Analytical solutions for the acoustic field in thin annular combustion chambers with linear gradients of cross-sectional area and mean temperature

Predictions of thermoacoustic instabilities in annular combustors are essential but difficult. Axial variations flow and thermal parameters increase the cost numerical simulations restrict application analytical solutions. This work aims to find approximate solutions for acoustic field ducts with linear gradients axially non-uniform cross-sectional area mean temperature. These can be applied low-order network models enhance ability methods solve instability problems real chambers. A modified WKB method is used wave equation field, an solution a wide range applications derived. The derivation equations requires assumptions such as low Mach number, high frequency small non-uniformity. Cases arbitrary distributions surface temperature solved by piecewise long satisfied along entire chamber.