Linear flow perturbations in nozzle flows with heat transfer

Solutions for the unsteady flow perturbations in duct flows with area variations are relevant to combustors, automotive exhausts, after-burners and air-intake diffusers. Analytical models for these perturbations were initially restricted to very low frequency and isentropic flows. More recent models extend to any frequency by using a Magnus expansion solution. The current work presents an analytical method which extends to any frequency and to non-isentropic nozzle flows – in this case undergoing steady heat transfer. The quasi-one-dimensional linearised Euler equations are cast in terms of the dimensionless mass, stagnation temperature and entropy fluctuations, which are invariants of the system at zero frequency and with no heat transfer. The resulting first-order system of differential equations is solved using the Magnus expansion, where the perturbation parameters are the normalised frequency and the volumetric heat transfer. This represents the first time that a measure of the flow non-isentropicity (in this case the steady heat transfer) is used as a Magnus expansion parameter. The solution method was applied to converging–diverging nozzle flows with constant heat transfer, showing good agreement with numerical predictions for both subcritical and supercritical flows.