A sound wave propagating in an inhomogeneous duct consisting of two semi-infinite
uniform ducts with a smooth transition region in between and which carries a steady
flow is considered. The duct walls may be rigid or compliant. For an irrotational
sound wave it is shown that the three properties of the title are closely related, such
that the validity of any two implies the validity of the third. Furthermore it is shown
that the three properties are fulfilled for lossless locally reacting duct walls provided
the impedance varies at most continuously. For piecewise-continuous wall properties
edge conditions are essential. By an analytic continuation argument it is shown that
reciprocity remains true for walls with loss. For rotational flow, energy conservation
theorems have been derived only with the help of additional potential-like variables.
The inter-relation between the three properties remains valid if one considers these
additional variables to be known. If only the basic gasdynamic variables in both half-ducts are known, one cannot formulate an energy conservation equation; however,
reciprocity is fulfilled.
Modelling and small-signal analysis of a grid connected doubly-fed induction generator
