Nonlinear Analysis of Rotordynamic Fluid Forces in the Annular Plain Seal by Using Extended Perturbation Analysis of the Bulk-Flow Theory (Influence of Whirling Amplitude in the Case With Concentric Circular Whirl)

Abstract

The bulk-flow theory for the rotordynamic (RD) fluid force has been investigated for many years. These conventional bulk-flow analyses were performed under the assumption and restriction that the whirl amplitude was very small compared to the seal clearance while actual turbomachinery often causes the large amplitude vibration, and these conventional analyses may not estimate its RD fluid force accurately. In this paper, the perturbation analysis of the bulk-flow theory is extended to investigate the RD fluid force in the case of concentric circular whirl with relatively large amplitude. A set of perturbation solutions through third-order perturbations are derived explicitly. It relaxes the restriction of conventional bulk flow analysis, and it enables to investigate the RD fluid force for the whirl amplitude up to about a half of the clearance. Using derived equations, the nonlinear analytical solutions of the flow rates and pressure are deduced, and the characteristics of the RD fluid force are investigated in both radial and tangential directions. The influence of the whirl amplitude on the RD fluid force is explained and validated by comparing with computational fluid dynamics (CFD) analysis. These results are useful for the analysis and prediction of frequency response of the vibration of the rotating shaft system considering the RD fluid forces.

Transient CFD Simulation on Dynamic Characteristics of Annular Seal under Large Eccentricities and Disturbances

“…Energies 2020, 13, x FOR PEER REVIEW 2 of 21 respectively; and M is direct mass coefficient. These five coefficients can be numerically computed by using the bulk flow model [6], CFD simulations by introducing moving reference frame [7,8] or transient method [9] and measured by perturbing the rotor or the stator [10]. (1) However, under actual condition, the static eccentricity of the rotor may exist in annular seal due to the misalignment during assembly process or the effects of various side loads (e.g., impeller weight).…”

“…San Andres and Jeung [17] presented an orbit analysis method based on extended Reynolds equation to investigate force coefficients valid over a wide frequency range of a squeeze film damper bearing with large amplitude and static eccentricity. Ikemoto et al [6] investigated the nonlinear fluid forces for the concentric seal with large whirl amplitude up to about a half of the clearance by using extended perturbation analysis of the bulk flow theory. Currently, the Muszynska's model proposed by Bently and Muszynska [18] is commonly used by researchers as a nonlinear dynamic model.…”

“…Due to the axial-symmetry of seal geometry, as shown in Figure 1, the force coefficients of concentric seals show symmetric or skew symmetric features, as shown in Equation 1, where F x , F y are the X and Y components of fluid forces respectively; K and k denote direct and cross stiffness coefficients, respectively; similarly, direct and cross damping coefficients are expressed as C and c, respectively; and M is direct mass coefficient. These five coefficients can be numerically computed by using the bulk flow model [6], CFD simulations by introducing moving reference frame [7,8] or transient method [9] and measured by perturbing the rotor or the stator [10].…”

Theoretical Solutions for Dynamic Characteristics of Liquid Annular Seals with Herringbone Grooves on the Stator Based on Bulk-Flow Theory

“…Hence, the inlet and outlet pressures of the middle plain part can be regarded as two boundary pressures b1 and b2 . Thus these two boundary pressures can be obtained by solving the conservation equation of the three parts shown as (13) using traversing method. The static characteristics including leakage flow rate and steady-flow velocities of the whole seal will be figured out with the solved boundary pressures.…”

“…Zhai [11,12] developed two different theoretical analysis methods for leakage rate and dynamic characteristics of herringbonegrooved liquid seals and validated the method through comparing the predicted leakage rates and hydraulic forces with the experimental results. Ikemoto [13] derived a set of perturbation solutions for the bulk-flow governing equations of annular plain seals through third-order perturbations. Through the derived equations, the nonlinear analytical solutions of the flow rates and pressure were deduced and the rotordynamic fluid forces in the case of concentric circular whirl with relatively large amplitude were solved and validated by comparisons with CFD results.…”