Wind Tunnel Measurements on an Aeroplane Model

Transcription

1 Wind Tunnel Measurements on an Aeroplane Model Akash Trivedi CID: Personal Tutor: Dr. P. Robinson Submission Date: 15/03/2011 In this experiment, wind tunnel measurements of the lift, drag and pitching moments were taken on a model. These were then reduced into quantities that could be analysed and used to determine the various parameters involved in the longitudinal static stability of an aircraft. The values obtained were then compared with those of Irving [3]. It was concluded that comparison was not ideal as not only were the two tests operating at greatly different Reynolds number, the models also had different geometry with respect to engine nacelles.

2 Contents Introduction... 3 Apparatus... 3 Procedure... 3 Data and Calculations... 3 Results... 5 Trimmed Lift Coefficients... 5 Static Margin, Stick Fixed... 7 Neutral Points, Stick Fixed... 7 Aerodynamic Centre... 7 Lift Coefficient Slopes Drag Factors... 9 Discussion Comparison Error Analysis Conclusion References P a g e

3 Introduction The wind tunnel is an important and useful apparatus in the Aeronautical Engineer s toolbox. Provided the model and wind tunnel abide to dynamic similarity requirements, a small model at sea level can be used to extensively study real life characteristics on a full size aircraft. In this experiment, the objective is to derive various quantities relating to the longitudinal static stability of the aircraft. Apparatus The model aircraft is mounted inversely on an accurate mechanical balance. This allows for the lift, drag and pitching moment to be measured. The model is inverted to allow for a clean upper surface that is not disturbed by the wake from the support structure. This is all placed inside the working section of a closed loop wind tunnel. Full details of the apparatus used can be found in the lab handout. [1] Procedure During the experiment, the lift, drag and pitching moment acting on the model are measured. This is done at seven incidences and three distinct tail configurations; without a tailplane, with the tailplane at +1 o, and with the tailplane at -3 o. Full details of the experimental procedure are given in the lab handout. [1] Data and Calculations The raw data collected during the experiment can be found in the appendix. The Betz reading on the manometer can be utilised to obtain the dynamic head via the hydrostatic equilibrium. Equation 1 In order to use this expression to obtain the wind speed, the air density must first be known. Equation 2 Upon substituting ρ from Equation 2 into Equation 1, it can be solved for V, the wind speed. Using the dynamic pressure, q, the lift, drag, and pitching moment coefficients can also be determined. Equation 3 3 P a g e

4 Equation 4 Equation 5 In the above three equations, the lift and drag forces are normalised by the dynamic pressure and the wing area, S, given as m 2. The pitching moment equation is slightly different. It is normalised with a further term called the mean chord. A reference length such that a rectangular wing of the same chord length as the mean chord would have the same lift and moment characteristics. Also, the pitching moment as read from the apparatus, M i, has to be corrected to exclude the effect of zero wind pitching moments. Equation 6 Equation 7 Furthermore, to correct for blockage effects imposed onto the model by the tunnel walls, a correction factor of 0.94 was applied to all three coefficients to make sure they represent true values. A further complication arising from the tunnel walls is the fact the flow streamlines are constraint to be straight; not the case in real life. Analysing this via image vortices shows that an upwash phenomenon is produced on the model. This means that for a given lift coefficient, the induced downwash as compared to a free-stream value is reduced. Therefore, due to this rotation of the lift vector, the true incidence would be greater than the geometric tunnel value. The corresponding increase in drag coefficient due to this phenomenon is given by the following equation. Another drag correction has to be made for the drag of the support structure and the interference between the model and support struts. Equation 8 Equation 9 An additional upwash correction has to be applied to the tail which affects the pitching moment. Overall, this means that the pitching moments measured in the tunnel are more negative than their free-stream counterparts. This means that the model appears to be more stable in the tunnel than it would be in free-stream. Equation 10 In Equation 10, is given by the following expression obtained by using the plot of vs and taking the values for an arbitrarily selected value of, P a g e

5 Equation 11 C MP C L No Tail Tail +1deg Tail -3deg Figure 1: Graph allowing the value of C M / η T to be obtained From Figure 1, it can be seen immediately that with tail-off, the aircraft is longitudinally statically unstable due to the positive gradient. Therefore, the two tail-on cases are stable. Using the above equations, the proper coefficient values have been determined. Using these along with the geometry of the aircraft model as a starting point, all the desired parameters relating to the static longitudinal stability of the aircraft model can be determined. Results Trimmed Lift Coefficients The trimmed lift coefficients are defined as the lift coefficients at the point such that when moments are taken about the centre of gravity of the aircraft, the net result is zero. This is the equivalent of saying the pitching moment coefficient about the CG position should be zero. The value of this coefficient about the strut pivots is already known. The conversion needing to be applied is given by the following. ( ) Equation 12 5 P a g e

6 C MG C L No Tail Tail +1deg Tail -3deg Figure 2: Graph of C MG against C L Once this conversion has been applied to all of the pitching moment coefficient values, a graph can be plotted of against for the two tailplane configurations, and the values for obtained for which. The values obtained using Figure 2 below, were as follows: Tail configuration η=1 o η=-3 o Table 1: Trimmed lift coefficients C MG C L Tail +1deg Tail -3deg Figure 3: Graph allowing for the determination of trimmed lift coefficients 6 P a g e

7 Static Margin, Stick Fixed The stick fixed static margin, K N, is related to the stick fixed stability of the aircraft in that it has a positive value of it is statically stable, and the greater the value is, the more stable the aircraft. The negative of the slopes of the curves given in Figure 2 evaluated at the point where give the values of K N. Neutral Points, Stick Fixed Tail configuration η=1 o η=-3 o Table 2: Stick fixed static margin Equation 13 The neutral point, H N, provides the information of the maximum possible distance of the centre of gravity from the leading edge that the aircraft can have, and still be stable. If the value exceeds H N, the aircraft is unstable. The neutral point is also related to the static margin in the following manner. Equation 14 Aerodynamic Centre Tail configuration η=1 o η=-3 o Table 3: Stick fixed neutral point The aerodynamic centre of an aircraft is the location (sometimes the quarter chord) where the aerodynamic moment is always constant regardless of angle of attack. This is the preferred point for averaging the aerodynamic force at rather than the centre of pressure, as this tends to move with incidence. Lift Coefficient Slopes Tail configuration η=1 o η=-3 o Table 4: Aerodynamic centre Equation 15 The lift coefficient slopes can be used to find out what the lift coefficient will be at a certain angle of attack. These slopes can be obtained from the plots of lift coefficient against angle of incidence. The values for the tail-on cases are equal to a(1+f), and the slope of the tail-off case refers to a. The slopes for both are found at the lift coefficient for which. 7 P a g e

8 1 0.8 C L No Tail Tail +1deg Tail -3deg α Figure 4: Graph for finding the lift coefficient slopes for which Tail-on slopes Tail-off slopes Table 5: Lift coefficient slopes To obtain the tail lift coefficient slope, the change in lift coefficient at a given α for the two tail settings is found by the following equation. ( ) Equation 16 It is possible to obtain the value of can be written as: by rearranging Equation 16 as the expression for Equation 17 α for which Table 6: Tail lift coefficient slope The rate of change of downwash angle with the incidence, or, is also an important parameter to obtain. Not only does it provide the relationship between downwash angle and incidence, it is also a required term in the trim equation. In order to obtain, firstly, the modified tail volume coefficient,, must be obtained. This is normally given by Equation 18, and in this experiment, this was in a slightly different form as evident in Equation P a g e

9 [ ] Equation 18 Equation 19 Once the modified tail volume coefficient is known, the expression given by Equation 20 can be rearranged to find. Drag Factors ( ) Tail configuration η=1 o η=-3 o Table 7: Modified tail volume coefficients and ε/ α Equation 20 The drag coefficient can often be expressed as. is the zero-lift drag coefficient and is the more interesting induced drag coefficient. Induced drag is proportional to the square lift, therefore plotting a graph of against will give a straight line whose y intercept is and the slope of which is given by the expression,. Here, k is the inverse of the Oswald efficiency factor, whose empirical expression is given in Equation 21 [2]. Equation 21 C D C L 2 Figure 5: Graph allowing the determination of induced drag factors No Tail Tail +1deg Tail -3deg Tail configuration η=1 o η=-3 o Tail-off C D k/πar k (Averaged) 1.35 Table 8: Induced drag factors 9 P a g e

10 Tail configuration η=1 o η=-3 o Tail-off Tail-on slopes Tail-off slopes α for which C D k/πar Table 9: Summary of relevant parameters Discussion Comparison Averaged Values Reference Values [3] Percentage Difference/% k/πar k Table 10: Comparison between experimental and reference values Overall, the experiment was quite successful in that all the relevant parameters related to longitudinal static stability were obtained. However, most of them had significant variations with respect to the reference values. The present experiment cannot possibly convey the properties of the aircraft in stability properly. One of the reasons why is because the reference values were obtained from testing at a Reynolds number of 12.8 million. This is two orders of magnitude higher than the test carried out in this experiment. Here, the Reynolds number was obtained to be around 10 P a g e

11 320,000. This lack of dynamic similarity means that any comparison made between the two experiments would not be very credible. Furthermore, in this experiment, there was the presence of the engine nacelles to be taken into account. In the reference, no engine nacelles were present. This would obviously affect values of drag, but also the pitching moments too. Therefore, the above comparison percentage differences should be taken with a pinch of salt as they are neither exact comparisons to theoretical values nor are they empirical values obtained under the same conditions. Error Analysis The data leading to the graphs may have errors. The accumulation of tolerance based inaccuracies from the mechanical balances, and fluctuations of the lift values of ±0.1 lbf during the experiment would have led to deviances from the true values for the lift coefficients. Turbulence in the flow itself could induce fluctuations in the velocity field leading to minor changes in values that accumulate as calculations are made upon them leading to greater variances. There was a human error during the experiment too. This involved not closing the wind tunnel doors tightly whilst testing for the second tail configuration. However, this did not seem to have significant effects on the overall results. Another source of error that creeps into this experiment is associated with a phenomenon called drift. When the wind tunnel is operated for a long amount of time, certain variables are constantly changing, such as the temperature, pressure, humidity, etc. This means that even though the mechanical scales are zeroed at the beginning of the experiment, they will not necessarily return to zero at the end. The values they end at are the drifted values. In the present experiment, the drift values that were obtained are as follows. Tail configuration Measured quantity η=1 o η=-3 o Tail-off Lift Drag Pitching moment Table 11: Drift values for the various tail configurations Conclusion This experiment has successfully allowed for measurements to be taken accurately on an aircraft model in a wind tunnel and then reduce the data into relevant quantities that would allow for the determination of various parameters relating to the longitudinal static stability. The obtained quantities were compared with reference values [3], however, they did not compare very well with percentage differences as high as 35.6%. Several reasons for this discrepancy were given, but the major ones were a highly different Reynolds number and a different geometry regarding engine nacelles. 11 P a g e

12 Ideally, this experiment could be repeated with the same geometry and Reynolds number but this would be impractical so the current values should suffice to give a rough comparison to the reference experiment. Longitudinal static stability is a very important aspect of flight dynamics and so wind tunnel testing is a great tool to assist engineers to understand the mechanics behind the mathematics. Appendix No Tail Incidence (Deg) Pressure (inhg) Temp Betz (mmh2o) Lift (lbf) Drag (lbf) Pitch (lbf.ft) Tail +1 o Tail -3 o Table 12: Raw data from wind tunnel measurements 12 P a g e

13 References [1] Lab handout. Wind Tunnel Measurements on an Aeroplane Model. [2] Anderson, J. D., Jr (2011). Fundamentals of Aerodynamics. 5th ed. Singapore: McGraw- Hill. p503. [3] Irving, F. G. Determination of Stick-fixed Static Margin 13 P a g e