.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/aerodynamics/compressible/plot_05_rankine_hugoniot_normal_shock.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_aerodynamics_compressible_plot_05_rankine_hugoniot_normal_shock.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_aerodynamics_compressible_plot_05_rankine_hugoniot_normal_shock.py:


Rankine-Hugoniot jump conditions across a normal shock
======================================================

W. J. Macquorn Rankine (1870) and Pierre-Henri Hugoniot (1887-1889) derived
the jump in state across a shock from conservation of mass, momentum and
energy alone. For a normal shock in a perfect gas the downstream Mach number
and pressure ratio are
:func:`~engineeringkit.aerodynamics.normal_shock_mach2` and
:func:`~engineeringkit.aerodynamics.normal_shock_pressure_ratio`. This example
reconstructs the full downstream state and checks the three conservation
laws, the entropy rise, and the loss of stagnation pressure.

.. GENERATED FROM PYTHON SOURCE LINES 16-25

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.aerodynamics import normal_shock_mach2, normal_shock_pressure_ratio, speed_of_sound, stagnation_pressure

    gamma, R = 1.4, 287.05287
    p1, T1 = 101325.0, 288.15
    M1 = np.linspace(1.0, 5.0, 81)








.. GENERATED FROM PYTHON SOURCE LINES 26-28

Reconstruct the downstream state
--------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 28-44

.. code-block:: Python


    rho1 = p1 / (R * T1)
    u1 = M1 * speed_of_sound(gamma, R, T1)
    p2 = p1 * normal_shock_pressure_ratio(M1, gamma)
    density_ratio = (gamma + 1) * M1**2 / ((gamma - 1) * M1**2 + 2)
    rho2 = rho1 * density_ratio
    T2 = p2 / (rho2 * R)
    u2 = normal_shock_mach2(M1, gamma) * speed_of_sound(gamma, R, T2)
    cp = gamma * R / (gamma - 1)

    mass = rho2 * u2 / (rho1 * u1) - 1
    momentum = (p2 + rho2 * u2**2) / (p1 + rho1 * u1**2) - 1
    energy = (cp * T2 + u2**2 / 2) / (cp * T1 + u1**2 / 2) - 1
    print(f"max conservation residuals: mass {np.max(abs(mass)):.1e}, momentum {np.max(abs(momentum)):.1e}, energy {np.max(abs(energy)):.1e}")
    assert np.allclose([mass, momentum, energy], 0, atol=1e-12)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    max conservation residuals: mass 3.3e-16, momentum 4.4e-16, energy 6.7e-16




.. GENERATED FROM PYTHON SOURCE LINES 45-47

Entropy rises and stagnation pressure falls
-------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 47-67

.. code-block:: Python


    entropy = cp * np.log(T2 / T1) - R * np.log(p2 / p1)
    p01 = stagnation_pressure(p1, M1, gamma)
    p02 = stagnation_pressure(p2, normal_shock_mach2(M1, gamma), gamma)
    assert np.all(entropy >= -1e-9)
    print(f"at M1 = 2: p02/p01 = {np.interp(2, M1, p02 / p01):.4f}, M2 = {float(normal_shock_mach2(2.0)):.4f}")

    fig, axes = plt.subplots(1, 3, figsize=(11, 3.3))
    axes[0].plot(M1, normal_shock_mach2(M1, gamma))
    axes[0].set(xlabel="$M_1$", ylabel="$M_2$", title="Downstream Mach")
    axes[1].plot(M1, p2 / p1, label="$p_2/p_1$")
    axes[1].plot(M1, density_ratio, label=r"$\rho_2/\rho_1$ (→ 6)")
    axes[1].plot(M1, T2 / T1, label="$T_2/T_1$")
    axes[1].set(xlabel="$M_1$", title="Static jumps")
    axes[1].legend()
    axes[2].plot(M1, p02 / p01)
    axes[2].set(xlabel="$M_1$", ylabel="$p_{02}/p_{01}$", title="Stagnation-pressure loss")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/aerodynamics/compressible/images/sphx_glr_plot_05_rankine_hugoniot_normal_shock_001.png
   :alt: Downstream Mach, Static jumps, Stagnation-pressure loss
   :srcset: /api/gallery/aerodynamics/compressible/images/sphx_glr_plot_05_rankine_hugoniot_normal_shock_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    at M1 = 2: p02/p01 = 0.7209, M2 = 0.5774





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.257 seconds)


.. _sphx_glr_download_api_gallery_aerodynamics_compressible_plot_05_rankine_hugoniot_normal_shock.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/aerodynamics/compressible/plot_05_rankine_hugoniot_normal_shock.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_05_rankine_hugoniot_normal_shock.ipynb <plot_05_rankine_hugoniot_normal_shock.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_05_rankine_hugoniot_normal_shock.py <plot_05_rankine_hugoniot_normal_shock.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_05_rankine_hugoniot_normal_shock.zip <plot_05_rankine_hugoniot_normal_shock.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_