def test_calculate_p_rho_h(self):
# Let's use figure 14.5a p. 610 Anderson to choose a good test point.
# Let's look at the 35900 ft curve at u1 = 10000 ft/s = 3048 m/s
# Looking at sentence above table IV in Huber (reference [165] in Anderson) we see that
# at 35900 ft then p1 = 0.2250 atm = 0.2250 * 1.013 Pa and T1 = 217 K.
# Air can be approximated pretty precisely as perfect at these conditions so let's
# use the perfect gas law to calculate rho1.
# Also, calculate h1 under the perfect gas assumption, h1 = c_p * T1.
u1 = 3048.
p1 = 0.2250 * 1.013E5
T1 = 217.
c_p = 1003.5
h1 = c_p * T1
R = 287.
rho1 = p1 / (R * T1)
rho2_guess = 10. * rho1
calculated_properties = calculators.calculate_p_rho_h(u1, p1, rho1, T1, h1, rho2_guess)
rho2_calculated = calculated_properties['density']
p2_calculated = calculated_properties['pressure']
h2_calculated = calculated_properties['enthalpy']
# Reading off figure 14.5a we estimate rho2_known as:
rho2_known = 7.8 * rho1
# Errors could be introduced through rho1 and h1 and reading of figure 14.5a.
# Allow for these error sources when choosing a value for rho_tolerance.
# A print statement on rho1 in a previous supplied rho1 = 0.366, which means that
# rho2 = 2.855. Allow for 5% error, i.e. 0.15 * 2.855 = 0.14.
rho_tolerance = 0.14
self.assertTrue(numpy.abs(rho2_known - rho2_calculated) < rho_tolerance)
def create_figures(u1_list_feet, engauge_list, figure_name, figure_type):
"""
Create one temperature figure and one density ratio figure (like in figures 14.4 and 14.5b
in Anderson pages 609 and 610), for a given input of upstream velocity absicca values.
:param u1_list_feet: A numpy array of upstream velocity values, in ft/s, to use as abscissa values
on the figures. Each line in the array corresponds to the velocity range of a single curve.
:param engauge_list: A list of n by 2 numpy arrays, where each array has n datapoints, generated by
Engauge, for one curve.
:param figure_type: 'temperature' or 'density' depending on which type of figure is to be plotted.
:param figure_name: The name of the output png file (excluding the .png ending).
"""
# Note: Altitude is in ft.
altitude = constants.altitude
number_of_curves = len(altitude)
# Pressure and temperature values are obtained from tables from Huber 1963
# (Anderson reference [165]).
p1_vector = constants.p1_upstream
T1_vector = constants.T1_upstream
# We can assume perfect gas before shock to calculate upstream properties.
rho1_vector = p1_vector / (constants.R * T1_vector)
h1_vector = constants.c_p * T1_vector
density_increase_guess = 10.
rho2_guess_vector = density_increase_guess * rho1_vector
# Need upstream velocity values in m/s to use in calculations.
# Also create a list of vectors to store computation results for temperature and density ratio.
# Since each curve has a different range of upstream velocities the number of values
# computed for temperature and density ratios is different for different curves.
u1_list = []
T2_list = []
rho_ratio_list = []
for i, u1_vector_feet in enumerate(u1_list_feet):
u1_vector = u1_vector_feet * constants.feet_to_m
u1_list.append(u1_vector)
vector_length = len(u1_vector_feet)
T2_vector = numpy.empty(vector_length)
T2_list.append(T2_vector)
rho_ratio_vector = numpy.empty(vector_length)
rho_ratio_list.append(rho_ratio_vector)
# Outer loop decides at what altitude we are at on the figure and so data for one curve is
# created for each passing through the outer loop.
# T2_array = numpy.empty([number_of_curves, vector_length])
# rho_ratio_array = numpy.empty([number_of_curves, vector_length])
for u1_vector, p1, rho1, h1, rho2_guess, T2_vector, rho_ratio_vector in \
zip(u1_list, p1_vector, rho1_vector, h1_vector, rho2_guess_vector, T2_list, rho_ratio_list):
# The inner loop loops over all the u1 velocities on the abscissa of the figure.
for j, u1 in enumerate(u1_vector):
out_dict = calculators.calculate_p_rho_h(u1, p1, rho1, h1, rho2_guess)
p2 = out_dict['pressure']
rho2 = out_dict['density']
T2 = calculators.srinivasan_T(p2, rho2)
T2_vector[j] = T2
rho_ratio_vector[j] = rho2 / rho1
if figure_type == 'temperature':
figure = pyplot.figure()
axes = figure.add_subplot(111)
for u1_vector_feet, T2_vector in zip(u1_list_feet, T2_list):
pyplot.plot(u1_vector_feet, T2_vector, 'b')
for engauge_array in engauge_list:
pyplot.plot(engauge_array[:,0], engauge_array[:,1], 'r')
# for i in range(engauge_list.shape[1]-1):
# curve_index = i+1
# pyplot.plot(engauge_list[:,0], engauge_list[:,curve_index], 'r')
xlabel = r'$u_{1}, ft/s$'
axes.set_xlabel(xlabel)
ylabel = r'$T_{2}, K$'
axes.set_ylabel(ylabel)
print 'Figure ' + figure_name + '.png' + ' has been created.'
pylab.savefig(figure_name+'.png')
if figure_type == 'density':
figure = pyplot.figure()
axes = figure.add_subplot(111)
for u1_vector_feet, rho_ratio_vector in zip(u1_list_feet, rho_ratio_list):
pyplot.plot(u1_vector_feet, rho_ratio_vector, 'b')
for engauge_array in engauge_list:
pyplot.plot(engauge_array[:,0], engauge_array[:,1], 'r')
xlabel = r'$u_{1}, ft/s$'
axes.set_xlabel(xlabel)
ylabel = r'$\frac{\rho_{2}}{\rho_{1}}$'
axes.set_ylabel(ylabel, rotation='horizontal')
print 'Figure ' + figure_name + '.png' + ' has been created.'
pylab.savefig(figure_name+'.png')
