w3 = cj_speed*rho4/driver_gas.density
u3 = [w3-cj_speed]
## Evaluate initial state for expansion computation
rho3 = [driver_gas.density]
P3 = [driver_gas.P]
T3 = [driver_gas.T]
S4 = driver_gas.entropy_mass
## compute unsteady expansion (frozen)
print('Generating points on isentrope P-u curve')
vv = 1/rho3[0]
while u3[-1] < u2[-1]:
vv = vv*1.01
driver_gas.SVX = S4,vv,driver_gas.X
if EQ_EXP:
# required for equilibrium expansion
driver_gas.equilibrate('SV')
a3.append(soundspeed_eq(driver_gas))
else:
# use this for frozen expansion
a3.append(soundspeed_fr(driver_gas))
P3.append(driver_gas.P)
T3.append(driver_gas.T)
rho3.append(driver_gas.density)
u3.append(u3[-1] - 0.5*(P3[-1]-P3[-2])*(1/(rho3[-1]*a3[-1]) + 1./(rho3[-2]*a3[-2])))
## Input limits for finding intersection of polars
# estimate maximum speed
wmax = np.sqrt(2*h0)
# initialize variables for computing PM properties and plotting
rho = []; a = []; P = []; T = []; h = []; mu = []; M = []; Me = []; u = []; ue = [];
v1 = 1/rho2 # lower limit to specific volume in PM fan
v2 = 50*v1 # upper limit to specific volume in PM fan
vstep = 1000
##
# Compute expansion conditions over range from minimum to maximum specific volume.
# User can adjust the increment and endpoint to get a smooth output curve and reliable integral.
# Could also try a logarithmic range for some cases.
for v in np.linspace(v1,v2,num=vstep):
rho.append(1/v)
x = gas.X # update mole fractions based on last gas state
gas.SVX = s2,v,x
gas.equilibrate('SV') # required for equilibrium expansion
h.append(gas.enthalpy_mass)
u.append(np.sqrt(2*(h0-h[-1]))) # flow speed within expansion
# Need to explicitly upcast to complex, otherwise get NaN:
ue.append(np.real(np.sqrt(2*(np.asarray(h1-h[-1],dtype=complex))))) # ideal axial velocity for RDE model
a.append(soundspeed_eq(gas)) # use this for equilibrium expansion, almost always the case for detonation products
#a.append(soundspeed_fr(gas)) # use this for frozen expansion
Me.append(ue[-1]/a[-1])
M.append(u[-1]/a[-1])
if M[-1] < 1:
# Sometimes the first M value has been observed to be ~0.999 which leads to errors
# in the arcsin and sqrt functions that follow
M[-1] = 1.00001
mu.append(np.arcsin(1/M[-1]))
T.append(gas.T)
# stagnation enthalpy
h0 = h1 + U1**2/2
# estimate maximum speed
wmax = np.sqrt(2*h0)
# initialize variables for computing PM properties and plotting
v2 = 200*v1
rho = []; a = []; h = []; u = []; M = []; mu = []; T = []; P = []; streamwidth = [];
##
# Compute expansion conditions over range from minimum to maximum specific volume.
# User can adjust the increment and endpoint to get a smooth output curve and reliable integral.
# Could also try a logarithmic range for some cases.
for v in np.linspace(v1,v2,num=1000):
rho.append(1/v)
x = gas.X # update mole fractions based on last gas state
gas.SVX = s1,1/rho[-1],x
if EQ:
# required for equilibrium expansion
gas.equilibrate('SV')
a.append(soundspeed_eq(gas))
else:
# use this for frozen expansion
a.append(soundspeed_fr(gas))
h.append(gas.enthalpy_mass)
u.append(np.sqrt(2*(h0-h[-1])))
M.append(u[-1]/a[-1])
if M[-1] < 1:
# Sometimes the first M value has been observed to be ~0.999 which leads to errors
# in the arcsin and sqrt functions that follow
M[-1] = 1.00001
a = np.zeros(npoints, float)
u = np.zeros(npoints, float)
T = np.zeros(npoints, float)
V[1] = V2
P[1] = P2
D[1] = D2
a[1] = a2_eq
u[1] = u2
T[1] = T2
print('Generating points on isentrope and computing Taylor wave velocity')
i = 1
while u[i] > 0 and i < npoints:
i = i + 1
vv = vv * 1.01
x = gas.X
gas.SVX = S2, vv, x
gas.equilibrate('SV')
P[i] = gas.P
D[i] = gas.density
V[i] = 1 / D[i]
T[i] = gas.T
a[i] = soundspeed_eq(gas)
u[i] = u[i - 1] + 0.5 * (P[i] - P[i - 1]) * (1. / (D[i] * a[i]) + 1. /
(D[i - 1] * a[i - 1]))
# estimate plateau conditions by interpolation on last two points
nfinal = i
P3 = P[nfinal] + u[nfinal] * (P[nfinal - 1] - P[nfinal]) / (u[nfinal - 1] -
u[nfinal])
a3 = a[nfinal] + u[nfinal] * (a[nfinal - 1] - a[nfinal]) / (u[nfinal - 1] -
u[nfinal])
V3 = V[nfinal] + u[nfinal] * (V[nfinal - 1] - V[nfinal]) / (u[nfinal - 1] -
