def no_losses(stator, rotor, one, two, thr, gamma, cp, R, GR, psi, DeltaH_prod, bounds_angles, RHT, mdot):
# 1.
# mach 3 converge until calculated value meets the initial guess
# inside of this function, alpha2 and beta 3 are also set so that the DeltaH is met
one, two, thr, stator, rotor = converge_mach3(one, two, thr, stator, rotor, gamma, cp, R, GR, psi, DeltaH_prod, bounds_angles)
# 1.2
# calculate loss coefficients
stator = f.losses(two.vel.V, two.vel.Vs, one.P0, two.P0, two.P, stator)
rotor = f.losses(thr.vel.W, thr.vel.Ws, two.P0r, thr.P0r, thr.P, rotor)
# 1.4
# compute total condtions
thr.T0, thr.P0 = f.total_conditions(thr.T, thr.vel.V, thr.P, cp, gamma)
# 2.
# establish geometry after assuming RHT
f.geometry(RHT, one, two, thr, mdot, R, gamma, cp)
# 2.2
# check limits
pass_limits = check_limits(two, thr)
stator.eta = (one.T0 - thr.T0)/(one.T0 - (thr.Ts+thr.vel.V**2/2/cp))
rotor.eta = (one.T0 - thr.T0)/(one.T0 - thr.Ts)
def f_etas(etas, stator, rotor, one, two, thr, gamma, cp, R, GR, psi,
DeltaH_prod, bounds_angles, RHT, mdot):
stator.eta = etas[0]
rotor.eta = etas[1]
# 1.
# mach 3 converge until calculated value meets the initial guess
# inside of this function, alpha2 and beta 3 are also set so that the DeltaH is met
one, two, thr, stator, rotor = converge_mach3(one, two, thr, stator,
rotor, gamma, cp, R, GR,
psi, DeltaH_prod,
bounds_angles)
# 1.2
# calculate loss coefficients
stator = f.losses(two.vel.V, two.vel.Vs, one.P0, two.P0, two.P, stator)
rotor = f.losses(thr.vel.W, thr.vel.Ws, two.P0r, thr.P0r, thr.P, rotor)
# 1.4
# compute total condtions
thr.T0, thr.P0 = f.total_conditions(thr.T, thr.vel.V, thr.P, cp, gamma)
# 2.
# establish geometry after assuming RHT
solve_geometry(RHT, one, two, thr, mdot, R, gamma, cp)
# efficiency calculations
stator.eta = (one.T0 - thr.T0) / (one.T0 -
(thr.Ts + thr.vel.V**2 / 2 / cp))
rotor.eta = (one.T0 - thr.T0) / (one.T0 - thr.Ts)
diff1 = abs(stator.eta - etas[0])
diff2 = abs(rotor.eta - etas[1])
return np.array([diff1, diff2])
def f_etas(etas, stator, rotor, one, two, thr, gamma, cp, R, GR, psi,
DeltaH_prod, bounds_angles, RHT, mdot):
stator.eta = etas[0]
rotor.eta = etas[1]
# 1.
# mach 3 converge until calculated value meets the initial guess
# inside of this function, alpha2 and beta 3 are also set so that the DeltaH is met
one, two, thr, stator, rotor = converge_mach3(one, two, thr, stator,
rotor, gamma, cp, R, GR,
psi, DeltaH_prod,
bounds_angles)
# 1.2
# calculate loss coefficients
stator = f.losses(two.vel.V, two.vel.Vs, one.P0, two.P0, two.P, stator)
rotor = f.losses(thr.vel.W, thr.vel.Ws, two.P0r, thr.P0r, thr.P, rotor)
# 1.4
# compute total condtions
thr.T0, thr.P0 = f.total_conditions(thr.T, thr.vel.V, thr.P, cp, gamma)
# 2.
# establish geometry after assuming RHT
solve_geometry(RHT, one, two, thr, mdot, R, gamma, cp)
# efficiency calculations
stator.eta = (one.T0 - thr.T0) / (one.T0 -
(thr.Ts + thr.vel.V**2 / 2 / cp))
rotor.eta = (one.T0 - thr.T0) / (one.T0 - thr.Ts)
# calculate reynolds numbers
f.reynolds(two, thr)
f.trailing_throat(two, thr)
# use kacker-okapuu to calculate losses in stator and rotor
stator.omegaKC = kackerokapuu('stator', two.geo.s, abs(one.alpha),
abs(two.beta), two.geo.c, two.geo.bx,
two.geo.h, one.vel.M, two.vel.M, one.P,
two.P, gamma, RHT, two.Re, two.geo.to)
rotor.omegaKC = kackerokapuu('rotor', thr.geo.s, abs(two.alpha),
abs(thr.beta), thr.geo.c, thr.geo.bx,
thr.geo.h, two.vel.M, thr.vel.M, two.P,
thr.P, gamma, RHT, thr.Re, thr.geo.to)
diff1 = abs(stator.omega - stator.omegaKC)
diff2 = abs(rotor.omega - rotor.omegaKC)
print(diff1, diff2)
return np.array([diff1, diff2])
def f_etas(etas, stator, rotor, one, two, thr, gamma, cp, R, GR, psi,
DeltaH_prod, bounds_angles, RHT, mdot):
stator.eta = etas[0]
rotor.eta = etas[1]
# 1.
# mach 3 converge until calculated value meets the initial guess
# inside of this function, alpha2 and beta 3 are also set so that the DeltaH is met
one, two, thr, stator, rotor = converge_mach3(one, two, thr, stator,
rotor, gamma, cp, R, GR,
psi, DeltaH_prod,
bounds_angles)
# 1.2
# calculate loss coefficients
stator = f.losses(two.vel.V, two.vel.Vs, one.P0, two.P0, two.P, stator)
rotor = f.losses(thr.vel.W, thr.vel.Ws, two.P0r, thr.P0r, thr.P, rotor)
# 1.4
# compute total condtions
thr.T0, thr.P0 = f.total_conditions(thr.T, thr.vel.V, thr.P, cp, gamma)
# 2.
# establish geometry after assuming RHT
f.geometry(RHT, one, two, thr, mdot, R, gamma, cp)
# calculate reynolds numbers
f.reynolds(two, thr)
# use kacker-okapuu to calculate losses in stator and rotor
kackerokapuu(one, two, thr, stator, rotor, gamma, RHT)
diff1 = abs(stator.omega - stator.omegaKO)
diff2 = abs(rotor.omega - rotor.omegaKO)
return diff1 + diff2
thr.beta = np.radians(-65) # rotor angle [deg->rad] RHT = 0.9 # ratio hub/tip radius mdot = 0.777482308 # total mass flow [kg/s] one.rho = 0.98317 # inlet density [kg/m^3] thr.geo.Rh = 0.106 # radius of hub at rotor exit [m] one.alpha = 0 # stator inlet angle (0 if asusmed axial) [rad] bounds_angles = ([np.radians(70),np.radians(-65)], [np.radians(75), np.radians(-60)]) one, two, thr, stator, rotor = converge_mach3(Mach3_init, one, two, thr, stator, rotor, gamma, cp, R, GR, phi, DeltaH_prod, bounds_angles) # stator kinetic loss coefficient # check loss inpose ??? ### # Total pressure loss # stator pressure loss coefficient, Total pressure loss down 02 xi_stator, loss_stator, tpl_stator, omega_stator = f.losses(two.vel.V, two.vel.Vs, one.P0, two.P0, two.P) # = (two.vel.Vs**2 - two.vel.V**2)/two.vel.Vs**2, = two.vel.V**2/two.vel.Vs**2, = (one.P0 - two.P0)/(one.P0 - two.P), = (one.P0 - two.P0)/(two.P0 - two.P) ### equation for xi is different in report and excel sheet (corregir) # rotor kinetic loss coefficient # check loss inpose ??? ### # Total pressure loss # rotor pressure loss coefficient, Total pressure loss down 02 xi_rotor, loss_rotor, tpl_rotor, omega_rotor = f.losses(thr.vel.W, thr.vel.Ws, two.P0r, thr.P0r, thr.P) # = (two.vel.Vs**2 - two.vel.V**2)/two.vel.Vs**2, = two.vel.V**2/two.vel.Vs**2, = (one.P0 - two.P0)/(one.P0 - two.P), = (one.P0 - two.P0)/(two.P0 - two.P) ### equation for xi is different in report and excel sheet (corregir) ### denominator no coincide entre excel and JS report DeltaH_T1 = thr.vel.U*(two.vel.Vu-thr.vel.Vu) # euler formulation
def converge_efficiencies_limits(etas, stator, rotor, one, two, thr, gamma, cp, R, GR, psi, DeltaH_prod, RHT, mdot, list_lb, list_ub):
def f_etas(etas, stator, rotor, one, two, thr, gamma, cp, R, GR, psi, DeltaH_prod, RHT, mdot):
stator.eta = etas[0]
rotor.eta = etas[1]
two.alpha = etas[2]
thr.beta = etas[3]
# 1.
# mach 3 converge until calculated value meets the initial guess
# inside of this function, alpha2 and beta 3 are also set so that the DeltaH is met
converge_mach3(one, two, thr, stator, rotor, gamma, cp, R, GR, psi, DeltaH_prod)
# 1.2
# calculate loss coefficients
stator = f.losses(two.vel.V, two.vel.Vs, one.P0, two.P0, two.P, stator)
rotor = f.losses(thr.vel.W, thr.vel.Ws, two.P0r, thr.P0r, thr.P, rotor)
# 1.4
# compute total condtions
thr.T0, thr.P0 = f.total_conditions(thr.T, thr.vel.V, thr.P, cp, gamma)
# 2.
# establish geometry after assuming RHT
f.geometry(RHT, one, two, thr, mdot, R, gamma, cp)
# efficiency calculations
stator.eta = (one.T0 - thr.T0)/(one.T0 - (thr.Ts+thr.vel.V**2/2/cp))
rotor.eta = (one.T0 - thr.T0)/(one.T0 - thr.Ts)
# calculate reynolds numbers
f.reynolds(two, thr)
# use kacker-okapuu to calculate losses in stator and rotor
stator.omegaKC = kackerokapuu('stator', two.geo.s, abs(one.alpha), abs(two.beta), two.geo.c, two.geo.bx, two.geo.h, one.vel.M, two.vel.M, one.P, two.P, gamma, RHT, two.Re, two.geo.to)
rotor.omegaKC = kackerokapuu('rotor', thr.geo.s, abs(two.alpha), abs(thr.beta), thr.geo.c, thr.geo.bx, thr.geo.h, two.vel.Mr, thr.vel.Mr, two.P, thr.P, gamma, RHT, thr.Re, thr.geo.to)
DeltaH_calculated = two.vel.U*(two.vel.Vu - thr.vel.Vu)
diff0 = abs(DeltaH_calculated - DeltaH_prod)
diff1 = abs(stator.omega - stator.omegaKC)
diff2 = abs(rotor.omega - rotor.omegaKC)
return np.amax(np.array([diff1, diff2, diff0]))
# def nlc_values(etas, stator, rotor, one, two, thr, gamma, cp, R, GR, psi, DeltaH_prod, bounds_angles, RHT, mdot):
def nlc_values(etas):
values = np.ones((1,8))
values[0,0] = np.degrees(abs(two.alpha - thr.alpha))
values[0,1] = np.degrees(abs(two.beta - thr.beta))
values[0,2] = thr.geo.A/two.geo.A
values[0,3] = two.vel.M
values[0,4] = two.vel.Mr
values[0,5] = thr.vel.M
values[0,6] = thr.vel.Mr
values[0,7] = np.degrees(two.beta)
arr = values.tolist()
# arr = [np.degrees(abs(two.alpha - thr.alpha)), np.degrees(abs(two.beta - thr.beta)), thr.geo.A/two.geo.A]
return arr[0]
def nlc_limits():
limits = np.ones((2,8))
limits[0:2,0] = [0,120] # turning alpha (alpha 2 - alpha 3) [deg]
limits[0:2,1] = [0,120] # turning beta (beta 2 - beta 3) [deg]
limits[0:2,2] = [1,1.36] # height ratio (h3 / h2) [-]
limits[0:2,3] = [0.85,1.2] # absolute mach at 2 [-]
limits[0:2,4] = [0,0.50] # relative mach at 2 [-]
limits[0:2,5] = [0,0.60] # absolute mach at 3 [-]
limits[0:2,6] = [0.85,1.2] # relative mach at 3 [-]
limits[0:2,7] = [45,50] # relative rotor inlet angle beta2 [-]
lb = limits[0,:].tolist()
ub = limits[1,:].tolist()
# lb = [0,0,1]
# ub = [120, 120,1.34]
return lb, ub
f_etas(etas, stator, rotor, one, two, thr, gamma, cp, R, GR, psi, DeltaH_prod, RHT, mdot)
lb, ub = nlc_limits()
# con = lambda x: [np.degrees(abs(two.alpha - thr.alpha)), np.degrees(abs(two.beta - thr.beta)), thr.geo.A/two.geo.A, two.vel.M, two.vel.Mr, thr.vel.M, thr.vel.Mr, np.degrees(two.beta) ]
constraints = NonlinearConstraint(nlc_values, lb, ub)
bounds = Bounds(list_lb, list_ub)
res = minimize(f_etas, etas, bounds=bounds, constraints=constraints, args=(stator, rotor, one, two, thr, gamma, cp, R, GR, psi, DeltaH_prod, RHT, mdot), options={'disp': True})
etas = res.x
stator.eta = etas[0]
rotor.eta = etas[1]
two.alpha = etas[2]
thr.beta = etas[3]
# 1.
# mach 3 converge until calculated value meets the initial guess
# inside of this function, alpha2 and beta 3 are also set so that the DeltaH is met
converge_mach3(one, two, thr, stator, rotor, gamma, cp, R, GR, psi, DeltaH_prod)
# 1.2
# calculate loss coefficients
stator = f.losses(two.vel.V, two.vel.Vs, one.P0, two.P0, two.P, stator)
rotor = f.losses(thr.vel.W, thr.vel.Ws, two.P0r, thr.P0r, thr.P, rotor)
# 1.4
# compute total condtions
thr.T0, thr.P0 = f.total_conditions(thr.T, thr.vel.V, thr.P, cp, gamma)
# 2.
# establish geometry after assuming RHT
f.geometry(RHT, one, two, thr, mdot, R, gamma, cp)
# 2.2
# check limits
lim_checks, lim_lb, lim_ub, lim_values = check_limits(two, thr)
stator.eta = (one.T0 - thr.T0)/(one.T0 - (thr.Ts+thr.vel.V**2/2/cp))
rotor.eta = (one.T0 - thr.T0)/(one.T0 - thr.Ts)
return res
# use initial values to begin study thr.vel.M = Mach3_init two.alpha = alpha2_init thr.beta = beta3_init stator.eta = eta_stator_init rotor.eta = eta_rotor_init # mach 3 converge until calculated value meets the initial guess # inside of this function, alpha2 and beta 3 are also set so that the DeltaH is met one, two, thr, stator, rotor = converge_mach3(one, two, thr, stator, rotor, gamma, cp, R, GR, psi, DeltaH_prod, bounds_angles) # loss coefficients (stator) stator = f.losses(two.vel.V, two.vel.Vs, one.P0, two.P0, two.P, stator) # loss coefficients (rotor) rotor = f.losses(thr.vel.W, thr.vel.Ws, two.P0r, thr.P0r, thr.P, rotor) # DeltaH_calculations DeltaH_calc = thr.vel.U*(two.vel.Vu-thr.vel.Vu) # euler formulation DeltaH_T = cp*(one.T0-thr.T0) # total temperatur formulation # compute total condtions thr.T0, thr.P0 = f.total_conditions(thr.T, thr.vel.V, thr.P, cp, gamma) # establish geometry after assuming RHT converge_geometry(RHT, one, two, thr, mdot, R, gamma, cp)
# density (from static quantities) rho2 = f.static_density(P2,T2,R) # = P2/T2/R # speed of sound and Mach a2, Mach2 = f.sonic(gamma, R, T2, V2) # = np.sqrt(gamma*R*T2), = V2/a2 # check if pressure calculated meets the restriction T02b = T2+V2**2/2/cp ### include this in the check loop P02 = f.T2P(P2, T02, T2, gamma) # = P2*(T02/T2)**(gamma/(gamma-1)) # stator kinetic loss coefficient # check loss inpose ??? ### # Total pressure loss # stator pressure loss coefficient, Total pressure loss down 02 xi_stator, loss_stator, tpl_stator, omega_stator = f.losses(V2, V2s, P01, P02, P2) # = (V2s**2 - V2**2)/V2s**2, = V2**2/V2s**2, = (P01 - P02)/(P01 - P2), = (P01 - P02)/(P02 - P2) ### equation for xi is different in report and excel sheet (corregir) # assume an alpha2 and project velocities V2x, V2u = f.velocity_projections(V2, alpha2) # assume a loading factor and calculate peripheral speed 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
