Fire plumes entrainment rate

At the instant of time shown, the entrainment of air into the fire plume is 300 g/s, the outflow of smoke through the door is 295 g/s and the liquid fuel evaporation rate of a spill burning on the floor is 10 g/s. What is the mass rate of smoke accumulation within the room ... 

In well-developed fires, the convective heat fraction is typically measured at more than about 65% of the total heat release rate (Heskestad, 2002). This heat is carried away by the plume above the flames. Prediction of plume velocity and temperatures above the flames serve as the basis for convective heat transfer calculations where overhead equipment exists. Widely used fire plume theory assumes a point source origin, and uniformity throughout the plume relative to air density, air entrainment, velocity profile, and buoyancy. 

Later Mayle, 1970 [400] continued their research by performing measurements of velocity and pressure within the fire whirl. He found that the behavior of the plume was governed by dimensionless plume Froude, Rossby, second Damkohler Mixing Coefficient and Reaction Rate numbers. For plumes with a Rossby number less than one the plume is found to have a rapid rate of plume expansion with height. This phenomenon is sometimes called vortex breakdown , and it is a hydraulic jump like phenomena caused by the movement of surface waves up the surface of the fire plume that are greater than the speed of the fluid velocity. Unfortunately, even improved entrainment rate type models do not predict these phenomena very well. 

Many formulations based upon these assumptions can be derived. One formulation can be converted into another using the definitions of density, internal energy and the ideal gas law. Though equivalent analytically, these formulations differ in their numerical properties. Each formulation can be expressed in terms of mass and enthalpy flow. These rates represent the exchange of mass and enthalpy between zones due to physical phenomena such as plumes, natural and forced ventilation, convective and radiative heat transfer, and so on. For example, a vent exchanges mass and enthalpy between zones in connected rooms, a fire plume typically adds heal to the upper layer and transfers entrained mass and enthalpy from the lower to the upper layer, and convection transfers enthalpy from the gas layers to the surrounding walls. 

If we had significant momentum or mass flow rate at the origin, the plume would resort to a jet and the initial momentum would control the entrainment as described by Equation (10.3). This jet behavior will have consequences for the behavior of flame height compared to the flame height from natural fires with negligible initial momentum. 

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