About the effect of turbulence on the performance of airfoils and the selection of the critical amplification factor for simulations

One of the scientific targets for the LEMFEV, our Martian UAV, can be the Martian planetary boundary layer.

The planetary boundary layer is usually defined as the layer of the atmosphere where the influence of friction, mechanical mixing, and thermal effects rising from the surface of the planet is significant (Ravi, 2012). Turbulence within the planetary boundary layer is characterized in terms of its intensity and integral length scale. The turbulence intensity quantifies the turbulent energy within the flow and is the ratio between the standard deviation and mean of the oncoming flow velocity.

The integral length scale characterizes the turbulent energy magnitude at each frequency through a measure of the average size of the largest turbulent eddy present within the flow.

On Earth, the turbulence intensities in urban terrain typically reach up to 10–20%, while integral length scales range from less than a meter to many tens of meters (Ravi, 2012).

Due to dusty flows with a transverse velocity gradient, the entire near-surface Martian atmosphere turns out to be highly turbulent (Petrosyan, 2011), with the turbulence intensity being as high as 20%.

If a UAV is much smaller compared with the integral length, the fluctuations induced by the largest eddies may be considered quasi-static changes in oncoming conditions with respect to the wing. Smaller-scale eddies and a reduced frequency of oscillation may have a larger influence on the airplane's aerodynamic performance. According to Herbst (Herbst, 2017), most influence is attributed to turbulent structures where the integral length scale is on the order of the wing chord.

As the turbulence intensity increases at low Reynolds numbers, the laminar bubble on the airfoil surface reduces in length, and the suction peak grows in absolute magnitude. According to Gopalarathnam (Gopalarathnam, 2003), this phenomenon closely resembles the effects obtained by increasing the chord Reynolds number.

Wind-tunnel tests revealed that turbulence has a considerably higher influence on the suction side as opposed to the pressure surface (Ravi, 2012). Also, it was sown that an increase in turbulence intensity from nominally smooth conditions to 7.8 % led to an increase in the maximum lift coefficient, a reduction in the lift curve slope, and a delay in stall. This phenomenon was attributed to the cambering effect of the leading-edge vortex, which weakens with increasing turbulence intensity.

To my best knowledge, the highest turbulence intensity modeled in wind tunnel tests with wings is 10% (these are the tests conducted by Ravi (Ravi, 2012)), which is much lower than the turbulence intensity expected to exist in the Martian planetary boundary layer (20%). Therefore, we can only extrapolate the trends for the variation of aerodynamic performance of wings with turbulent intensity from the available data.

In our effort to automatically select a proper airfoil for various configurations of the LEMFEV, we use XFOIL, where the only parameter that can be set to adjust the turbulence intensity is the critical amplification factor. By default, it is set to 9, which corresponds to a low-turbulence condition. For a high-turbulence condition, it can be set to be less than 1. In our studies, to take into account the high-turbulence Martian atmosphere, we use the amplification factor of 0.24 (for a rocket-engine single-flight version of the UAV) calculated for the known turbulence intensity using equations from Drela (Drela, 1998).