Mobius transformation between reflection coefficients at upstream and downstream sides of flame in thermoacoustics systems

• An alternative approach to assess the conditions for the onset of thermoacoustics combustion instability is proposed. The method is based on the analysis of the relation between the reflection coefficient of combustor upstream section (subsystems) with respect to the burner/flame, Rup, and the input reflection coefficient, Rin, as observed from the inlet of the burner with flame and all downstream subsystems of a combustion appliance. The instability of the combustor can be determined by evaluating the system dispersion relation expressed in the terms of these two reflection coefficients. The properties of the relation between Rin, the reflection coefficient of the burner downstream subsystems, Rdn, and elements of the flame transfer matrix, TM, of the burner are investigated. This relation has the form of the well-known Mobius transformation. Using the well-developed theory of the transformation, we derive the necessary conditions of Rdn to ensure that the magnitude of Rin becomes less than 1 in a frequency range. This condition results in a passive thermoacoustics stability of the system's operation. Furthermore, an optimum value of Rdn is derived which provides a minimum value of Rin at given entries of the burner TM. The practical application of the developed theory provides suitable criteria and guidelines for designing passive acoustic properties at the downstream side of the combustion appliance.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Energiteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Energy Engineering (hsv//eng)

Nyckelord

Combustion

Flame transfer function

Instability

Passive termination

Acoustic properties

Combustors

System stability

Thermoacoustics

Transfer matrix method

Burner flames

Combustion instabilities

Condition

Down-stream

Flame transfer functions

Input reflection coefficient

Mobius transformations

Thermoacoustic combustion

Thermoacoustic systems

Reflection

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