ENGINEERING AND CFD

Recently there has been a large push in the aircraft industry to reduce its carbon footprint. Laminar flow control and Natural Laminar Flow (NLF) wing design have been proposed as one of the main options for reducing the drag on the airplane and hence its fuel consumption. One of the important aspects of aircraft design concerns dynamic stability and an understanding of the unsteady behavior of NLF airfoils is important for predicting the stability characteristics of the aircraft. Recent experimental studies on NLF airfoils have shown that their dynamic behavior differs from that of turbulent airfoils and that classical linearized models for unsteady airfoils fail to predict the unsteady behavior of NLF airfoils. Most notably, NLF airfoils exhibit non-linear aerodynamic responses to small-amplitude pitch oscillations whereas the classical theories predict only a linear response. In the current work we investigate the dynamics of pitching airfoils to understand the flow phenomenon which causes the breakdown of classical models, and also attempt to describe a new simplified model which takes into account the non-linearities observed in the NLF airfoils.

Introduction

Dynamic stability is an important concern for aircraft designers and the occurrence of an aeroelastic instability in mid-flight can have catastrophic consequences. For the prediction of such an instability early in the design process, simplified mathematical models are used which were laid down in the early 1930s in the works of [1], [2] etc. However, the effects of air transport on climate and global warming have forced the aerospace industry to consider alternate airfoil designs, called Natural Laminar Flow (NLF) airfoils, which have the potential to reduce the fuel consumption of commercial aircrafts and thereby lower the carbon footprint of the industry.

Recent experimental results at DLR [3] and KTH [4]  have shown that the classical unsteady models for the prediction of dynamic stability are no longer valid for these NLF airfoils. This failure of the classical models has been traced to the point of transition on the airfoil where flow changes state from laminar to turbulent. The flow state affects the point at which the flow separates from the airfoil which in turn affects the point of transition itself. Thus, these two boundary layer characteristics – point of transition and point of separation - are coupled and lead to new dynamic behavior in unsteady cases which is not modeled by the classical theories.

In this work we study the dynamic coupling between these boundary layer characteristics for unsteady airfoils with the aim to create an improved mathematical model to predict the aeroelastic stability characteristics of airfoils.

Methodology and Results

The dynamics of flow around airfoils depends on the Reynolds number (Re) which is a parameter defining the ratio of the largest to the smallest spatial scales in the flow. Commercial aircrafts fly at Reynolds numbers of the order of 10⁶-10⁷. On the other hand, aeroelastic instabilities typically exhibit long time scales. Computationally this becomes challenging since a large range of spatial scales must be simulated to get accurate predictions of boundary layer transition and separation, and the simulation must also evolve over long time scales for the relevant aeroelastic instabilities. In our work we numerically simulate a pitching wing at a Reynolds number of 750,000 which is very close to the Reynolds number range of high-altitude long-endurance aircraft. A high-order Spectral-Element Method code Nek5000 is used for the numerical simulation [5] and 1.4 x 10⁹ grid points were necessary to discretize the problem.

The time varying boundary layer transition and separation is tracked throughout the simulation. Figure 1 and Figure 2 show the instantaneous flow states at the minimum and maximum angles of attack.