JOURNAL OF PROPULSION AND POWER Vol. 15, No. 4, July– August 1999 Technical Note TECHNICAL NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes cannot exceed 6 manuscript pages and 3 gures; a page of text may be substituted for a gure and vice versa. After informal review by the editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contributions (see inside back cover ). Determination of Unsteady Heat Release Distribution in Unstable Combustor from Acoustic Pressure Measurements Timothy C. Lieuwen, ¤ Yedidia Neumeier, † and Ben T. Zinn ‡ Georgia Institute of Technology, Atlanta, Georgia 30332-0150 Introduction D ETRIMENTAL combustion instabilities in propulsion or power generation systems often occur when oscillations in heat release excite one or more of the natural acoustic modes of the combustion chamber. 1 Determining the characteristics of combus- tion driving processes in these unstable combustors remains one of the most important and unresolvedproblems in the eld of combus- tion instability. Developing such an understanding often requires characterizing a number of processes occurring in the combustion zone, including chemical kinetics, uid mechanics, and transport processes. Clearly, measuring the oweld variables, e.g., veloc- ity, temperatures,and species concentrations,that will characterize these processes in the combustion zone of an unstable combustor would tax the capabilitiesof most laboratoriesand would be impos- sible in practical combustors where optical windows and access for the required number of probes are not available. Consequently, ap- proachesfordeterminingthecharacteristicsoftheunsteadycombus- tion processthatdo not requireextensivemeasurementsare needed. Unsteady heat addition in a combustor affects the characteris- tics of the combustor’s acousticpressure,velocity,temperature,and densityelds. Because it is often much easier to measure the charac- teristicsof the excited acousticpressure eld, this Note exploresthe possibility of using acoustic pressure measurements to determine information about the unknown combustion process heat source. Specically, the feasibility of recovering the spatial distribution of the amplitude and phase of the unsteady combustion process heat release in an unstable combustor from measurements of the spatial dependence of the acoustic pressure is investigated. Such a technique was rst attempted by Ramachandra and Strahle 2 andRamachandra 3 to determinethe distributionof the uc- tuating heat release rate in an open premixed ame. They measured the spatial distributionof the acoustic pressure and then used linear acoustictheorytodeterminethespatialdistributionoftheuctuating heatrelease.Theaccuracyofthiscalculatedheatreleasedistribution Received 13 September 1997; revision received 27 February 1999; ac- cepted for publication 16 March 1999. Copyright c ° 1999 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. ¤ Graduate Research Assistant, Mechanical Engineering. Student Member AIAA. † Senior Research Engineer, Aerospace Engineering. Member AIAA. ‡ David S. Lewis, Jr., Chair and Regents’ Professor, Aerospace and Me- chanical Engineering. Fellow AIAA. was assessed by comparison with radicals radiation measurements. Although encountering difculties due to the sensitivity of the so- lution to measurement errors, they 2,3 reported that the technique was successfullyused to recover the heat release distribution in the investigated ame. Subsequently, Chao and Strahle 4 and Chao 5 attempted to extend the techniqueto recoverthe heat releasedistributionin a gas turbine combustor.Theyfoundthattheywere ableto recovertheheatrelease distribution only in certain frequency bands and concluded that the method was generally not feasible. In his thesis, Chao 5 commented that “the reasons why such poor results were obtained. . . are still not very clear.” Unfortunately, without a clear understandingof his results, it is difcult to ascertain whether his conclusions are appa- ratus specic or reect general limitations of the technique. Thus, the applicabilityof his results to other applicationsand combustion congurations is unclear. This Note reconsiders this problem to better understand the pre- viousresultsand to arrive at some generalconclusionsregardingthe feasibility of the technique.The “Theoretical Background” section beginsfrom a generalformulationof theconservationequationsand demonstrates that it is theoretically possible to recover the heat re- lease from pressure measurements. In the Analysis and Discussion sections, issues of sensitivity of the solution to measurement errors are considered and the physical processes responsible for the prior experimentalresultsare explained.The Noteclosesby drawingcon- clusionsaboutthe feasibilityof usingthe techniquein otherunstable combustors such as those used in rocket motors or afterburners. Theoretical Background This section describes a theoretical analysis showing that, given certain assumptionsto be outlined, it is theoreticallypossibleto de- termine the spatial distribution of the unsteady heat release from acoustic pressure measurements. The investigated combustor is as- sumed to consist of a long and narrow duct of constantcross section and is shown in Fig. 1. A description of the unsteady oweld in this combustor can be obtained from the mass, momentum, and energy conservation equations. 6 By the assumption that there is a one-dimensional,inviscid, perfect gas ow and that only a combus- tion process heat addition source is present in the combustor, the conservation and state equations may be written in the following form: Fig. 1 Schematic of a proposed experimental setup for determining the unsteady combustion process heat addition from acoustic pressure measurements. 613