Finding the operating point of Eulerian flow machines

Examples of Eulerian flow machines (EFM) are turbomachines, jet pumps and vortex amplifiers working with incompressible non-cavitating flow. They are ‘Eulerian’ in the sense used by Paynter² in his work on turbomachines subject primarily to dynamic flow forces. Efficient methods are specified in this paper for finding the operating point of an EFM from its characteristics and any two state-defining variables. A trivial example is to find the torque and pressure of a pump when the speed and flow are given. This is simple because the usual constant-speed characterisation favours the solution, but if other pairs of variables are given, the problem is less simple. For jet pumps or the many ‘power fluidic’ devices the variety of problems is much greater because of combinatorial aspects, although the fluid mechanics is analogous to that of the turbomachine. Solution procedures are specified first for turbomachines; there are six ‘algorithms’. For general ‘3-terminal’ EFM (jet-pumps etc) it is shown that there are 108 characterisation formats and that the 30 listed algorithms enable any of them to be solved given any possible variable-pair. Graphical and computational implementations are described