def __init__(self, OC, surrogate_model, relative_thickness=.12, camber=0., Sref=1., Lref=1., sweep=0., surrogate_fcs=None):
Airfoil.__init__(self, OC, Sref, Lref, relative_thickness, sweep, camber)
if not surrogate_fcs:
self.__coefs = SurrogateCoefs(surrogate_model)
else:
self.__coefs = surrogate_fcs
self.__surrogate_model = surrogate_model
def __init__(self,
OC,
surrogate_model,
relative_thickness=.12,
camber=0.,
Sref=1.,
Lref=1.,
sweep=0.,
surrogate_fcs=None):
Airfoil.__init__(self, OC, Sref, Lref, relative_thickness, sweep,
camber)
if not surrogate_fcs:
self.__coefs = SurrogateCoefs(surrogate_model)
else:
self.__coefs = surrogate_fcs
self.__surrogate_model = surrogate_model
class MetaAirfoil(Airfoil):
"""
A meta model based on 2D CFD data
Provide lift, drag and moment coefficients
Provide sensitivities of aerodynamic surrogate function w.r.t. input parameters
"""
POW_COS = 1.0
def __init__(self, OC, surrogate_model, relative_thickness=.12, camber=0., Sref=1., Lref=1., sweep=0., surrogate_fcs=None):
Airfoil.__init__(self, OC, Sref, Lref, relative_thickness, sweep, camber)
if not surrogate_fcs:
self.__coefs = SurrogateCoefs(surrogate_model)
else:
self.__coefs = surrogate_fcs
self.__surrogate_model = surrogate_model
def Cl(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal = Mach*np.cos(sweep)**self.POW_COS
ToC=self.get_rel_thick()/np.cos(sweep)*100.
Cl = self.__coefs.meta_Cl(ToC, self.get_camber(), alpha, Mach_normal)
sweep_corr = np.cos(self.get_sweep())**(2.*self.POW_COS)
return Cl*sweep_corr
def ClAlpha(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal= Mach*np.cos(sweep)**self.POW_COS
ToC=self.get_rel_thick()/np.cos(sweep)**self.POW_COS*100.
dCl_dAoA = self.__coefs.grad_Cl(ToC, self.get_camber(), alpha, Mach_normal)[2]
sweep_corr = np.cos(self.get_sweep())**(2.*self.POW_COS)
return dCl_dAoA*sweep_corr
def Cd(self, alpha, Mach):
Cdf = self.__Cd_friction(alpha, Mach)
Cdp = self.Cdp(alpha, Mach)
return Cdf + Cdp
def Cdp(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal= Mach*np.cos(sweep)**self.POW_COS
ToC=self.get_rel_thick()/np.cos(sweep)**self.POW_COS*100.
Cd = self.__coefs.meta_Cd(ToC, self.get_camber(), alpha, Mach_normal)
Cds = self.Cd_spurious(alpha, Mach)
Cdp = max([Cd-Cds, 0.])
return Cdp
def CdpAlpha(self, alpha, Mach):
Cdp = self.Cdp(alpha, Mach)
if Cdp == 0.:
dCdp_dAoA = 0.
else:
Cdsalpha = self.CdsAlpha(alpha, Mach)
sweep=self.get_sweep()
Mach_normal= Mach*np.cos(sweep)**self.POW_COS
ToC=self.get_rel_thick()/np.cos(sweep)**self.POW_COS*100.
dCdp_dAoA = self.__coefs.grad_Cd(ToC, self.get_camber(), alpha, Mach_normal)[2] - Cdsalpha
return dCdp_dAoA
def CdAlpha(self, alpha, Mach):
dCdp_dAoA = self.CdpAlpha(alpha, Mach)
dCdf_AoA = self.__dCd_friction_dAoA(alpha, Mach)
return dCdp_dAoA+dCdf_AoA
def Cm(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal= Mach*np.cos(sweep)**self.POW_COS
ToC=self.get_rel_thick()/np.cos(sweep)**self.POW_COS*100.
Cm = self.__coefs.meta_Cd(ToC, self.get_camber(), alpha, Mach_normal)
sweep_corr = np.cos(self.get_sweep())**(2.*self.POW_COS)
return Cm*sweep_corr
def dCl_dchi(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal = Mach*np.cos(sweep)**self.POW_COS
ToC=self.get_rel_thick()/np.cos(sweep)**self.POW_COS*100.
Cl = self.__coefs.meta_Cl(ToC, self.get_camber(), alpha, Mach_normal)
dsweep=self.get_sweep_grad()
sweep_corr = np.cos(self.get_sweep())**(2.*self.POW_COS)
dsweep_corr = -2.*self.POW_COS*np.sin(sweep)*dsweep*np.cos(sweep)**(2.*self.POW_COS-1.)
dCl_dToC= self.gradCl(alpha, Mach)[0]
dToC_dchi = 100.*(self.get_rel_thick_grad()*np.cos(sweep)**self.POW_COS+self.POW_COS*self.get_rel_thick()*np.sin(sweep)*dsweep*np.cos(sweep)**(self.POW_COS-1.))/np.cos(sweep)**(2*self.POW_COS)
dCl_dMach = self.gradCl(alpha, Mach)[3]
dMach_dchi = -self.POW_COS*Mach*np.sin(sweep)*dsweep*np.cos(sweep)**(self.POW_COS-1.)
return (dCl_dToC*dToC_dchi + dCl_dMach*dMach_dchi)*sweep_corr + Cl*dsweep_corr
def dCd_dchi(self, alpha, Mach):
dCdf_dchi = self.__dCd_friction_dchi(alpha, Mach)
dCdp_dchi = self.dCdp_dchi(alpha, Mach)
return dCdf_dchi + dCdp_dchi
def dCdp_dchi(self, alpha, Mach):
Cdp = self.Cdp(alpha, Mach)
if Cdp != 0:
sweep=self.get_sweep()
Mach_normal = Mach*np.cos(sweep)**self.POW_COS
ToC=self.get_rel_thick()/np.cos(sweep)**self.POW_COS*100.
Cd = self.__coefs.meta_Cd(ToC, self.get_camber(), alpha, Mach_normal)
dsweep=self.get_sweep_grad()
dCdp_dToC = self.gradCd(alpha, Mach)[0]
dToC_dchi = 100.*(self.get_rel_thick_grad()*np.cos(sweep)**self.POW_COS+self.POW_COS*self.get_rel_thick()*np.sin(sweep)*dsweep*np.cos(sweep)**(self.POW_COS-1.))/np.cos(sweep)**(2*self.POW_COS)
dCdp_dMach = self.gradCd(alpha, Mach)[3]
dMach_dchi = -self.POW_COS*Mach*np.sin(sweep)*dsweep*np.cos(sweep)**(self.POW_COS-1.)
dCdsdchi = self.dCds_dchi(alpha, Mach)
dCdpdchi = dCdp_dToC*dToC_dchi + dCdp_dMach*dMach_dchi - dCdsdchi
else:
dCdpdchi = 0.
return dCdpdchi
def Cdf(self, alpha, Mach):
return self.__Cd_friction(alpha, Mach)
def __Cd_friction(self, alpha, Mach):
# Re= V_corr*Lref_corr/nu=Mach*cos(sweep)*c*Lref/cos(sweep)/nu = Mach*c*Lref/cos(sweep)
OC = self.get_OC()
sweep = self.get_sweep()
c = OC.get_c()
nu = OC.get_nu()
L = self.get_Lref()
Re = Mach*np.cos(sweep)*c*L/nu
toc = self.get_rel_thick()/np.cos(sweep)
thick_coeff = 1.+2.1*toc # a rough guess since 1.21 for 10% relative thickness
if Re < 1.e-12:
# Prevent division by 0. Drag is null at zero Re number anyway
Cdf = 0.
elif Re < 1.e5:
# Laminar flow
Cdf=1.328/math.sqrt(Re)*thick_coeff
else:
# Turbulent flow
Cdf=0.074*Re**(-0.2)*thick_coeff
return Cdf
def CdfAlpha(self, alpha, Mach):
return self.__dCd_friction_dAoA(alpha, Mach)
def __dCd_friction_dAoA(self, alpha, Mach):
return 0.
def dCdf_dchi(self, alpha, Mach):
return self. __dCd_friction_dchi(alpha, Mach)
def __dCd_friction_dchi(self, alpha, Mach):
OC = self.get_OC()
sweep = self.get_sweep()
dsweep = self.get_sweep_grad()
c = OC.get_c()
nu = OC.get_nu()
L = self.get_Lref()
dL = self.get_Lref_grad()
Re = Mach*np.cos(sweep)*c*L/nu
dRe = Mach*np.cos(sweep)*c*dL/nu-Mach*np.sin(sweep)*c*L/nu*dsweep
toc = self.get_rel_thick()/np.cos(sweep)
dtoc = (self.get_rel_thick_grad()*np.cos(sweep)+self.get_rel_thick()*np.sin(sweep)*dsweep)/np.cos(sweep)**2
thick_coeff = 1.+2.1*toc
dthick_coeff = 2.1*dtoc
if Re < 1.e-6:
# Prevent division by 0. Drag is null at zero Re number anyway
dCdf = 0.
elif Re < 1.e5:
# Laminar flow
dCdf=-0.664/(Re**1.5)*dRe*thick_coeff+1.328/math.sqrt(Re)*dthick_coeff
else:
# Turbulent flow
dCdf=-0.0148*Re**(-1.2)*dRe*thick_coeff+0.074*Re**(-0.2)*dthick_coeff
return dCdf
def Cd_spurious(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal = Mach*np.cos(sweep)
ToC=self.get_rel_thick()/np.cos(sweep)*100.
Cl = self.__coefs.meta_Cl(ToC, self.get_camber(), alpha, Mach_normal)
k, coef = self.k_coef()
Cl0 = self.Cl0()
Cds = k + coef*(Cl - Cl0)**2.
return Cds
def CdsAlpha(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal = Mach*np.cos(sweep)
ToC=self.get_rel_thick()/np.cos(sweep)*100.
Cl = self.__coefs.meta_Cl(ToC, self.get_camber(), alpha, Mach_normal)
Cl_alpha = self.__coefs.grad_Cl(ToC, self.get_camber(), alpha, Mach_normal)[2]
k, coef = self.k_coef()
Cl0 = self.Cl0()
Cds_alpha = coef*2.*(Cl - Cl0)*Cl_alpha
return Cds_alpha
def dCds_dchi(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal = Mach*np.cos(sweep)
ToC=self.get_rel_thick()/np.cos(sweep)*100.
Cl = self.__coefs.meta_Cl(ToC, self.get_camber(), alpha, Mach_normal)
#dCldchi = self.dCl_dchi(alpha, Mach)
dCl_dToC = self.gradCl(alpha, Mach)[0]
dToC_dchi = 100.*(self.get_rel_thick_grad()*np.cos(sweep)+self.get_rel_thick()*np.sin(sweep))/np.cos(sweep)**2
dCl_dMach = self.gradCl(alpha, Mach)[3]
dsweep = self.get_sweep_grad()
dMach_dchi = -Mach*np.sin(sweep)*dsweep
dCldchi = dCl_dToC*dToC_dchi + dCl_dMach*dMach_dchi
k, coef = self.k_coef()
dk_dchi, d_coef_dchi = self.d_k_coef_dchi()
Cl0 = self.Cl0()
dCl0dchi = self.dCl0_dchi()
dCdsdchi = dk_dchi + d_coef_dchi*(Cl - Cl0)**2. + 2.*coef*(Cl - Cl0)*(dCldchi - dCl0dchi)
return dCdsdchi
def k_coef(self):
k = 0.0045235
coef = 0.03132053
return k, coef
def d_k_coef_dchi(self):
return 0., 0.
def Cl0(self):
Cl0 = 0.16372357
return Cl0
def dCl0_dchi(self):
return 0.
def gradCl(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal= Mach*np.cos(sweep)
ToC=self.get_rel_thick()/np.cos(sweep)*100.
gradCl = self.__coefs.grad_Cl(ToC, self.get_camber(), alpha, Mach_normal)
return gradCl
def gradCd(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal= Mach*np.cos(sweep)
ToC=self.get_rel_thick()/np.cos(sweep)*100.
gradCd = self.__coefs.grad_Cd(ToC, self.get_camber(), alpha, Mach_normal)
return gradCd
def gradCm(self, alpha, Mach):
sweep=self.get_sweep()
Mach_normal= Mach*np.cos(sweep)
ToC=self.get_rel_thick()/np.cos(sweep)*100.
gradCm = self.__coefs.grad_Cm(ToC, self.get_camber(), alpha, Mach_normal)
return gradCm
# def dCl_dthickness(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCl_dthic = self.__coefs.grad_Cl(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[0]*100.
#
# return dCl_dthic*sweep_corr
#
# def dCl_dcamber(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCl_dcamb = self.__coefs.grad_Cl(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[1]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCl_dcamb*sweep_corr
#
# def dCl_dMach(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCl_dM = self.__coefs.grad_Cl(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[3]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCl_dM*sweep_corr
#
# def dCd_dthickness(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCd_dthic = self.__coefs.grad_Cd(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[0]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCd_dthic*sweep_corr
#
# def dCd_dcamber(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCd_dcamb = self.__coefs.grad_Cd(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[1]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCd_dcamb*sweep_corr
#
# def dCd_dalpha(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCd_dAoA = self.__coefs.grad_Cd(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[2]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCd_dAoA*sweep_corr
#
# def dCd_dMach(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCd_dM = self.__coefs.grad_Cd(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[3]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCd_dM*sweep_corr
# def dCm_dthickness(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCm_dthic = self.__coefs.grad_Cm(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[0]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCm_dthic*sweep_corr
#
# def dCm_dcamber(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCm_dcamb = self.__coefs.grad_Cm(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[1]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCm_dcamb*sweep_corr
#
# def dCm_dalpha(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCm_dAoA = self.__coefs.grad_Cm(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[2]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCm_dAoA*sweep_corr
#
# def dCm_dMach(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCm_dM = self.__coefs.grad_Cm(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[3]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCm_dM*sweep_corr
def get_scaled_copy(self, OC=None, Sref=None,Lref=None, rel_thick=None, camber=None, sweep=None):
if Sref is None:
Sref=self.get_Sref()
if Lref is None:
Lref=self.get_Lref()
if rel_thick is None:
rel_thick = self.get_rel_thick()
if camber is None:
camber = self.get_camber()
if sweep is None:
sweep = self.get_sweep()
if OC is None:
OC = self.get_OC()
return MetaAirfoil(OC, self.__surrogate_model, relative_thickness=rel_thick, camber=camber, Sref=Sref, Lref=Lref, sweep=sweep, surrogate_fcs=self.__coefs)
class MetaAirfoil(Airfoil):
"""
A meta model based on 2D CFD data
Provide lift, drag and moment coefficients
Provide sensitivities of aerodynamic surrogate function w.r.t. input parameters
"""
POW_COS = 1.0
def __init__(self,
OC,
surrogate_model,
relative_thickness=.12,
camber=0.,
Sref=1.,
Lref=1.,
sweep=0.,
surrogate_fcs=None):
Airfoil.__init__(self, OC, Sref, Lref, relative_thickness, sweep,
camber)
if not surrogate_fcs:
self.__coefs = SurrogateCoefs(surrogate_model)
else:
self.__coefs = surrogate_fcs
self.__surrogate_model = surrogate_model
def Cl(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)**self.POW_COS
ToC = self.get_rel_thick() / np.cos(sweep) * 100.
Cl = self.__coefs.meta_Cl(ToC, self.get_camber(), alpha, Mach_normal)
sweep_corr = np.cos(self.get_sweep())**(2. * self.POW_COS)
return Cl * sweep_corr
def ClAlpha(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)**self.POW_COS
ToC = self.get_rel_thick() / np.cos(sweep)**self.POW_COS * 100.
dCl_dAoA = self.__coefs.grad_Cl(ToC, self.get_camber(), alpha,
Mach_normal)[2]
sweep_corr = np.cos(self.get_sweep())**(2. * self.POW_COS)
return dCl_dAoA * sweep_corr
def Cd(self, alpha, Mach):
Cdf = self.__Cd_friction(alpha, Mach)
Cdp = self.Cdp(alpha, Mach)
return Cdf + Cdp
def Cdp(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)**self.POW_COS
ToC = self.get_rel_thick() / np.cos(sweep)**self.POW_COS * 100.
Cd = self.__coefs.meta_Cd(ToC, self.get_camber(), alpha, Mach_normal)
Cds = self.Cd_spurious(alpha, Mach)
Cdp = max([Cd - Cds, 0.])
return Cdp
def CdpAlpha(self, alpha, Mach):
Cdp = self.Cdp(alpha, Mach)
if Cdp == 0.:
dCdp_dAoA = 0.
else:
Cdsalpha = self.CdsAlpha(alpha, Mach)
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)**self.POW_COS
ToC = self.get_rel_thick() / np.cos(sweep)**self.POW_COS * 100.
dCdp_dAoA = self.__coefs.grad_Cd(ToC, self.get_camber(), alpha,
Mach_normal)[2] - Cdsalpha
return dCdp_dAoA
def CdAlpha(self, alpha, Mach):
dCdp_dAoA = self.CdpAlpha(alpha, Mach)
dCdf_AoA = self.__dCd_friction_dAoA(alpha, Mach)
return dCdp_dAoA + dCdf_AoA
def Cm(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)**self.POW_COS
ToC = self.get_rel_thick() / np.cos(sweep)**self.POW_COS * 100.
Cm = self.__coefs.meta_Cd(ToC, self.get_camber(), alpha, Mach_normal)
sweep_corr = np.cos(self.get_sweep())**(2. * self.POW_COS)
return Cm * sweep_corr
def dCl_dchi(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)**self.POW_COS
ToC = self.get_rel_thick() / np.cos(sweep)**self.POW_COS * 100.
Cl = self.__coefs.meta_Cl(ToC, self.get_camber(), alpha, Mach_normal)
dsweep = self.get_sweep_grad()
sweep_corr = np.cos(self.get_sweep())**(2. * self.POW_COS)
dsweep_corr = -2. * self.POW_COS * np.sin(sweep) * dsweep * np.cos(
sweep)**(2. * self.POW_COS - 1.)
dCl_dToC = self.gradCl(alpha, Mach)[0]
dToC_dchi = 100. * (
self.get_rel_thick_grad() * np.cos(sweep)**self.POW_COS +
self.POW_COS * self.get_rel_thick() * np.sin(sweep) * dsweep *
np.cos(sweep)**(self.POW_COS - 1.)) / np.cos(sweep)**(2 *
self.POW_COS)
dCl_dMach = self.gradCl(alpha, Mach)[3]
dMach_dchi = -self.POW_COS * Mach * np.sin(sweep) * dsweep * np.cos(
sweep)**(self.POW_COS - 1.)
return (dCl_dToC * dToC_dchi +
dCl_dMach * dMach_dchi) * sweep_corr + Cl * dsweep_corr
def dCd_dchi(self, alpha, Mach):
dCdf_dchi = self.__dCd_friction_dchi(alpha, Mach)
dCdp_dchi = self.dCdp_dchi(alpha, Mach)
return dCdf_dchi + dCdp_dchi
def dCdp_dchi(self, alpha, Mach):
Cdp = self.Cdp(alpha, Mach)
if Cdp != 0:
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)**self.POW_COS
ToC = self.get_rel_thick() / np.cos(sweep)**self.POW_COS * 100.
Cd = self.__coefs.meta_Cd(ToC, self.get_camber(), alpha,
Mach_normal)
dsweep = self.get_sweep_grad()
dCdp_dToC = self.gradCd(alpha, Mach)[0]
dToC_dchi = 100. * (
self.get_rel_thick_grad() * np.cos(sweep)**self.POW_COS +
self.POW_COS * self.get_rel_thick() * np.sin(sweep) * dsweep *
np.cos(sweep)**
(self.POW_COS - 1.)) / np.cos(sweep)**(2 * self.POW_COS)
dCdp_dMach = self.gradCd(alpha, Mach)[3]
dMach_dchi = -self.POW_COS * Mach * np.sin(
sweep) * dsweep * np.cos(sweep)**(self.POW_COS - 1.)
dCdsdchi = self.dCds_dchi(alpha, Mach)
dCdpdchi = dCdp_dToC * dToC_dchi + dCdp_dMach * dMach_dchi - dCdsdchi
else:
dCdpdchi = 0.
return dCdpdchi
def Cdf(self, alpha, Mach):
return self.__Cd_friction(alpha, Mach)
def __Cd_friction(self, alpha, Mach):
# Re= V_corr*Lref_corr/nu=Mach*cos(sweep)*c*Lref/cos(sweep)/nu = Mach*c*Lref/cos(sweep)
OC = self.get_OC()
sweep = self.get_sweep()
c = OC.get_c()
nu = OC.get_nu()
L = self.get_Lref()
Re = Mach * np.cos(sweep) * c * L / nu
toc = self.get_rel_thick() / np.cos(sweep)
thick_coeff = 1. + 2.1 * toc # a rough guess since 1.21 for 10% relative thickness
if Re < 1.e-12:
# Prevent division by 0. Drag is null at zero Re number anyway
Cdf = 0.
elif Re < 1.e5:
# Laminar flow
Cdf = 1.328 / sqrt(Re) * thick_coeff
else:
# Turbulent flow
Cdf = 0.074 * Re**(-0.2) * thick_coeff
return Cdf
def CdfAlpha(self, alpha, Mach):
return self.__dCd_friction_dAoA(alpha, Mach)
def __dCd_friction_dAoA(self, alpha, Mach):
return 0.
def dCdf_dchi(self, alpha, Mach):
return self.__dCd_friction_dchi(alpha, Mach)
def __dCd_friction_dchi(self, alpha, Mach):
OC = self.get_OC()
sweep = self.get_sweep()
dsweep = self.get_sweep_grad()
c = OC.get_c()
nu = OC.get_nu()
L = self.get_Lref()
dL = self.get_Lref_grad()
Re = Mach * np.cos(sweep) * c * L / nu
dRe = Mach * np.cos(sweep) * c * dL / nu - Mach * np.sin(
sweep) * c * L / nu * dsweep
toc = self.get_rel_thick() / np.cos(sweep)
dtoc = (
self.get_rel_thick_grad() * np.cos(sweep) +
self.get_rel_thick() * np.sin(sweep) * dsweep) / np.cos(sweep)**2
thick_coeff = 1. + 2.1 * toc
dthick_coeff = 2.1 * dtoc
if Re < 1.e-6:
# Prevent division by 0. Drag is null at zero Re number anyway
dCdf = 0.
elif Re < 1.e5:
# Laminar flow
dCdf = -0.664 / (
Re**1.5) * dRe * thick_coeff + 1.328 / sqrt(Re) * dthick_coeff
else:
# Turbulent flow
dCdf = -0.0148 * Re**(-1.2) * dRe * thick_coeff + 0.074 * Re**(
-0.2) * dthick_coeff
return dCdf
def Cd_spurious(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)
ToC = self.get_rel_thick() / np.cos(sweep) * 100.
Cl = self.__coefs.meta_Cl(ToC, self.get_camber(), alpha, Mach_normal)
k, coef = self.k_coef()
Cl0 = self.Cl0()
Cds = k + coef * (Cl - Cl0)**2.
return Cds
def CdsAlpha(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)
ToC = self.get_rel_thick() / np.cos(sweep) * 100.
Cl = self.__coefs.meta_Cl(ToC, self.get_camber(), alpha, Mach_normal)
Cl_alpha = self.__coefs.grad_Cl(ToC, self.get_camber(), alpha,
Mach_normal)[2]
k, coef = self.k_coef()
Cl0 = self.Cl0()
Cds_alpha = coef * 2. * (Cl - Cl0) * Cl_alpha
return Cds_alpha
def dCds_dchi(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)
ToC = self.get_rel_thick() / np.cos(sweep) * 100.
Cl = self.__coefs.meta_Cl(ToC, self.get_camber(), alpha, Mach_normal)
#dCldchi = self.dCl_dchi(alpha, Mach)
dCl_dToC = self.gradCl(alpha, Mach)[0]
dToC_dchi = 100. * (
self.get_rel_thick_grad() * np.cos(sweep) +
self.get_rel_thick() * np.sin(sweep)) / np.cos(sweep)**2
dCl_dMach = self.gradCl(alpha, Mach)[3]
dsweep = self.get_sweep_grad()
dMach_dchi = -Mach * np.sin(sweep) * dsweep
dCldchi = dCl_dToC * dToC_dchi + dCl_dMach * dMach_dchi
k, coef = self.k_coef()
dk_dchi, d_coef_dchi = self.d_k_coef_dchi()
Cl0 = self.Cl0()
dCl0dchi = self.dCl0_dchi()
dCdsdchi = dk_dchi + d_coef_dchi * (Cl - Cl0)**2. + 2. * coef * (
Cl - Cl0) * (dCldchi - dCl0dchi)
return dCdsdchi
def k_coef(self):
k = 0.0045235
coef = 0.03132053
return k, coef
def d_k_coef_dchi(self):
return 0., 0.
def Cl0(self):
Cl0 = 0.16372357
return Cl0
def dCl0_dchi(self):
return 0.
def gradCl(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)
ToC = self.get_rel_thick() / np.cos(sweep) * 100.
gradCl = self.__coefs.grad_Cl(ToC, self.get_camber(), alpha,
Mach_normal)
return gradCl
def gradCd(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)
ToC = self.get_rel_thick() / np.cos(sweep) * 100.
gradCd = self.__coefs.grad_Cd(ToC, self.get_camber(), alpha,
Mach_normal)
return gradCd
def gradCm(self, alpha, Mach):
sweep = self.get_sweep()
Mach_normal = Mach * np.cos(sweep)
ToC = self.get_rel_thick() / np.cos(sweep) * 100.
gradCm = self.__coefs.grad_Cm(ToC, self.get_camber(), alpha,
Mach_normal)
return gradCm
# def dCl_dthickness(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCl_dthic = self.__coefs.grad_Cl(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[0]*100.
#
# return dCl_dthic*sweep_corr
#
# def dCl_dcamber(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCl_dcamb = self.__coefs.grad_Cl(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[1]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCl_dcamb*sweep_corr
#
# def dCl_dMach(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCl_dM = self.__coefs.grad_Cl(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[3]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCl_dM*sweep_corr
#
# def dCd_dthickness(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCd_dthic = self.__coefs.grad_Cd(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[0]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCd_dthic*sweep_corr
#
# def dCd_dcamber(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCd_dcamb = self.__coefs.grad_Cd(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[1]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCd_dcamb*sweep_corr
#
# def dCd_dalpha(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCd_dAoA = self.__coefs.grad_Cd(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[2]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCd_dAoA*sweep_corr
#
# def dCd_dMach(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCd_dM = self.__coefs.grad_Cd(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[3]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCd_dM*sweep_corr
# def dCm_dthickness(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCm_dthic = self.__coefs.grad_Cm(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[0]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCm_dthic*sweep_corr
#
# def dCm_dcamber(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCm_dcamb = self.__coefs.grad_Cm(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[1]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCm_dcamb*sweep_corr
#
# def dCm_dalpha(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCm_dAoA = self.__coefs.grad_Cm(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[2]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCm_dAoA*sweep_corr
#
# def dCm_dMach(self):
# sweep=self.get_sweep()
# Mach_normal= Mach*np.cos(sweep)
# dCm_dM = self.__coefs.grad_Cm(self.get_rel_thick()*100., self.get_camber(), alpha, Mach_normal)[3]
# sweep_corr = np.cos(self.get_sweep())**2
#
# return dCm_dM*sweep_corr
def get_scaled_copy(self,
OC=None,
Sref=None,
Lref=None,
rel_thick=None,
camber=None,
sweep=None):
if Sref is None:
Sref = self.get_Sref()
if Lref is None:
Lref = self.get_Lref()
if rel_thick is None:
rel_thick = self.get_rel_thick()
if camber is None:
camber = self.get_camber()
if sweep is None:
sweep = self.get_sweep()
if OC is None:
OC = self.get_OC()
return MetaAirfoil(OC,
self.__surrogate_model,
relative_thickness=rel_thick,
camber=camber,
Sref=Sref,
Lref=Lref,
sweep=sweep,
surrogate_fcs=self.__coefs)