Posted: June 20th, 2021

Pressure Management on a supercritical aerofoil in transonic flow Abstract-At transonic speeds an aerofoil will have flow accelerate onwards from the leading edge to sonic speeds and produce a shockwave over the surface of its body. One factor that determines the shockwave location is the flow speed. However, the shape of an aerofoil also has an influence. The experiment conducted compared Mach flow over a supercritical aerofoil (flattened upper surface) and a naca0012 aerofoil (symmetrical).

Despite discrepancies, the experiment confirmed the aerodynamic performance of a supercritical aerofoil being superior to a conventional aerofoil. A comparison of the graphical distributions demonstrates the more even pressure distribution on a supercritical aerofoil and a longer delay in shockwave formation. All of which, reflects the theory. Table of Contents Introduction3 Apparatus3 Induction Wind Tunnel with Transonic Test Section3 Mercury Manometer4 Procedure4 Theory and Equations5 Results6 Discussion10 Theory of Transonic Flight10 Relating the Theory to the Experiment11

Effectiveness of Supercritical aerofoils……………………………………………………………………… 11 Limitations and Improvements12 Appendix13 References14 Introduction For any object travelling through a fluid such as air, a pressure distribution over all of its surface exists which helps generate the necessary lift. Lift is an aerodynamic force which is perpendicular to the direction of the aerofoil. Transonic speeds result in the formation of shockwaves over the top surface of the aerofoil. This is due to accelerated flow over the surface region. We say this region is approximately between 0. 8-0. . Since the flow must accelerate and then will lose velocity following the shockwave the aerofoil will have a subsonic and sonic region. For the majority of commercial airlines this is not a desired region to cruise at given the instantaneous pressure distribution which passengers would otherwise experience. Particularly, the formation of shock induced boundary layer separation. Supercritical aerofoils are more efficient designed for higher Mach speeds and drag reduction. They are distinct from conventional aerofoils by their flattened upper surface and asymmetrical design.

The main advantage of this type of aerofoil is the development of shockwaves further away then traditional aerofoils and thus greatly reducing the shock induced boundary layer separation. In order to truly understand the effectiveness of a supercritical aerofoil an experiment gathering supercritical aerofoil performance and raw data of a naca0012 aerofoil will be extensively analysed and compared. Following the calculation and procedureit will be assessed whether a supercritical aerofoil is more effective. Apparatus

A wind tunnel with a transonic test section was used in this experiment to study transonic flow around an aerofoil. The test section consists of liners which, after the initial contraction, are nominally parallel apart from a slight divergence to compensate for growth of the boundary layers on the wall. In order to reduce interference and blockage at transonic speeds, the top and bottom liners are ventilated by longitudinal slots backed by plenum chambers. The working section has a height and width of 178mm and 89mm respectively. The stagnation pressure, p0? in the tunnel is close to atmospheric pressure, and therefore it can be taken to be equal to the settling-chamber pressure as the errors are only small. To minimise the disturbance due to the model itself, the reference stagnation pressure, p? , is taken from a pressure tapping in the floor of the working-section, well upstream of the model. The nominal ‘free-stream’ Mach number, M? , in the tunnel can be calculated from the ratio p? /p0?. The Mach number in the tunnel can be controlled by varying the pressure of the injected air, pj. The maximum Mach number that the tunnel can achieve is about 0. 8 Mercury Manometer A multi-tube manometer with mercury was used to measure the pressure at stagnation, the aerofoil tappings and atmosphere. The manometer is equipped with a locking mechanism which allows the mercury levels to be ‘frozen’ so that readings can be taken once the flow has been stopped. Also, the angle of the manometer can be adjusted. For this experiment, it was set to 45 degrees (Motellebi, F. ,2012). Procedure Before conducting the experiment, the barometric pressure, Pat, was recorded, in inches of mercury and the atmospheric temperature, in degrees Celsius, was also recorded.

For a range of values of Pj from 10 – 110 lb/in2, in intervals of 20lb/in2, Pj was then recorded along with the manometer 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 (Iat), all in inches of mercury (Motellebi, F. ,2012). Results- Raw data in appendix x/c Figure 1b Cp against x/c at M= 0. 85 Figure 1a -Cp against x/c at M=0. 85 The experimental data was converted to absolute pressure values using Equation x ( units are inches of mercury).

For a given value of the pressure injector (Pinjector) we can find the value of the Mach number using Equation y. Also Equation Z calculates Cp( or pressure coefficents) which reflect the measurements of the surface of the aerofoil. These results are displayed in figure x. This was done for both the supercritical aerofoil and the NACCA 0012 aerofoil. What follows is a comparison and analysis of the data. ( Figure 2b Cp against x/c at Mach speed 0. 8 Figure 2a -Cp against x/c at Mach speed 0. 81 x/c x/c Figure 3b- -Cp against x/c at Mach speed 0. 72 Figure 3a –Cp against x/c at Mach speed 0. 3 Figure 4b –Cp against x/c at Mach speed 0. 61 Figure 4a –Cp against x/c at Mach speed 0. 61 Figure 5a- -Cp against x/c at Mach speed 0. 45 Figure 5b- -Cp against x/c at Mach speed 0. 44 Note that for both supercritical and naca0012 aerofoils the supercritical cases ( where M is equal to 0. 77, 0. 83 and 0. 840) the approximate value of x/c % where the shock occurs over the aerofoil is shown in red line. For the point below where Cp and the Cpcritical and hence the drop in Cp is greatest gives the location of where the shockwave occurs on the surface of the aerofoil. Cp and Cp* vs M? naca0012 aerofoil) Cp and Cp* vs M? (supercritical aerofoil) It is worth noting that for both the supercritical and Naca0012 aerofoil the results are somewhat similar. That is the critical Mach numbers for both are around 0. 72. Therefore the Minimum Mach number for a local shockwaves on both the supercritical and conventional aerofoil can be assumed to be the same. It is worth noting that Mach number 0. 41 for the supercritical aerofoil does not produce a shockwave, whereas the Naca0012 aerofoil does. Mach number| Supercritical Aerofoil Approx position of shock| naca0012 Approx position of shock| 0. 5| -| -| 0. 61| -| -| 0. 72-0. 73| -| 0. 25x/c%| 0. 85-0. 86| 0. 70x/c%| 0. 40x/c%| Basic transonic theory An aerofoil or any object for that matter travelling through a medium (air) at low Mach numbers ( typically between 0. 30-0. 40) has flow is subsonic and can be considered incompressible. This means that any change in pressure or density is significant. The speed of sound (a) is dependent on the altitude of the aerofoil/object and the Mach number M is the ratio of velocity: M=va , a=? RT ?is a specific heat ratio, T is thel absolute temperature and R is the gas constant.

The combination of these two equations above leads to: M=v? RT Sound is essentially a series of consecutive weak pressure waves emitted from a given source. These waves travel at the local speed of sound. If we assume the aerofoil is travelling towards the source, the source can notice the disturbances beforehand giving enough time for flow to adjust around the object. When the source begins to approach near the speed of sound, pressure waves move closer together in front of the object, therefore inadequate information from the source/disturbance is propagated upstream and the flow will not be able to react in time.

The pressure waves merge together to produce a shockwave in front of the object. The flow encountering the shockwave will experience changes in temperature, static pressure and gas density as well as a lower Mach number. The transonic region is special because although flight speed is below sonic speed as the information is propagated upstream on the surface of the aerofoil the flow accelerated to the speed of sound. Thus forming a shockwave over the aerofoil. The position of this shockwave depends on the initial entry speed to the aerofoil.

Therefore what we have in the transonic region is an aerofoil which has sonic speeds early upstream and subsonic speed towards the end of the aerofoil or downstream. This means it is complicated to accurately analyse transonic flow over an aerofoil as a different set of equations must be used on the leading edge, upper surface and trailing edge. The critical upstream Mach number is the minimum value of a given Mach number for which a shockwave will be produced on the surface of an aerofoil. In other words, supersonic flow.

Below this threshold a shockwave will not appear. Drag or the aerodynamic force in the transonic region again depends on the speed of the object travelling. At subsonic speeds the main component of drag are Skin friction, pressure drag and lift induced drag. At sonic speeds (approaching or exceeding) there is the addition of wave drag. The drag increases dramatically, and as a result a higher thrust is needed to sustain acceleration. Also, at this point the shockwave will interact with the boundary layer, thus causing it to separate upstream of the shock.

Figure 6Demonstration of transonic flight-(Scott, J. , 2000) The aerofoils The two aerofoils Naca0012 and Supercritical aerofoil are different in design and purpose. The Naca0012 is a basic symmetrical aerofoil used primarily for rudder and elevator movements. Aerodynamic performance is not taken into consideration and is thus reflected by the simple aerodynamic design. It is worth noting that there are better aerofoils. The Supercritical aerofoil is a performance aerofoil designed for higher Mach speeds and drag reduction.

They are distinct from conventional aerofoils by their flattened upper surface and asymmetrical design. The main advantage of this type of aerofoil is the development of shockwaves further away then traditional aerofoils and thus greatly reducing the shock induced boundary layer separation. Relating the Theory to the Experiment The critical Mach number for both the supercritical aerofoil and NACA0012 aerofoil was found to be in the region of 0,72. There is a difference to the nearest 10th but for all intents and purposes we can assume they are the same.

This indicates that the minimum Mach number for a shockwave to be produced on the surface of the aerofoils is equal and not influenced via the shape. The pressure distributions of the supercritical aerofoil ( especially at Higher Mach) in comparison to the Naca0012 are more evenly distributed. The experiment confirms the theory that the supercritical aerofoil in comparison ro a conventional aerofoil generates more lift due to an even distribution of pressure over the upper surface. (http://en. wikipedia. org/wiki/Supercritical_airfoil) Effectiveness of Supercritical aerofoils.

At a Mach number of 0. 45 both aerofoils do not display a shockwave. This is evident from the fact the Cp and Cp* graphs do not intersect at all. We already know this because the critical Mach number is 0. 72 for both. This indicates that either a shockwave was not produced (unlikely), or that the shockwave was produced beyond the trailing edge This means we cannot assess the effectiveness of the supercritical aerofoil at Mach speeds 0,45 and 0. 61. The supercritical Mach numbers show varying results. When the experiment took place at Mach ) 0. 72-0. 3 ( the critical Mach number) the supercritical aerofoil did not produce a shockwave ( Cp and Cp* do not intersect) whereas the naca0012 aerofoil did. The lack of a shockwave formation indicates either the critical Mach number for the supercritical aerofoil is higher then the conventional aerofoil experimental accuracy is lacking. At the supercritical mach numbers ( 0. 81-0. 86) in both the naca0012 aerofoil and the supercritical aerofoil Cp and Cp* intersect. The large drop in pressure coefficient is evidence of the formation of a shockwave.

However, the pressure drop in the supercritical aerofoil is occurring at a pressure tapping further downstream. This confirms the theory that a shockwave is produced further downstream in a supercritical aerofoil This seems to confirm the theory that a supercritical aerofoils design does allow for development of shockwaves further away then traditional aerofoils and thus greater reduction in the shock induced boundary layer separation. In regards to the amount of drag (aerodynamic force) acting on the aerofoils it is worth noting that the pressure distribution at 0. 5 Mach for the supercritical aerofoil is more evenly distributed and ‘flatter’ then the naca0012 aerofoil. There is no indication of a large instantaneous increase in drag taking over. This would therefore confirm the theory that a supercritical aerofoil is effective in greatly reducing the shock induced boundary layer separation. Notes for limitations The experiment is a success since results obtained confirm the capabilities of supercritical aerofoils and their advantages over conventional aerofoils. However, there are a few discrepancies which regarding experimental error and the different aerofoils.

First of all the mach numbers tested at 0. 72 and 0. 73 created an inaccurate experiment. Normally, this would not be a problem. However, since the critical mach numbers for both aerofoil’s were in the vicinity of 0. 72 it was expected this was the minimum threshold for a shockwave to be produced over the aerofoil. A shockwave was not produced for the supercritical aerofoil despite the critical mach number value. Therefore, we can conclude that at this speed there are too many inaccuracies to understand what is really going on.

We also did not really see a difference in performance at subsonic flow. Granted, the supercritical aerofoil was primarily designed for supercritical mach speed. No useful information was obtained from here. The fact the pressure tappings have different coordinates means that each aerofoil is showing the pressure distribution at a different set of coordinates. This of course, is not as accurate if the aerofoils had the same pressure tappings. For instance, the naca0012 has a pressure tapping at 6. 5% of the aerofoil section and the last ends 75% the rest is unaccounted for.

Since the supercritical aerofoil has different pressure tappings it means both aerofoils have different areas which are unaccounted for. This means it is not certain whether or not the graphs are a reliable source of information, yet alone to compare. A digital meter should also be connected that displays the pressure in the two tappings so the aerofoil can be appropriately adjusted to bring it to zero incidence. This digital meter can also be used to display the value of the mercury levels for other pressure tappings, reducing any human errors.

In order to increase the accuracy of the pressure distribution over the aerofoil surface, more pressure tappings can be made on the aerofoil. These will improve the pressure coefficient graphs by allowing more points to be plotted, in turn, yielding better information for the position of the shockwave in the supercritical cases and also the critical Mach number for a shock to occur. References 1) http://www. southampton. ac. uk/~jps7/Aircraft%20Design%20Resources/aerodynamics/supercritical%20aerofoils. pdf 2) http://www. nasa. gov/centers/dryden/pdf/89232main_TF-2004-13-DFRC. pdf 3)

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