Compressor Maps and Coupling: Symmetry, Paradox, and Clarity

The most common compressor map framework, referred to here as the β-framework, will be shown to suffer from limitations that grow more troublesome in the multiple-map environment. When maps are coupled in series in the β-framework, it is very common to find operating points that are physically unrealizable, but these cannot generally be avoided without first generating them. A feasible situation is described in which the β-framework leads to an apparent physical paradox. In the proposed S-framework, the map itself is recast in terms of independent variables (corrected speed and exit corrected flow) and dependent variables (inlet corrected flow and temperature ratio). The propagation of information in map coupling is split into an upstream-marching corrected flow ‘flux’ and a downstream-marching temperature ‘flux’. Finding the equilibrium operating point requires only finding a simple intersection between curves. The S-framework is then developed further into a more compact S’-framework that exhibits a natural set of qualitative symmetries. The S- and S’-frameworks are shown to simplify compressor map expression, resolve the problems shown with the β-framework, and aid intuition with regard to off-design phenomena. The resolution of the paradox using the S’-framework is a new description of multistage compressor performance hysteresis.