def __init__(self, left, right):
self.left = left
self.right = right
import math
u1 = left[0]
u2 = right[0]
# r1 = left[1];
# r2 = right[1]
T1 = left[1]
T2 = right[1]
p1 = left[2]
p2 = right[2]
# T1 = p1 / r1 / Rg();
# T2 = p2 / r2 / Rg()
r1 = p1 / Rg() / T1
r2 = p2 / Rg() / T2
k1 = k_Justi(T1)
k2 = k_Justi(T2)
a1 = math.sqrt(k1 * p1 / r1)
a2 = math.sqrt(k2 * p2 / r2)
print("-" * 100)
print("{0:^50}|{1:^50}".format("ul=%.5gm/s" % u1, "ur=%.5gm/s" % u2))
print("{0:^50}|{1:^50}".format("rhol=%.5gkg/m^3" % r1,
"rhor=%.5gkg/m^3" % r2))
print("{0:^50}|{1:^50}".format("pl=%sPa" % p1, "pr=%sPa" % p2))
print("{0:^50}|{1:^50}".format("Tl=%sK" % T1, "Tr=%sK" % T2))
print("-" * 100)
def openEnd(p, p0=1.e5, T0=300, R=None, k=None):
from GasProperty import k_Justi, Rg
from math import sqrt
if R is None:
R = Rg()
if k is None:
k = k_Justi(T0)
return sqrt(2 * k * R * T0 / (k - 1) * (1 - pow(p / p0, (k - 1) / k)))
def openEnd2(u, p0=1.e5, T0=300, R=None, k=None):
from GasProperty import k_Justi, Rg
from math import sqrt
if R is None:
R = Rg()
if k is None:
k = k_Justi(T0)
temp = 2 * k * R * T0 / (k - 1)
temp2 = 1 - u ** 2 / temp
return p0 * pow(temp2, k / (k - 1))
def airFlowExample(self, p1, T1, p2=None, T2=None, K2=None):
from GasProperty import Rg, k_Justi
R1 = Rg(T1)
R2 = Rg(T2)
k1 = k_Justi(T1)
k2 = k_Justi(T2)
step = 1.e-3 * p1
import numpy as np
for i in np.arange(0, p1, step):
self.data.append([i / p1, self.__massFlowRate(p1, T1, R1, k1, i)])
if p2 is not None and T2 is not None:
step2 = 0.01 * p2
for i in np.arange(0.5 * p2, p2, step):
self.data.append([
p2 / i,
self.__massFlowRate(i, T1, R1, k1, p2, T2, R2, K2)
])
return self.data
def eqnozzle(p, u, p0=1.e5, T0=300, phi=1, R=None, k=None):
from GasProperty import k_Justi, Rg
from math import sqrt
if R is None:
R = Rg()
if k is None:
k = k_Justi(T0)
temp = 2 * k * R * T0 / (k - 1)
temp2 = pow(p / p0, (k - 1) / k) - 1
temp3 = 1 / pow(phi, 2) * pow(p / p0, 2. / k) - 1
# return u ** 2 * temp3 - temp * temp2
return u ** 2 - temp * temp2*temp3
def nozzle(p, p0=1.e5, T0=300, phi=0.5, R=None, k=None):
from GasProperty import k_Justi, Rg
from math import sqrt
if R is None:
R = Rg()
if k is None:
k = k_Justi(T0)
temp = 2 * k * R * T0 / (k - 1)
temp2 = pow(p / p0, (k - 1) / k) - 1
temp3 = 1 / pow(phi, 2) * pow(p / p0, 2. / k) - 1
return sqrt(temp * temp2 / temp3)
def nozzle2(u, p0=1.e5, T0=300, phi=0.9, R=None, k=None):
from GasProperty import k_Justi, Rg
if R is None:
R = Rg()
if k is None:
k = k_Justi(T0)
pinit = 1.1 * p0
def fun(p):
# return nozzle(p,p0,T0,phi,R,k)-u
return eqnozzle(p, u, p0, T0, phi, R, k)
h = p0 / 1.e4
# print(fun(pinit))
while abs(fun(pinit)) > 1.e-5:
# print(fun(pinit))
# print(fun(pinit+h)-fun(pinit-h))
pinit -= fun(pinit) / ((fun(pinit + h) - fun(pinit - h)) / 2. / h)
return pinit
def solve(self, U=None, A=1, AFAK=1.e8):
from GasProperty import Rg
from GasProperty import k_Justi
if U is None:
U = self.U
else:
self.U = U
self.rho = U[0] / A
self.u = U[1] / U[0]
self.e = U[2] / U[0] - 1. / 2. * pow(U[1] / U[0], 2)
T = self.e * (1.4 - 1.) / Rg(AFAK)
# def kite(T):
# return self.e - Rg(AFAK) * T / (k_Justi(T, AFAK) - 1)
#
# h = 1.
# while abs(kite(T)) > 1.e-5:
# T -= kite(T) / ((kite(T + h) - kite(T - h)) / 2. / h)
self.T = T
self.k = k_Justi(T, AFAK)
self.p = Rg(AFAK) * T * self.rho
def AnalyticalSolution(t, left=[], right=[], xlim=None):
import math
u1 = left[0]
u2 = right[0]
# r1 = left[1];
# r2 = right[1]
T1 = left[1]
T2 = right[1]
p1 = left[2]
p2 = right[2]
# T1 = p1 / r1 / Rg();
# T2 = p2 / r2 / Rg()
r1 = p1 / Rg() / T1
r2 = p2 / Rg() / T2
k1 = k_Justi(T1)
k2 = k_Justi(T2)
a1 = math.sqrt(k1 * p1 / r1)
a2 = math.sqrt(k2 * p2 / r2)
# print("-" * 100)
# print("{0:^50}|{1:^50}".format("ul=%.5gm/s" % u1, "ur=%.5gm/s" % u2))
# print("{0:^50}|{1:^50}".format("rhol=%.5gkg/m^3" % r1, "rhor=%.5gkg/m^3" % r2))
# print("{0:^50}|{1:^50}".format("pl=%sPa" % p1, "pr=%sPa" % p2))
# print("{0:^50}|{1:^50}".format("Tl=%sK" % T1, "Tr=%sK" % T2))
# print("-" * 100)
def function(pbar, pj, rhoj, gamma=1.4):
if pbar == pj:
return 0
elif pbar > pj:
import math
aj = math.sqrt(gamma * pj / rhoj)
return (pbar - pj) / rhoj / aj / math.sqrt(
(gamma + 1) / 2. / gamma * pbar / pj +
(gamma - 1) / 2. / gamma)
elif pbar < pj:
import math
aj = math.sqrt(gamma * pj / rhoj)
return 2. * aj / (gamma - 1.) * (pow(pbar / pj,
(gamma - 1) / 2. / gamma) - 1)
def F(p):
return function(p, p1, r1, k1) + function(p, p2, r2, k2)
pbar = (p1 + p2) / 2
h = 10.
while abs(u1 - u2 - F(pbar)) > 1.e-5:
pbar -= (u1 - u2 - F(pbar)) / ((-F(pbar + h) + F(pbar - h)) / 2. / h)
# print(pbar)
ubar = (u1 + u2 - function(pbar, p1, r1, k1) +
function(pbar, p2, r2, k2)) / 2.
# print(ubar)
A1 = r1 * a1 * math.sqrt((k1 + 1.) / (2. * k1) * pbar / p1 +
(k1 - 1) / 2. / k1)
A2 = r2 * a2 * math.sqrt((k2 + 1.) / (2. * k2) * pbar / p2 +
(k2 - 1) / 2. / k2)
if pbar >= p1:
Z1 = u1 - A1 / r1
else:
Z1 = u1 - a1
if pbar >= p2:
Z2 = u2 + A2 / r2
else:
Z2 = u2 + a2
if pbar >= p1:
Z1star = Z1
elif pbar > 0:
a1star = a1 + (k1 - 1) / 2. * (u1 - ubar)
Z1star = ubar - a1star
else:
Z1star = u1 - 2. * a1 / (k1 - 1)
if pbar >= p2:
Z2star = Z2
elif pbar > 0:
a2star = a2 - (k2 - 1) / 2. * (u2 - ubar)
Z2star = ubar + a2star
else:
Z2star = u2 + 2 * a2 / (k2 - 1)
r1bar = r1 * A1 / (A1 - r1 * (u1 - ubar))
r2bar = r2 * A2 / (A2 + r2 * (u2 - ubar))
# print("Z1=", Z1)
# print("Z1star=", Z1star)
# print("ubar=", ubar)
# print("Z2star=", Z2star)
# print("Z2=", Z2)
if xlim is None:
Zlaggest = abs(Z1) if abs(Z1) > abs(Z2) else abs(Z2)
xlim = [-1.5 * t * Zlaggest, 1.5 * t * Zlaggest]
# print("Will draw air state between [{},{}]".format(xlim[0],xlim[1]))
def fun(t, x):
if x / t > Z2:
return u2, r2, p2
elif x / t < Z1:
return u1, r1, p1
elif Z1star < x / t < ubar:
return ubar, r1bar, pbar
elif ubar < x / t < Z2star:
return ubar, r2bar, pbar
elif Z1 < x / t < Z1star:
a = (k1 - 1) / (k1 + 1) * (u1 - x / t) + 2 * a1 / (k1 + 1)
u = x / t + a
p = p1 * pow(a / a1, 2 * k1 / (k1 - 1))
r = k1 * p / a / a
return u, r, p
elif Z2star < x / t < Z2:
a = (k2 - 1) / (k2 + 1) * (x / t - u2) + 2 * a2 / (k2 - 1)
u = x / t - a
p = p2 * pow(a / a2, 2 * k2 / (k2 - 1))
r = k2 * p / a / a
return u, r, p
result = ArrayTable(5, 0)
result.setTableHeader(
["x", "Velocity", "Density", "Pressure", "Temperature"])
result.setTableUnit(["m", "m/s", "kg/m^3", "Pa", "K"])
import numpy as np
step = (xlim[1] - xlim[0]) / 1000.
xx = np.arange(xlim[0], xlim[1], step)
for each in xx:
u, r, p = fun(t, each)
result.append([each, u, r, p, p / r / Rg()])
return result
def fun(pt):
Rge=Rg(setting["过量空气系数"])
k=k_Justi(Tt,setting["过量空气系数"])
temp=setting["涡轮当量流通面积,m^2"]*flowUnitArea(pt,Tt,Rge,k,Pt0)
print("涡前压力{},流量{}".format(pt,temp))
return (temp-ma)/ma