Buffeting of an airfoil in transonic flow

As part of my Computational Fluid Dynamics (CFD) class at Purdue, I collaborated with three colleagues to conduct an investigation utilizing Ansys for turbulent flow analysis on a NACA 0012 airfoil. Our specific focus was on the airfoil's behavior under transonic flow conditions. The study revealed the emergence of shock waves during transonic flow, leading to noticeable fluctuations in lift values.

This phenomenon was found to be particularly prevalent within a specific angle of attack window, approximately ranging from 3.5 to 5.5 degrees. The induced shock wave introduced a consistent oscillation at a fixed frequency, directly impacting the lift coefficient (Cl) graph by introducing persistent fluctuations.

These research findings contribute significantly to our understanding of the dynamic response of the NACA 0012 airfoil under transonic conditions. The implications extend to aerodynamic performance considerations and design insights for real-life applications.

To initiate our research, we commenced by creating a two-dimensional sketch of a NACA 0012 symmetric airfoil with a chord length of 1 meter. Subsequently, we constructed a computational domain in the shape of a 'C' around the airfoil. The 'C' domain featured a radius of 35 meters, and the rectangular portion had a length of 70 meters. This design choice was informed by insights from prior research, indicating that the rear portion of the computational domain should be elongated to effectively account for vortices and wake effects. 

To create the mesh for the domain, we first determined the number of divisions and bias factors for the coarse grid. This involved utilizing an online y+ calculator and equations from our lectures. Using the online y+ calculator, we inputted the physical parameters and desired characteristics of the problem (as shown below) to obtain the estimated wall distance. Subsequently, this estimated wall distance, along with the domain length and a desired growth rate of 1.2, was used to determine the number of divisions using the provided equation (Calculation 1, Blaisdell, Lecture 6). Finally, the bias factor was calculated based on the growth rate and the number of divisions. An illustrative example of this calculation for the 'C' portion of the domain is provided below. 

Once the desired values were established, we proceeded to develop the coarse mesh within Ansys. For the 'C' portion of the domain each half consisted of 350 divisions with a bias factor of 10. The leading edge had larger divisions, while the trailing edge had smaller ones. This same approach was applied to the airfoil, divided into upper and lower halves. The bias factor was determined through trial and error to minimize skewness towards the trailing edge while maintaining a curved leading edge. It also aided in smoothing the transition from the 'C' portion to the rectangular portion.

The number of divisions was primarily determined through trial and error to strike a balance between achieving high accuracy and avoiding a drastic increase in computational time. The skewness of our mesh was kept reasonably low, with an average around 0.224 and the majority of nodes exhibiting skewness under 0.3. This was considered within acceptable tolerance levels for our simulation.

The straight vertical and frontal lines of the domain (Index 2 in Figure 2) had 85 divisions and a bias factor of about 4.48e+6 which were found using a y+ calculator and the method detailed previously. This led to a y+ value of less than 0.5 along the airfoil which is within the tolerance of less than 1.

The computational settings employed for our simulation are outlined below: 

The results for each test case are captured below: 

3.5 Angle of attack: No Buffeting observed

4.0 Angle of attack: Buffeting observed

5.5 Angle of Attack: Initial buffeting that dies out

To Conclude, in our comprehensive testing, we conducted three main cases utilizing both coarse and fine grids. Throughout these cases, we maintained consistent physical parameters and computational methods, with the variation lying in the angle of attack of the airfoil. Specifically, we investigated angles of 3.5°, 4.0°, and 5.5°, while keeping the freestream Mach number at approximately 0.75.

Our findings revealed the formation and dissipation of shocks over the top of the airfoil, leading to oscillating lift values within this angle of attack range, commonly referred to as buffeting. Importantly, our observations align closely with previous research on this topic ("Balakumar, P., Prahladh Iyer, and Mujeeb R. Malik. 2023. Turbulence Simulations of Transonic Flows over an NACA-0012 Airfoil... AIAA SciTech Forum,") , validating the accuracy and reliability of our results.

Software skills: Ansys (Fluent)