Combustion dynamics and control: Progress and challenges

Proceedings of the Combustion Institute, Volume 29, 2002/pp. 1–28

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES SE´BASTIEN CANDEL Laboratoire EM2C, CNRS Ecole Centrale Paris 92295 Chaˆtenay-Malabry, France

Combustion dynamics constitutes one of the most challenging areas in combustion research. Many facets of this subject have been investigated over the past few decades for their fundamental and practical implications. Substantial progress has been accomplished in understanding, analysis, modeling, and simulation. Detailed laboratory experiments and numerical computations have provided a wealth of information on elementary dynamical processes such as the response of flames to variable strain, vortex rollup, coupling between flames and acoustic modulations, and perturbed flame collisions with boundaries. Much recent work has concerned the mechanisms driving instabilities in premixed combustion and the coupling between pressure waves and combustion with application to the problem of instability in modern low NOx heavyduty gas turbine combustors. Progress in numerical modeling has allowed simulations of dynamical flames interacting with pressure waves. On this basis, it has been possible to devise predictive methods for instabilities. Important efforts have also been directed at the development of the related subject of combustion control. Research has focused on methods, sensors, actuators, control algorithms, and systems integration. In recent years, scaling from laboratory experiments to practical devices has been achieved with some success, but limitations have also been revealed. Active control of combustion has also evolved in various directions. A number of experiments on laboratory-scale combustors have shown that the amplitude of combustion instabilities could be reduced by applying control principles. Full-scale terrestrial application to gas turbine systems have allowed an increase of the stability margin of these machines. Feedback principles are also being explored to control the point of operation of combustors and engines. Operating point control has special importance in the gas turbine field since it can be used to avoid operation in unstable regions near the lean blowoff limits. More generally, closed loop feedback concepts are useful if one wishes to improve the combustion process as demonstrated by applications to automotive engines. Many future developments of combustion will use such concepts for tuning, optimization, and emissions reduction. This article proposes a broad survey of these fast-moving areas of research.

survey of research, the identification of problems, trends, and perspectives, a tutorial style, and compact writing. It was stimulating and worthwhile to read again some of the previous lectures and see how this was accomplished by former speakers [1–5]. This reading also helped in selecting the topic of this lecture. It appeared timely to deal with ‘‘combustion in the system’’ and address the critical issues of dynamics and control. Other reasons for choosing this subject are listed below:

Introduction As engineers and scientists working in combustion, we often deal with specialized problems. While some of us emphasize fluid flow and turbulence, others consider kinetics in their finest details, while still others envisage pollutant, soot, sprays, droplets, flame structures detonations, fires, solids, and propellants. A complex phenomenon, combustion features a maze of processes. To unravel its threaded elements requires the individual and collective intelligence of generations of scientists. The Combustion Symposia have played a major role in the advancement of this field by allowing our mutual interactions, and many of us have had their lives synchronized by these periodic events. This lecture bears the name of Hoyt Hottel, one of the founders of the Combustion Institute and of this tradition. It is an occasion for synthesis and for reflection on the past and the future. As a unique opportunity to speak to the assembly in its entirety, the conference requires a balanced but synthetic

• A multidisciplinary field, combustion dynamics and control (CDC) is quite suitable for such a circumstance. It exemplifies much of our activity as scientists, involving a subtle combination of intuition, theoretical analysis, modeling, simulation, and experimentation implying advanced diagnostics, sensors, and actuators. • As a topic of continued interest, CDC has evolved during the past 50 years from phenomenology to a situation where it is amenable to simulation. 1

2

HOTTEL LECTURE

External perturbations

Combustion

Flow (a)

Acoustics

External perturbations

Combustion

Flow Acoustics Controller (b)

Fig. 1. (a) Schematic diagram of combustion instability coupled by acoustic feedback. (b) An active control loop is used to stabilize the system.

• As an area of research, CDC belongs to ‘‘Pasteur’s quadrant’’ advocated in Irv Glassman’s Hottel lecture [1] of 2 years ago to describe the type of focused research aiming at the advancement of science and applications simultaneously. • The positive connotation of the word dynamic hopefully characterizes the activity of this community of scientists and engineers, and this lecture is intended as a contribution to the momentum of this symposium. It is also possible to establish some relations with Hottel’s contributions. Fifty years ago, Hottel with two of his students, Weddell and Hawthorne (see Ref. [6]), studied the visible radiation of jet flames, concluded that length depended on jet momentum and much less on fuel composition, and gave the first criteria for liftoff and blowoff. This classical analysis indicated the prevalence of dynamical processes in combustion. This point of view is adopted in what follows. This paper begins with an historical perspective and some background material. Current problems are underlined next, and the contents of this review are described at the end of this section. Historical Perspective and Background Combustion scientists laid the ground of modern CDC during the early fifties and sixties [7–16]. An account of much of this research was assembled in Ref. [17]. This was a time in which jet propulsion applications to rockets and aircraft were encountering stability problems. Dynamics and control had always been issues in the technical application of combustion, but the problem became more severe in these new high-performance devices. Combustion control became critical in these new areas. A complex, nonlinear, closely coupled process, combustion was not well understood and not simple to describe mathematically. This was compounded with problems associated with the harsh conditions prevailing

in combustors and difficulties in taking measurements and integrating sensors and actuators in practical devices. During the early period in which jet propulsion was being developed for aeronautical and space applications, the occurrence of instability led to some dramatic failures. Many accidents resulted from various types of resonant motions often leading to explosions. Failures caused by oscillations also affected power plants or various industrial processes. While combustion had often been the driving mechanism of instabilities in propulsion, it is not the only possible cause. Other components may be responsible for divergence from steady-state operation to a strongly unstable motion. For example, the rotating stall in jet engine compressors has often had damaging consequences. Because instability problems were particularly acute during the initial development of high-performance propulsion systems, a considerable amount of research was expended to identify the driving and coupling mechanisms and develop methods for their control [17–19]. The important design objective was to keep the combustion process under control and avoid runaway, oscillation, flashback, blowout, flame acceleration, and transition. While instabilities have been a standing point of concern in propulsion, the problem has been encountered more recently in heavy-duty low NOx gas turbine applications, and this has motivated much of the current research on this topic [20–32]. In general, instabilities are driven by a variety of flow and combustion processes and they are usually coupled by acoustic resonant modes (Fig. 1a) [33]. A driving process generates a perturbation of the flow; a feedback process couples this perturbation to the driving mechanism and produces the resonant interaction which may lead to oscillatory combustion. The driving mechanism itself involves a wide variety of elementary processes as shown schematically in Fig. 2. The feedback generally relates the downstream flow to the upstream region and it is in most cases acoustic in nature. The coupling may also involve convective modes like entropy waves. Flames themselves feature instabilities which do not require an acoustic coupling. It is known, for example, from the work of Darrieus [34] and Landau [35] that premixed fronts are hydrodynamically unstable. These and other intrinsic instabilities have been studied extensively (see Refs. [36–39] and the review of Clavin [40]), and they will not be considered here to focus on processes coupled by system or chamber modes. Standard reasons advocated to explain why combustion is so succeptible to instabilities are listed below. 1. The energy density associated with combustion is quite sizable, so that a small fraction of this energy is sufficient to drive the oscillation [41–42]. For example, in a modern liquid rocket engine, the mean pressure is typically p¯  10 MPa and the

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES

3

Acoustics

Upstream dynamics

Flame wall interactions

Atomization/ vaporization/ mixing

Feed line dynamics Injection Impedance conditions Mixing

Downstream dynamics Stabilization flame holding Organized vortex structures

Heat release Entropy waves

Exhaust impedance conditions

Flame/ vortex interactions

Acoustics

Fig. 2. Basic interactions leading to combustion instabilities.

mean power density reaches Ec  50 GW m3. If an instability develops, the rms pressure perturbation may typically reach 1%–10% of the mean pressure. For a 10% fluctuation, the power density associated with the unsteady motion is Ea  0.1 MW m3 which is clearly a minute fraction of the density of energy in the system: Ea/Ec ⯝ 106. Oscillations may be driven by a small amount of the heat released in the combustor. 2. Combustion involves time lags. Reactants introduced in the chamber at one instant are converted into burnt gases at a later time. Systems with delays are more readily unstable as can be shown by considering a second-order model featuring a linear damping and a restoring force with a delay: d2x dx  2fx0  x02x(t s)  0 dt2 dt

(1)

Assuming that the delay s is small and developing this expression in a Taylor series to first order yields d2x dx  x0(2f x0s)  x02x(t)  0 (2) dt2 dt This system has a negative damping coefficient if x0s
2f. If the time lag is long enough, the amplitude will grow exponentially. Systems with time lags are inherently unstable. The sensitive time lag (STL) theory developed during the fifties and sixties is based on the further observation that the lag is not constant but depends on physical parameters like pressure or temperature in the chamber [7–10,43]. In the simplest case, if one reactant is injected as a spray, an increase in pressure will augment the ambient density, and this will decrease the droplet size. The droplet vaporization will proceed faster and the conversion of reactants into products will take place sooner. Thus, an increase in pressure will produce a decrease of the time delay s between injection

and combustion. Assuming that the reactant is injected at a constant rate and that only pressure influences the time lag, one may show that the relative change in the mass rate of burnt gases lb ¯˙ b)/m ¯˙ b may be expressed in terms (t)  (m ˙ b m of the relative change in pressure u  (p p¯)/p¯: lb (t)  n [u(t) u(t s)], where the interaction index n describes the sensitivity of the combustion process to pressure. According to this expression, the relative change of mass rate of production of burnt gases is proportional to the difference in pressures at times t and t s. 3. Resonant interactions may readily occur in the confined and weakly damped geometries used in most practical combustors. Among the possible coupling modes, acoustics is dominant. Resonance is sharp because the damping is limited. Energy losses are related to viscous dissipation at the walls, radiation from inflow and outflow, various relaxation processes in flows with particles or droplet sprays. The corresponding attenuation is weak and the gain in the system exceeds the losses. If resonance takes place in the low-frequency range, the wavelength exceeds the typical transverse dimension and wave propagation is essentially longitudinal and involves the full system giving rise to ‘‘system instabilities’’. If resonance features a higher frequency ( f
1 kHz), the wavelength is of the order or less than the tranverse dimension and the coupling usually involves a transverse mode of the chamber [15]. These ‘‘chamber instabilities’’ are found in systems where the combustor is well decoupled from upstream and downstream systems (reactant supply lines, turbomachinery, vessels). 4. There are numerous mechanisms which may feed energy in the perturbed motion. A gain is obtained if, according to the Rayleigh criterion, the heat-release fluctuation is in phase with pressure or more exactly if  p q dt
0 [44,45]. The flow

4

HOTTEL LECTURE

perturbations which may initiate the process involve vortex rollup, shear instabilities, flame acceleration, collective interactions between reactant streams, collisions with boundaries [33]. If the feed lines are not well decoupled from the chamber, instabilities can also be driven by the differential response of the injection system when it is submitted to incident perturbations giving rise to inhomogeneities in reactant content. The previous factors all favor the development of unstable oscillations. This may be counteracted by changing the balance between gain and losses, a principle which has been exploited to devise passive control methods (PCM). In PCM, one tries to remove energy from the oscillation or change the design to damp the modes of oscillation which could most effectively couple with the combustion process. PCM rely on one or a combination of the following actions: (1) Modification of the injection system to change the characteristic delay and modify the resonance conditions, (2) deployment of acoustic liners to augment the energy losses and reduce the level of organized perturbation in the system, (3) insertion of resonators to diminish the resonance level of a given mode by augmenting acoustic losses, and (4) integration of baffles to protect the combustion zone from the oscillating flow and to eliminate the most destructive transverse modes. Baffles only allow standing modes which have velocity nodes at the baffle blades. Proposals were already made during the 1950s to introduce closed-loop control to stabilize the combustion process [8–10]. (The concept is sketched in Fig. 1b.) These ideas were explored on a theoretical basis but did not find a practical demonstration. Knowledge was gathered but progress was limited by the state of the art in sensors, and control hardware. Combustion science had not reached an advanced state of maturity, and some fundamental questions were not well understood or described. Early research in combustion instability was strongly driven by practical needs but was limited by technology. (1) Diagnostics were mainly pressure sensors, photomultipliers, and high-speed film cameras. The main imaging techniques were based on shadowgraph and Schlieren; (2) lasers were yet to be invented and their applications in probing and imaging came much later; (3) computers occupied large volumes, their memory, performance, and reliability were limited; (4) data acquisition and storage was based on multichannel FM magnetic tape recorders and processing was essentially done with analog electronics with restricted performance and flexibility. One can admire the ingenuity of researchers working in this field during the early period and appreciate how much was learned despite the technical and computational limitations. Remarkable theoretical developments were made, and the fundamental experimentation carried out during these

early days provided many clues on the coupling phenomena. Instability problems were solved one by one with a variety of methods combining scientific analysis, phenomenological reasoning, and engineering know-how. The more detailed approach to the understanding of CD phenomena had to wait until recently [33]. Considerable insight in the processes driving instabilities was obtained from experiments carried out from the late 1970s to this day. During that period also, active control of instabilities was demonstrated in small-scale experiments. (See Ref. [46] for a review.) Many elementary processes were investigated, such as the effect of unsteady strain on laminar premixed and non-premixed flames, flame/vortex interactions (see Ref. [47] for a review), the sensitivity of droplet combustion to unsteady pressure, flame acceleration by pressure waves [48–50], dynamics of spray flames [51–54], and this effort has been continued in recent years. Current Dynamics and Control Problems Combustion dynamics and control remain central issues in key technological developments in energy and propulsion. For stationary gas turbines, the requirement for lower emission of nitric oxides has lead to the development of premixed burners. The technological shift from non-premixed ‘‘diffusion’’ combustors to premixed systems provides an important reduction of nitric oxide emissions but also results in reduced stability of the flame which is more succeptible to acoustic disturbances [21]. Close to the lean blowoff limit where the combustor must operate, the pressure fluctuations may feature sizable amplitudes which in some cases reach levels of the order of a few percent of the mean pressure corresponding to rms values of the order of 0.1 MPa or more. Such unacceptable levels must be reduced to avoid incidents or restrictions in the operational domain of the machine. The dynamics of the lean premixed combustion instabilities has been the subject of intensive research in academia and industry. Fig. 3 gives a view of the possible interactions in such devices. Investigations have focused on the identification of the driving mechanisms, the modeling of the unsteady flame motion, the description of system dynamics, and related development of active and passive control methods. The premixed mode of combustion now favored in stationary gas turbines is also considered for jet engines because of its low NOx capability. Premixed combustion requires an accurate control of the operating point. The equivalence ratio (EQR) ␾  (m ˙ f/m ˙ a)/(m ˙ f/m ˙ a)st must be fixed with precision [56– 58]. If it is too low, the flame may be blown out, a serious incident for a gas turbine. If it is too high, nitric oxide emissons increase and one loses the advantages of lean premixed combustion. The main

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES Burner flow turbulence

Burner flow instabilities Velocity fluctuations

Burner heat release

Pressure fluctuations

Equivalence ratio

Pressure fluctuations

Air supply

Entropy waves

Combustion chamber

Fig. 3. Thermoacoustic interactions in gas turbine combustors. Adapted from Ref. [55].

difficulty in controlling the equivalence ratio is that the mass flow rate of air through the combustor is not known with precision. It is then necessary to use closed-loop control concepts in which a sensor or a set of sensors operating on the chamber or on the gas exhaust return information to the fuel regulation system. Work along these lines has been carried out and demonstrations of operating point control concepts have been reported (see the recent review by Docquier and Candel [58]). Studies are generally developed on model-scale combustors [59–62]. Scale up and operation under real conditions are less common (see, however, Refs. [2,63] for an application of modern sensors to waste incineration). Closed-loop operating point control implies systematic sensor testing, design, and experimentation of control loops under representative conditions (high pressures, preheat temperatures in excess of 600 K) and integration activities. Research in gas turbine combustion is aimed at achieving stable, clean, and efficient combustors. This will require progress in classical areas of combustion science (understanding and modeling of elementary mechanisms, numerical modeling in simple situations and in the practical geometries). One will also have to examine aspects which imply the complete system: (1) dynamical phenomena leading to instabilities, (2) active combustion control (ACC)

Detailed studies of elementary processes

Model scale investigations Sensor and actuator development

5

for instability reduction and passive control methods, and (3) operating point control (OPC) for combustion tuning and optimization. Active control is extensively investigated as already apparent from some earlier reviews [33,46,64]. A number of papers in the last symposia focus on this topic and it was the subject of a recent NATO/RTO Symposium in Braunschweig. In what follows, we try to sort out current trends and future perspectives. Contents CDC has many complexities which cannot be covered exhaustively. This area is characterized by a broad range of activities (see Fig. 4). Some key aspects already surveyed in previous reviews will not be envisaged and a synthesis is also not attempted. Selected problems are considered to highlight some current efforts. The next section is concerned with elementary processes. It focuses on dynamical interactions and reviews investigations aimed at a fundamental understanding. The theoretical description of CD is treated next. Approaches to the problem are identified. The numerical simulation of CD is then illustrated in a separate section with calculations of premixed turbulent flames in various configurations. It is shown that considerable progress has been achieved in the large-eddy simulation of turbulent flames and that this will allow realistic descriptions of combustion dynamics in practical devices. Active control was treated in previous reviews. Much of the recent effort has focused on the modeling of control. This is emphasized here with specific attention to the new possibilities and difficulties of multidimensional simulations (MDS) of active control. This is illustrated with multidimensional calculations of vortex driven instabilities in solid-propellant rockets. The final section concerns OPC. The subject is briefly discussed because it is covered extensively in recent reviews [58,65]. Elementary Processes An understanding of combustion dynamics may be founded on detailed studies of elementary processes.

Low order Low-order modeling modeling, Multidimensional simulations

Control algorithms and technological developments

Integration, scale-up and application to real systems Fig. 4. Activities in combustion dynamics

6

HOTTEL LECTURE F

F+O

ε(t)

Flame

F+O

ε(t)

F

Vortex Flame

Flame

(d) O

P

O Flame

Flame

(c)

(b)

(a)

Flame

Flame Plate

Flame (e)

(f) Plane acoustic waves

(g) Plane acoustic waves

(h) Plane acoustic waves

Equivalence ratio perturbation

Fig. 5. Elementary processes. (a) Unsteady strained diffusion flame; (b) unsteady strained premixed flame; (c) premixed flame/vortex interaction; (d) strained diffusion flame/vortex interaction; (e) acoustically modulated conical flame; (f) acoustically modulated V-flame; (g) perturbed flame interacting with a plate; (h) equivalence ratio perturbation interacting with a premixed flame.

On the fundamental level, one wishes to analyze the flame response to perturbations and its coupled motion in acoustic wavefields. Among the many possible interactions which take place in combustors, some processes are of special dynamical importance: (1) unsteady strain effects on diffusion or premixed flame elements; (2) flame/vortex interactions, vortex enhanced mixing, and subsequent combustion; (3) acoustic flame coupling; (4) interactions of perturbed flames with boundaries; (5) flame response to incident composition inhomogeneities. These processes are illustrated schematically in Fig. 5. There are many other processes which deserve attention, some of which have already been surveyed in Ref. [33]. Flame acceleration by shocks or weakpressure fronts is typically important when flames travel in ducts (for example, see Refs. [49,50]), the interaction between acoustic waves or shocks and droplets or sprays has profound effects by inducing breakup of the liquid phase, thus augmenting the rate of vaporization (a process of importance in liquid propellant rocket engines, see Ref. [19]). These mechanisms will not be considered to keep this review under reasonable limits. Results obtained in studies of elementary processes only depict one aspect of the unstable motion but may be used to establish a comprehensive model of the process. This, however, requires that links be established between the elementary system and the more complex real device, a relation which is not often made explicit. Dynamics of Unsteady Strained Flames The flame response to strain rate is a central issue in laminar flame analysis and in turbulent combustion (see Refs. [66–68]). Investigations have mainly

concerned effects of steady strain rates with many early experiments by Tsuji and his coworkers [69,70]. A large-scale unstable motion in a combustor produces at the local level a field of time-dependent strain rates. This will modify the flame structure, the burning velocity in the case of premixed flames, and the rates of reaction per unit flame area in the nonpremixed case as shown experimentally in Refs. [71– 75]. The response of flames to such external strainrate modulations is clearly of interest. There are many studies of this topic, mostly relying on direct calculations using time-dependent solutions of strained flames with complex chemistry [76–81]. It is found that flames behave like low-pass filters when the perturbed strain-rate fluctuations do not exceed the extinction value. Analytical expressions of the flame response have also been worked out using asymptotics [82–84]. A simple analysis may be developed by considering strained diffusion flames submitted to small variations of the strain rate (Fig. 5a). Assuming infinitely fast chemistry and a singlestep reaction between fuel and oxidizer, one may derive a complete expression for the flame response to an arbitrary strain rate e(t) [85–87]. This yields an analytical relation for the rate of reaction per unit flame surface which will be used here as a starting point. m ˙ (t) ⯝

D ps

1/2

冢 冣

t

冢冮 edt冣

exp

0

(3)

where D is the diffusion coefficient and s

t

冮

0

冤 冢冮

t1

dt1 exp 2

0

冣冥

edt

(4)

Assuming a sinusoidal strain rate around a mean

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES

value e(t)  e0  e1 cos xt, and considering that the amplitude of the strain rate perturbation e1 is small compared with e0, one finds that the relative oscillation of the rate of reaction may be cast in the form m ˙ (t)  m ˙0 1 e1 1  m ˙0 2 e0 1  (x/2e0)2

冤cos xt  冢2e 冣 sin xt冥 x

(5)

0

The flame-transfer function defined in the frequency domain as the ratio of the relative reaction rate modulation to the relative strain-rate perturbation ˜˙ m(x) m ˙0 F(x)  m ˙0

冢

e˜ (x)  e0 e0

冣冫冢

冣

(6)

takes the form of a low-pass filter: F(x) 

1 1 2 1  i(x/2e0)

(7)

The cutoff angular frequency of this filter is xc  2e0( fc  e0/p), and the phase angle between the strain-rate modulation and the reaction rate is given by u  arctan(x/2e0). This phase tends to p/2 as x takes large values. The 1/2 factor appearing in the transfer function reflects the functional relation of the steady-state rate of reaction per unit flame surface m ˙ ⯝ (e)1/2. The effect of unsteady strain on premixed flames cannot be described in such simple terms [88–90]. It is convenient in that case to plot the ratio of the consumption speed to the laminar burning velocity Sc/SL as a function of a reduced strain rate Ka(t)  dfe(t)/SL where df and SL are the unstrained flame thickness and burning velocity. Numerical calculations [90] indicate that the reponse takes the form of cycles around the steady-state line. The size of the cycle diminishes as the frequency increases. A convenient definition of the flame response consists in taking the ratio T(x) 

冤

冥冫冤

Sc(x) 1 SL

冥

Madf e(x) SL

(8)

where Ma is a Markstein number of the mixture. The magnitude of the response is close to unity in the low-frequency range. This is so because for weak strain rates, Sc ⯝ SL Madfe in the quasi-steady state. The amplitude is attenuated as the product x*  xdf/SL exceeds a reduced cutoff frequency of the order of unity x*, c which depends to a certain extent on the equivalence ratio x*c  x*( c ␾). Another mechanism which may influence the dynamics of turbulent flames is the mutual interactions of neighboring reactive fronts. This has been identified as a fundamental process limiting the flame surface area. The rapid consumption of reactants

7

trapped between two adjacent flames may also produce a heat-release pulse and the emission of pressure waves. If this interaction is properly phased with respect to a pressure eigenmode, it may drive the unstable motion. The mutual interaction of strained diffusion flames is now well understood [85–93], but the possibility of having synchronized interactions leading to instability is not generally considered. The process has been observed experimentally at least in Ref. [94]. Flame/Vortex Interactions Vortex structures drive various types of combustion instabilities. In many circumstances the ignition and delayed combustion of these structures constitute the sustaining mechanism by which energy is fed into the oscillation. Vortex rollup often controls the transport of fresh reactants into the burning regions and this process determines the non-steady rate of conversion of reactants in the flow and the amplitude of the pressure pulse resulting from the vortex burnout. Because problems of flame/vortex interactions are so pervasive, they have been studied extensively (see Ref. [47] for a review). Much of the experimental work has concerned vortices impinging on a progressive premixed flame (Driscoll and coworkers [95–97]) or an established strained diffusion flame (by Rolon and coworkers [98,99]). However, instability experiments indicate that vortex rollup takes place while the flame develops. The vortex entrains a mass of fresh reactants and hot products and ignites at a later time producing a pulse which may feed energy in one of the resonant modes of the combustor. This process is more difficult to study experimentally and is less well documented. Interactions between adjacent reactive vortices and collisions of flames rolled up in vortices with boundaries are also less well covered but often observed in premixed devices [100]. Flame Response to Incident Inhomogeneities Experiments and theoretical analysis indicate that instabilities in lean premixed combustors may be driven by perturbations in the fuel and air ratio [22,25,101,102]. Pressure oscillations in the combustor interact with the fuel supply line. A positive pressure excursion produces a decrease of the fuel supply at a later instant. This causes a negative perturbation in the equivalence ratio ␾ which is convected by the flow to the flame zone. This will produce a heat-release perturbation which, if properly phased with the pressure, may feed energy in the resonant acoustic mode involved in the process. This mechanism is described schematically in Fig. 6. One assumes first that a pressure oscillation is established in the system. Three time delays appear in the process. The first si corresponds to the phase

8

HOTTEL LECTURE p Fuel

Flame

τi

Pressure at the flame Pressure at the fuel injector

Air

φ’

(a)

L inj L flame

(b)

τ conv

Equivalence ratio at the fuel injector Equivalence ratio at the flame

τcomb

Q’

Heat release

Fig. 6. Instability driven by equivalence ratio perturbations. (a) Combustor model; (b) time traces of pressure, equivalence ratio, and heat release in the flame. (Adapted from Ref. [22].)

shift between the pressure oscillations at the injector and the fuel mass flow rate m ˙ F. Oscillations in this flow rate induce fluctuations in the equivalence ratio ␾. The inhomogenous mixture is convected to the reaction zone and the corresponding delay is sconv. The response of the flame to the incoming fluctuations ␾ introduces a combustion delay scomb. Oscillations will be sustained by this process if the pressure and heat-release fluctuations are in phase. This is achieved if the total delay is an odd multiple of the half period si  sconv  scomb  (2n 1)T/2. In many cases, the dominant delay is that associated with convection, and the previous condition becomes sconv ⯝ (2n 1)T/2. One fundamental aspect of this process is the response of the flame to incoming equivalence ratio perturbations [103]. Coupled Flame Motion under Acoustic Perturbation The response of laminar flames to acoustic modulations constitutes one of the simplest cases of combustion/acoustics interactions: (1) It allows detailed observations of the coupling mechanisms, (2) the interaction may be modeled from basic principles without the closures required for descriptions of turbulent flames, (3) experimental data may be used to check computational tools for combustion dynamics, and (4) practical applications exist in which the flame is quasi-laminar (domestic boilers, radiant heaters, and industrial dryers). Theoretical studies of the response of premixed conical flames may be found in early work [104] and in recent studies motivated by active control analysis [105-107]. Systematic experiments on laminar flame dynamics have been carried out in the case of flames anchored on a cylindrical burner [108]. (The same experimental geometry may be used to produce cylindrical flames and observe the collapse of these structures and burning under at high levels of curvature [109].) The flame is submitted to a sinusoidal modulation created by one or several actuators set

inside the burner (Fig. 5d). The burner comprises a cylindrical tube, 20 cm in length, followed by a convergent nozzle. The outlet diameter is 3 cm. The driver unit placed at the bottom of the burner generates pressure waves in the range 20 Hz–5 kHz. Similar configurations were studied in Refs. [104,110,111]. The use of modern diagnostic techniques has provided more recently novel information concerning the geometry of the flame front [112], the velocity field at the burner exhaust and in the flowfield, the local and global heat release rates, and direct measurements of the flame transfer function [108]. The typical flame shapes displayed in Fig. 7 are visualized with instantaneous four-color Schlieren images. Without excitation, the flame is conical. Under low-frequency excitation, the flame front is wrinkled by the velocity modulation. The number of undulations is directly connected to the frequency. This is true as far as the frequency remains low (in this experiment, between 30 and 400 Hz). The flame deformation is created by hydrodynamic perturbations initiated at the base of the flame and convected along the front. When the velocity modulation amplitude is low, the undulations are sinusoidal and weakly damped as they proceed to the top of the flame. When the modulation amplitude is augmented, a toroidal vortex is generated at the burner outlet and the flame front rolls over the vortex at the base of the burner. But the consumption speed is fast enough to suppress the winding as the structure is convected away from the outlet and a cusp is formed toward burnt gases. Cusp formation is known to occur when a flame interacts with hydrodynamic perturbations. This mechanism requires some duration and it is obtained when the flame is elongated [113]. If the acoustic excitation levels remain low (typically, v/v¯  20%), the flames oscillate at the modulation frequency. The wave crests move at a velocity v¯ cos ␣ as indicated in Ref. [110] and verified in Refs. [108,114]. Direct measurements of the flame transfer function may be compared with theory [108]. The transfer function is defined as the ratio of the relative

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES

9

Fig. 7. Methane/air premixed flame modulated by acoustic perturbations. fe  75 Hz, x  15, v/v¯  0.2, * ␾  0.95.

heat-release fluctuation to the relative velocity perturbation: F(x) 

Q(x)/Q0 v(x)/v¯

(9)

Theoretical arguments indicate that this quantity will depend on a reduced frequency x*  xR/(SL cos ␣), where R is the burner radius and ␣ is the flame halfangle. Assuming that the velocity perturbation is uniform upstream of the flame yields the following result: F(x*) 

2 [1  exp(ix )  ix ] * * x2*

(10)

The experimental and theoretical transfer function amplitudes essentially agree, but this is not the case for the phase. The experimental phase increases with frequency while the theoretical phase tends to p/2. It is also found that the first-order filter models which have been used to represent flame dynamics in many recent theoretical studies of control concepts are not quite suitable. The difference analyzed in a separate paper stems from the description of the velocity perturbation as a bulk oscillation [115]. This assumption becomes invalid as frequency is increased. Using a convective model for the velocity perturbation, the results are notably improved. It is also possible to derive a new expression for the transfer function by making use of an earlier analysis of perturbed oblique flames [116]. It is shown in Ref.

[117] that this function depends on two parameters x and SL/v¯ and retrieves the experimental data and * more specifically the phase. The V-flame shown in Fig. 5f is another generic configuration. A two-dimensional V-flame is considered by Boyer and Quinard [116]. The flame anchored at the outlet of a rectangular burner is submitted to longitudinal waves generated by a driven unit and to a Ka`rma`n vortex street. The phase speed is found to be roughly equal to the velocity component parallel to the mean flame front v¯ cos ␣, where ␣ is the flame cone half-angle. This is explained in Ref. [114] with a kinematic calculation, and it is retrieved in Ref. [116] when the V-flame is confined inside a rectangular duct and submitted to an acoustic modulation. A traveling perturbation propagating inside a stationary envelope is observed in this case. The velocity of the propagating wave corresponds to the tangential convective velocity, and the nodes of the stationary envelope are multiples of the wavelength of the propagating wave. The flame response is different when the flame is confined or unconfined, because of the velocity boundary conditions. Inside the burner, the propagation is purely acoustic, whereas outside the burner, the jet undergoes an adaptation and a radial component is created. When the modulation amplitude is increased, the wrinkling becomes more pronounced leading to cusps on the burnt-gas side. In this situation, the response does not depend linearly on the level of excitation.

10

HOTTEL LECTURE

Fig. 8. Temperature fields at four instants during a cycle. A premixed laminar flame is modulated from upstream by acoustic waves. x  15, ␾  0.95. *

Water cooled plate

z

CCD camera

Perturbed flame Microphone

Burner Photomultiplier

Premixed gases

Fig. 9. Experimental setup. A premixed flame interacts with a plate. At the burner outlet, the mean velocity is v¯. A sinusoidal perturbation velocity is v(t) is imposed by a driver unit located at the bottom of the burner. From Ref. [94].

Experiments on acoustic/laminar flame interactions provide information on basic mechanisms. The data may be used to test numerical modeling [118,119]. The typical example of calculation shown in Fig. 8 nicely reproduces the qualitative features observed experimentally. This may be used to check the validity of computational tools for CDC and to envisage various numerical simulation issues in wellcontrolled situations.

Perturbed Laminar Flames Interacting with Boundaries Recent studies in which a premixed flame impinges on a flat plate have revealed some remarkable interactions. Phenomena described in detail in Ref. [94] are summarized in what follows. A premixed flame is anchored on an axisymmetric burner. This burner comprises a cylindrical tube, 16 cm in length, followed by a convergent nozzle. The outlet diameter is 22 mm (Fig. 9). The flow is modulated around its mean value v¯ by a driver unit set at the bottom of the tube. This produces a well-controlled harmonic velocity perturbation v(t)  v sin 2p fet at the burner outlet which wrinkles the surface of the flame front A(t). Sound measurements are carried out when the flame is perturbed at different driving frequencies fe. Figure 10 shows the overall pressure level recorded by a microphone located at 0.25 m from the burner axis in the plane of the plate. Over a broad range of driving frequencies fe, the sound emitted in the case of a perturbed impinging jet flame is always 10–20 dB louder than that produced by the same upstream perturbation, but without combustion or without the plate. The pressure field is only generated by combustion, when the flame interacts with the plate. The mechanism investigated in detail in Ref. [94] is controlled by the periodic collision of the flame with the wall. One remarkable feature of this configuration is the strong generation of harmonics as indicated by the

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES

100 WP-WC

Sound level (dB)

NP-WC

90

WP-NC NP-NC LAB

80 70 60 50 0

50

100 150 fe (Hz)

200

250

Fig. 10. Overall sound level as a function of the driving frequency. Mean axial velocity, U¯  1.44 m/s; equivalence ratio, ␾  0.95; nozzle-to-plate distance z  7.6 mm. The convention adopted in the caption is: WP, with plate; NP. without plate; WC, with combustion; NC, without combustion; and LAB, mean background noise in the laboratory. From Ref. [94].

90

PSD (dB)

80

11

detector. The sudden change in surface area when the flame impinges on the plate is responsible for the significant noise output from the flame and the rich spectral content of the noise emitted in this process. This is analyzed in further detail in Ref. [94] using measurements of the flame light emission I(t), direct estimations of the flame surface area A(t) (using Abel transformed sequences of images), and measurements of the far-field pressure signals p. The fast rate of extinction of the flame area at the cold boundary induces the significant acoustic pressure signature measured by the microphone. This should be compared with the relatively slow rate of growth of the flame surface which only induces a limited pressure rise. This experiment indicates that flame-wall quenching could be a strong source of pressure perturbation. In the case of a closed system (in the acoustic sense), where a periodic unsteady flame-wall collision takes place, this will constitute a source of acoustic energy feeding the natural modes of oscillation of the system. This may lead to a resonant feedback process driven by the flame-wall interaction mechanism. Such self-sustained oscillations constitute a simple but remarkable example of the coupling between combustion, acoustics, and solid boundaries [122].

70 60

Theoretical Description of Combustion Instabilities

50

The theoretical description of combustion instabilities is usually approached by emphasizing one of the processes in this closely coupled phenomenon.

40 30 20 0

500

1000

1500

f (Hz) Fig. 11. Power spectral density of pressure radiated by a perturbed flame interacting with a plate. Nozzle-to-plate distance z  7.6 mm; driving frequency, fe  101 Hz; flow velocity v¯  1.20 ms1. Methane/air mixture at an equivalence ratio ␾  0.95. From Ref. [94].

power spectral density of the signal recorded by the microphone (Fig. 11). The sources of sound are located where the flame interacts with the plate and one may relate the far-field radiated pressure p to the time-retarded rate of change of the flame surface area A(t) [120,121]: p(r, t) 

冢

冣 冤 冥

q qu dA  1 SL 4pr qb dt

t  s

(11)

In this equation, q, qu, qb are, respectively, the farfield air, the reactant gas, and the burned gas densities, s is the time required by the sound to propagate over a distance r from the sources to the

• Considering acoustics as the central mechanism, one may write a wave equation for the reacting flow and derive a unified framework for the analysis of combustion oscillations. While this is an attractive approach, it tends to hide the difficult problem of describing the response of the flame to the wave motion. • Considering combustion as the central process, the modeling tries to represent the flame response to acoustic waves. The analysis emphasizes the fluid mechanics, the flame motion in a field of perturbations, the differential response of the cold and hot streams of gases. The modeling of premixed combustion dynamics has most often relied on a kinematic equation (G equation) to represent the flame motion. These distinct viewpoints are briefly outlined in what follows. It is also possible to merge these approaches into combined models as described later. The unified analytical framework of combustion oscillations established by Culick and his coworkers (see the reviews [41,123]) uses an eigenfunction projection method equivalent to the Galerkin procedure

12

HOTTEL LECTURE

introduced initially by Zinn [124,125]. The starting point is the formulation of a boundary value problem for acoustic perturbations in a reactive medium: 2p 

1 2p c2 t2

 h(v¯, p¯, v, p; . . .)

with n • p  f

(12)

Inhomogeneous Neumann boundary conditions are used in this formulation, but other conditions could be used as well. Using simplifying assumptions, one may show that h  [(c  1)/c2]q/t which indicates that the source term is proportional to the nonsteady rate of heat release. The acoustic field is then expanded in a series of normal modes: 

p(x, t)  p¯

兺 gn(t)Wn(x) n1

(13)

The eigenfunctions Wn(x) satisfy a homogeneous Helmholtz equation and corresponding homogeneous boundary conditions: 2Wn  (xn2/c2)Wn  0 with n • Wn  0

(14)

where xn designates the modal eigenfrequency. The amplitudes gn of the normal mode expansion then satisfy a set of second-order differential equations: d2gn dt2

 xn2gn  Fn where Fn  

冤冮 hW dV  冮 fw dA冥 V

n

A

n

c2

movement becomes the central issue while the acoustics of the system define the boundary conditions. If the system is premixed, one may track the flame position and distinguish the dynamics of the fresh mixture on the upstream side from that of the hot stream on the burnt side. This was recognized in the thin flame sheet (TFS) model of Marble and Candel [133] where a flame stabilized in a duct is described as a front which is thin compared with the wavelength. The flame moves with respect to the fresh gases at a normal flame speed w1. Its location is described by its distance g(x,t) with respect to the duct centerline. In the TFS model, the flame separates the incoming fresh gases (density q1) from the hot combustion products (density q2). The model has been used to investigate the response of ducted flames to incident perturbations and possible resonant interactions between the flame and longitudinal acoustic modes of the system [134]. The description of the flame as a thin front forms the basis of many current analytical or semianalytical models and it is used in turbulent combustion modeling. Most studies rely on a kinematic description of the motion of this front based on the G equation [67,135,136]. The flame is an isolevel G  G0 of a function G describing the propagation of a front featuring a normal velocity Sd. One considers for example that G  0 in the fresh gases and G  1 in the reacted mixture, and one has to solve the firstorder equation G  v • G  Sd|G| t

p¯E2n (15)

This formulation emphasizes the wave motion and provides a framework for the determination of the modal amplitudes gn. The central difficulty is to specify the source terms arising from the distributed coupling process between acoustics and combustion and formally represented in the previous equations by the functions h(v¯, p¯, v, p;. . .) and f. Another difficulty is encountered in developing a suitable representation of source terms associated with control. It is difficult to derive a nonlinear formulation for these terms and they usually appear as additive sources, h and f, respectively, becoming h  hc and f  fc. These are approximate expressions of the subtle interactions taking place between control sources and the unstable motion. The unified framework is however valuable for theoretical investigations [126,127] and may be used to devise ‘‘low-order models’’ of combustion dynamics and control [128–131]. If one adopts the second viewpoint, which emphasizes the flow and combustion dynamics, there is no unique framework. The general objective is to describe the non-steady motion [132]. The flame

(16)

The use of this equation is illustrated in Fig. 12 with simulations of a conical flame submitted to an upstream velocity modulation. The flame motion is very close to that observed in the experiment, but this result requires a suitable definition of the perturbation velocity field (see Ref. [115]). Another interesting result may be deduced by assuming that the unsteady flow velocity component and the flame displacement with respect to the steady state are both small perturbations. The G equation may be expanded by writing G  G0(x)  g1(x,t) and v  v0(x)  v1(x,t). Retaining terms up to first order one finds g1  (v0  Sdn0) • g1  v1 • G0 t

(17)

where n0  G0/|G0| is the local unit normal to the steady flame position. In addition v0 • n0  Sd and the perturbed G equation may be cast in the compact form g1  v0t • g1  v1n|G0| t

(18)

where v0t  v0  (v0 • n0)n0 is the mean velocity component in the tangential flame direction and v1n

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES

13

40

Y

30

20

10

0 -20

-10

0

10

20 -20

-10

0

10

20 -20

X

X

-10

0

10

20 -20

-10

0

X

10

20

X

Fig. 12. Simulation based on the G equation of a premixed flame modulated by a convective field of velocity perturbations. Flow velocity, v¯  1.3 ms1; relative perturbation amplitude, vrms /v¯  0.155; driving frequency, fe  75 Hz. The mixture of methane and air at an equivalence ratio ␾  1.05 has a laminar burning velocity SL  0.39 ms1. Details in Ref. [115]. Flame holder r

ξ(r,t) x

(a)

Flames

(d)

(b)

(e)

(c)

(f)

Fig. 13. Periodic motion of a premixed flame stabilized in a duct. The inlet flow velocity modulation is sinusoidal and its amplitude exceeds the mean flow velocity uE(t)  u¯b sin (xt), b  1.15, Sd  0.09u¯. Adapted from Ref. [137].

is the perturbation velocity normal to the steady flame direction. This indicates that the flame perturbations move along the flame at a convection velocity v0t (a result already mentioned in studies of modulated conical and V-flames) and that the motion is determined by the normal velocity perturbations. In most analytical studies based on the G equation, the change in density across the flame front is neglected. Various arguments are used to justify an assumption which is obviously not quite right, but is often made in combustion and has the considerable advantage of simplifying the analysis. One interesting example of application is that of an axisymmetric flame stabilized on a central body in a channel [137] (Fig. 13). Using n(r,t) to describe the axial position of the flame at a radius r and at time t, the flame surface is given by G  x n(r,t)  G0. Substituting in the G equation one obtains n n n  uv  Sd 1  t r r



冤

2 1/2

冢 冣冥

(19)

Now, if the density change across the flame may be neglected, the velocity just upstream of the flame is that imposed by the incoming flow. One may assume

for example that (u,v)  (uE, 0) where uE is imposed. This yields a simplified kinematic equation: n n  uE  Sd 1  t r

冤

2 1/2

冢 冣冥

(20)

Solving this equation for n(r,t), one may then obtain the instantaneous flame area from A(t) 

n

2 1/2

冮2pr冤1  冢r冣 冥

dr

(21)

If Sd is constant, one may assume that the heat release is proportional to the instantaneous flame area: Q(t)  quYuSd (Dh0f ) A(t) and establish the relation between the incoming perturbations and the non-steady heat release. Equation 20 is usually solved by first linearizing around a steady-state solution. This yields a transfer function between external velocity modulations and the resulting heatrelease fluctuations. A nonlinear treatment is also possible but generally requires a numerical solution. One model due to Dowling [137] attempts to describe the dynamics of the flame when the incoming modulation has large amplitudes so that at certain instants the flame displacement speed exceeds the

14

HOTTEL LECTURE

incoming flow velocity. It is then not possible to consider that the flame is anchored on the central body outer edge, that is, to impose n(a,t)  0 where a is the flameholder radius. Indeed, if one considers equation 20 and uses the last condition, one gets Sdn/r  [u2E S2d]1/2 on r  a which has no solution for Sd
uE. One then has to distinguish instants during the cycle where Sd
uE from those where Sd  uE. At the switching instant where Sd  uE, the flame leaves the central body in the normal direction since n/r  0 on r  a at that instant. This finally yields the following conditions: Sd

n 2  [uE  S2d]1/2 and r n(a, t)  0 for uE ⱖ Sd

(22)

n  0 if n(a, t)  0 or uE ⱕ Sd r

(23)

When the modulation velocity on the upstream side of the flame uE has an amplitude in excess of the mean flow velocity, the flame progresses in the upstream direction during part of the cycle and the previous set of conditions at the flameholder yield the flapping motion displayed in Fig. 13. The semianalytical models based on flame kinematics are limited to simple cases. The numerical treatment of the G equation may be combined with the unified approach to formulate dynamical loworder models. The more complex situations of practical interest can only be tackled with more refined numerical tools. Numerical Combustion Dynamics While computational combustion has been extensively developed during the past three decades, mainly for steady laminar and turbulent combustion problems, numerical methods for dynamical problems are less well established. We will first identify the modeling levels and some of the specific problems encountered in the description of wave motion. Turbulent flame dynamics are then considered and illustrated with numerical calculations. Modeling Levels for Combustion Dynamics Diverse combinations of methods may be used to describe the flame motion and the coupled acoustics of the system. The following modeling levels may be identified: • Direct simulation of the flame motion, characteristic boundary conditions, or time domain impedance models to describe incoming and outgoing acoustic waves. • Large eddy simulation (LES) of the flame motion, time-domain impedance conditions to represent

the acoustical response of upstream and downstream elements. • Large eddy simulation for the flame motion, analytical or linearized Euler description of the wave motion outside the flame zone. • Low-order models for the flame zone, analytical or linearized Euler description of wave motion in the outer regions. Direct numerical simulation (DNS) is limited to small computational domains and relatively low Reynolds numbers, because the flame and the smallest scales must be resolved on the grid (Fig. 14a and b), which usually requires large computer resources [138]. LES methodologies must be used for most practical purposes [139]. The central difficulty is to represent the flame on a coarse grid (Fig. 14c–e). This will be combined with various treatments of the acoustic motion. It is also possible to use low-order models for the flame zone, but this will be limited by the many assumptions needed to establish these models. Numerical Methods for Acoustic Modulation One aspect which deserves special attention is related to the modulation of a given system to study the forced response of the flow to external perturbations. One such problem is treated in detail in Ref. [140]. Consider for example a sinusoidal velocity perturbation u  u0 cos xt injected in the system at the upstream boundary. This modulation is introduced at time t  0 in a region which is initially free of perturbations. The system will respond to this perturbation by exhibiting a forced motion, but it will also feature a free motion which compensates the mismatch that exists between the forced motion and the perturbation-free initial state. As a consequence, the modulation excites the natural modes of the system, and the amplitudes of the eigenmodes which are closest to the perturbation frequency will have finite values of the same order of magnitude as the response at the excitation frequency. If the numerical viscosity is small, as it should be to deal with acoustic wave problems, the modes excited in the process will decay slowly and the oscillations of these modes will be sustained for a long period of time. This scenario has been verified by calculations in which a duct is submitted to an incoming perturbation. The acoustic response obtained numerically coincides with that predicted in terms of a modal expansion. Methods which may be used to deal with this problem are discussed in Ref. [140]. Boundary Conditions Another issue of considerable importance is related to boundary conditions. It is known from numerical fluid dynamics that the treatment of inflow,

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES

δ f

Flame

15

Small scale turbulent eddies

η

k

(b)

(a)

Sd

Sd

Sd

Flame (c)

∆x

Thin front ( d)

Thickened flame (e)

Fig. 14. (a, b) In DNS, the flame and the smallest scales of the flow must be resolved on the grid. (c) In LES, the grid is often too coarse to resolve the flame; (d) the flame may be replaced by a thin front; (e) the flame may be thickened artificially and resolved on the coarse grid.

outflow conditions, together with conditions at the walls, essentially determines the quality of the solution (see, for example, Refs. [68,141]). In combustion instability simulations, one has to establish boundary conditions for the fluid flow but simultaneously impose conditions on the various waves involved in the process. The two types of conditions may not be compatible. To illustrate this point, consider an outflow boundary. This is usually treated by imposing a constant static pressure. In doing so, one makes the implicit assumption that the specific acoustic impedance vanishes at the boundary (f  Z/(qc)  (1/qc)(p/v • n)  0). In other words, this implies that the pressure perturbations must vanish at the outflow. Now, this may not be the case and one should be able to impose other types of conditions at this boundary. Similarly, one generally imposes the mass flow rate at the inflow. This implies a condition on the specific impedance f  1/M, where M designates the mean flow Mach number. Again this condition may not suitably describe the response of the upstream region to acoustic waves

generated in the system and impinging on the inflow boundary. Large Eddy Simulation for Turbulent Flame Dynamics There are now well-established LES and subgrid scale models (SGM) for non-reactive flows (see, for example, the recent articles of Refs. [142–145]. Combustion LES is less well developed and constitutes a relatively new field not much older than about a dozen years [68]. An important motivation for the development of LES is that it may provide a route to an improved modeling of combustion and is specifically well suited to the description of the unsteady dynamical phenomena envisaged here. Some important advances have been made in the numerical modeling of flame dynamics using largeeddy simulations [146–165]. The topic is also extensively covered in Ref. [166]. Among the many problems encountered in the application of LES to combustion dynamics, the most prominent are: (1)

16

HOTTEL LECTURE

the description of the flame motion, (2) the modeling of combustion at the subgrid scale level, (3) the reduction of numerical dissipation and dispersion to acceptable levels, and (4) the treatment of boundary conditions. One difficulty with combustion LES stems from the fact that the chemical conversion takes place in thin layers which cannot be captured on the relatively coarse grid used for LES (see Fig. 14c). It is therefore necessary to adapt the flame description to the LES framework. In the premixed case, this has been achieved by following two distinct routes: • The flame is represented as a thin front and its motion is calculated by a front tracking technique or with a G equation formulation (Fig. 14d). • The flame is artificially thickened while preserving its displacement speed (Fig. 14e). The first method, based on the theoretical work [135], was initially explored in the LES context by Menon and Jou [167]. The reactive layer is considered to be infinitely thin with respect to the size of the turbulent structures, and it is represented by a propagative surface separating fresh and reacted gases. This surface is located at an isolevel of a field variable G which obeys the kinematic equation 16 with G  0 in the fresh stream and G  1 in the burned gases. The displacement speed of the flame front with respect to the fresh gases Sd may be expressed as a function of the local flow conditions. Menon and Jou [167] used this approach by taking a constant Sd to calculate ramjet combustion instabilities. A subgrid model for combustion in LES based on a G equation in each grid cell has been proposed more recently by Menon and his coworkers [168]. One difficulty with the level set approach based on the original G equation 16 is that the release of heat and the consumption of species is not easily included. The gas-expansion effects are represented for example by the potential flows induced by volume sources placed at the flame. Another possibility is to define a region of finite thickness around the flame front (the surface corresponding to one value G  G0) and confine heat release in this region. The prescribed thickness is of course selected to be larger than the grid spacing adopted for the simulation. This idea may be implemented in various ways. One possibility is the forward estimation of temperature (FET) method of Piana et al. [149]. This method is based on a temperature prediction relying on the field estimates of G. The G equation is first advanced in time, before the Navier-Stokes equations. The new G field at G(x, t  Dt) defines the location of the flame through its isolevel G  G0. From this new flame location, one may deduce a forward estimate of the temperature field T * obtained by imposing a prescribed temperature distribution around the flame location T * (G G0, d)

where d is an adjustable thickness parameter allowing a variation of the stiffness of the estimated temperature T *. The energy release term x˙ is deduced from the fields T* (x,t  Dt) and T(x,t). This source term is then injected in the energy equation and the Navier-Stokes equations are advanced in time. In this model, the G equation provides the location of the flame, and a reaction rate which is compatible with the propagation speed of the flame. By keeping an energy equation in the system, it is possible to include compressibility effects or energy losses at boundaries. Computational results obtained with the G  FET method closely follow DNS results [149]. More recently, Chakravarthy and Menon [169] have abandoned the conventional flame speed model for a filtered version of the G equation: (qG) ¯˜   • qvG ¯ ˜  q¯ 0SL0 |G| t  ˜   • [q(vG ¯  v˜G)]

(24)

This equation describes the transport of the progress variable G with G  0 in the reactants and G  1 in the burnt products. In this equation, q0 is the reference density and S0L represents the laminar burning velocity. Effects of subgrid turbulence are included in the second term on the right-hand side ˜ |, which may be written as q¯ 0SL0 |G|  q0uf |G where uf is a burning velocity including subgrid scale effects. This velocity is determined, for example, using a model due to Yakhot [170] in which uf appears as the solution of an implicit equation: uf  S0L exp((u)2/u2f ) The second representation of premixed combustion in the LES framework consists in artificially thickening the reaction zone, while keeping its propagative properties unchanged (Fig. 14e). The idea, originally developed in Refs. [171,172] for the computation of laminar flames in complex geometries, has been applied in many recent largeeddy simulations of premixed combustion (for example, Refs. [153,159,160,163]). The method may be explained by considering that a single-step irreversible reaction takes place between fuel and oxidizer and that the reaction kinetics follows an Arrhenius law, ␣0

␣F

qY 冢qY W 冣 冢W 冣

w ˙  B

0

0

F

F

冢 TT 冣

exp 

a

(25)

where Ta is the activation energy, WF and WO are, respectively, molar masses of fuel and oxidizer, and B is a pre-exponential factor. The classical Zeldovich, Frank-Kamenetski analysis of premixed laminar flames indicates that the laminar burning velocity SL takes the general form SL 冪DB

(26)

where D and B are, respectively, the molecular diffusivity and the pre-exponential factor. The corre-

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES

Fig. 15. Schlieren visualization of vortex pattern during unstable operation of the premixed combustor at a frequency of 530 Hz. m ˙ air  78 g s1; ␾  0.83; left, t4  0.92 ms; right, t5  1.15 ms. From Ref. [173].

sponding flame thickness df is then estimated by df  D/SL 冪D/B. This thickness can be increased at constant SL by multiplying D and dividing B by the same coefficient F [172]. The flame thickness is then multiplied by the factor F. This technique can be used to compute a laminar flame on a coarse mesh, and it is of interest in LES. However, the flame thickening has some drawbacks. It diminishes the flame response to small structures and enhances the flame sensitivity to curvature and strain. The thickened flame will be easier to quench than the original reactive layer. Now, this will be compensated in part by the fact that the largest stretch rates in a turbulent flow are associated with small turbulent scales which are only modeled in LES. Also, quenching of premixed flames mainly takes place in the presence of heat losses. Although flame thickening diminishes the extinction strain rate, it might be possible to compensate this effect by suitably reducing the heat losses from the burnt gases [153]. Fine tuning of the thickened flame model has been devised to account for combustion taking place in the small scales [159,160]. An efficiency function E is used to incorporate the effects of the unresolved scales on the resolved reaction rate. The balance equation for one of the chemical species mass fraction Yk becomes: qY ¯ ˜k   • (qvY ¯ ˜ k) t E ¯ w ˙ (27) F k In this equation, the tilde designates mass-weighted, spatially averaged variables, while the bar corresponds to standard spatial averages. The thickening approach including the efficiency function E allows suitable representations of the flame front as it is convected, wrinkled, and distorted by the large structures of the flow as illustrated in two rather different configurations. In the first case, the geometry is that of a multiple-injector premixed dump combustor. ˜ k)    • (qDFEY ¯

17

Instabilities observed in this situation [173] were shown to be driven by large-scale vortex patterns shed from the lips of the injection slots. At a later time, adjacent vortices interacted forming an amount of fine-grained turbulence and generating a pulse of heat release (Fig. 15). It was shown that such a pulse, when properly phased with respect to the pressure perturbation, could feed energy in the acoustic mode, thus sustaining the oscillation. The simulation of this mechanism is not yet complete but it has been possible [163] to represent the vortex shedding and the subsequent motion using the LES framework. This is shown in Figs. 15 and 16. The calculation is carried out by imposing a velocity oscillation in the injection slot [163]. The vortex pattern is close to that observed in the experiment but it is obtained in the ‘‘forced mode’’ (i.e., by modulating the upstream flow). The simulation of the instability, including the coupling with acoustics, remains a challenge. In the second example, a premixed turbulent flame is stabilized on a bluff obstacle placed in a duct [174]. Two driver units are located on the upstream manifold feeding the combustor with a fresh mixture of air and propane. These units generate plane acoustic waves, which propagate in the duct, impinge on the flame, and wrinkle the reactive front (Fig. 17). The large-scale organized structures which are observed in the experiment (Fig. 17) are well retrieved numerically (Fig. 18). A more detailed analysis [160] shows, however, that the agreement is not perfect and that the subgrid scale model developed to account for combustion in the small scales does not feature the expected spatial distribution. This in turn will induce a phase difference between the incident perturbations and the flame response. Now, in combustion instability, the phase between the pressure fluctuation and the non-steady heat release determines whether amplification or dissipation takes place. According to Rayleigh’s criterion, amplification takes place when pressure and heat release are in phase, while dissipation corresponds to pressure and heat release in phase opposition. It is then clear that more work is needed to improve current subgrid scale models. Efforts are now made to devise more elaborate schemes applicable to combustion instability problems. The next example concerns a premixed combustor developed by the University of Cambridge to model an industrial gas turbine unit. The airflow enters the injector through an annular section and is then divided into two streams which flow through concentric channels. Vanes are placed in these channels to create a rotating velocity component (‘‘swirl’’) with an opposite sign. Gaseous fuel is injected in the airflow through cylindrical bars fitted with two 0.45 mm diameter holes. The swirler unit is plugged on a 70 mm diameter quartz tube. Burned gases are exhausted

18

HOTTEL LECTURE

Fig. 16. Simulation of vortex driven instability. The temperature field is shown at five different instants during the cycle. (from Ref. [163]).

Fig. 17. Schlieren visualizations of the flame at two instants during a period of oscillation. An acoustic modulation is generated upstream by two driver units. Uinlet  39 m s1; ␾  0.75; f  1210 Hz. From Ref. [174].

Fig. 19. Enlargement of the mesh at the outlet of the swirler unit. Fig. 18. Result of large-eddy simulation of a ducted flame submitted to acoustic modulations generated in the upstream duct. (Calculation by C. Nottin.)

from this 1 m long tube at atmospheric pressure. Simulations of the complete system (air supply, fuel supply, swirler unit, and combustion chamber) would require an excessive amount of computer resources. It is therefore assumed that (1) the flow beyond the injection vanes is perfectly premixed, (2)

the rotating component uh of the flow created by the vanes is proportional to the axial flow velocity and to the tangent of the vane angle, and (3) uh is a constant in a given section. The system is considered to be axisymmetric, and the calculations are carried out over a sector corresponding to a 10 angle around the symmetry axis. Fig. 19 shows a view of the unstructured mesh required to represent the injector [165]. A typical distribution of reaction rate is displayed in Fig. 20. Recirculation in the central part of the

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES

Fig. 20. Temperature distribution at one instant during an instability cycle. From Ref. [165].

chamber provides a continuous source of ignition, and the flame spreads from the lower border of the internal channel in a region of reduced flow velocities. Snapshots of temperature field and reaction rate fields show that vortices develop and the flame-stabilization position moves when these structures are shed. This causes fluctuations in the flame surface which may lead to instabilities [165]. At certain instants in time, the flame propagates inward along the internal channel separation, a process which could eventually lead to flashback The last example is the most complex geometrically (Fig. 21). This illustrates a full three-dimensional large-eddy simulation of the premixed flame formed by a swirl combustor. The calculation uses the thickened flame model together with an efficiency correction function. It has been used to demonstrate the possible transition between a lifted

19

flame formed dowstream, as in Fig. 21, and a flame attached inside the premixer after flashback. This simulation indicates that it is now possible to envisage LES of combustion instabilities in the relatively complex geometries found in practice. The previous calculations and many others in the recent literature indicate that LES may be used to investigate combustion dynamics and that it will be a central block in predictive methods for combustion instabilities. Active Control Concepts, Experimentation, and Low-Order Modeling Methods which may be used to suppress or attenuate combustion instabilities can be divided in two classes. In the first group, one finds passive methods (PCM), which require a physical understanding of the phenomenon and involve careful modifications of the combustion system. Active methods belong to the second class and originate from the early work of Refs. [8,10]. In the 1950s, these authors devised the sensitive time lag (STL) model to analyze rocket motor instabilities. This theory could not provide a detailed explanation of the complicated physical processes involved, but it helped design global strategies

Fig. 21. Large-eddy simulation combustion. Air and methane flow through a premixer including two swirlers. The flame formed downstream is displayed on a scale of grey levels. (From T. Poinsot.)

20

HOTTEL LECTURE

to deal with the problem. The stabilization method consisted in actively injecting perturbations into the combustor using an actuator in order to decouple the physical processes responsible for the combustion oscillations. Although the principles of active control of instabilities were described in these early studies, the practical, demonstration of the concept was only achieved in the recent past (see Ref. [46] for a review). Most of the development of active-control strategies has relied on experiments on model-scale combustors. These studies have revealed the potential of ACC and the technical limitations of the controlsystem components (sensors, algorithms, and actuator). The actuator effectiveness constitutes the most critical issue and introduces a complicated tradeoff between bandwidth and power. For gaseous fuel, it is possible to modulate the flow using direct-drive valves, but the bandwidth is limited to about 400 Hz [31,175]. Liquid injection is more difficult to modulate [53]. Fuel injection timing is an interesting method of depositing energy at the right moment during an instability cycle [52,54,176–178]. Many recent efforts have tried to use control concepts in theoretical analyses of generic situations. Low-order modeling is exploited in many studies [102,106,107,128–132,179–181]. Block diagrams are used extensively to formalize the control problem and allow theoretical control analysis. A few examples are gathered in Fig. 22. One generally distinguishes the combustion process and the acoustical coupling as in Fig. 22 a and b. One may also consider that the combustor constitutes a plant to be controlled but without a detailed description of its behavior (Fig. 22c). The block diagram representation of the control loop is less straightforward. In Fig. 22 a and b, the controller acts on the acoustics of the system but the representation implies that the path between actuator and sensor is also the path which induces the coupled motion in the unstable operation of the system. This is not always the case. The actuator modulates in many circumstances a secondary fuel injection, and it is the chemical conversion of the injected fuel which induces an acoustic wave. This wave then combines with the acoustic motion associated with the instability in the system (see Fig. 22 d). Many studies also try to look at the problem from the point of view of control theory. This is exemplified in Ref. [182] which uses state space descriptions of combustor and controller in a robust control framework including many disturbances and uncertainties affecting the process. Adaptive techniques have also been extensively investigated with much of the recent work focusing on self-tuning adaptive regulators. Multidimensional Simulation of Active Control While most of the theoretical effort has relied on low-order models, some recent investigations have

been directed at a full simulation of control with the objective of testing and improving control algorithms. Time-dependent one-dimensional calculations are reported in Refs. [183,184]. Multidimensional simulations are carried out in Refs. [148,185,186]. Simulation complements experimentation and it has potential in the development of combustion control methods. The aim of this section is to underline some of the problems arising when one wishes to couple a flow solver with a control algorithm. The illustration is based on research directed at the control of vortex-driven instabilities found in solid segmented rocket motors [187–189]. An adaptive controller is used in this simulation [190,191], and the conceptual principle is shown schematically in Fig. 23. In practice, segmented solid rocket motors develop low-amplitude pressure and thrust oscillations at frequencies of the first longitudinal acoustic modes. Because of the rocket motor size, the oscillation is at low frequency and it may couple with the launcher structural modes. The driving mechanisms are linked with internal flow instability. A strong coupling with acoustic modes generates large-scale coherent vortices. This process is here simulated in a small-scale geometry, and the corresponding frequency is near 2.5 kHz. The vortices are shed in this case from the edge of the solid propellant. These vortices are convected downstream, and impinge on the nozzle producing a pressure signal which feeds energy into one of the longitudinal modes. To control this process, a sensor is placed close to the region where vortices are shed and its signal serves as input to a controller which drives an actuator. This scheme is typical of many active control applications and the present simulation is, in this sense, generic. The Navier-Stokes flow solver has been used extensively to analyze vortex instabilities in configurations of interest in solid-propellant propulsion. It provides the space-time simulation needed by active control. A first issue which deserves special care is to devise a suitable representation of the actuator or of the set of actuators which would be used to drive the flow. It is shown in Ref. [185] that this may be accomplished by distributing sources in the field. This representation is close to the possible use of a controlled injection of an evaporating and/or reacting substance in an actual motor. Such a physical device would provide a distributed source of mass and a source or sink of energy. Momentum exchange might also take place depending on the type of injection geometry but is usually less effective than mass injection. A series of open-loop tests not shown here indicate that the sources operate as expected. Problems related to the coupling of the flow simulation module with the control algorithm must be treated next. There is a large mismatch between the time stepping of the flow solver and the sampling

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES

H(s)

Combustion

Q +

u

+

Acoustics

G(s)

+

+ Actuator

21

p

Qc

A(s)

Sensor

B(s) V(s)

Controller (a)

(b) G +

+ +

Combustor

Actuator

+ Sensor

S1

Sensor

Adaptive controller

(c)

H +

S2 yr

d

e =d- yr

W

(d)

S

LMS

Fig. 22. (a) Block diagram representation of combustor coupled to an external control loop; (b) transfer function description of the system shown in a; (c) general principle of adaptive instability control; (d) block diagram representation of adaptive control of combustion H coupled by acoustic feedback G. W is the LMS filter, S1, S2 represent the actuator transfer function, and part of the secondary path between actuator and sensor S  S1S2, Sˆ is a filter representing the secondary path S.

period of the controller, and, as shown in Ref. [185], some precautions must be taken. The input and output of the control routine should be low-pass filtered to prevent a growth of high-frequency perturbations which after a short duration will disrupt the calculation. The simulation methodology is illustrated by a calculation of vortex-driven instabilities in a small rocket motor and control of these instabilities using an adaptive algorithm. In the situation considered, the controller input is a pressure signal provided by a sensor located near the nozzle, while the actuator is placed near the motor head. A typical flow configuration is shown in Fig. 24. Large-scale vortices are shed from the solid propellant edge and interact with the nozzle producing a resonant pressure field in the motor. There are typically two vortices between the propellant edge and the nozzle. When the controller is on, the flowfield is modified, vortices are still present, but the number of vortices in the cavity is now around four, the frequency is shifted to a higher value, the amplitude is lower, and the level of pressure oscillations is reduced to about 20% of its initial value (Fig. 25). This example serves to show that multidimensional calculations may be used to study active control strategies and examine the modification of the flow under control.

Operating Point Control Most combustion systems are controlled without feedback in an open loop mode, that is, without feedback of information to the injection system. The combustor parameters are set by determining the required power output and using a lookup table to determine the mass flow rates. This does not allow a precise optimization of the process. The absence of closed-loop control poses serious problems in advanced systems. It is recognized that new combustion technologies will have to integrate feedback controllers (see, for example, Refs. [57,58]). Control of emissions in automotive applications is already based on closed-loop concepts, which allow a fine tuning of the operating conditions (Fig. 26a). A conceptual view of the control system for future directinjection gasoline engines is shown in Fig. 26b. The control system will have to continuously adapt the fuel injection strategy to take into account the status of the exhaust aftertreatment devices. Similar concepts are being explored in other areas. The adjustement of operating conditions with sensors monitoring the flame or the exhaust gas stream is considered in various applications including biomass combustion, waste incineration, glass manufacturing, and gas turbines. In this last area, a notable reduction of NOx emissions can be achieved by operating in the premixed mode. The flame temperature is reduced and the level of NOx is diminished

22

HOTTEL LECTURE

Actuator Symmetry axis

Nozzle Sensor

Propellant Adaptive controller

Flow solver f = 4.1 MHz

Solid rocket motor

(a)

Output files

Active control routine Identification Output filters

Instability control

Input filter

(b)

f = 20.5 kHZ Fig. 23. Active control of a solid rocket motor. (a) Principle; (b) coupling between the flow solver Sierra and the adaptive controller ‘‘ACR’’. Adapted from Ref. [185].

to a great extent. However, premixed combustion requires a precise determination of the equivalence ratio [56]. If the incoming flow is too lean, blowout may take place. If the flow is too rich, the level of NOx emission increases. The determination of the EQR is made difficult, in most cases, because the airflow rate through the gas turbine is not known with sufficient accuracy. The gas composition and the air humidity also affect the temperature. It is then logical to try to deduce the equivalence ratio or the flame temperature from measurements on the combustor and on the gaseous exhaust and use these measurements in a feedback loop [59–62,192–195]. The problem of detection is not a simple one, however. Fast, reliable, and preferably low-cost sensors are required. At present, only some of the combustion parameters of interest can be detected easily (e.g., pressure and oxygen mole fraction of exhaust gases), but new solid-state gas sensors are developed and advances have been made in laser diode-based methods (see Ref. [65] for a survey) allowing measurements of temperature and mole fractions of different species. Another possibility is to use the light emission from the flame but the method should be made immune to obscuration of the optical access. (One possible scheme is described in Ref. [196].) State observation and performance estimation are central issues in combustion control. The sensor systems needed in this context must be accurate, have a suitable bandwidth, and cope with the tough environment of combustion processes. While some applications of OPC exist, for example, in automotive engines, the widespread use of sensor-based closed-loop control will require further research. Precision is generally insufficient and there are many practical problems posed by the severe conditions found in practical combustors. The main issues are: (1) sensor integrity, (2) immunity to obscuration for optical sensors, (3) sensor integration (optical access to the combustion chamber, flow channeling for solid-state gas sensors), (4) resistance

to poisoning (solid-state gas sensors), (5) durability and lifetime. It is clear that new sensor concepts and more research is needed to develop the required technology for OPC. Conclusions and Perspectives This article has focused on combustion dynamics and control. These topics have been extensively investigated over the past few decades. While the initial effort was limited by experimental techniques, the lack of computers and the rudimentary methods of diagnostic and data processing, it laid the ground for detailed studies undertaken during the latter two decades. Many aspects of the problem were elucidated, but the prediction of combustion instability has remained elusive and still poses important scientific and technical challenges. Progress has been made in this area with many calculations of unsteady laminar flames, the development of methodologies for large-eddy simulation, application of LES to dynamical problems, calculations of externally modulated laminar and turbulent flames, and some initial attempts at directly calculating instabilities. One scientific objective for the future will be to continue the development of combustion LES, and specifically improve the first generation of subgrid scale models. This will require combined efforts in modeling, simulation and experimentation oriented toward LES needs. Further progress will also be needed in the treatment of boundary conditions and in the integration of boundary conditions describing the mean flow as well as the wave motion. Suitable representations of the response of components placed on the upstream and downstream sides of the combustor will be needed to obtain full description of the combustor dynamics. The control of combustion instability has also progressed in many ways. While the initial demonstrations were carried out on small laboratory combustors, active control has been implemented in some

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES

23

Fig. 24. Simulated vorticity field inside the rocket motor. Controller is off. Adapted from Ref. [185].

Fig. 25. Simulated vorticity field inside the rocket motor. The controller is operating. It modifies the vorticity field and reduces the level of pressure oscillations inside the motor. Adapted from Ref. [185].

Intake manifold

Three Way Catalyst

Cylinder

Intake manifold

Oxydation catalyst

NOx Trap Exhaust

Air

Air Fuel

Cylinder

Exhaust

Control unit

(a)

Stoichiometric ratio

Fuel flow rate

Fuel

Lambda probe

b)

φ

Fuel flow command

Tc - Tair

Air flow rate

HC/CO or T* sensor

O2 sensor

φd

Tc Tair

+ _

G f

G c

Gb

Geqr

Fuel metering unit

(d) Preheater controller

(e)

Fiber

Controller

Turbine

Air Low emission burner

Water drop out

CH4

Air

Filter and PM

NOx CO

Pressure controller

Flowrate controller

Optical temperature sensor

CH 4

Compressor NO converter

Fuel injection

φ

CH emission signal

Controller

Combustor

(c)

NOx sensor

Tair

φ

AFR

Control unit

Tf (f)

mCH4

X O2

XCO

Control system

Exhaust gases

Gas sensors

Bypass valve XNOX p

Tair

Fig. 26. (a) Conventional automotive engine control (adapted from Ref. [58]); (b) control scheme for new gasoline direct-injection engines, (c) premixed gas turbine/operating point control by fuel regulation using calculated airflow rate, measured hygrometry and fuel properties (adapted from Ref. [56]); (d) block diagram of equivalence ratio control system based on CH chemiluminescence (adapted from Ref. [192]); (e) model gas-fired combustor (15 kW): optimization by fuel flow actuation and CO2* measurements; (f) model gas turbine combustor control using light emission from flame and gas sensors. (Adapted from Ref. [62]).

24

HOTTEL LECTURE

larger-scale systems and has been put in operation on high-power gas turbines. A considerable amount of research has been made to study the problem with the tools of modern control theory. Theoretical instability models have been devised to this purpose, and many control strategies have been explored. Investigations have used rational analysis based on simple low-order essentially linear instability models. This research has been mostly theoretical with limited demonstrations on practical devices. One challenge for the future will be to apply theoretical strategies (state feedback, robust control, model-based adaptive control) to real systems. One important technical aspect of the problem is related to the performance of actuators and integration of these units into practical injectors. This is recognized as a critical technology and some progress has been made, essentially by exploiting highperformance valves to modulate the flow of reactants. There are, however, bandwidth and amplitude level limitations. Advances are clearly needed to augment the operating range, develop advanced concepts, and override the current obstacles. The actuator/injector integration also constitutes a central challenge which is not often identified but deserves consideration. The multidimensional simulation (MDS) of active control (the simulation based on a full description of the combustion dynamics relying on unsteady Navier-Stokes flow solvers) has also become an important area of research. The objective of this type of simulation is to allow complete (and realistic) software studies of control concepts. This problem combines the difficulties of the description of the dynamics to those of coupling with a control scheme. Early developments of such a capability were quite limited. Some more recent efforts have uncovered some of the difficulties. MDS of control requires a suitable description of the actuator and a careful coupling of the flow solver and controller. One solution to the first problem is to represent the actuator with a distribution of sources. To deal with the coupling problem one has to suitably filter the input and output of the controller to deal with the mismatch in sampling frequencies of the Navier-Stokes solver and controller. Further progress in MDS of ACC may be foreseen with advances in combustion LES and active control methodologies. Another technical aspect of concern is that of sensors. The sensor problem is most critical for control of the operating point. Requirements in terms of sensors are not always fulfilled by current technology. For certain applications, like automotive engines, oxygen gas sensor technology has allowed the remarkable development of catalysts for exhaust gas treatment, but there are needs for further improvements. In other areas of application, the sensor technology does not match the level of accuracy and reliability needed for practical usage. Research efforts

and systematic testing are needed to fill the gap and allow closed-loop control of combustion. Further developments are also required in control algorithms for increased performance and reduced sensitivity to noise and parameter variability. Acknowledgments I am grateful to Professors Foreman Williams and Jurgen Troe for their kind invitation to give this lecture. Our work on combustion dynamics and control has been decisively influenced by Frank Marble and by the friendly advice of the late Marcel Barre`re. It has benefited from interactions with many colleagues and among others P. Clavin, G. Searby, N. Peters, F. Williams, A. Lin˜a`n, K. Bray, C.K. Law, F. Culick, B. Zinn, J. Driscoll, A. Ghoniem, V. Yang, A. Karagozian, B. Cetegen, K. Yu, K. McManus, and F. Vuillot. I also wish to acknowledge the contributions of Drs. T. Poinsot, D. Veynante, F. Lacas, D. The´venin, D. Durox, C. Rolon, N. Darabiha, E. Esposito, S. Ducruix, D. Thibaut, M. Mettenleiter, and N. Docquier and those of C. Nottin, T. Schuller and C. Rey. The generous support from Snecma, Aerospatiale (now MBDA), CNES, DGA, CNRS and the European Community is gratefully acknowledged. Computational examples were provided by S. Ducruix, T. Schuller, T. Poinsot, and C. Nottin. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12.

13. 14. 15. 16. 17.

Glassman, I., Proc. Combust. Inst. 28:1–10 (2000). Wolfrum, J., Proc. Combust. Inst. 27:1–41 (1998). Bray, K. N. C., Proc. Combust. Inst. 26:1–26 (1996). Marble, F. E., Proc. Combust. Inst. 25:1–12 (1994). Williams, F. A., Proc. Combust. Inst. 24:1–17 (1992). Hottel, H. C., Proc. Combust. Inst. 4:97–113 (1952). Crocco, L., J. Am. Rocket Soc. 21:163 (1951). Tsien, H. S., J. Am. Rocket Soc. 22:256–263 (1952). Marble, F. E., and Cox Jr., D. W., J. Am. Rocket Soc. 23:63–81 (1953). Crocco, L., and Cheng, S. L., Theory of Combustion Instability in Liquid Propellant Rocket Motors, Butterworths Science Publication, London, 1956. Barre`re, M., and Bernard, J. J., Proc. Combust. Inst. 6:487–492 (1956). Barre`re, M., and Corbeau, J., ‘‘Les instabilite´s de combustion dans les fuse´es a` propergol liquide,’’ in Combustion and Propulsion, Fifth Agard Colloquium (R. P. Hagerty, A. L. Jaumotte, O. Lutz, and S. Penner, eds.), Pergamon, Oxford, 1963, pp. 637–692. Levine, R. S., Proc. Combust. Inst. 10:1083–1099 (1964). Crocco, L., Proc. Combust. Inst. 10:1101–1128 (1964). Barre`re, M., and Williams, F. A., Proc. Combust. Inst. 12:169–181 (1968). Crocco, L., Proc. Combust. Inst. 12:85–99 (1968). Harrje, D. T., and Reardon, F. H. (eds.), Liquid Propellant Rocket Combustion Instability, report NASA SP-194, NASA, 1972.

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES 18. Culick, F. E. C., ‘‘Combustion Instabilities in LiquidFueled Propulsion Systems,’’ in AGARD CP-450, AGARD, 1989, pp. 1–73. 19. Yang, V., and Anderson, R., (eds.) Liquid Rocket Engine Combustion Instability, Progress in Astronautics and Aeronautics, Vol. 169, AIAA, Washington, 1995. 20. Keller, J. J., AIAA J. 33:2280–2287 (1995). 21. Correa, S. M., Proc. Combust. Inst. 27:1793–1807 (1998). 22. Lieuwen, T. C., and Zinn, B. T., Proc. Combust. Inst. 27:1809–1816 (1998). 23. Paschereit, C. O., Gutmark, E., and Weisenstein, W., Proc. Combust. Inst. 27:1817–1824 (1998). 24. Broda, J. C., Seo, S., Santoro, R. J., Shirhattikar, J., and Yang, V., Proc. Combust. Inst. 27:1849–1856 (1998). 25. Venkatamaraman, K. K., Preston, L. H., Simons, D. W., Lee, B. J., Lee, J. G., and Santavicca, D. A., J. Propul. Power 15:909–918 (1999). 26. Cohen, J. M., Rey, N. M., Jacobson, C. A., and Anderson, T. J., J. Eng. Gas Turbines Power 121:281– 284 (1999). 27. Hermann, J., ‘‘Combustion Dynamics: Applications of Active Instability Control to Heavy Duty Gas Turbines,’’ in Proceedings of the Combustion Institute of the RTO/VKI Special Course Active Control of Engine Dynamics (VKI), Rhode Saint Genese, Belgium, 2001, pp. 7.1–7.16. 28. Lee, S. Y., Seo, S., Broda, J. C., Pal, S., and Santorro, R. J., Proc. Combust. Inst. 28:775–782 (2000). 29. Sattinger, S. S., Neumeier, Y., Nabi, A., Zinn, B. T., Amos, D. J., and Darling, D. D., J. Eng. Gas Turbines Power 122:262–269 (2000). 30. Lee, J. G., Kim, K., and Santavicca, D. A., Proc. Combust. Inst. 28:739–746 (2000). 31. Bernier, D., Ducruix, S., Lacas, F., Candel, S., Robart, N., and Poinsot, T., ‘‘Identification of the Transfer Function in a Model Gas Turbine Combustor: Application to Active Control of Combustion Instabilities,’’ in Proceedings of the Eighteenth ICDERS Seattle, 2001. 32. Paschereit, C. O., Flohr, P., and Schuermans, B., Prediction of Combustion Oscillations in Gas Turbine Combustors, AIAA paper 2001–0484. 33. Candel, S., Proc. Combust. Inst. 24:1277–1296 (1992). 34. Darrieus, G., ‘‘Propagation d’un front de flamme,’’ in Proceedings of La Technique Moderne August 1939, p. 15. 35. Landau, L., Acta Physicochimica, USSR 19:77–85 (1945). 36. Markstein, G. H., Nonsteady Flame Propagation, Pergamon, London, 1964. 37. Buckmaster, J. D., and Ludford, G. S. S., Theory of Laminar Flames, Cambridge University Press, Cambridge, 1982. 38. Sivashinsky, G. I., Annu. Rev. Fluid Mech. 15:179– 199 (1983).

25

39. Williams, F. A., Combustion Theory, Benjamin/Cummings, Menlo Park, 1985. 40. Clavin, P., Proc. Combust. Inst. 28:569–585 (2000). 41. Culick, F. E. C., ‘‘Combustion Instabilities in Propulsion Systems,’’ in Unsteady Combustion (F. E. C. Culick, M. V. Heitor, and J. H. Whitelaw, eds.), Kluwer, Dordrecht, 1996, pp. 173–241. 42. Yang, V., ‘‘Introductions-Stability Characteristics and Control Approach,’’ in Proceedings of the Combustion Institute of the RTO/VKI Special Course Active Control of Engine Dynamics (VKI), Rhode Saint Genese, Belgium, 2001, pp. 1.1–1.17. 43. Summerfield, M., J. Am. Rocket Soc. 21:108 (1951). 44. Lord Rayleigh, J. W. S., Nature 18:319–321 (1878). 45. Putnam, A. A., Combustion Driven Oscillations in Industry, Elsevier, New York, 1971. 46. McManus, K. R., Poinsot, T., and Candel, S., Prog. Energy Combust. Sci. 19:1–29 (1993). 47. Renard, P. H., The´venin, D., Rolon, J. C., and Candel, S., Prog. Energy Combust. Sci. 26:225–282 (2000). 48. Leyer, J. C., Acta Astronaut. 14:445–451 (1969). 49. Searby, G., and Rochewerger, D., J. Fluid Mech. 231:529–543 (1991). 50. Dobashi, R., Hirano, T., and Tsuruda, T., Proc. Combust. Inst. 25:1415–1422 (1994). 51. Haile, E., Delabroy, O., Lacas, F., Veynante, D., and Candel, S., Proc. Combust. Inst. 26:1079–1086 (1996). 52. Yu, K. H., Wilson, K. J., and Schadow, K. C., Proc. Combust. Inst. 26:2843–2850 (1996). 53. Hermann, J., Gleis, S., and Vortmeyer, D., Combust. Sci. Technol. 118:1–25 (1996). 54. Yu, K. H., Wilson, K. J., and Schadow, K. C., Proc. Combust. Inst. 27:2039–2046 (1998). 55. Paschereit, C. O., Schuermans, B., and Campos-Delgado, D., Active Combustion Control Using an Evolution Algorithm, AIAA paper 2001-0783. 56. Corbett, N. C., and Lines, N. P., ‘‘Control Requirements for the RB 211 Low Emission Combustion Systems,’’ paper 93-GT-12, Proceedings of the International Gas Turbine and Aeroengine Congress and Exposition, Cincinnati, OH, 1993. 57. Docquier, N., and Candel, S., ‘‘Sensor Requirements for Combustion Control,’’ in Applied Combustion Diagnostics (K. Kohse Ho¨inghaus and J. B. Jeffries, eds.), Taylor and Francis, New York, 2002. 58. Docquier, N., and Candel, S., Prog. Energy Combust. Sci. 28:107–150 (2002). 59. St. John, D., and Samuelsen, G. S., Proc. Combust. Inst. 25:307–316 (1994). 60. Furlong, E. R., Baer, D. S., and Hanson, R. K., Proc. Combust. Inst. 26:2851–2858 (1996). 61. St. John, D., and Samuelsen, G. S., Combust. Sci. Technol. 128:1–21 (1997). 62. Docquier, N., Lacas, F., and Candel, S., Operating Point Control of Gas Turbine Combustor, AIAA paper 2001-0485.

26

HOTTEL LECTURE

63. Ebert, V., Fitzer, J., Gerstenberg, I., Pleban, K.-U., Pitz, H., Wolfrum, J., Jochem, M., and Martin, J., Proc. Combust. Inst. 28:1301–1308 (2000). 64. Haile, E., Delabroy, O., Durox, D., Lacas, F., and Candel, S., ‘‘Combustion Enhancement by Active Control,’’ in Flow Control, Fundamentals and Practices (M. Gad el Hak, A. Pollard, and J. P. Bonnet, eds.), Springer, New York, 1998, pp. 467–499. 65. Allen, M. G., Furlong, E. R., and Hanson, R. K., ‘‘Tunable Diode Lasers and Combustion Control,’’ in Applied Combustion Diagnostics (K. Kohse-Ho¨inghaus, and J. B. Jeffries, eds.), Taylor and Francis, New York, 2002. 66. Law, C. K., Proc. Combust. Inst. 22:1381–1402 (1988). 67. Peters, N., Turbulent Combustion, Cambridge University Press, Cambridge, 2000. 68. Poinsot, T., and Veynante, D., Theoretical and Numerical Combustion, Edwards, Philadelphia, 2001. 69. Tsuji, H., and Yamaoka, I., Proc. Combust. Inst. 11:979 (1966). 70. Tsuji, H., and Yamaoka, I., Proc. Combust. Inst. 13:723 (1970). 71. Saitoh, T., and Otsuka, Y., Combust. Sci. Technol. 12:135–146 (1976). 72. Aguerre, F., Darabiha, N., Rolon, C., and Candel, S., transl. from Russian, Combust. Explos. Shock Waves 29:311–315 (1993). 73. Brown, T. M., Pitz, R. W., and Sung, C. J., Proc. Combust. Inst. 27:703–710 (1998). 74. Yoshida, K., and Takagi, T., Proc. Combust. Inst. 27:685–692 (1998). 75. Welle, E. J., Roberts, W. L., Decroix, M. E., Carter, C. D., and Donbar, J. M., Proc. Combust. Inst. 28:2021–2027 (2000). 76. Darabiha, N., Combust. Sci. Technol. 86:163–181 (1992). 77. Ghoniem, A. F., Soteriou, M. C., Cetegen, B. M., and Knio, O. M., Proc. Combust. Inst. 24:223–230 (1992). 78. Egolfopoulos, F. N., Proc. Combust. Inst. 25:1365– 1373 (1994). 79. Kim, J. S., and Williams, F. A., Combust. Flame 98:279 (1994). 80. Im, H. G., Bechtold, J. K., and Law, C. K., Combust. Sci. Technol. 106:345–361 (1995). 81. Egolfopoulos, F. N., and Campbell, C. S., J. Fluid Mech. 318:1–29 (1996). 82. Joulin, G., Combust. Sci. Technol. 97:219–229 (1994). 83. Im, H. G., Law, C. K., Kim, J. S., and Williams, F. A., Combust. Flame 100:21 (1995). 84. Cuenot, B., Egolfopoulos, F. N., and Poinsot, T., Combust. Theory Model. 4:77–97 (2000). 85. Carrier, G. F., Fendell, F. E., and Marble, F. E., SIAM J. Appl. Math. 28:463–500 (1975). 86. Haworth, D. C., Drake, M. C., Pope, S. B., and Blint, R. J., Proc. Combust. Inst. 22:589–597 (1988). 87. Cetegen, B. M., and Bogue, D. R., Combust. Flame 86:359–370 (1991).

88. Hirasawa, T., Ueada, T., Matsuo, A., and Mizomoto, M., Proc. Combust. Inst. 27:875–882 (1998). 89. Lauvergne, R., and Egolfopoulos, F. N., Proc. Combust. Inst. 28: (2000). 90. Im, H. G., and Chen, J. H., Proc. Combust. Inst. 28:1833–1840 (2000). 91. Gerk, T. J., and Karagozian, A., Proc. Combust. Inst. 26:1095–1102 (1996). 92. Petrov, C. A., and Ghoniem, A., Combust. Flame 115:180–194 (1998). 93. Kollmann, W., and Chen, J. H., Proc. Combust. Inst. 27:927–934 (1998). 94. Schuller, T., Durox, D., and Candel, S., Combust. Flame 128:88–110 (2002). 95. Roberts, W. L., and Driscoll, J. F., Combust. Flame 87:245–256 (1991). 96. Mueller, C. J., Driscoll, J. F., Reuss, D. L., and Drake, M. C., Proc. Combust. Inst. 26:347–355 (1996). 97. Sinibaldi, J. O., Mueller, C. J., and Driscoll, J. F., Proc. Combust. Inst. 27:827–832 (1998). 98. Rolon, C., Aguerre, F., and Candel, S., Combust. Flame 100:422–429 (1995). 99. Renard, P. H., Rolon, C., The´venin, D., and Candel, S., Combust. Flame 117:189–205 (1999). 100. Smith, D. A., and Zukoski, E. E., Combustion Instability Sustained by Unsteady Vortex Combustion, AIAA paper 85-1248. 101. Lee, J. G., Kim, K., and Santavicca, D. A., Proc. Combust. Inst. 28:415–421 (2000). 102. Hathout, J. P., Fleifil, M., Annaswamy, A. M., and Ghoniem, A. F., Proc. Combust. Inst. 28:721–730 (2000). 103. Marzouk, Y. M., Ghoniem, A. F., and Najm, H. N., Proc. Combust. Inst. 28:1859–1866 (2000). 104. Blackshear, P. L., Proc. Combust. Inst. 4:553–566 (1952). 105. Fleifil, M., Annaswamy, A. M., Ghoneim, Z. A., and Ghoniem, A. F., Combust. Flame 106:487–510 (1996). 106. Annaswamy, A. M., El Rifai, O. M., Fleifil, M., Hathout, J. P., and Ghoniem, A. F., Combust. Sci. Technol. 135:213–240 (1998). 107. Hathout, J. P., Annaswamy, A. M., Fleifil, M., and Ghoniem, A. F., Combust. Sci. Technol. 132:99–138 (1998). 108. Ducruix, S., Durox, D., and Candel, S., Proc. Combust. Inst. 28:765–773 (2000). 109. Durox, D., Ducruix, S., and Candel, S., Combust. Flame 125:982–1000 (2001). 110. De Soete, G., Revue de l’Institut Franc¸ais du Pe´trole 19:766–785 (1964). 111. Matsui, Y., Combust. Flame 43:199–209 (1981). 112. Bourehla, A., and Baillot, F., Combust. Flame 114:303–318 (1998). 113. Baillot, F., Bourehla, A., and Durox, D., Combust. Sci. Technol. 112:327–350 (1996). 114. Baillot, F., Durox, D., and Prud’homme, R., Combust. Flame 88:149–168 (1992).

COMBUSTION DYNAMICS AND CONTROL: PROGRESS AND CHALLENGES 115. Schuller, T., Ducruix, S., Durox, D., and Candel, S., Proc. Combust. Inst. 29:107 (2002). 116. Boyer, L., and Quinard, J., Combust. Flame 82:51–65 (1990). 117. Schuller, T., Durox, D., and Candel, S., unpublished data, 2002. 118. Le Helley, P., ‘‘Etude the´orique et expe´rimentale des instabilite´s de combustion et de leur controˆle dans un foyer pre´me´lange´,’’ Ph.D. thesis, Ecole Centrale Paris, 1994. 119. Ducruix, S., ‘‘Dynamique des interactions acoustique-combustion,’’ Ph.D. thesis, Ecole Centrale Paris, 1999. 120. Abugov, D. I., and Obrezkov, O. I., Combust. Explos. Shock Waves 14:606–612 (1978). 121. Clavin, P., and Siggia, E. D., Combust. Sci. Technol. 78:147–155 (1991). 122. Durox, D., Schuller, T., and Candel, S., Proc. Combust. Inst. 29:69 (2002). 123. Culick, F. E. C., ‘‘Dynamics of Combustion Systems: Fundamentals, Acoustics and Control,’’ in Proceedings of the RTO/VKI Special Course Active Control of Engine Dynamics (VKI), Rhode Saint Genese, Belgium, 2001, pp. 6.1–6.133. 124. Zinn, B. T., Proc. Combust. Inst. 13:491–503 (1970). 125. Zinn, B. T., and Lores, E. M., Combust. Sci. Technol. 4:269–278 (1972). 126. Awad, E., and Culick, F. E. C., Combust. Sci. Technol. 46:195–222 (1986). 127. Yang, V., and Culick, F. E. C., Combust. Sci. Technol. 72:37–65 (1990). 128. Yang, V., Sinha, A., and Fung, Y. T., J. Propul. Power 8:66–73 (1992). 129. Yang, V., and Fung, Y. T., J. Propul. Power 8:1282– 1289 (1992). 130. Annaswamy, A. M., Fleifil, M., Hathout, J. P., and Ghoniem, A. F., Combust. Sci. Technol. 128:131–180 (1997). 131. Koshigoe, S., Komatsuzaki, T., and Yang, V., J. Propul. Power 15:383–389 (1999). 132. Candel, S., Huynh Huu, C., and Poinsot, T., ‘‘Some Modeling Methods of Combustion Instabilities,’’ in Unsteady Combustion (F. E. C. Culick, M. V. Heitor, and J. H. Whitelaw, eds.), Kluwer, Dordrecht, 1996, pp. 83–112. 133. Marble, F. E., and Candel, S., Proc. Combust. Inst. 17:761–769 (1978). 134. Poinsot, T., and Candel, S., Combust. Sci. Technol. 61:121–153 (1988). 135. Kerstein, A. R., Ashurst, W. T., and Williams, F. A., Phys. Rev. A 37:2728–2731 (1988). 136. Rhee, C. W., Talbot, L., and Sethian, J. A., J. Fluid Mech. 300:87–115 (1995). 137. Dowling, A. P., J. Fluid Mech. 394:51–72 (1999). 138. Poinsot, T., Candel, S., and Trouve´, A., Prog. Energy Combust. Sci. 21:531–576 (1996). 139. Candel, S., The´venin, D., Darabiha, N., and Veynante, D., Combust. Sci. Technol. 149:297–337 (1999).

27

140. Ducruix, S., Candel, S., Nicoud, F., and Poinsot, T., ‘‘Conditions aux limites permettant l’injection d’ondes acoustiques dans une simulation numerique,’’ in Proceedings of the Combustion Institute of the 14 e`me Congre`s Franc¸ais de Me´canique Toulouse, 1999. 141. Poinsot, T., and Lele, S. K., J. Comput. Phys. 101:104–129 (1992). 142. Ferziger, J., ‘‘Large Eddy Simulation: An Introduction and Perspective’’ in New Tools in Turbulence Modelling (O. Metais, and J. Ferziger, eds.), SpringerVerlag, New York, 1997, pp. 29–47. 143. Lesieur, M., ‘‘Recent Approaches in Large-Eddy Simulations of Turbulence’’ in New Tools in Turbulence Modelling (O. Metais, and J. Ferziger, eds.), SpringerVerlag, New York, 1997, pp. 1–28. 144. Ghosal, S., and Moin, P., J. Comput. Phys. 1995:24– 37 (1995). 145. Meneveau, C., and Katz, J., Annu. Rev. Fluid Mech. 32:1–32 (2000). 146. Kailasanath, K., Gardner, J. H., Boris, J. P., and Oran, E. S., J. Propul. Power 3:525–533 (1987). 147. Kailasanath, K., Gardner, J. H., Boris, J. P., and Oran, E. S., J. Propul. Power 5:165–171 (1989). 148. Menon, S., Combust. Sci. Technol. 84:51–79 (1992). 149. Piana, J., Veynante, D., Candel, S., and Poinsot, T., ‘‘Direct Numerical Simulation Analysis of the GEquation in Premixed Combustion,’’ in Proceedings of the Second ERCOFTAC Workshop on Direct and Large-Eddy Simulation (J. P. Chollet, P. R. Voke, and L. Kleiser, eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996. 150. Yamashita, H., Shimada, M., and Takeno, T., Proc. Combust. Inst. 26:27–34 (1996). 151. Piana, J., Ducros, F., and Veynante, D., ‘‘Large Eddy Simulations of Turbulent Premixed Flames Based on the G-Equation and a Flame Wrinkling Description,’’ in Proceedings of the Eleventh Symposium on Turbulent Shear Flows (F. Durst, N. Kasagi, B. E. Launder, F. W. Schmidt, and K. Suzuki, eds.), SpringerVerlag, Berlin, 1997, pp. 21.13–21.18. 152. Veynante, D., and Poinsot, T., ‘‘Reynolds Average and Large Eddy Simulation Modeling for Turbulent Combustion,’’ in New Tools in Turbulence Modelling (O. Metais and J. Ferziger, eds.), Springer-Verlag, New York, 1997, pp. 105–140. 153. Thibaut, D., and Candel, S., Combust. Flame 113:51– 65 (1998). 154. Angelberger, C., Veynante, D., Egolfopoulos, F., and Poinsot, T., ‘‘Large Eddy Simulation of Combustion Instabilities in Turbulent Premixed Flames,’’ in Proceeding of Summer Program, Center for Turbulence Research, Stanford, 1998, pp. 61–82. 155. Weller, H. G., Tabor, G., Gosman, A. D., and Fureby, C., Proc. Combust. Inst. 27:899–907 (1998). 156. Pierce, C. D., and Moin, P., Phys. Fluids 10:3041– 3044 (1998). 157. Fureby, C., Proc. Combust. Inst. 28:783–791 (2000).

28

HOTTEL LECTURE

158. Pitsch, H., and Steiner, H., Proc. Combust. Inst. 28:41–49 (2000). 159. Colin, O., Ducros, F., Veynante, D., and Poinsot, T., Phys. Fluids 12:1–21 (2000). 160. Nottin, C., Knikker, R., Boger, M., and Veynante, D., Proc. Combust. Inst. 28:67–73 (2000). 161. Hawkes, E. R., and Cant, R. S., Proc. Combust. Inst. 28:51–58 (2000). 162. Nwagwe, I. K., Weller, H. G., Tabor, G. R., Gosman, A. D., Sheppard, C. G. W., and Wooley, R., Proc. Combust. Inst. 28:59–65 (2000). 163. Angelberger, C., Veynante, D., and Egolfopoulos, F., Flow Turbulence Combust. 65:205–222 (2001). 164. Hawkes, E. R., and Cant, R. S., Combust. Flame 126:1617–1629 (2001). 165. Ducruix, S., Poinsot, T., and Candel, S., ‘‘Large Eddy Simulations of Combustion Instabilities in a Swirled Combustor,’’ in Turbulent Mixing and Combustion (A. Pollard, and S. Candel, eds.), Kluwer, Dordrecht, 2002, p. 357. 166. Pollard, A., and Candel, S., (eds.), Turbulent Mixing and Combustion, Proceedings of the IUTAM Symposium, Kluwer, Dordrecht, 2002. 167. Menon, S., and Jou, W., Combust. Sci. Technol. 75:53–72 (1991). 168. Menon, S., and Calhoon, W. H., Proc. Combust. Inst. 26 (1996). 169. Chakravarthy, V. K., and Menon, S., Flow, Turbulence Combust. 65:133–161 (2000). 170. Yakhot, V., Combust. Sci. Technol. 60:191–214 (1988). 171. O’Rourke, P. J., and Bracco, F. V., J. Comput. Phys. 33:185–203 (1979). 172. Butler, T. D., and O’Rourke, P. J., Proc. Combust. Inst. 16:1503–1515 (1976). 173. Poinsot, T., Trouve´, A., Veynante, D., Candel, S., and Esposito, E., J. Fluid Mech. 177:265–292 (1987). 174. Yu, K., Trouve´, A., and Candel, S. M., “Combustion Enhancement of a Premixed Flame by Acoustic Forcing with Emphasis on Role of Large Scale Vortical Structures,” AIAA paper 91-0367. 175. Hermann, J., Orthmann, A., Hoffmann, S., and Berenbrink, P., ‘‘Combination of Active Instability Control and Passive Measures to Prevent Combustion Instabilities in a 260 MW Heavy Duty Gas Turbine,’’ in Proceedings of the NATO/RTO Symposium on Active Control Technology (RTO), Braunschweig, Germany, May 8–12, 2000. 176. Haile, E., Lacas, F., and Candel, S., Comptes Rendus de l’Acade´mie des Sciences, Serie II b 325:203–209 (1997). 177. Yu, K. H., ‘‘Active Control of Engine Dynamics: Fundamentals and Fluid Dynamics,’’ in Proceedings of

178. 179. 180. 181. 182. 183.

184. 185.

186. 187. 188. 189. 190. 191.

192. 193. 194.

195. 196.

the RTO/VKI Special Course Active Control of Engine Dynamics (VKI), Rhode Saint Genese, Belgium, 2001, pp. 2.1–2.29. Yu, K. H., and Wilson, K. J., J. Propul. Power 18:53– 60 (2002). Fung, Y. T., Yang, V., and Sinha, A., Combust. Sci. Technol. 78:217–245 (1991). Evesque, S., and Dowling, A. P., Combust. Sci. Technol. 164:65–93 (2001). Hathout, J. P., Fleifil, M., Annaswamy, A. M., and Ghoniem, A. F., J. Propul. Power 18:390–399 (2002). Boe-Shong, H., Yang, V., and Ray, A., Combust. Flame 1999:91–106 (1999). Neumeier, Y., and Zinn, B. T., Active Control of Combustion Instabilities with Real Time Observation of Unstable Combustor Modes, AIAA paper 96-0758. Mohanraj, R., Neumeier, Y., and Zinn, B. T., J. Propul. Power 16:485–492 (2000). Mettenleiter, M., Vuillot, F., and Candel, S., ‘‘Numerical Simulation of Active Control in Unstable Solid Rocket Motors,’’ in Proceedings of the NATO/ RTO Symposium on Active Control Technology (RTO), Braunschweig, Germany, May 8–12, 2000. Mettenleiter, M., Vuillot, F., and Candel, S., AIAA J. 40:860–868 (2002). Blomshield, F., and Mathes, H. B., J. Propul. Power 9:217–221 (1993). Vuillot, F., J. Propul. Power 1995:626–639 (1995). Dotson, K. W., Koshigoe, S., and Pace, K. K., J. Propul. Power 13:197–206 (1997). Mettenleiter, M., Haile, E., and Candel, S., J. Sound Vib. 230:761–789 (2000). Mettenleiter, M., and Candel, S., ‘‘Developments of Adaptive Methods for Active Instability Control,’’ in Proceedings of the NATO/RTO Symposium on Active Control Technology, Braunschweig, Germany, May 8–12, 2000. Scott, D. A., King, G. B., and Laurendeau, N. M., J. Propul. Power 18:376–382 (2002). Jackson, M. D., and Agrawal, A. K., J. Eng. Gas Turbines Power 121:437–443 (1999). Miyasato, M. M., McDonell, V. G., and Samuelsen, G. S., ‘‘Active Optimization of the Performance of a Gas Turbine Combustor,’’ in Proceedings of the NATO/RTO Symposium on Active Control Technology (NATO/RTO), Braunschweig, May 8–12, 2000. Scott, D. A., King, G. B., and Laurendeau, N. M., Combust. Sci. Technol. 159:129–146 (2000). Docquier, N., Lacas, F., and Candel, S., Proc. Combust. Inst. 29:139 (2002).