Mathematical model of brush seals for gas turbine engines: A nonlinear analytical solution

Presented herein is a mathematical model employing differential equations formulation for brush seals used in gas turbine engines. These components are used to seal the bearing chamber from the environment and reduce the loss of lubricant in the atmosphere, ensuring a MTBR long enough to have required the change the seals only during the engine overhaul operation. The model assumes a single curved bristle loop in the form of a curved-bridge beam subjected to the influences of complex external loads (static and dynamic). Further, a model for clustered bristles is proposed. Specifically, the static forces acting on the curved-bridge beam include the weight of the oil capillary attached to the beam, the weight of the beam itself, the capillary force developed between the surfaces of the bristles in the brush and the temperature gradient. The dynamic forces include the leakage oil pressure and the rotation of the shaft. This complex loading induces a nonlinear large deflection on the curved-bridge beam. Also, the temperature gradient present on the bristles during the gas turbine engine operation generates a change in the geometry of the beam and in the magnitude of the forces acting on the bristles modeled as beams. In the present model, the weights are assumed as uniformly distributed forces on the surface of the beam while the capillary forces and the force generated by the rotating shaft are considered to be non-uniform. The equation expressing the curvature of the beam under general loading force is developed and one can choose the appropriate method of solving the generated differential equation after the expression of the general force is defined. Hence, the ordinary differential equation describing the nonlinear large deflection of the curved-bridge beam will be derived using general nonlinear elasticity theory.

Rotating Brush Seal Design and Performance Testing

Brush seals are widely used in various turbomachinery applications because they provide reduced leakage than labyrinth seals in a compact space. Brush seals are generally mounted on static components and their flexible bristle tips engage the rotor to form a dynamic seal. In this paper, development of a brush seal mounted on a rotor is discussed. Benefits of this enhancement to brush seal include avoiding localized rubs on the rotor, which reduces heating of a local spot and resulting rotor bow and instabilities. The bristles are angled circumferentially instead of axially and are supported by a conical backplate. Under rotation, the bristles are pushed towards the backplate by the centrifugal force. Seal configurations are designed to fit into interstage and inter-shaft locations. A modeling approach for predicting stiffness and operating stresses in these seals also is outlined. A test setup is developed to characterize the performance of rotating brush seals under engine-representative centrifugal force and pressure differentials. Presented results demonstrate that brush seal can achieve tight effective gaps and desired performance after undergoing initial wear.

Numerical Investigations on the Leakage Flow Characteristics of Brush Seal Based on the Three-Dimensional Staggered Tube Bundle Model

To accurately predict the leakage flow and resistance characteristics of brush seals, the multiblock structured mesh and the mesh motion technique are applied to the three-dimensional (3D) staggered tube bundle model of brush seals. The multiblock structured mesh can easily add nodes and set boundary layers in the interbristle gap between adjacent bristles, which can ensure good mesh quality (orthogonal angle and expansion ratio). The mesh motion technique realizes the overall axial compactness of the bristle pack. The effects of pressure ratio Rp, sealing clearance c, and bristle pack compactness on the leakage flow and resistance characteristics are investigated. To analyze the aerodynamic resistance of the brush seals, Euler number (Eu) is applied in this study. The numerical results are in good agreement with the experimental data. Thus, the accuracy of the presented numerical method is validated. For the contacting brush seal, ΔSx, i has a significant effect on the leakage flow rate reduction. For the clearance brush seal, ΔSx, i has little effect on the leakage flow rate reduction. The leakage flow passing through the sealing clearance keeps almost constant. As for aerodynamic resistance, the presence of the sealing clearance can effectively convert the pressure energy of the leakage flow into the kinetic energy. As a result, the leakage flow velocity exiting the bristle pack of the clearance brush seal is 1.5 to 2.0 times larger than that of the contacting brush seal. Although the existence of the sealing clearance obviously increases the leakage flow rate, it effectively reduces the aerodynamic forces acting on the bristles. The developed numerical approach based on the three-dimensional staggered tube bundle model and multiblock structured mesh can serve as a technical method for analysis of the sealing mechanisms of brush seals.

A Three-Dimensional Tube Bundle Model Analysis for Leakage Flow Characteristics of Variable Bristle Diameter Brush Seals With Bristle Pack Stratification

The leakage flow characteristics of the variable bristle diameter (VBD) brush seals are numerically investigated using the three-dimensional (3D) tube bundle model with consideration of bristle pack stratification. The discretization of the computational domain applies the multiblock structured mesh, which ensures that there is no need to set interfaces between the fluid domains of the bristle pack and the cavities to eliminate interpolation errors. The bristle pack stratification is achieved by using mesh motion technique from the point of cause-effect. The effects of pressure ratio (Rp=1.5, 2.5, 3.5), axial rows of bristles (Nx=9–21), sealing clearance (c=0, 0.1 mm), bristle pack arrangements, and bristles gapping (gi=0, 0.005, 0.010, 0.015 mm) on the leakage flow characteristics and aerodynamic forces are conducted. The recorded leakage flow of the 3D tube bundle model is multiplied by circumferential loop number (Ncl) to determine total leakage flow rate of the brush seal. The numerical results agreed well with the experimental data, which verifies the reliability of the numerical method. The numerical results indicate that the leakage flow rate increases linearly with the pressure ratio. The increase of Nx has a distinctly different effect on the relative rate of leakage flow for the contacting and clearance brush seals. The use of large diameter bristles weakens the sealing performance of the brush seals, particularly in the rear region. Bristle pack stratification can improve the sealing performance of the brush seals. The large diameter bristles increase the porosity and reduce the flow resistance coefficients. On the contrary, the bristle pack stratification decreases the porosity and rises the flow resistance coefficients in the rear region. The results of this article indicate when designing VBD brush seals, the effects of bristle diameter and bristle density on the sealing performance and pressure loading capacity of the brush seals should be fully considered.

Oil Brush Seals in Turbomachinery: Flow Analyses and Closed-Form Solutions

Brush seals are one of the most important dynamic seals used in oil and oil mist applications in industrial turbines and aviation. Flexible bristle structure is the main structural superiority of brush seals, which enables precise clearance control and high performance in compensating rotor transients. The viscous medium between the high-speed rotor surface and brush seal bristles generates a hydrodynamic lifting force that determines seal clearance and leakage rate in oil sealing applications. Shear heating at moderate and high rotor surface speeds results in an increase in temperature and stabilization of lifting force, which is known as high-speed lift stabilization. Strong temperature–viscosity dependency of lube oils possesses the need for a detailed analysis and understanding of the effect of shear heat on hydrodynamic lift of brush seals in oil applications. To provide a better understanding about the critical balance of hydrodynamic lift force with rotor speed, temperature, and pressure, this work presents an analytical study to investigate pressure profile and shear heat temperature rise in liquid sealing medium within the hydrodynamic lift clearance. A closed-form solution to pressure and temperature distribution in axial and radial directions has been obtained by solving continuity, Navier–Stokes, and thermal energy equations for brush seals. The thermal and pressure functions are evaluated for linear and nonlinear pressure drop approaches, and the results are compared with each other. Deviation in nonlinear and linear pressure, resulting temperature level differences, and effect of rotor speed are detailed within the content of this study. The provided closed-form functions for pressure and temperature profiles are useful for designers since these can be utilized for turbine operation conditions. Dynamic test rig design for high-speed leakage performance measurement of turbomachinery seals is detailed, where the test rig can also be adopted for stiffness, frictional heat, power loss, torque loss, and bucket tip stability testing in oil and air environment. The test setup can also be used for testing dynamic seals other than brush seals.

Measured Influence of Clearance and Eccentricity on Brush Seal Leakage Characteristics

Brush seals are used in turbomachinery for reduced leakage as compared to conventional seals such as labyrinth seals. Early applications tended to favor having a line-to-line to a slight interference fit of the bristles to the shaft, but more recent applications have favored the use of a slight initial clearance fit for the purpose of reducing bristle wear. In these brush seals with clearance, the phenomenon of bristle blow-down largely negates the leakage degradation due to clearance, with bristles bending to reduce the clearance gap. This paper presents experimental results for a 10.5 inch bore brush seal with 0.0028 inch bristle diameter. Bristle blow-down is characterized with measurements at three different clearances then compared to a calibrated brush seal leakage model. Tolerances in brush installation may lead to a brush seal bore that is eccentric to the rotor. The influence of this seal eccentricity on measured leakage performance is also characterized in the paper. Seal eccentricities up to 55% of brush fence height are tested. Effective clearances for eccentric operation are estimated from the measurements. Brush seals are described as unidirectional seals because the bristles have a lay angle in the direction of rotation. This paper also investigates the influence of rotation direction on measured leakage performance of brush seal. This influence is characterized by non-pressurized reverse rotation operation and measurement of leakage performance prior to and after reverse rotation operation.

Factors of Influence on the Leakage of Brush Seals

Based on previous research from the authors a modeling approach for brush seals is developed further. Each individual bristle is reproduced in both the fluid dynamics and the structural mechanics model. An investigation regarding the influence of the free bristle height and the sealing gap on the leakage mass flow rate is carried out. Results are compared to experimental and literature data. Furthermore, preliminary results of the segregated fluid-structure interaction model are presented briefly, and matched to literature data.