Geometric Parametrization

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 n0012.dat.

Navigate to the directory airfoilopt/ffd in your tutorial folder. Copy the airfoil data from airfoilopt/mesh:

cp ../mesh/n0012.dat .

Create the following empty runscript in the current directory.


Import Packages

import numpy as np

Load Airfoil

airfoil = np.loadtxt("n0012.dat")
npts = airfoil.shape[0]
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.

xmargin and ymargin specify the closest distance from the airfoil to place the FFD box. xslice, yupper, and 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 FFDbox variable. 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("", "w") as f:
    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]))

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.


3D view of the FFD volumes


2D view of the FFD volume, together with the embedded airfoil