# RCAIDE/Methods/Aerodynamics/Airfoil_Panel_Method/hess_smith.py
#
#
# Created: Dec 2023, M. Clarke
# Modified: Apr 2023, N. Nanjappa
# ----------------------------------------------------------------------------------------------------------------------
# IMPORT
# ----------------------------------------------------------------------------------------------------------------------
# RCAIDE imports
from .panel_geometry import panel_geometry
from .infl_coeff import infl_coeff
from .velocity_distribution import velocity_distribution
# pacakge imports
import numpy as np
from scipy.linalg import solve
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# hess_smith
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[docs]
def hess_smith(x_coord,y_coord,alpha,Re,npanel):
"""Computes the incompressible, inviscid flow over an airfoil of arbitrary shape using the Hess-Smith panel method.
Assumptions:
None
Source: "An introduction to theoretical and computational
aerodynamics", J. Moran, Wiley, 1984
Inputs
x - Vector of x coordinates of the surface [unitess]
y - Vector of y coordinates of the surface [unitess]
alpha - Airfoil angle of attack [radians]
npanel - Number of panels on the airfoil. The number of nodes [unitess]
is equal to npanel+1, and the ith panel goes from node
i to node i+1
Outputs
cl - Airfoil lift coefficient [unitless]
cd - Airfoil drag coefficient [unitless]
cm - Airfoil moment coefficient about the c/4 [unitless]
x_bar - Vector of x coordinates of the surface nodes [unitless]
y_bar - Vector of y coordinates of the surface nodes [unitless]
cp - Vector of coefficients of pressure at the nodes [unitless]
Properties Used:
N/A
"""
ncases = len(alpha[0,:])
ncpts = len(Re)
alpha_2d = np.repeat(alpha.T[np.newaxis,:, :], npanel, axis=0)
# generate panel geometry data for later use
l,st,ct,xbar,ybar,norm = panel_geometry(x_coord,y_coord,npanel,ncases,ncpts)
# compute matrix of aerodynamic influence coefficients
ainfl = infl_coeff(x_coord,y_coord,xbar,ybar,st,ct,npanel,ncases,ncpts) # ncases x ncpts x npanel+1 x npanel+1
# compute right hand side vector for the specified angle of attack
b_2d = np.zeros((npanel+1,ncases, ncpts))
b_2d[:-1,:,:] = st*np.cos(alpha_2d) - np.sin(alpha_2d)*ct
b_2d[-1,:,:] = -(ct[0,:,:]*np.cos(alpha_2d[-1,:,:]) + st[0,:,:]*np.sin(alpha_2d[-1,:,:]))-(ct[-1,:,:]*np.cos(alpha_2d[-1,:,:]) +st[-1,:,:]*np.sin(alpha_2d[-1,:,:]))
qg = np.zeros((npanel+1, ncases, ncpts))
for i in range(ncases):
for j in range(ncpts):
A = ainfl[i, j, :, :]
B = b_2d[:, i, j]
qg[:, i, j] = solve(A, B)
# compute the tangential velocity distribution at the midpoint of panels
vt = velocity_distribution(qg,x_coord,y_coord,xbar,ybar,st,ct,alpha_2d,npanel,ncases,ncpts)
return xbar,ybar,vt,norm
