def error_in_velocity(p3p4, state4=state4, state1=state1):
"Compute the velocity mismatch for a given pressure ratio across the expansion."
# Across the expansion, we get a test-gas velocity, V3g.
p3 = p3p4*state4.p
V3g, state3 = finite_wave_dp('cplus', 0.0, state4, p3)
# Across the contact surface.
p2 = p3
print "current guess for p3 and p2=", p2
V1s, V2, V2g, state2 = normal_shock_p2p1(state1, p2/state1.p)
return (V3g - V2g)/V3g
def error_in_velocity(p5p2, state2=state2, V2g=V2g, state10=state10):
"Compute the velocity mismatch for a given pressure ratio across the expansion."
# Across the expansion, we get a test-gas velocity, V5g.
V5g, state5 = finite_wave_dp('cplus', V2g, state2, p5p2 * state2.p)
# Across the contact surface, p20 == p5
p20 = p5p2 * state2.p
print "current guess for p5 and p20=", p20
V10, V20, V20g, state20 = normal_shock_p2p1(state10, p20 / state10.p)
return (
V5g - V10
) / V5g # V10 was V20g - lab speed of accelerator gas - we now make the assumption that this is the same as the shock speed
def main():
#build some gas objects
print "pure He driver gas"
state4 = Gas({'He': 1.0}, inputUnits='moles', outputUnits='moles')
state4.set_pT(2.79e+07, 2700.0)
print "state1:"
state4.write_state(sys.stdout)
print "Air test gas"
state1 = Gas({
'Air': 1.0,
})
state1.set_pT(3000.0, 300.0)
print "state1:"
state1.write_state(sys.stdout)
#
print "Air accelerator gas"
state5 = Gas({'Air': 1.0})
state5.set_pT(10.0, 300.0)
print "state10:"
state5.write_state(sys.stdout)
print "Steady expansion of driver"
#for 100%He condition mach number terminating steady expansion is 2.15
#need to work out the corresponding pressure for this to put into
#the function
M4dash = 2.15 #mach number terminating steady expansion
(state4dash,
V4dash) = expand_from_stagnation(1.0 / (p0_p(M4dash, state4.gam)), state4)
print "state4dash:"
state4dash.write_state(sys.stdout)
print "V4dash = {0} m/s".format(V4dash)
#I think we need to start guessing shock speeds to be able to keep going here
print "Start working on the shock into the test gas"
print "Guess US1 of 5080 m/s"
state2 = state1.clone()
V2, V2g = normal_shock(state1, 5080.0, state2)
print "state2:"
state2.write_state(sys.stdout)
print "Checks:"
print "p2/p1=", state2.p / state1.p
print "rho2/rho1=", state2.rho / state1.rho
print "T2/T1=", state2.T / state1.T
print "V2g = {0} m/s".format(V2g)
print "Unsteady expansion from state 4dash to state 3"
print "Well, giving it a go for now anyway"
(V3, state3) = finite_wave_dp('cplus',
V4dash,
state4dash,
state2.p,
steps=100)
print "state3:"
state3.write_state(sys.stdout)
print "V3 = {0} m/s".format(V3)
print "Start working on the shock into the accelerator gas"
print "Guess US2 of 11100 m/s"
state6 = state5.clone()
V6, V6g = normal_shock(state5, 11100.0, state6)
print "state6:"
state6.write_state(sys.stdout)
print "Checks:"
print "p2/p1=", state6.p / state5.p
print "rho2/rho1=", state6.rho / state5.rho
print "T2/T1=", state6.T / state5.T
print "V6g = {0} m/s".format(V6g)
print "Unsteady expansion from state 2 to state 7"
print "Well, giving it a go for now anyway"
(V7, state7) = finite_wave_dp('cplus', V2g, state2, state6.p, steps=100)
print "state7:"
state7.write_state(sys.stdout)
print "V7 = {0} m/s".format(V7)
M7 = V7 / (state7.gam * state7.R * state7.T)**(0.5)
print "M7 = {0}".format(M7)
"""
def main():
print "Helium driver gas"
state4 = Gas({'He':1.0})
state4.set_pT(30.0e6, 3000.0)
print "state4:"
state4.write_state(sys.stdout)
#
print "Air driven gas"
state1 = Gas({'Air':1.0})
state1.set_pT(30.0e3, 300.0)
print "state1:"
state1.write_state(sys.stdout)
#
print "\nNow do the classic shock tube solution..."
# For the unsteady expansion of the driver gas, regulation of the amount
# of expansion is determined by the shock-processed test gas.
# Across the contact surface between these gases, the pressure and velocity
# have to match so we set up some trials of various pressures and check
# that velocities match.
def error_in_velocity(p3p4, state4=state4, state1=state1):
"Compute the velocity mismatch for a given pressure ratio across the expansion."
# Across the expansion, we get a test-gas velocity, V3g.
p3 = p3p4*state4.p
V3g, state3 = finite_wave_dp('cplus', 0.0, state4, p3)
# Across the contact surface.
p2 = p3
print "current guess for p3 and p2=", p2
V1s, V2, V2g, state2 = normal_shock_p2p1(state1, p2/state1.p)
return (V3g - V2g)/V3g
p3p4 = secant(error_in_velocity, 0.1, 0.11, tol=1.0e-3)
print "From secant solve: p3/p4=", p3p4
print "Expanded driver gas:"
p3 = p3p4*state4.p
V3g, state3 = finite_wave_dp('cplus', 0.0, state4, p3)
print "V3g=", V3g
print "state3:"
state3.write_state(sys.stdout)
print "Shock-processed test gas:"
V1s, V2, V2g, state2 = normal_shock_p2p1(state1, p3/state1.p)
print "V1s=", V1s, "V2g=", V2g
print "state2:"
state2.write_state(sys.stdout)
assert abs(V2g - V3g)/V3g < 1.0e-3
#
# Make a record for plotting against the Eilmer3 simulation data.
# We reconstruct the expected data along a tube 0.0 <= x <= 1.0
# at t=100us, where the diaphragm is at x=0.5.
x_centre = 0.5 # metres
t = 100.0e-6 # seconds
fp = open('exact.data', 'w')
fp.write('# 1:x(m) 2:rho(kg/m**3) 3:p(Pa) 4:T(K) 5:V(m/s)\n')
print 'Left end'
x = 0.0
fp.write('%g %g %g %g %g\n' % (x, state4.rho, state4.p, state4.T, 0.0))
print 'Upstream head of the unsteady expansion.'
x = x_centre - state4.a * t
fp.write('%g %g %g %g %g\n' % (x, state4.rho, state4.p, state4.T, 0.0))
print 'The unsteady expansion in n steps.'
n = 100
dp = (state3.p - state4.p) / n
state = state4.clone()
V = 0.0
p = state4.p
for i in range(n):
rhoa = state.rho * state.a
dV = -dp / rhoa
V += dV
p += dp
state.set_ps(p, state4.s)
x = x_centre + t * (V - state.a)
fp.write('%g %g %g %g %g\n' % (x, state.rho, state.p, state.T, V))
print 'Downstream tail of expansion.'
x = x_centre + t * (V3g - state3.a)
fp.write('%g %g %g %g %g\n' % (x, state3.rho, state3.p, state3.T, V3g))
print 'Contact surface.'
x = x_centre + t * V3g
fp.write('%g %g %g %g %g\n' % (x, state3.rho, state3.p, state3.T, V3g))
x = x_centre + t * V2g # should not have moved
fp.write('%g %g %g %g %g\n' % (x, state2.rho, state2.p, state2.T, V2g))
print 'Shock front'
x = x_centre + t * V1s # should not have moved
fp.write('%g %g %g %g %g\n' % (x, state2.rho, state2.p, state2.T, V2g))
fp.write('%g %g %g %g %g\n' % (x, state1.rho, state1.p, state1.T, 0.0))
print 'Right end'
x = 1.0
fp.write('%g %g %g %g %g\n' % (x, state1.rho, state1.p, state1.T, 0.0))
fp.close()
return
def main():
print "Titan gas"
state1 = Gas({
'N2': 0.95,
'CH4': 0.05
},
inputUnits='moles',
outputUnits='moles')
state1.set_pT(2600.0, 300.0)
print "state1:"
state1.write_state(sys.stdout)
#
print "Air accelerator gas"
state10 = Gas({'Air': 1.0})
state10.set_pT(10.0, 300.0)
print "state10:"
state10.write_state(sys.stdout)
#
print "Incident shock"
state2 = state1.clone()
V2, V2g = normal_shock(state1, 4100.0, state2)
print "V2=", V2, "Vg=", V2g, "expected 3670.56"
print "state2:"
state2.write_state(sys.stdout)
print "Checks:"
print "p2/p1=", state2.p / state1.p, "expected 166.4"
print "rho2/rho1=", state2.rho / state1.rho, "expected 9.5474"
print "T2/T1=", state2.T / state1.T, "expected 14.9"
#
print "\nNow do unsteady expansion..."
# For the unsteady expansion of the test gas, regulation of the amount
# of expansion is determined by the shock-processed accelerator gas.
# Across the contact surface between these gases, the pressure and velocity
# have to match so we set up some trials of various pressures and check
# that velocities match.
def error_in_velocity(p5p2, state2=state2, V2g=V2g, state10=state10):
"Compute the velocity mismatch for a given pressure ratio across the expansion."
# Across the expansion, we get a test-gas velocity, V5g.
V5g, state5 = finite_wave_dp('cplus', V2g, state2, p5p2 * state2.p)
# Across the contact surface, p20 == p5
p20 = p5p2 * state2.p
print "current guess for p5 and p20=", p20
V10, V20, V20g, state20 = normal_shock_p2p1(state10, p20 / state10.p)
return (
V5g - V10
) / V5g # V10 was V20g - lab speed of accelerator gas - we now make the assumption that this is the same as the shock speed
p5p2 = secant(error_in_velocity, 0.01, 0.011, tol=1.0e-3)
print "From secant solve: p5/p2=", p5p2
# It would have been faster and the code closer to Hadas' spreadsheet if we had
# stepped down in pressure until we found the point where the velocities matched.
# The expansion along the u+a wave would have appeared in the code here.
V5g, state5 = finite_wave_dp('cplus', V2g, state2, p5p2 * state2.p)
print "Expanded test gas, at end of acceleration tube:"
print "V5g=", V5g
print "state5:"
state5.write_state(sys.stdout)
V10, V20, V20g, state20 = normal_shock_p2p1(state10, state5.p / state10.p)
print V10
print "Done."
return