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Tharikaa Ramesh Kumar and Dr. Joseph Majdalani Auburn University, Department of Aerospace Engineering Photo Acknowledgements: SLS Rocket: <http://www.nasa.gov/sites/default/files/thumbnails/image/sls_wireframe_1_dac3.jpg> Background: <http://i.imgur.com/8xXfKkj.jpg> ► COMBUSTION ACOUSTIC INTERACTION These interactions cause enhanced heat transfer rates and resonance resulting in structural vibrations, increased noise levels to serious mechanical failure. 0 100 200 300 400 500 600 0.1 0.2 0.3 0.4 0.5 0 Unsteady Axial Wave (m/s) f r (Hz) FFT Present Acoustic 168.4 337.8 507.4 170.1 340.3 510.4 ► Continuity, Momentum and Energy Equations ► Nondimensionalization ► Perturbation ► The Biglobal Stability Approach ► Majdalani Mean Flowfield ( Compressible, Closed-form, Cylindrical ) ► Eigenvalue Problem ( ) 0 t ρ ρ ∂ +∇⋅ = ∂ u ( ) 4 3 D ( ) D P t ρ µ µ = −∇ − ∇× ∇× + ∇ ∇⋅ u u u 2 D D D D p T P c T t t ρ κ = +Φ+ ∇ 2 ; ; ; ; ; ; ; ; ; ; w w w w w x z r r z z w w w w w w c z r P T z r t t a p T a a a a c T U u u U U u u U u V u W u v w U U U c c c θ θ θ θ ρ θ ρ ρ ρ ′ ′ = = = = ∇= ∇ = = = = = = = = = = = = 1 1 1 1 1 1 1 1 1 = ; = = ; = ; = ; = z w r w w u u U u MU uu v V v MV v u w W w MW w p P pT T T θ ρ ρ ρ = + = + = + = + = + = + + + + ( ) ( ) 1 , exp( ) exp i r g gzr t im t ω θ ω = − ( ) { } ( ) 2 2 2 2 2 1 1 1 w 2 4 3 sin 1 1 cos( ) 2 x r M x r ψ π π π = − + + ij i ij i Af Bf ω = , , , , , , , , , , , , , , , , , , , , , , , , , continuity -momentum = -momentum -momentu z r cu cv cw c cT zu zv zw z zT ru rv rw r rT ij u v w T eu ev ew e eT U U U T A A A A A A A A A A z A A A A A A r A A A A A A A A A A θ ρ ρ ρ θ θ θ θρ θ ρ ρ θ ↓ ↓ ↓ ↓ ↓ → → → → m energy → ˆ = + + + u U u u u = + u U u BASE UNSTEADY (TRADITIONAL) One swoop strategy! (lesser work, time and cost) Cylindrical Compressible Navier-Stokes Solver - a more reliable predicting scheme Predicted Vorticoacoustic and hydrodynamic modes without the need to decompose the equations using the same eigensolver with the accurate prediction of frequency shifts due to mean flow effects. Capturing the fully coupled response between the hydrodynamic and acoustic waves is more reliable than the traditional way of prediction. ONERA’s Cold flow facility When wall injection is turned on, ► When mean flow speed is increased, a leftward shift in frequencies is observed. ► An increase in Reynolds number is accompanied by a slight amplification in temporal growth rate. We also observed that viscosity is a stabilizing factor as it leads to damping in the vorticoacoustic waves. ► Considering the aspect ratio, it is evident that the frequency of the vorticoacoustic modes lower proportionately, but their stability remains unaffected. ► Conversely, hydrodynamic modes become less stable in more elongated chamber. ► PREDICTING COMBUSTION INSTABILITIES During the developmental stages of Titan IV, Ariane 4 and 5, Ares and Reusable SRM, strong vorticoacoustic waves have been reported. So, the stability schemes are targeted towards predicting the various frequency modes in cold flows.
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