On the thermodynamic process in the bulk-flow model for the estimation of the dynamic coefficients of labyrinth seals

The influence of sealing components on the stability of turbomachinery has become a key topic because oil and gas market is increasingly requiring high rotational speed and high efficiency, which implies the clearance reduction in the seals. The accurate prediction of the effective damping of the seals is critical to avoid instability issues. In recent years, "negativeswirl" swirl brakes have been employed to reverse the circumferential direction of inlet flow, changing the sign of the cross-coupled stiffness coefficients and generating stabilizing forces. Industries started to investigate, by experiments, the dynamical behavior of labyrinth seals. The experimental results of a 14 teeth-on-stator labyrinth seal with nitrogen, performed in the high-pressure seal test rig owned by GE Oil&Gas, are presented in the paper. Both experimental tests with positive and negative pre-swirl values were performed in order to investigate the pre-swirl effect on the cross-coupled stiffness coefficients. Concerning with the dynamic characterization of the seal, the fluid-structure interaction into the seal can be modelled by the bulk-flow numeric approach that is still more time efficient than computational fluid dynamics (CFD). Dealing with the onecontrol volume bulk-flow model, the thermodynamic process in the seal is considered isenthalpic, despite an expected enthalpy variation along the seal cavities, both for gas and steam applications. In this paper, the authors improve the state-of-the-art onecontrol volume bulk-flow model [1], by introducing the effect of the energy equation in the zero-order solution. In this way, the real gas properties are evaluated in a more accurate way because the enthalpy variation, expected through the seal cavities, is taken into account in the model. The authors, considering the energy equation only in the zero-order solution, assume that the enthalpy is not a function of the clearance perturbation (i.e. of the rotor perturbed motion). The energy equation links the continuity and the circumferential momentum equations. The density, in the leakage correlation, depends on the enthalpy, which is calculated (in the energy equation) on the basis of the circumferential velocity and of the fluid/rotor shear stress. Therefore, the leakage mass-flow rate and the fluid thermodynamic properties depend, indirectly, on the shear stresses. This fact is proved in the literature by several CFD simulations that investigate the leakage in the straightthrough labyrinth seals, hence, the energy equation allows to better characterize the physics of the problem. Overall, by taking into account the energy equation, a better estimation of the coefficients in the case of negative pre-swirl ratio has been obtained (as it results from the comparison with the experimental benchmark tests). The numerical results are also compared to the state-of-the-art bulk-flow model developed by Thorat and Childs (2010), highlighting the improvement obtained.