
:html_theme.sidebar_secondary.remove:

.. py:currentmodule:: cantera


.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/python/thermo/sound_speed.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_python_thermo_sound_speed.py>`
        to download the full example code.

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

.. _sphx_glr_examples_python_thermo_sound_speed.py:


Sound speeds
============

Compute the "equilibrium" and "frozen" sound speeds for a gas

Requires: cantera >= 3.0.0, matplotlib

.. tags:: Python, thermodynamics, equilibrium

.. GENERATED FROM PYTHON SOURCE LINES 11-55

.. code-block:: Python


    import cantera as ct
    import math
    import numpy as np
    import matplotlib.pyplot as plt


    def equilSoundSpeeds(gas, rtol=1.0e-8, max_iter=5000):
        """
        Returns a tuple containing the equilibrium and frozen sound speeds for a
        gas with an equilibrium composition.  The gas is first set to an
        equilibrium state at the temperature and pressure of the gas, since
        otherwise the equilibrium sound speed is not defined.
        """

        # set the gas to equilibrium at its current T and P
        gas.equilibrate('TP', rtol=rtol, max_iter=max_iter)

        # save properties
        s0 = gas.s
        p0 = gas.P
        r0 = gas.density

        # perturb the pressure
        p1 = p0*1.0001

        # set the gas to a state with the same entropy and composition but
        # the perturbed pressure
        gas.SP = s0, p1

        # frozen sound speed
        afrozen = math.sqrt((p1 - p0)/(gas.density - r0))

        # now equilibrate the gas holding S and P constant
        gas.equilibrate('SP', rtol=rtol, max_iter=max_iter)

        # equilibrium sound speed
        aequil = math.sqrt((p1 - p0)/(gas.density - r0))

        # check against the built-in sound speed function
        afrozen2 = gas.sound_speed

        return aequil, afrozen, afrozen2








.. GENERATED FROM PYTHON SOURCE LINES 56-57

Calculate sound speed at a range of temperatures

.. GENERATED FROM PYTHON SOURCE LINES 57-70

.. code-block:: Python

    gas = ct.Solution('gri30_highT.yaml')
    gas.X = 'CH4:1.00, O2:2.0, N2:7.52'
    T_range = np.arange(300, 5901, 200)
    data = []
    print('   T     Equilibrium  Frozen manual  Frozen built-in')
    print('  [K]       [m/s]         [m/s]           [m/s]')
    print('-------  -----------  -------------  ---------------')
    for T in T_range:
        gas.TP = T, ct.one_atm
        aequil, afrozen, afrozen2 = equilSoundSpeeds(gas)
        data.append((T, aequil, afrozen, afrozen2))
        print(f'{T:6.1f}  {aequil:12.2f}  {afrozen:13.2f}  {afrozen2:15.2f}')





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

 .. code-block:: none

       T     Equilibrium  Frozen manual  Frozen built-in
      [K]       [m/s]         [m/s]           [m/s]
    -------  -----------  -------------  ---------------
     300.0        351.82         351.82           351.83
     500.0        450.54         450.54           450.54
     700.0        528.57         528.57           528.58
     900.0        594.39         594.39           594.39
    1100.0        653.02         653.03           653.03
    1300.0        706.54         706.64           706.64
    1500.0        755.61         756.33           756.34
    1700.0        800.09         803.03           803.04
    1900.0        839.27         847.59           847.60
    2100.0        873.72         891.07           891.07
    2300.0        906.65         934.86           934.86
    2500.0        942.15         980.70           980.70
    2700.0        982.98        1030.52          1030.52
    2900.0       1030.57        1086.41          1086.41
    3100.0       1086.27        1150.69          1150.69
    3300.0       1151.17        1224.86          1224.87
    3500.0       1224.11        1307.11          1307.11
    3700.0       1300.74        1390.78          1390.78
    3900.0       1375.91        1467.77          1467.77
    4100.0       1446.46        1533.98          1533.99
    4300.0       1509.89        1590.28          1590.29
    4500.0       1562.67        1639.67          1639.68
    4700.0       1603.00        1685.06          1685.07
    4900.0       1633.63        1728.73          1728.74
    5100.0       1659.84        1772.45          1772.45
    5300.0       1686.34        1817.70          1817.70
    5500.0       1716.15        1865.92          1865.92
    5700.0       1751.02        1918.55          1918.55
    5900.0       1792.09        1977.10          1977.10




.. GENERATED FROM PYTHON SOURCE LINES 71-72

Plot results

.. GENERATED FROM PYTHON SOURCE LINES 72-80

.. code-block:: Python

    data = np.array(data)
    fig, ax = plt.subplots()
    ax.plot(data[:,0], data[:,1], label='Equilibrium')
    ax.plot(data[:,0], data[:,2], label='Frozen (manual)')
    ax.plot(data[:,0], data[:,3], linestyle='none', marker='.', label='Frozen (built-in)')
    ax.set(xlabel='T [K]', ylabel='Sound Speed [m/s]')
    ax.legend()
    plt.show()



.. image-sg:: /examples/python/thermo/images/sphx_glr_sound_speed_001.png
   :alt: sound speed
   :srcset: /examples/python/thermo/images/sphx_glr_sound_speed_001.png, /examples/python/thermo/images/sphx_glr_sound_speed_001_2_00x.png 2.00x
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 1.065 seconds)


.. _sphx_glr_download_examples_python_thermo_sound_speed.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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