CONTROL-ORIENTED HIGH-FREQUENCY TURBOMACHINERY MODELING - SINGLE-STAGE COMPRESSION SYSTEM ONE-DIMENSIONAL MODEL

In this paper, a one-dimensional unsteady compressible viscous flow mo del of a generic compression system previously developed by the author s is applied to a multistage axial compressor experimental rig configu red for single-stage operation. The required model parameters and maps are identified from experimental data. The resulting model is an expl icit system of nine first-order ODEs. The model inputs are compressor speed, nozzle area, compressor discharge bleed area, plenum bleed area , inlet total pressure and entropy, and nozzle and bleed exit static p ressures. The model and experimental data are compared with respect to both open-loop uncontrolled and closed-loop controlled behaviors. The se comparisons focus on (i) forced transients and (ii) global nonlinea r dynamics and bifurcations. In all cases the agreement between the mo del and experimental data is excellent. Of particular interest is the ability of the model, which does not include any hysteretic maps, to p redict experimentally observed hysteresis with respect to the onset an d cessation of surge. This predictive capability of the model manifest s itself as the coexistence of a stable equilibrium (rotating stall) a nd a stable periodic solution (surge) in the model at a single fired s et of system input values. Also of intel est is the fact that the cont rollers used for closed-loop comparisons were designed directly from t he model with no a posteriori tuning of controller parameters. Thus, t he excellent closed-loop comparisons between the model and experimenta l data provide strong evidence in support of the validity of the model for use in di, ect model based controller design. The excellent agree ment between the model and experimental data summarized above is attri buted in large part to the use of effective lengths within the model, as functions of axial Mach number and nondimensional compressor rotati onal speed, as prescribed by the modeling technique. The use of these effective lengths proved to be far superior to the use of physical len gths. The use of these effective lengths also provided substantial imp rovement over the use of physical lengths coupled with fixed first-ord er empirical fags, as proposed by other authors for the modeling of ob served compressor dynamic lag. The overall success of this model is be lieved to represent a positive first step toward a complete experiment al validation of the approach to control-oriented high-frequency turbo machinery modeling being developed by the authors.