Flow models reduced parameter approach

Correlation between liquid behavior at thermodynamic equilibrium and that during flow follows from the mean-field approach, which assumes that liquids are structureless and that the dynamic behavior can be considered a semiequilibrium state. Evidently, this approach is unable to explain kinetic phenomena. The S-S lattice-hole mean-field theory does not consider polymeric chain structure, but its effects are reflected in the values of the characteristic reducing parameters, P, T, V, and tlie L-J interaction parameters. Characteristically, the PVT data rarely show secondary transformation temperatures at about 0.8r and 1.2r, which are evident in derivative properties (see Figures 6.1 and 6.2). By contrast, all flow models (e.g., reptation, cell structures, hole jumping) implicitly postulate that such configurational or conformational changes affect liquid dynamic behavior. 

Progress has been made in both reduced-order modeling and model-based control of combustion dynamics. Advances in modeling were obtained by investigating shear-flow driven combustion instability. The authors of this chapter determined that shear-layer instability occurs when an absolutely unstable mode is present. This mode can be predicted and matched to experimental data. Also, it is shown that the temperature profile determines a transition to absolutely unstable operation. Parameters of the shear-flow modes together with a POD-based approach led to the derivation of a new reduced-order model that sheds light on the interactions between hydrodynamics, acoustics, and heat release. A RePOD... 

In other terms, above a critical shear stress, it flows as a Newtonian fluid of (constant) viscosity t). It follows that a fluid obeying the Herschel-Bulkley model is sometimes called a generalized Bingham fluid, since with n=1 and K=r in Equation 5.3, one obviously obtains Equation 5.4. The three fit parameters of the Herschel-Bulkley equation can be reduced to two, when considering that n=0.5. This was in fact the approach used by Casson in proposing the following model ... 

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