Prediction models for the dynamical behaviour of multi-phase annular seals

Increasing interest has been devoted in the last two decades in the study and development of multiphase pumps. Multiphase pumps elaborate mixtures of immiscible fluids (both compressible and not) at high speed and power density per stage in order to reduce size and cost. These peculiarities make this kind of turbomachinery very attractive in different industrial sectors such as Oil&Gas, both for subsea and topside applications, chemical and pharmaceutical industry. Of primary importance, in the machine design phase, is the evaluation of the turbomachinery rotordynamic stability, to ensure high reliability and service continuity especially when maintenance works are difficult and expensive. In this respect, the evaluation of the seal rotordynamic coefficients is usually achieved through simplified bulk flow models, based on the Navier-Stokes equations averaged over the fluid meatus (i.e. the rotor-stator clearance); the problem closure is achieved with the aid of both numerical and experimental correlations. Bulk flow models are characterized by some important peculiarities such as ease of use and fastness. They show however some weakness. In the specific case of multiphase pumps, for example, the application of the single-phase correlations to the multiphase field can lead to inaccuracy and misleading results. In this regard, the aim of this doctoral research is to propose a new bulk flow model for the characterization of the structural response of an annular pressure seal operating in the multiphase flow regime. The proposed model is based on the major hypothesis of a smooth stratification of the two fluids. It is hypothesized that the liquid is centrifuged toward the stator, leaving the rotor in contact only with the gas. This assumption allows deriving a two-layer bulk model for each of the two phases.