42/mm. Hg Intercept on calibration curve at a readiiig of 925 Free stream Mach number a 2.41
Theoretical shook wave angle (degrees): 30.2 Mach number downstream of initial shock: 1.451
Theoretical reflected shock wave angle (degrees): 53*5 Optical boundary layer thickness (mm): 6 m 0.236 inches Station Y » 13.97 nmi. » 0.55 inches
Reflected shock at Xs/delta s 20.291
First Mach line in F>m expansion fan at Xs/delta » 11.135
i M c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+ TAPPING NG. * PRESSURE CMM. H G ) ' * P R E S S . CGEFF. * P / P l * XS/DELTA *
• t * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * k * * * te * * * + * • 1 : * * * k * * * * + * 1 2 3
4
5
6 7 8 9 10 11 1 2 1 3 1 4 1 5 1 6 1 7 18 19 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 30 * * * * * * * * * + * * * * * * * * * * • ^ * M * * * * * * * 5 6 . 6 8 5 9 . 4 6 6 1 . 4 7 6 2 . 9 1 6 3 . 8 7 6 4 ^ 5 4 6 5 . 2 1 6 5 . 6 9 6 6 . 0 7 6 6 . 4 6 6 6 . 8 4 6 7 . 4 2 6 7 . 9 0 6 8 . 4 7 6 8 . 9 5 6 9 . 2 4 6 9 . 6 2 7 0 . 2 0 7 0 . 3 9 7 0 . 3 9 6 0 . 4 3 6 3 . 7 7 6 1 . 8 5 6 0 . 3 2 5 9 . 5 5 5 0 . 2 7 5 9 . 4 6 5 9 . 8 4 6 0 . 0 3 6 0 . 2 2 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 0 . 0 3 3 5 0 . 0 4 7 2 0 . 0 5 7 2 0 . 0 6 4 3 0 . 0 6 9 0 0 . 0 7 2 3 0 . 0 7 5 6 0 . 0 78 0 0 . 0 7 9 9 0 . 0 8 1 8 0 . 0 8 3 6 0 . 0 8 6 5 0 . 0 8 8 8 0 . 0 9 1 7 0 . 0 9 40 0 . 0 9 5 5 0 . 0 9 7 4 0 . 1 0 0 2 0 . 1 0 1 1 0 . 1 0 1 1 0 . 0 9 6 4 0 . 0 6 8 5 0 . 0 59 1 0 . 0 5 1 5 0 . 0 4 7 7 0 . 0 4 6 3 0 . 0 4 7 2 0 . 0 4 9 1 0 . 0 5 0 1 0 . 0 5 1 0 * * * * * * * * * * * * * * * * * * * * 1 * ] * ] * * * 1 * 1 * * 1 * 1 * i e ^ c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * « * : 4 c * * ^ I . 1 3 6 * 1 . 1 9 2 * 1 . 2 3 2 * 1 . 2 6 1 * I . 2 8 0 * 1 . 2 9 4 * I . 3 0 7 * L . 31 7 * I . 3 2 4 * I . 3 3 2 * 1 . 3 4 0 * 1 . 3 5 1 * 1 . 3 6 1 * 1 . 3 7 3 * I . 38 2+ I . 3 8 8 * I . 3 9 6 * L . 4 0 7 * [ . 'i 1 1 + L . 4 1 1 * i . 3 0 2+ L . 2 7 8 * L . 2 4 0 * 1 . 2 0 9 * I . 1 9 4 * . 1 8 8 * [ . 1 9 2 * . 1 9 9 * L . 2 0 3 * i . 2 0 7 * e * * * * * * - 8 . 0 4 4 * - 1 . 4 0 9 * - 0 . 7 7 4 * - 0 . 1 3 9 * 0 . 4 9 5 * 1 . 1 3 0 * 1 . 7 6 5 * 8 . 4 0 0 * 3 . 0 3 5 * 3 . 6 7 0 + 4 . 3 0 5 * 4 . 9 / 1 0 * 5 . 5 7 5 * 6 . 2 1 0 * 6 . 8 4 5 * 7 . 4 8 0 * 8 . 1 1 5 + ° ; . 7 5 0 * 9 . 3". B '•• 1 0 . 0 2 0 * 1 0 . 6 5 '•i •= 1 1 . 2 9 0 i= 1 1 . 0 8 5 * , . 1 2 . 5 6 0 + 1 3 . 1 9 5 + 1 3 . 8 3 0 * 1 4 . 4 6 5 * 1 5 . 1 0 0 * 1 5 . 7 3 5 + 1 6 . 3 7 0 * 4 c * * * * * * * * *V;DRKIM(^ S E C T I G M R E Y N G L D S MUMPER = 1 0 . 1 5 X 10T6 /M = 2 . 5 7 X 1 0 t 5 / IMCH
TABLE- E2 Pressure distribution for deflection angle of 7° at Station Y «= 0.55 inches
Deflection angle (degrees) : 9
Atmospheric pressure (mm. Hg): 758.6 Atmosi>heric temperature (degs. C ) : 16.6 Vao\xum reference (mm. H g ) : 0.05
Scanning valve calibration factor ; 10.42/mm. Hg Intercept on calibration curve at a reading of Free stream Mach number « 2.40
Theoretical shock wave angle (degrees): 32 Hach number downstream of initial shook: 1.426 Theoretical reflected shock wave angle (degrees):
922
61 O p t i c a l boundary l a y e r t h i c k n e s s (mm):
s t a t i o n Y > 13*97 nm. « 0.55 inches Reflected shock a t X s / d e l t a « 17.785
F i r s t Mach l i n e i n P / H expansion fan a t X s / d e l t a s
0.236 inches 10.915 * : • ! : * • - • : * 1; * * * * It * k * k k * * + * * * * * * * * (c * * • * * * T A P P I - ^ G •t •: : ; l; i !- ;: 1 2 3 4 5 6 7 8 9 10 11 1 2 1 3 1 4 1 5 1 6 1 7 18 19 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 • •: •: •: f: i. M G . * * * + * * * + * * * * * * * * * * * * • * * * * * * * * * * * * * PRESSU?.K ( T ' . 10) • ;= P R E S S . CGEFF. •(:.(: .ie * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * it !: * * * * *: * * * * «c + * * * * * * * * * * * * + * * * * * * •i 1 . •') 7 6 4 . 3 6 6 6 . 2 7 6 7 . 9 1 6 8 . 6 7 60 .• 54 7 0 . 3 0 7 1 . 4 5 7 2 . 2 2 7 3 . 2 8 7 4 . 3 3 7 5 . 5 8 7 6 . 6 3 7 7 . 2 1 7 7 . 7 8 78 . 1 7 7 8 . 4 6 7 8 . 6 5 7 8 . 6 5 7 8 . 2 6 7 1 . 1 7 69 . 1 5 68 . 1 0 6 7 . 2 3 6 6 . 4 7 6 6 . 0 8 6 5 . 9 9 6 6 . 1 8 6 6 . 0 8 6 6 . 2 7 * * * •It * * * * * * * • * * * * * * * * * * * * * * * * * * 0 . 0 5 7 6 0 . 0 7 0 3 0 . 0 8 0 3 0 . 0 8 8 3 0 . 0 9 2 1 0 . 0 9 6 4 0 . 1 0 0 1 0 . 1 0 58 n . 10 0 6 0 . 1 1 4 8 0 . 1 2 0 0 0 . 1 2 6 1 0 . 1 3 1 3 0 . 1 3 4 2 0 . 1 3 70 0 . 1 3 8 9 0 . 1 4 0 3 0 . 1 / 1 1 3 0 . 1 /«1 3 0 . 1 3 9 4 0 . 1 0 4 4 0 . 0 9 4 5 0 . 0 8 9 3 0 . 0 8 50 0 . 0 8 1 2 0 . 0 79 3 0 . 0 789 0 . 0 798 0 . 0 79 3 0 . 0 8 0 3 ( : ( , • • . » : • • •; •: ••: ^ic •;: k * P / P l * * * * i * 1 * 1 * 1 * J * 1 • 1 + * 1 * 1 * 1 * 1 * 1 * * * * 1 * 1 * * * * * 1 * * * 1 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ' ( 1; 1: I; Jc * * * k •* * X S / D E L T A * : !; k .-<« <<: * * <t * * * * * * 4c * * . 2 34+ . 88 7* .326'!= . 3 58 + .37/1+ . 3 9 1* . 4 0 6+ . 4 2 9 * L.4/45* ./16 6+ . 4 8 7* . 5 1 2 * . 5 3 3 * 1 . 5 4 5 * . 5 5 6 * . 5 6 4 * L . 5 7 0 * 1 . 5 7 3 * 1 . 5 7 3 * 1 . 5 6 6 * I . 4 2 4 * I . 38 3 * 1 . 3 6 2 * L . 3 4 5 * 1 . 3 3 0 * I . 3 2 2 * 1 . 3 2 0 * I . 3 2 4 * 1 . 3 2 2 * 1 . 3 2 6 * K * * * * * * - 1 . 7 7:1 •• = - 1 . 1 3 5 * - f' . 5 0 0 •><•. 0 . 1 3 4 * 0 . 7 6 9 * 1 . 4 0 4 k 8 . 0 3 9 + 8 . 6 7 4 + 3 . 3 0 9 + 3 . 9 4 4 + 4 . 5 7 0 * 5 . 8 1 4 + 5 . 8 4 0 •<: 6 . 4 8 4 * 7 . 1 1 9 * 7 . 7 5 4 + 8 . 3 3 9 * 9 . 0 2 4 + 9 . 6 50 * 1 0 . 2 9 4 * 1 0 . 0 2 0 + 1 1 . 5 6 / 4 * 1 2 . 1 9 0 * 1 2 . 8 3 4 + 1 3 . 4 6 0 * 1 4 . 1 0 4 * 1 4 . 7 3 9 * 1 5 . 3 7 4 * 1 6 . 0 00 + 1 6 . 6 4 4 + * * * * * * * * * *
vnRKIMG SECTION! REYMGLDS NUMBER = 1 0 . 1 5 X 1 0 t 6 / M = 2 . 5 8 X 1 0 t 5 / IMCH TABLE E3 Pressure d i s t r i b u t i o n f o r d e f l e c t i o n angle of 9
p Theoretical location of
(p J 1** Mach line in trailing
•^ L edge expansion
<^jr Theoretical location of
I- reflected shock wave
VJ1
VO
'15
Figure E.2. Pressure distribution along side wall.
Deflection angle (degs.) : 5
Atmospheric pressure (mm. H g ) : 758.6 Atmospheric temperature (degs. C ) : 16.6 Vacuum reference (mm. Hg): 0.05
Scanning valve calibration factor • 10.42/am. Hg Intercept on calibration curve at a reading of 914 Free stream Mach number « 2.40
Theoretical shock wave angle (degrees): 28.5 Mach number downstream of initial shock: 1.474
Theoretical reflected shock wave angle (degrees): 49 Optical boundary layer thickness (mm): 6 ~ 0.236 inches Station Y = 20.32 mm. « 0.80 inches
Reflected shock at Xs/delta = 19.510
First Mach line in P/M expansion fan at Xs/delta « 10,428
. . . — • • * * * * * * * * * ; f : i c : t : = t c * * * * > | c > ( c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * : ( ( * * * T.-^PIMG NG. * P R E S S U R E CMM. HGV * P R E S S . C G E F F . * P / P l * X S / D E I . T A * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * + * * * * * * * * * * * * * * * * • * : * 1 2 3 4 5 6 7 8 9 10 1 1 1 2 1 3 1 4 1 5 1 6 1 7 18 19 2 0 S I 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 30 * * * * * * * * * * * * * * * * * * * * * * * * * * * * • * * * * + * * * * * * * + * * t:;) 5 0 . 4 6 5 1 . 7 0 5 3 . 5 2 5 5 . 4 4 5 6 . 8 8 5 8 . 2 3 5 9 . 0 9 5 9 . 8 6 6 0 . 0 5 6 0 . 1 4 6 0 . 5 3 6 1 . 0 1 6 1 . 3 9 V 6 1 . 6 8 6 1 . 8 7 6 2 . 1 6 6 2 . 3 5 6 8 . 6 4 6 3 . 0 2 6 3 . 1 2 6 3 . 4 1 6 2 . 8 3 6 1 . 1 0 5 8 . 8 0 5 6 . 5 0 5 4 . 7 7 5 3 . 6 2 5 3 . 3 3 5 3 . 2 4 5 3 . 0 5 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * - 0 . 0 0 0 4 0 . 0 0 5 6 0 . 0 1 4 5 0 . 0 2 3 9 0 . 0 3 1 0 0 . 0 3 7 6 0 . 0 4 1 8 0 . 0 4 5 5 0 . 0 4 6 5 0 . 0 4 7 0 0 . 0 4 8 8 0 . 0 5 1 2 0 . 0 5 3 1 0 . 0 5 4 5 0 . 0 5 5 4 0 . 0 5 6 8 0 . 0 5 78 0 . 0 5 9 2 0 . 0 6 1 1 0 . 0 6 1 5 0 . 0 6 2 9 0 . 0 6 0 1 0 . 0 5 1 7 0 . 0 4 0 4 0 . 0 2 9 1 0 . 0 2 0 6 0 . 0 1 5 0 0 . 0 1 3 6 0 . 0 1 3 1 0 . 0 1 2 2 * C * ] * 1 * 1 * ] * ] * 1 * ] * ] * ] * ] * 1 * 1 * ] * 1 * ] * 1 * * 1 * * * ] * 1 * 1 * * * * * * 1 < * * * * * * ) ( ( * * * * * * * * * * * * * * * * * * * * * * * * * * * * * : ( ) . 9 9 8 * 1 . 0 2 2 * 1 . 0 5 8 * . 0 9 6 * 1 . 1 2 5 * . 1 5 1 * 1. 1 6 8 * . 1 8 4 * . 18 7 * . 1 8 9 * . 1 9 7 * . 2 0 6 * 1 . 2 1 4 * . 2 8 0 * 1 . 2 2 3 * 1 . 2 2 9 * 1 . 2 3 3 * 1 . 2 3 9 * 1 . 2 4 6 * 1 . 2 4 8 * 1 . 2 5 4 * 1 . 2 4 2 * 1 . 2 0 8 * 1 . 1 6 3 * 1 . 1 1 7 * 1 . 0 8 3 * 1 . 0 6 0 * 1 . 0 5 5 * L . 0 5 3 * 1.0 4 9 * t*****it - 3 . 6 4 6 * - 3 . 0 1 1 * - 2 . 3 7 6 * - 1 . 7 4 1 * - 1 . 1,06 * - 0 . 4 7 1 * 0 . 1 6 3 + 0 . 7 9 8 * 1 . 4 3 3 * 2 . 0 6 8 * 2 . 7 0 3 * 3 . 3 3 8 * 3 . 9 7 3 * 4 . 6 0 8 * 5 . 2 4 3 * 5 . 8 78 * 6 . 5 1 3 * 7 . 1 48 * 7 . 7 8 3 * 8 . 4 1 8 * 9 . 0 5 3 + 9 . 6 8 8 * 1 0 . 3 2 3 * 10 . 9 5 8 + 1 1 . 5 9 3 + 1 2 . 2 2 8 * 1 2 . 8 6 3 * 1 3 . 4 9 8 + 1 4 . 1 3 3 * 1 4 . 7 6 8 + * * * * * * * * * * *
V.'DJK! ^J(i .">:•^<:!TTn^J REYMGLDS MUMPER - 10.19 X 10 T6 /M = 8.^0 x 10 t5 / I MC'-I TABLE E4 Pressure distribution for deflection angle of 5°
