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336    CHAPTER 15 COMBUSTION AND FLAMES




             FIGURE 15.9
             Schematic diagram of turbulent flame in spark-
             ignition engine.


















             The parameters governing the extinction of the laminar flame are the Lewis and Karlovitz numbers,
             defined below.
                Measurements have shown that the turbulence intensity at the time of combustion tends to be about
             half the mean piston speed. Since the turbulent burning velocity is related to the laminar flame speed
             by the turbulence intensity then the mass burning rate in the cylinder for the majority of the combustion
             period (say, from 10% to 90% of the in-cylinder charge) is almost independent of engine speed.
             Heywood quotes that the turbulent to laminar flame area is about 10 at 2000 rev/min. As the flame
             approaches the wall it is slowed down by heat transfer to the wall and also the smaller scales of
             turbulence existing close to the wall. There have been theories of flame quench at the wall but these are
             not very well understood in the context of engine combustion.
                The flame in a spark-ignition engine propagates as a local laminar flame whose speed is enhanced
             by the effects of turbulence. The laminar flame speed is a function of a number of parameters,
             including the fuel, the equivalence ratio, temperature and pressure. The turbulent flame speed is a
             function of all of the parameters which affect the laminar flame speed plus the effect of turbulence in
             the cylinder. It was stated above that the flame is a wrinkled one, which basically means that the
             Kolmogorov scale of turbulence must be larger than the laminar flame thickness. This means that the
             laminar flame structure is maintained and that the turbulent flame is simply a distorted laminar one. If
             the distortion becomes too large it is possible for the flame to be extinguished. This tendency can be
             assessed by examining the Lewis and Karlovitz numbers. The Lewis number (Le) is the ratio of
             thermal to molecular diffusivity (defined in Eqn (15.12)), and was used to examine the basic flame
             propagation mechanisms.
                         Le ¼ a=D; where a ¼ thermal diffusivity; and D ¼ mass diffusivity  (15.12)
                The Karlovitz number is the product of the turbulent strain rate and the transit time for flow through
             the laminar flame, s L , giving
                                                             0

                                               1 dF L       u   d L
                                        K ¼          s L ¼                               (15.13)
                                              F L dt       [ T  S L
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