Representing mixtures with State objects

The State object provides a full picture of the themochemical state of a gaseous mixture. It can be used to extract missing thermochemical quantities, or to keep a meaningful thermochemical state while modifying individual state variables. A State does not contain any velocity or numerical information.

State initialization

A State object can be initialized in two ways:

  • From the temperature, pressure, and species mass fractions \((T, P, Y_k)\) through the default constructor:

    state = State(T, P, Yk)

  • From conservative variables \((\rho, \rho E, \rho Y_k)\) through the from_cons constructor:

    state = State.from_cons(rho, rhoE, rhoYk)

\(E\) is the total energy defined as the sum of the sensible and chemical (formation) energies ([TNC] p. 3)

The constructor arguments \((T, P, Y_k)\) or \((\rho, \rho E, \rho Y_k)\) can be scalars or multidimensional arrays.

Warning

When initializing from conservative variables, \(T\) is determined by a Newton-Raphson method to ensure that the mixture energy matches the input energy. This is an expensive step that may take a long time for large inputs.

The following flowchart details how from_cons works

../_images/fromcons_flowchart.png

State transformations

After a State has been initialized, \(T\), \(P\) and \(Y_k\) can independently be set to new values (e.g. myState.temperature = newTemperature) and the other state variables are modified accordingly:

  • When setting a new value for \(T\), the other state variables are modified assuming an isobaric and iso-composition transformation from the previous state.

  • When setting a new value for \(P\), the other state variables are modified assuming an isothermal and iso-composition transformation from the previous state.

  • When setting a new value for \(Y_k\), the other state variables are modified assuming an isothermal and isobaric transformation from the previous state.

State transformations always satisfy the perfect gas equation of state

\[P = \rho \frac{R}{W_{mix}} T\]
TNC

Poinsot, T.; Veynante, D. Theoretical and Numerical Combustion, 3rd ed.; 2011.