Transient simulation of gas labyrinth seal
Funded by national high-tech Research and development Program (863) of China. No. 2009AA04Z413
Traditionally, Labyrinth seal is utilized in turbo-machinery of high speed and huge capacity. Sometimes, the labyrinth seal can result in unstability of seal-rotor system. Circumferential flow in seal is regarded as the main reason, which causes large cross-stiffness. Excitational force due to flow in seal is used to calculate rotor dynamic coefficient of seal. This force is produced by the non-uniform pressure distribution in seal. Although many research have already been conducted on labyrinth seal, it is found that these research focus mostly on steady simulation. Few research involve with transient simulation of labyrinth seal. My work is trying to find the law of excitational force when rotor is whirling in the gas labyrinth seal. The whirling orbit can be linear, circle and ellipse.
Seal model
Fig 1, two dimensional model of
labyrinth seal
A four teeth straight labyrinth seal consisting of a rotor with flat surface is studied. There are six parameters influencing the seal form, shown in Fig 1. The clearance without eccentircity is 0.2mm. The rotor diameter is 170mm. The small size of clearance and large diameter make simulation difficult. Dense mesh grid can capture important flow phenomenon in the narrow channel, while this fine grid leads to a large mesh file. Because there are requriement on the quality of mesh, the lenght-width ratio cannot be too large. When increasing grid number in the clearance, the circumferential grid number should also be added. For example, if dividing the clearance into four parts (0.2/4 = 0.05)and keeping the clearance and circumferential size equal, the circumferential size need be divided into 3400 parts (170/0.05 = 3400). Adding one more part in the clearance (0.2/5 = 0.04) means increasing the increasing 850 circumferential parts. For fine mesh grid, very large mesh file will be created (larger than 1GB). This mesh file can often not be calculated because of RAM limitation. Choosing sparser grid can Lower mesh size, while the grid quality should not be too bad, otherwise it is hard for simulation to converge. This mesh problem of labyrinth seal can be solved through trying various grid combinations and finding a acceptable choice both for grid number and converging ability.
Conducting CFD simulation, mesh independence should always be considered. Too sparse mesh number leads to inaccurate result, while too dense mesh number costs too much calculation time and requies high performance computer. To perform mesh independence test, I tried to keep only one size change so as to figure out its influence on the simulation result. I took the gas excitational force on the rotor surface as the criterion because this force is essential to calculate rotor dynamics coefficient of labyrinth seal.
Conducting CFD simulation, mesh independence should always be considered. Too sparse mesh number leads to inaccurate result, while too dense mesh number costs too much calculation time and requies high performance computer. To perform mesh independence test, I tried to keep only one size change so as to figure out its influence on the simulation result. I took the gas excitational force on the rotor surface as the criterion because this force is essential to calculate rotor dynamics coefficient of labyrinth seal.
Dynamic mesh method
Fig 2, three dimensional model of labyrinth seal
The small clearance between rotor and seal makes it difficult to realize transient simulation of labyrinth seal. Three dynamic mesh methods provided by FLUENT can not be applied to this small clearance because negative volume will appear. Other solution need be found to perform transient simulation. Using User defined function (UDF) in FLUENT, transient simulation can be performed in straight labyrinth seal with structured mesh. The seal can be divided into two part. One part is the dynamic mesh domain and other part is the cavity domain (see Fig 2). The dynamic mesh domain is actually a annulus volume. For structured mesh, grid point is regularly arranged in this volume. The coordinate of each point is determined by the grid number in clearance and rotor eccentricity. Using a algorithm to find coordinate of each point, it is easy to perform desired mesh motion in each time step. In this way, the linear motion, circle and ellipse whirling of rotor in seal can be realized. Monitering the excitational force in each time step, the law of excitational force in straight labyrinth seal can be figured out. One demo about the dynamic mesh method can be seen in blow video.
Result
The unsteady calculation belongs to calculation of differential equations with initial parameters. It's necessary to investigate the influence of different initial parameters on calculation results. A straight linear whirl of rotor is taken and two different initial conditions were applied to investigate the influence. Through calculating 100 time steps, the results can be seen in Fig. 3 and Fig.4. Apparently, unsteady calculation results will be affected by the initial condition. The first unsteady calculation was started from a converged steady result. Comparably, the other unsteady case was started directly without being steadily calculated. At the beginning, results of the two unsteady calculation are different. When time increases, the influence of initial condition decreases and the force trend become similar . However, the final results are a little different,which may be caused by the fluctuation of calculation.
Whirl around eccentric position
Former research have also simulated circle whirl of rotor at seal, but the circle center can only be the chamber center which is assumed to be balanced position. Rotor dynamic coefficients of labyrinth seal are different when rotor is in different eccentricity position. In practice, the balanced position is rarely in chamber center. It always has some eccentricity. It is meaningful to calculate circle whirl around eccentric position and its dynamic coefficient.
In transient simulation, time step is set as 5×10-4s and the whirl radius is 0.02 mm. One case with 50 percent eccentricity is used to investigate how excitational forces change around eccentric position. Fig.5~Fig.6 show whirl orbit and corresponding forces. The asymmetric shape of force is caused by initial perturbation. More iteration steps can improve prediction accuracy.
In transient simulation, time step is set as 5×10-4s and the whirl radius is 0.02 mm. One case with 50 percent eccentricity is used to investigate how excitational forces change around eccentric position. Fig.5~Fig.6 show whirl orbit and corresponding forces. The asymmetric shape of force is caused by initial perturbation. More iteration steps can improve prediction accuracy.
Notice
Some results of this section has already been published in International journal "Advanced Material Research" (EI Compendex). Back to list >>
Some results of this section has already been published in International journal "Advanced Material Research" (EI Compendex). Back to list >>