Stepwise Discontinuity problem

Alan Kang

I have analysis NACA23012 using FEM fortran software where there is a stepwise discontinuity on upper surface of the NACA23012. We find that the coefficient of pressure of the cut surface is lower compared to the basic airfoil of NACA23012. Why this will happen when the upper surface is being cut on 50%chord and 50% depth? Besides, we have analysis also that the stepwise discontinuity of NACA23012 at 45% and 55%chord of the upper surface. From result, the 45%showed the best lift coefficient from others when the angle of attack is higher than 3 degree. Why the stepwise discontinuity at lower percent of chord having the better lift coefficient? What is the best percent of chord for stepwise discontinuity for NACA23012 so that the best lift coefficient can be obtained.

The mesh we used is using triangular element and the domain or the boundary is for x direction is 20 times chord length and for y direction is 100 times maximum thickness of the airfoil. This airfoil is analysed by solving the equation of stream function and the equation of Bernoulli equation is also applied to calculate the lift coefficient. This analysis is for airfoil in inviscid flow. The following result is what we get for different percent of stepwise discontinuity for the lift coefficient:

0deg 3deg 5deg 8deg 10deg 50% 0.14 0.28 0.46 1.15 1.38 45% 0.03 0.33 0.56 1.31 1.85 55% -0.13 0.15 0.38 0.94 1.15 basic -0.2 0.06 0.33 0.76 0.98