SPM Airflow Analyzer
####################
This analyzer is designed to determine how much supplemental axial airflow is needed to cool the rotor to a specified ``max_temp``. 

Model Background
****************

The SPM rotor is modeled using the thermal resistance network described in :doc:`SPM Rotor Thermal Analyzer <SPM_rotor_thermal_analyzer>`. The implementation of the resistances and nodal locations can be found in the source code of the ``create_resistance_network`` method of ``SPM_RotorThemalAnalyzer``. In this analyzer, the axial airflow is varied to increase the convection rate on the rotor in order to improve cooling.

The problem class for the ``AirflowAnalyzer`` contains the :doc:`Rotor Thermal Analyzer <SPM_rotor_thermal_analyzer>` which is used to calculate the magnet temperature as a function of the axial airflow. The ``AirflowAnalyzer`` solve a single objective minimization problem subject to a constraint that the magnet temperature is less than ``max_temp``.

Inputs from User
************************************

The airflow analyzer utilizes the same ``mat_dict`` and ``losses`` dictionary as the SPM Rotor Thermal Analyzer (see :ref:`here <mat-dict-therm>`). In addition, the following inputs must be defined for the problem class. The location of these inputs are shown on this :ref:`figure <therm-geo>`:
   
.. csv-table:: Input dimensions and operating conditions for rotor thermal problem 
   :file: inputs_dimensions_rotor_airflow.csv
   :widths: 70, 70, 30
   :header-rows: 1
 

The following code demonstrates how the eMach thermal analyzer for the rotor can be used to calculate the required airflow to cool a rotor. 

.. code-block:: python

    import numpy as np
    from eMach.mach_eval.analyzers.mechanical.rotor_thermal import AirflowProblem,AirflowAnalyzer

    # Example Machine Dimensions
    r_sh=5E-3 # [m]
    d_m=3E-3 # [m]
    r_ro=12.5E-3 # [m]
    d_ri=r_ro-r_sh - d_m # [m]
    d_sl=1E-3 # [m]
    l_st=50E-3 # [m]
    l_hub=3E-3 # [m]
    r_si=r_ro+d_sl+1E-3 # [m]

    # Define Material Dictionary
    mat_dict= {'shaft_therm_conductivity': 51.9, # W/m-k ,
               'core_therm_conductivity': 28, # W/m-k
               'magnet_therm_conductivity': 8.95, # W/m-k ,
               'sleeve_therm_conductivity': 0.71, # W/m-k,
               'air_therm_conductivity'     :.02624, #W/m-K
               'air_viscosity'              :1.562E-5, #m^2/s
               'air_cp'                     :1, #kJ/kg
               'rotor_hub_therm_conductivity':205.0} #W/m-K}

    # Operating Conditions
    T_ref=25 # [C]
    omega=120E3*2*np.pi/60 # [rad/s]
    losses={'rotor_iron_loss':.001,'magnet_loss':135}
    max_temp=80

    # Create an AirflowProblem object
    afp=AirflowProblem(r_sh, d_ri, r_ro, d_sl, r_si, l_st, l_hub, T_ref, losses,
                       omega, max_temp, mat_dict)
    # Create an Airflow Analyzer
    ana=AirflowAnalyzer()

Outputs to User
****************************************
 
The ``AirflowAnalyzer`` returns a results object with the following keys:

* ``Message``: returns false if magnets exceed the specified maximum temperature.
* ``Magnet Temp``: In Celsius
* ``Required Airflow``: in m/s
 
The following code demonstrates how to use the airflow analyzer to solve the airflow problem. 

.. code-block:: python


    # Analyze problem for required airflow
    results=ana.analyze(afp)
    print(results)
    
The ``results`` object returned by the analyzer for this example is shown below:

.. code-block:: python

    {'Message': True,
     'Magnet Temp': array([73.43703021]),
     'Required Airflow': array([1.23618711e-08])}