Confined Swirling Flows with Heat Release and Mixing

Abstract

A simpli ed model is used to illustrate global features and ow regimes encountered in swirling ows with combustion, as an approach to providing an overall interpretation of the behavior of primary zone ows in leanpremixed-prevaporized gas turbine combustors. As one example of this, the physical mechanisms that characterize the interactions between swirl and heat addition are described, including the differing effects on recirculation zone formation for low and high values of swirl. The model, which is based on a quasi-one-dimensional control volume formulation, contains many approximations for the relevant ow processes. Nevertheless, comparisons of this simpli ed model with results from an axisymmetric Navier-Stokes code support the utility of the approach for gaining physical insight into the overall behavior of these parametrically complex ows. Nomenclature A= control volume area b 0 = planar shear layer growth rate C p = speci c heat of air at constant pressure E = Eckert number, (u 1 ¡ u 2 ) 2 / C p t T 1 h = enthalpy L = duct length M = Mach number = momentum, Çmu Çm = mass ow Pr t = turbulent Prandtl number p = static pressure R = radius of duct Re b = Reynolds number based on shear layer thickness, D U b/ m t r = velocity ratio, u 1 / u 2 s = density ratio, q 1 / q 2 T = static temperaturē U = average axial velocity of core and outer streams u = velocity in axial direction v = velocity in circumferential direction w = velocity in radial direction z = coordinate in axial direction a = area ratio, A D / A 1 C = circulation D U = velocity difference, u 1 ¡ u 2 d = radius of vortex core g = ratio of speci c heats at constant pressure, C p1 / C p2 m t = effective turbulent viscosity N = mixing coef cient q = density s = temperature ratio, T 1 / T 2 u = equivalence ratio X = swirl ratio, C / 2p d u 1 Subscripts c = centerline D = duct m = mixing pr = product formation due to chemical reaction

Correspondence Between “Stable” Flame Macrostructure and Thermo-acoustic Instability in Premixed Swirl-Stabilized Turbulent Combustion

“…The jet forms a narrower angle in the mean flow sense for the cold flow and, as the equivalence ratio increases, the angle increases. This effect has been previously numerically studied [23]. This trend is reversed for flame IV.…”