a mechanism of combustion

8/3/2019 A Mechanism of Combustion

1/11


2/11

Prior theoretical studies by the authors suggested that heatrelease oscillations excited by fluctuations in the compositionof the reactive mixture entering the combustion zone were the

dominant mechanism responsible for the instabilities observedin these combustors [lo- 121. However, limited experimentalevidence was available to critically assess the theory.Furthermore, the developed theory could not account for the

observed dependence of the combustor stability upon flamestructure. This paper describes recent work of the authors thatextends the theory to account for flame structure effects, aswell as comparisons of the theory with measurements at severalfacilities.

The following section presents the mechanism ofinstability proposed by the authors, necessary conditions underwhich it will cause self-excited oscillations, and an analysis thatcan be used to predict the conditions under which combustorsbecome unstable. Next, it presents results that illustrate theagreement between the predictions of the developed theory andexperimental data. The paper closes with a discussion ofpossible approaches for passive control and of other potentialinstability mechanisms.

2. Mechanism of LP Combustion Instability

The primary difficulty in combustion instability studies isunderstanding the interactions between the unsteady heatrelease processes and the disturbances that drive them. Thistask is difficult because these heat release oscillations may bedue to oscillations of the velocity, pressure, temperature, andreactants composition that are present simultaneously incombustion systems. Though heat release oscillations may beexcited by a host of disturbances, there are two conditionswhich must be met for self-excited, combustion driven

oscillations to occur. First, the unsteady heat release processesmust be in phase with the fluctuating acoustic pressure so thatenergy is added to the unsteady motions (i.e., Rayleighscriterion) [lo]. Second, the rate of energy addition must exceedthe rate of energy dissipation.

This section describes a mechanism that appears to beresponsible for LP combustion instabilities, shows whatoperating ranges will satisfy the conditions discussed above,and consequently, predicts the regions under which instabilitieswill be observed. A schematic of the feedback process uponwhich the proposed mechanism is based on is shown in Fig. 2.Its main elements are the generation of heat release oscillations

by periodic variations in $I of the reactive mixture that entersthe flame, and the formation of @ oscillations in the inletsection by velocity and pressure oscillations in the vicinity ofthe fuel injector. These processes are described in more detailin the following subsections.

2.1 Response of LP systems to $ oscillationsThis study was partially motivated by observations that

properties of premixed combustion systems, such as flame

thickness, flame speed, and reaction rate become increasingl

sensitive to variations in $ as the combustion processtoichiometry becomes leaner [lo]. Moreover, systemoperating near the lean limit are acutely sensitive t

r$ perturbations since they may cause periodic extinction of thcombustion process. To further examine these observations, aunsteady well stirred reactor (WSR) model was developed anits response to @perturbations in its inlet conditions wastudied [lo]. Figure 3 presents a result from this study. shows that the response of the WSRs reaction rate tperturbations in the inlet (9 significantly increases (by tworders of magnitude) as the mean value of Q decreases. Thiresult strongly suggests that 4 oscillations could drivsubstantial heat release oscillations under lean operatin

conditions. It also suggests that 4 oscillations are unlikely tdrive instabilities near stoichiometric conditions because of thnegligible response of the reaction rate at this operatincondition. Some experimental observations that the oscillatinpressure amplitude in LP combustors is relatively small undestoichiometric conditions and becomes progressively larger a

$ is reduced [l] appear to support these assertions and thtrends depicted in Fig. 3.

2.2 Formation of 41 oscillations

The discussion in Section 2.1 suggests that the sensitivit

of LP systems to $ oscillations could be responsible for theiunstable behavior. While random $ fluctuations undoubtedloccur in LP combustors (e.g., due to turbulent mixing),fluctuations can only play a role in an instability mechanism they are driven by the combustion process and the resultinpressure and velocity oscillations, thus closing the feedbacloop needed to maintain an instability, see Fig. 2

Consequently, it is necessary to consider how tl~ fluctuations caarise, and to elucidate the feedback mechanism between theand heat release oscillations that drive the instability. Th

following equation, derived from the definition of Q, suggestsmechanism for the formation of 4 oscillations in the inlesection due to velocity and pressure perturbations:

mr m,4 z--z-=(4 1+5-m.

(1

In Eq. (l), the subscripts f and o denote fuel and oxidize(assumed to be air from this point on), respectively, and m th

mass flow rate. This equation shows that t$ oscillations can bformed by air and/or fuel flow oscillations (that are present the fuel injector). Furthermore, for the low Mach number flowtypical of these systems, this equation implies that sma

acoustic fluctuations can generate significant I$ fluctuatione.g., for M= 0.05 and a choked fuel injector (i.e., m,=O

2


3/11


4/11


5/11

measured dependence of the instability regions on the upstreamboundary condition in Fig. 5 are well described by the theory.

Figure 7 shows pressure data obtained by Straub andRichards [3] and the instability regions predicted by Eq. (2). Itcan be seen that their data collapses into bands when

normalized by a,JT, as predicted in the preceding discussion.Furthermore, since the inlet section of the combustor wasconnected to a plenum (see [3]), the upstream boundarycondition may be approximated as a pressure node. Then, Eq.(2) predicts that instabilities should occur in the vicinity of

= 0.75, 1.75, . . . . The figure shows that this predictionis in agreement with the measured data, particularly for the firstregion of instability. It can be seen that the agreement is not asgood for the second band of oscillations; however, this is likelydue to distributed flame effects and is discussed further below.

Figure 8 shows unsteady pressure data obtained at PennState [2,19]. Since the upstream boundary of the inlet sectionin this facility is essentially nonreflecting, Eq. (4) predicts that

instabilities should occur when r~&T = 0, 1, . . . . Figure 8shows that the measured data agrees well with this prediction.

Figure 9 shows unsteady pressure data obtained atGeorgia Tech (a description of the experimental setup andadditional results can be found in [17]). Since the upstreamboundary of the inlet section is rigid, Eq. (3) predicts that

instabilities should occur when ~,,JT = 0.25, 1.25, . . . .Figure 9 shows that most of the large amplitude pressureoscillations occur in the predicted region, However, it shouldbe noted that instabilities were observed in four test runs thatare well outside of the predicted unstable region (i.e.,

An examination of Figs. 7-9 reveals that some of the

measured instabilities occurred in zCORYCC~ regions that lie to theleft of the predicted regions. As the discussion below Eq. (8)

indicates, this consistent leftward bias is to be expected,however, because regions of instability should actually occur

where z,,,,/T * (0.7-l)C, = C, ; i.e., between zero and thirtypercent to the left of those shown in Fig. 5. The shift ofapproximately twenty five percent in the DOE data (see Fig. 7)and twenty percent in the Georgia Tech data (see Fig. 9)suggests that these discrepancies are simply due to

correlating the measure data with rW,,,(T instead ofr,O,,JI.The above comparisons between the theoretical

predictions and the experimental data clearly demonstrate that

LP instabilities occur at specific ranges of the parameter T,,,,Significantly, the demonstrated agreement between the

theorys predictions and measurements strongly suggests thatthe mechanism discussed in this paper is responsible for LPinstabilities.

One issue that is not clear, however, is the lack of unstableoscillations in bands that are predicted to be unstable. Forexample, no oscillations have been observed in the Georgia

Tech facility in the O


6/11


7/11


8/11


9/11


10/11


11/11

a mechanism of combustion

Documents