.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermodynamics/cycles/plot_09_brayton_regeneration_intercooling.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_09_brayton_regeneration_intercooling.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_09_brayton_regeneration_intercooling.py:


Brayton's cycle with regeneration, intercooling and reheat (1872)
=================================================================

A simple gas turbine throws its hot exhaust away and spends much of its
turbine work on the compressor. A regenerator heats the compressed air with
the exhaust. Splitting the compression with intercoolers and the expansion
with reheaters moves both towards isothermal processes. With many stages and
a perfect regenerator the cycle becomes Ericsson's, whose efficiency is
Carnot's (:func:`~engineeringkit.thermodynamics.brayton_cycle`).

.. GENERATED FROM PYTHON SOURCE LINES 14-19

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.thermodynamics import brayton_cycle, brayton_efficiency, carnot_efficiency








.. GENERATED FROM PYTHON SOURCE LINES 20-25

A gas turbine with imperfect components
---------------------------------------

Air at 300 K, turbine inlet 1300 K, pressure ratio 8, an 80% compressor and
an 85% turbine (the cold-air-standard form of Çengel and Boles's Example 9-6).

.. GENERATED FROM PYTHON SOURCE LINES 25-45

.. code-block:: Python


    simple = brayton_cycle(8.0, 300.0, 1300.0, compressor_efficiency=0.8, turbine_efficiency=0.85)
    regenerated = brayton_cycle(8.0, 300.0, 1300.0, compressor_efficiency=0.8, turbine_efficiency=0.85, regenerator_effectiveness=0.8)
    print(f"ideal {brayton_efficiency(8.0):.3f}; with losses {simple.efficiency:.3f}, back-work ratio {simple.back_work_ratio:.2f}")
    print(f"80% effective regenerator: {regenerated.efficiency:.3f}, saving {regenerated.heat_regenerated / 1e3:.0f} kJ/kg of fuel heat")
    assert regenerated.efficiency > simple.efficiency and np.isclose(regenerated.net_work, simple.net_work)

    staged = brayton_cycle(
        8.0,
        300.0,
        1300.0,
        compressor_efficiency=0.8,
        turbine_efficiency=0.85,
        regenerator_effectiveness=0.8,
        compressor_stages=2,
        turbine_stages=2,
    )
    print(f"two-stage compression and expansion with regeneration: {staged.efficiency:.3f}")
    fig, ax = staged.plot()




.. image-sg:: /api/gallery/thermodynamics/cycles/images/sphx_glr_plot_09_brayton_regeneration_intercooling_001.png
   :alt: Brayton cycle, η = 45.0%
   :srcset: /api/gallery/thermodynamics/cycles/images/sphx_glr_plot_09_brayton_regeneration_intercooling_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    ideal 0.448; with losses 0.274, back-work ratio 0.61
    80% effective regenerator: 0.356, saving 161 kJ/kg of fuel heat
    two-stage compression and expansion with regeneration: 0.450




.. GENERATED FROM PYTHON SOURCE LINES 46-51

Towards Ericsson and Carnot
---------------------------

With ideal components and a perfect regenerator, more stages close the gap
to Carnot's bound between 300 K and 1300 K.

.. GENERATED FROM PYTHON SOURCE LINES 51-63

.. code-block:: Python


    stages = [1, 2, 3, 5, 10, 30, 100]
    etas = [brayton_cycle(8.0, 300.0, 1300.0, regenerator_effectiveness=1.0, compressor_stages=n, turbine_stages=n).efficiency for n in stages]
    fig, ax = plt.subplots(figsize=(6, 3.5))
    ax.semilogx(stages, etas, "o-", label="ideal, perfect regenerator")
    ax.axhline(carnot_efficiency(1300.0, 300.0), color="gray", ls=":", label="Carnot (Ericsson limit)")
    ax.set(xlabel="stages of compression and of expansion", ylabel="efficiency", title="Intercooling and reheat, pressure ratio 8")
    ax.legend()
    fig.tight_layout()
    assert np.all(np.diff(etas) > 0) and carnot_efficiency(1300.0, 300.0) - etas[-1] < 0.01

    plt.show()



.. image-sg:: /api/gallery/thermodynamics/cycles/images/sphx_glr_plot_09_brayton_regeneration_intercooling_002.png
   :alt: Intercooling and reheat, pressure ratio 8
   :srcset: /api/gallery/thermodynamics/cycles/images/sphx_glr_plot_09_brayton_regeneration_intercooling_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.230 seconds)


.. _sphx_glr_download_api_gallery_thermodynamics_cycles_plot_09_brayton_regeneration_intercooling.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_09_brayton_regeneration_intercooling.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_09_brayton_regeneration_intercooling.ipynb <plot_09_brayton_regeneration_intercooling.ipynb>`

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

      :download:`Download Python source code: plot_09_brayton_regeneration_intercooling.py <plot_09_brayton_regeneration_intercooling.py>`

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

      :download:`Download zipped: plot_09_brayton_regeneration_intercooling.zip <plot_09_brayton_regeneration_intercooling.zip>`


.. only:: html

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

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