Acoustic Analysis of Gas Turbine Combustion Instability
Department of Mechanical Engineering
• Back ground Unsteady flow motions in combustion chambers, commonly known as combustion instabilities, represent one of the most serious problems in the development of gas turbine engines.
PENNSTATE
Acoustic Analysis of Gas Turbine Combustion Instability
Department of Mechanical Engineering
Time Elapsed
• Frequency spectra of pressure oscillations in unstable combustors
Frequency
PENNSTATE
Acoustic Analysis of Gas Turbine Combustion Instability
Department of Mechanical Engineering
• Consequence of combustion instability – – – –
Excessive vibration Enhanced heat transfer Reduced operating regime Negative impact on NOx emission control
• Project goal – To establish a generalized methodology for predicting, understanding, and analyzing gas turbine combustion instability
• Objectives – To determine linear stability characteristics of combustion chambers – To assess the effects of all known processes on chamber dynamics
PENNSTATE
Classical Approach for Combustor Stability Analysis (1/2)
Department of Mechanical Engineering
•• assumptions: assumptions: 1. 1. simple simple geometry geometry 2. 2. small small Mach Mach number number and and mean-flow mean-flow variations variations ∞
•• normal-mode normal-mode expansion: expansion: p′(r, t ) = p ∑η n (t )ψ n (r ) n =1
nπ L
ψ n ( r ) = cos
•• spatial spatial averaging averaging 2 d ηn 2 + ω η n = Fn where 2 dt
cos ( mθ ) x J m (κ ms r ) sin ( mθ )
a2 Fn = − { hψ n dV + ∫∫ fψ n dS} pEn2 ∫
PENNSTATE
Classical Approach for Combustor Stability Analysis (2/2)
Department of Mechanical Engineering
Nonlinear Nonlinear behavior behavior Linear Linear Stability Stability Behavior Behavior
η n (t ) = ηˆ n e ia K
nt
where
K n = ( Ω n − iα n ) / a
a2 hˆ ( r ) fˆ ( r ) Ωn = ωn + { ψ n dV + ∫∫ ψ dS } 2ω n p E n2 ∫ ηˆ n ηˆ n n
a2 hˆ ( i ) fˆ ( i ) αn = − { ψ n dV + ∫∫ ψ n dS } 2ω n p E n2 ∫ ηˆ n ηˆ n
Ref: Culick, F. E. C., and Yang, V. (1995), “Overview of Combustion Instabilities in Liquid Propellant Rocket Engines”, Liquid Rocket Engine Combustion Instability, Progress in Aeronautics and Astronautics, Vol.169, pp. 3-37.
PENNSTATE
Acoustic Analysis of Gas Turbine Combustion Instability
Department of Mechanical Engineering
• Technical approach – Derivation of a wave equation governing unsteady motions in two-phase mixtures – Discretization of combustion chamber into small cells – Decomposition of flow variables in three modes - acoustic
- vortical
- entropy
– Implementation of interfacial boundary conditions to determine complex wave numbers characterizing chamber acoustic characteristics
PENNSTATE
Acoustic Analysis of Gas Turbine Combustion Instability
• Results obtained – Mechanistic understanding and quantitative prediction of acoustic instabilities in gas turbine combustors – Optimization of combustor design in terms of acoustic stability behavior
Acoustic Field in Penn. State Lean Premixed Combustor
PENNSTATE
(first longitudinal mode)
Department of Mechanical Engineering natural gas choked venturi
hot compressed air
swirl injector
24 mm
combustion chamber
choked exit
45 mm x 584 mm
x=0
Pressure (exptl.) Pressure Velocity
1.2 1 0.8 0.6 0.4
0.2 choked venturi 0
0.1
0.2
dump plane 0.3
0.4
0.5
Axial coordinate
0.6
acoustic properties with premixer damping
Normalized amplitudes
Normalized amplitudes
acoustic properties without premixer damping 1.4
0.7
0.8
178 to 356 mm
38 mm
1.5
Pressure (exptl.) Pressure Velocity
1
0.5
choked venturi 0
0.1
0.2
dump plane 0.3
0.4
0.5
Axial coordinate
0.6
0.7
0.8
PENNSTATE
Acoustic Field in Penn. State Lean Premixed Combustor (first tangential mode)
Department of Mechanical Engineering
A-A A-A
Ω = Ω r + iΩi frequency: frequency: 11310 11310 (Hz) (Hz) growth growth constant: constant: 3.3 3.3 (s (s-1-1))
B-B B-B
C-C C-C
PENNSTATE
Acoustic Field in Penn. State Lean Premixed Combustor (first radial mode)
