M. Fleifil

Response of a laminar premixed flame to flow oscillations: A kinematic model and thermoacoustic instability results

Combustion instability is a resonance phenomenon that arises due to the coupling between the system acoustics and the unsteady heat release. The constructive feedback between the two processes, which is known to occur as a certain phase relationship between the pressure and the unsteady heat release rate is satisfied, depends on many parameters among which is the acoustic mode, the flame holder characteristics, and the dominant burning pattern. In this paper, we construct an analytical model to describe the dynamic response of a laminar premixed flame stabilized on the rim of a tube to velocity oscillation. We consider uniform and nonuniform velocity perturbations superimposed on a pipe flow velocity profile. The model results show that the magnitude of heat release perturbation and its phase with respect to the dynamic perturbation depend primarily on the flame Strouhal number, representing the ratio of the dominant frequency times the tube radius to the laminar burning velocity. In terms of this number, high-frequency perturbations pass through the flame while low frequencies lead to a strong response. The phase with respect to the velocity perturbation behaves in the opposite way. Results of this model are shown to agree with experimental observations and to be useful in determining how the combustion excited mode is selected among all the acoustic unstable modes. The model is then used to obtain a time-domain differential equation describing the relationship between the velocity perturbation and the heat release response over the entire frequency range.

Impact of Linear Coupling on the Design of Active Controllers for the Thermoacoustic Instability

Analysis of combustion instability has traditionally been based on the assumption that linear coupling among acoustic modes is insignificant. While this is reasonable when one is interested in determining the unstable mode frequency and growth rate, in this paper we show that this assumption in a model-based active control design may lead to serious errors. To explain the origin of these errors, we employ both analysis and numerical examples to investigate the effect of linear coupling on the resonance and anliresonance properties of a benchlop premised combuslor in the presence of external excitation. The analysis is carried out using one-dimensional flow dynamics in the presence of an oscillating heal release source based on laminar premised flame kinematics, and an external actuator in the form of a loudspeaker. We show that, for certain sensor-actuator configurations, a controller designed on the basis of a model where linear coupling is neglected may fail to suppress the thermoacoustic instability wh...

A Model-Based Active Control Design for Thermoacoustic Instability

Abstract Active control has been pursued vigorously for combating thermoacoustic instabilities in combustion processes. Most experimental investigations employ empirical design procedure for determining the characteristic parameters of the filter and phase-shifter of the controller. Such procedure has been observed to result in resonance at frequencies which were not excited in the power spectrum of the uncontrolled combustor, though the dominant thermoacoustic instability was suppressed. In this paper, we present an alternative design methodology which is based on the underlying physical model of the combustor and modern control theory. We show that using this methodology, one can avoid the generation of secondary peaks and achieve short settling time using small control energy. The physical model takes into account multiple acoustic modes, the heat release dynamics of a premixed flame, and the effect of an actuator such as a loudspeaker, on the flow variables over a wide range of frequencies. The model-...

The Origin of Secondary Peaks with Active Control of Thermoacoustic Instability

This paper deals with the generation of new peaks in the pressure spectrum in controlled combustors in experimental investigations of active control of thermoacoustic instabilities. Typically, the reported experiments have demonstrated that the dominant thermoacoustic instability can be suppressed, but secondary peaks at different frequencies which were not excited in the uncontrolled combustor appear. We develop a physically-based model of an actively controlled premixed laminar combustor which takes into account (a) laminar flame kinematics, (b) linear acoustic dynamics with coupling between the acoustic modes, and (c) actuation using side-mounted and end-mounted loudspeakers. Using this model, we analyze some of the experimental controllers proposed in the literature and explain the origin of secondary peaks observed in these studies. Secondary peaks are created while using these controllers due to resonant coupling between various mechanisms in the combustor that are distinct from those responsible fo...

Combustion Instability Active Control Using Periodic Fuel Injection

Active control using periodic fuel injection has the potential of suppressing combustion instability without radically changing the engine design or sacrificing performance. A study is carried out of optimal model-based control of combustion instability using fuel injection. The model developed is physically based and includes the acoustics, the heat-release dynamics, their coupling, and the injection dynamics. A heat-release model with fluctuations in the flame surface area, as well as in the equivalence ratio, is derived. It is shown that area fluctuations coupled with the velocity fluctuations drive longitudinal modes to resonance caused by phase-lag dynamics, whereas equivalence ratio fluctuations can destabilize both longitudinal and bulk modes caused by time-delay dynamics. Comparisons are made between the model predictions and several experimental rigs. The dynamics of proportional and two-position (on-off) fuel injectors are included in the model. When the overall model is used, two different control designs are proposed. The first is an linear quadratic Gaussian/loop transfer recovery controller, where the time-delay effect is ignored, and the second is a positive forecast controller, which explicitly accounts for the delay. Injection at 1) the burning zone and 2) farther upstream is considered. The characteristics of fuel injectors including bandwidth, authority (pulsed-fuel flow rate), and whether it applies a proportional or a two-position (on-off) injection are discussed. We show that increasing authority and increasing bandwidth result in improved performance. Injection at location 2 compared to location 1 results in a tradeoff between improved mixing and increased time delay. It is also noted that proportional injection is more successful than on-off injection because the former can modulate both amplitude and phase of the control fuel.

A Model-based Self-tuning Controller forThermoacoustic Instability

Abstract Active Control of thermoacoustic instabilities in continuous premixed combustion processes is being increasingly investigated for operating at lean low NOx conditions. Recently, we have developed a model-based approach for active control design which accounts for the underlying acoustics, heat release dynamics, and sensor and actuator dynamics. While this model captures a number of the dominant dynamic features of a premixed laminar combustor, there are a number of uncertainties associated with it as well. In this paper, we study the sensitivity of this model with respect to parametric uncertainties, and the efficacy of a fixed control design for suppressing pressure oscillations. We show that under certain conditions, the fixed controller is inadequate and present a self-tuning controller which is capable of delivering the desired performance in the presence of these uncertainties. The controller proposed is based on a rigorous analytical foundation, and is shown through simulation results to le...

Heat-release actuation for control of mixture-inhomogeneity-driven combustion instability

A low-order heat-release model, which accounts for the impact of flame surface area and the equivalence ratio oscillations, was used in conjunction with system acoustics to design a hierarchy of control strategies designed to mitigate combustion instability. The model assumes premixed combustion which burns a mixture with a temporally dependent equivalence ratio at high Damkohler number and low turbulence intensity (i.e., a wrinkled laminar flame). When the acoustic field is of the Helmholtz-resonator type, the instability is dominated by the ratio of the convective time lag between the primary fuel injection and the burning zone and the time constant of the resonant acoustics. The model was applied to a practical combustor, and the instability condition predicted agreed with the measurements. The model structure was then utilized to design several active control approaches which incorporated periodic fuel injection at an arbitrary location between the primary injector and the burning zone. We showed that by exploiting the instability mechanism, as captured by the model, one can add flexibility and robustness to the control design (e.g., where the injector is located, how much fuel is introduced, the settling time). Several control algorithms, including an integral controller located at the fuel supply, an integral-plus-proportional controller located at the burning zone, and a Posi-Cast controller located at an arbitrary location in between, are proposed. While we find that the secondary injector can be successful in suppressing the instability, irrespective of its location with respect to the flame zone, results show that the control effort and the robustness against uncertainty and changes in operating conditions depend on the delay associated with the combustion of the extra control fuel (i.e., the location of the injector and the control algorithm).

Role of Actuation in Combustion Control

This paper presents analysis of the effect of actuation on combustion dynamics. Two different categories of actuators are examined: flow sources, e.g., acoustic speakers, and heat sources, e.g., fuel injectors. These sources are modeled in the conservation equations and a finite dimensional model is obtained. Two methods of analysis are used to gain insight into the physics of actuation, and its stabilizing/destabilizing effect on the combustor through feedback control. The first is the energy method which is used here in a novel way to explain work exchange between the different dynamic components of the system: the acoustics, the flame, and the actuator. Energy analysis is also used to quantify the “Useful” and “wasted” work generated by actuators. The second method of analysis is the dynamic method in which the combustor is represented as an oscillator. This method is used as a basis of any optimal control design.

Low-order nonlinear models of thermoacoustic instabilities and model-based control

We present three low order nonlinear models which depict limit-cycle behavior that is ubiquitous in thermoacoustic pressure oscillations. All three nonlinear models are shown to result in periodic solutions and exhibit trends similar to those observed in a bench-top combustor rig. We also analyze the behavior of a linear controller based on a model without the nonlinearities and discuss the conditions under which the controller can be successful in stabilizing the pressure despite the nonlinear mechanisms. Numerical simulations and experimental results are presented to support the nonlinear model as well as the linear controller.

Model-based analysis and design of active control of thermoacoustic instability

Thermoacoustic instability arises due to the two-way coupling between the heat release dynamics and acoustics in continuous combustion systems, especially those designed to run at lean premixed conditions. While suppression or damping of oscillation is possible under some circumstances, active control promises to provide more flexibility in terms of design, operating conditions and robustness. Optimum designs of the latter must rely on accurate modeling of the underlying mechanisms governing combustion dynamics and a good understanding of the tight and often subtle coupling between actuators, combustion dynamics, acoustics, control algorithms and observers. In this paper, we use an input-output reduced order model of a controlled combustor to illustrate one aspect of such coupling, namely the dependence of the zero dynamics on the relative location of the heat release zone, the actuator and the sensor. We also use the model to design the controller using a linear quadratic Gaussian (LQG) approach. We show that the model response is similar to that obtained using the governing partial differential equations simulations of the process. We also verify the performance of the same controller experimentally using a 1 KW benchtop combustor rig.