Lift and Drag

• Ivy Lewney and Spencer Goudswaard; Spring 2021

Introduction

This lab was split into two sections: starting vortices in water, and lift and drag in a wind tunnel. Both of the experiments look at the characteristics of an airfoil in a fluid.

Starting Vortex

The amount of circulation held by an airfoil determines the location of stagnation points where the oncoming stream attaches to and separates from the airfoil’s surface. When the air foil begins to move, the lower surface fluid moves towards the stagnation point on the upper surface. When the fluid reaches the trailing edge it begins curling around. However, for an airfoil with a sharp trailing edge, the kinetic energy of the fluid will not be enough to fully curl around the edge. Instead the fluid will separate with a certain amount of circulation. This separated circulation is what causes the starting vortex. Eventually, this curling motion generates enough circulation at the trailing edge to move the stagnation point to the tip of the trailing edge. Once the stagnation point is at the trailing edge, the fluid moving along the lower side can separate without curling. This means the airfoil no longer generates circulation at the trailing edge and is the reason why there is not a continuation of vortices in the wake of the airfoil. However, changes to the velocity or angle of attack during the movement also create starting vortices.

The net circulation of the fluid in a closed system of inviscid flow must remain constant according to Kelvin’s circulation theorem. Since the airfoil generates circulation around its trailing edge, there must be an equal and opposite circulation to keep the net circulation constant. This opposite signed circulation is called a starting vortex and is formed near the airfoil’s starting location. When the airfoil stops moving it will also create a stopping vortex that is equal and opposite to the starting vortex.

Lift and Drag, Angle of Attack

For this portion of the lab we observed the responses of streamlines over an airfoil with varying levels of attack, and briefly touched on the equations governing the lift and drag of airfoils travelling through a fluid.

Lift and Drag

The superposition of a translational flow and a rotating flow over an airfoil can be described with the Kutta–Zhukhovsky Lift Theorem, where the lift in a steady irrotational flow can be described as: $𝐋 = 𝝆𝐔𝚪$, with $\rho$ and $𝐔$ being the flows respective density and velocity, and 𝚪 is the circulation about the airfoil, given by 𝚪 = ∲𝐔 · 𝑑𝑆 This shows that ideally, the lift of an airfoil is proportional to the velocity of the fluid squared, 𝐋∝𝐔². The Kutta-Zhukovsky theorem, although written for an ideal fluid, can be used to estimate the lift of an airfoil in real-life applications. However, drag in this ideal flow should be zero, which we know not to be true in real-life estimations.

Angle of Attack

In further derivations of the Kutta-Zhukovsky theorem, we can find the relation between attack angle and lift with the lift coefficient 𝐂𝐋 which for a Zhukhovsky airfoil is given by: $𝐂_𝐋 = L(\frac{1}{2}\rho U^2c)^{-1} \approx 2\pi(\alpha + \beta)$ , where $\alpha$ is the angle of attack, and β is the angle at which lift is zero.

This equation shows a linear relationship between $𝐂_L$ and $\alpha$ for the idealized airfoil, and this linear relationship is shown for real applications as well. For non-ideal scenarios, there is an additional aspect that we must consider in this relationship, and that is the critical angle of the airfoil. If the angle of attack exceeds this critical angle, the stagnation point of the flow has travelled up to the leading edge of the foil, and the steep adverse pressure gradient on the upper surface of the airfoil leads the boundary layer (and thus the flow) to separate. This separation causes a sudden drop in lift, and is known as a stall.

For this experiment, we seek to demonstrate the reaction of our stream with varying the angle of attack, and achieve this stall in our foil.

Procedure

Starting Vortex

An airfoil is placed in a tub of water which has less depth than the airfoil. A few drops of ink are placed at the trailing edge of the airfoil. The airfoil is then pulled forward through the water. The steps are repeated with different angles of attack.

Angle of Attack

A wind tunnel was constructed to allow for the airfoil placed in the stream could vary in angle of attack. One thing to note about the construction of the wind tunnel is the importance of the “flow straightener”: a honeycomb of short cylinders to minimize the turbulence of the airflow into the tunnel (in this case, straws). A diagram of the constructed windtunnel can be seen below. The airfoil was placed into the streamline, and recorded to demonstrate the response of the flow with zero attack angle. Then, without disturbing the flow, the airfoil’s angle of attack was increased by pressing down on the trailing edge, until stall was achieved. This was demonstrated twice, then a negative angle of attack was demonstrated to show the flow’s response over the top of the foil.

Results

Starting Vortex

The starting vortex was very visible. Above an approximately 5 degree angle of attack the vortex rotated in a clockwise direction and rotated in a counter clockwise direction below 5 degrees. In addition, there were no noticeable changes in the size of the vortex as the angle of attack was varied.

Angle of Attack

For the initial observation of the foil in the tunnel, we could see a clear “sticking” of the streamlines to the outer edge of the airfoil, showing there was some type of boundary layer formation around the foil.

When varying the angle of attack, we can see the boundary layer separation moving up towards the leading edge of the foil, until the foil reaches the critical angle, and a stall is achieved. The separation of the flow is clearly demonstrated, as well as the backflow of the streamlines in response to the pressure gradient on the upper surface of the foil.

Discussion

Starting Vortex

Unfortunately, in this experiment we weren't able to hold the initial acceleration constant. Ideally, we would be able to keep the acceleration constant and also observe the change in vortex size as the acceleration is varied. As well, there are several models of airfoils that exist and their starting vortex characteristics could be studied. Another phenomena that could be observed during this experiment is a stopping vortex. Dropping ink in the region where the airfoil stops should show the formation of the stopping vortex.

4.2 Angle of Attack

Although the response of the streamlines were demonstrated well, ideally for this experiment we would be able to measure lift and drag with varying attack angles, specifically for observing the drop in lift once a stall had been achieved.

Another improvement to the lab could be in the construction of the airfoil used in the windtunnel. As cool steam was used as the tracer for the airflow, water collected quickly on the surface of the airfoil, and that in combination with the irregular surface induced very low boundary layer control. This lack of boundary layer control aided in achieving a stall, but it would be interesting to see how a flow reacts over a more ideal foil.