Investigation of the Dynamic Characteristics of an Eccentric Annular Seal on the Basis of a Transient CFD Method with Three Whirl Models

Many annular seals suffer eccentricity because of rotor–stator misalignment or the deflection of a flexible rotor, which has a strong influence on the vibration characteristics and stability of rotating machines. In this article, a transient CFD method based on three whirl models is employed to research the dynamic characteristics of annular seals at various static eccentricities. The influence of the whirl amplitude on the dynamic characteristics of eccentric annular seals are also explored. The results of the transient CFD method are compared with the bulk flow model results and the experimental results. It is shown that the transient CFD method possesses high prediction precision for direct damping, with a maximum error of 25%. Negative kyx increases by 166% when the static eccentricity ratio is increased from 0 to 0.5. The dynamic characteristics of the annular seal operating at high static eccentric ratio are sensitive to whirl amplitude, and the model with an amplitude of 1% Cr has great advantages for the prediction of direct virtual-mass, while the model with an amplitude of 10% Cr has great advantages for the prediction of cross-coupled damping.

Static Performance of Smooth Liquid Annular Seals in the Transition and Turbulent Regimes

Static test results are presented for smooth annular seals with a length-to-diameter ratio of 0.50, radius R = 51.00 mm, at the nominal radial clearance Cr = 0.2032 mm. Tests were conducted for angular shaft speeds; ω = 2, 4, 6, 8 krpm, axial pressure drops; ΔP = 2.1, 4.13, 6.21, 8.27 bars, and eccentricity ratios ϵ0 = e0/Cr = 0.00, 0.27, 0.53, 0.8 where e0 is the static eccentricity. Three pre-swirl inserts were used to target zero, medium, and high (0., 0.4, and 0.8) pre-swirl ratios for a set of pre-determined operating conditions with ISO VG 2 oil at 46.1°C. Pitot tubes measured the circumferential velocity at separate upstream and downstream seal locations and were used to calculate pre-swirl ratio, PSR = vinlet/Rω, and outlet-swirl ratio, OSR = voutlet/Rω. For all tested pre-swirl inserts, PSR tended to converge to 0.4∼0.5 as ω increased. PSR and OSR were poorly correlated. Volumetric leakage rate Q ˙ versus pressure differential ΔP was measured. The measured vector Reynolds number Re, combining the axial and circumferential Reynolds numbers ranged from ∼1000 to ∼3500. Based on Zirkelback and San Andrés 1996 publication, almost all of the flow regime is predicted to lie in the transition regime, with fewer points in the turbulent regime. Generally, the seals’ static centering properties were obtained by applying a static load Fs and measuring the resulting displacement vector e0. At many low-speed, low-ΔP test conditions, the seal would not remain in the desired centered or near-centered position and had to be forced into place with a centering force Fs. The authors believe that the observed de-centering effects resulted from test operations in the transition flow regime where the friction factor λ does not drop with increasing ΔP and increasing Re. A positive centering Lomakin effect requires that λ drop with increasing axial Reynolds number. The seals had positive centering effects over a large portion of the predicted transition flow regime, supporting the view that the shift from transition-to-turbulent flow regularly occurred at lower Re values than the Re = 3000 boundary used by Zirkleback and San Andrés.

Orbit Decomposition Method for Rotordynamic Coefficients Identification of Annular Seals

The elliptical orbit whirl model is widely used to identify the frequency-dependent rotordynamic coefficients of annular seals. The existing solution technique of an elliptical orbit whirl model is the transient computational fluid dynamics (CFD) method. Its computational time is very long. For rapid computation, this paper proposes the orbit decomposition method. The elliptical whirl orbit is decomposed into the forward and backward circular whirl orbits. Under small perturbation circumstances, the fluid-induced forces of the elliptical orbit model can be obtained by the linear superposition of the fluid-induced forces arising from the two decomposed circular orbit models. Due to that the fluid-induced forces of circular orbit, the model can be calculated with the steady CFD method, and the transient computations can be replaced with steady ones when calculating the elliptical orbit whirl model. The computational time is significantly reduced. To validate the present method, its rotordynamic results are compared with those of the transient CFD method and experimental data. Comparisons show that the present method can accurately calculate the rotordynamic coefficients. Elliptical orbit parameter analysis reveals that the present method is valid when the whirl amplitude is less than 20% of seal clearance. The effect of ellipticity on rotordynamic coefficients can be ignored.

Numerical Analyses of Static Characteristics of Liquid Annular Seals Based on 2D LBM-LES Model

Static characteristics and leakage flow rates of liquid annular seals have great influences on the hydraulic efficiency of turbomachinery. In this paper, a two-dimensional (2D) mathematical model for predicting the leakage flow rates and static characteristics of liquid seal is established, based on the lattice Boltzmann method (LBM) combined with the D2G9 velocity model for incompressible fluid and large eddy simulation (LES) turbulence model, in which the transformation equation of reference pressure is developed with the Bernoulli equation. Moreover, the proposed model is validated by comparing with the experimental results, calculation results based on the finite volume method (FVM), and the results based on the empirical method of three seals under different operating conditions. The comparisons show that the maximum deviation in leakage prediction of the calculating model based on 2D LBM is 4%, and this calculating model will effectively improve the leakage prediction accuracy of the seals compared with the FVM and theoretical method.

Transient simulation on dynamic response of liquid annular seals

Transient change of the operating parameters has a serious influence on the stability of liquid annular seals. Take the liquid annular seals as a research object, a numerical method based on six-degree-of-freedom (6DOF) to analyze the dynamic response of liquid annular seals under gravity impact load. The variations of the force of liquid seal and pressure as well as the axis trajectory in time history are investigated. The influence of different sealing clearance、different liquid viscosity and different rotor speed is also studied. The results show that the maximum sealing pressure and sealing force of gravity direction will increase greatly in a very short time and then reduce rapidly. When sealing clearance increases, the displacement response amplitudes of axis trajectory, the maximum sealing force of gravity direction and maximum sealing pressure also increase. When liquid viscosity increases, the displacement response amplitudes of axis trajectory, the maximum sealing force of gravity direction and maximum sealing pressure decrease. We also found that different rotor speed has almost no influence on the maximum sealing force of gravity direction and maximum sealing pressure.

A Comparison of Static and Rotordynamic Characteristics for Two Types of Liquid Annular Seals With Parallelly Grooved Stator/Rotor

Liquid annular seals with parallelly grooved stator or rotor are used as replacements for smooth plain seals in centrifugal pumps to reduce leakage and break up contaminants within the working fluid. Parallelly grooved liquid annular seals have advantages of less leakage and smaller possibility of abrasion when the seal rotor–stator rubs in comparison to smooth plain seals. This paper deals with the static and rotordynamic characteristics of parallelly grooved liquid annular seals, which are limited in the literature. Numerical results of leakage flow rates, drag powers, and rotordynamic force coefficients were presented and compared for a grooved-stator/smooth-rotor (GS-SR) liquid annular seal and a smooth-stator/grooved-rotor (SS-GR) liquid annular seal, utilizing a modified transient computational fluid dynamics-based perturbation approach based on the multiple-frequency elliptical-orbit rotor whirling model. Both liquid annular seals have identical seal axial length, rotor diameter, sealing clearance, groove number, and geometry. The present transient computational fluid dynamics-based perturbation method was adequately validated based on the published experiment data of leakage flow rates and frequency-independent rotordynamic force coefficients for the GS-SR and SS-GR liquid annular seals at various pressure drops with differential inlet preswirl ratios. Simulations were performed at three pressure drops (4.14 bar, 6.21 bar, and 8.27 bar), three rotational speeds (2 krpm, 4 krpm, and 6 krpm) and three inlet preswirl ratios (0, 0.5, and 1.0), applying a wide rotor whirling frequency range up to 200 Hz, to analyze and compare the influences of operation conditions on the static and rotordynamic characteristics for both the GS-SR and SS-GR liquid annular seals. Results show that the present two liquid annular seals possess similar sealing capability, and the SS-GR seal produces a slightly larger (∼2–10%) drag power loss than the GS-SR seal. For small rotor whirling motion around a centered position, both seals have the identical direct force coefficients and the equal-magnitude opposite-sign cross-coupling force coefficients in the orthogonal directions x and y. For all operation conditions, both the GS-SR and SS-GR liquid annular seals possess negative direct stiffness K and positive direct damping C. The GS-SR seal produces purely positive Ceff throughout the whirling frequency range for all operation conditions, while Ceff for the SS-GR seal shows a significant decrease and transitions to negative value at the crossover frequency fco with increasing rotational speed and inlet preswirl. From a rotordynamic viewpoint, the GS-SR liquid annular seal is a better seal concept for pumps.

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

Annular seals of turbomachinery usually suffer from various degrees of eccentricities and disturbances due to the rotor–stator misalignment and radial loads, while the discussion of annular seal under both large static eccentricities and dynamic disturbances is relatively limited. In this paper, the applicability of linear assumption and reliability of nonlinear dynamic model for eccentric annular seals under large eccentricities and disturbances is discussed based on the investigation of seals with various rotor motions through computational fluid dynamics (CFD). After the validation of transient CFD methods by comparison with experimental and bulk theory results, the dynamic behaviors of annular seal are analyzed by adopting both direct transient simulations and the nonlinear Muszynska model. The results show that the nonlinear dynamic model based on rotor circular whirls around seal center can predict the fluid excitations of different types of rotor motions well under small static eccentricities, while it is limited severely with large static eccentricities, which indicates that the dynamic characteristics of annular seal under large eccentricities are related with the rotor’s motion ways. The paper provides a reference for studies of rotor–seal system with complex rotor motions considering radial loads or running across the resonance region.