Analytical development of non-ideal effects for control volume based mixer models

Many researchers have modeled ideal mixing and entrainment phenomena using control volume methods. The simplicity, robustness and generally useful results make this one dimensional (1D), quasi-1D approach a viable and attractive methodology, especially for preliminary design work. However, to extend modeling capability beyond simple ideal mixing models remains a challenge. This is even more the case when we limit the extension to analytically based expressions with a minimum of empirical information. Here, we develop a family of models that extend to include non-ideal effects such as skin friction. Comparison to available aerodynamic nozzle data is presented to illustrate the viability of these methodologies.