Airfoil Simulation – Plotting lift and drag coefficients of an airfoil at different angles of attack

Airfoils are specifically designed structures that generate lift force when air flows over it. This has led to a whole new branch in the field of mechanical engineering and has allowed us to explore the atmosphere and space. when an airfoil travels through air, lift is produced.  Simultaneously, the flow of air over the body also generates a resistance called drag. To calculate the lift and drag forces acting on a body, we use certain aerodynamic numbers called as lift and drag coefficients.

In this project here, we are going to simulate airflow over an airfoil and calculate the lift and drag coefficients generated for different angles of attack.

 

Objective

The objective here is to simulate an airfoil and calculate drag co-efficient and Lift Co-efficient at different angle of attacks (0⁰, 5⁰, 10⁰and 15⁰) to compare the drag co-efficient and lift co-efficient for all angles of attacks.

 

Steps to be done

• Understand the theory behind drag force and lift force
• Derive the formula to calculate drag co-efficient and lift co-efficient.
• Build geometry for an airfoil in CAD software.
• Set up steady-state simulation and transient state simulation
• Calculate drag co-efficient and lift co-efficient and make plots from the post-processed data.

 

Formulas Used

Formula for calculating drag co-efficient and lift co-efficient

• Formula for Drag Co-efficient:

Where Fd is the Pressure force along X-direction (Px)

• Formula for Lift Co-efficient:

Where Fl is the Pressure force along Y-direction (Py)

• Dynamic Pressure:

 

 

Formula used to simulate airflow:

• Formula for Reynolds’s Number:

• Formula for flow-through time (used to calculate end time in transient flow simulation):

 

Deriving the Drag & Lift Coefficients

When an airfoil is subjected to airflow, the front section and the bottom section of the airfoil encounters most of the flow.

• While calculating Drag Coefficient, we should take an area as observed from Front View since drag force affects this section the most.
• While calculating Lift Coefficient, we should take an area as observed from Bottom View since lift force acts in that direction.

 

When you observe the front view and the bottom view, you will see a rectangular structure like this:

 

 

Calculating Drag Coefficient:

To calculate the Drag Coefficient, we use the formula mentioned above:

 

Since CONVERGE always calculates force per unit length (for 2D case), the formula can be re-written as:

[Fd/L is the force per unit length, as calculated by CONVERGE, we multiply L with the factor Fd/L so that the force can be calculated in Newton]

With reference to Figure 1, we can substitute the area as the multiplication of length and height of the rectangular structure:

Since we are calculating the drag force for only a unit length,

Hence, we can re-write the formula as

 

Calculating Lift coefficient

To calculate the Lift Coefficient, we use the formula mentioned above:

Since Converge always calculates force per unit length (for 2D case), the formula can be re-written as:

[ FL/L is the force per unit length, as calculated by CONVERGE, we multiply L with the factor FL/L  so that the force can be calculated in Newton]

With reference to Figure 1, we can substitute the area as the multiplication of length and height of the rectangular structure:

 

Since we are calculating the lift force for only a unit length,

 

Hence, we can re-write the formula as

 

 

Simulating the Airfoil

Software used: CONVERGE CFD

We can now create the geometry for the airfoil. The dimensions of the airfoil by enabling the bounding box in CONVERGE STUDIO, like shown in the below image. the bounding box is used to determine the dimensions of any geometry. Then, the geometry must be imported into CONVERGE STUDIO as a .stl file. It is then diagnosed for errors like intersection errors or open edges or non-manifold edges.

 

 

The case is then set up for steady-state and transient simulation.

 

Result Discussion:

Steady-State Simulation results:

In practical situations, a steady-state does not occur as there is always turbulence present. However, we still simulate steady flow since we always take an industrial approach to any problem. The result obtained is as follows:

 

 

As you can see in the result above, the solution converged for the first 15000 cycles and then blew up due to excessive errors. This scenario is impracticable in real life. When we post-process the data into ParaView to visualize the scenario. You can watch the results in the video here. At the ninth second, you will see that the flow turned spontaneous and irregular:

 

  

 

Plotting Angles of Attack Vs Drag Coefficient (Steady State):

 

 

Plotting Angles of Attack Vs Lift Coefficient (Steady State):

 

Transient State Simulation results:

On simulating transient airflow over the airfoil in CONVERGE, the results appeared to converge at 2 seconds.

The result was averaged for the last 0.5 seconds for simplification purposes:

 

On extracting this result to ParaView, the flow was visualized as shown below. As you can see, the fluctuation in the pressure and velocity was great when the AoA was increased. It also gave rise to a flow separation region (colored in blue) that caused a drop in static pressure.

 

 

 

Plotting Angles of Attack Vs Drag Coefficient (Transient State)

 

Plotting Angles of Attack Vs Lift Coefficient (Transient State)

 

Conclusion:

• In steady-state simulation, we observed that the values for Drag force (Px) and Lift force (Py) are fluctuating a lot and are not getting converged at the end of the steady-state simulation. Hence, there is a need to perform transient state simulation of the same airfoil.
• In the Transient state simulation, values for Drag force and Lift force are getting converged. In fact, those values are getting converged quite before the end time of the simulation. Hence we can decrease the value for an end time for the transient simulation.

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