Numerical Analysis of the Flow Around an Airfoil with Serrated Trailing Edge
Using Dynamic Mode Decomposition
N. Thomareis, G. Papadakis
Department of Aeronautics, Imperial College London
Dynamic mode decomposition (DMD) is applied to the flow field over a NACA 0012 airfoil at Re=50,000 and 5o angle of attack. The
DMD method decouples the spatial and temporal behaviour of the flow dynamics, and allows the detailed study of the effect of different
trailing edges on the flow. The analysis is initially performed on a simple 2D case in order to assess the behaviour of the method, and
then in three different 3D cases, one with a straight trailing edge, one with a truncated trailing edge and one with triangular serrations.
The insertion of the serrations was found to attenuate the shedding from the exposed blunt part by decorrelating the spanwise coherence
of the vortices. This has a direct impact on the lift and drag coefficients of the serrated airfoil, both of which show a significant reduction
of fluctuations, and a reduction in the mean value of the drag coefficient, as compared to the blunt trailing edge airfoil.
1.Introduction
Performance improvement of lifting devices has always been a challenge for the aerospace industry. Early investigations showed a
potential improvement of the maximum lift coefficient with a simple truncation of the rear part of the airfoil, albeit with an increase in the drag
due to the exposed bluntness and a Karman vortex shedding [1]. More recent investigations have demonstrated additional benefits of the flatback
airfoil profile, both experimentally and numerically [2]-[4] , such as increased lift curve slope, optimized structural characteristics and decreased
sensitivity to leading-edge transition, which is important in low to medium Reynolds numbers applications such as unmanned air vehicles or
wind turbine blades. Despite the aforementioned improvements in certain aerodynamic characteristics, the adverse effect of the exposed blunt
part of the airfoil, that leads to increased pressure drag due to shedding, is severe. Several researchers have tried to identify ways by which to
mitigate this effect while maintaining the beneficial ones. Tanner et al.[5] used M-shaped serrations at the trailing edge of a blunt profile and
found a decrease in the base pressure of up to 64% compared to the straight blunt trailing edge. A more recent work by Krentel et al.[8] on a
truncated NACA 0012 airfoil using various geometrical patterns, showed a decrease in the drag by 29% for a specific Reynolds number
(44,000). The latest study in this area by Nedic et al.[9] has shown that the effect of serrated trailing edges can be further improved by adding a
self-similar repeating pattern in smaller scales (multiscale pattern). It was shown that the single scale triangular serrations reduced the intensity
of vortex shedding and improved the lift-to-drag ratio for higher angles of attack, and that the addition of a multiscale pattern reduced even more
the shedding energy without affecting the improved aerodynamic characteristics.
2.Simulated Airfoils
A standard NACA 0012 airfoil and two modified airfoils (one with a truncated and one with a serrated trailing edge) were simulated.
The blunt trailing edge airfoil is formed by truncating the original NACA 0012 airfoil at a distance δx = 0.133C from the trailing edge, thus
exposing a bluntness of approximately 0.037C. The airfoil with the serrated trailing edge geometry is formed by cutting inside the airfoil,
exposing a blunt part in their troughs which tappers towards the peak. The maximum bluntness is set equal to the bluntness of the flatback
airfoil.
3.Results
The dynamic mode decomposition method works by extracting the dominant spatial modes of the flow field and the corresponding
temporal frequency (Schmid [10]). We initially applied the DMD method in a simple 2D case which shows a strong and well defined shedding.
The temporal frequencies for each mode were compared with the frequency content of velocity signals probed at the near wake of the airfoil. In
Figure (1) the first four dominant modes are shown. Figure (2) demonstrates that the frequencies computed from the DMD (a) and Fourier
analysis (b) match. The eigenvalue of 0th mode (corresponding to the time-average flow) is located on the real axis since its frequency
(imaginary part) is zero. The other frequencies correspond to the shedding and its harmonics.
The method was then applied to 3D cases and was able to identify the dominant structures. For the straight trailing edge the flow is
characterized by the shedding of the separated shear layer (Figure (3)). In addition to the shear layer shedding (Fig. 4b), the flatback airfoil
shows highly energetic shedding from the exposed blunt part (Fig. 4a). In Figure (5) the DMD spectra of all three 3D cases are plotted together.
It can be observed that by inserting the triangular serrations the shedding peak is attenuated by almost 20%. The spatial structure of the dominant
modes corroborates this observation with no apparent shedding originating from the trailing edge despite an exposed blunt part at the troughs
(Figure 6). This has a direct implication on the level of fluctuations of the forces exerted on the wing, whose RMS value was reduced by 56%
and in the base pressure drag which was reduced by approximately 15% (compared to the flatback airfoil).
4.References
[1] Smith, H.A., Schaefer R.F., ”Aerodynamic Characteristics at Reynolds Numbers of 3.0 · 106 and 6.0 · 106 of Three Airfoil Sections Formed by Cutting Off
Various Amounts from the Rear Portion of the NACA 0012 Airfoil Section”, NACA Technical Note, NACA TN 2074, 1950
[2] Standish, K.J., Van Dam, C.P., ”Aerodynamic Analysis of Blunt Trailing Edge Airfoils”, Journal of Solar Energy Engineering, Vol. 125(4), 2003, pp. 479-487.
[3] Baker, J.P., Mayda, E.A., Van Dam C.P., ”Experimental Analysis of Thick Blunt Trailing-Edge Wind Turbine Airfoils”, Journal of Solar Energy Engineering,
Vol. 128(4), 2006, pp. 422-431.
[4] Xu, H., Shen, W., Zhu, W., Yang, H., Liu, C., ”Aerodynamic Analysis of Trailing Edge Enlarged Wind Turbine Airfoils”,Journal of Physics: Conference Series,
Vol. 524 No.1 IOP Publishing, 2014
[5] Tanner M., ”A Methods for Reducing the Base Drag of Wings with Blunt Trailing Edge.”, Aeronautical Quarterly, Vol. 23, 1972, pp. 15-23
[8] Krentel, D., Nitsche W., ”Investigation of the Near and Far Wake of a Bluff Airfoil Model with Trailing Edge Modifications Using Time-Resolved Particle
Image Velocimetry”, Experiments in Fluids, Vol. 54.7, 2013, pp. 1-16.
[9] Nedi´c, J., Vassilicos, J.C., ”Vortex Shedding and Aerodynamic Performance of an Airfoil with Multiscale Trailing Edge Modifications”, AIAA Journal (to be
published).
[10]Schmid, P.J., ”Dynamic Mode Decomposition of Numerical and Experimental Data”, Journal of Fluid Mechanics, Vol. 656, 2010, pp. 5-28
Figure 1: Spatial structure of the first 4 dominant modes for the 2D case.
Figure 2: Eigenvalues of the DMD method (a) and power spectral density of the streamwise velocity component in the near wake (b).
Figure 3: 2nd dominant mode of the straight trailing edge case.
Figure 4: Dominant modes of the blunt trailing edge case. Figure (a) corresponds to the mode of the Karman -type
shedding while figure (b) to the shedding from the separated shear layer.
Figure 5: DMD spectra for all three 3D
cases. The peak located at approximately
St=0.4 corresponds to the shedding from the
blunt TE, and it can be seen that it greatly
attenuates in the serrated case, giving rise to
more broadband spectrum.
Figure 6: 2nd dominant mode for the serrated trailing edge case. The left figure corresponds to the trough location where the
bluntness takes its maximum value, while the right figure corresponds to the peak location.