Design and Analysis of CFD Experiments for the Development of Bulk-Flow Model for Staggered Labyrinth Seal

Nowadays, bulk-flow models are the most time-efficient approaches to estimate the rotor dynamic coefficients of labyrinth seals. Dealing with the one-control volume bulk-flow model developed by Iwatsubo and improved by Childs, the “leakage correlation” allows the leakage mass-flow rate to be estimated, which directly affects the calculation of the rotor dynamic coefficients. This paper aims at filling the lack of the numerical modelling for staggered labyrinth seals: a one-control volume bulk-flow model has been developed and, furthermore, a new leakage correlation has been defined using CFD analysis. Design and analysis of computer experiments have been performed to investigate the leakage mass-flow rate, static pressure, circumferential velocity, and temperature distribution along the seal cavities. Four design factors have been chosen, which are the geometry, pressure drop, inlet preswirl, and rotor peripheral speed. Finally, dynamic forces, estimated by the bulk-flow model, are compared with experimental measurements available in the literature

Thermo-elasto bulk-flow model for labyrinth seals in steam turbines

Over the last few decades, the increasing demand on efficiency and performance for steam turbines has resulted in OEMs operating machines near critical conditions of their structural and thermal capabilities. In this paper, a new thermo-elasto bulk-flow model for labyrinth seals has been introduced. The model includes the bulk-flow model for estimating the dynamic coefficients, heat transfer model for evaluating the temperature distribution in the rotating and stationary parts and structural-mechanics model for calculating the radial growth. By considering a staggered labyrinth seal installed in the balancing drum of a steam turbine, different operating conditions, such as the boundary pressure, rotational speed and inlet pre-swirl ratio, as well as the stability of the seal are investigated in this study

Rotordynamic Characterization of a Staggered Labyrinth Seal: Experimental Test Data and Comparison With Predictions

As well known, the stability assessment of turbomachines is strongly related to internal sealing components. For instance, labyrinth seals are widely used in compressors, steam and gas turbines and pumps to control the clearance leakage between rotating and stationary parts, owing to their simplicity, reliability and tolerance to large thermal and pressure variations. Labyrinth seals working principle consists in reducing the leakage by imposing tortuous passages to the fluid that are effective on dissipating the kinetic energy of the fluid from high-pressure regions to low-pressure regions. Conversely, labyrinth seals could lead to dynamics issues. Therefore, an accurate estimation of their dynamic behavior is very important. In this paper, the experimental results of a long-staggered labyrinth seal will be presented. The results in terms of rotordynamic coefficients and leakage will be discussed as well as the critical assessment of the experimental measurements. Eventually, the experimental data are compared to numerical results obtained with the new bulk-flow model (BFM) introduced in this paper

Sensitivity analysis of the one-control volume bulk-flow model for a 14 teeth-on-stator straight-through labyrinth seal

Since the 80s, academic research in the rotordynamics field has developed mathematical treatment for the prediction of the dynamic coefficients of sealing components. Dealing with the straight-through labyrinth seal, Iwatsubo [1], at a first stage, and Childs [2], later on, have developed the one-control volume bulk flow model. The model allows evaluating the surrounding fluid forces acting on the rotor, analyzing the fluid dynamics within the seal: the continuity, circumferential momentum and energy equations are solved for each cavity. To consider axial fluid dynamics, correlations, aiming to estimate the leakage and the pressure distribution, are required. Several correlations have been proposed in the literature for the estimation of the leakage, of the kinetic energy carry-over coefficient (KE), of the discharge coefficient and of the friction factor. After decades of research in the field of seal dynamics, the bulk-flow model has been confirmed as the most popular code in the industries, however, it is not clear which is the best set of correlations for the prediction of seal dynamic coefficients. This paper allows identifying the most accurate combination of correlations to be implemented in the bulk-flow model. The correlations are related to: the leakage formula, the flow coefficient, the KE and the friction factor. Investigating the results of several models (32 models), which consider different sets of correlations, in comparison to the experimental data (performed by General Electric Oil & Gas), it is possible to observe the dependence, of the model correlations, on the operating conditions. The experimental results, performed using a 14 teeth-onstator labyrinth seal, investigate several operating conditions of pressure drop

Rotordynamic Characterization of Labyrinth Seals in Steam Turbines: Effects of Thermal and Mechanical Loads

Over the last few decades, the increasing demand on efficiency and performance for steam turbines has resulted in OEMs operating machines near critical conditions of their structural and thermal capabilities. Consequently, a more accurate estimation of the dynamic behavior of the machine has become mandatory as well as the stability assessment. Steam turbines are subjected to high temperatures, high pressures and centrifugal forces that could change the nominal geometry, especially the clearance profile in correspondence of the sealing components, occasionally generating a convergent or divergent annulus. In this paper, a new thermo-elasto bulk-flow model for labyrinth seals has been introduced. The model includes the bulk-flow model for estimating the dynamic coefficients, heat transfer model for evaluating the temperature distribution in the rotating and stationary parts and structural-mechanics model for calculating the radial growth. By considering a staggered labyrinth seal installed in the balancing drum of a steam turbine, different inlet pre-swirl ratios, as well as the stability of the seal are investigated in this paper. The model can be extremely useful for the dynamic characterisation of a wide class of labyrinth seals considering the effect of the surrounding environment on the rotordynamic coefficient prediction

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