Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling

Chapter 12: Physics of Premixed Combustion-Acoustic Wave Interactions

Overview

Timothy C. Lieuwen [*]
Georgia Institute of Technology, Atlanta, Georgia
Copyright 2005 by the author. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

Nomenclature

A FL

= flame-surface area

A LC

= limit-cycle amplitude

c

= speed of sound

d

= flame thickness

E

= energy

E a

= overall activation energy

f

= frequency

F

= flame-transfer function

G

= flame-area-transfer function

h

= enthalpy

? h R

= heat of reaction per unit mass of reactant

? I a

= net acoustic energy flux out of the flame

k

= wave number

Ka

= Karlovitz number

Le

= Lewis number

L F

= flame length

= mass flow rate

M

= Mach number

= total mass

Ma

= Markstein number

N

= dimensionless length scale defined in Eq. (12.34)

p

= pressure

Q

= heat-release rate

r

= radial coordinate

R

= jet or flame radius

= reflection coefficient

s

= flame coordinate along the nominal flame surface

S c

= stretched flame speed

S 1 , s L

= laminar flame speed

S t

= Strouhal number (= fL f/ u 0)

St 2

= modified Strouhal number defined in Eq. (12.23)

St c

= convective Strouhal number (= ?L f/ u c)

t

= time

T

= temperature

= transmission coefficient

T b

= burned-gas temperature

u

= velocity

u c

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