/
propeller.py
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/
propeller.py
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" propeller model "
from numpy import pi
from gpkit import Model, Variable,Vectorize,parse_variables, SignomialsEnabled, SignomialEquality
from gpkit.constraints.tight import Tight as TCS
from gpfit.fit_constraintset import XfoilFit
import os
import pandas as pd
class ActuatorProp(Model):
""" Propeller Model
Variables
---------
T [lbf] thrust
Tc [-] coefficient of thrust
etaadd .7 [-] swirl and nonuniformity losses
etav .85 [-] viscous losses
etai [-] inviscid losses
eta [-] overall efficiency
z1 self.helper [-] efficiency helper 1
z2 [-] efficiency helper 2
lam [-] advance ratio
CT [-] thrust coefficient
CP [-] power coefficient
Q [N*m] torque
omega [rpm] propeller rotation rate
omega_max 10000 [rpm] max rotation rate
P_shaft [kW] shaft power
M_tip .5 [-] Tip mach number
a 295 [m/s] Speed of sound at altitude
"""
def helper(self, c):
return 2. - 1./c[self.etaadd]
def setup(self, static, state = None, rho = None, V = None):
exec parse_variables(ActuatorProp.__doc__)
V = state.V
rho = state.rho
R = static.R
constraints = [eta <= etav*etai,
Tc >= T/(0.5*rho*V**2*pi*R**2),
z2 >= Tc + 1,
etai*(z1 + z2**0.5/etaadd) <= 2,
lam >= V/(omega*R),
CT >= Tc*lam**2,
CP <= Q*omega/(.5*rho*(omega*R)**3*pi*R**2),
eta >= CT*lam/CP,
omega <= omega_max,
P_shaft == Q*omega,
(M_tip*a)**2 >= (omega*R)**2 + V**2,
static.T_m >= T
]
return constraints
class Blade_Element_Performance(Model):
""" Single element of a propeller blade
Variables
---------
dT [lbf] thrust
eta_b [-] local efficiency
dQ [N*m] torque
omega [rpm] propeller rotation rate
Wa [m/s] Axial total relative velocity
Wt [m/s] Tangential total relative velocity
Wr [m/s] Total relative velocity
va [m/s] Axial induced velocity
vt [m/s] Tangential induced velocity
G [m^2/s] Circulation
c [m] local chord
cl [-] local lift coefficient
cd [-] local drag coefficient
cdp [-] local drag coefficient
B 3 [-] number of blades
r [m] local radius
lam_w [-] advance ratio
eps [-] blade efficiency
AR_b [-] blade aspect ratio
AR_b_max 50 [-] max blade aspect ratio
Ut [m/s] tangential freestreem
Re [-] blade reynolds number
f [-] intermediate tip loss variable
F [-] Prandtl tip loss factor
cl_max .9 [-] max airfoil cl
dr [m] length of blade element
FF [-] form factor
t_c .1 [-] airfoil t/c
C_f [-] skin friction coefficient
M [-] Mach number
a 295 [m/s] Speed of sound at altitude
"""
def setup(self,parent, state):
exec parse_variables(Blade_Element_Performance.__doc__)
V = state.V
rho = state.rho
R = parent.R
mu = state.mu
path = os.path.dirname(__file__)
fd = pd.read_csv(path + os.sep + "dae51_fitdata.csv").to_dict(
orient="records")[0]
constraints = [#TCS([Wr**2 >= (Wa**2+Wt**2)]),
#Ut == omega*r,
TCS([G == (1./2.)*Wr*c*cl]),
#TCS([f+(r/R)*B/(2*lam_w) <= (B/2.)*(1./lam_w)]), #.2 = 1-.8 = 1-r/R
F == (2./pi)*(1.02232*f**.0458729)**(1./.1), #This is the GP fit of arccos(exp(-f))
M == Wr/a,
lam_w == (r/R)*(Wa/Wt),
va == vt*(Wt/Wa),
eps == cd/cl,
#TCS([1 >= etai*(1+va/V)+vt/Ut]),
#TCS([1 >= etap*(1+eps*Wt/Wa)+eps*Wt/Wa]),
TCS([dQ >= rho*B*G*(Wa+eps*Wt)*r*dr]),
#Wa == V,
#Wt == omega*r,
AR_b == R/c,
AR_b <= AR_b_max,
Re == Wr*c*rho/mu,
#eta == T*V/(Q*omega),
eta_b == (V/(omega*r))*(Wt/Wa),
#TCS([cd >= cl**2/(pi*AR_b*.85) + cdp]),
#TCS([FF >= 1. + .3*t_c + (100*t_c)**.4]),
#C_f == .027/(Re**(1./7.)),
#cdp >= FF*C_f*(2.+.4*t_c),
XfoilFit(fd, cd, [cl,Re], name="polar"),
cl <= cl_max
]
with SignomialsEnabled():
constraints += [TCS([Wa>=V + va]),
#SignomialEquality(Wa, V+va),
SignomialEquality(Wr**2,(Wa**2+Wt**2)),
#TCS([Wr**2 >= (Wa**2+Wt**2)]),
SignomialEquality(Wt,omega*r-vt),
#TCS([Wt<=omega*r-vt]),
TCS([dT <= rho*B*G*(Wt-eps*Wa)*dr]),
SignomialEquality(vt**2*F**2*(1.+(4.*lam_w*R/(pi*B*r))**2),(B*G/(4.*pi*r))**2),
#TCS([vt**2*F**2*(1.+(4.*lam_w*R/(pi*B*r))**2)<=(B*G/(4.*pi*r))**2]),
#TCS([f+(r/R)*B/(2*lam_w) <= (B/2.)*(1./lam_w)]),
SignomialEquality(f+(r/R)*B/(2*lam_w),(B/2.)*(1./lam_w))
#SignomialEquality(1,etap*(1+eps*Wt/Wa)+eps*Wa/Wt),
#SignomialEquality(1,etai*(1+va/V)+vt/Ut),
#SignomialEquality(dQ,rho*B*G*(Wa+eps*Wt)*r*dr),
#SignomialEquality(dT,rho*B*G*(Wt-eps*Wa)*dr),
]
return constraints, state
class MultiElementProp(Model):
""" Performance for a propeller with multiple elements
Variables
---------
Mtip .5 [-] tip mach number
"""
def setup(self,parent, state, N = 4):
#exec parse_variables(Multi_Element_Propeller_Performance.__doc__)
T = self.T = Variable('T', 'lbf', 'Overall thrust')
Q = self.Q = Variable('Q', 'N*m', 'Overall torque')
eta = self.eta = Variable('eta', '-', 'Overall efficiency')
omega = self.omega = Variable('omega', 'rpm', 'rotation rate')
omega_max = Variable('omega_max',10000, 'rpm', 'rotation rate')
Mtip = Variable('Mtip', .5, '-', 'Tip Mach')
with Vectorize(N):
blade = Blade_Element_Performance(parent, state)
constraints = [blade.dr == parent.R/(N),
blade.omega == omega,
blade["r"][0] == parent.R/(2.*N)]
with SignomialsEnabled():
for n in range(1,N):
constraints += [TCS([blade["r"][n] >= blade["r"][n-1] + parent.R/N]),
#SignomialEquality(blade["r"][n],blade["r"][n-1] + parent.R/N),
blade["eta_b"][n] == blade["eta_b"][n-1]
]
constraints += [TCS([T <= sum(blade["dT"][n] for n in range(N))]),
TCS([Q >= sum(blade["dQ"][n] for n in range(N))]),
eta == state.V*T/(omega*Q),
blade["M"][-1] <= Mtip,
#parent.T_m>=T
omega <= omega_max
]
return constraints, blade
class SimpleQProp(Model):
""" Propeller Model
Variables
---------
T [lbf] thrust
etaadd 0.7 [-] swirl and nonuniformity losses
etap [-] viscous losses
etai [-] inviscid losses
eta [-] overall efficiency
Q [N*m] torque
omega [rpm] propeller rotation rate
omega_max 10000 [rpm] max rotation rate
P_shaft [kW] shaft power
M_tip .5 [-] Tip mach number
a 295 [m/s] Speed of sound at altitude
Wa [m/s] Axial total relative velocity
Wt [m/s] Tangential total relative velocity
Wr [m/s] Total relative velocity
va [m/s] Axial induced velocity
vt [m/s] Tangential induced velocity
G [m^2/s] Circulation
c [m] local chord
cl .4 [-] local lift coefficient
cd [-] local drag coefficient
B 2 [-] number of blades
r [m] local radius
lam_w [-] advance ratio
eps [-] blade efficiency
AR_b [-] blade aspect ratio
AR_b_max 18 [-] max blade aspect ratio
Ut [m/s] tangential freestreem
Re [-] blade reynolds number
f [-] intermediate tip loss variable
F [-] Prandtl tip loss factor
cl_max 1.3 [-] max airfoil cl
eta_check [-] efficiency check
"""
def helper(self, c):
return 2. - 1./c[self.etaadd]
def setup(self, static, state):
exec parse_variables(SimpleQProp.__doc__)
V = state.V
rho = state.rho
R = static.R
mu = state.mu
path = os.path.dirname(__file__)
fd = pd.read_csv(path + os.sep + "dae51_fitdata.csv").to_dict(
orient="records")[0]
constraints = [TCS([eta <= etap*etai]),
omega <= omega_max,
P_shaft == Q*omega,
Ut == omega*r,
TCS([G == (1./2.)*Wr*c*cl]),
r == .8*R, #Assume 80% chord is representative
f == (B/2.)*.2*(1./lam_w), #.2 = 1-.8 = 1-r/R
F == (2./pi)*(1.02232*f**.0458729)**(1./.1), #This is the GP fit of arccos(exp(-f))
lam_w == (r/R)*(Wa/Wt),
va == vt*(Wt/Wa),
eps == cd/cl,
TCS([1 >= etai*(1+va/V)+vt/Ut]),
TCS([1 >= etap*(1+eps*Wt/Wa)+eps*Wt/Wa]),
TCS([Q >= rho*B*G*(Wa+eps*Wt)*R**2]),
TCS([(M_tip*a)**2 >= Wa**2 + Wt**2]),
AR_b == R/c,
AR_b <= AR_b_max,
Re == Wr*c*rho/mu,
eta == T*V/(Q*omega),
XfoilFit(fd, cd, [cl,Re], name="polar"),
static.T_m >= T,
cl <= cl_max
]
with SignomialsEnabled():
constraints += [TCS([Wa>=V + va]),
SignomialEquality(Wr**2,(Wa**2+Wt**2)),
#SignomialEquality(Wa,V+va),
SignomialEquality(Wt,omega*r-vt),
#TCS([Wt>=omega*r-vt]),
TCS([T <= rho*B*G*(Wt-eps*Wa)*R]),
SignomialEquality(vt**2*F**2*(1.+(4.*lam_w*R/(pi*B*r))**2),(B*G/(4.*pi*r))**2),
#TCS([vt**2*F**2*(1.+(4.*lam_w*R/(pi*B*r))**2)>=(B*G/(4.*pi*r))**2]),
#SignomialEquality(1,etap*(1+eps*Wt/Wa)+eps*Wa/Wt),
#SignomialEquality(1,etai*(1+va/V)+vt/Ut),
#SignomialEquality(Q,rho*B*G*(Wa+eps*Wt)*R**2),
#SignomialEquality(T,rho*B*G*(Wt-eps*Wa)*R),
]
return constraints, state
class Propeller(Model):
""" Propeller Model
Variables
---------
R [ft] prop radius
W [lbf] prop weight
K 4e-4 [1/ft^2] prop weight scaling factor
T_m [lbf] prop max static thrust
Variables of length N
---------------------
c [ft] prop chord
"""
flight_model = SimpleQProp
def setup(self, N = 1):
exec parse_variables(Propeller.__doc__)
self.N = N
return [W >= K*T_m*R**2]
class Multi_Element_Propeller(Model):
""" Propeller Model
Variables
---------
R [ft] prop radius
W [lbf] prop weight
K 4e-4 [1/ft^2] prop weight scaling factor
T_m [lbf] prop max static thrust
"""
flight_model = MultiElementProp
def setup(self):
exec parse_variables(Multi_Element_Propeller.__doc__)
constraints = [W >= K*T_m*R**2]
return constraints