Kinetics Class 12 Pdf

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Ophelia Gurin

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Aug 5, 2024, 12:32:59 AM8/5/24

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Thisclass serves as a base class to derive 'kinetics managers', which are classes that manage homogeneous chemistry within one phase, or heterogeneous chemistry at one interface. The virtual methods of this class are meant to be overloaded in subclasses. The non-virtual methods perform generic functions and are implemented in Kinetics. They should not be overloaded. Only those methods required by a subclass need to be overloaded; the rest will throw exceptions if called.

Kinetics derivatives are calculated with respect to temperature, pressure, molar concentrations and species mole fractions for forward/reverse/net rates of progress as well as creation/destruction and net production of species.

Forward/reverse rate expressions $ k_f,i $ and $ k_r,i $ are implemented by ReactionRate specializations; forward/reverse stoichiometric coefficients are $ \nu_ji^\prime $ and $ \nu_ji^\prime\prime $. Unless the reaction involves third-body colliders, $ \nu_M,i = 0 $. For three-body reactions, effective ThirdBody collider concentrations $ C_M $ are considered with $ \nu_M,i = 1 $. For more detailed information on relevant theory, see, for example, Perini, et al. [31] or Niemeyer, et al. [29], although specifics of Cantera's implementation may differ.

Partial derivatives are obtained from the product rule, where resulting terms consider reaction rate derivatives, derivatives of the concentration product term, and, if applicable, third-body term derivatives. ReactionRate specializations may implement exact derivatives (example: ArrheniusRate::ddTScaledFromStruct) or approximate them numerically (examples: ReactionData::perturbTemperature, PlogData::perturbPressure, FalloffData::perturbThirdBodies). Derivatives of concentration and third-body terms are based on analytic expressions.

Species creation and destruction rates are obtained by multiplying rate-of-progress vectors by stoichiometric coefficient matrices. As this is a linear operation, it is possible to calculate derivatives the same way.

All derivatives are calculated for source terms while holding other properties constant, independent of whether equation of state or $ \sum X_k = 1 $ constraints are satisfied. Thus, derivatives deviate from Jacobians and numerical derivatives that implicitly enforce these constraints. Depending on application and equation of state, derivatives can nevertheless be used to obtain Jacobians, for example:

While some applications require exact derivatives, others can tolerate approximate derivatives that neglect terms to increase computational speed and/or improve Jacobian sparsity (example: AdaptivePreconditioner). Derivative evaluations settings are accessible by keyword/value pairs using the methods getDerivativeSettings() and setDerivativeSettings().

They are designed primarily for carrying out sensitivity analysis, but may be used for any purpose requiring dynamic alteration of rate constants. For each reaction, a real-valued multiplier may be defined that multiplies the reaction rate coefficient. The multiplier may be set to zero to completely remove a reaction from the mechanism.

For heterogeneous mechanisms, one of the phases in the list of phases represents the 2D interface or 1D edge at which the reactions take place. This method returns the index of the phase with the smallest spatial dimension (1, 2, or 3) among the list of phases. If there is more than one, the index of the first one is returned. For homogeneous mechanisms, the value 0 is returned.

It is typically used so that member functions of the ThermoPhase object may be called. For homogeneous mechanisms, there is only one object, and this method can be called without an argument to access it.

Kinetics manager classes return species production rates in flat arrays, with the species of each phases following one another, in the order the phases were added. This method is useful to find the value for a particular species of a particular phase in arrays returned from methods like getCreationRates that return an array of species-specific quantities.

k is an integer from 0 to ktot - 1, where ktot is the number of species in the kinetics manager, which is the sum of the number of species in all phases participating in the kinetics manager. If k is out of bounds, the string "" is returned.

For example, if this method is called with the array of standard-state molar Gibbs free energies for the species, then the values returned in array deltaProperty would be the standard-state Gibbs free energies of reaction for each reaction.

Array 'g' must have a length at least as great as the number of species, and array 'dg' must have a length as great as the total number of reactions. This method only computes 'dg' for the reversible reactions, and the entries of 'dg' for the irreversible reactions are unaltered. This is primarily designed for use in calculating reverse rate coefficients from thermochemistry for reversible reactions.

The computed values include all temperature-dependent and pressure-dependent contributions. By default, third-body concentrations are only considered if they are part of the reaction rate definition; for a legacy implementation that includes third-body concentrations see Cantera::use_legacy_rate_constants(). Length is the number of reactions. Units are a combination of kmol, m^3 and s, that depend on the rate expression for the reaction.

This method is called automatically when the first reaction is added. It needs to be called directly only in the degenerate case where there are no reactions. The base class method does nothing, but derived classes may use this to perform any initialization (allocating arrays, etc.) that requires knowing the phases.

If throw_err is true, then an exception will be thrown if either any unmarked duplicate reactions are found, or if any marked duplicate reactions do not have a matching duplicate reaction. If throw_err is false, the indices of the first pair of duplicate reactions found will be returned, or the index of the unmatched duplicate will be returned as both elements of the pair. If no unmarked duplicates or unmatched marked duplicate reactions are found, returns (npos, npos).

For homogeneous kinetics applications, this vector will only have one entry. For interfacial reactions, this vector will consist of multiple entries; some of them will be surface phases, and the other ones will be bulk phases. The order that the objects are listed determines the order in which the species comprising each phase are listed in the source term vector, originating from the reaction mechanism.

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