Influence of Chemical Kinetics and Unmixedness on Burning in Supersonic Hydrogen Flames

Good agreement has been obtained between published profiles of composition and pitot pressure with the calculated results from a computer program in which finite rate chemistry was used. Significant differences are noted between results calculated using 7 species and 8 reactions and those calculated using 12 species and 25 reactions. Differences are also found between results in which the effect of unmixedness on reaction in turbulent flow is applied or is not applied. ULTI-REACTION finite-rate chemistry has been used for many years in computer simulation of complex flowfields, and results have been good in laminar flows. Mixing of fuel and air is faster in turbulent flows than in laminar flows, but in turbulent flows the folding together of large volumes of fluid alternately rich in either fuel or oxygen produces the phenomenon of "unmixedness" in which the time-averaged temperature and composition at a point do not represent correctly the degree to which fuel and air are mixed on a molecular scale. Thus, the use of time-averaged values of temperatures and concentrations in the finite-rate chemistry equations is incorrect and can lead to serious errors in calculated results. This by no means rules out the use of time- averaged values, since the effects of unmixedness may be small for many turbulent, reacting flows. One purpose of this paper is to demonstrate that this is so by calculating some results with and without the effects of unmixedness. Another purpose of the paper is to report improvement in the ability of a computer program to simulate burning of H 2 in a super- sonic air stream when an eddy breakup chemistry model is replaced with one in which finite reaction rates, corrected for unmixedness, are used. In a prior investigation,1 the usefulness of a parabolic marching computer program was evaluated by comparing computed results with data from five experimental test cases. Mixing of fuel and oxidant was computed for parallel in- jection of H2 using a two-equation turbulence model, and the extent of chemical reaction was deduced by comparing the data with results obtained from three different assumptions: 1) no reaction, corresponding to zero combustion efficiency; 2) complete burning of all fuel mixed with oxygen, corresponding to combustion efficiency = 1; and 3) finite-rate burning based on the rate of decay of large turbulent eddies into small ones. The last of these assumptions, the eddy- breakup (EBU) model,2 provided a means for obtaining combustion efficiency values intermediate between 0 and 1 and is believed to be useful as a tool to account for the effects of unmixedness on chemical reaction in turbulent flows if chemical reaction rates are large enough so that the production of combustion products is limited by the mixing rate. In this paper three of the experimental test cases used in the previous computer program evaluation are reanalyzed using the same program but with a finite-rate chemistry system reported by Spiegler. 3 In this chemistry system the effect of unmixedness on individual reactions is modeled by decreasing any rate for which one or more of the species involved goes negative during fluctuation of its concentration about the average value. (Temperature fluctuations are not considered.) In addition to calculations using Spiegler's system of 7 species and 8 reactions, calculations were also made using 12 species and 25 reactions. The latter system required the solution of twice as many differential equations for chemical species, but this was judged to be necessary in order to examine the effect of the added equations on the generation rates of radicals such as H, O, and OH. The elemental reactions by means of which H2 and O2 are transformed into H2O provide multiple paths between the reactants and the product, most of which depend on the presence of high concentrations of radicals. The relative importance of the paths changes as conditions in the flow change, and it is important not to neglect any path which might be a large source or sink for one or more of the radicals, since such a path might be critical for prediction of ignition.