.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermodynamics/cycles/plot_05_diesel_cycle.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_thermodynamics_cycles_plot_05_diesel_cycle.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_thermodynamics_cycles_plot_05_diesel_cycle.py:


Diesel's compression-ignition cycle (1893)
==========================================

Rudolf Diesel's *Theorie und Konstruktion eines rationellen Wärmemotors*
(1893) set out to approach Carnot's efficiency by compressing air alone so
hard that injected fuel ignites by itself. Because there is no fuel in the
cylinder during compression, a diesel cannot knock and can use compression
ratios of 15-22. The fuel burns while the piston moves, which the
air-standard Diesel cycle idealizes as heat added at constant pressure up
to a cutoff ratio :math:`r_c = v_3/v_2`
(:func:`~engineeringkit.thermodynamics.diesel_efficiency`).

.. GENERATED FROM PYTHON SOURCE LINES 16-21

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.thermodynamics import diesel_efficiency, isentropic_temperature_ratio, otto_efficiency, thermal_efficiency








.. GENERATED FROM PYTHON SOURCE LINES 22-27

Four states from the first law
------------------------------

Compression ratio 18, cutoff ratio 2. Heat in is :math:`c_p(T_3 - T_2)`
at constant pressure, heat out :math:`c_v(T_4 - T_1)` at constant volume.

.. GENERATED FROM PYTHON SOURCE LINES 27-39

.. code-block:: Python


    R, gamma, r, rc, T1 = 287.0, 1.4, 18.0, 2.0, 300.0
    cv, cp = R / (gamma - 1), gamma * R / (gamma - 1)
    T2 = T1 * r ** (gamma - 1)
    T3 = T2 * rc
    T4 = T3 * (rc / r) ** (gamma - 1)
    eta = thermal_efficiency(cp * (T3 - T2), cv * (T4 - T1))
    print(f"T2 = {T2:.0f} K (autoignition), T3 = {T3:.0f} K, T4 = {T4:.0f} K")
    print(f"efficiency from the states {eta:.4f}, from the formula {diesel_efficiency(r, rc):.4f}")
    assert np.isclose(eta, diesel_efficiency(r, rc))
    assert np.isclose(T2 / T1, isentropic_temperature_ratio(r**gamma, gamma))





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

 .. code-block:: none

    T2 = 953 K (autoignition), T3 = 1907 K, T4 = 792 K
    efficiency from the states 0.6316, from the formula 0.6316




.. GENERATED FROM PYTHON SOURCE LINES 40-47

Diesel against Otto
-------------------

At the *same* compression ratio the Otto cycle wins: constant-pressure
heat addition takes in part of the heat at a lower temperature. A longer
cutoff (more fuel, more power) costs efficiency. But a diesel at 18 beats
a petrol engine held to 10 by knock.

.. GENERATED FROM PYTHON SOURCE LINES 47-62

.. code-block:: Python


    ratios = np.linspace(5, 24, 96)
    fig, ax = plt.subplots(figsize=(6, 3.5))
    ax.plot(ratios, otto_efficiency(ratios), "k", label="Otto ($r_c$ = 1)")
    for cutoff in (1.5, 2.0, 3.0):
        ax.plot(ratios, [diesel_efficiency(x, cutoff) for x in ratios], label=f"Diesel, $r_c$ = {cutoff:g}")
    ax.plot(10, otto_efficiency(10), "s", color="C3", label="petrol engine limited by knock")
    ax.plot(r, diesel_efficiency(r, rc), "o", color="C1", label="diesel at r = 18")
    ax.set(xlabel="compression ratio", ylabel="ideal efficiency", ylim=(0.4, 0.75))
    ax.legend(fontsize=8)
    fig.tight_layout()
    assert all(diesel_efficiency(x, 2.0) < otto_efficiency(x) for x in ratios)
    assert diesel_efficiency(r, rc) > otto_efficiency(10)

    plt.show()



.. image-sg:: /api/gallery/thermodynamics/cycles/images/sphx_glr_plot_05_diesel_cycle_001.png
   :alt: plot 05 diesel cycle
   :srcset: /api/gallery/thermodynamics/cycles/images/sphx_glr_plot_05_diesel_cycle_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.046 seconds)


.. _sphx_glr_download_api_gallery_thermodynamics_cycles_plot_05_diesel_cycle.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/thermodynamics/cycles/plot_05_diesel_cycle.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_05_diesel_cycle.ipynb <plot_05_diesel_cycle.ipynb>`

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

      :download:`Download Python source code: plot_05_diesel_cycle.py <plot_05_diesel_cycle.py>`

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

      :download:`Download zipped: plot_05_diesel_cycle.zip <plot_05_diesel_cycle.zip>`


.. only:: html

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

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