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Show species field via the strained dissipation and reaction laye r mapping approach [Dahm & Bish 1993: Bish & Dahm 19951. This mapping approach begins with the fact t~at each of the conserved scalar mLxture fraction variables ~I can be written as a linear sum over the chemical species and enthalpy fields Y/x.r) as ,V SI(X,l) = Ial • 1 Y/X,l) i = 1,2, .. . ,m (9) 1= 1 where tV- I is the number of chemical species and In the number of elements involved in the chemical system. Each of the conserved scalars ~I in (9) satisfies a locally onedimensional advection-diffusion equation similar to (2). Since scalar dissipation layers in turbulent flows do not generally involve pure fuel or pure air on either side of the layer, the correct locaL boundary values are Sl ~ s,± as fl ~ ioo. Replacing the ~,'s in (2) with their definitions in terms of the chemical species fields in (9) then leads to locally one-dimensional advection-diffusion-reaction equations for the chemical species fields Y/x,t). Thus the one-dimensionality of the conserved scalar field across each strained dissipation layer implies a locally one-dimensional structure for the underlying chemical species fields within the layer, though owing to the local boundary conditions this does not imply that the resulting Y/x .r) fields must be layerlike . The resulting quasi-steady solutions Y/fl;cr) can be equivalently given as mappings of the form Y/S. V'~·V'S; S±). The scalar and scalar dissipation values thus determine the local chemical composition at each point in the flow. It is shown in [5] that this mapping approach produces thin (flamelet-like) mass fraction and reaction rate fields under conditions of relatively weak chemical nonequilibrium (Le. fast chemical reactions). and the natural emergence and dominance of broad (distributed) species concentration and reaction rate fields for increasing chemical equilibrium departures (i.e. slow chemical reactions). Thus. the model provides a physicallyba ·<..:d framework that reconciles these two widely disparate views of the coupling between the fluid dynamics and reaction chemistry in turbulent combustion. The layer-like scalar dissipation structures at the core of the LIM model. together with thi ' trained dissipation and reaction layer formulation . accounts for both the "Il d olelet" and "distributed" combustion regimes under differing equilibrium d partures and locations in the flow . 4. LIM MODEL VALIDATIONS Figures 5-16 show sample results obtained when the LIM model described in the prcvious section is applied to a series validation problems of successively increasing complexity . In the simplest of these problems. sho\\..'n in Figures 5 and 6, direct nUlnerical simulation results can be obtained for coolparison with LIM model results. A two-dimensional time-evolving mixing layer fonns between parallel fuel and oxidizer streams moving at different speeds, and finite-rat chemical rea tions pro eed between the reactants where they have mixed rnol ularly . The Arrhenius teolperature dependence of the reaction rate produces a wid ran e of finit rate h mistry effects that are coupled dire tly to the mixing r t produ d by the underlying flow. Results are shown h re for two diff ren S', on corresponding to relatively low now speed (or fast chemistry) onditions orr sp nding to global Uamkbhlt:r nuolber Da = 300. and the oth r Lo high -spc 'c1 (or low hemistry) conditions giving Da = 30. Comparisons bctw n LIM mod I r'sults and dir ct s im u lation results for the fuel conc ntration field arc shown in Fi rure 5a. Not that. |
