Response of a Rotor Under the Influence of Seal Forces

In fluid seals found in axial compressors, two types of fluid forces can be distinguished. The first type of force directly opposes the lateral motion of the rotor, and it is modeled using equivalent direct stiffness and damping coefficients. The second force type acts in the circumferential direction of the rotor. This force is modeled with cross stiffness and damping coefficients. The first type of force always tends to stabilize the rotor, whereas the second type may have destabilizing effects under certain conditions.

In this example, an axial compressor is modeled using the Beam Rotor interface. The compressor has ten impeller stages with a seal located near each impeller. The compressor model also includes a balance piston seal located at the end of all impeller stages. The time-dependent response of the compressor is studied for a gradually increasing rotor speed. In order to compare the effect of the seals on the rotor response two studies are performed, one without and one with the seals included. In this case, the seals have a stabilizing effect on the compressor as the displacement amplitude is significantly smaller in the presence of the seals.

Model Definition

The model consists of an axial compressor with ten impeller stages. The overall configuration is shown in Figure 1. The rotor is supported with two hydrodynamic bearings. Each impeller stage is accompanied by a seal to avoid flow leakage. In addition, there is a balance piston seal at the end of the impeller stages. The rotor’s weight is supported by the bearings and the seals. The impellers are modeled with small mass eccentricities.

Figure 1: Rotor geometry.

Shaft Properties

The diameter of the rotor shaft varies along its length. Thus, to more easily apply different properties, the rotor axis is divided into multiple segments separated by various support points. Some of these points separate segments with different shaft diameters, and others mark the locations of seals, impellers and bearings. The coordinates of the various stations are given in Table 1.

Table 1: Station Coordinates.
Station	Coordinate
1	0
2	0.04 m
3	0.172 m
4	0.413 m
5	0.663 m
6	1.943 m
7	2.459 m
8	2.653 m
9	2.715 m
10	2.850 m

The shaft diameters for the different segments are given in the Table 2.

Table 2: Shaft Diameters.
Shaft Segment	Diameter
Station 1–2	72 mm
Station 2–3	92 mm
Station 3–4	105 mm
Station 4–5	110 mm
Station 5–6	115 mm
Station 6–7	110 mm
Station 7–8	105 mm
Station 8–9	75 mm
Station 9–10	60 mm

Impeller Properties

The properties of the impellers are given in the Table 3.

Table 3: Impeller properties.
Impeller	Mass	Diametral Moment of Inertia	Polar Moment of Inertia	Eccentricity
1	15 kg	0.131 kg·m2	0.262 kg·m2	0.01 mm
2–9	13 kg	0.114 kg·m2	0.228 kg·m2	0.01 mm
10	14 kg	0.122 kg·m2	0.244 kg·m2	0.01 mm

All impellers are located between stations 5 and 6, and they are equidistantly spaced in this shaft segment. The first impeller is located at a distance of 62 mm from station 5. The axial length of each impeller is 80 mm.

Bearing Properties

The rotor is supported on two plain hydrodynamic journal bearings. The first bearing is located in the middle of stations 3 and 4. The second bearing is located adjacent to station 8 such that the right end of the bearing touches this station. The length of each bearings is 96 mm. The radius of both bearings is 52.5 mm and the radial clearance in each bearing is 0.15 mm. The viscosity of the bearing lubricant is 0.0414 Pa·s.

Seal Properties

The properties of the seals are given in the Table 4.

Table 4: Seal Properties.
Seal	Diameter	Clearance	Length	Pressure Drop
Annular seals 1–10	195 mm	0.5 mm	22 mm	3.2 MPa
Balance piston seal	80 mm	0.5 mm	165 mm	32 MPa

The annular seals are equidistantly spaced between stations 5 and 6 on the rotor with the left end of the first seal starting at station 5. The right end of the balance piston seal is located at station 7. The density and viscosity of the seal fluid are 800 kg/m3 and 0.02 Pa·s, respectively.

Results and Discussion

Figure 2 shows the von Mises stress in the rotor after including the seal forces at t=2 seconds. The response appears to be similar to the first bending mode of the rotor. The rotor geometry is also shown below the stress plot.

Figure 2: von Mises stress in the rotor with seals at t=2 secconds.

The orbit of the rotor near the left bearing is shown in Figure 3. In the presence of seals, the displacement amplitude of the whirl is considerably smaller. The orbit plot indicates a growing whirl amplitude in the absence of seals towards the end of the simulation.

Figure 3: Orbit of the rotor in the bearing with and without seals.

The stiffness and damping coefficients of seals play an important role in dictating the rotor stability. The direct and cross stiffnesses for the balance piston seal are shown in Figure 4. Clearly, the direct rotor stiffness decreases with rotor speed whereas the cross stiffness increases. Also, the change in the cross stiffness is more sensitive to the change in speed as compared to the direct stiffness.

Figure 4: Stiffness of the balance piston seal.

The vertical displacement at impeller 5 is compared with and without seals in Figure 5. From this plot also we can deduce that the vibration amplitudes of the rotor are significantly larger without seals. At higher rotor speeds, the amplitude of the displacement is growing without seals.

Figure 5: Comparison of the vertical displacement of the rotor at impeller 5.

Rotordynamics_Module/Tutorials/rotor_stability_with_seal

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters: Stations

Start by importing the parameters for the rotor, bearings, seals and impellers.

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file rotor_stability_with_seal_stations.txt.

In the text field, type Parameters: Stations.

Parameters: Rotor Diameters

In the toolbar, click

and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file rotor_stability_with_seal_rotor_dia.txt.

In the text field, type Parameters: Rotor Diameters.

Parameters: Bearings

In the toolbar, click

and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file rotor_stability_with_seal_bearing.txt.

In the text field, type Parameters: Bearings.

Parameters: Impellers

In the toolbar, click

and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file rotor_stability_with_seal_impellers.txt.

In the text field, type Parameters: Impellers.

Parameters: Seals

In the toolbar, click

and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file rotor_stability_with_seal_seal_properties.txt.

In the text field, type Parameters: Seals.

Geometry 1

Polygon 1 (pol1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Use the station coordinates together with location of bearings, seals and impellers to create a 1D representation of the rotor.

In the text field, type x1 x2 x3 xb1 x4 x5 xs1 xd1 xs2 xd2 xs3 xd3 xs4 xd4 xs5 xd5 xs6 xd6 xs7 xd7 xs8 xd8 xs9 xd9 xs10 xd10 x6 xp x7 xb2 x8 x9 x10.

In the text field, type 0.

Click

Definitions

You can specify the diameter of the rotor between different stations by using as many nodes as rotor segments. You can avoid many such nodes by using the interpolation function for the axial variation of the rotor diameter. You can use a small axial tolerance in the interpolation data to create the steps in the diameter near the stations.

Interpolation: Diameters