We present you an example of flow past NACA0012 airfoil with experimental validation. In this example we will simulate the turbulent flow past the mentioned airfoil for the series of Reynolds numbers and several angles of attack. Simulations are carried out using our QuickerSim CFD Toolbox for MATLAB. The solver is Finite Element Method-based and steady.
In nature we deal with plenty of cases when the flow corresponds to Re = 40000 – 400 000. Such flight regime can be considered relevant for drones, RC aircraft or birds. Calculations are performed for Reynolds numbers 40 000, 80 000, 160 000 and 360 000 since we have a direct reference experimental results [2].
Turbulence in our problem is modeled with one-equation CITM (Constant Intensity Turbulence Model). It assumes constant turbulence intensity at the large distance from the airfoil whereas it can be computed in the boundary layer vicinity.
Calculations for two types of mesh have been compared. The basic mesh comprises 4771 nodes and 9542 elements. The second one is twice as dense with 9007 nodes and 18014 elements. Mesh is properly densed towards the airfoil. Additionally, basic input meshes are modified inside the script to apply elements of very low thickness in the boundary layer. For both types of meshes the results are very close, hence we conclude that the basic resolution is sufficient and the results are mesh-independent.
The structure of the code is very simple. To calculate all the variations of flow past an airfoil MATLAB requires just two for loops: one of them changes angles of attack depending on our desired range and point distribution. Notice that due to the symmetry of the profile ew investigate only non-negative angles. The second loop repeats procedure for the array of Reynolds numbers.
% Specify Reynolds number Re = [40000 80000 160000 360000]; % Specify range of angles of attack aoa_start = 0; aoa_finish = 10; % Specify number of angles between the limiting values and their distribution steps = 11; AOA = linspace(aoa_start, aoa_finish, steps);
Results generated by the code for 5° angle of attack and Re = 160 000 are presented below. They present just the zoomed-in region in the vicinity of the airfoil. Notice the obvious features of the aerodynamic flows, namely the presence of stagnation point just below the leading edge.
Flow past NACA 0012 at Re = 160 000 and 5-degree angle of attack- pressure distribution
Flow past NACA 0012 at Re = 160 000 and 5-degree angle of attack- velocity distribution
Results obtained by QuickerSim CFD Toolbox for MATLAB agree within uncertainty range with experimental values below some limiting value of angle of attack. In particular, uur code predicts almost linear relation between lift coefficient and angle of attack. It does not predict flow separation which appears for angles of attack increasing with Reynolds number increase. Experimental and simulation data for Reynolds numbers 40 000 and 160 000 can be compared in the figures below.
Variation of the lift coefficient with the angle of attack at Re=40 000. Notice that the experimental results show the flow separation. That is not seen in the CFD simulation, however.
Variation of the lift coefficient with the angle of attack at Re=160 000. Notice that the experimental results show the flow separation. It occurs at larger angle than in the case of Re=40 000
Although there are more advanced models available already (such as k-epsilon or k-omega), CITM model proves sufficiently accurate in this benchmark. More samples on the advanced models will be released very soon.
The script (with the basic mesh) will run properly in the Student Basic version and can be generated by a simple modification to our Tutorial 12. Apart from valdation purposes, it will serve as a great teaching and demonstration example for students.
For more information about CITM model please refer to the first bibliography position.
References:
- Van Driest, E.R., 1956, “On Turbulent Flow near a Wall,” J. Aero. Sci., Vol. 23, pp. 1007-1011
- Robert E. Sheldahl, Paul C. Klimas, Aerodynamic Characteristics of Seven Symmetrical Airfoil Sections Through 180-Degree Angle of Attack for Use in Aerodynamic Analysis of Vertical Axis Wind Turbines, Sandia Energy Reports 1981