Dynamics of a Longitudinally Forced, Bluff Body Stabilized Flame

Abstract

This paper describes an investigation of the response of bluff body stabilized flames to harmonic oscillations. This problem involves two key elements: the excitation of hydrodynamic flow instabilities by acoustic waves, and the response of the flame to these harmonic flow instabilities. In the present work, data were obtained with inlet temperatures from 297 to 870 K and flow velocities from 38 to 170 m=s. These data show that the flame-front response at the acoustic forcing frequency first increases linearly with downstream distance, then peaks and decays. The corresponding phase decreases linearly with axial distance, showing that wrinkles on the flame propagate with a nearly constant convection velocity. These results are compared with those obtained from a theoretical solution of the G-equation excited by a harmonically oscillating, convecting disturbance. This kinematic model shows that the key processes controlling the response are 1) the anchoring of the flame at the bluff body, 2) the excitation of flame-front wrinkles by the oscillating velocity, 3) interference of wrinkles on the flame front, and 4) flame propagation normal to itself at the local flame speed. The first two processes control the growth of the flame response and the last two processes control the axial decrease observed farther downstream. These predictions are shown to describe many of the key features of the measured flame response characteristics. Nomenclature A = flame area D = burner depth d = bluff body width f = frequency f o = forcing frequency f BvK = Bénard-von Kármán instability frequency f KH = Kelvin-Helmholtz frequency G = isoscalar contour variable describing flame position H = burner height I t = edge detection threshold k = wave number L = flame position L 0 = fluctuation of flame position jL 0 j = gain of Fourier transformed flame position Q = heat release R 2 = goodness-of-fit parameter Re = Reynolds number S = distance along time-averaged flame front S L = laminar flame speed S T = turbulent flame speed t = time u = flow velocity in the x-direction u 0 = unsteady axial flow velocity u 0 = mean flow velocity u c;eff = effective convection velocity of a flame disturbance u c;v = convective velocity of a flow disturbance u 0 n = fluctuating flow velocity normal to the flame u t;0 = mean flow velocity tangential to the flame V = excitation voltage v = flow velocity in the y-direction W = burner width x = position along mean flow direction y = position perpendicular to mean flow direction = parametric flame-front angle " = nondimensionalized disturbance amplitude = time-averaged flame-front angle c = convective wavelength, u o =f 0 f = phase of a flame wrinkle x = phase of velocity perturbations in the x-direction y = phase of velocity perturbations in the y-direction ! = disturbance radial frequency

Nonlinear self-excited thermoacoustic oscillations of a ducted premixed flame: bifurcations and routes to chaos

“…For this reason, the perturbation velocity is modelled as a travelling wave that originates at the burner lip (Ducruix, Durox & Candel 2000;Preetham, Hemchandra & Lieuwen 2008;Kashinath et al 2013b). Experiments on laminar premixed flames (Boyer & Quinard 1990;Baillot et al 1992;Durox, Schuller & Candel 2005;Birbaud, Durox & Candel 2006;Kornilov, Schreel & de Goey 2007;Karimi et al 2009;Shanbhogue et al 2009) and turbulent premixed flames (Shin et al 2011;O'Connor & Lieuwen 2012), and direct numerical simulations (DNS) in our previous work (Kashinath et al 2013b), have shown that the phase speed of these velocity perturbations is not equal to the mean flow velocity. It is a function of the forcing frequency but is independent of the forcing amplitude.…”

Coordinate Systems and Integration Limits for Global Flame Transfer Function Calculations

“…For example, past studies have defined the flame position with respect to the axial coordinate [13,14], transverse coordinate [2,3,8] or in a coordinate system normal to the time averaged flame position [7,9,15]. To illustrate, the resulting expression written in the axial coordinate system is: (2) Here, x A ≡ x A (x, z, t).…”

“…Shin et al [13] and Shanbhogue et al [14] used the axial coordinate system for their study, as the position of shallow angle flames remains a single valued function of the coordinate for much larger amplitudes in that coordinate system. We focus attention for the rest of this note on the linearized flame area dynamics.…”

A numerical investigation on the mechanism of bluff-body lean blowout

“…As experimental chemical luminescence images illustrated [12] , the flames did not directly attach to the bluff body. According to the theory of flame propagation, anchoring points are essential for flame existence.…”