Project Design Methods and Goals
Three main tools were used to design new airfoils: the Eppler and Somers design code20, the ISES code written by Drela and Giles21’22, and the wind tunnel described previously. The Eppler and Somers code formulates the design problem in a way that allows quick and easy manipulation of the airfoil shape. With a minimum number of parameters, almost any desired velocity distribution can be obtained. However, because this code does not accurately predict the performance of airfoils in the Reynolds number range considered here, it was used mainly to obtain the inviscid velocity distributions and to give an estimate of the transition point behavior.
The ISES code solves the two-dimensional Euler equations coupled with a momentum integral boundary layer formulation using a global Newton method. Over the Reynolds number range considered in this investigation, it predicts airfoil performance more accurately than the current version of the Eppler and Somers code. In particular, the agreement with the experiment at Reynolds numbers of 200k and greater is very good. However, the agreement depends on the choice of the n value used in the en transition criterion. While the ISES code provided a relatively good estimate of the performance, wind tunnel results were the ultimate test of an airfoil.
The design approach was to generate an airfoil with the desired inviscid velocity distribution using the Eppler. and Somers code, and then predict the performance at a Reynolds number of 200k using the ISES code. If the performance was poor, the new airfoil was redesigned and the process repeated. Upon reaching a suitable design through this iteration process, a wind tunnel model was built and tested. Based upon the wind tunnel results, the new airfoils were further refined and the process repeated.
Before discussing airfoil design, it should be pointed out that for any aircraft in straight and level flight the relation between C and chord Reynolds number is given by:
This relation emphasizes the fact that the Сд should be minimized for a value of Ci and the corresponding Rn. Thus, the optimum airfoil design is clearly dependent upon the configuration and desired tasks of the aircraft for which it is designed. The designs discussed below are based upon RC sailplane
configurations; however, the general principles apply to any type of low-Reynolds number aircraft.
A popular RC soaring, cross-country airfoil is the E374. It is commonly used on aircraft intended for high speeds, with relatively little importance placed on the performance at low speeds. The experimentally determined drag polars for this airfoil are shown in Figs. 12.24-12.29. This airfoil works well at high speeds because of the small values of the drag coefficient at the higher Reynolds numbers throughout a range of low C values. At lower Reynolds numbers, the drag increases dramatically as C moves from 0.0 to 0.5, and then decreases from 0.5 to 0.8. This behavior indicates the formation of a large laminar separation bubble on the upper surface.
The inviscid velocity distribution about the E374 for a Ci of 0.55 is shown in Fig. 4.1. A “kink” in the upper-surface velocity distribution beginning at 40% separates it into two distinct regions. Over the forward 40%, the velocity changes little, and the majority of recovery takes place over the aft 50% with a relatively strong adverse pressure gradient. At low Reynolds numbers, this pressure gradient results in a large laminar separation bubble. To reduce the drag, the pressure gradient should be reduced. However, if the same pressure differential is to be recovered, then the recovery region must start farther upstream, as shown by the dashed line in Fig. 4.1. This longer region of smaller adverse pressure gradient is termed a bubble ramp. Before this point is discussed further, it is important to observe the behavior of the transition point on the upper surface with increasing Ci.
As a result of the kink in the velocity distribution at 40% chord, the transition point moves rapidly forward with C as shown in Fig. 4.2. (Of course, transition does not occur at a point but rather over some finite distance.) In this case the point refers to the location at which transition was predicted to occur by the Eppler and Somers code using a method based on the boundary layer shape factor for Rn of 200,000. Knowledge of the shape of the transition-point curve is helpful when designing with the Eppler and Somers code because it is similar to the distribution of design parameters which specify the airfoil (a* with i/)20. In the “redesign” of the E374, the kink in the velocity distribution was removed to define a new airfoil—the SD6060. The resulting transition point behavior and velocity distribution are shown by the dashed lines in Figs. 4.1 and 4.2, respectively. Removing the kink shifted the transition point farther forward for Ci greater than 0.5. In this case, separation will occur earlier because of the steeper initial gradient, but with the transition point farther forward, the separation bubble will be shorter and the drag will be lower.
A comparison between the experimentally determined drag polars for the E374 and SD6060 is shown in Fig. 4.3. There has been a reduction in drag throughout the central portion of the polars for all Reynolds numbers because the bubble ramp has reduced the length of the separation bubble. (Some of this
reduction in drag is due to a thinning of the airfoil; the E374 is 10.9% thick and the SD6060 is 10.4% thick.) In addition to the decrease in drag in the central region, the increase in drag as Ci approaches 1.0 is more gradual in the case of the SD6060, which is consistent with the smoother forward movement of the transition point.
A further example illustrating the effectiveness of a bubble ramp in the upper – surface velocity distribution can be seen by comparing the E205 and the S302123. The E205 is usually used as a “multi-task” airfoil because of its relatively good performance at both high and low lift. This airfoil has an upper-surface velocity distribution which is similar to the E374 in that it also contains a kink. The velocity distribution of the S3021 is essentially the same as that of the E205 except the kink has been replaced with a bubble ramp as in the SD6060. Figure
4.4 shows a comparison between the drag polars of the E205 and S3021 at several Reynolds numbers. The differences are similar to those noted between the E374 and SD6060, that is, at all Reynolds numbers the drag of the S3G21 is lower than that of the E205 in the central region of the polars. However, at the highest Reynolds number (300k) the E205 has lower drag than the S3021 for Ci = 0.9. As discussed earlier, as the speed increases, the lift coefficient decreases so that for typical low Reynolds number configurations, at 300k the lift coefficient would be considerably less than 0.9. Thus, for low Reynolds number aircraft, the S3021 will perform better than the E205.
These examples illustrate that significant improvements can be made over existing designs by relatively minor changes in the velocity distributions (which, of course, directly alter the airfoil shape). Other airfoils, such as the SD70Q3, demonstrate that if sufficient attention is paid to the control of the bubble, it is possible to design entirely new, low Reynolds number airfoils that show little or no evidence of increased drag due to the bubble, even at 60k. What is not known at this "point is how far this design philosophy can be “pushed”. Even though improvements have already been demonstrated, the optimum shape and location of the ramp remain to be determined. Employing airfoils with bubble ramps on model aircraft will provide further insight into the benefits of this type of design and will help guide further study.
E205B-PT and S3021A-PT
и Rn = 100,000 – E205B-PT v Rn = 300,000 ^ Rn = 100,000 – S3021A-PT д Rn = 300,000