Transonic report DEN 302

8/14/2019 Transonic report DEN 302

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Surface Pressure Measurements on an

Aerofoil in Transonic FlightIntroduction

This report details the study of transonic flight over an aerofoil. The investigation first takesplace by measuring, for a range of free-stream Mach numbers from subsonic, to supercritical, thesurface pressure distribution on an aerofoil mounted in a transonic wind tunnel. Thesemeasurements are then used to assess the validity of the Prandtl - Glauert Law, which relates thepressure coefficient at point on the surface of an aerofoil in sub-critical, compressible flow tothat at the same point in incompressible flow. Furthermore, the results are then used as a basisfor a discussion of the changes which occur in the character of flow over an aerofoil as the Mach

number increases into the transonic regime.

Apparatus


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Induction wind Tunnel with Transonic Test Section

The tunnel used in this experiment is equipped with a transonic test section having liners whichare nominally parallel apart (after initial contraction) from a slight divergence to compensate forgrowth of the boundary layers on the wall. The top and bottom liners are ventilated bylongitudinal slots backed by plenum chambers, to reduce interference and blockage at transitionspeeds. The working section has a width of 89mm and a height of 178mm.

The stagnation pressure, p0, in the tunnel is close to atmospheric pressure, and (with onlya small error) can be taken to be the same as the settling chamber pressure. The referencestagnation pressure, p, is taken from a pressure tapping in the floor of the working section, wellupstream of the model to minimise the disturbance due to the model itself. The nominal freestream Mach number, M, in the tunnel can be calculated from the ratio p / p0.

The tunnel Mach number is controlled by varying the pressure of the injected air, pj. Themaximum Mach number which can be achieved is about 0.88.

The model

The untapered, unswept model has the well known NACA 0012 symmetric section1, and spansthe tunnel. The model has a chord length of 90mm and a maximum thickness/chord ratio of 12%.

Pressure tappings, numbered 1 to 8, are provided on the upper surface of the model at thechordwise positions given in table 1.1, and there is an additional tapping 3a in the lower surfaceat the same chordwise position as tapping 3; this is to enable the model to be set at zeroincidence by equalising the pressures at tappings 3 and 3a.

Fig 1.0 the model

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Mercury Manometer


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A multitube mercury manometer is provided, with a locking mechanism which allows themercury levels to be frozen so that reading can be taken after the flow has been stopped. Themanometer bank should be set at a slope of 45 degrees.

Fig 2.0 The mercury manometer

Procedure


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As a preliminary, the barometric pressure, Pat was recorded, in inches of mercury. For a range ofvalues of Pj, from 10 110lb/in

2 in intervals of 20lb/in2, Pj was then recorded along with themanometer readings, corresponding to stagnation pressure (I0), the reference static pressure(I),airfoil pressure tappings (In, n=1 to 8 and 3a) and the atmospheric pressure(I at)(at all inches).

*

Fig 3.0 Pictorial representation of manometer

Theory


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The typical reading, I, on the sloping manometer can be converted to an absolute pressure, p,using the equation:

p=pat|I-Iat|sin (1)

Where is the slope angle of the manometer, which will be set to 45.

For isentropic flow of a perfect gas with = 1.4, the mach number, M, is related to the ratio ofstatic/ stagnation pressures, p/ po, by the equation:

M=2-1ppo--1-1 (2)

The pressure coefficient, Cp, is defined as:

Cp=p-p12U2 (3)

For compressible flow, this can more conveniently be re-written in the form:

Cp=2M2pp-1 (4)

According to the Prandtl- Glauert law the pressure coefficient, Cpc, at a point on anaerofoil in sub-critical, compressible flow is related to the pressure coefficient, Cpi, at the samepoint in incompressible flow by the relation:

Cpi=Cpi1-M2 (5)

This relation is based on thin-aerofoil theory. It is therefore not exact, but is quiteaccurate for reasonably thin aerofoils at small incidence. It breaks down completely in super-critical flow, when regions of locally supersonic flow occur and shock waves begin to form.

The theoretical pressure distribution for inviscid flow over the NACA 0012 section in

incompressible flow is included as the last column in Table 1. The value of the critical pressurecoefficient, Cp*, corresponding to locally sonic conditions, is given by2:

Cp*=10.7M25+M263.5-1 for = 1.4 (6)

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2Motellebi, F. Surface Pressure Measurements on an Aerofoil in Transonic Flighthandout,

Queen Mary Pubs., London

Results

Fig 3.1 - -cp vs x/c for M = 0.32


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Fig 3.2 - -cp vs x/c for M = 0.52

Fig 3.3 - -cp vs x/c for M = 0.65

Fig 3.4 - -cp vs x/c for M = 0.74

Fig 3.5 - -cp vs x/c for M = 0.80


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Fig 3.6 - -cp vs x/c for M = 0.84

Critical Mach number and shockwave analysis

Fig 4.0 graph showing crossings of two graphs representing Mcritical

Fig 4.1 graph showing close-up of crossings of two graphs representing Mcritical


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From these graphs, it can be shown that the M critical value is 0.7253. this value is the thresholdlevel required for the NACA 0012 wing profile to experience local shockwaves on the surface ofthe aerofoil. Hence, mach numbers below (or equal to) this value will not experience enoughacceleration near the aerofoil leading edge to experience a shockwave along the surface. Hence,Mach numbers 0.32, 0.52 and 0.65 will not experience a local shockwave.

Discussion

Transonic flow

As an aeroplane is in motion at subsonic velocities, the air is treated as incompressible flow. Asthe velocity increases, however, the air loses its incompressible behaviour. The question arises asto how fast an aeroplane must be moving before compressibility is taken into account.

A disturbance in the air will send pressure pulses or waves out into the air at the localspeed of sound. For example, take a cannon fired at sea level. A person observing situated atsome distance from the cannon will see the flash almost immediately, but the sound wave isheard (or pressure wave is felt) some time later. The observer can easily calculate the speed ofsound by dividing the distance between him and the cannon by the time it takes the sound toreach him. The disturbance propagates out and away from the cannon in an expandinghemispherical shell.

The speed of sound varies with altitude. It depends upon the square root of theabsolute temperature. At sea level under standard conditions (i.e. T = 288.15 K) the speed ofsound is approximately 340.3 m/s, but at an altitude of 15 km when the temperature isapproximately 216.7 K, the speed of sound reduces to 295 m/s. This difference indicates that anaeroplane flying at this altitude encounters the speed of sound at a slower speed, thus comes upagainst the effects of compressibility sooner.

a=RT

Where a = local speed of sound, = ratio of specific heats (1.4 for air), R = molar gas constant,T = local temperature in Kelvin

An aeroplane flying below the speed of sound creates a disturbance in the air andsends out pressure pulses in all directions. Air ahead of the aeroplane receives these "messages"before the aeroplane arrives and the flow separates around the aeroplane. However as the plane


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approaches the speed of sound, the pressure pulses merge closer and closer together in front ofthe aeroplane and little time elapses between the time the air gets a warning of the plane'sapproach and the plane's actual arrival time At the speed of sound, the pressure pulses move atthe same speed as the plane. They merge ahead of the aeroplane into a "shock wave" that is analmost instantaneous line of change in pressure, temperature, and density. The fluid has no

warning of the approach of the aeroplane and abruptly passes through the shock system. There isa tendency for the air to break away from the aeroplane and not flow smoothly about it; hence,there is a change in the aerodynamic forces from those experienced at low incompressible flowspeeds.

The Mach number is a measure of the ratio of the aeroplane speed to the speed ofsound. In other words, it is a number that may relate the degree of warning that air may have toan aeroplane's approach. The Mach number is named after Ernst Mach, an Austrian professor(1838 - 1916).

M=Va

Where V = local velocity of object in m/s, a = local speed of sound in m/s

For Mach numbers less than one, one has subsonic flow, for Mach numbers greaterthan one, supersonic flow, and for Mach numbers greater than 5, the name is hypersonic flow.Additionally, transonic flow pertains to the range of speeds in which flow patterns change fromsubsonic to supersonic or vice versa, about Mach 0.8 to 1.2. Transonic flow presents a specialproblem area as neither equations describing subsonic flow nor those describing supersonic flowmay be accurately applied to the regime.

At subsonic speeds, drag was composed of three main componentsskin-frictiondrag, pressure drag, and induced drag (or drag due to lift). At transonic and supersonic speeds,

there is a substantial increase in the total drag of the aeroplane due to fundamental changes in thepressure distribution.

This drag increase encountered at these high speeds is called wave drag. The drag ofthe aeroplane wing, or for that matter, any part of the aeroplane rises sharply, and large increasesin thrust are necessary to obtain further increases in speed. This wave drag is due to the unstableformation of shock waves that transforms a considerable part of the available propulsive energyinto heat, and to the induced separation of the flow from the aeroplane surfaces. Throughout thetransonic range, the drag coefficient of the aeroplane is greater than in the supersonic rangebecause of the erratic shock formation and general flow instabilities. Once a supersonic flow hasbeen established, however, the flow stabilizes and the drag coefficient is reduced.

The total drag at transonic and supersonic speeds can be divided into two categories:(1) zero-lift drag composed of skin-friction drag and wave (or pressure-related) drag of zero liftand (2) lift-dependent drag composed of induced drag (drag due to lift) and wave (or pressure-related) drag due to lift. In the early days of transonic flight, the sound barrier represented a realbarrier to higher speeds. Once past the transonic regime, the drag coefficient and the dragdecrease, and less thrust is required to fly supersonically. However, as it proceeds toward highersupersonic speeds, the drag increases (even though the drag coefficient may show a decrease).


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It is a large loss in propulsive energy due to the formation of shocks that causes wavedrag. Up to a free-stream Mach number of about 0.7 to 0.8, compressibility effects have onlyminor effects on the flow pattern and drag. The flow is subsonic everywhere. As the flow mustspeed up as it proceeds about the airfoil, the local Mach number at the airfoil surface will behigher than the free-stream Mach number. There eventually occurs a free-stream Mach number

called the critical Mach number at which a supersonic point appears somewhere on the airfoilsurface, usually near the point of maximum thickness, and indicates that the flow at that pointhas reached Mach 1. As the free-stream Mach number is increased beyond the critical Machnumber and approaches Mach 1, larger and larger regions of supersonic flow appear on theairfoil surface. In order for this supersonic flow to return to subsonic flow, it must pass through ashock (pressure discontinuity). This loss of velocity is accompanied by an increase intemperature, that is, a production of heat. This heat represents an expenditure of propulsiveenergy that may be presented as wave drag. These shocks appear anywhere on the aeroplane(wing, fuselage, engine nacelles, etc.) where, due to curvature and thickness, the localized Machnumber exceeds 1.0 and the airflow must decelerate below the speed of sound. For transonicflow, the wave drag increase is greater than would be estimated from a loss of energy through theshock. In fact, the shock wave interacts with the boundary layer so that a separation of the

boundary layer occurs immediately behind the shock. This condition accounts for a largeincrease in drag that is known as shock-induced (boundary-layer) separation.


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Fig. 4.2+ diagram showing transonic regime with Mcrit= 0.8

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+http://www.centennialofflight.gov/essay/Theories_of_Flight/Transonic_Flow/TH19G6.htm

The free-stream Mach number at which the drag of the aeroplane increases markedly is calledthe drag-divergence Mach number. Large increases in thrust are required to produce any furtherincreases in aeroplane speed. If an aeroplane has an engine of insufficient thrust, its speed will belimited by the drag-divergence Mach number. The prototype Convair F- 102A was originallydesigned as a supersonic interceptor but early flight tests indicated that because of high drag, itwould never achieve this goal. It later achieved its goal through a redesign.
http://www.centennialofflight.gov/essay/Theories_of_Flight/Transonic_Flow/TH19G6.htmhttp://www.centennialofflight.gov/essay/Theories_of_Flight/Transonic_Flow/TH19G6.htm


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3Anderson, Jr., John D.A History of Aerodynamics, Cambridge University Press, Cambridge,

England4Wegener, Peter P. What Makes Airplanes Fly? Springer-Verlag, New York

Analysis

As previously mentioned, we have concluded from observations made from fig. 4.1 that thecritical Mach number is approximately 0.7253. Thus, in the Cp vs x/c graphs for M = 0.74, 0.80and 0.84, we should expect a shockwave along the body of the aerofoil, progressively movingmore downstream as the free steam mach number increases. To identify this, first we must lookback at the definition of Cp. We know that:

Cp=p-p12U2

Hence, as p is assumed constant, as the static pressure in the test section remains constant, asthe Psi remains costant, and = U = constant. Hence we can say:

Cp=p-const.const.

Hence, as it is known that a normal shockwave results in a discontinuity in flow properties. Inparticular, the stagnation pressure is lowered by a substantial amount. Hence, the pressure loss isdetected by the different pressure tappings. Hence, -Cp will show a large drop in the graph whena shock occurs. Below shows the graph of the suspected regions of shock occurring, highlightedby red regions.


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Fig 5.0 shock roughly between 0.16 to 0.36 x/c


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Hence we can say:

M Position of shock (x/c, approximation)

0.84 0.35 - 0.55

0.80 0.25 - 0.45

0.74 0.16 - 0.36

Thus, our hypothesis regarding the shock moving more downstream as M increases, is correct asit can be shown above.

The theoretical values were designed using the Prandtl Glauert Law, and there wereseveral assumptions made. Firstly, it is based on the thin aerofoil theory. It is not exact, andhence the theoretical values are not as accurate as desired. When observing figs. 3.1 to 3.6, theexperimental data does not completely follow the theoretical graph exactly, however at smallerMach numbers they correlate closer than that at higher M numbers. This is possibly because athigher Mach numbers there are larger losses. As mentioned in the transonic regime section,during supersonic flight, drag is induced from several sources; particularly wave drag, pressuredrag and skin friction. As the flow velocity increases the skin friction increases as the shearingwith the surface of the NACA 0012 body and neighbouring fluid particles is relatively high.Another factor is the fact that the pressure drag will increase as the Reynolds number increasesthus resulting in more separated flow as M increases. Finally, the shockwaves generated duringthe highest three Mach flows creates a large difference between the theory graph andexperimental graph. This is because the theoretical graphs do not take shockwaves into account,as the theory breaks down completely in super-critical flow, when regions of locally supersonicflow occur and shock waves start to form. Hence when M = Mcrit, the theory graphs are useless.

The inaccuracies for the lower M speeds is noticeable mainly in the regions of x/c from 0.2 to0.6.

The experiment was successful in terms of determining accurate information, such as theposition of the shockwave and the value of Mcritical. However, the accuracy of the experimentcould have been greater due to general human inaccuracies and limitations in the experimentalequipment available. For example, the pressure tappings began from x/c of 6.5 % and the lastpressure tapping was at x/c position of 75%. Hence, these tappings are not centralized relative tothe leading edge and trailing edge. Hence, it is impossible at the current status to determine howmuch pressure is conserved, i.e. as the aerofoil is placed at 0 incidence, the pressure at the tip ofthe LE should be equal to the pressure at the tip of the TE. Hence as an improvement, thereshould be more pressure tappings covering the whole length of the aerofoil. This would also

provide more points to plot on the above graphs hence providing more accurate data.


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Conclusion

Overall, the experiment was successful, as the experimental data resulted in reasonablegraphs which comply with aerodynamic laws of transonic flight. The theoretical graphs followeda trend with Mach numbers below Mcritical, but after this critical value, the theoretical values had

no correlation with the experimental data. The shockwaves produced after the critical Machnumber showed a sharp drop in the graphs, and the location of the shockwaves moved furtherdownstream as M increased, which is true for transonic flight. The experiment has satisfactoryequipment to produce sound results, but can be improved by increasing the number of pressuretappings to cover the entire aerofoil surface, hence yielding more accurate information. Themercury manometer could also be replaced with a device which could read pressure and havedigital values as outputs, further increasing accuracy of the experiment.

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Transonic report DEN 302