| OCR Text |
Show OPTIMIZATION PROCEDURE The systematic optimization procedure used to produce the GRI-Mech mechanisms involves the following steps: 1. Assemble a reaction model consisting of a complete set of elementary chemical reactions. 2. Assign values to their rate constants from the literature or by judicious estimation. Treat temperature and pressure dependences in a proper and consistent manner. Also evaluate error limits, and the thermodynamics used for the equilibrium reverse rate constants. 3. Search the literature for reliable experiments that relate to natural gas combustion and N O formation and reburn; find various shock tube experiments, flame measurements, flame speeds, ignition studies, flow reactor studies, etc., that depend on some or all of the rate and transport parameters in the model. These experiments should include key combustion properties that the mechanism is to predict. Evaluation is again required, although the optimization process itself typically will reveal inconsistencies with the other data. A final selection criterion is that the experimental results be readily modelable - uncertainties in other model parameters, or the model itself, for the actual experiments should not approach those of the kinetics w e anticipate optimizing as a result. 4. Use a computer model to solve the reaction mechanism kinetics and any necessary transport equations, computing values for the observables of these "target" experiments. Also apply sensitivity analysis to determine h o w the model input rate constants affect the result. The sensitivity coefficient S = dX/X / dk/k = dlnX / dink. Compare computed results with data. Since the first solution often yields a computed value that does not match observation, normally the next activity is to adjust input parameters (within error limits), individually or in combinations, to bring the computed value into agreement with the observation. The problem with this approach is that the change in input parameters used to match one observation does not take into account other data sensitive to the same parameters. This other data will not be matched by the model, or m a y simply be ignored. O n e must either iterate, or sacrifice reliable predictability for the mechanism. A process that is systematic, simultaneous, and inclusive is required instead. 5. Choose experimental targets sensitive to a representative cross-section of the rate parameters, under a representative set of conditions. Many parameters will apply to more than one target. Also select, according to sensitivities and uncertainties, those parameters making the largest impacts on a given target. These are the potential optimization parameters. 6. M a p the model response by repeating computations of the target observables for a minimum subset of combinations of these variables - within their appropriate error limits - according to a central composite factorial design. W e typically try to include all "active" (i.e., significant) variables. 7. Create, using the results of these factorial-design-directed calculations, the polynomial functions (the response surface) that mimic the results of the computer simulation for each target. This solution mapping technique in essence creates a representation of the predicted target values for the set of possible mechanisms within stated error estimates. The rate constants are normalized on a logarithmic scale, and a second order polynomial expression is typically created by regression analysis of the appropriate factorial design 3 |
