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df0618fbf1
Provide better explanations of what the example is showing, and add plots of the temperature and pressure to better illustrate the resulting flow characteristics.
73 lines
2.2 KiB
Python
73 lines
2.2 KiB
Python
"""
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Converging-Diverging Nozzle
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===========================
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Calculate the area ratio vs. Mach number curve for a mixture accelerating to supersonic
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speed through a converging--diverging nozzle, assuming isentropic, adiabatic flow.
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The calculations are done for a 10:1 hydrogen/nitrogen mixture with stagnation
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temperature of 1200 K and a stagnation pressure of 10 atm.
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Requires: cantera >= 2.5.0, matplotlib >= 2.0
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.. tags:: Python, thermodynamics, compressible flow, plotting
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"""
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import cantera as ct
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import math
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import numpy as np
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import matplotlib.pyplot as plt
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# %%
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# Set initial conditions and get stagnation state parameters:
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gas = ct.Solution('h2o2.yaml')
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gas.TPX = 1200.0, 10.0*ct.one_atm, 'H2:1, N2:0.1'
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s0 = gas.s
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h0 = gas.h
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p0 = gas.P
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T0 = gas.T
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# %%
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# To calculate the state at different points, we can take pressure as the independent
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# variable and set the state of the gas based on that pressure and the entropy, which is
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# constant (:math:`s = s_0`) by the isentropic assumption. Assuming an adiabatic flow,
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# the total enthalpy is constant, which gives us an equation that can be solved for the
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# velocity:
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#
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# .. math:: h_0 = h + \frac{v^2}{2}
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#
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# Finally, conservation of mass requires:
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#
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# .. math:: \rho v A = \dot{m} = \textrm{constant}
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#
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# which gives us an equation that can be solved for the area.
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mdot = 1 # arbitrary
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n_points = 200
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data = np.zeros((n_points, 4))
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for i, p in enumerate(np.linspace(0.01 * p0, 0.99*p0, n_points)):
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# set the state using (s0, p)
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gas.SP = s0, p
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v = np.sqrt(2.0*(h0 - gas.h)) # h + V^2/2 = h0
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area = mdot / (gas.density * v) # rho*v*A = constant
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Ma = v/gas.sound_speed
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data[i, :] = [area, Ma, gas.T/T0, p/p0]
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# Normalize by the minimum area (nozzle throat)
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data[:, 0] /= min(data[:, 0])
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# %%
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# Plot the results:
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fig, ax = plt.subplots()
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h1 = ax.plot(data[:, 1], data[:, 3], 'C1', label='$P/P_0$')
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h2 = ax.plot(data[:, 1], data[:, 2], 'C2', label='$T/T_0$')
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ax.set(xlabel='Mach Number', ylabel='Temperature / Pressure Ratio',
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ylim=(0, 1.05))
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ax2 = ax.twinx()
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h3 = ax2.plot(data[:, 1], data[:, 0], label='$A/A^*$')
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ax2.set(ylabel='Area Ratio', ylim=(0,None))
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ax.legend(handles=[h1[0], h2[0], h3[0]], loc='upper center')
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plt.show()
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