Surface Pressure Measurements on an Aerofoil

DEN 302 Applied Aerodynamics SURFACE PRESSURE MEASUREMENTS ON AN AEROFOIL IN TRANSONIC FLOW Abstract The objective of this form is to measure the jam distribution across the surface on an control surface in a wind cut into. The open is mental tested under several(prenominal) different Mach bets from sub sonic to super diminutive. The purpose of measuring the mash distributions is to respect the validity of the Prandtl-Glauert law and to discuss the changing chracteristics of the issue as the Mach image increases from subsonic to transonic.As a result of the experiment and computation of data, the airfoil was rear to have a detailed Mach spell of M=0. 732. Below this freestream Mach image the Prandtl-Glauert law predicted results very successfully. However, above this value, the law completely breaks down. This was found to be the result of topical anesthetic realms of ultrasonic play and local shockwaves. Contents Abstract2 Apparatus2 1. induction Wind Tunnel wi th sonic Test Section2 2. Aerofoil sit down3 3. Mercury manometer3 Procedure3 Theory3 Results4 Discussion8 Transonic Flow8 Analysis9 Conclusion11 Bibliography11Apparatus 1. Induction Wind Tunnel with Transonic Test Section The tunnel used in this experiment has a transonic test partitioning with liners, which, after the contraction, remain nominally parallel bar a dismiss divergence to accommodate for boundary layer growth on the walls of the test section. The liners on the top and bottom be ventilated with retentiveitudinal slots back by plenum chambers to reduce interference and blockage as the Mach add together increase to transonic speeds. The working section dimensions be 89mm(width)*178mm(height). The stagnation pressure , p0? is close to the atmospheric pressure of the lab and with only a sensitive error ,is taken to be equal to the settling chamber pressure. The destination staticpressure, p? , is measured via a pressure tapping in the floor of the working sectio n, well upstream of the simulate so as to reduce the mental disturbance due to the model. The freestream Mach identification number, M? , can be calculated by the ratio of static to stagnation pressure. The tunnel airspeed is controlled by varying the pressure of the injected air, with the highest Mach number that can be achieved by the tunnel being 0. 88. 2. Aerofoil modelThe model used is untapered and unswept, having the NACA 0012 symmetric section. The model chord length, c, is 90mm and the model has a amphetamine limit chord/thickness ratio of 12%. Non-dimensionalised co-ordinates of the aerofoil model are abandoned in table 1 below. Pressure tappings, 1-8 , are displace on the upper surface of the model at the positions detailed in table 1. An additional tapping, 3a, is placed on the abase surface of the aerofoil at the like chordwise position as tapping 3. The reason for including the tapping on the lower surface is so that the model can be set at zero incidence by equalizing the pressures at 3 and 3a 3.Mercury manometer A multitube mercury manometer is used to record the measurements from the tappings on the surface of the model. The manometer has a locking apparatus which allows the mercury levels to be frozen so that readings can be taken after the bleed has stopped. This is useful as the wind tunnel is noisy. The lurch of the manometer is 45 degrees. Procedure The atmospheric pressure is first recorded, pat, in inches of mercury. For a range of injected pressures, Pj, from 20 to 120Psi, the manometer readings are recorded for stagnation pressure (I0? , destination static pressure (I? ), and surface pressure form tappings on the model (In, for n=1-8 and 3a). Theory These compares are used in order to consider and discuss the raw results achieved from the experiment. To convert a reading, I, from the mercury manometer into an absolute pressure, p, the following(a) is used p=patl-latsin? (1) For isentropic prey of a double-dyed(a) g as with ? =1. 4, the freestream Mach number,M? , is related to the ratio amidst the static and stagnation pressures by the comparison M? =2? -1p? p0? -? -1? -1. 0(2) Pressure coefficient, Cp , is given byCp=p-p? 12?? U? 2(3) For compressible flow this can be rewritten as Cp=2? M? 2pp? -1(4) The Prandtl-Glauert law states that the pressure coefficient, CPe, at a point on an aerofoil in compressible, sub-critical flow is related to the pressure coefficient, CPi, at the same point in in incompressible flow by the comparability CPe=CPi1-M? 2(5) Due to its basis in on thin aerofoil conjecture, this equation does non win an exact solution. However it is deemed reasonably accurate for cases much(prenominal) as this in which thin aerofoils are tested at scurvy incidence.The law does not hold in super-critical flow when local regions of ultrasonic flow and shockwaves appear. The value of the critical pressure coefficient, Cp*, according to local sonic conditions is calculated by Cp*= 10. 7M? 25+M? 263. 5-1for? =7/5(6) The co-ordinates for the NACA 0012 section are as follows prototype 1-Co-ordinates for aerofoil (Motallebi, 2012) Results Given atmospheric conditions of Patm=30. 65 in-Hg Tatm=21C The following results were achieved Figure 2-Pressure coefficient vs x/c for M=0. 83566 Figure 3-Pressure coefficient vs x/c for M=0. 3119 Figure 4-Pressure coefficient vs x/c for M=0. 79367 Figure 5-Pressure coefficient vs x/c for M=0. 71798 Figure 6-Pressure coefficient vs x/c for M=0. 59547 Figure 7-Pressure coefficient vs x/c for M=0. 44456 Figure 8-Cp* and Cpminvs Mach itemize From figure 7 the critical Mach number is able to be determined. The critical Mach number (the maximum velocity than can be achieved before local shock conditions arise) occurs at the point where the curves for Cp* and Cpmin cross. From figure 7 we can face that this value is, M? =0. 732. Discussion Transonic FlowTransonic flow occurs when in that location is miscellaneous sub and superso nic local flow in the same flow field. (Mason, 2006) This generally occurs when free-stream Mach number is in the range of M=0. 7-1. 2. The local region of supersonic flow is generally terminated by a habitual shockwave resulting in the flow slowing down to subsonic speeds. Figure 8 below shows the typical progression of shockwaves as Mach number increases. At both(prenominal) critical Mach number (0. 72 in the case of Figure 8), the flow becomes sonic at a single point on the upper surface of the aerofoil.This point is where the flow reaches its highest local velocity. As seen in the figure, increase the Mach number further, results in the development of an area of supersonic flow. Increasing the Mach number further again then moves the shockwave toward the trailing edge of the aerofoil and a normal shockwave will develop on the lower surface of the aerofoil. As seen in figure 8, approaching very close to Mach 1, the shockwaves move to the trailing edge of the aerofoil. For M> 1, the flow behaves as expected for supersonic flow with a shockwave forming at the leading edge of the aerofoil.Figure 9-Progression of shockwaves with increasing Mach number (H. H. Hurt, 1965) In normal subsonic flow, the run is composed of 3 components-skin friction drag, pressure drag and induced drag. The drag in transonic is markedly increase due to changes to the pressure distribution. This increased drag encountered at transonic Mach come is known as wave drag. The wave drag is attributed to the formation of local shockwaves and the general instability of the flow. This drag increases at what is known as the drag divergence number (Mason, 2006).Once the transonic range is passed and true supersonic flow is achieved the drag decreases. Analysis From figure 7, the conclusion was reached that the critical Mach number was 0. 732. This path ultimately that in the experiment local shockwaves should be experienced someplace along the aerofoil for Mach numbers M=0. 83566, 0. 831 19 and 0. 79367. According to transonic hypothesis, these shockwaves should be moving further along the length of the aerofoil as the freestream Mach number increases. To determine the approximate position of the shockwaves it is useful to look again at equation (4).Cp=2? M? 2pp? -1 Assuming constant p? , as static pressure in the test section is assumed to be constant and constant free stream Mach number as well, equation (4) may be written as Cp=const. pconst. -1 Normal shockwaves usually stage themselves as discontinuous data, particularly in stagnation pressure where in that respect is a large land. To detect the rough position of the shockwave on the aerofoil surface it is useful to look at the detected pressure by the different tappings and scrutinize the Cpvs x/c graph to see where the drop in pressure occurs.Investigating the graphs for the supercritical Mach numbers yields these approximate positions M x/c, % 0. 835661 40-60 0. 831199 35-55 0. 793676 25-45 Figure 10- Ta ble showing approximate position of shockwave According to the theory described earlier, these results are correct as it demonstrates the shockwave moving further along the aerofoil as the Mach number increases. As seen in figure 8, given a sufficiently high Mach number, a shock may to a fault occur on the lower surface of the wing. This can be seen for M=0. 835661, in figure 1, where there is a marked difference in pressure between tappings 3 and 3a.The hypothetic curves on each Cpvs x/c graph were designed using the Prandtl-Glauert law. As mentioned earlier, this law is found on thin aerofoil theory, meaning it is not exact and there are sometimes large errors between the proposed theoretical set and the data-based values achieved. These large errors are seen most clearly in the higher(prenominal) Mach numbers. This is because in the transonic range, where there is a mixture of sub and supersonic flow, local shockwaves occur and the theoretical curves do not take shockwaves int o account.Hence, the theory breaks down when the freestream Mach number exceeds the critical Mach number for the aerofoil. At lower Mach numbers, the theoretical values line up reasonably well with those achieved through experiment. there only seems to be some error between the two, mainly arising in the 15-25% range. However, overall the Prandtl-Glauert law seems to be reasonably accurate as long as the Mach number remains sub-critical. The experiment itself was successful. The rough position of the shockwave and the critical Mach number were able to be identified.There are however some sources of inaccuracy or error that can be addressed of the experiment is to be recurrent for bettter results. Aside from the normal human errors made during experimentation the apparatus itself could be improved. Pressure tapping 1 (the appressed to the leading edge) and pressure tapping 8 (the closest to the trailing edge) were placed at 6. 5% and 75% respectively. What this means is that they are not centralized relative to the leading and trailing edge effectively meaning it is not able to be determined whether or not the pressure is conserved.At a zero angle of incidence, the pressure at the gunpoint of the leading edge should be equal to the pressure at the pinch of the trailing edge. To improve this pressure tappings should exist at the LE and TE and possibly more pressure tappings across the aerofoil surface to provide more points for recording. Another source of improvement could be using a larger test section so that there is absolutely no disturbance in measuring the static pressure. However, this may only relieve oneself a minute difference in the data and may not be worthwhile for such little gain. ConclusionAs desired, a symmetric aerofoil was tested in transonic flow and the experimental results were compared to the theoretical values predicted by the PrandtlGlauert law. In the cases where there was a large disparity between experimental and theoretical r esults, an explanation was given, relying on the theory behind transonic flow. Bibliography H. H. Hurt, J. (1965). Aerodynamics for Naval Aviators. Naval Air Systems Command. Mason. (2006). Transonic aerodynamics of airfoils and wings. Virginia Tech. Motallebi. (2012). cake Pressure Measurements on an Aerofoil in Transonic Flow. London promote Mary University of London.