Dynamics of Practical Premixed Flames, Part II: Identification and Interpretation of CFD Data

Abstract

In Part I of this paper, a multiple-input, single-output (MISO) model for the dynamics of practical premixed flames has been proposed. A corresponding method for identification of model coefficients was developed and validated against test data generated with a linear time-domain model, designed to be qualitatively representative of a practical premix burner.The method for system identification of a MISO model is now applied to time series data generated with Computational Fluid Dynamics (CFD) simulation in the presence of broadband forcing. The CFD model represents a generic, practical premixed swirl burner with multiple fuel injection stages. Fuel injectors are assumed to be acoustically "non-stiff ", such that pressure fluctuations will modulate the fuel mass flow rates. The flame dynamics is therefore influenced by fluctuations of the equivalence ratio as well as the mass flow rate of premixture at the burner exit.Results obtained demonstrate that system identification based on correlation analysis is well capable of differentiating between the various interaction mechanisms. Unit impulse and flame transfer functions corresponding to different signal-response relations can be determined in a quantitative manner from a single CFD run. A detailed analysis and physical interpretation of the response functions has been carried out. The results allow to draw non-trivial conclusions concerning a) the interactions of flame front kinematics and equivalence ratio fluctuations and b) flame transfer functions with an amplitude above unity.

A Discrete-Time, State-Space Approach for the Investigation of Non-Normal Effects in Thermoacoustic Systems

“…A very simple configuration with h k = n for k = 10, 11, 12 and h k = −n for k = 13,14 was set up. The low-frequency limit of the corresponding flame transfer function is the same as for the n-τ model, but an intermediate peak and subsequent decay of the gain are observed (not shown), as it is typical for premix flames [29,30,35]. With a large interaction index n = 2.5, the system with distributed time lags is linearly unstable at intermediate frequencies.…”

“…The cycle increment Γ m of an eigenmode m with temporal evolution ~ exp (-iω m t) may be defined as the relative increment in amplitude per period of oscillation T m = 2π/ᑬ(ω m ), (29) …”

“…In particular, the time lag need not be small, such that larger, more realistic values of τ can be chosen. Furthermore, a spread in time lags, as it is often observed in flame transfer functions [29,30] can also be considered. Results for such cases will be presented in the next section.…”

“…7, which shows rather erratic behavior with large jumps in operator norm every 10 time advances due to the large time increment of that case, the increased temporal resolution resulted in physically more plausible behavior. Finally, a heat source with a spread of time lags [26,29,30,33,34],…”

Computation of Acoustic Transfer Matrices of Swirl Burner with Finite Element and Acoustic Network Method

“…The acoustic behaviors of these elements are characterized by their transfer matrices [7], which are linked at their inputs and outputs of the respective pressure and velocity fluctuations. The network model for stability analysis requires the flame transfer function (FTF) describing the coupling of the unsteady heat release offunction of modulation frequency, inlet velocity, fuel injection location, and fuel injector impedance [13]. Swirl burner composing of fuel injectors, swirlers and mixing sections, is necessary to determine the flame transfer function, but it's not easy to directly measure the velocity oscillations at the swirl passages for the complexity of the swirl burner.…”