An experimental investigation of laminar boundary layer profiles in a weak adverse pressure gradient at an incident mach number of three

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..

AN EXPERIMENTAL INVESTIGATION OF LAMINAR BOUNDARY LAYER PROFILES IN A WEAK ADVERSE

PRESSURE GRADIENT AT AN INCIDENT MACH NUMBER OF THREE

BY

E. A. RACICOT

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..

The author wishes to express his thanks to Dr. G. N. Patterson for the opportunity to pursue this investigation and for his interest in its progress , to Professor B. Etkin who gave freely of his time for discussion and advice and to Mr. B . G . Dawson for his prompt and careful work with the instrumentation .

This work was made possible through the financial assistance of the Defence Research Board.

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SUMMARY

Experimental pitot pressure profiles through a laminar boundary layer in supersonic flow and under a weak adverse pressure gradient are compared with the predictions of the theory of G. M. Low.

Some information is presented about the effects of probe geometry on the shape of the measured profile.

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• TABLE OF CONTENTS NO TA TION 1. INTRODUCTION Il. TEST F ACILITIES 1. 2. 3. 4. 5. Wind Tunnel Model

Pressure Measuring Equipment Pitot Probes

Press ure Gradient Generator

lIl. EXPERIMENTAL PROCEDURES

1. 2. 3. 4. 5. Probe Zeroing Model Temperature

Determination of the Pressure Distribution Routine in Obtaining a Profile

Pressure Fluctuations

IV. EXPERIMENTAL RESULTS AND DISCUSSION

1. 2. 3. Pressure Distribution Profiles Concluding Remarks -REFERENCES ApPENDIX 1. 2. 3.

4 .

TABLE 1

Spurious Wave System Prebe Effects Model Position Goncluding Remarks FIGURES 1 to 18 ii 1 1 1 Z 2 3 4 5 5 5 6 6 7 7 8 9 10 13 13 13 _, 14 15

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:J

-..

H P

"Ó

M t z x y h

&

Subscripts r th av 00 '{ ïi ) NOTATION pitot pressure statie pressure

ratio of the specific heats of the gas Mach number

coefficients of the polynomial defining the statie pressure distribution over the model

time

displacement from plane surface as read by the centre leg of the curvature gauge

distance along the surface of the plate or of the pressure gradient generator

vertical distance from the surface of the plate to the physical centre of a probe face

height of a probe

boundary layer thickness

reference conditions , taken as those of the incident flow

theoretical ave rage

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..

1. INTRODUCTION

With the advent of supersonic flight the problem of the

separation of the boundary layer induced by astrong pressure rise, for example by shock waves, reached great practical importance. The strength of that pressur~ rise which would just separate the boundary layer was sought, at first by using weak waves incident upon the boundary layer and later by examining the rise in pressure at the front of a separ-ated region which had been caused by a stronger shock wave or by a step in the wal!. With the exception of that by Drougge (Ref. 22) there was little published on the boundary layer growth under a simple distributed pressure gradient. Some of the papers on these experimeri al invest-·' igations are listed as References 10 to 25.

The aim of the present thesis is to present pitot profiles in a laminar boundary layer under a weak adverse pressure distribution. The pressure gradient was obtained by having an inward curving wal! immediately downstream of a Mach three supersonic nozzle. From this wall a family of coalescing wavelets cross the flow to be reflected at a flat plate which extends under the laminar boundary layer under test .

Il. TEST FACILITIES 1. Wind Tunnel

This research program was carried out in the UTIA five by seven inch supersonic wind tunnel. The tunnel has an atmospheric pressure inlet and exhausts into an evacuated sphere. A description of this equipment is contained in References 1 and 2. See also Figure 1.

With the acquisition of a new pressure transducer of fast response, which is described below, it became possible to obtain timé

resolved pressure records. This instrument showed that the total heád was fluctuating in the subsonic section immediately ahead of the nozzle blocks. Pressure fluctuations of a similar shape had been found in the wal! boundary layers of the supersonic wind tunnels at the N. A. E. in Ottawa. Lukasiewicz

(Ref. 3) reported that these were believed to be caused by vortex shedding from the lip of the subsonic c.ontraction horn. These fluctuations were reduced by the addition of high-drag screens about tha.mouths of these horns. In the tunnel here the flow turns a two inch radius corner af ter leaving the heating tower and before entering the subsonic section of the tunnel proper. The flow could gave. been separating intermittently here. The existing 14 mesh screen was removed and first one and thtm two 60 mesh screens were mounted about the upstream gate valve, Figure 1. The resultant changes in the time variation of the total head in the sub-sonic section downstream of the screens is shown in Figure 2. The tunnel flow was not considered satisfactory with the large pulsations evident in the uppermost curve of Figure 2. The addition of the two 60 mesh screens reduced these fluctuations to an acceptable level. Figure 3 shows the total head through the boundary layer on the side wal! in the same region.

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The relative humidity of the supply air is eontinuously

measured. Test runs were made only if the supply air tested was below the minimum reading of the instrument, i. e. O. 30/0.

2. Model

The testing surface was a flat plate. It spanned the tunnel and was of suffieient length (6 in. ) to inc1ude the expected run of laminar

boundary layer. There were six statie pressure holes along the eentre line of the model at one inch intervals beginning 0.89" from the leading edge. The leading edge average thiclmess was O. 0017". The plate was supported from the floor of the tunnel by a central longitudinal mounting post.

The traversing gear eonsisted of one of three members which slid vertieally in the aft portion of the plate mounting post. To these could be attached the various stings which held the pitot probes. The three slides differed in the location of the sting positioning pins, these being on the centre line and one quarter or one half inch from the centre line of the three different slides. With any particular sting

i"

changes in longitudinal position eould be made by interchanging the three slides. One position was obtained with that slide which had its positioning pins on the centre line. Two other positions,

i

and

i

inch aft of this could be obtained with those slides having their pins removed from the center line. An additional two positions came from rotating either of the slides with off-centre pins through' 180 degrees. This WGuld bring the positioning pins to the other side of the slide and hence 1/8" from the plate centre line but also to a position

i

or

i

inch ahead of that reached from the slide with the pins on the centre line.

Larger fore and aft changes in test station were obtained by intereliá.~-ie;i:lg the ~ :ings which carried the pitot probes. These stings were flat steel pieces cut in the shape of right angle triangles. Their leading edges were sharpenèè. The pitot probes were affixed in a grove along the bottom of the sting. Each sting had its own probe.

Figure 4 shows a generaJ. view of the complete model. 3. Pressure Equipm ent

Th~ ;>Fimary pressure standard for the wind tunnel is a "Wallaee and Tiernen Precision Mereurial Barometer". There are two of these instruments at the installation. One was used to m easure the atmospherie pressure and the other was used to measure the reference

pressure for the pressure transdueer. The manufaeturer states the accuraey of these instruments as one part in one thousand of full scale. Full scaie is eight hundred millimeters of Mercury. The instrument has a vernier which reads direetly to one tenth_ of a millimeter but the next decimal plaee may be estimated. As both the setting of the zero and the reading of the seale involve an error, the aeeuracy is considered

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to be plus or minus 0.16 mmo Hg. Before each day's running the instruments were degas'sed and compared in their reading of the atmospheric pressure .

Most of the pressure measurements in the tunnel were made with a pressure transducer which is described by the manufacturer as follows. "The Northam Model DP-7 Pressure Transducer is a sensitive instrument for the measurement of differential pressure in terms of an electrical output". "Electrically the Model DP-7 consists of two variabie induc~ances, which change in opposite directions with the application of pressure . The conversion of pressure to inductance is brought about through a variation in air gap in two magnetic circuits with the motion of

a pressure sensing diaphragm'.'\: The gauge is used as half of a bridge which is in balance when there is no press ure difference across the diaphragm. The unbalance of the bridge is calibrated with the press ure differential. With the exception of the pressure transducer and the

solenoid valvethe physical elements of the system were the same as those used by Pridmore-Brown and Ludwig (Refs. 4 and 5). The calibration of the transducer system repeated to within

10/0

of the twenty millimeters of Hg. which represented full scale deflection of the potentiometer scale used.

4. Pitot Probes

Originally it had been decided to use rectangular probes . It was believed that if the probes were thin then they would disturb the flow very little. By making the probes wide the frontal area of the probe

opening could be made large enough to give a useable response time. The probe height was kept less than one quarter of the boundary layer thickness. Such a criterion had been suggested in References 8 and 9.

The work of Ludwig (Ref. 5) and the early results obtained in this program demonstrated that the rectangular probes would not give acceptable res ults. Circular probes were therefore made to replace the rectangular ones.

The circular probes were ground by hand with a fine stone from stainless steel hypodermic tubing spinning in a collet chuck of a small lathe giving a truncated cone-cylinder shape. The tubing was 0.016" O. D. x 0.004" wall. Although each sting had its own probe they were nearly the same ~.iameter. Later, attempts were made to make a smaller probe using the next and smallest size of hypodermic tubing available to us. This was 0.014"

o

.

D. x 0.004" wall. The 1. D. of this tubing is 0.006" and hence to get a much smaller tube than 0 .007" 0 . D. some swaging of the tip is necessary. This led~,to_adilemma·. . If the residual material at the tip was left thick and hence strong the inside diameter af ter working was so small that the response time of the probe became prohibitive. If the tip was made thin then it would crack and in use would read something less than the pitot pressure .

The dimensions of the circular probes used are given in

Table 1. The rectangular probe for which data is also given is the one for which a profile will later be shown to provide a comparison between the probe effects of the circular and rectangular probes .

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The Reynolds number of the inside diam eter of the circular probes based on average free stream conditions is 1000. Errors caused by viscous effects do not become apparent until Reynolds numbers of less than 200 are reached.

5. Pressure Distribution Generator

The pressure distribution over the flat plate was generated by a curved liner aft of the two-dimensional nozzle blocks, (See Fig. 5).

For a given pressure distribution over a reflecting surface the character-istic family could be found. From this net the shape of the curved llner could be inferred. Such a net was constructed graphically for the .case of a linear adverse pressure gradient. To the accuracy of the construction the surface was a parabola. Numerical calculation of the net w,ould have improved the accuracy but considering the corrections for the wall bourrl ary layer, the accuracy obtainable in construction, and that in the end the dis-tribution would have to be measured at the plate it was decided that the surface should be made of this shape and of sufficient flow deflect~on.

The manufacturer suggested as a method of constructing the liner the bonding together of a thin ground steel sheet to a massive base. It would be undesirable to have a wavy surface. If the con~our of the liner were specified at several points then the finished surface may well have risen and fallen between these points. 1t waS decided to specify the be-ginning and end of the curved surface and to specify the curvature between. The liner waS designed to have

two.

possible gradiE~nts of different strengths,

obtained~by turriingit end for end. The base had a short pier at each end

which specified the beginnings of the respective curves and a higher roof-shaped central pier each side of which set the end point~ of the curve. Between these piers the base was cut back to avoid contact with the ground sheet. Thin beam theory predicts that a cantilevered beam with pure end moments will have the shape of a 'parabola. For the positioning of the thin sheet before bonding, it was this. r~tilt, ·that was in mind. The thin sheet was clamped -rigidl~' to one of the short piers ne ar the' end of the base. This end -would act as the fixed end of the beanL The other end was grad-ually clarnped to the Surface of the centre pedestal. This pedestal was not only at the correct position to define the end of the curved liner.,.but it was also tangential to the desired parabola at that point. If the thin sheet were Îree to slide between the clamping, blocks at this end then the applied force system would be a couple i. e. a pure e~d moment. The curvature of the surface could be checked when the clamping was finished. The sheet wàs bonded to the base with a thermo-setting cement. Such regions as were adjudged poor on the basis of the curvat'\lre reaqings ·were improved by hand rubbing.

The curvature gauge is shown in Figure 6 and the curved wall itself is shown in Figures 7 and 8.

To the accuracy of the curvature gauge the dial reading should be constant for the desired shape. The measur,ed values,,-, for the strong and the weak llneTs are presented in Figure 9 for that region where the

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'w

gauge has all three legs on the curved portion. The gauge has three legs in line and one inch apart. The variation of the central leg from a line through the tip of the other two is plus or minus O. 0004" over the first eight inches of the strong pressure gradient side and plus or minus

O. 0002" for the first five inches of the weak pressure gradient side. Such variation as there was, was extended over several inches.

III EXPERIMENTAL PROCEDURES

1. Probe Zeroing

The first technique used to zero the probes was electrical. The probes were set with a thermo-setting cement in a small groove along the base of the sting. The resistance between the probe and the plate was measured with an ohmmeter. Ideally there should have been zero resistance at contact and infinite resistance when the probe was not touching the surface. In practice over a distance of about one thousandth of an inch the resistance would have some mid-scale value. The repeat-ability was poor and the scatter was large.

The second method and the one finally used was to look at the probe with a low power microscope from outside the tunnel at at a very sm all angle to the surface of the plate. Figure 10 shows the tip of a rectangular probe as seen through the microscope with flow in the tunnel.

The difference in micrometer setting between each of these photographs

is O. 0003". The figures shows the probe and its reflection in the plate.

The change from position to position is sufficiently marked that the probe can be zeroed with an accuracy of plus or minus O. 0002".

The practice was to set the probe in some position and to observe the separation while the tunnel was running. The probe would deflect towards the plate as the flow was established but would remain steady during the run. Repeat runs would, as far as the eye could tell,

have the same separation. A new setting would be made and the probe observed again as the tunnel was running. This was continued until the zero was passed. Each setting of the slide would be measured by the micrometer fitted to the bottom of the slide. When a profile had been

finished the probe would be returned to the zero setting and to the accuracy stated above the zero would repeat

2. Model Temperature

The temperature of the model was measured by a thermocouple which was clamped by one of the screws which attached the plate to the

-vertical mount. During the zeroing runs and the first one or two runs when the probe was near the wall the temperature of the model would drop about ten Fahrenheit degrees. Af ter this and during the remaining runs the temperature would stay approximately at the value that it had reached during the early runs. The temperature of the model would rise while the probe was being reset and then fall during the run, all within the range of

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some four Fahrenheit degrees. This situation would last over the two or

three hours it took 't~t complete a profile. The theory assumes that the wall

is isothermal. In the ca1culations from theory it was this temperature

about which the model drifted that was used as the wall temperature.

3. Determination of the Pressure Distribution

The pressure distribution ove~ the model was inferred from

two groups of data . . These were the wall static pressure distribution and

the pitot pressure distribution. The pitot pressure distribution was that

measured by the probes when they were sufficiently far out of the boundary

layer to be free from probe-boundary layer interference effects. To use

the pitot probe data it was necessary to know the stagnation pressure of the

supply air. This was measured by a total head tube down-stream of the

screens and in the subsonic section of the tunnel. It was expressed as a

fraction of the atmospheric pressure. Having calibrated the loss across

the screens the stagnation pressure was caiculated as needed from the

atmospheric pressure.

4. Routine in Obtaining a Profile

The probe was first zeroed and the pressure measurements

begun at the wall. When a measurement was made the ave rage ofthe chart

trace would be estimated and the pressure calculated. These points were

plotted on a monitoring graph. A line sketched through these points enabled

an estimate to be made of the next reference pressure required to keep the

potentiometer on scale. The spacing between the height settings would depend

on the slope of the curve. The tunnel waS then opened, the probe reset to

the next height and the tunnel resealed. When the sphere pressure had been

pumped down far enough for the next run the temperature of the model was

read and the run begun. At the end of a run the data i. e. model temperature,

stagnation temperature, atmospheric pressure and reference pressure were

read. Having traversed through the boundary layer a few check points were

taken two or three boundary layer thicknesses out into the free stream. ''J,

Usually an additional two or three points were obtained in the region of

hlghli!'str gradfeht~ Firtally the zero was cheeked. ' .(-_

5. Pressure Fluctuations

The pressure as measured in the \boundary layer was not steady.

The fluctuations were most marked with the ~è~'tangular probes that were

initially used. With the circular probes, with which the final data present-ed herein was obtained, this effect was much smaller. In most cases the

trace could be averaged by eye. For the exceptional cases the area to one

side of the trace was integrated with a planimeter and a time average was

taken.

These fluctuations were not in that part of the boundary layer

where the pressure was changing most rapidly with height but out at the

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alone then the changes in position required should have been observable

through the zerolng< micToscope, but they were not seen. Also the duration

of a particular fluduation was long compared with the natural frequency of the probe.

The response time of the circular probes was two or three times that of the rectangular proOes. This probably accounts for the attenuation of the fluctuations recorded with these probes.

It is felt that these fluctuations are related to the structure of

the flow in the tunnel as a whoie. The jumps in the pressure trace often

seemed to be coincident with the changes in the sound of the tunnel. This

same effect is more clearly marked in the UTIA 16 x 16 inch tunnel.

IV EXPERIMENTAL RESULTS AND PISCUSSION

I

1. Pressure Distrihution

'The pressure distribution over the plate is presented in

Figure 11. This curve was fitted with a polynomial. The coefficients of

the polynomial were found by fairing a curve through the experimental

data and then fitting this curve with a series expansion in Chebyshev

polynomials. On changing the independent variabie in the expansion from

Chebyshev polynomials to x, the distance along the plate, the coefficients

of powers greater then two were found ~o be negligible. The terms of the

expansion up to the seco~d order wer:e taken as an analytic statement of

the distribution.

From this curve and the stagnation pressure of the tunnel the

incident Mach number could be found. Expressing the distribution in the

form that appears in G. M. Low's paper (Ref. 7).

'2

n

\ - CS

M(

f.

E:

o.N

X

N

gave the coefficients required fOl~ the theory i. e.

The above pressure distribution actually provided by the

tunnel liner is substantially lower than that for which it was designed,

i. e.

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The isentropic core of the tunnel may be thought of as being

turned by the displacement thickness of the wall boundary layer. The liner

protrudes into the flow at its greatest height 0.5" whereas the wall boundary

layer itself is 0.8" thick. The obstacle presented to the boundary layer by

the liner is of the same height as the boundary layer itself. Considering

this and the shape of the pressure distribution it seems that the wall

boundary layer did not begin to respond to the presence of the liner until

it was downstream of the point where the wall began to curve. The

boundary layer seems to have masked the curvature of the wall, and thus

the press ure rise obtained was not as great as des igned.

2. Profiles

To provide a comparison with other flat plate experiments in

a zero pressure gradient a profile was taken with probe #2 with the plate

mounted in the first test rhombus of the tunnel. The theoretical profile,

as predicted by Chapman and Rubesii:L (Ref. 6) and the experimental results

are shown in Figure 12. The experimental profile shows the same type of

discrepancy as other experiments have shown. There is a slightly higher

pressure near the wall but a slightly lower pressure throughout the rest of

the profile resulting in an apparent increase in boundary layer thickness.

The pressure distribution over the model is shown in Figure 13.

Figure 18 illustrates the effect of the pressure gradient on the

shape of the pit ot press ure profile. There are two theoretical profiles shown

of pitot pressure divided by the local free stream pitot pressure and plotted

against the vertical distance from the plate. One is that predicted by the

theory of G. M. Low (Ref. 7) for the experimentally determined longitudinal

pressure gradient at a station 2.70 in. from the leading edge. The other

is that predicted by the theory of Chapman and Rubesin (Ref. 6) at the same

station and with free stream conditions which are the same as those found

locally at this station in the pressure gradient cas er .. It can be seen that the

applied pressure gradient is sufficient to produce a noticeable difference.

Four profiles wer.e obtained in the boundary layer under the

adverse pressure distribution. These are shown in Figures 14, 15, 16 and

17. The graphs show the pitot pressure divided by the incident static pressure

plotted against the distance from the physical centre of the probe to the wall.

The theoretical curves shown on the graphs are calculated from the theory

of G. M. Low, (R ef. 7).

The profile taken with probe #3 at the most aft station is

characteristic of a transitional boundary layer, (Fig. 14).

Figure 15 shows the information for the next station forward.

The experimental points were obtained using probe #2.

At the next forward station two sets of experimental data were

taken, (Fig. 16). As well as presenting the data obtained with the circular

probe #1 there is also presented the measurements obtained with a

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L

theory is for the case of the adverse pressure gradient.

F:igure 17 shows the theory and experiment for the most forward station. Circular probe #1 was used for this station.

For the two laminar profiles where the probe is less than 1/4 of the theoretical boundary layer thickness the difference between the theory and the experiment is small for most of the profile; the main difference occurring at the outer edge of the boundary layer. The

character of this difference is the same as thát found with the zero pressure gradient profile. For the more forward station where the probe height to boundary layer thickness ratio is larger distortion of the boundary layer is more marked.

3. Concluding Remarks

The theory of Low (Ref. 7) for the compressible laminar boundary layer is obtained by a method of perturbation on the flat pla!e solution of Chapman and Rubesin (Ref. 6) for the case of an isothermal wall. The theory constitutes, in effect, the first two terms of a

Maclaurin series expansion of the èxact solution for arbitrary pressure gradient. Thus it should be applicable for weak pressure gradients.

In the present investigation employing a weak adverse pressure gradient of a second degree monotonie shape the theory of Low has predicted well the pit ot pressure distribution through the boundary layer in a Mach three flow.

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1. Ruptash, J. 2. Patterson, A. M. 3. Lukasiewicz, J. 4. Pridmore-Brown, N. B. 5 . Ludwig, G. R. 6. Chapman,D. R. and Rubesin, M. W. 7. Low, G. M. 8. Davies , F. V. 9. OrDonnell, R. M. 10. Lee, J. D. ( 10 ) REFERENCES

"Boundary Layer Measurements in the UTIA 5 by 7 inch Supersonic Wind Tunneî" , UTIA Report No. 16, July, 1952

"Factors Affecting the Performance of Supersonic Diffusers", UTIA Report No. 23, December, 1952

"Elimination of Flow Instabilities in Two High Speed Wind Tunnels by Means of High-Drag Screens", NAE Lab. Report LR - 83, November, 1953

"Heat Transfer in a Laminar Boundary Layer at Mach 2.5 From a Surface Having a Temperature Distribution" , UTIA Report No. 45, February, 1957

"Effects of Probe Size on Measurements in a Läminar Boundary Layer in

Supersonic Flow", UTIA Technical Note NQ. 9, November, 1956

"Temperature and Velocity Profiles in the Compressible Laminar Boundary Layer with Arbitrary Distribution of Surface Temperature", Jour. Aero. Sci. Vol. 16 #9, September, 1949

"The Compressible Laminar Boundary Layer with Heat Transfer and Small Pressure Gradient", NACA TN 3028, Qctober, 1953

"Some Effects of Pitot Size on the Measurement of Boundary Layers in

S~personic Flow", Tech. Note Aero 2179, RAE Farnborough, August, 1952

",Experimental Investigation at a Mach lNumber of 2.41 of Average Skin-Friction Coefficients and Velocity Profiles for Laminar and Turbulent Boundary Layers

~nd an Assessment of Probe Effects ",

NACA TN 3122, January, 1954

"The Influence of High Adverse Pressure Gradients on Boundary Layers in

Supersonic Flows", UTIA Report No. 21, October, 1952

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11 . Bardsley, D. and Mair, W. A. 12. Barry, F : W., Shapiro, A. H., and Neumann. E . P . 13. Bursnall, W. J ., and Lof tin, L . K. 14. Liepmann, H. W. , Roshko, H. , 15. 16. 17. 18. 19. 20. and Dhawan, S. Moeckel, W. E. Bogdonoff, S. M., and Solarski, A. M . Johannesen, N. H. Donaidson, C. DuP. , and Lange, R . H. Drougge, G. Bogdonoff,. S. M., Kepler, C. E., and Sanlorenzo, E .

"The Interaction Between an Oblique Shoçk Wave and a Turbulent Boundary

Lay~r", Philosophical Magazine, Ser. 7

Vol. XLll, P 29, January, 1951

"The Interaction of Shock Waves with Boundary Layers on a Flat Plate",

Jour. ~ero. Sci., Vol. 18, No. 4, 1951

"Experimental Investigation of Localized

Regions of Laminar Boundary Layer

Separation", NACA TN 2338, April,

1951

"On the Reflection of Shock Waves from Boundary Layers", NACA TN 2335, April, 1951

"Flow Sep~ration Ahead of Blunt Bodies

at Superso~ic Speeds", NACA TN 2418,

July, 1951

"A Preliminary Investigation of a Shock Wave-Turbulent Boundary Layer

Interaction" , Princeton University

Report No. 184, November, 1951

"Experiments on Two Dimensional Supersonic Flow in Corners and Over

Concave Surfaçes", Philosophical

Magazine, Ser. 7, Vol. XLll p. 567,

May, 1952

"Study of the Pressure Rise Across Shock

Waves Required to Separate Laminar and

Turbulent Boundary Layers", NACA TN

2770, September, 1952

"Experimental Investigation of the

Influence of Strong Adverse Pressure

Gradients on Turbulent Boundary Layers

at Supersonic Speeds", 8th International Congress on Theoretical and Applied

Mechanics, Istanbul, 1952

"A Study of Shock Wave Turbulent

Boundary Layer Interactions at M Equals

Three", Princeton University, Dept. Aero.

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• 21 . Kepler, C. E. , and Bogdonoff, S. M. 22. Drougge, G. 23. Barry, F. W., Shapiro, A. H., and Neumann, E . P. 24. Bogdonoff, S. M. , and Kepier, C. E. 25. Lange, R . H. ( 12 )

"lnteraction oLa Turbulent .Boundary Layer with . .a Step at M Equals Three" , Princeton University, Dept. Aero . .E,;ng. ,

Report #238, September, 1953

"AI\ Experimental lnvestigation of the lnfluence of Strong Adverse Pressure Gradients on Turbulent Boundary Layers at Supersonic Speeds", The Aviation Research lnstitute of Sweden, Report No. 43, 1953

"Same Experiments on the lnteraction of

Shoc~ Waves with Boundary Layers on a Flat :plate", Jour. Appl. Mech. , Paper

No. '1t9-A3, 1953

"The ·Separation of a Supersonic

Turbulent Boundary Layer", lnst. Aero.

Sci. , Preprint No. 441, January_I , 1954 "Present Status of lnformation Relative to the frediction of Shock lnduced

Boundary Layer Separation" , NACA TN 3065, ~ebruary, 1954

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APPENDIX

There are certain difficulties that arose during the development of the final test arrangement whieh provided some

- experienee that. may be of use if future work is done with this model.

1. Spurious Wave $ystem

When the model was first obtained it was mounted with the

tunnel in its conventional form. It was in this configuration that the

first profiles were taken for the zero pressure gradient case. There

was. nothing untoward about the flow.

For the nen stage the nozzle bloeks were moved upstream

and the pressure gradient liners mounted between the nozzle blocks and the diffuser. The empty tunnel provided clean flow when observed by the schlieren system. However, when the model w.as mounted in the

tunnel a .spurious wave system appeared about the model. It looked

like the lambda feet of a normal shock in a tunnel but without the normal

portion ..

.A series of tests with a mock plate of sheet steel and

_plywood indicated the direction of the necessary changes in model

thickness .and height required to eliminate the waves. The bow angle of

themount was made .smaller to lessen the strength of the bow shock.

When these removals of material had progressed about as far as was

structurally safe for the model the tunnel gave flow free from any

apparent wave system.

The boundary layers are thicker on the walls of the tunnel

when the pressure gradient liner is in position because of the longer run

from the nozzle throat. When they are further thickened by the bow

shock of the mount and the intrusion of the liner they effect area

reductions which together with those of the model prohibit shock free flow.

2 . Probe Effects

When the first profiles were taken in the zero pressure

gradient case they were found to fit the theoretical profiles predicted

by Chapman and Rubesin (Ref. 6) if the theoretical height coordinate

was given a percentage increase. This type of agreement had been

found before and so the work was commeneed on the adverse pressure

gradient case.

Coincident with this Ludwig (Ref. 5) had been studying the

'effect of probe height on the shape of the pitot profile measured. He

found the same type of agreement as noted above but the percentage

factors required were much smaller. The only marked differenee

between the two sets of probes is in their widths. Those that were used

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height is leEs than one quarter of the boundary.layer thickness then the distortion of the profile is basically due to the bow wave system of the probe. The wider the pfobe the more of the boundary layer is

influenced by it.

As the profiles that were being obtained in the pressure gradient case were considerably different from theory a small circular probe was made and one of the profiles waS repeated. The circular and rectangular profiles agreed.

Following up another set of clues about the cause of the

difference between experiment and theory a more serious' shortcoming

of the experimental arrangement was found. When this had been

corrected, as noted below, the circular profile was found to agree weU

with theory while the rectangular one did not, (see Fig. 16).

For the remainder of the work circular probes were used.

These probes all had nearly the same height. Again it was found that as the probe height to boundary layer thickness ratio was increased, this time by changing the boundary layer thickness rather than the probe height as Ludwig had done, the difference between theory and

experiment grew.

3. Model Position

The pus.itionof the model with respect to the liner had been

computed from Mach waves assumed to emanate from the beginning of the curved section. When clean flow was finally obtained this

positioning was checked. Electrician's tape was stuck to the liner and

the resulting waves observed in the schlieren system. Those waves

which marked the beginning and end of the curved part of the liner were positioned properly with respect to the model.

The pressure distributicm was measured along the model. The pressure rises obtained were not as large as had been expected nor were the distributions of good shape. To gain more information about the distribution the pitot pressure data from the outer edge of the boundary layer was used. Profiles were taken at about ten stations in

the laminar region. It became apparent that near the leading edge there

was an expansion-compression wave system.

To avoid this wave system the model was moved 2 1/2 inches down stream. Lamp black painted on the model did not show any wave system crossing the plate except that from the tips of the leading edge. The pressure distribution measured now was monotonic although not linear.

The multiplicity of test stations developed in the above work and provided by the three slides and the different positioning holes on

the stings were nqt used in the final sequence of experiments. The

(20)

to warrant their use. , _ l

.

' .

4. Concluding Remarks

Rectangular probes will n<?t gi ve truly representatlve shapea for the profiles . For circular probes with a probe height to boundary

layer thickness ratio of 0.19 there is some residual difference between theory and experiment.

If this geometry is used again and if more control is desired over the pressure distribution then more work will have to be done first on the response of turbulent boundary layers to a slightly curved wall.

.. ~

. ( ' .

.

, ;

. .

(21)

PROBE NO. 1R PROBE NO. 1 2 3 ( 16 ) TABLE I RECTANGULAR PROBE OUTSIDE DIMENSIONS

o.

0586 x

o.

0043 in. CIRCULAR PROBES OUTSIDE DIAMETER 0.0075 in. O. 0077 in. 0.0073 in. INSIDE DIMENSIONS O. 0439 x O. 0011 in. INSIDE DIAMETER 0.0064 in. 0.0064 in. 0.0064 in.

(22)

Air

Drier

Heating

Tower

Dry Air

Storage Room

Working

Sectlon

Diffuser

Section

. . -

----

...

-

..

-

1t1

.

-

....

--\

...

.,'

-

...

-

--

--.1'-"'" ... ___ . ___ __

liJ ... - -- - - .... - __

Upstream Gate Volve

a

Screens

FIGURE 1

,

Vacuum

Sphere

(23)

14 Mesh Screen

One 60 Mesh Screen

Two 60 Mesh Screens, 1.6" Apart

Pi tot Pressure , Subsonic Part of Test Section. t Sec. FIGURE 2

2 o

4

· H

mmo

Hg.

(24)

·017

---~-~~

---·041

---·078

·103

·203---

__

-·303

·403

y,

in. Pitot Pressure Near Wall of Subsonic Part of Test Section. FIGURE 3

t

2

sec.

4 H

mmo

Hg.

(25)

~ ~ Cl 0 ~ ~ ~

:s

P-4 <o:t4 ~ ril

:s

0::

::>

~ ~ ~

...

~ ~

~

P-4 ~ 0 U ril ::Il ~

(26)

/

v

/ / / / Q) VI o U

-

c .~ "0 o ~ (!) ~ o

-

c o ~ o ~ :::I 0'

-

C o U Q) c c ~ "0 C

(27)

~ 0

::>

~ 0 til co 0:= fiI

::>

0:= E-t

::>

~ C!)

>

1-1 0:=

rx..

::>

U til ~ ~

(28)

(29)

~ ...:l

~

co I

,

, Cl ~ lil ~

:>

~ p:: C!) ~ 1-4 ~ U ~ tI: E-4

(30)

-000

z

·002

in

-004

·000

z

·002

in.

-004

I L

o

Curvoture Gauge Readings

Weak Curve

I .f'\

n

) ...

Strong Curve

0

2 ----Direction

( )

I'"

f \ .f). I

0 ₀

0

4 x tin.

FIGURE 9

LxJ

-.n

I'"

"" 0

0 f

J

I

0 _.o....U"\

0

0 0

0

()

₀

6

8

10

(31)

~ j:Q 0 0

re

~ ~ ril ::ti

~

E-4 C!)

g

Z t-4 ~ 0 p:: ~ N

(32)

Statie Pressure Distribution

o

Direct

M ea surement

() Inferred From Pitot

a

Stagnation Pressures

1-40

I

From Chebyshev Polynomials

P

-Pr

1-20

I :;;< ()

1-00 '

_o

2 x in

_,

3

4

FIGURE 11

5

(33)

· .

1'60,

A

Statie Pressure Distribution

o

Direct Measument

() Inferred From Pitot

a

Stagnation Pressures

1.40 I

From Chebyshev Polynomials

P

-Pr

1·20

I

, <

() I'OO~'~~---~---~---~---~---~

o

2 x,

i n : 3

4

5

FIGURE 11

(34)

Pitot Profile

·080

Zero Pressure Gro dien f

Probe 2

x

=

2 '70 in.

'070

h -111 '17 8th.

o

Experiment -Theory ·060 y

,050

I in '040

'030

'020 . ·0 10

~

cY"

cS

k(

10

'000 I

o

2

4

('

~

po 6

H

8 Pr

FIGURE 12 ) ()

~

V

10

12 14

(35)

-

c CD CD

...

:I

•

CD

...

Q. o

...

CD N c

o

.-

-:I .a

.-

-

...

•

Cl CD

...

:I

.,

•

CD ~ Q. C>

.-

-

-=--

en

-0

I T

<Q

c

~

o

.

-0

-ft)

.

~

-

,.

)( N

-o

0 CJ)

6

(36)

-080

Pitot Profile Prob e 3

'070

x= 3-76 in.

o

E)(periment - Theory

-060

y

·050

in.

·040

·030

'020

V

-0 10

/

0 '000

o

2

~

I..

0

4 ~

l.--cJ"

6 H 8

Pr

FIGURE 14

0 p

v

V

10

12

14

(37)

·090

pltot Profile

'080

Pro be 2 x

=

2·70 In. h

-=

·19

8

_th ·070

o

Experi ment y - Theory

·060

in. ·050 ~

·040

r

·030

·020

0/

• _~

~

..rY"

V

y

·0 10 /

t

.

·000

I

o

2

4

6 H

8

10 12 14

Pr

FIGURE 15

(38)

Pitot Profile ·080

)( =

I· 70 in. h

1 -=

·24

8

_th.

o

Experiment, Circulor '070

h

-=

·14

8

_th

() E)( peri ment, Rectongulor ·060 - Theory

_tt

y ·050

IC)

in. ·040

<-·030

~

V

<D

,

Kt

_~

r.

----·02..0

b-"'"

Cl

_~

(

V

() ·0 10

(

..

'0 0

0

0 2 4 6

-

H 8 12 14 Pr FIGURE 16

(39)

'090 ·080 '070 '060 y ·050 in. '040 ·030 ·020 -OIO ·000

o

Pitot Profile Probe I x I: 0·70 in

1L

=

'38 8_th

o

Experiment - Theory

0

0 D

,...

' /

~

-;Y"

2 4 6

li

8 Pr FIGURE 17 10 12 14

(40)

'050 ·040

·030

Y in. '020 ·010 ·000

o

'" <

"

Theoretical Proflies For Local ---- And Overall -Pressure Gradient Conditions

~

-~

~-~

-L----::-=

~-

-~-::::

/

,.,-~

1/

--I

-2

·3

_'4

H

·5

-6

-7

-8 '9 H

co

FIGURE 18

.

)

~ I

-1,0

(41)

·

.

UTIA REPORT NO. 46

Institute of Aerophysics, lJnivenity of Toronto

"

An Ex:perimental Investigation of Profiles Laminar Boundary Layer in a weak

Adverse Pressure Gradient at an Incident Mach number of Three E. A. Racicot, March, 1957,

1. Flow, Laminar

3. Pressure Measurements

Racicot, E. A.

16 pp., 18 figs., 1 table

2. Boundary Layer, Internal Aerodynamics

IJ UTIA Report No. 46

Experimental pitot pressure profiles through a laminar boundary layer in supersonic flow and Illider a weak adverse pressure gradient are compared

with the predictions of the theory of G. M. Low. Some information is

pre-sented about the effects of probe geometry on the shape of the m-easured profile

Copies obtoinable from: Institute of Aerophysics, University of Toronto, Toronto 5, Ontorio UTIA REPORT NO. 46

Institute of Aerophysics, University of T oronto

"

An Ex:perimental Investigation of Profiles Laminar Boundary Layer in a weak

Adverse Pressure Gradient at an Incident Mach Number of Three E. A. Rac ic ot, Mareh, 1957, 16 pp., 18 figs. , 1 table

1. Flow, Laminar 2. Boundary Layer, Internal Aerodynamics 3. Pressure Measurements

Racicot, E. A. II UTIA Report No. 46

Ex:perimental pitot pressure profiles through a laminar boundary layer in

supersonic flow and under a weak adverse pressure gradient are compared

with the predictions of the theory of G. M. Low. Some information is pre-sented abw t the effects of probe geometry on the shape of the measured profile.

Copies obtoinoble from: Institute of Aerophysics, lJniversity of Toronto, Toronto 5, Ontorio

~

UT IA REPORT NO. 46

"

Institute of Aerophysics, University of Toronto

An Experimental Investigation of Profiles Laminar Boundary Layer in a weak Adverse Pressure Gradient at an Incident Mach Number of Three

E. A. Racicot, March, 1957, 16 pp., 18 figs., 1 table

Experimental pitot pressure profiles through a laminar boundary layer in supersonic flow and under a weak adverse pressure gradient are compared

with the predictions of the theory of G. M. Low. Some information is

pre-sented about the effects of probe geometry on the shape of the measured

profile.

Copies obtoinable from: InstÏlute of Aerophysics, University of Toronto, Toronto 5, Oniario UTIA REPORT NO. 46

"

An Experimental Investigation of Profiles Laminar Boundary Layer in a weak

Adverse Pressure Gradient at an Incident Mach Number of Three

E. A. Racicot, March, 1957, 16 pp., 18 figs., 1 tab Ie

I Racicot, E. A. II UTIA Report No. 46

Experimental pitot pressure profiles through a laminar boundary layer in supersonic flow and under a weak adverse pressure gradient are compared with the predictions of the theory of G. M. Low. Some information is pre-sented about the effects of probe geometry on the shape of the measured profile.

(42)

UTIA REPORT NO. 46

•

Adverse Pressure Gradient at an Incident Mach number of Three E. A. Racicot, March, 1957,

1. Flow, Laminar

3. Pressure Measurements Racicot, E. A.

II UTIA Report No. 46

Experimental pitot pressure profiles through a laminar boundary layer in supersonic flow and UI,der a weak adverse pressure gradient are compared

with the predictions of the theory of G. M. Low. Some information is pre-sented about the effects of probe geometry on the shape of the m-easured

profile

Copies obtainable from: Institute of Aerophysics, University of Toronto, Toronto 5, Ontario UTIA REPORT NO. 46

"

Adverse Pressure Gradient at an Incident Mach Number of Three E. A. Racicot, March, 1957,

1. Flow, Laminar

Racicot, E. A.

II UTIA Report No. 46

with the predictions of the theory of G. M. Low. Some information is pre-sented abw t the effects of probe geometry on the shape of the measured

profile.

Copies obtainable from: Institute of Aerophysics, University of Toronto, Toronto 5, Ontario

UTIA REPORT NO. 46

•

E. A. Racicot, March, 1957, 16 pp., 18 figs. , 1 table

1. Flow, Laminar 2. Boundary Layer, Internal Aerodynamics

with the predictions of the theory of G. M. Low. Some information is pre-sented about the effects of probe geometry on the shape of the measured profile.

Copies obtainable fram: Institute af Aeraphysics, University of Toranto, Toranto 5, Oniario

UTIA REPORT NO. 46

•

E. A. Racicot, March, 1957, 16 pp., 18 figs., 1 table

l. Flow, Laminar 2. Boundary Layer, Internal Aerodynamics 3. Pressure Measurements

Experimental pitot press.ure profiles through a laminar boundary layer in supersonic flow and under a weak adverse pressure gradient are compared

with the predictions of the theory of G. M. Low. Some information is pre-sented about the effects of probe geometry on the shape of the measured profile.