A fitted algebraic model for wet CO ignition

The first application of the polynomial approximation to combustion systems describes the temperature and CO and O2 concentration profiles during the ignition of a wet carbon monoxide-air mixture. The detailed mechanism was identical to the CO mechanism that has been used as an example in ILDM calculations [6]. All in all, 300 initial conditions, uniformly distributed between ambient temperatures of 990 and 1010 K and fuel-to-oxygen ratios 0.5 to 1.5, were used in spatially homogeneous simulations. Temperature and mole fractions of CO and O2 were recorded every 

The values of temperature, [CO] and [O2] at the time (f -l- 10 ) s were fitted as a function of the three variables at time t. The fitted functions were fourth-order polynomials with between 22 and 25 non-zero parameters. The average deviations between the results of detailed simulations and values calculated from the polynomial were below 0.26% over the range of conditions covered. A FORTRAN program was used to convert the polynomial coefficients into FORTRAN functions optimized for multiplications. An example of such a computer-generated function is given in Fig. 4.17. 

An alternative version of the FORTRAN function-generator program has also been elaborated. In this version, the powers of variables are calculated sequentially and then applied to the independent calculation of 

Concentration-time and temperature-time curves calculated from the polynomial approximation are in close agreement with the simulation results from the detailed kinetic model (see Fig. 4.19). Calculation of the curves with the polynomial approximation was 11,700 times faster. This gain in computer-time is unexpectedly high, although a lO -times increase in calculation speed has been reported in another application of repromodelling [230]. 

Fitting small mathematical models to kinetic data is an alternative to the reduction of large kinetic models. The mathematical models can be systems of ordinary differential equations (odes) or algebraic equations (including systems of difference equations) and the kinetic data may be either simulation results of a detailed model or experimental data. When simulation results are fitted, the original experimental information might be distorted by the inaccurate large model. However, experimental data 

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