Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

PDF, beta

Turbulent mixing is primarily responsible for fixing the rate at which the composition PDF evolves in time. Molecular diffusion, on the other hand, determines the shape of the composition PDF at different time instants. In fact, binary mixing of an inert scalar is well represented by a beta PDF. [Pg.84]

Figure 5.8. The mixture-fraction PDF in turbulent flows with two feed streams (binary mixing) can be approximated by a beta PDF. [Pg.194]

The beta PDF is widely used in commercial CFD codes to approximate the mixture-fraction PDF for binary mixing. This choice is motivated by the fact that in many of the canonical turbulent mixing configurations (Fig. 5.8) the experimentally observed mixture-fraction PDF is well approximated by a beta PDF. However, it is important to note that all of these flows are stationary with Nmf = A m — 1 = 1, i.e., no linear mixture exists between the inlet conditions. The unmixed PDF is thus well represented by two peaks one located at % = 0 and the other at % = 1, which is exactly the type of behavior exhibited... [Pg.194]

Figure 5.9. The unmixed mixture-fraction PDF in turbulent flows with two feed streams has two peaks that can be approximated by a beta PDF. However, with three feed streams, the unmixed PDF has three peaks, and is therefore poorly approximated by a beta PDF. [Pg.195]

Thus, if a presumed beta PDF is employed to represent / (f x, t), the finite-rate one-step reaction can be modeled in terms of transport equations for only three scalar moments (f), (f 2), and (7). The simple closure based on linear interpolation thus offers a highly efficient computational model as compared with other closures. [Pg.229]

A two-term power series expression can be derived to handle this case, but it will again fail in cases where the skewness depends on x, but the mean and variance are constant. However, note that the beta PDF can be successfully handled with the two-term form since all higher-order moments depend on the mean and variance. By accounting for the entire shape of the mixture-fraction PDF, (5.318) will be applicable to all forms of the mixture-fraction PDF. [Pg.234]

The procedure followed above can be used to develop a multi-environment conditional LES model starting from (5.396). In this case, all terms in (5.399) will be conditioned on the filtered velocity and filtered compositions,166 in addition to the residual mixture-fraction vector = - . In the case of a one-component mixture fraction, the latter can be modeled by a presumed beta PDF with mean f and variance (f,2>. LES transport equations must then be added to solve for the mixture-fraction mean and variance. Despite this added complication, all model terms carry over from the original model. The only remaining difficulty is to extend (5.399) to cover inhomogeneous flows.167 As with the conditional-moment closure discussed in Section 5.8 (see (5.316) on p. 215), this extension will be non-trivial, and thus is not attempted here. [Pg.258]

Truncating the power series at second order implies that only the means and covariances will be needed to specify the coefficients. The beta PDF has this property, and thus we can speculate that the stationary PDF predicted by the FP model with these coefficients should be the same as (5.147). [Pg.302]

For example, a beta PDF can be found from (6.148) by using the shape function given by the uni-variate version of (6.130) ... [Pg.305]

Baurie, R. A., G. A. Alexopoulos, H. A. Hassan, and J. P. Drnmmond. 1992. An assumed joint-beta PDF approach for snpersonic tnrbnlent combnstion. AlAA Paper No. 92-3844. [Pg.154]


See other pages where PDF, beta is mentioned: [Pg.230]    [Pg.257]    [Pg.129]    [Pg.161]    [Pg.194]    [Pg.194]    [Pg.194]    [Pg.195]    [Pg.195]    [Pg.195]    [Pg.225]    [Pg.233]    [Pg.233]    [Pg.236]    [Pg.237]    [Pg.251]    [Pg.251]    [Pg.255]    [Pg.255]    [Pg.284]    [Pg.344]    [Pg.110]    [Pg.175]    [Pg.175]    [Pg.175]    [Pg.176]    [Pg.176]    [Pg.176]    [Pg.176]    [Pg.206]    [Pg.214]   
See also in sourсe #XX -- [ Pg.65 , Pg.110 , Pg.175 , Pg.176 , Pg.206 , Pg.210 , Pg.214 , Pg.215 , Pg.217 , Pg.218 , Pg.232 , Pg.236 , Pg.239 , Pg.265 , Pg.276 , Pg.283 , Pg.286 , Pg.325 ]

See also in sourсe #XX -- [ Pg.139 ]

See also in sourсe #XX -- [ Pg.65 , Pg.110 , Pg.175 , Pg.176 , Pg.206 , Pg.210 , Pg.214 , Pg.215 , Pg.217 , Pg.218 , Pg.232 , Pg.236 , Pg.239 , Pg.265 , Pg.276 , Pg.283 , Pg.286 , Pg.325 ]




SEARCH



Pdf

© 2024 chempedia.info