A simplified model for the investigation of acoustically driven combustion instabilities

D. Dane Quinn *Dept. of Mechanical EngineeringThe University of AkronAkron, OH 44325-3903Daniel E. Paxson tNASA Lewis Research CenterMS 77-1Cleveland, OH 44135ABSTRACTA simplified one-dimensional model of reactive flow ispre_ented which captures features of aeropropulsion sys-tems, including acoustically driven combustion instabil-ities. Although the resulting partial differential equa-tions are one-dimensional, they qualitatively describeobserved phenomena, including resonant frequencies andthe admission of both steady and unsteady behavior.A number of simulations are shown which exhibit bothsteady and unsteady behavior, including flame migrationand thermo-acoustic instabilities. Finally, we present ex-amples of unsteady flow resulting from fuel modulation.NOMENCLATURESc = & viscosityD mass diffusion coefficient'Le = (_/cp) thermal diffusion coefficientD mass diffusion coefficient '= (Q/c_)vo heat-release,To8 = _ activation energy,RTo# = __a = _ acoustic time scaleco to characteristic time scale'6 = v_..p_.._ = _ characteristic time scalepozo_o td diffusive time scale 'A K= characteristic time scale= _o--_e---_tr reactive time scale '7 = _ specific-heat ratio,*Summer Faculty Fellow at NASA Lewis Research Center,quinn@ uakron.edu*Member AIAA, dpaxson@lerc.nasa.govINTRODUCTIONThe current drive toward lean operating, low-emission,low-loss combnstors in next generation aeropropulsionsystems makes them susceptible to various instabilitiesand makes the understanding of those instabilities crit-ical. Combustion instabilities, specifically acousticallydriven instabilities, often arise from the interaction be-tween the energy released by the chemical reactions andthe underlying fluid flow. This coupling can dramaticallyalter the dynamical behavior of the combustion process,and result in unstable behavior. Typical combustion in-stabilities in propulsion systems can often be chaxacter-ized by oscillatory pressure fluctuations coupled with anunsteady heat release. This instability can lead to flameblowout, reduced performance, and decreased engine life.