Static and Rotordynamic Characteristics for Two Novel Hole-Pattern Annular Liquid Seals With Circumferentially- /Axially- Oblique Hole Cavities

Non-contacting annular damper seals, such as hole-pattern seals are gradually used in the multiple-stage centrifugal pumps, as a replacement of the conventional labyrinth seal to reduce the fluid leakage and stabilize the rotor-bearing system.The hole-pattern seal (HPS) possesses numerous radial hole cavities on the seal stator, and the geometric constructions of the hole cavity (such as the hole depth and diameter) have been demonstrated to have significant influences on the leakage and rotordynamic characteristic for hole-pattern seals. Due to the inevitable manufacturing variability, particulate impurity deposition and abrasion during operation, these hole cavities can be non-radial, which may affect the performance of the hole-pattern seal. However, the effects of the non-radical hole cavities on the performance of the hole-pattern seal are still unknown due to the lack of numerical or experimental research. Thus, in this paper, two types of novel hole-pattern seals possessing circumferentially- or axially-oblique hole cavities (C-HPS, A-HPS) with various oblique angles were designed and assessed to better understand the influences of the non-radial hole cavities. To assess the leakage and rotordynamic characteristics of the novel liquid hole-pattern seals, a proposed 3D transient CFD-based perturbation method was utilized for the predictions of seal rotordynamic forces coefficients, based on the multi-frequency one-dimensional rotor whirling model and mesh deformation technique. The accuracy and reliability of the present steady and transient numerical methods were demonstrated based on published experimental data of leakage and rotordynamic force coefficients for an experimental hole-pattern seal with radial hole cavities. The leakage and rotordynamic force coefficients were presented for the novel hole-pattern seals with various circumferentially-oblique angle (α = −30°∼30°) or axially-oblique angle (β = −30°∼30°) at various rotational speeds (n = 0.05, 2.0, 4.0, 6.0 krpm), and compared with the ideal hole-pattern seal with radial hole cavities. Numerical results show that the non-radial hole cavity can result in a modest deviation (∼10%) from the design value for the seal leakage, and the oblique direction is crucial for the sealing performance. The flow field in hole cavities and the pressure distribution in the seal clearance suggest that the oblique hole cavities with positive α or β can strengthen the vortex-dissipation of kinetic energy in the hole cavities, thus reduce the leakage (about 5% ∼ 10%). The non-radial cavity with a positive oblique angle results in a modest increase (∼15% for the circumferentially-oblique angle α = 30°, ∼ 6% for the axially-oblique angle β = 30°) in the effective stiffness of the hole-pattern seal, but shows very weak influence (< 4.0%) on the effective damping of the hole-pattern seals, especially for the circumferentially-oblique hole. Therefore, in view of the inevitable manufacturing variability and abrasion effects, a designed non-radial hole with suitable positive α or β (10°∼20°) is beneficial to be applied to new designs in early design phases for the robust design of hole-pattern seals.

A Review of Journal Bearing Induced Nonlinear Rotordynamic Vibrations

Nonlinear elements found in fluid film journal bearings and their surrounding structures are known to induce sub- and super-synchronous, chaos and thermally induced instability responses in rotor-bearing systems. The current review summarizes the literature on journal bearing induced nonlinear, rotordynamic forces, and responses. Nonlinear, thermo-elasto-hydrodynamic (TEHD) aspects of journal bearings has become increasingly important in high-performance turbomachines. These have significant influence on bearing dynamic performance and thermally induced, rotordynamic instability problems. Techniques for developing TEHD bearing models are discussed in the second section. Nonlinear solution methodology, including bifurcation determination and time and frequency domain methods such as harmonic balance, shooting and continuation, etc., is presented in the third section. Numerical tools to determine nonlinear vibration responses, including chaos, along with examples of bearing induced nonlinear vibrations are presented in the fourth and fifth sections, respectively.

Numerical Investigation on the Static and Rotordynamic Characteristics for Two Types of Novel Mixed Helical Groove Seals

Non-contracting annular seals, such as helical groove seals, are widely used between the impeller stages in the liquid turbomachinery to reduce the fluid leakage and stabilize the rotor-bearing system. However, previous literature has expounded that the helical groove seals possess the poor sealing property at low rotational speed condition and face the rotor instability problem inducing by negative stiffness and damping, which is undesirable for liquid turbomachinery. In this paper, to obtain the high sealing performance and the reliable rotordynamic capability for full operational conditions of the machine, two novel mixed helical groove seals, which possess a hole-pattern/pocket-damper stator matching with a helically-grooved rotor, were designed and assessed for a multiple-stage high-pressure centrifugal liquid pump. In order to assess the static and rotordynamic characteristics of these two types of mixed helical groove seals, a three-dimensional (3D) steady CFD-based method with the multiple reference frame theory was used to predict the seal leakage and drag power loss. Moreover, a proposed 3D transient CFD-based perturbation method, based on the multi-frequency one-dimensional stator whirling model, the multiple reference frame theory and a mesh deformation technique, was utilized for the predictions of seal rotordynamic characteristics. The accuracy of the numerical methods was demonstrated based on the experiment data of leakage and rotordynamic forces coefficients of published helical groove seals and hole-pattern seal. The leakage and rotordynamic forces coefficients of these two mixed helical groove seals were presented at five rotational speeds (0.5 krpm, 2.0 krpm, 4.0 krpm, 6.0 krpm, 8.0 kpm) with large pressure drop of 25MPa, and compared with three types of conventional helical groove seal (helical grooves on rotor, stator or both), and two types of damper seals (hole-pattern seal, pocket damper seal with smooth rotor). Numerical results show that the mixed groove seals possess generally better sealing capacity than the conventional helical groove seals, especially at low rotational speed conditions. The circumferentially-isolated cavities (hole or pocket) on the stator enhance the “pumping effect” of the helical grooves for mixed helical groove seals, what is more, the helical grooves also strengthen the dissipation of kinetic energy in the isolated cavities, thus the mixed helical groove seal offers less leakage. Although the mixed helical groove seals possess a slightly larger drag power loss, it is acceptable in consideration of reduced leakage for the high-power turbomachinery. The present novel mixed helical groove seals have pronounced stability advantages over the conventional helical groove seal, due to the obvious large positive stiffness and increased damping. The mixed helical groove seal with the hole-pattern stator and the helically-grooved rotor (HPS/GR) possesses the lowest leakage and the largest effective damping, especially for the high rotational speeds. From the viewpoint of sealing capacity and rotor stability, the novel mixed groove seals are better seal concepts for liquid turbomachinery.

Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor—Part 2: Analysis

An integrated analytical model to predict non-axisymmetric flow fields and rotordynamic forces in a shrouded centrifugal compressor has been newly developed and validated. The model is composed of coupled, conservation law-based, bulk-flow submodels, and the model takes into account the flow coupling among the blades, labyrinth seals, and shroud cavity. Thus, the model predicts the entire flow field in the shrouded compressor when given compressor geometry, operating conditions, and eccentricity. When compared against the experimental data from part 1, the new model accurately predicts the evolution of the pressure perturbations along the shroud and labyrinth seal cavities as well as the corresponding rotordynamic stiffness coefficients. For the test compressor, the cross-coupled stiffness rotordynamic excitation is positive; the contribution of the shroud is the highest; the contribution of the seals is less than but on the same order of magnitude as that of the shroud; and contribution of impeller blades is insignificant. The new model also enables insight into the physical mechanism for pressure perturbation development. The labyrinth seal pressure distribution becomes non-axisymmetric to satisfy mass conservation in the seal cavity, and this non-axisymmetry, in turn, serves as the influential boundary condition for the pressure distribution in the shroud cavity. Therefore, for accurate flow and rotordynamic force predictions, it is important to model the flow coupling among the components (e.g., impeller, shroud, labyrinth seal, etc.), which determines the non-axisymmetric boundary conditions for the components.

Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor—Part 1: Measurement

Centrifugal compressors can suffer from rotordynamic instability. While individual components (e.g., seals, shrouds) have been previously investigated, an integrated experimental or analytical study at the compressor system level is scarce. For the first time, non-axisymmetric pressure distributions in a statically eccentric shrouded centrifugal compressor with eye-labyrinth seals have been measured for various eccentricities. From the pressure measurements, direct and cross-coupled stiffness coefficients have been determined. Thus, the contributions of the pressure perturbations in the shroud cavity and labyrinth seals have been simultaneously investigated. The cross-coupled stiffness coefficients in the shroud and labyrinth seals are both positive and one order of magnitude larger than the direct stiffness coefficients. Furthermore, in the tested compressor, contrary to the common assumption, the cross-coupled stiffness in the shroud is 2.5 times larger than that in the labyrinth seals. Thus, not only eye-labyrinth seals but also shrouds need to be considered in rotordynamic analysis.

Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor: Part 1 — Measurement

Centrifugal compressors can suffer from rotordynamic instability. While individual components (e.g., seals, shrouds) have been previously investigated, an integrated experimental or analytical study at the compressor system level is scarce. For the first time, non-axisymmetric pressure distributions in a statically eccentric shrouded centrifugal compressor with eye-labyrinth seals have been measured for various eccentricities. From the pressure measurements, direct and cross-coupled stiffness coefficients in the shrouded centrifugal compressor have been determined. Thus, the contributions of the pressure perturbations in the shroud cavity and labyrinth seals have been simultaneously investigated. The cross-coupled stiffness coefficients in the shroud and labyrinth seals are both positive and one order of magnitude larger than the direct stiffness coefficients. Furthermore, in the tested compressor, contrary to the common assumption, the cross-coupled stiffness in the shroud is 2.5 times larger than that in the labyrinth seals. Thus, the shroud contributes more to rotordynamic instability than the eye-labyrinth seals.