Next, the FFD (Free-Form Deformation) file has to be generated in PLOT3D format. This file contains the coordinates of the FFD points around the airfoil. These are control points that are fitted to the airfoil using B-splines, which are used to deform the airfoil.
The coordinates for the NACA0012 airfoil are in the file
Navigate to the directory
airfoilopt/ffd in your tutorial folder.
Copy the airfoil data from
cp ../mesh/n0012.dat .
Create the following empty runscript in the current directory.
import numpy as np
airfoil = np.loadtxt("n0012.dat") npts = airfoil.shape nmid = (npts + 1) // 2
The following two functions are used to get the upper and lower points of the airfoil.
def getupper(xtemp): myairfoil = np.ones(npts) for i in range(nmid): myairfoil[i] = abs(airfoil[i, 0] - xtemp) myi = np.argmin(myairfoil) return airfoil[myi, 1] def getlower(xtemp): myairfoil = np.ones(npts) for i in range(nmid, npts): myairfoil[i] = abs(airfoil[i, 0] - xtemp) myi = np.argmin(myairfoil) return airfoil[myi, 1]
FFD Box Creation
The FFD box can now be set up.
nffd = 10 FFDbox = np.zeros((nffd, 2, 2, 3)) xslice = np.zeros(nffd) yupper = np.zeros(nffd) ylower = np.zeros(nffd) xmargin = 0.001 ymargin1 = 0.02 ymargin2 = 0.005 for i in range(nffd): xtemp = i * 1.0 / (nffd - 1.0) xslice[i] = -1.0 * xmargin + (1 + 2.0 * xmargin) * xtemp ymargin = ymargin1 + (ymargin2 - ymargin1) * xslice[i] yupper[i] = getupper(xslice[i]) + ymargin ylower[i] = getlower(xslice[i]) - ymargin
nffd signifies the number of chordwise slices.
we pre-allocate an array of generic size (a,b,c,3) to set up an empty FFD box. In this example, a=nffd (number of chordwise sections), b=c=2 (number of spanwise and thickness-wise sections respectively) and the final 3 is “fixed” as we are using 3D coordinates for each point
An empty FFD box is created.
ymargin specify the closest distance from the airfoil to place the FFD box.
ylower store the x- and y- coordinates of the control points for each slice along the chord, taking into account the margins from the airfoil.
# X FFDbox[:, 0, 0, 0] = xslice[:].copy() FFDbox[:, 1, 0, 0] = xslice[:].copy() # Y # lower FFDbox[:, 0, 0, 1] = ylower[:].copy() # upper FFDbox[:, 1, 0, 1] = yupper[:].copy() # copy FFDbox[:, :, 1, :] = FFDbox[:, :, 0, :].copy() # Z FFDbox[:, :, 0, 2] = 0.0 # Z FFDbox[:, :, 1, 2] = 1.0
The x- and y- coordinates are transferred to the
Since the airfoil slices are the same along the z-direction, the x- and y- coordinates are copied over.
The z-coordinates are updated to 0 and 1.
Writing to File
with open("ffd.xyz", "w") as f: f.write("1\n") f.write(str(nffd) + " 2 2\n") for ell in range(3): for k in range(2): for j in range(2): for i in range(nffd): f.write("%.15f " % (FFDbox[i, j, k, ell])) f.write("\n")
Run it yourself!
You can now run the python file with the command:
The above script writes the FFD coordinates to a PLOT3D
.xyz file, which will be used for optimization.