Chemical source term fluctuating

As seen above, the mean chemical source term is intimately related to the PDF of the concentration fluctuations. In non-premixed flows, the rate of decay of the concentration fluctuations is controlled by the scalar dissipation rate. Thus, a critical part of any model for chemical reacting flows is a description of how molecular diffusion works to damp out... 

Figure 5.21. Scatter plot of concentration in a turbulent reacting flow conditioned on the value of the mixture fraction. Although large fluctuations in the unconditional concentration are present, the conditional fluctuations are considerably smaller. In the limit where the conditional fluctuations are negligible, the chemical source term can be closed using the conditional scalar means. 

Thus, the turbulent-reacting-flow problem can be completely closed by assuming independence between Y and 2, and assuming simple forms for their marginal PDFs. In contrast to the conditional-moment closures discussed in Section 5.8, the presumed PDF method does account for the effect of fluctuations in the reaction-progress variable. However, the independence assumption results in conditional fluctuations that depend on f only through Tmax(f ) The conditional fluctuations thus contain no information about local events in mixture-fraction space (such as ignition or extinction) that are caused by the mixture-fraction dependence of the chemical source term. 

The multi-environment conditional PDF model thus offers a simple description of the effect of fluctuations about the conditional expected values on the chemical source term. 

In Section 4.2, the LES composition PDF was introduced to describe the effect of residual composition fluctuations on the chemical source term. As noted there, the LES composition PDF is a conditional PDF for the composition vector given that the filtered velocity and filtered compositions are equal to U and 0, respectively. The LES composition PDF is denoted by U, 0 x, /), and a closure model is required to describe it. 

Hence, it is not necessary to solve a separate LES transport equation for the filtered compositions. Indeed, in the limit of one environment, (5.422) reduces to the LES model for the filtered compositions with the simplest possible closure for the chemical source term (i.e., one that neglects all SGS fluctuations). 

The composition PDF thus evolves by convective transport in real space due to the mean velocity (macromixing), by convective transport in real space due to the scalar-conditioned velocity fluctuations (mesomixing), and by transport in composition space due to molecular mixing (micromixing) and chemical reactions. Note that any of the molecular mixing models to be discussed in Section 6.6 can be used to close the micromixing term. The chemical source term is closed thus, only the mesomixing term requires a new model. 

For higher-order reactions, a model must be provided to close the covariance source terms. One possible approach to develop such a model is to extend the FP model to account for scalar fluctuations in each wavenumber band (instead of only accounting for fluctuations in In any case, correctly accounting for the spectral distribution of the scalar covariance chemical source term is a key requirement for extending the LSR model to reacting scalars. 

Abstract. The quality in the prediction of turbulent reactive flows requires mainly two essential ingredients, namely an appropriate treatment of the fluctuating nature of turbulence in the calculation of averaged chemical source-terms and a realistic model of chemical kinetics for the case of homogeneous reaction. The first one is most generally established by the usage of Probability-Density-Functions (PDF s), the second one is provided by the application of detailed reaction mechanisms. 

The values of raw materials and products can be found in trade journals such as Chemical Marketing Reporter (published by Schnell Publishing Company), European Chemical News and Asian Chemical News (published by Reed Business Information). However, the values reported in such sources will be subject to short-term fluctuations, and long-term forecasts will be required for investment analysis. 

Consideration will be restricted to dilute sprays, so that the statistical fluctuations in the flow, which are induced by the random motion of individual particles, may be neglected. Therefore, our objective is to obtain the hydrodynamic equations for the (local) average properties of the gas. These equations will be derived by phenomenological reasoning and will be shown to be equivalent to the ordinary equations of fluid dynamics, with suitably added source terms accounting for the average effect of the spray. For the sake of generality, allowance will be made for M different kinds of droplets and N different chemical species in the gas. 

When chemical reactions are slow (with respect to mixing) it is not necessary to employ additional models to close the reaction source terms. For slow reactions (Da 1), turbulent mixing will be complete before the reaction can take place. The contributions of fluctuating concentrations may be neglected. Therefore, the time-averaged reaction source term can be related to the time-averaged temperature and species concentrations ... 

---