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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_gallery_plot_initial_temperature_model_example.py:


Initial Temperature Model
==========================

This example demonstrates the PulseInitialTemperatureModel which computes initial gas
temperature accounting for energy-to-temperature conversion, cylindrical thermal diffusion,
and relaxation between pulses.

The model supports different heat capacity approaches via the cp_model parameter.

.. GENERATED FROM PYTHON SOURCE LINES 11-66



.. image-sg:: /auto_examples/gallery/images/sphx_glr_plot_initial_temperature_model_example_001.png
   :alt: Temperature Evolution Over One Pulse Cycle
   :srcset: /auto_examples/gallery/images/sphx_glr_plot_initial_temperature_model_example_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Initial Temperature T_0: 501.0 K
    Peak Temperature T_max: 501.8 K
    Temperature Rise ΔT: 201.8 K
    Relaxation Time τ: 4929.4 μs






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np
    import openmdao.api as om

    from paroto.models.initial_temperature import PulseInitialTemperatureModel

    # Create OpenMDAO problem
    # cp_model=2200 uses constant Cp (low fidelity, faster)
    # cp_model=CanteraEnergyModel uses Cantera (high fidelity, requires Cantera)
    prob = om.Problem()
    prob.model.add_subsystem("temp", PulseInitialTemperatureModel(cp_model=2200.0))
    prob.setup()

    # Set parameters for typical operating conditions
    prob.set_val("temp.energy_per_pulse", 10e-3)  # 10 mJ
    prob.set_val("temp.pulse_frequency", 50e3)  # 50 kHz
    prob.set_val("temp.thermal_diameter", 0.002)  # 2 mm arc diameter
    prob.set_val("temp.arc_length", 0.01)  # 10 mm arc length
    prob.set_val("temp.gas_density", 0.717)  # kg/m³ (CH4)
    prob.set_val("temp.gas_heat_capacity", 2200.0)  # J/(kg·K)
    prob.set_val("temp.thermal_conductivity", 0.08)  # W/(m·K)
    prob.set_val("temp.ambient_temperature", 300.0)  # K
    prob.set_val("temp.pulse_duration", 1e-6)  # 1 μs

    # Run model
    prob.run_model()

    # Extract results
    T_0 = prob.get_val("temp.T_0")[0]
    T_max = prob.get_val("temp.T_max")[0]
    delta_T = prob.get_val("temp.delta_T_pulse")[0]
    tau = prob.get_val("temp.relaxation_time")[0]

    print(f"Initial Temperature T_0: {T_0:.1f} K")
    print(f"Peak Temperature T_max: {T_max:.1f} K")
    print(f"Temperature Rise ΔT: {delta_T:.1f} K")
    print(f"Relaxation Time τ: {tau * 1e6:.1f} μs")

    # Plot temperature evolution over one pulse cycle
    t_cycle = 1.0 / 50e3  # s
    t_points = np.linspace(0, t_cycle, 100)
    T_points = 300.0 + delta_T * np.exp(-t_points / tau)

    plt.figure(figsize=(8, 5))
    plt.plot(t_points * 1e6, T_points, "b-", linewidth=2)
    plt.axhline(y=T_0, color="r", linestyle="--", label=f"T_0 = {T_0:.0f} K")
    plt.axhline(y=300, color="gray", linestyle=":", label="Ambient")
    plt.xlabel("Time (μs)")
    plt.ylabel("Temperature (K)")
    plt.title("Temperature Evolution Over One Pulse Cycle")
    plt.grid(True, alpha=0.3)
    plt.legend()
    plt.tight_layout()
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.164 seconds)


.. _sphx_glr_download_auto_examples_gallery_plot_initial_temperature_model_example.py:

.. only:: html

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

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

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

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

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

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

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