A semi-analytical solution for acoustic wave propagation in varying area ducts with mean flow

A semi-analytical solution is developed for the propagation of plane acoustic waves in a varying area duct, sustaining 1-D mean flow with temperature gradient. The can be non-isentropic, such that axial variation and prescribed independently. case an isentropic flow, which are linked, discussed. second order differential equation (ODE) pressure derived from linearised Euler equations frequency domain, neglecting communication between entropy disturbances. This ODE has axially coefficients solved using iterative WKB approximation method. obtained wave-like expressed as superposition downstream upstream propagating wave amplitudes. thus is, at any location, function thermodynamic mean-flow properties wave-number, applied to ducts arbitrarily profiles. For validation model, two shapes linear gradient considered, further simplified depend only on local spatial coordinate inlet conditions. solutions valid “high” frequencies, frequencies considered must both low enough predominantly one-dimensional field, large validity solutions. each geometry, analytical presented along range its validity. predictions compared numerical (LEEs), either account or neglect - coupling; this allows coupling effect evaluated. Within ranges their validity, perform well up Mach-numbers around 0.3. fluctuations ~ 1% mean, acoustic-entropy accuracy prediction was found insignificant Mach numbers less than