Effects of heat release on turbulent shear flows. Part 3. Buoyancy effects due to heat release in jets and plumes

An integral method is presented for determining effects of buoyancy due to heat release on the properties of reacting jets and plumes. This method avoids the Morton entrainment hypothesis entirely, and thus removes the ad hoc 'entrainment modelling' required in most other integral approaches. We develop the integral equation for the local centreline velocity u_c(x), which allows modelling in terms of the local flow width δ(x). In both the momentum-dominated jet limit and buoyancy-dominated plume limit, dimensional arguments show δ(x) ∼ x, and experimental data show the proportionality factor c_δ to remain constant between these limits. The entrainment modelling required in traditional integral methods is thus replaced by the observed constant c_δ value in the present method. In non-reacting buoyant jets, this new integral approach provides an exact solution for u_c(x) that shows excellent agreement with experimental data, and gives simple expressions for the virtual origins of jets, plumes and buoyant jets. In the exothermically reacting case, the constant c_δ value gives an expression for the buoyancy flux (x) that allows the integral equation for u_c(x) to be solved for arbitrary exit conditions. The resulting u_c(x) determines the local mass, momentum and buoyancy fluxes throughout the flow, as well as the centreline mixture fraction ζ_c(x) and thus the flame length L. The latter provides the proper parameters Ω and Λ that determine buoyancy effects on the flame, and provides power-law scalings in the momentum-dominated and buoyancy-dominated limits. Comparisons with buoyant flame data show excellent agreement over a wide range of conditions.