Leakage performance of hybrid brush seals under high differential pressure conditions

A three-dimensional axial fluid-porous medium-flow field model was designed for the sealing properties of the hybrid brush seal (HBS) seal structure under complex operating conditions. Using a computational fluid dynamics model in view of non-Darcy porous media, the pressure and velocity distributions of the sealing medium in the flow path were simulated, and the flow characteristics of the hybrid brush seal were analysed to obtain the leakage of the hybrid seal structure. The results show the implication of pressure ratio (Rp) on the labyrinth brush seal leakage rate and pressure distribution. Compared with typical brush seal test results, as the inlet and outlet pressure ratio (Rp) increases, the more obvious the hybrid brush seal sealing effect is, when the pressure ratio is 3 bar, the spillage of the hybrid brush seal is reduced by about 39%.


Introduction
Gas sealing technology has become a key technology for the development of low consumption and high reliability turbomachinery [1] .In turbomachinery seals, loss due to leakage is a major challenge and pain point, and the power consumption due to leakage in a representative turbine take possession of about 30% of the total power consumption [2] , so reducing leakage has been the focus of academic explorations in related fields.Previously, labyrinth seals were widely used to reduce leaks in working fluids, but the continued demand for higher performance aero-engines has led to extensive improvements in various turbine components and brush seals have emerged and taken a prominent place in pneumatic systems.Compared to conventional labyrinth seals, brush seals leak 1/5 as much as labyrinth seals [3] .Compared with labyrinth seals, brush seals have better sealing performance, but are limited by contact speed, friction and pressure-bearing capacity, etc., which can produce hysteresis effects and frictional heat effects.By replacing the labyrinth teeth in a labyrinth seal with a brush filament bundle, a hybrid brush seal is formed, which not only has excellent and durable sealing performance, but also has a high pressure-bearing capacity [4] .
HUANG Shouqing [5] investigated the influence of the amount of brush filament rows on spillage as well as the details and patterns of flow in the brush filament gap and temperature distribution in the brush and filament gap.Deville Lilas [6] conducted experiments on a 38 mm diameter brush seal under operating conditions with an air pressure difference of 7 bar and a rotation frequency of 500 Hz to verify the effect of radial interference on seal performance, and the experimental results showed the important effect of radial interference on leakage.Yunseok Ha [7] studied the impact of the gap between the rotor and hybrid brush seal of a turbine plant on the leakage flow, focusing on the effect of axial offset and wear on the seal performance, using a turbine plant turbine equipment.An 11% improvement in accuracy was achieved using a CFD model that accounted for the gap variation.Ma Dengqian [8] used the k-ω SST turbulence model to investigate the effect of brush seal leakage flow and aerodynamic characteristics under different rotational speeds.
Hybrid brush seals combine the characteristic of labyrinth seals and typical brush seals, but there are few comprehensive studies on the leakage flow characteristics of hybrid brush seals.To further improve the comprehensive performance and reliability of hybrid brush seal technology, it is necessary to carry out research on the application of hybrid brush seals in aero-engines.In view of the numerical solution method of porous medium model, this paper calculates the leakage of hybrid brush seals under three different pressure ratios, investigates the influence of the Rp on the leakage behaviour of typical brush structures and composite seal structures, and carries out a detailed study on the leakage rate pattern and pressure transfer pattern inside the brush filament bundle.

Simulation model and geometric parameters
Figure 1 gives a sketch of the operation of the hybrid brush seal, which is mounted on a rotor and static sub-piece with a diameter of 200 mm and which consists mainly of a brush seal and labyrinth seal with three teeth.Figure 2 shows a diagram of the CFD fluid model characterising the flow field of a composite brush seal.Table 1 lists the detailed structural parameters of the brush filament bundles and labyrinth teeth in hybrid brush seals.
Table 1.Geometry parameters of hybrid brush seal.Hybrid brush seal Tooth height [Hh] 7.9

Calculation methods
The brush pack in a brush seal consists of closely spaced and irregularly arranged bristles with complex flow between them [9] .The difficulty of numerical analysis lies in describing the irregular flexible behaviour of the brush filament bundle under gas forces and the fact that the gas passing through the seal will lead to a change in the actual breadth of the brush filament strand due to the presence of the inlet and outlet pressure drops.Therefore, simplification of the seal calculation model is a necessary means of operational process, and the porous media model is an efficient and reasonable method to achieve similar simulation results with high accuracy.
A numerical method is adopted for simulating the gas flow characteristics within a hybrid brush seal structure by means of a numerical method based on a non-Darcy porous media model, by adding a resistance source term S = [ Sz, Sn, Sm ] T to the momentum equation of the set of RANS equations to represent the resistance of the brush filament to the flow of the fluid, as shown in equation ( 1) and (2).
The matrices of viscous and inertial drag coefficients are each represented by A = diag {az, an, am} and B = diag {bz, bn, bm}, where the spatially anisotropic drag coefficients (az, an, am, bz, bn, and bm) are calculated according to equations (3) and (4).The porosity ε is the ratio of the pore volume in the brush bundle structure to the total volume of the brush bundle, and is one of the most important parameters describing the resistance to flow of the medium, as shown in Equation (5).
ANSYS Fluent is used for the numerical analysis of the HBS and the numerical model uses a realizable k-epsilon model turbulence model for calculating the fluid components outside the brush beam region.The working fluid is a compressible ideal air, which is easy to calculate and handle.The inlet and outlet boundary conditions are based on differential pressure and temperature simulations of actual operating conditions.

Method validation and pre-processing
In the radial position, the grid near the rotor wall and porous media area needs to be increased to meet the impact of shear force changes brought about by the wall fluid on the numerical calculation and to improve the precision of the results; when the residual term of the numerical calculation does not converge in part, the inlet and outlet leakage can be used as the basis for judgment, when the inlet and outlet leakage is about 1% of the inlet and outlet flow, the calculation is considered to be completed.The calculation is considered to be finished and the influence of the calculation error on the calculation results is very small.The total number of meshes for the hybrid brush seal calculation was verified to be approximately 910,000 by grid independence, which has a small impact on the calculation results.

Characteristics of the sealed flow field
Figures 3(a, b, c) show the pressure distribution of a hybrid brush seal at different Rp for a composite brush seal with 3 teeth.In all three seal cases, the pressure drop is gradual in general, with the inlet pressure decreasing by approximately 1/3-1/4 as it passes through the brush seal.In contrast, the pressure drop in the flow field is more uniform when passing through three consecutive labyrinth seal teeth.4 (a, b, c).The velocity of the leakage jet increased dramatically in the interval between the brush seal outlet and the tip of the seal teeth for the three different pressure drop cases, suggesting that most of the potential energy of the gas is transformed into high-velocity kinetic energy in the small clearance through which it passes.The leak jet then diverges, with a portion of the high velocity leak jet maintaining axial flow into the next gap, while the remainder disperses towards the cavity wall, moving within the cavity to form a large counter-clockwise vortex, generating kinetic energy dissipation.In addition, as the pressure ratio increases, the potential energy of the gas in the stream field increases, and the maximum speed of the stream field increases significantly, which will also be detrimental to the sealing performance, and the maximum velocity is mainly present between the third tooth near the outlet.

Spill volume analysis
In order to keep the data stable and reliable, the fluctuations of mass flow rates were monitored at different pressure ratios, as shown in Figures 5(a, b, c).The initial fluctuation of the flow rate difference varies significantly, and the fluctuation becomes slow rapidly at about 1ms, and then the fluctuation is very small and maintained in a very small interval.In Fig. 7, the numerical results of the leakage coefficients of the CFD hybrid brush seals at different pressure ratios Rp are compared with the leakage coefficients obtained from the typical brush seal experiments [10] according to the relevant data support, which will visually and efficiently show the performance of the typical seal structure and the new seal structure.Under a variety of initial pressure conditions, the leakage of the hybrid brush seal is smaller than that of the typical brush seal with a certain radial gap; with the grow of pressure ratio, the sealing effect of the typical brush seal gradually deteriorates, and the leakage increases significantly, whereas the increase in leakage of the HBS is less than that of the typical brush seal, and the sealing performance is better under the situation of larger pressure ratio.

Conclusions
This research investigates the implication of different pressure ratios on the leakage of hybrid brush seals and compares it with the experimental results of typical brush seals, which will contribute to the development of work on new seal constructions and help to improve the energy efficiency and performance of aero engines.The main findings are as follows: (1) On the basis of the pressure and velocity distribution characteristics of the flow field, it can be found that the pressure-bearing capacity and sealing behaviour of the brush seal is stronger than that of the labyrinth seal, and improving the interdental configuration near the outlet can improve the sealing performance to a certain extent.A reasonable increase in the number of teeth of the labyrinth seal will also reduce the leakage problem caused by excessive local flow velocity to a certain extent, and the addition of auxiliary teeth at the front end of the flow field is a desirable attempt.
(2) Hybrid brush seals provide less leakage than typical brush seal test results, with hybrid brush seal configurations reducing leakage by approximately 25% at a pressure ratio of 2 bar and approximately 39% at a high pressure ratio (Rp) of 3 bar.For aero-engine equipment that operates with high pressure differentials, hybrid brush seals are clearly of wider value and research interest.
(3) three-dimensional CFD analysis of the hybrid brush seal provided in this paper can be utilised for the observation of the overall flow field characteristics, and the leakage coefficients can be more accurately derived for data analysis, which can be applied to the design of the structural parameters of various interstage annular seals for steam turbines, aero-engines or gas turbines, to further reduce the energy consumption due to gas leakage.

Figure 1 .
Figure 1.Configuration of HBS planar and 3D profile structures.

Figure 2 .
Figure 2. CFD Hybrid Brush Seal.Table 1 lists the detailed structural parameters of the brush filament bundles and labyrinth teeth in hybrid brush seals.Table 1.Geometry parameters of hybrid brush seal.Hybrid brush seal Tooth height [Hh] 7.9[mm] Tooth pitch [B] 5[mm] Tooth width[b] 0.3[mm] Number of labyrinth teeth 3 [ea] Brush diameter [d] 0.1 [mm]

Figure 6 .
Figure 6.Line graph of the difference mass flow rates at different Rp.In Fig.7, the numerical results of the leakage coefficients of the CFD hybrid brush seals at different pressure ratios Rp are compared with the leakage coefficients obtained from the typical brush seal experiments[10] according to the relevant data support, which will visually and efficiently show the performance of the typical seal structure and the new seal structure.Under a variety of initial pressure conditions, the leakage of the hybrid brush seal is smaller than that of the typical brush seal with a certain radial gap; with the grow of pressure ratio, the sealing effect of the typical brush seal gradually deteriorates, and the leakage increases significantly, whereas the increase in leakage of the HBS is less than that of the typical brush seal, and the sealing performance is better under the situation of larger pressure ratio.

Figure 7 .
Figure 7. leakage flows for HBS with typical brush seal experiments at different Rp.

Table 2 .
Table 2 lists the values of the numerically calculated boundary conditions.Operating conditions.