Aerodynamics

Let pick a problem from the [Anderson] textbook.

Consider a normal shock wave in air. The upstream conditions are given by \(M_1 = 3, P_1 = 101 [kPa]\) and \(\rho_1 = 1.23 [kg/m3]\). Calculate the downstream values \(M_2, P_2, \rho_2\).

Open your favorite python instance, for this case I will open IPython and in IPython I will add the following lines.

import haot

downstream = haot.normal_shock_relations(3.0)

dowstream # Print dictionary values

>> {'mach_2': 0.4751909633114914,
    'pressure_r': 10.333333333333334,
    'temperature_r': 2.6790123456790123,
    'density_r': 3.857142857142857,
    'pressure_s': 0.32834388819073684}

The output is a dictionary, but the variable names may not be very intuitive. To gather more information, you can use Python’s help() function or consult the documentation in the modules section under the Aerodynamics module. However, for this example, we will rely solely on standard Python techniques.

help(haot.normal_shock_relations)

>> Calculates normal shock relations

    Parameters:
        mach_1: pre-shock mach number
        adiabatic_indx: adiabatic index, 1.4 (default)

    Returns:
        dict: A dictionary containing:
            - mach_2: post-shock mach number
            - pressure_r: pressure ratio (post-shock / pre-shock)
            - temperature_r: temperature ratio (post-shock / pre-shock)
            - density_r: density ratio (post-shock / pre-shock)
            - pressure_s: stagnation pressure ratio (post-shock / pre-shock)

    Reference:
        Normal Shock Wave - NASA (https://www.grc.nasa.gov/www/k-12/airplane/normal.html)

Now we can calculate the downstream values by multiplying the upstream values to the results provided by the module

print(downstream['pressure_r'] * 101)

>> 1043.6666666666667

print(downstream['density_r'] * 1.23)

>> 4.744285714285715

print(downstream['mach_2'])

>> 0.4751909633114914

[Anderson]

Modern Compressible Flow: With Historical Perspective (4th), Aderson J., ISBN: 978-1260471441