R. & M. No. 2863(13,509,13,789,13.947)

A.R.C. Teclmical RellOzt

MINISTRY OF SUPPLY

AERONAUTICAL RESEARCH COUNCIL

REPORTS AND MEMORANDA..--' ,,', ' -'~···r·'-~>,:;~j,~-~'·"'-'·" .-:1

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Tests at High Subsonic Speeds on a10 per cent Thick Pressure-plotting

Aerofoil of RAE 1°4 SectionBy

E. W. E. ROGERS, D.LC., B.Sc.,- C. J. BERRY,

andR. F. CASH, A.F.R.Ae.S.

Crown Copyright Rmroed

LONDON: HER MAJESTY'S STATIONERY OFFICE

I956THIRTEEN SHILLINGS NET

per cent104 Section

Tests at High Subsonic Speeds on a I 0

Thick Pressure-plotting Aerofoil of RAE

By

E. W. E. ROGERS, D.LC., B.Sc., C. J. BERRY, and R. F. CASH, A.F.R.Ae.S.,

of the Aerodynamics Division, N.P.L.

Reports and Memoranda No.' 2863*

April, 1951

1. Summary and Introduction.-A series of tests has been made in the National Physical Laboratory 20-in. X 8-in.High Speed Wind Tunnel on a two-dimensional pressure-plotting aerofoil of five inches chord and RAE 104 section.The work included:

(a) A comparison of the results obtained with and without spanwise bulges on the aerofoil surface (Ref. 1).(b) A comparison (to show the effects of a change in Reynolds number at high speeds) with measurements made

in the same tunnel on a pressure-plotting aero foil of similar profile but having a chord of two inches (Ref. 2).(c) An investigation of the pressure distribution and flow around the aerofoil at high incidences for various Mach

numbers.(d) A determination of the force coefficients, surface pressures and flow patterns for the aerofoil through a range

of Mach number at incidences up to 8 deg.

The present report is concerned with thislast item.

2. The Aerofoil.-The five symmetrical aerofoils designed by Squire in 1945 and described byhim in a note of limited circulation were originally referred to as ' Sections A to E '. Slightlydifferent versions of aerofoils B, E and A were tested on a balance in the Royal Aircraft Establish­ment High Speed Tunnel and are called' H.S. 6, 7 and 8 ' in the report" on that work. Subsequentlyhowever, the Squire sections were designated' RAE 100 to 104 '. The ordinates and theoreticalpressure distributions are given in Ref. 4.

RAE 104 (or Squire E) has a maximum thickness/chord ratio of 10 per cent occurring at42 per cent chord. The rear section of the aerofoil beyond. about 80 per cent of the chord iswedge shaped. At zero lift, the theoretical pressure distribution is almost constant back to60 per cent chord and then falls uniformly to the trailing edge.

For the present tests the aerofoil was made with a finite trailing-edge thickness of 0·00064chord and this modifies very slightly some of the ordinates given in Ref. 4. The actual modelordinates are given in Table 1 and the profile isshown in Fig. 1.

The model had seventeen pressure holes on the upper surface, fourteen on the lower surface,one at the leading edge and one at the trailing edge. Table 2 gives the chordwise positions ofthe pressure holes.

>i< Published with permission of the Director, National Physical Laboratory.(1522) A

3. Tests.-(a) Method of Testing.-Using a large multi-tube manometer, measurements of thesurface pressure distribution were made at various incidences from 0 deg to 8 deg for a Machnumber range of from 0·4 to the limiting speed of the tunnel. The flexible walls of the tunnelwere' streamlined' in the standard manner". In addition, several pressure distributions weretaken at negative incidences to check the symmetry of the flow and the accuracy of the zeroincidence setting; these were satisfactory in all cases.

At the higher incidences, the model slightly affects the reading of the tunnel-speed hole 1· 7chords upstream of the leading edge and to allow for this a correction has been applied, wherenecessary, to the nominal free-stream Mach number.

Wake traverses were also made at one chord behind the trailing edge of the model for sixincidences, the Mach number range being the same as for the pressure distributions.

The Reynolds number of the tests varied with Mach number between 1· 1 and 1· 9 million.

(b) Reduction of the Observations.-The coefficients CL and C; were found in the usual way byintegrating the pressure distribution curves; the profile-drag coefficients (CD) were obtained fromthe wake pitot-traverse curves by means of a shortened method of Ref. 6.

(c) Flow Visualisation.-Schlieren and direct-shadow photographs of the flow were obtained atmost angles of incidence and free-stream Mach numbers. For the schlieren photographs, thecut-off was parallel to the aerofoil chord.

(d) Condition of Boundary Layer.-The tests were first made with the boundary-layer transitiontaking place naturally. Later the transition position was fixed on both surfaces at about O· 14chord by means of a narrow band of cellulose lacquer (see section 7).

4. Presentation of Results.-The experimental pressure distributions obtained with the naturaltransition position are given in Figs. 3 to 15*; two methods of plotting these results are used:

(a) In terms of the pressure coefficient C, [= (P - Po)/ipU2].

(b) In terms of the ratio P/H for certain incidences.

(The stream total head and static pressure are denoted by H and Po, and p is the measured surfacepressure.)

A comparison with the theoretical pressure distributions at four angles of incidence for Machnumbers near 0·4 is made in Fig. 2.

The resulting lift and quarter-chord moment curves and their derivatives, together with thedrag results are given in Figs. 17 to 30; a comparison with RA.E. tests on a wing of aspect ratio5·5 is also made (Figs. 32 to 34).

The results obtained with the boundary-layer transition artificially fixed at about 0·14 chordare presented in Figs. 35 to 43. Finally, direct-shadow and schlieren flow photographs for bothconditions of the boundary layer are reproduced as Figs. 45 to 51.

5. Discussion of Results (Transition Free).-(a) IX = 0 deg (Figs. 3, 45 and 46).-Fig. 2 showsthat at M = O·4 agreement between the calculated and experimental pressure distributions isreasonably good over most of the aerofoil surface. Between O·6 and 0·7 chord there is a smalldiscrepancy between the two curves, due to a kink in the experimental pressure distributioncurve. This kink becomes accentuated with increase of Mach number (Fig. 3) and its positioncorresponds roughly with that of a local separation of the laminar boundary layer which wasfirst detected by means of oil deposited on the model surface at a Mach number of O·65. Transi­tion occurs at about 0·75 chord, after reattachment of the boundary layer; the evidence of thedirect-shadow photographs on this matter was subsequently confirmed by evaporation testsusing cc-monochlorhydrin as the indicator.

* Tabulated values of Cp or P/H for the various pressure distributions may be obtained on application to theSuperintendent, Aerodynamics Division, N.P.L.

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The experimental pressure-critical Mach number at zero incidence is 0,785, although Fig. 45cshows that small wavelets, presumably moving against the stream, are visible at M = 0·750.No sudden change takes place in the flow pattern as the free-stream Mach number is raisedabove the critical, the diffuse band of wavelets slowly giving place to a series of shock-wavesinclined forward into the stream. Each compression wave is followed by a small expansion,presumably as a 'result of undergoing reflection from the laminar boundary layer, which wasfound to be separated from the surface in this region. The number of these shock-waves decreasesrapidly with increasing Mach number. For example, at M = 0·810 (Fig. 46b) there are five orsix separate waves visible between O'4 chord and O: 7 chord; this is reduced to three or fourinclined waves followed by a small normal wave in Fig. 46c (M = 0,820), to one inclined wavefollowed by a normal wave at M = 0·840 (Fig. 46e). It is between M = 0·800 and 0·820 thatthe rapid increase in drag coefficient occurs; by M = 0,840, CD is twice its low-speed value andthe loss of momentum through the shock-system has become appreciable. The value of C; atthe trailing edge also begins to decrease rapidly at this speed, indicating an increase in boundary­layer thickness at this position. (Separation of the turbulent boundary layer was not observeduntil about 0·88 (Fig. 16a).)

This change in the flow pattern modifies the shape of the pressure distribution curves until atM = 0·840, there is the type of curve usually associated with a locally detached laminar layerupstream of the main shock-wave. These results are compared below with those obtained fromthe aero foil with transition fixed on both surfaces at about 0·14 chord; in this case, there is nolocal separation of the boundary layer and 'the type of shock-pattern described above is absent.The local velocity continues to increase up to the final recompression and thus the' truncated'type of pressure distribution is not observed.

As the free-stream Mach number is increased beyond 0·840, the pressure distribution curvesremain similar in general shape, apart from the rearward movement of the recompression position.The flow photographs however show that the shock-pattern obtained at M = 0·840 gives placeto a normal shock-wave as the Mach number is raised to 0·860 (Figs. 45n and 46g). The laminarboundary layer separates upstream of the main wave and a weak compression wave springsfrom this point to join the main wave some distance from the aerofoil surface, Fig. 45n suggeststhat transition to turbulent flow in the separated, or vortex layer does not occur until just beforethe wave. Oil deposited on themodel surface did not indicate any reversed flow in the turbulentboundary layer but the schlieren photograph (Fig. 46g) suggests that this layer may have beenseparated or about to separate.

The weak inclined compression waves* appear also in the schlieren photograph at M = 0·89(Fig. 46i). In this case there is a gradual compression immediately upstream of the foot of themain wave which now resembles a bifurcated wave, but with its front branch' softened '. Thereis now definitely no attachment after transition to turbulent flow, the oil indicating reversed flowfrom the trailing edge to the foot of the shockwave for Mach numbers of 0·88 and above. Thepresence of turbulent separation is also suggested by Fig. 46i.

(b) IX = 1 deg (Fig. 4).-At this incidence the low-speed pressure distribution has a smallsuction peak on the upper surface near the leading edge. With increasing Mach number, the peakgradually disappears and the curve becomes similar in shape to that observed at the higher Machnumbers at zero incidence, with a favourable pressure gradient back to about O· 5 chord.

The lift coefficient increases continuously up to a Mach number of about O'82, when sonicvelocity is reached on the lower surface. The subsequent rapid growth in the local supersonicregion on this surface and the associated decrease in pressure, are greater than the correspondingeffects on the upper surface and as a result, the lift decreases.

* The weak compression waves are not very clear (at least near the surface) in the direct-shadow photographs (Figs.45n, 45p, and 45q). This is probably due to the continuous nature of the compression and suggests that both types ofpictures are necessary if a detailed knowledge of the flow around the aerofoil is required.

3(1522) A*

(c) o: = 2 deg (Figs. 5, 6, 47 and 48).-As was observed at o: = 1 deg, the low-speed pressuredistribution (in good agreement with theory, see Fig. 2) gives place to a curve having a favourablepressure gradient back to about 0·5 chord, as the Mach number is increased. Further the fall-offin CL again occurs just after sonic velocity has been reached on the lower surface; the decreasein C; takes place a little earlier, when the low-pressure supersonic region, originally situated atthe nose, spreads beyond the quarter-chord position.

The flow photographs show a similar sequence of events to that observed at 0 deg, althoughthis occurs at different Mach numbers on the two surfaces. A forward-inclined shock-wavereflecting as an expansion from the locally separated laminar boundary layer and followed by anormal shock gives place to a strong normal wave. The increased pressure rise at the foot of theshock causes marked boundary-layer thickening and leads to a very thick layer over the rear ofthe aerofoil and a rapid increase in drag. The trailing-edge pressure coefficient begins to decreaserapidly after M = 0·83 (Fig. 16b). On the lower surface, Figs. 47d, 47e and 47f, show the reduc­tion in the number of the forward-inclined waves with increasing Mach number.

(d) rt. = 2·5 deg and 3 deg (Figs. 7 and 8).-The chief difference between the results obtainedat these incidences is in the shape of the Cccurve near its peak (Fig. 17). This peak is markedat o: = 2· 5 deg, but is replaced at the higher incidence by a region of almost constant lift coefficientextending over a range of Mach number from 0·74 to 0·82. In both cases the fall in CL takesplace just after the speed of sound has been reached on the lower surface.

On the upper surface between itt = O·75 and O·80, the increasing region of low pressure causedby the rearward movement of the shock-wave is offset to some extent by the disappearance ofthe forward suction peak. The peak is higher, and the loss of lift resulting from its disappearanceis greater, at 3 deg incidence than at IX = 2·5 deg.

(e) rt. = 4 deg (Figs. 9, 10 and 49).-Fig. 2 shows that agreement between the theoretical andexperimental pressure distributions is not as good at o: = 4 deg than at the lower incidences,especially over the rear half of the aerofoil. Sonic velocity first occurs on the upper surface ofthe aerofoil, near the nose, at a Mach number of 0·550. The drag coefficient rises slowly as thisspeed is exceeded. As the shock-wave moves back, it takes with it the boundary-layer transitionposition and it is possible that the shallowness of the drag rise is due in part to the increasedlosses through the shock-wave being offset by the reduced skin friction. The local Mach numberon the aerofoil surface ahead of the shock-wave is reasonably constant being between 1·3 and 1·4for a wide range of Mach number (0,685 to 0,838). This is shown in Fig. lOa.

The fall in Cm once more occurs when the shock-wave moves back past the quarter-chordposition. On the lower surface the pressure decreases more rapidly with increase in Mach number(Fig. 9b), than was the case at the lower incidence; this tends to reduce to some extent the rateat which the lift coefficient rises with increasing tunnel speed. The pressure-critical Mach numberfor the lower surface is about 0·80, corresponding approximately to the Mach number at whichthe lift coefficient begins to decrease.

At Mach numbers greater than about O·75, the shape ofthe upper surface pressure distributioncurves suggests that a local laminar separation takes place about O· 1 chord upstream of thenormal shock-wave. (This separation was in fact confirmed by oil tests.) A small recompressionoccurs at this point and is visible as a faint black band, inclined to the stream direction, in theschlieren photographs. At the higher Mach numbers, there is a peculiar bulge in the upper­surface pressure distribution curve between 0·8 chord and 0·95 chord. A similar though lessmarked effect occurs at 3 deg incidence (Fig. 8a) and the phenomenon persists up to the highesttest incidence. Increase in free-stream Mach number causes the bulge to disappear at someincidences, presumably when severe separation takes place over the rear of the aerofoil. It isdifficult to account for this bulge; oil deposited on the surface at this position gave little directevidence For example, at IX = 4 deg the bulge begins to be apparent in the pressure distribution

4

taken at M = 0·763 and persists until M = 0·829. An oil test* at about a Mach number of0·79 indicated no local separation in this region, whilst at about M = 0,81, the surface flow wasreversed from the trailing edge to about 0·6 chord.

(f) o: = 6 deg and 7 deg (Figs. 11, 12 and 50; 13).-The flow around the aerofoil at 6 deg incidenceis similar in many respects to that obtained at 4 deg. The drag coefficient begins to rise soon afterthe pressure-critical Mach number (0' 430) has been exceeded, the transition position movingback from the nose with the shock-wave. In the direct-shadow photograph taken at M = O' 594(Fig. 50a) small' lambda' waves are visible near the leading edge.

The bulges in the upper surface pressure distribution curves near the trailing edge are verymarked at this incidence (Fig. 11a).

Three pressure distributions were taken at 7 deg in order to find the low-speed lift-curve slopein this region and also the low-speed drag coefficient. These pressure distributions are plotted inFig. 13; the step in the curve near the nose suggests that the stall is beginning and in fact dCLldrxdoes begin to decrease (see Fig. 18).

(g) ex = 8 deg (Figs. 14, 15 and 51).-Because of the high suction peak, and the 'stepped'shape of the curve in this region, the pressure-critical Mach number is difficult to estimate. Atlow speeds the flow separates locally near the nose and reattaches as a thick turbulent layer.Fig. 51a shows that several small waves are visible in this region at M = 0·591 and by M = 0·640,a well-defined lambda shock has developed, the forward leg of which is caused by the separatingboundary layer. It should perhaps be pointed out that a series of shock-waves which appearto be consecutive in a photograph, may in fact be distributed along the chord since the flow maynot be entirely two-dimensional at high incidence. The schlieren photograph at M = 0·640(Fig. SId) shows that the boundary layer has fully separated behind the shock-wave.

This is the Mach number at which the drag coefficient reaches a local maximum (Fig. 27), areduction taking place until M = 0·680. The laminar boundary layer adheres over the frontpart of the model (local laminar separation occurs at O· I chord at M = O'665 and about 0·01chord at M = O·60), and thus the turbulent boundary layer is initially thinner and the subsequentturbulent separation less severe. A comparison of Figs. 5Id and 51£ shows a small decrease inthe width of the wake. Moreover above M = 0·690 the flow adheres around the nose and thepressure distribution curve becomes smooth back to the shock (Fig. I5a).

The beginning of the drop in CD corresponds approximately to a marked rise in the liftcoefficient, which reaches its peak at M = 0·74. This rise, which was not observed at 6 degincidence, seems to be due to a rapid backward movement of the shock-wave combined withthe attainment of higher local Mach numbers at the nose of the aerofoil. By M = 0·765, theshock-wave has only moved a little to the rear of its position at a Mach number of 0·737 (Figs.14 and 15). Further, the velocity distribution up to the shock is similar in both cases (a localMach number of about 1· 6 being obtained at the nose) and hence the pressure coefficient inthis region is increased. There is also a relatively large decrease in the lower-surface pressurecoefficient, and the net result is a decrease in C£0 Fig. 15a shows that the bulge in the pressuredistribution curve between 0·8 chord and 0·95 chord on the upper surface appears at the threehighest test Mach numbers.

The variation with Mach number of the trailing-edge pressure coefficient at this incidence isgiven in Fig. 16f. Up to a Mach number of 0 '64, the value of Cpu. slowly decreases; beyondthis Mach number the drag coefficient decreases, and there is a rapid increase of CPT.E.. Theinitial decrease in CPT.E. corresponds to the thickening of the boundary layer and separation withMach number. The rapid increase corresponds to the adherence of flow over the nose of the model,which causes a thinner boundary layer or wake at the trailing edge. The rise in CL and decreasein drag coefficient is due directly to this effect. A further boundary-layer separation or thickeningoccurring at a Mach number of about 0·7 causes a reduction in CPT.E. and a final drag rise.

* The oil tests mentioned in this report were made by H. H. Pearcy during an investigation on the stallingcharacteristics of this aerofoil; except at 0 deg incidence the tunnel walls were not streamlined but were adjusted foruniform pressure along the empty tunnel. It is therefore difficult to relate precisely the Mach numbers of the two tests.

5(1522) A*2

6. Brief Discussion of Integrated Results (Transition Free).-(a) Lift.-It is interesting to notein Fig. 17, at the lower incidences the agreement between the experimental rise of CL withincreasing Mach number and that predicted by the Glauert law. The falling-off in CL is delayeduntil after the pressure critical Mach number has been exceeded, and is preceded by a markedpeak in the curves for o: = 1 deg, 2 deg and 2· 5 deg. At 3 deg however this sharp peak is replacedby a flat top extending over a considerable range of Mach number and as a result the lift-curveslope in this region alters appreciably.

At the higher angles of incidence no agreement can be expected with the Glauert law, becausethe pressure-critical Mach number is low. At rx = 8 deg, there is in fact, a large and rapid increasein CL between M = 0·6 and 0·725 probably due to the rearward movement of the shock-waveand of the position of flow separation (see above).

The CL vs. o: curve exhibits a change of slope in the region rx = 0 deg to 2 deg even at lowspeeds. Similar effects have been observed in earlier tests and can be attributed to the forwardmovement of the upper-surface transition point in' this range; the value of dCL/drx thus varieswith incidence (see curves of Fig. 23). A further decrease in the lift-curve slope occurs at thehighest incidence; in this case it is probably due to turbulent separation over the rear of theaerofoil.

(b) M oment.-Except at the lowest incidence, the increase in Cm with Mach number (Fig. 19)is everywhere greater than that predicted by the Glauert law and by Hilton's empirical formula".The maximum value of C; is, in general, quite well defined and occurs at progressively decreasingMach numbers as the incidence increases.

The variation of C; with incidence or lift coefficient is relatively small at low Mach numbersbut becomes less so as the speed is increased.

(c) Drag.-At incidences of 2 deg and 4 deg (but not at 0 deg) the final rapid rise in drag isdelayed until well beyond the pressure critical Mach number (Fig. 27). The drag rise is in factdelayed until approximately the' crest critical Mach number' is reached". This is when sonicvelocity is first achieved at the position where the aerofoil surface is tangential to the free-streamdirection. At 4 deg there is a peculiar discontinuity in the curve near M = O·80, the dragcoefficient actually reducing slightly as the Mach number increases. The effect was confirmedwhen the observations were repeated later. The wake-traverse curves suggest that thisreduction is due to a decrease in the loss through the shock-wave (which is quite well developed)but the reason for such a decrease is not clear a present.

A similar type of curve but with a much more marked discontinuity was obtained at o: = 8 deg,a well-defined reduction in CD occurring between M = 0·64 and 0·69; this point was discussedin section 5 (g) above. Similar reductions in CD occurring at the same incidence and aboutthe same Mach number, have been observed in many American tests on 10 per cent thicksymmetrical sections.

The theoretical profile-drag coefficient values" for different mean transition positions are alsoplotted in Fig. 27. Using the evidence" of the direct-shadow photographs transition for 0 degwas found to take place at about 0·75 chord at low speeds. The measured value of CDwas 0·0048 and this agrees well with theory if the latter is extrapolated to estimate transitionposition at O·75 chord.

(d) Comparison with R.A.E. Res~tlts.-An early version of a 10 per cent RAE 104 aerofoil,having a rounded trailing edge* has been tested on a balance in the R.A.E. High Speed Tunnel"at a Reynolds number of one million. The model used was rectangular with an aspect ratio of5·5 and for comparison the N.P.L. results have been reduced to the same aspect ratio by themethod of Ref. 12.

* This early version (H.S.7) had almost the same trailing-edge angle as the present RAE 104 but was slightly thickerbeyond about O·5 chord for a given x]c position. The trailing-edge thickness was reduced to zero by rounding the wedgetail after 0·975 chord. Until recently the RAE 104 section was known at the N.P.L. as H.S.7a.

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It appears from Fig. 32, which compares the CL vs. IX curves, that although agreement is goodat a Mach number of 0·4, the lift-curve slope of the N.P.L. results is less than that given by theRA.E. tests at the higher Mach numbers. Reasonably good agreement in the curves of C;against CL is obtained for the two sets of results (Fig. 33), with the exception of near the stallat M = 0·4. Here the divergence may be due to the different nature of the stall in the two casesof finite and infinite aspect ratio.

The drag results from the R.A.E. tests are not given in Ref. 3, but are included in a later paper.A comparison between the CD vs. Mach number curves is given in Fig. 34, the N.P.L. resultshaving been reduced to an aspect ratio of 5·5. The differences between the two sets of curvesmay be due partly to the effect of Reynolds number and partly to uncertainty in allowing forthe effect of aspect ratio, particularly at the higher Mach numbers. Moreover, the R.A.E. winghad square-cut ends (the usual rounding of the section being omitted in this case) and it is under­stood that there was some uncertainty regarding the strut interference corrections to dragcoefficient at high speeds.

7. Tests with Fixed Boundary-Layer Transition Position.-In the tests considered above, theboundary-layer transition was allowed to occur naturally and thus the layer was laminar up tothe foot of the shock-wave system, when this was present on the aerofoil surface. At the ratherlow Reynolds numbersof the experiment (1,1 to 1·9 million), local separations of the laminarboundary layer tended to occur at some incidences and Mach numbers, giving rise to a characteristictype of shock-pattern and pressure distribution. Since the extent and magnitude of theseoperations (and their effect on the aerofoil surface pressures and forces) is known to vary withReynolds number- 13, becoming less pronounced as this quantity is increased, results obtained witha natural transition position are difficult to extrapolate to a higher Reynolds number. Shouldthe transition occur near the nose, so that the boundary layer ahead of the shock-wave isturbulent, then the present' transition free' results may actually be misleading.

It was therefore felt that if transition could be fixed near the leading edge on both surfaces, acomparison of the results thus obtained with the earlier tests would be of interest.

Earlier experiments in the 20-in. X 8-in. Tunnel in which the boundary-layer transition positionwas fixed on an aerofoil were made by Pearcey"*, Shaw", and Fage and Sargent". In the testsdescribed in Ref. 14, spanwise wires were attached to the model in order to cause transition.It was concluded that for an aero foil of 5-in. chord, this method was rather unsuitable due to theformation of shock-waves at the wires for comparatively low free-stream Mach numbers. Byusing a one-foot chord model (thus increasing the Reynolds number) the compressibility effectsat the wires were found to be of less importance]. This model size however is too large for normalexperimental work in the 20-in. X 8-in. Tunnel.

For the results obtained in Ref. 15, tests were made with the aerofoil in thewake of a fine wire(0·025-in. diameter) stretched across the tunnel 0·75 aerofoil chords upstream of the model andparallel to its leading edge; turbulent boundary layers were therefore caused on both surfacesof the aero foil. The main objections to such a technique are:

(a) The drag of the model is difficult to measure by the wake-traverse method (the tunnelhas no balance).

(b) The aerofoil is tested in a narrow non-uniform stream (the wake of the wire) whose meanMach number is lower than that of the free stream.

(c) The flow just outside the boundary layer is more turbulent than would normally be thecase had transition taken place at the leading edge in the absence of the wire. Thismay cause a more rapid growth in the boundary-layer thickness than would occurnaturally.

* Pearcey has also made extensive tests on an aerofoil with turbulent and laminar boundary layers. These resultsare as yet unpublished.

t It was also found from tests in another tunnel of the N.P.L. High Speed Laboratory that spanwise grooves wereineffective in fixing transition on a 2-in. chord model.

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Nevertheless, the results obtained from tests of this type are valuable in indicating the natureof the flow changes that occur when the boundary layer of the model is made turbulent at theleading edge. The effect of items (b) and (c) on the general flow pattern and the surface pressuredistribution is difficult to assess and may well prove to be negligible.

Fage and Sargent" achieved a satisfactory method of causing transition by injecting air intothe boundary layer at the required position through a spanwise row of small holes in the surfaceof a hollow aero foil. By controlling the airflow, transition could be made to take place withoutdisturbing the external flow. The method requires a specially constructed model and a chordwisevariation of the transition position on a particular aero foil is difficult. Moreover, on as-in.chord pressure-plotting model, these transition holes are normally only obtained by slightlyreducing the number of chordwise pressure holes. The construction of a model of this designis not easy and its use in the wind tunnel may entail certain experimental difficulties.

I t was therefore considered worthwhile attempting to fix transition by means of the methoddescribed below, which uses a narrow band of cellulose lacquer deposited near the leading edgeto disturb the boundary layer.

(i) Experimental Details and Range of Tests.-Two spanwise parallel strips of cellulose tapewere placed on the aero foil surface with their edges about O·03 chord apart and a thin coat(about O·0015-in. thick) of Frigilene* applied over the inner edges of the strips and the surfacebetween them. When this first application was dry, the process was repeated, the numbers ofseparate coats varying between two and five and depending on the chordwise position of the tapesand the free-stream Mach number of the tests (see below).

With the removal of the tapes a band of Frigilene was left which had sharply defined edges.It was found that, in general, a sharp forward edge to the band was essential for causing transition.When this edge became smoothed (for example, after several tunnel runs), the band was nolonger effective.

Transition was fixed in this way on both surfaces of the aerofoil at a mean position of 0·14chord. During the subsequent tests, the free-stream Mach number was varied between 0·4 andits limiting value for three values of incidence, 0 deg, 2 deg and 4 deg. Pressure distributions(Figs. 35 to 37) were recorded in order to determine CL and C',I (Fig. 38), the drag coefficient(Fig. 39) being found by integrating the curves of total-head loss in the wake, one chord behindthe trailing edge. In addition schlieren and direct-shadow photographs were taken of the flowaround the model.

At free-stream Mach numbers where the local flow at 0·14 chord is supersonic, it proveddifficult, though not impossible, to obtain a band of sufficient thickness to cause transition butnot to produce small shock-waves at the band position. It was decided not to attempt to eliminatethe waves completely but to reduce their magnitude and extent. Those visible in the photographsdo not seem to affect appreciably the general flow, and in no case could an irregularity be detectedin the readings of the neighbouring pressure holes. The addition of carborundum powder to theFrigilene, although causing transition even when the sharp forward edge of the band had wornaway, greatly increased the size of the waves and this method was not used to obtain any of theresults presented in the present note.

Tests were also made at two Mach numbers (0,4 and 0,725) for zero incidence, the profiledrag being measured for various chordwise transition positions. The results obtained arecompared with theory in Fig. 44.

At 0 deg incidence, for a given chordwise position, a thicker band was needed to causetransition at the lower speeds (and hence lower Reynolds number) than at the higher free-streamvelocities, the pressure gradient being favourable back to at least 0·5 chord for all Mach numbers.The disturbance required to promote transition increased as the band position was moved tothe rear of the model.

* A proprietary brand of cellulose lacquer.

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At incidences of 2 deg and 4 deg and without a transition band, transition occurs near the noseon the upper surface at low speeds; as the main shock-wave moves back with increasing free­stream Mach number, it carries the transition point with it. In this case then, a transition bandsituated at 0·14 chord would only begin to be effective after the local velocity at that point wassupersonic. The thickness required at any particular free-stream Mach number was about thesame as at 0 deg. On the lower surface, transition occurs well towards the rear of the aerofoilif no band is present. The band thickness necessary to cause transition at 0·14 chord on thissurface was greater at low speeds.

The effectiveness of the band in provoking transition along the whole span of the model waschecked at frequent intervals throughout the experiment by observing the evaporation of a thinfilm of glycerol-u-monochlorhydrin''. A well-defined transition front at the Frigilene band wasalways obtained. (The same chemical, applied more thickly so that its movement could be observedwas also used in the earlier tests to detect local separations of the laminar boundary layer.)Similar observations made when transition was fixed at 0·14 chord failed to reveal any separationof the turbulent layer, except at the highest Mach number, where the oil flow on the aero foilsurface was reversed in direction from the trailing edge to about 0·8 chord.

(ii) Discussion of Results-Transition Band at 0·14 Chord.-It has been suggested by H. H.Pearcey that at relatively low Reynolds numbers, the differences in the general flow patternwhen the boundary layer is either laminar or turbulent are due very largely to the presence ofextensive local separations in the former case, which are absent when the boundary layer isturbulent. Such differences are much less noticeable when the laminar separations are smallerin extent and this occurs when the Reynolds number or the free-stream turbulence is increased(see, for example, Refs. 2 and 13).

It is proposed here merely to present the data obtained during the tests described above andto discuss the results briefly. The free-stream turbulence was low, and the test Reynolds numberwas also comparatively small (1,1 to 1·9 million).

(a) oc = 0 deg (Figs. 35, 45 and 46).-The pressure distribution curves obtained with eitherfixed or ( natural' transition positions are shown in Figs.' 35a to 35j ; specimen photographs ofthe flow pattern are given in Figs. 45 and 46.

At low speeds, the chief difference in the pressure-distribution curves occurs in the regionbetween 0·6 chord and the trailing edge, the distribution with fixed transition position being inbetter agreement with theory' (Fig. 41). Above M = 0·6, a local laminar separation wasobserved in the original tests between about 0·6 chord and 0·7 chord by means of «-mono­chlorhydrin deposited on the aerofoil surface.

From M = 0·820 to 0·880, the pressure distributions obtained with a laminar boundary layerhave the characteristic truncated appearance associated with a local separation ahead of theshock-wave system. With a turbulent boundary layer no such separation occurs and the mainrecompression on the aerofoil surface takes place more abruptly (e.g., Figs. 35h to 35j). Themain recompression systems in the two cases are situated at approximately the same chordwiseposition (Fig. 42a).

The shock-patterns in this Mach number range are dissimilar. For example at M = 0·820,as was mentioned above, with a laminar boundary layer, there is a series of small compressionwaves, inclined upstream slightly, and each reflecting as an expansion from the separated layer(Fig. 46c), whilst with a turbulent boundary layer (Fig. 46d) , the main compression wave isquite well-defined, normal to the surface and followed by a fairly rapid thickening of the boundarylayer. In both cases the drag coefficient at this Mach number has increased by about the sameamount above the value at M = 0·4 (see Fig. 40).

Perhaps the most striking difference between the shock-patterns occurs at M = 0·840 (Figs.46e and 46f). In the original tests, the compression system consists of a forward-inclined wavereflecting as an expansion from the detached laminar layer, subsonic flow being finally reached

9

through a small normal shock; the boundary layer reattaches to the surface in a turbulent state.When transition is made to occur at 0·14 chord, the main shock-wave is inclined downstreamslightly at the surface, and becomes normal to the incident flow some distance from the aerofoil.This pattern is again observed at M = 0·860 (Fig. 46h) but the backward inclination of theshock-wave near the surface is more marked. With a laminar boundary layer, the maincompression wave has straightened and grown in extent; the expansion region has disappeared,but separation still occurs some distance ahead of the main wave, giving rise to weak inclinedcompression waves and a softening at the foot of the main wave.

For the highest test Mach number at this incidence (M = 0,880), the main compression wavesare situated at about the same chordwise position in both tests, and are both inclined backwardsnear the aero foil surface. The laminar boundary layer separates about 0·2 chord upstream ofthe main shock, causing (as before) weak inclined waves. These compression waves cause asmall decrease in the local Mach number at that position (Fig. 35j). With a turbulent boundarylayer, separation only takes place after the shock, the local Mach number increasing continuouslyup to the foot of the shock-wave.

(b) ex = 2 deg (Figs. 36 and 48).-At the lower speeds, the main difference between the twosets of pressure distribution curves at this incidence is the small increase in lower surface pressureswhen the boundary layer is turbulent from 0·14 chord. This discrepancy is greatest over thelast 0·4 chord and in some cases (e.g., Figs. 36c, 36d and 36e) the negative pressure-loop observedwith a laminar boundary layer completely disappears. As a result, the lift coefficient is increasedand the quarter-chord pitching-moment coefficient reduced (Fig. 38). On the upper surface theboundary layer is turbulent from near the nose in both cases and agreement is good over most ofthe surface.

The pressure-critical Mach number at ex = 2 deg is 0·720 but the flow patterns are similar upto about M = 0'770; apart from small waves caused by transition band, only diffuse waveletscan be seen. By about M = 0·80 the main shock-wave has become well-defined when theboundary layer is turbulent and the state of the boundary layer upstream of the shock-waveposition is now important in determining the flow pattern and pressure distribution. NearA{ = 0,82, for example (Figs. 48e and 48f), the shock-waves on the upper surface and theassociated pressure distributions differ in a similar manner to that observed at 0 deg. Thecontinuous decrease in pressure back to the shock-wave, which occurs with a turbulent boundarylayer, causes an increase in the lift coefficient (Fig. 38).

On the lower surface where the local velocity at about 0·55 chord is just supersonic at thisMach number, the pressure distribution curves in this region are in each case similar in type tothose observed on the upper surface around O·5 chord (Fig. 36g).

The pressure-distribution curves at M = 0·840 and 0·841 (Fig. 36h) illustrate well thecharacteristic difference in shape obtained with the two states of the boundary layer.

The increase in drag coefficient above the value obtained at M = 0·4 is slightly greater witha turbulent boundary layer at Mach numbers above O· 75. The final drag rise occurs earlier, thedifference in free-stream Mach number being about 0·02 (Fig. 40).

(c) ex = 4 deg (Figs. 37 and 49).-In general, the differences between the two sets of resultsat this incidence are similar to those observed at ex = 2 deg. At all speeds, the lift coefficient ishigher when transition is fixed on both surfaces. At low Mach numbers, this is due to smallchanges in Cp , particularly on the lower surface. For higher free-stream Mach numbers, thiseffect is augmented by the lower pressure just upstream of the main shock-wave when theboundary layer is turbulent and the change in the pressure distribution to the rear of this position.The bulge in the upper surface pressure distribution between 0·8 and 0·9 chord observed witha laminar boundary layer ahead of the shock, disappears when transition is fixed at 0·14 chord(see Figs. 37f and 37g).

Between about 0·15 and 0·45 chord, the upper surface of the aero foil is obscured by the holesin the glass tunnel wall, through which pass the model support pins. A comparison of the basesof the shock-waves and their interaction with the aerofoil boundary layer in the two cases, is

10

difficult until about M = 0·77. Figs 4ge and 49f show that with a laminar boundary layer themain compression wave is inclined forward slightly into the stream; with transition fixed at0·14 chord, the shock-wave is inclined slightly downstream near the surface. The correspondingpressure distributions (Fig. 37e) suggest that a local laminar separation takes place at about0·15 chord upstream of the main shock-wave in the former case.

Near M = O·SO, the flow behind the shock-wave system is different in the two tests, a morerapid thickening of the boundary layer occurring with a fixed transition position. Some thickeningof the boundary layer also occurs ahead of the shock in this case giving rise to a region ofcontinuous compression. This region grows in extent as the free-stream Mach number is increased.When the boundary layer is laminar upstream of the shock-wave, this continuous compressionstill exists (cj. Figs. 37g and 37h), although it is more gradual and is spread over a larger fractionof the chord. I t begins at the forward limit of the local laminar separation and a faint compressionwave originating from this point can just be seen in Figs. 49i and 49k.

The drag rise occurs earlier and the subsequent rate of increase of CD with M appears to begreater when transition is fixed (Fig. 43).

(c) Discussion of Results-Transition Band at Various Chordwise Positions.-The variation ofmeasured CD with Mach number at zero incidence is plotted in Fig. 43 for the two cases of' natural'and' fixed' transition positions. The theoretical values" of CD for various transition positionsare also given and it is seen that these predict a position nearer the trailing edge than was actuallythe case. The discrepancy is greater at the lower Mach numbers.

Transition was therefore fixed by means of a Frigilene band at five additional chordwise stationsat a free-stream Mach number of 0·4 and the profile-drag coefficient measured. A linear reductionof CD with rearward movement of transition position was observed (Fig. 44a). The correspondingtheoretical curve gives everywhere a higher value of CD for a given transition position, thedifference between the two lines reducing with rearward movement of the band. Similar curveswere obtained at M = 0·725, but only one additional transition position was investigated(Fig. 44b).

A difference of the same order between the experimental and theoretical results has beenobserved earlier by Dowlen" (wind-tunnel tests) and R. C. Lock" (flight tests). The latterreport discusses the matter at some length. without reaching any definite conclusions. Dowlenattributes the discrepancy to the fact that at the low Reynolds number of his tests (1·1 X 106

) ,

transition took place over an appreciable chordwise region (about O·2 chord) and was notimmediately provoked by the disturbing wire. In the tests described in the present note (whichare at the same-Reynolds number as Dowlen's at M = 0·4), a sharp well-defined transition frontwas given by the indicator and it is considered unlikely that transition could extend over about0·15 chord-the requisite chordwise distance at M = 0·4.

S. Concluding Remarks.-These tests made in the 20-in. X S-in. High Speed Wind Tunnelwith a 10 per cent thick RAE 104 aerofoil, in addition to providing data on the behaviour of thesection for a range of Mach numbers and incidence, show that large differences in flow pattern,pressure distribution and force coefficients can be obtained by fixing boundary-layer transitionnear the nose on both surfaces. These changes are mainly due to the suppression (or at least,reduction in chordwise extent) of the local boundary-layer separations observed near the feetof the shock-waves in the original tests",

There is evidence to suggest that the influence of these local laminar separations on the aero­dynamic characteristics of an aerofoil decreases with increase of Reynolds number, even thoughthe boundary layer remains laminar up to the shock-wave system. Tests planned in the newpressurised IS-in. X 14-in. Tunnel (R }lP to 6 million) on a 5-in. chord pressure-plotting aerofoilof the same section and thickness/chord ratio as the present tests, will therefore be of interest.

11

The Frigilene-band technique described in this report, though easy to apply, requires constantvigilance on the part of the tunnel operators as the band tends to become ineffective after a littletime. Small shock-waves are difficult to eliminate and the band thickness necessary to causetransition varies with Mach number (linked with Reynolds number in the 20-in. X 8-in. Tunnel)and chordwise position of the band.

The method therefore, can be said to be useful when various transition positions are requiredor when only a limited amount of work with a fixed transition position is contemplated. Forroutine tests in which transition position remains constant and in which careful control of thedisturbance is necessary, the introduction of air into the boundary layer through small surfaceholes would seem to be best*. More definite conclusions will be possible after the tests on the6 per cent RAE 104 aerofoil have been completed.

9. Acknowledgement.-The authors wish to acknowledge the assistance given by Miss B. M.Davis both during the experimental work and in the preparation of the figures and photographs.

REFERENCESNo. Author

1. J. A. Beavan, E. W. E. Rogers andR Cartwright.

2. E. W. E. Rogers, A. Chinneck andR F. Cash.

3. R Hills and H. E. Gamble

4. R C. Pankhurst and H. B. Squire ..

5. C. N. H. Lock and J. A. Beavan ..

6. J. A. Beavan and A. R Manwell ..

7. A. Fage and R F. Sargent

8. E. W. E. Rogers and C. White

9. W. F. Hilton

10. N. E. Winterbottom and H. B.Squire.

11. H. H. Pearcey

12. A. D. Young

13. R Hills

14. H. H. Pearcey

15. R. A. Shaw . .

16. A. Fage and R F. Sargent

Title, etc.High Speed Wind Tunnel tests on an aerofoil with and without two­

dimensional bulges. C.P.78. February, 1951.A comparison of results obtained at high subsonic speeds on two aero foils

of similar section but differing chord. A.RC. 13,628. December, 1950.(Unpublished.)

Preliminary note on three 10 per cent thick aerofoils (H.S.6, 7, 8) in theRAE. High Speed Tunnel. RAE. Tech. Note Aero. 1926. A.RC.11,117. December,1947. (Unpublished.)

Calculated pressure distributions for the RAE 100-104 aerofoil sections.C.P.SO. March, 1950.

Tunnel interference at compressibility speeds using the flexible walls ofthe Rectangular High Speed Tunnel. R & M. 2005. September, 1944.

Tables for use in the determination of profile drag at high speeds by thepitot traverse method. R & M. 2233. September, 1941.

Shock wave and boundary layer phenomena near a flat surface. Proc.Roy. Soc. A, Vol. 190. 1947.

Force and pressure measurements up to Mach number 0·88 on a 10 percent thick modified NACA 16 seriespropeller section A.RC. 11,114.24th December, 1947. (Unpublished.)

Empirical laws for the effect of compressibility on quarter-chord momentcoefficient, and for the choice of an aerofoil with small compressibilityeffects on centre of pressure. R & M. 2195. March, 1943.

Note on further wing profile drag calculations. RA.E. Report B.A.1634.A.RC. 4781. October, 1940.

The indication of boundary layer transition on aerofoils in the N.P.L.20-in. X S-in. High Speed Wind Tunnel. C.P.lO. December, 1948.

Note on the effect of compressibility on the lift curve slope of a wing offinite span. R & M. 2767. August, 1943.

Use of wind tunnel model data in aerodynamic design. ].R. Ae. Soc.,Vol. 55, pp. 1 to 19. January, 1951.

Aerofoils with and without spanwise wires or grooves. R & M. 2252.August, 1942.

Adhesion of flow beyond the shock stall on an E.C.1250 aero foil with25 per cent concave control flap. Further tests with turbulent boundarylayer. R & M. 2436. April, 1949.

An air-injection method of fixing transition from laminar to turbulentflow in a boundary layer. R & M. 2106. June, 1944.

* Subsequent experiments have confirmed this view.

12

No. Author17. E. M. Dowlen

18. R. C. Lock

19. R. F. Cash

REFERENCES-continuedTitle, etc.

Acomparisonof the calculated profile drag coefficients of various low-dragwing sections. College of Aeronautics Report No. 35. A.R.C. 13,224.April, 1950.

Note on profile drag calculations for low-drag wings with cusped trailingedges. R. & M. 2419. April, 1946.

Application of suggested drag-rise criterion to some N.P.L. and D.V.L.drag measurements on two-dimensionalaerofoils at high subsonic Machnumbers. A.R.c. 13,689. January, 1951. (Unpublished.)

TABLE 1Ordinates of RAE 104

x]» y/c x/c y/c »[c y/c

0 0 0·10 0·03234 0·58 0·045900·001 0·00344 0·12 0·03498 0·60 0·044640·002 0·00486 0·14 0·03724 0·62 0·043100·003 0·00596 0·16 0·03924 0·64 0·041360·004 0·00688 0·18 0·04100 0·66 0·039480·005 0·00768 0·20 0·04256 0·68 0·037460·006 0·00840 0·22 0·04394 0·70 0·035340·007 0·00908 0·24 0·04516 0·72 0·033120·008 0·00970 0·26 0·04622 0·74 0·030860·010 0·01082 0·28 0·04714 0·76 0·028540·012 0·01184 0·30 0·04790 0·78 0·026200·014 0·01276 0·32 0·04856 0·80 0·023820·016 0·01364 0·34 0·04908 0·82 0·021480·018 0·01446 0·36 0·04948 0·84 0·019120·020 0·01520 0·38 0·04976 0·86 0·016780·025 0·01696 0·40 0·04994 0·88 0·014420·030 0·01852 0·42 0·05000 0·90 0·012080·035 0·01994 0·44 0·04994 0·92 0·009720·040 0·02126 0·46 0·04976 0·94 0·007380·050 0·02362 0·48 0·04944 0·96 0·005020·060 0·02568 0·50 0·04902 0·98 0·002680·070 0·02756 0·52 0·04846 1·00 0·000320·080 0·02928 0·54 0·047760·090 0·03086 0·56 0·04692

TABLE 2Position of Pressure Holes

Hole No.»[c

Hole No.x/c

Upper I Lower Upper I . Lower

L.E. 0 0 10 0·50 0·621 0·002 0·005 11 0·56 0·682 0·01 0·02 12 0·62 0'743 0·04 0·10 13 0·68 0·834 0·10 0·16 14 0·74 0·955 0·16 0·26 15 0·806 0·26 0·36 16 0·887 0·30 0·44 17 0·958 0·36 0·50 T.E. 1·00 1·009 0·44 0·56

13

Ztil

C/I \II ."

,-

(ll J 0

(ll

(ll Q, ,

~~'U ~.

Q.

5O'o{T

~

-/1'(ll -'0C/I ~_-f\

(ll....... 3\l1

Q..Ul

'ill (ll

(ll

::J 0 "'1

:>o.-+,~

" -0"'1

9

" 'ill~'U g" ,

~,0

"'1

" xC

(ll

\ 3' /1'

I,JI 0(J> "'1

l." --C 0.. 9('T

~

"'1 -.N

~(\)

~

(ll JIII

;;:J(T

'}

fTj o (ll0

<.0~ *"lJl ,,;.

o'0" ::J

:;l 0

-q

IU1

......."'1

0 ~. I.Il~ 0

-+,(l ,

)

:-:J!!,""

=r tf>

0t"JJ

c..e: (ll0.

.......o 9

~ co

0""11<1'

::J (ll

>l"-

(\)

P>0

I \II

(1l

J0- J

'i0

o Q

\ll ~

...,"'1 '

r :J(ll

~ 0..0-

Q.........)(

-i

<:TI

~

=i

,9

"

S'n

~

.....,'-I

0<

o

-i-o J

::r0

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a9

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0>

Q...0

(II

"'1

)<

IIIQ.

\)

C

0

II'

~,

~

~. Q

~

0

---:J

0

'?""11

0

"0

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0

(tl

.,.II'lPC"'1(tl

J2-(ll(,0

-5

0'9 J'O

3/>!:')

.555)

/'0

"0

t-o

o-e

0'9

0'9

0'10

0'10

0'8

0'7

0'7

0'7

0'"

0'"

0-5 X/C O'b

0'4 X/c 0'5

0'4 :x./c 0'5

0'4

0"5

0':\

0'3

0'2

0'2

0'2

0'1

0"

O'j

I I 1 I I

If- I a. =- 0°' C =o· M = 0'400 ""~--,-L..-' ""<:l,

?> (IncreaSed b':J GJauer-t. fr-om M=Oi CL=O) ~

I I I I I

<, a. = 2°' C = 0'195' M=O'398I__ '_L___ J

I--.r.. (tncreaeec 0':j Glauer-t:. f.-om -~

~~M=O; c ..= 0'/79)

~-x---l(- -l( ~_..,.~

'",x- ..... ~

,- .......r-,"

11 1 , '{--uppe": SurfaceI I-- Calculaeed-1-4 ~ -- - L.ower Surface

1 '- -1'2 -t- Observed {o Upper Surface -f---x L.ower Surrace

- ,.- -1'0

\ a.~4°;CL=O'~02, M=o':\95Cp

, ~ -.0'8

~ (Incr;aSed by 0lauert.- from M=Oi CL,=O-I >- -o'/>

ro--~I- >- -0'4

0--

~'-~ -0-2

--x- -l(- X- x- x-x 1-0"--..r-;~o r>

x-'1t __

,.x... x-

l 0·2L-..x...... 0 0'/ 0'2 0'5 0-4% 0'5 oe 0'7 0,3

,r-, I I J

a. =£10 - C =0'/>02' 1>1= 0':\9£1___ '_L___ '

~ (Increased D':j Glauert from M =OiCL=- 0

-0-r-o-5--

~~ <,

~x-..._x- X-x -= <,

x .....--x x-.......

,~ ...... ~- -

o

0'4o

o

0'2o

0-2o

oCp0-2

-0'£1

-2,4

-2'0

-/'8

-2'

-1-4

-2'

-0'4

Cp-0'2

-O'b

-0'4

-0'2

-/-2

-0'2

-0'4

FIG. 2. Comparison of calculated and observed pressure distributions.

-I'b

-1'0Cp

-0'&

-3-0n-- -"cll 1 i , Iii iii i

-,j:::.. -2'

1'00';'

o

-I-O'-I--'--,--I--,------,,------r--,------,---.

- 0'8 t-.:......---It---j---+---+---+-----b M = 0 '797

-0'2 H-+--f-

M = O'B~O

0'80'70';'

M; 0'800

M: 0'775M: O'bOOM = 0'400

0'20'1

o H------j---

0'2 f---+----j----f----li---f---+----+---f---""-/;:--

0'4 '--_-'-__--'-__-f-__-..J'-__-'-__--'--__-'-__--' '- J

o

-I·O,.---y----,.---r---...----,----,----,----,----..---...,

-0' b I---t---t----t----t-~"""'''f':-___j:>t__''''''::::::_f_.::

:J2-b:<:

It0.24-'!::

-o·~I---+----+-----!----!---+--+--+----b"---r----t ~ ~:J of>

~:e~

\\--t-----l-O·750

0'5 :C/c O'b0'40-;'0'20"

0-411J'--1--1---t---.L---L---.l-_+__+-__~-_J

)'3

'-2

I"

0'70'30'/

1'0 f--.........J'-_--'__--!__---L__-L__-L__....L...__...l..-__.L-_----lo

0'8 ff-----jI---j---t---j-----+---+---+---t---==+-=---1

FIG. 3. 10 per cent RAE 104 aerofoil: pressure distributionsat ex =Odeg.

FIG. 4. 10 per cent RAE 104 aerofoil: pressure distributionsat ex = 1 deg.

\'2

\-0

I·'

II

12.

10

1-0080-70-,3 0-4 0'5 xlc ()-6

(a) Upper SurFace0'20·1

Loc.alMbeForethe

MoO-81':) enock

/; M'0~52

MOQ-MI

.Ai .-:: M·O-7~ .. r-.\ ~1\IF ........<,

f- ::-::--::~r--- ......-~- K\:~

-- ---M"O-774

MOQ7~~~~~<,~

r-«:I-- ~~~M·005~ -- ~-------r-- ---MoO-398 -

0-2

0-'0

~o

0-0

0-7

0·8

0'9

0-4

0-8 tfIf"'"7'Y---+--+--+--+---+---+---+-=-+-=---I

0'9 J-:~!==F==i==~~=t===t====jF==l--=k::::::::1

10

Value of CPC",T(For spsciFic. M)

0·60·4 0-5 "7c 0·6 0-7

(a) Upper SurFace

o-~0-2.0"

O~-+---+----1f-----+--+----1f-----+-4~~+----i

-"0

+0'40

-Hl-21---+--+---I--+--+---I---+--+--t--~~

-o-e 0'743

0·7750-796

-0'4 0·8190-8410-852

-0-2

Cp

0

Cp

-0,2

0'-'750'795

*0-4~r--lr::::::''i~~j~~!=--=t::::~~t;::"-1\~:-t--t--1°'619I 0·8410'652

-OJ

090·8070-3 0-4 O-S X/c. 0-6

(b) Lower SurFa.c.e

0-20-1r-0O~--'----"----~--"----"---_.L.-_--'-----'--_-L__--J

\'0o·g0·50-4 0-5 Xfc. 0-6 0'/

(t» Lower 5urFace0-3(}20·1

Q·eLL_-.L__.L_--l__--L__L-_-l.-:-_--::"-::=--_-:l-:-_--:!L::-_-:-lo

FIG. 5. 10 per cent RAE 104 aerofoil: pressure distributionsat IX = 2 deg.

FIG. 6. 10 per cent RAE 104 aerofoil : pressure distributionsat IX = 2 deg.

0'744

1'00'80'5 o-eXfc

0'4-0';;0'20-1

(/\.. 1>1= 0'?'!}7

r--.... ~ M =0'818

~~~

~M=O'835

Va-Iue ofC

b..-----~ it' __v"\~... (for specirrc

fIX:.~~\ \ \1\M'~ ~ \CC:r---=::::r--- --~~1;1=0'5% l\M =0'398-

~1'-1=0'744

~(a) ~pper Surface. <,

~I I I

o

02o

-0'1)

Cp

-o»

O'7'!}?

-0'4 0-8180'835

-0-2

c,?

0

0'2

-O-b

0'7990·821

0-839

0'751

',0

1-0

0,<)

0·9

. Value of CPCRIT

for 5peciFic M)

0'5

0'8

0·4 0·5 -:r./c 0'0 0·7(a) Upper SurFace

0-4 C-5 "'-/c 0-6 0'7

('b) Lower SurFace

0·3

0·2.

0·2

0'1

0·1

M=o-a3~

~---1'1=0'821

~ ./" -.M=(}79~

~~V~~\d ~

A'~--:::--- /7 -:::::~~~ ~1'1=0·751

I V M=0'698~M=O-598 'j

~M=0'399

( "I0,,,

o

0-4

o

0·2

o·21---r--+--+--+---t----+--_+--_J._--I_-~

-1·0,-------,----,----r--__.~-__.--_r--__r_--_._~-_,_-_____,

OI---+--+--+--+---t----+--_+---=:c>ko~~I_-__+

-0,2

Cp

-0 -21+-----l-----l-----1

-0'6

-04

-0' 6I/f;HYp'<;:----1p-....~---1---I---+-_\___+\__4__+--_+_--_J._--+o_751

Cp

- OA"-H---j-----1----=""---I=---t-A~_J._=_==~...._1r___f\._-_+_--_J._--+0'799" 0082.1

0'839

......."'-l -0'8

FIG. 7. 10 per cent RAE 104 aero foil : pressure distributionsat rx = 2·5 deg.

FIG. 8. 10 per cent RAE 104 ae.rofoil: pressure distributionsat rx = 3 deg.

1'0

1'0

0·80'7

M·O'588

0'5 0'.X/c

0'3

(b) Lower Surface-

0'2

0'1

0-1

/, 0 L-_--.JL-_-l__-L__--.L__-L-__"---:_---' ---'-__-L_~.....J

o

0-9WJ,L+-=-+-~f====F==I===\===F===l=_-_l==~

L0= I Iv! beforet.he shock

( a) '::!PrJsr Surface_

0- 8 1----"<,----11----+---+- M =0-395

0-9 f----+--+--+------j-----1---+---I----===t~-_=I===_l

0-5

0-4,------,----,------r----,---,---,.-------'-----r--, 1'2-

0-7

%o

0-.W--~+---+==+=~~;""~::==+::~~~~~;;::;~,------j'%0

-737

-7b3

-795-815-829-838

-b85

~)

0-568

0-7b3

J-O

J-O

O'~O'B0-7

0'5 x./c ()-b

0-4

O'7~5

t---J-----t,..,;,..",,4::-----f'...--+---+----~0:g~0-8;3

0-.30-1

\\ Value ofC Pc( for specJf; c

r- -- <,

~\\ ---""\. '-.............~

~~~ M>'''y,J~ [ot'\ M: 0-7~~

'I\~~

~M=0-815-, ~ M = 0-629 0

10:0-301~~~~S fmM = 0 -6 380

~~ ~ 00

M = 0-538 \......--' "::::~--........::::

~~""'"0

/VI: 0-b851 0

~"<, M= 0-815

~~'<:::::

~(a) ~p~er Surface 10= 0-795

1 I I I I

o

0-2

o

-0-8

-0- b ,...-----,------,----,--..,---,---,----,-----,------,-----,

- 0-41-----+

Cp

-0·21----+

....00 -0-1

FIG. 9. 10 per cent RAE 104 aerofoil: pressure distributionsat rl = 4 deg.

FIG. 10. 10 per cent RAE 104 aerofoil: pressure distributionsat rl = 4 deg,

\-1

\·2

'-0

',3

\·6

1'5

\.4-

to0908

0-8

---- --- ---- /-0

M=0-3':l6

0-70·4 0·5 :c/c 0'6

{bl Lower- SurFace

04 0-5 "'Ie 0·& 07

(a) Upper-SurFace.

0-3

0·3

0-20-/

Local M~ before

G t::.he

1\ <,1\\

M=0'B20 E>hoc.k

f\ 1\ M M=0-797M=0'771M=0-74~

M=0-687h \ \ ~o~-\ ----~--\ ----~ --\ :~ ------- ----

-, ~ ---......<; -- ~

.:>

~r---- --.. -:---r--- r-;

~M";'S':l"l-- r---.

~-------- f-- -M-0-396 - -

1'0o

M=0'7?1M=0'743

0-5,...----r--,---,---,-------,---,--,----..,---r-----,

0-3

0-9

0-6

0-4

0-5

P/H

0'7

0'8

'594

·771

'797'820

'1:>87

0'9

0-8

0'6

0'7

0-7

(b) Lower Surface

0'4

0'4 '% 0'5

-+---1---d--~-',==::;:::==~--L0-620

0'5

V Cpma,x=-5·51.

,t'"CPmax =-2 -48

I r\ -II

I~II r-,

~V- I"-../1'1=0-743

) 1" \. M = 0-77/0

==\S~ M= O'?97\

'~- '\1\\V M = 0 -820

f\

" \ \ \\ 0

"'"~ \\ \\br-; f-o

.~ ~ I-\-~t\M=0-b87 /

~0

0

r--- , M=0-59Y

~0

1'1 =0'59b

2

.. ,~

(~) ~pp'er~

Surface.

"2 I I I

-1'4

-I-b

-2-0

-0'

o

0-1

-0-21-----+­Cp

Ol---t---+-:#n:;.s..-s..-j;;;~::::::'"

-0'

-O'41-'---t--

-1'0

Cop

-0'5

......'.t:D -eN)

FIG_ 11. 10 per cent RAE 104 aerofoil: pressure distributionsat 0: = 6 dog.

FIG, 12, 10 per cent RAE 104 aerofoi1: pressure distributionsat 0: = 6 deg.

'591

'49,3

'.40

'b90

'737

,7.5

IT

M)

0'70-4 0'5 X/c

o-e

M'O'7b5

O'?0'1

Value of CPCF'.

(for specific

\\ M: 0'690 0

/ I

33~M 00'737

y-i.. 1M. O'7b5"-

\~~~~

0

M:0'393~~~0

10.0'493& ~0

~ j-oM~0'5Y ""'"'~~ f::::",....

~M ~ O'b40~ r-,

"""-.

(a) l::!ppe'- SurFace

I I I

o

oeo

Cp

-4'0

-2,0

-1'0

o

c.RtT

eM)

Yc

'0

O.

M ·O'39b

//

Value ofC p

0 (for specifi

/10 ·0·49/l

P Vert-ical Sea-Ie half-

NBChat. of Rrecedingf!9~

0

~ M • 0'597

\ ~

t\ [o

( a ) ~pper Surface

""~~ t--

M· 0'3%/ --=::::::::::::M· O'498} ~r--M • 0'597 I r----

0 0'1 O·? 0'3 0'4 0'5 oX O'b 0'7 0'8 0'9~'o

c

-s-

-5

IM .O'498}M ·0'597 '<,

~..- I " ' ---M·0·397

V (b) Lower Surface

c-s0'7

(b) Lower Sur'face

0'30-20-1

0'5 L..__le:-_-.J__......l__---l.__--L__-'-__-'-__...l-__.L.-_--.J

oJ'O0'80'70'5 Xlc 0'1,0'30-1

o

0'5o

-0'5

FIG. 13. 10 per cent RAE 104 aerofoil: pressure distributionsat C( = 7 deg.

FIG, 14. 10 p-Or cent RAE 104 aerofoil: pressure distributionsat C( = 8 deg.

1·0

I,"

~ M=Q·64() Local Ml-o

V ~ -=:::::::~ /, M'O'690 before

M=00737 l::he

~ 1\ \\ 1/ M=O'765 6hock

~I/;-,r-~\ \

~! -, r-,---- ->, -~

~--~<: ---- --- ---- ---

~ "" r-; t:--<,

r-, A

i'---~--I--::::-------~M=Qo59 I ---l... r--- r---

-, M~ ---I--- -- <,r-- -- -;:""

r-, r--- - I---a~ - --- "'-- -

0·4

0'7

0·;<

0·9

,,0o 0" 0'2 0'4 0'5 :r./c 0'6 0'7

(a) Upper- SurFace

0'8

0'5 .------,.----.-----r----r---,-----,---...------,---.--~1'0

~o0'4 0'5 0'6 0'7'Xjc

(bi Lower- Sur-rac.e.

0·1

0·61---+--+-----1

0.7~--+--_+-----:~fs:::::::::t=~~-=t==-.L,--:::t:==i:::::::~pHo

O' 8 f--#::;"'4;:::"":::::::::::=b:::=o---¥::::::::==j:..---+--LJ.--=+======I==~

FIG. 15. 10 per cent RAE 104 aerofoil: pressure distributionsat 0( = 8 deg.

21(1522) B

Mo·B,,·a.1'0

0·6,.4

0'5,1-2

~'! \

! r-,

/yf .' Glauert- Law

a: eo ~ V r-.I0- 'p-

I ---- " ,,6 '0a = 7° 0---- , / /'

I /" ..---.::a » 6° -::.:-c---I

/"f-o-'~

l-6 ~

~~ ,,-"--<r

a;:. 4." // 0

I .-' P,

~~ l;9' ).-~ #<

a-=-;)O0- .-----r -}-,-..--< -

a'2'/2"C- - .....b-'''''' PI ---- Glauert- La""

a, 2°0- A1""-<

....--- "' \a = ,0

IObe.er-vecr pressure M ericl I

(Upper SurFace) MarKed t71u'" ",a-0°j' I I I I I I I I I'"o

D·)

,0

0'7

0-':1

oe

0-6

0·"

0·4

0,)

0'1

0.2

1'0

"0

1-0

o-s

0-9

0'3

0'8

0·8

0'8

0·80-6 M 0.7

0'6 M 0·7

0-6 M 007

0'6 M 0·7

0-6 M 0-70'5

0'5

0·5

j §k41 I0-5

0'4

0'4

J(a)a=o· Aopr-ox rme.c.e Maen NUmbeC? i

for- Forw=<.rd Flow from t;het-r-alling edge, as given b~ oil 1depo:;it::ed on aerofoi! 5Ur ace

I I J JGlauert; La0 i --_I I

;:';c.h~ber.Pressure Cribical

~

(Fla = B O

....,..-Dh :7-0- \ /c~

----,--------,-Ii H I I

o

0'4­0')

0-3

-0.1

0-20·3 0-4 0'0 0·6 M 0-7 0·8 0'!3 "0

FIG. 17. Variation of CL with Mach number at constantincidence.

FIG_ 16. Variation of pressure coefficient at the trailing edgewith Mach number for a range of incidence.

1'00·9

J.I

0(."

Obser-voo pr-"<osu.-,, Mc ..il} Mar-ked lhlJ'" I(Upper- su r-race)

Obs¢r-ved pr-e<o~ur-a. Meril} Mar-ked(uppcz.r' 5U'-"«.ce) lhu'i> I

o

0·03 r----,----..,-----,----::=-r---,--i-----,

-0·02

FIG. 19. Variation of Cn> with Mach number at constant incidence.

~-o·o I 1-----+-----;o~'--

D·'

0'6

0'5

0·8

o6°

to M: 0-860° \0

Incidence

FIG. 18. Variation of CL with incidence at constantMach number.

M:0·80

1---+--+-71l'~~f--+---;>"7t"--M:0'82

I1---+---7-/f;67'y--+_~",--_+M:: o-84

/·0

0·9

0'8

0'7

0'6M = 0'4C

L M=O·5M = 0·6

0'5 M:: 0·65M:: 0·70

~ 0'4CN

0'3

0'2

0'1

FIG. 20. Variation of Cn> with Mach number constant at CL •

0'7 M 0,8

0'7, I 0'8D'S M O'b

0'5

, \

a "-40 I 'i .: I

f

ex. e 3° - - --~ -~ \. -~ \..,

-Q.,:,o - ---~\\ex. ./0~

-::=.. \ 7 '\ex. =1>0

Glauert. law ~, I \I-ex.:e,o~ V

,C

L: £:4 '-I 1"\

f I \.I I Ib

C L ~ 0 ------r-fr(\, I

--.y fDJ ~,~/

C L • 0'5 k::-::-::- - J -~ }::~"'..j, :1-""'" I ,

C L .0', /' ~V--' \\7" ,~:o /- C ·0'6 •

-, L / .C

L: 0'7

Glauer-t law..........+-.... .-' r· II

-- - II I

I

O'Ob

0'0403

0'/4

0'/2

0'08

O-Ob

0'0403

0'08

0'/8

0"1

0"0

FIG, 21. Variation of Cm with incidence at constant Mach number.

Q'04

0'05

0'02

0'01

em0

-0'01

-0' 02

-0'0"0° 1°

FIG, 23. Variation of dCL/de.: with M at constant CLor «.

0'80'7

0'7

05

0-5

o 4-

~BO'~/ ':.:.....,.-1-... '/X r\a. : 1>0,"-'7'

/

1'\'-,<, a..4- 0 \

a. ./0 i., ..'-~~\........ '\

f\, , I '\ !\

\ 1

5 CL

• oe~ CL'~ CL';O'~~~k:CL;' 0-2

CL

,;:.0-3 --d== - <,1'-----..\.. r--..'-C L • O'~~ --.......... '\i, ,"

\ ~,\ .

0'/0

-0'1503

-0'/0

0' 10

0'15

-0'/505

0'0

clCm. 0

cia.00'05

0'05

dC""Cia 0

-0'05

O'D!II

FIG. 24. Variation of aCm/de.: with M at constant CLore.:.

02

ern,o

FIG. 22. Variation of Cm with CL at constant Mach number.

0'0" I---f----I---+-----hc----r-'"

O'04~__~--~-----,.----r----r-----,---r---r-----'

-00 I I-__+- +-__:':l'--_=--+--+"'"-~_t_

. 0·021---+-----+--------1

/

I

0·8"8I

J

III

fI

007I'b1

06

IIMeRIT1M8l"Ked jlhLlS l.

1·4I

05I'ZI

04

Co

0·0601---+---f----+-..,.,.--I----1I----J

O·090r---,-----,----,----,----.----,

0·070 - Observed Pressure(Upper Surface)

0'030 ;!I-----+-/_¥_~ -------w-~/---+-l--l--l

0'020 ~ I

/ /$60 ------r/---t---+-------

Theoretical CO ILE.-'-'-'-~ ~ I0·2e. • . - . . . 0/=40 H(Refl0) for mean 0·40-- " ~ -=: _ I - . . '-. 4-11--,--1transition POSition O·6c. 0 °1 I I ·l-·_·~J

at:-

I ----1\ ./,A--_<:(.'6°ci = ,0 -, '~_(;(.=2° <,

<, "<:(.,~~ 1/ClC.: 4Cl~

-;

,."

I---CL = 0CL = 0-6

Ct' 0·2 --L \ f\~\7 '\J

CL=O'!> } CL.'O'~ J\CI.'0·4 I' d

_0'10

0-0'5

-0·\5

0'10

FIG. 25. Variation of CmIC" (centre of pressure distance forwardof quarter-chord) with M at constant incidence and lift

coefficient.

0-10

0'05 ClC.:::; 8°

em~

0

-0,0'5 O·Go.s M

0'10

0-05

CrnCL =0·2CL = o-s

CL. CL =0'4

a CL =a."} C L =0-6 CL =0'6

CL =0-4

-0-0'50'0 0·4 0''5 0'6 M 0'7 o-s o·g

0'05dC mdCL 0

-o-oe

dCmdeL 0

-()o05

FIG. 26. Variation of dCmldCL (aerodynamic-centre positionforward of quarter-chord) with M at constant incidence and

lift coefficient.

-0,1",0-0 er4 0-6 M' 0'7 0'8

FIG. 27. Variation of CD with Mach number at constant incidence.

0·0 7 r------,r-----r-----,-----r-~_,

0'06 I---I----f---f----tt-----j

0-0;'

0'02

0-80'6 'M 0'70·5

OL-_--.JL-_.---l__-----l__--'-__--'

04 ~q

FIG. 28. Variation of CJ) with M at constant CL •

010

0'09

O'OB

0'07 0'07

0'06 0'00

CD CD

0'05 0'05

0'0 0-04

0'03 0-03

0'0,2 0-02

0-01 0-01

0-1 0-3 0'6 0·7 0'8

FIG. 29. Variation of CJ) with CL at constant Mach number.

26

FIG. 30. Variation of CD with incidence at constant Mach number.

r-- ..............

~

'\.C<

~~"'"<tcc

'Z.-,

-,\

Lowepe.ed c. ..(ExcrapOlatoed co MoO b':j \Grlauerc)

,0-3 0-4 0-",

,0-\ 0-2 0-0 ,

7°20

, LiFto tv'lc.ritot-..... (\5eginning oF- F-a.11lx

r-o....7~ """"~ZMfri~ -. <, --......

Momento( be~llnnin9 of

!""4; "'iFall)

/ ~s~ Ne.re~'bu?e Mc..rit

A,.;-Drag Mc.rito

(Experimental) ~C't'~ (increase of<, 0'005 on low-speed value_)

<,"R

\\

0-7

O-B

0'6

0-7

0-6

0'5

0-8

0-5

0-4

0-4

Mc.ril;,

tv'l' 01:>75

M·O-65

M·070

o

o·04f----t---t-~-+~--+_---H'---+-+--_Y'5Ift1'_f-fl

o

0-02 M=0-54

0-05f----f---f---+---+---+--++---I-f----,H-+I

o ·o,f----+---+---+---A"T"-I'..-:"-:-""'++---f-HN-7'-d-------f"

o-05f----+---+---+---t----f----+---++---,I

o -071---1---t---+_--+_--+---+---+--+-1

o-o8.-----~----.---,---,------.----,--,----,

0-2o 0'1 0-2 0'4- 0'0 0'7

Ob",erved C.. at spec.iFic. Mc.rit.

FIG. 31. Variation of critical Mach number with liftcoefficient and incidence.

0-7o-e0-50·;00'20·'o

--- - ---- --------- --x---~--- M: 0-84--",

M;O-e,O- .~ - -- -

~

M;O·76

--- - -- -" - -x-

....---

___ ""liI.- ___" ~--.-,<. ----

--------

--- -" - - -- ..-- , M;0·4

,""- N.PL. '"2 dirnene;lona\ ,--- re&ults reduced to ~

As.pec.t. Rat:;io !>·5 \,(R: 1·1 t>o 1·9XJO")

I I I :0:.___x___ RAE Te:.ts 3 0n W'ing of

IAepece Ra.bio 5-5 (R; 1·0><'0")

o

o

o

o

o

-0'05

-0'05

-0·05

-0·05

12°10°

I

---x---

4°2°

0·7 ,..----,----,----,--..,."......,-----,-----,----,

0·' iI''//Jf 1//I'. '/ / J

M;O'B 4--o .....+---!f-A7<--r+t--++----+---t----+---!

1///1./M::o.ao-o~VI /1

1/ /

1/ 2dimensiona.l N.P.L. result.~

" I j ;,' --- reduced co Aepec.c Rat.io

1f_-r'-t/L-\-,.;'t--\ -.-__5_.5---._(_R_:_I_.',,C_O_'._9_X-,-IO_6_l_--1

M;O·7o-0 ..... r-

1)/ 1/11 ,f

FIG. 32. Comparison of N.P.L. and R.A.E. tests onRAE 104 at aspect ratio 5·5.

FIG. 33. Comparison of N.P.L. and R.A.E. results on RAE104 aerofoil.

I I I I II

r- 2. dirnenstorral NPL Results I

/ reduced to Aspect Ratio 5,5 IJ

I- (R= II to I~X 106)

//RAE. Tests sI

on W,'n.9 ef I/ Aspect Rotio S'S II- ,

(R= 1X lOb) ,,IIII III I,I I

ICL~ 0,4 !

--~. '!AI,I--- II

'l4 "';.;P''I/,

1r-- CL

=L:~- II I

----e-. ~J,Cl-O ---- ---- ----- --_ ....')

0'02

0'0

0'05

0'04

0'06

o0'3 0'4 05 O'B

FIG. 34. Comparison of N.P.L. and RA.E. tests on RAE 104 at aspect ratio 5·5.

29

'00·80-4 OC/CO-G0-2

c)k-..

/-- --

"""/ \

II ~,~

~,'\

(d) M= 0-750

o

0·2

-0'4Cp-0-2

- O.B

-0,6

'·00-50-4 x/c O.G0-2

I Cp I(Local M=ll_

/,

II ~~"":~

(c] M = 0-700

o

0·2

-0·6

- 0-8

-0-4

Cp-0-2

H)o-eer4 "Ole 0-60·2

8

0

I

/ I r--.....( ~,

"'"'~(b) M = 0600

0-2

-0.4­

Cp-0-2

-0-

- 0-

o

'-00-80 ... "'Ie 0-6Q.2

i- --- =--

I,

"<,

~(0) ,M= oaoo

-O-G

0-2

°

0-4o

-0-4

Cp-0-2

-0-8

IC *-

-/" '\/

I ~

""~,(e) M = 0-775

I I I

--, c'*- , .......

/ '\

I t, -,il "-\ '"',

(F) M =0-800i I I

/'00'80'4X/C O'G

-,.-<

,,,~~ Ip ~-

,,, c*-\

I ' \( \I

,~,,

(h) M= 0540" I I

0·2

o

-0·6

-0·8

-0-4

Cp-0-2

',0o-e0-4 zclc erG0'2

8

-,

.-/.-' .'\ c

l"- \ '\ p

/ \\I ~

~~

(9) M ~ 870 "'\I 1 I

o

0·'2

-0-4

Cp-0·2

-0'

'-00-80-4 x/c 0-60-2

0·2

o

-0,8

-OG

-004­

Cp-0'2

'-00-80-4 tete 0-&0-2

0-2

-08

-0-4

Cp-0-2

-0,6

Na.tural transition position

-~---- -Fixed traflsii;k>n pO$i~iof'l

/·0ers0·4 ;x;/e O-G0-2

P",,./ \~

~?

\ \~

/ C*\

P \ ,

I \I

(j) M = 0-880I

o

0·7

-o.{;

-08

-0-4

Cp-().2

/-00'80-4 x/c O-G0-2

,~ \

'----'

.-/,..-/ :\

/' \ Co"'

/ -,

( \:'-,

ei.l M = 0-8600-4o

0-2

o

-0-8

-0-0

-04

Cp

- 0-2

FIG. 35. Comparison of pressure distributions obtained on the aerofoil with and without artificial transition: ex = 0 deg.

I'D

1-008

0-8

0'2

r ........... '"Cp--r-~ M= 0'74"I--...

1\Sl::=--I..--

~-/'" ~

I ~ -,1/ ( d)

T T- M = 0-840- -

~ l?" ........ "':(M = 0-841"....-

II I........ lrRA '",s- C p

k<-'" \~ff

V ~ ....

I ~I( (h)

o

o

-1-0

0-2

-0'8

-O-b

Cp-0'4

-0'8

-O'b

Cp-0'4

0'41-0 0

0'4-/-0 0

0-8

0'80-2

TCD"

I'. Loca.l M =I

:--r-M,~700_ - ~--~~

~~7 '"~

rT (c;

--I,..-' \ .. M=O'81/~I--

"'v -...j M=0-81'11,/

11 ,- l.\ cp'"

l/ - ~~./

V ~ .../ ~f\-

1 (9)

-1·0

o

o

-0'8

-0' ..

Cp-0-4

-1'0

-0-&

-0- ..Cp

-0'4-

0'4J-O 0

0'4r-o 00'&

0-8

0'2

IA.

r--...I---f--

~~o~:~:~-....e-,-

V~ - ....~~

I "'-II (b)

- - vMI=0~7%1 .t./ r-,

~ M= 0-7':'9 _~ Cp"

I----' - ~.4~ 1'-.

~ I'\;I '.;::

"II (of )

o

0'4­o

0-2

o

-'-0-0·8

- 0'"Cp-0'4

-0-2

- 0'&

-O'bCp

-0'4

/-0

0-4"0 0

-1,0

0-8

0-(;0'4 0-":tic

/" -......IT '\ ,

"""'- C llt_

~ M=O;~-=r-....- r-,

I--;: ~

I~,

I~

7 ""<::r'\.

1 (e)

Upper surf"oM;,e

\ M' 0' 3"<, I" "I"

~M= 0'.3'(;~

I.,:.-:: -= ~~~

7 Lower 5urofa.ce r-,II (a)

0-4­o

-0'2

0'2

o

o

-0'"Cp

-0'4

-0"(;

-0'(;

-0'"Cp

-0-4

-0-&

-o':?

o

,.-".. M =~.&",

1,..-'7 \ 1-c, - -... /

\

/,

;' ....

I ,/ cri'"..

/

I

/ (j )

Nat-ur.;l../ T...ansicion Position

Fixed Tran5ic;on Posicion

0·8

FIG. 36. Comparison of pressure distributions obtained on the aero foil with and without artificial transition: Ct. = 2 deg.

1'0

Nacural Transjt;ionPosit-ion

Fixec:l Transit-ionPosicion

0'2

I I Irf = 0-835 - ~

',,1M = 0'S3e f--

l--l-I--'<;~l.-

II 1\/ N,

C p""-

/"!r"

.\ 10.

/ " '\ -i\:'V "'7 (h)

I

ir- -- --f\1 M: 0'74f>

II" M: 0-757I

rrr Cp"

1\\ --r-..\..V '"V v "'~

/' ~

/ '~~

I I(d?

-0-8

o

0'2

o

-0-8

-o-eCp-0-4

-0-2

-0'0Cp

-0-4

0'4I'D 00-8

0'8

0'2

In

\ ,.. ,....... p

\ I

"--I- r-,

M=0'f>S5 f'>-M =0,,~9~i-.::=' -"':::

~ r-,

:/~r-,

/ (c)

I I- r-, vM: 0-814 1

-I.- -- fi /~: 0-8151/

\\

b

1\ \ Cp"

V, r, ,

-,

v 0' r\ :zsIf ~

( (9)0-2

-1'0

o

o

-0'2

-0'8

-1'4

-0'Cp-0-4

- HI

- 0-8

- O'bCp

-0'4

- 0'2

-I- 0

0-41-0 0

0-4/·0 0

-/'4

0-8

0'8

0-2

Cp"(Loc,aJ M=I)_

"\ 1 I~ /M: 0'588 II~ k';M:0'';93

r-r--. r-....

~~ - """'-~~ ".6

1/ "'" r-,( ( b)

I 1 IvM:0797 - ~

.......,~-[7 IV: 0795 ~

bl ~

\\ c "p

l..?v.::~"-~

71.....

~~L# ~

I (f)

-0'2

0-4o

o

o

0'2

0'2

0'4o

-I' 0

-0-8

-1-2

-1·4

-)'2

-0'

C"-0-4

-1,8

-0'0

-0'8

/·0o-e

0'8

Lipper s",rface

\M :0'~"5

,./ t-1: O'~98

~~:.~~

- '-~-i-'""

/'..-- ' ~,Lower stJrfac.e

l I(a)

If - "t----, " VM: 0'770\;

M e 0'7f>5 - ~

%II Cp"-

\'--~~~

~V ~

~"V '"

7 (e)

o

0-2

0'4o

0·4­o

o

0'2

-0'2

-)'4

-0'8

-I- 2

-0-2

-0-8

-1'0

-O'bCp-0'4

FIG. 37_ Comparison of pressure distributions obtained on the aero foil with and without artificial)ransition: IX = 4 deg.

0·9O-B0-70-5

yI

~

I

III

I~I

--<>-- NO\.l:.ural I::-r6tn &iI::ion I I-,- .,":} III

Tr-6tV1Slbor'l I___""'__ G\- Z

fixed--I

-- --)t- - 0(; o'

JII

Observed PressureI

Mer-it; I 1-- MarKeel thus - ,.

/I1

I

I I

I I ~I I -of I

j"~/

! :1t\~ 'j=t"- ------//; I I

II I

\= s: -= =-~- -='f -----\~-=-' =~~7 ~~=.:: ~'~~--

1\ \

o0-,

FIG. 39. Variation of Cn with M for the two sets of tests.

0-010

O' 020

0-040

_J·o~6

o-s0-7M

0-60·4

A.

Q= 4(~~ ~~ tt

-+---1 " '\ \" x,- - - ~--- ----- .-1-- -<'"Q=.2° -..\.-4-V;f

" J\x'-6-- Natural Tran~It:.lon

"\

---.-0-- Natural TranSlcion---;---- FIxed Tr a rte rci o n---)(--- Fi"ed Tr'an5ition

I I ex ': 0°'\.1

-+-'Gtao erE

/ \-RI~e I / \

"'x/ /:"'-A. \

- f'('" ~-..:;\

a = 4.°",--~

;;:_r~ }b

-- - ~-----

G-Izl-Uert- Rise / \\ A' \

a = 2°, \ ~

~7/j~\~- ~..:::::-

:;:...::;----'~ \~

Ob",erved Pre'O'Oure M C R IT marked thu",- I

Q = 0°<,

0-1

o0-3

ac",

0-2

0:3

0-4

0-5

0-01

004

0-03

0-02

- 0·01

- 0-02

- 0'03

- 0-04

06 07 0-8

FIG.38. Variation of CL and Cm with M for the two sets of tests.

-o---Nal:;ura.l Tranv\c'\on- - - - - - - --Tran",H::;ion Fixed ,

lICo = (C D\.,,- (CO)M=O·4II

II'I

I II,I I:,

rp J: [Fd,: I0\-

I

: J /I

f' ff ,'fi1

ar:O O / a= ?O:j ex:: 4-0 /1

~ f! ~Y'"

~...;YiJ ~ ..dJ.- -- -- - - - --

0'030

0'025

0'02.0

0'010

0-005

o

0'002'"0-4 0'0 0-7 0'5

0'4

0'9

0'6 M

0'4

0'13

0'0

0'9

0'6 M 0·7 0'13

FIG.-40. Variation of LIen with Mach number for the two tests.

- tl

r r ,,--r-,I'" Transil:ion band posicion (O,14c). -,

I

'~ "-'~~

I

~ }i~,\

\X

- 0'2

0·3

- 0'3

- o·

c 0p

o·

0·4

1·00,90'704 O,S 0'6

re/c

M == O' 600, a = 0°.

0'3020·'

o Transit:ion Fixed}Experimenl:al

-----)(---- Transition Free

----- Theorccica! (ReF.4) augmencad From

incompressible values b\:J Karman­

Tsien Ia.w.

FIG. 41. Comparison of two experimental pressure distributions with theoretical.

34

,·O,...-------;r----,----..,......,r-------".cr----..------,-----,---.....,

0·4f------l----I-----I-----l----.J.----l-----+----l

M CRIT

0'9

0·6

0·8

Q'14 chor-d

M

M

0'7

-rr-a.m:;Il::-ion POEdl;.loncliff iculb 1:;0 lZsbima.-ba..f'r-om dil""lZ-cb- shadowFlow photoghaphs.ab t;,hi... incidlZ~~~

(e) 0(. = 4°( Upper- Sur-face)

(0) ~= 2° I .. Let(Uppel"" SUI"" f ace)

.J. I.Lirnibe

?~1:.00 dif,u~

Tl""ansl Ion posll:.ion.~..MIII-difFicul1J 1:.0 e...l:.ima.be

fl""otn dir-ecl;- shadowFlow phol::-oghaph"3 ~or-

the lower- Ma.ch riurnber-sf-a.l:. thr incidence II

IOb5,fr-vedI pr-¢5 s i ",e MeRI;

Tr-an'5il:.i;Jr1 f"i l(lZ.d a.E0·2f----+-I----l----+----+---+----f-..----+--~

---- Li~- f----

00,,,

o-e

0 0'6

0'8 r----....-----,-----.----....-----,-,-.------:---.:----...,

0·4

0-; M 0-8

FIG. 42. Variation with Mach number of approximate extent of recompression systems alongthe aerofoil surface for the two tests.

35

'I

""

"I,"

I I

I'

IP051tion oftheoretical tranSition ---1-----1----+--<1-1---1

LE ,Co

" ,O·2e I--.

W~~~·thi;_tt:;:r_a;!!;;;s~·,!:r;:io~n~Fi::xe:d0a~t:=;0'i':.T.14r.:=C=.=F=::::;::::f'i==i:==j0'4e I-. ----- - ----

0'0,0

II

I ,\

0'70·6 M0'4

0·6 c il-.---li--+---+----,-f¥:---~

FIG. 43. Comparison of measured values of CD with theoretical values of Ref. 10 (oc = 0 deg.)

0·015,----,-.:.......--,.-----,---,-----,---,----...,-----,

(0) M=04

Natural transition

--0__----0__

Experime~t.al -0

(Wake traverse met:hod).

N.B. Pressure Merit: = O'7e~

0·0051-----+---+---I-----f---+---+------===-=!'--=7"\c="'"!

0'--__-'-__~ .L...___'______1 .L___-L _

Natural t.r ansicior'--t_

0·01011-----=F=--=:-I 1heo,. 1::.--~-+----+-===+::===-+--~--1-__ e Ical

Experiment:I/­(Wake traverse method).

O·Oool-----+---+---+-----+----+-----l-~~~-==1~"-=-_I

0·10 0·20 0·30 0·40 0'50 0·60Mean posicion or transibon band.

0·70 0·80

FIG. 44. Variation of profile CD with position of transition. (oc = 0 deg.)

36

Natural transition position

(a) M = 0·600

(c) ."[= 0 · 750

(e) M = 0·775

Fixed transition position(Frigilene band at 0 ·14 chord on

both surfaces)

(b) M = 0 ·600

(d) M = 0· 750

(1522)

FI G. -IS. 10 per cent RAE 104 aerofoil. Direct-shadow photographs at IX = 0 deg.

37c

Natural t ran siti on position

(f) il l = 0 ·790

Fixed t ransiti on posit ion(Frigilene band at 0 ·14 chord on

both surfaces)

Observed pressure Merl, = 0 ·785

(g) M = 0 ·800 (h) iv[ = 0 ·800

(i) M = 0 ·810

FIG. 45- continued. 10 per cent RAE 104 aerofoil. Direct-shadow ph otographs at IX = 0 deg.

38

Natural t ransiti on positi on

(j) ill = 0·820

(1) AI = 0·840

(n) M = 0 ·860

Fixed t ransition position(Frigilene band at 0 ·14 chord on

both surfaces)

(k) ill = 0 ·820

(m) M = 0·840

(0) M = 0 ·860

(1522)

FIG. 45- continued. 10 per cent RAE 104 aerofoil. Direct-shadow phot ographs at ex = 0 deg.

39C'

Natural tran siti on posit ion

(p) 111 = 0·880

(q) M = 0·890

FIG. 4S':- continued., ~,;

10 per cent R;AE 104 aero foil. Direct-shadow photographs at C( = 0 deg.

40

Natural transition position

(a) M = 0·400

Fixed t ransition position(Fri gilene band at 0· 14 chord on

both surfaces)

Observed pressure M erit = 0· 785

(b) M = 0 ·810

(c) M = 0 ·820 (d) M = 0·820

FIG. 46. 10 per cent RAE 104 aerofoil. Schlieren photographs at a. = 0 deg.

41

Natural transition position

(e) "vI = 0·840

(g) "vI = 0·860

(i) M = 0·890

Fixed t ransiti on position(Frigilene band at 0·14 chord on

both sur faces)

(f) M = 0 ·840

(h) M = 0 ·860

FI G. 46-continu ed. 10 per cent RAE 104 aerofoil. Schlieren phot ographs at IX = 0 deg.

42

Nat ura l transition positi on.

(a) M = o<l9H (b) !If = 0·699

Observ ed pressure Men' = 0 ·720.

(c) M = 0 '774

(e) M = 0 ·841

(d) i\{ = 0 ·809

(f) M = 0·852

(1522)

FIG. 47. 10 per cent RAE 104 aerofoil. Dir ect- shadow photographs at IX = 2 deg.

43D

Natural transiti on position

(a) M = 0·398

(b) M = 0· 749

(c) M = 0 ·799

Fixed transiti on position(Frigilene band at 0 ·14 chord on

both sur faces)

(d) M = 0·796

FIG. 48. 10 per cent RAE 104 aerofoil. Schlieren photographs at ex = 2 deg.

44

Natural transiti on position

(e) M = 0 ·819

(g) M = 0 ·84 1

(i) M = 0 ·852

Fixed transition position(Frigilene band at O·14 chord on

both sur faces)

(f) M = 0 ·818

(h) M = 0 ·840

FIG. 48- continued. 10 per cent. RAE 104 aerofoil, Schlieren photographs at Ct. = 2 deg.

45

Natural transition position

(a) 1"[ = 0 ·685

Fi xed transit ion posit ion(Frigilene band at 0 ·14 chord on

both sur faces)

(b) M = 0·689

Observed pressure M crl t = 0 ·550

(c) M = 0·737

(e) M = 0 · 763

(el) M = O·74G

(f) M = 0·770

FI G. 49. 10 per cent RAE 104 aerofoil. Schlieren phot ographs at ex = 4 deg.

46

Natural transiti on position

(g) M = 0'795

(i) Al = 0·815

(k) M = 0 ·838

Fi xed transiti on position(Frigilene band at 0·14 chord on

both surfaces)

(h) M = 0 ·797

(j) M = 0 ·814

(1) M = 0 ·835

F IG. 49-contin ued. 10 per cent RAE 104 aerofoil. Schlieren photographs at C( = 4 deg.

47

Natural transition position.

(a) M = 0 ' :'94 (b) il l - 0·722

Observed pressure M erit = 0·530

(c) M = 0·797

(e) M = 0·797

(d) M = 0 ·722

(f) M = 0·820

FIG. 50. 10 per cent RAE 104 aerofoil. Direct-shadow and Schlieren phot ographs at IX = 6 deg.

48

Natural transition posit ion .

(a) M = 0 ·59 1

(c) M = 0 ·640

(e) M = 0 ·665

(b) M = 0 ·591

(d) M = 0 ·640

(f) M = 0 ·665

FIG. 51. RAE 104 aerofoil. Direct-shadow and Schlieren photographs at ex = 8 deg.

49(1522) W I. 18/9 296 K7 I I /56 Hw. PRIN TED IN OREAT BIlIUDI

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