def f_angles(angles, one, two, thr, stator, rotor, gamma, cp, R, GR, psi,
DeltaH_prod):
alpha = angles[0]
beta = angles[1]
# assume an two.alpha and project velocities
two.vel.Vx, two.vel.Vu = f.velocity_projections(two.vel.V, alpha)
# assume a loading factor and calculate peripheral speed
two.vel.U = np.sqrt(DeltaH_prod / psi)
# velocity triangle (pithagoras)
two.vel.Wu = two.vel.Vu - two.vel.U
two.vel.Wx = two.vel.Vx
two.vel.W = f.mag(two.vel.Wu, two.vel.Wx)
# relative inlet angle and relative Mach number
two.vel.Mr = two.vel.W / two.vel.a
# relative total quantities at rotor inlet
two.T0r, two.P0r = f.relative_temperature_pressure(
two.T, two.P, two.vel.Mr, gamma)
############ ROTOR #############
# in the rotor, the relative total temperature is constant (se conservan rotalpías)
thr.T0r = two.T0r
# ideal outlet temperature, real outlet temperature
# assuming the expanse to thr.P, calculated with the assumed M3
thr.Ts = f.P2T(thr.T0r, thr.P, two.P0r,
gamma) # = thr.T0r*(thr.P/two.P0r)**((gamma-1)/gamma)
thr.T = f.stage_efficiency(
rotor.eta, thr.T0r,
thr.Ts) # = thr.T0r - rotor.eta*(thr.T0r - thr.Ts)
# velocities
thr.vel.W = f.isen_velocity(cp, thr.T0r,
thr.T) # = np.sqrt(2*cp*(thr.T0r - thr.T))
# velocity projections, axial and tangential
thr.vel.Wx, thr.vel.Wu = f.velocity_projections(thr.vel.W, beta)
# constant radius, constant peripheral speed
thr.vel.U = two.vel.U
# tangential outlet speed
thr.vel.Vu = thr.vel.Wu + thr.vel.U
# V3u_euler = -DeltaH_prod/two.vel.U + two.vel.Vu
# find work, check for angle iteration
DeltaH_calculated = two.vel.U * (two.vel.Vu - thr.vel.Vu)
diff = DeltaH_calculated - DeltaH_prod
return np.array([diff[0], 0])
def f_mach3(Mach3, one, two, thr, stator, rotor, gamma, cp, R, GR, phi,
DeltaH_prod, bounds_angles):
thr.vel.M = Mach3
# using mach, find static pressure
thr.P = f.static_pressure(
thr.P0, gamma, thr.vel.M
) # = thr.P0/(1+(gamma-1)/2*thr.vel.M**2)**(gamma/(gamma-1))
thr.Ts = f.P2T(thr.T0, thr.P, thr.P0,
gamma) # = thr.T0*(thr.P/thr.P0)**((gamma-1)/gamma)
# find intermediate static pressure
two.P = one.P0 * ((GR - 1) * (1 - (thr.P / one.P0)**(
(gamma - 1) / gamma)) + 1)**(gamma /
(gamma - 1)) # GP rp definition
### where does that definition come from? doublecheck GR definition
# isentropic evolution in stator: absolute total temperature is same
two.T0 = one.T0
two.Ts = f.P2T(one.T0, two.P, one.P0,
gamma) # = one.T0*(two.P/one.P0)**((gamma-1)/gamma)
two.vel.Vs = f.isen_velocity(
cp, two.T0, two.Ts) # = np.sqrt(2*cp*(two.T0 - two.Ts))
# assume rotor efficiency
two.T = f.stage_efficiency(
stator.eta, two.T0,
two.Ts) # = two.T0 - stator.eta*(two.T0-two.Ts)
two.vel.V = f.isen_velocity(cp, two.T0,
two.T) # = np.sqrt(2*cp*(two.T0 - two.T))
# density (from static quantities)
two.rho = f.static_density(two.P, two.T, R) # = two.P/two.T/R
# speed of sound and Mach
two.vel.a, two.vel.M = f.sonic(
gamma, R, two.T,
two.vel.V) # = np.sqrt(gamma*R*two.T), = two.vel.V/two.vel.a
# get initial guess for angles
angles_init = np.array([two.alpha, thr.beta])
angles = solve_angles(angles_init, one, two, thr, stator, rotor, gamma,
cp, R, GR, phi, DeltaH_prod, bounds_angles)
two.alpha = angles[0]
thr.beta = angles[1]
two.vel.Vx, two.vel.Vu = f.velocity_projections(two.vel.V, two.alpha)
# assume a loading factor and calculate peripheral speed
two.vel.U = np.sqrt(DeltaH_prod / phi)
# velocity triangle (pithagoras)
two.vel.Wu = two.vel.Vu - two.vel.U
two.vel.Wx = two.vel.Vx
two.vel.W = f.mag(two.vel.Wu, two.vel.Wx)
# relative inlet angle and relative Mach number
two.vel.Mr = two.vel.W / two.vel.a
# relative total quantities at rotor inlet
two.T0r, two.P0r = f.relative_temperature_pressure(
two.T, two.P, two.vel.Mr, gamma)
############ ROTOR #############
# in the rotor, the relative total temperature is constant (se conservan rotalpías)
thr.T0r = two.T0r
# ideal outlet temperature, real outlet temperature
# assuming the expanse to thr.P, calculated with the assumed M3
thr.Ts = f.P2T(thr.T0r, thr.P, two.P0r,
gamma) # = thr.T0r*(thr.P/two.P0r)**((gamma-1)/gamma)
thr.T = f.stage_efficiency(
rotor.eta, thr.T0r,
thr.Ts) # = thr.T0r - rotor.eta*(thr.T0r - thr.Ts)
# velocities
thr.vel.W = f.isen_velocity(cp, thr.T0r,
thr.T) # = np.sqrt(2*cp*(thr.T0r - thr.T))
# speed of sound and relative mach number
thr.vel.a, thr.vel.Mr = f.sonic(gamma, R, thr.T,
thr.vel.W) # = np.sqrt(gamma*R*thr.T)
# velocity projections, axial and tangential
thr.vel.Wx, thr.vel.Wu = f.velocity_projections(thr.vel.W, thr.beta)
# constant radius, constant peripheral speed
thr.vel.U = two.vel.U
# tangential outlet speed
thr.vel.Vu = thr.vel.Wu + thr.vel.U
# V3u_euler = -DeltaH_prod/two.vel.U + two.vel.Vu
# assume axial speed constant
thr.vel.Vx = thr.vel.Wx
thr.vel.V = f.mag(
thr.vel.Vx, thr.vel.Vu) # = np.sqrt(thr.vel.Vx**2 + thr.vel.Vu**2)
Mach3_calculated = thr.vel.V / thr.vel.a
return Mach3_calculated - Mach3
def converge_mach3(one, two, thr, stator, rotor, gamma, cp, R, GR, psi,
DeltaH_prod):
def f_mach3(Mach3, one, two, thr, stator, rotor, gamma, cp, R, GR, psi,
DeltaH_prod):
thr.vel.M = Mach3
# using mach, find static pressure
thr.P = f.static_pressure(
thr.P0, gamma, thr.vel.M
) # = thr.P0/(1+(gamma-1)/2*thr.vel.M**2)**(gamma/(gamma-1))
thr.Ts = f.P2T(thr.T0, thr.P, thr.P0,
gamma) # = thr.T0*(thr.P/thr.P0)**((gamma-1)/gamma)
# find intermediate static pressure
two.P = one.P0 * ((GR - 1) * (1 - (thr.P / one.P0)**(
(gamma - 1) / gamma)) + 1)**(gamma /
(gamma - 1)) # GP rp definition
### where does that definition come from? doublecheck GR definition
# isentropic evolution in stator: absolute total temperature is same
two.T0 = one.T0
two.Ts = f.P2T(one.T0, two.P, one.P0,
gamma) # = one.T0*(two.P/one.P0)**((gamma-1)/gamma)
two.vel.Vs = f.isen_velocity(
cp, two.T0, two.Ts) # = np.sqrt(2*cp*(two.T0 - two.Ts))
# assume rotor efficiency
two.T = f.stage_efficiency(
stator.eta, two.T0,
two.Ts) # = two.T0 - stator.eta*(two.T0-two.Ts)
two.vel.V = f.isen_velocity(cp, two.T0,
two.T) # = np.sqrt(2*cp*(two.T0 - two.T))
# density (from static quantities)
two.rho = f.static_density(two.P, two.T, R) # = two.P/two.T/R
# speed of sound and Mach
two.vel.a, two.vel.M = f.sonic(
gamma, R, two.T,
two.vel.V) # = np.sqrt(gamma*R*two.T), = two.vel.V/two.vel.a
## ANGLE CONVERGENCE FOR ALPHA2 AND BETA3
solve_angles(one, two, thr, stator, rotor, gamma, cp, R, GR, psi,
DeltaH_prod)
two.vel.Vx, two.vel.Vu = f.velocity_projections(two.vel.V, two.alpha)
# assume a loading factor and calculate peripheral speed
two.vel.U = np.sqrt(DeltaH_prod / psi)
# velocity triangle (pithagoras)
two.vel.Wu = two.vel.Vu - two.vel.U
two.vel.Wx = two.vel.Vx
two.vel.W = f.mag(two.vel.Wu, two.vel.Wx)
# relative inlet angle and relative Mach number
two.vel.Mr = two.vel.W / two.vel.a
# relative total quantities at rotor inlet
two.T0r, two.P0r = f.relative_temperature_pressure(
two.T, two.P, two.vel.Mr, gamma)
############ ROTOR #############
# in the rotor, the relative total temperature is constant (se conservan rotalpías)
thr.T0r = two.T0r
# ideal outlet temperature, real outlet temperature
# assuming the expanse to thr.P, calculated with the assumed M3
thr.Ts = f.P2T(thr.T0r, thr.P, two.P0r,
gamma) # = thr.T0r*(thr.P/two.P0r)**((gamma-1)/gamma)
thr.T = f.stage_efficiency(
rotor.eta, thr.T0r,
thr.Ts) # = thr.T0r - rotor.eta*(thr.T0r - thr.Ts)
# velocities
thr.vel.W = f.isen_velocity(cp, thr.T0r,
thr.T) # = np.sqrt(2*cp*(thr.T0r - thr.T))
# speed of sound and relative mach number
thr.vel.a, thr.vel.Mr = f.sonic(gamma, R, thr.T,
thr.vel.W) # = np.sqrt(gamma*R*thr.T)
# velocity projections, axial and tangential
thr.vel.Wx, thr.vel.Wu = f.velocity_projections(thr.vel.W, thr.beta)
# constant radius, constant peripheral speed
thr.vel.U = two.vel.U
# tangential outlet speed
thr.vel.Vu = thr.vel.Wu + thr.vel.U
# V3u_euler = -DeltaH_prod/two.vel.U + two.vel.Vu
# assume axial speed constant
thr.vel.Vx = thr.vel.Wx
thr.vel.V = f.mag(
thr.vel.Vx, thr.vel.Vu) # = np.sqrt(thr.vel.Vx**2 + thr.vel.Vu**2)
Mach3_calculated = thr.vel.V / thr.vel.a
return Mach3_calculated - Mach3
thr.vel.M = fsolve(f_mach3,
thr.vel.M,
args=(one, two, thr, stator, rotor, gamma, cp, R, GR,
psi, DeltaH_prod))[0]
# speed of sound and relative mach number AT 3
thr.vel.a, thr.vel.Mr = f.sonic(gamma, R, thr.T,
thr.vel.W) # = np.sqrt(gamma*R*thr.T)
# using mach, find static pressure
thr.P = f.static_pressure(
thr.P0, gamma,
thr.vel.M) # = thr.P0/(1+(gamma-1)/2*thr.vel.M**2)**(gamma/(gamma-1))
thr.Ts = f.P2T(thr.T0, thr.P, thr.P0,
gamma) # = thr.T0*(thr.P/thr.P0)**((gamma-1)/gamma)
# find intermediate static pressure
two.P = one.P0 * ((GR - 1) * (1 - (thr.P / one.P0)**(
(gamma - 1) / gamma)) + 1)**(gamma / (gamma - 1)) # GP rp definition
# isentropic evolution in stator: absolute total temperature is same
two.T0 = one.T0
two.Ts = f.P2T(one.T0, two.P, one.P0,
gamma) # = one.T0*(two.P/one.P0)**((gamma-1)/gamma)
two.vel.Vs = f.isen_velocity(cp, two.T0,
two.Ts) # = np.sqrt(2*cp*(two.T0 - two.Ts))
# assume rotor efficiency
two.T = f.stage_efficiency(stator.eta, two.T0,
two.Ts) # = two.T0 - stator.eta*(two.T0-two.Ts)
two.vel.V = f.isen_velocity(cp, two.T0,
two.T) # = np.sqrt(2*cp*(two.T0 - two.T))
# density (from static quantities)
two.rho = f.static_density(two.P, two.T, R) # = two.P/two.T/R
# speed of sound and Mach
two.vel.a, two.vel.M = f.sonic(
gamma, R, two.T,
two.vel.V) # = np.sqrt(gamma*R*two.T), = two.vel.V/two.vel.a
two.P0 = f.T2P(two.P, two.T0, two.T,
gamma) # = two.P*(two.T0/two.T)**(gamma/(gamma-1))
# assume an two.alpha and project velocities
two.vel.Vx, two.vel.Vu = f.velocity_projections(two.vel.V, two.alpha)
if two.vel.Vx == 0:
two.vel.Vx = 0.00000001
# assume a loading factor and calculate peripheral speed
two.vel.U = np.sqrt(DeltaH_prod / psi)
# velocity triangle (pithagoras)
two.vel.Wu = two.vel.Vu - two.vel.U
two.vel.Wx = two.vel.Vx
two.vel.W = f.mag(two.vel.Wu, two.vel.Wx)
# relative inlet angle and relative Mach number
two.beta = np.arctan(two.vel.Wu / two.vel.Vx)
two.vel.Mr = two.vel.W / two.vel.a
# relative total quantities at rotor inlet
# (add relative speed to static conditions)
# two.T0r = two.T*(1 + two.vel.Mr**2*(gamma-1)/2) # total temperature is conserved
# two.P0r = two.P*(1 + (gamma-1)/2*two.vel.Mr**2)**(gamma/(gamma-1))
two.T0r, two.P0r = f.relative_temperature_pressure(two.T, two.P,
two.vel.Mr, gamma)
############ ROTOR #############
# in the rotor, the relative total temperature is constant (se conservan rotalpías)
thr.T0r = two.T0r
# ideal outlet temperature, real outlet temperature
# assuming the expanse to thr.P, calculated with the assumed M3
thr.Ts = f.P2T(thr.T0r, thr.P, two.P0r,
gamma) # = thr.T0r*(thr.P/two.P0r)**((gamma-1)/gamma)
thr.T = f.stage_efficiency(
rotor.eta, thr.T0r, thr.Ts) # = thr.T0r - rotor.eta*(thr.T0r - thr.Ts)
# velocities
thr.vel.W = f.isen_velocity(cp, thr.T0r,
thr.T) # = np.sqrt(2*cp*(thr.T0r - thr.T))
thr.vel.Ws = f.isen_velocity(cp, thr.T0r,
thr.Ts) # = np.sqrt(2*cp*(thr.T0r - thr.Ts))
# density
thr.rho = f.static_density(thr.P, thr.T, R) # = thr.P/thr.T/R
# speed of sound and relative mach number
thr.vel.a, thr.vel.Mr = f.sonic(gamma, R, thr.T,
thr.vel.W) # = np.sqrt(gamma*R*thr.T)
# total absolute pressure
thr.P0r = f.T2P(thr.P, thr.T0r, thr.T,
gamma) # = thr.P*(thr.T0r/thr.T)**(gamma/(gamma-1))
# assume a value for thr.beta
# velocity projections, axial and tangential
thr.vel.Wx, thr.vel.Wu = f.velocity_projections(thr.vel.W, thr.beta)
# constant radius, constant peripheral speed
thr.vel.U = two.vel.U
# tangential outlet speed
thr.vel.Vu = thr.vel.Wu + thr.vel.U
# V3u_euler = -DeltaH_prod/two.vel.U + two.vel.Vu
# assume axial speed constant
thr.vel.Vx = thr.vel.Wx
thr.vel.V = f.mag(thr.vel.Vx,
thr.vel.Vu) # = np.sqrt(thr.vel.Vx**2 + thr.vel.Vu**2)
thr.alpha = np.arctan(thr.vel.Vu / thr.vel.Vx)
U2 = np.sqrt(DeltaH_prod/phi) # velocity triangle (pithagoras) W2u = V2u - U2 W2x = V2x W2 = f.mag(W2u, W2x) # relative inlet angle and relative Mach number beta2 = np.arctan(W2u/V2x) Mach2r = W2/a2 # relative total quantities at rotor inlet # (add relative speed to static conditions) # T02r = T2*(1 + Mach2r**2*(gamma-1)/2) # total temperature is conserved # P02r = P2*(1 + (gamma-1)/2*Mach2r**2)**(gamma/(gamma-1)) T02r, P02r = f.relative_temperature_pressure(T2, P2, Mach2r, gamma) ############ ROTOR ############# # in the rotor, the relative total temperature is constant (se conservan rotalpías) T03r = T02r # ideal outlet temperature, real outlet temperature # assuming the expanse to P3, calculated with the assumed M3 T3s = f.P2T(T03r, P3, P02r, gamma) # = T03r*(P3/P02r)**((gamma-1)/gamma) T3 = f.stage_efficiency(eta_rotor, T03r, T3s) # = T03r - eta_rotor*(T03r - T3s) # velocities W3 = f.isen_velocity(cp, T03r, T3) # = np.sqrt(2*cp*(T03r - T3)) W3s = f.isen_velocity(cp, T03r, T3s) # = np.sqrt(2*cp*(T03r - T3s)) # density
U2 = np.sqrt(DeltaH_prod / phi)
# velocity triangle (pithagoras)
W2u = V2u - U2
W2x = V2x
W2 = f.mag(W2u, W2x)
# relative inlet angle and relative Mach number
beta2 = np.arctan(W2u / V2x)
Mach2r = W2 / a2
# relative total quantities at rotor inlet
# (add relative speed to static conditions)
# T02r = T2*(1 + Mach2r**2*(gamma-1)/2) # total temperature is conserved
# P02r = P2*(1 + (gamma-1)/2*Mach2r**2)**(gamma/(gamma-1))
T02r, P02r = f.relative_temperature_pressure(T2, P2, Mach2r, gamma)
############ ROTOR #############
# in the rotor, the relative total temperature is constant (se conservan rotalpías)
T03r = T02r
# ideal outlet temperature, real outlet temperature
# assuming the expanse to P3, calculated with the assumed M3
T3s = f.P2T(T03r, P3, P02r, gamma) # = T03r*(P3/P02r)**((gamma-1)/gamma)
T3 = f.stage_efficiency(eta_rotor, T03r,
T3s) # = T03r - eta_rotor*(T03r - T3s)
# velocities
W3 = f.isen_velocity(cp, T03r, T3) # = np.sqrt(2*cp*(T03r - T3))
W3s = f.isen_velocity(cp, T03r, T3s) # = np.sqrt(2*cp*(T03r - T3s))