Pressure modeling of fires controlled by radiation

Mathematical modeling of natural convection in fire—A state of the art review of the field modelling of variable density turbulent flow

“…Eqn ( 5 ) ) , of the molecular motion, and is therefore absorbed normally in the unknown p / p (replacing p / p by o / p + $ k ) if an explicit equation for k is not involved. (It should be noted that Eqn (17) reduces to the identity k = k for i = j , and thus cannot be used for the determination o f k.)…”

“…The first part of the model can be obtained from Eqns (17) and (19): with a constant of proportionality being unity and (L=)l,,, being the mixing length of turbulent motion analogous to the molecular mean-free path. The second part conceives the following form for the velocity scale:…”

“…The eddy viscosity hypothesis has also been extended to higher levels of complexity for nonequilibrium boundary layers (where turbulent transport = production -dissipation# 0 locally) whereby the eddy viscosity or the associated characteristic scales of turbulent motion are solved through the transport equations. Following Mellor and Herring,55 mean velocity field (MVF) models include all those eddy viscosity models (algebraic and transport) which provide information only about the mean velocity profile, in addition to the turbulent shear stresses (through Eqns (17) and (19)), whereas mean turbulent energy (MTE) models include all other (transport but not necessarily eddy viscosity) models that provide additional information about the kinetic energy of turbulent motion. The models of Saffman and W i l~o x ,~~ and Nee and Kovasznay7' are put5' in the category of MVF models, since their transportable parameters (such as vt) are themselves models of turbulent flows and not physically realizable quantities like k. The lack of popularity of these models compared with MTE models thus seems quite obvious.…”

“…MTE models, reviewed recently by Harsha,'" have been classified into two groups. PK models, proposed by Prandt17" and K~l m o g o r o v ,~~ use the eddy viscosity hypothesis (Eqns (17) and (19)) with the scale of velocity fluctuations specified according to for the eddy viscosity in PK models becomes With Eqn (22) ) (27) ak eddy diffusivity hypothesis…”

“…Tennekes and L~m l e y~~) . The correlation uirui' implicit in the term p k is modelled according to Eqn (17). The term E(V) represents the 'average' (kinematic) dissipation rate of turbulent (kinetic) energy, i.e.…”