Sensitivity Analysis of the Static and Rotordynamic Characteristics on Geometric Parameters for a Supercritical Carbon Dioxide Hole-Pattern Damper Seal
Authors: Li Zhigang , Zhang Zihan , Li Jun 
Published: August 2024

Abstract
Hole-pattern damper seal (textured stator with numerous circular-hole cavities and smooth rotor) is a typical annular damper seal that is gradually used in modern turbomachinery as a replacement of the conventional labyrinth seal to reduce the fluid leakage and stabilize the rotor-bearing system. It has been demonstrated that hole geometric design parameters (hole diameter and hole depth) have a decisive influence on the sealing capability and rotordynamic performance of hole-pattern damper seals, especially for the balance piston seal of high pressure turbomachinery where the seal sustains the quite high pressure difference and fluid density. In this paper, geometric configurations of hole-pattern damper seal with various hole diameter and depth were designed for the balance piston in a 14-MW supercritical CO2 turbine. To enhance the seal net damping capability at high inlet preswirl condition, a straight swirl brake also was designed and employed at seal entrance for each seal configuration. To better understand the sensitivity of geometric design parameters (hole diameter and depth) on the leakage and rotordynamic characteristics of the hole-pattern seals with inlet preswirl, a leakage computational model based on mesh deformation technology was proposed to predict the leakage flowrate with continuously varying hole depth, and a transient computational fluid dynamics (CFD)-based perturbation method based on the multiple-frequency elliptical-orbit rotor whirling model also was proposed to predict the frequency-dependent rotordynamic force coefficients. To take into account of real gas effect with high accuracy, a table look-up procedure based on the National Institute of Standards and Technology (NIST) database was implemented, using an in-house code, for the fluid properties of CO2 in both supercritical and subcritical conditions. The accuracy and availability of the present numerical methods and seal model were demonstrated based on the published experimental data of the leakage and force coefficients of hole-pattern damper seals with different hole diameters and depths. The leakage flow rates were predicted for hole-pattern seals with five hole diameters (D = 3.2 mm, 4.8 mm, 6.4 mm, 9.6 mm, and 12.8 mm) and continuously varying hole depth, the rotordynamic forces coefficients and response force vectors were presented for seals with the present five types of hole diameters and five hole depths (H = 0.8 mm, 1.6 mm, 3.2 mm, 4.8 mm, and 6.4 mm). Results show that the aspect ratio (Ar, the ratio of hole depth to diameter) is the key parameter affecting the seal leakage performance. Although the supercritical carbon dioxide (sCO2) hole pattern seal with smaller diameters (D = 3.2 mm, 4.8 mm) possesses the best sealing performance, especially at the range of Ar = 0.15–0.5, the leakage characteristics show a strong sensitivity to the aspect ratio: when Ar is less than 0.15 or more than 0.5, the leakage flowrate has a sharp increase (&gt;14%). The hole depth and hole diameter possess a significant influence on the rotordynamic characteristics of sCO2 hole-pattern seals. For the present seal configurations in this paper, the seal with the shallower hole depth (H = 0.8 mm) or the larger hole diameter (D = 12.8 mm) has the best rotordynamic behavior, which possess the lower direct stiffness Kxx and larger effective damping Ceff.