A method for modeling the dynamics of industrial pumping systems is presented. The approach extends existing models for aero-engine like applications to capture dynamic features of interest in industrial, ground-based, applications. Those include the driver-driven (e.g., turbine-pump or compressor) interaction, the driver speed regulation subsystem, and their impact on stability. The method utilizes a lumped parameter modeling approach that involves developing and analyzing a set of nonlinear ordinary differential equations which describe the system dynamics.
A model of a baseline industrial pumping system comprised of a turbine driving a process compressor is formulated first. Components in the compressor flow path include an inlet duct, a plenum, and a discharge valve. The resulting model captures the system’s instability onset point, the post-stall behavior, and the sensitivity to system parameters. Two non-dimensional groups are found to play a dominant role in characterizing the overall dynamics: the ratio of fluid compliance to fluid inertia on the compressor side (B-parameter), and the ratio of the mechanical inertia of the rotating assembly to the fluid inertia. Low values of the B-parameter have a strong stabilizing effect and are associated with high frequency surge oscillations. In contrast, low values of the mechanical to fluid inertia ratio have a stabilizing effect only in a limited region of the compressor operating range, and have little effect on surge frequency. For the baseline system considered in this study, stabilizing effects of these two ratios were observed at values less than 0.4 and 0.2 respectively.
The baseline system model is then expanded to include a turbine speed controller. This allows examination of large transient events such as station shutdown and the phenomena of turbine hunting. It is found that the parameters of the turbine speed controller can affect the stability during such transients, but have little impact on the post-stall behavior.