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Airfoil design

The glide ratio, or the ratio between the lift and the drag coefficient, is one of the most important aerodynamic characteristics of an airfoil. It represents the aerodynamic efficiency of the airfoil and affects aircraft’s flight performance values such as the maximum range or angle of a climb after take-off.

Challenge

The main goals for new airfoil design were to increase the glide ratio (efficiency) and decrease the sensitivity of airfoil’s aerodynamics to manufacturing tolerances and imperfections of its surface. Therefore, it was necessary to create a mathematical model describing dependencies between the glide ratio of the airfoil on its geometry.

The geometry was parameterized with a slightly modified PARSEC method. There were ten geometrical parameters in the task together with the Reynolds number describing flight conditions. Airfoil aerodynamics was analyzed in the panel method software Xfoil.

One computation in the Xfoil takes about 20 seconds; thus, this task was also suitable for validation of the mathematical model against the results of the Monte Carlo simulation. Result values interpolated from the metamodel were compared with the results of computations performed with the Xfoil.

Solution

In the beginning, we coupled the UptimAI tool with the panel method code Xfoil, with no need to interfere with its code or features. Then, the UptimAI tool began to set combinations of inputs for the Xfoil. It used the UptimAI algorithm to process computation results into the metamodel of the airfoil aerodynamics.

As shown in the UptimAI histogram and its probability density function, ranges of input parameters were set broad enough to conclude in the large variance of resulting values of the maximum glide ratio. It demonstrates possibilities of the chosen parameterization method and the capability of the Xfoil software to converge when solving aerodynamics of airfoils with multiple curvatures. A comparison of probability distribution of results, based on the glide ratio computed in Xfoil coincided well with the distribution of the modeled values of the maximum glide ratio, proving the accuracy of the metamodel. For the comparison, around  40,000 Xfoil computations were made in total with randomized values of input parameters (the Monte Carlo method). In contrast, the metamodel was created from only 161 Xfoil computations.

UptimAI sensitivity analysis showed the influence of each input parameter on the maximum glide ratio. It confirmed the major effect of inputs describing the upper surface of the airfoil, especially its maximum thickness. On the other hand, the influence of the trailing edge taper was lower than expected, but this could be a result of the defined range of this input parameter. The leading edge radius of the upper surface did not affect the glide ratio either.

Then, direct response of the maximum value of the glide ratio to changes in each of the influential inputs was examined using the UptimAI increment plot. The shape of these functions was key to the airfoil design. This can be demonstrated on the position of the maximum thickness on the airfoil’s upper surface. For this input parameter, the range of values could be identified with a low response in result values as well as the region with a steep gradient of the output. For the first range, the glide ratio becomes insensitive to surface imperfections. The second one leads to significant aerodynamic improvements, only when the manufacturing of the airfoil is flawless.

Benefits

  • Deeper insight into the statistical effect on the airfoil aerodynamics.
  • Increase in the average value of the glide ratio from 113 to 166. All of the newly designed airfoils have a maximum glide ratio higher than 125.
  • Validation of the metamodel – probability distribution of interpolates results coincide with results computed in Xfoil.



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