The CFD database for most of the cases were built using the HMB Time Marching method. However, the Harmonic Balance method was used for the BERP rotor case because of its much faster clock time in obtaining high-fidelity results. The HB method used was able to obtain a snapshot at every 10 degrees of azimuth. The only limitation was the memory required. With higher number of modes and higher grid resolution, the memory increases rapidly, hence, for the same number of snapshots as in the TM method, which requires a set number of modes and for a limited amount of memory, the grid resolution is sometimes reduced. Nevertheless, the results obtained were shown to be very similar to that obtained by time marching and any change in values was relative resulting in the same outcome.
The metamodel of choice was mostly the ANN and in some cases, the kriging method. These two methods were most popular because of their ability to model the design space accurately without overfitting or underfitting the data with changes in their parameters. Metamodels were checked aposteriori against HMB solutions. The optimiser developed was a GA. While a number of different evolutionary techniques could have been used, such as Simulated Annealing, Particle Swarm etc., from the literature, GAs are one of the most successful techniques in terms of im- plementation, ability to find the global optimum and relative efficiency. Within the objectives of this project, it performed well. Future work will include testing it against other non-gradient techniques.
The parameterisation techniques used were dependent on each case. The choice of parameters and their values depended on the experience of the user, the objectives required and the initial design.
For example, in the case of the transonic aerofoil optimisation, the RAE 2822 aerofoil was parame- terised using Chebyshev polynomials. Six coefficients were required to define the shape. However, only the first three were optimised as they controlled the thickness, the camber and the position of maximum camber, which are known to significantly change the lift-to-drag ratio. The final design had more or less the same thickness and camber but with the camber pushed further backwards creating more favourable pressure gradients.
For the wing, the parameters were simply the chord length and position at two spanwise sta- tions and the position of the tip. This effectively controlled the sweep and taper of the wing and
the objective was to obtain as close to elliptic loading as possible. The final design removed the forward sweep of the full wing, tapered the end a bit more and maintained the backward sweep at the tip. This reduced the loading more outboards which resulted in a lift distribution closer to an elliptic distribution due.
For the rotor section optimisation, a parameterisation technique already existed since NACA aerofoils were used. Again, the important characteristics chosen were the thickness and camber of the aerofoils. The optimum selection was for thick, cambered aerofoils, such as the NACA 33015, inboard of the rotor (r/R = 0.5) and thinner (9% thickness), more symmetrical (9% camber) aerofoils, outboards (r/R = 0.9). This is a well-known and tested theory since inboards the Mach number is slower therefore thicker aerofoils can be used. High camber is also advantageous because of the high angles of attack experienced inboard due to the twist of the blade. Outboards, the flow is more compressible and so the optimum tends to avoid shock effects. This case was a good case to use as a starting point to develop the optimisation method since the results expected were more or less known.
Similarly for the hovering rotor, high twist is expected to be the optimum for obtaining good Figure of Merit (FM). The compromise was between obtaining a high single point FM or a lower FM but for a bigger range of thrust. The optimum selected had 11 degrees of twist, which was less than the maximum twist tested of 12 degrees, showing that a wide design space was selected. The optimum also removed stall from the tip when compared to the untwisted blade.
For the UH60-A and the BERP-like rotors, twist as well as anhedral were optimised in hover. In both cases, however, forward flight was the main condition optimised for since this is the main condition that these rotors were designed for. Hover performance was then improved or constrained. In the UH60-A case, the parameters, sweep and anhedral were first optimised for forward flight, then the new design was tested in hover and found to maintain good performance. Nevertheless, twist was optimised for hover as well, and found to be approximately the same as the original rotors hover. Much more anhedral was added to the tip (11 degrees) which helped reduce the drop in moment on the advancing side which reduced the overall average moment. The sweep was slightly reduced (14.5%) since not as much of it was required as the anhedral off-loaded the tip of the rotor.
For the BERP-like rotor, a simulation of a typical fast flying, moderate thrust rectangular ro- tor with sweep was the baseline point. This planform was converted to a BERP-like tip using a parameterisation technique that used parabolic and sigmoidal curves. Using this technique, three important features of the BERP-like tip could be captured viz. the sweep, the notch gradient and the notch position. However, this baseline BERP-like tip had a lower performance in hover. Therefore, the twist and anhedral were first optimised in hover to obtain the same performance of the original rectangular swept rotor. More anhedral was added to offload the tip and a higher twist was added to regain the load more inboards. Once this blade was obtained, the planform was then optimised for forward flight. The parameter that had the biggest effect in load distribution was the sweep. The position of the notch had an effect on the peak-to-peak pitching moment and average moment. It also amplifies the effect of the BERP-like part of the blade since a more inboard notch means a larger BERP-like tip i.e. a lower rise in torque, a bigger rise in moment and so on. The notch gradient has a smaller effect on the performance, although a higher notch gradient reduces the torque slightly.
Overall, the optimum selection was a highly swept tip, with a high notch gradient and the ini- tiation of the notch in between the two extremes. The reason for this was because its average pitching moment was very close to zero. Torque and peak-to-peak did not change much with notch position. Peak-to-peak moment was mainly affected by the sweep, where lower sweep was preferable. However, the effect was not large compared to the gain in average moment with higher sweep. A higher notch gradient also favoured a large decrease in the average moment. This rotor
was then tested in hover and maintained good hover performance over a range of thrust. In terms of the parameters used in Chapter 10, the optimum had a sweep of 0.21 (same as the baseline), a notch gradient of 35 (40% higher than the baseline) and a notch position of 11.75 (about 2% more inboards).
A further case that was run, was the JMRTS fuselage. The objective was to optimise the wind screen gradient for drag. Therefore, the parameters were linked to a single value that controlled this gradient. The automation of the grid generation part made it easy to modify this parameter and obtain results quickly. The final design was the one that had the least gradient, which was approximately 24% less than the baseline in terms of the parameterisation coefficient. This case was mainly performed for the parameterisation part for future work.
Overall, the method works well in fine-tuning parameters for improved aerodynamic performance efficiently. Some understanding of rotor design is still necessary and the aim was not to replace, but assist the designer in obtaining optimal designs. There is still much work that can be carried out for this endeavour as described below.