Mitsubishi Heavy Industries Technical Review Vol. 60 No. 1 (March 2023)
1Visualization of Labyrinth Seal Force Acting on Rotating
Machinery Using Pressure Sensitive Paint

SHINGO NISHIDA*1

MAKOTO IWASAKI*1

NAOTO OMURA*2

For improving the reliability of rotating machinery, it is extremely important to predict fluid
force acting during the machine operation. Recently, CFD (Computational Fluid Dynamics)
analysis technology has been applied to the evaluation of fluid forces. In order to verify CFD
analysis and improve its accuracy, visualization and measurement technology of fluid forces are auseful tool. Regarding the verification technology, Mitsubishi Heavy Industries, Ltd. (MHI) has
been working on the visualization of unsteady fluid forces using pressure sensitive paint (PSP). In
this study, we improved this technology to enable measurement in narrow sections, and applied it
to a seal of rotating machinery and compared the results with those of CFD analysis. As a result ofthe measurement, we were able to obtain a detailed pressure distribution, which led to a better
understanding of the mechanism of fluid force generation. In addition, we verified the differencebetween the measurement using PSP and the CFD analysis, which led to the improvement ofevaluation methods for the future.

|1. Introduction
In order to suppress leakage of the working fluid from shafts and blade tips of rotatingmachinery and improve the efficiency, labyrinth seals are used. A labyrinth seal has a fin structure
as shown in Figure 1, and the narrow section of the fin suppresses leakage from blade tips andshafts leakage. To increase the efficiency of the equipment, it is desirable to minimize the clearance
at the tips of these fins, however at the same time, it is known that an increase in fluid force thatcauses self-induced vibration of the shaft of the rotating machinery occurs at the seal. With theincrease in capacity and efficiency of rotating machinery, the working fluid has increased inpressure and the seal dimensions have also become larger in recent years. Therefore, the need fordetailed evaluation of the fluid force at seals, which is the cause of self-induced vibration, hasincreased.

Figure 1

Example of labyrinth seal structure

Conventionally, it has been possible to evaluate the fluid force by using a theoretical formulafor a simple-shape seal structure. However, as the performance of seals improves, more complex*1Vibration Research Department, Research & Innovation Center, Mitsubishi Heavy Industries, Ltd.

*2

Turbomachinery Research Department, Research & Innovation Center, Mitsubishi Heavy Industries, Ltd.

Mitsubishi Heavy Industries Technical Review Vol. 60 No. 1 (March 2023)
2seal structures are being used, and there are limitations to using only theoretical formulas forevaluation. In addition, because of the complexity of the flow inside the seal, the reproducibility
with CFD evaluations, which have been rapidly expanding to use in recent years, can beproblematic in some cases. Therefore, in order to improve the evaluation with CFD, it is highly
desirable to visualize the details of pressure fluctuation inside the seal.
In this study, we measured pressure fluctuations using a fast-responding
polymer-ceramic-type pressure sensitive paint (PC-PSP) to visualize pressure distribution insideseals. By illuminating the pressure sensitive paint with excitation light from the opposite side of thepressure acting surface and measuring with a high-speed camera, we succeeded in making unsteadymeasurements in a complex channel such as the inside of a seal. Using the detailed visualization
results of unsteady pressure fluctuations obtained in this study, it was found that the pressure
distribution calculated by CFD and that measured with the pressure sensitive paint differedsignificantly near the position where the flow separation occurs, which is an important result as afundamental finding for improving turbulence models used in CFD.

|2. Measurement of seal excitation force
2.1

Seal excitation force

The equation of the motion of shaft vibration of rotating machinery can be expressed by a
two-degree-of-freedom system with respect to two directions of shaft deflection as follows:
M++=(1)Since the seal excitation force is a fluid force that is generated in response to the shaft
vibration response, it can be represented as the added stiffness and added damping of this vibration
system and can be matrixed as in the following equation.
=−−(2)The seal excitation force is a problematic force that contributes to shaft vibration and isgenerated by the swirling flow entering a seal narrow section as shown in Figure 2. By
understanding the stiffness matrix and damping matrix in equation (2) and performing a stability
analysis, it is possible to calculate whether self-induced vibration occurs over the whole of the rotor
system.

Figure 2

2.2

Mechanism of shaft vibration generated by rotor whirling

Rotational test equipment

Figure 3 shows rotational test equipment for measuring seal excitation force. This equipment
has two disks on one rotor, and is equipped with seal fins to be used for measurement at the tips ofthe disks. Compressed air supplied from the center of the two disks passes through the left and rightMitsubishi Heavy Industries Technical Review Vol. 60 No. 1 (March 2023)
3seal fins to balance the differential pressure in the axial direction. The rotor is supported by
cage-type springs via rolling bearings. By using an electromagnetic actuator at the shaft end tovibrate the rotor in a whirling manner, an excitation force is generated at the seals, which ismeasured by a load cell. Figure 4 shows the seal used in this test. The strength of the swirling flowat the inlet of the seals was measured using a three-hole pitot tube. The seal used is an interlocking
seal (ILS), which has fins on the rotor side and stator side protruding alternately.

Figure 3

Rotational test equipment for measuring seal excitation force

Figure 4

Structure of tested seal

2.3

Result of excitation force measurement

In this test, excitation was performed while changing the strength of the swirling flow into
the seal fins. Figure 5 shows the measurement results. It was observed that the magnitude of theoff-diagonal term in the seal excitation force stiffness matrix, which is the cause of unstablevibration, increased in proportion to the strength of the swirling flow.

Mitsubishi Heavy Industries Technical Review Vol. 60 No. 1 (March 2023)
4

Figure 5

Measurement result of seal excitation force added
stiffness coefficient|3. Measurement using pressure sensitive paint
3.1

Pressure sensitive paintPressure sensitive paint consists of a dye, the luminescence intensity of which changes
according to oxygen concentration, indicating changes in the partial pressure of oxygen due tochanges in the static pressure of the air. Pressure sensitive paint, with which static pressure can bemeasured as a change in its luminescence intensity, is applied to pressure measurement. For thistest, a polymer-ceramic-type pressure sensitive paint containing a platinum porphyrin dye andmixed with ceramic powder to increase the response speed was used. This paint was provided by
the Japan Aerospace Exploration Agency (JAXA). Figure 6 shows a schematic diagram of themeasurement using pressure sensitive paint. When a pressure sensitive paint is applied to thesurface of an object to be measured and then irradiated with excitation light such as ultraviolet
light, luminescence is produced at a wavelength according to the characteristics of each dye and at
an intensity corresponding to the oxygen concentration. By measuring this with a high-speed
camera, unsteady pressure can be visualized and measured.

Figure 6 Principle of measurement using pressure sensitive paint3.2

Measurement setup

Figure 7 shows the measurement part of pressure sensitive paint. The measurement ofpressure sensitive paint requires evaluation of the change in luminance from a reference image, and
it is therefore more advantageous that the object to be measured remains stationary from thestandpoint of measurement accuracy. For this reason, the wall surface of the seal cavity on thecasing side was used as the object to be measured. However, the conventional measurement
method requires that the pressure acting surface coated with the pressure sensitive paint (thesurface to be measured) and the directions of the excitation light irradiation and camera installation
coincide, which makes it impractical to measure the narrow inner surface of the seal cavity.
Therefore, in this test, we made a modification by optimizing the composition of the pressure
sensitive paint and irradiating the excitation light from the opposite side of the pressure receiving
surface (i.e., outside of the test equipment) so that measurement with a camera can be performed.
The tested seal has five seal cavities: cavity #1 to cavity #5 from the upstream side. Among them,
we used cavities #1 and #2, which are strongly affected by the swirling flow and prone to relatively
large destabilizing forces, as the cavities to be visualized and measured using pressure sensitivepaint.

Mitsubishi Heavy Industries Technical Review Vol. 60 No. 1 (March 2023)
5Figure 7

3.3

Setup of measurement using PSPMeasurement result

We installed a small pressure sensor inside the seal cavity to verify the measurement accuracyof the pressure sensitive paint. Figure 8 compares the result of measurement using the pressure
sensitive paint and the result of measurement using the pressure sensor in the excitation test. It isindicated that the level of pressure fluctuation with respect to the vibration frequency is in good
agreement between the two. We averaged the result of measurement using the pressure sensitive
paint with the rotor displacement phase in order to clarify the relationship between the rotor
eccentricity position and the pressure fluctuation due to excitation. In addition, for the purpose of
averaging the uneven dispersion of the pressure sensitive paint dye, etc., we averaged and evaluatedthe measurement results at each measurement position, taking into account the change in rotor
phase. Figure 9 shows the averaging method schematically. Figure 10 shows the averaged
measurement results. The measurement result clearly indicates the mechanism that a high-pressurepart of the seal excitation force exists in a phase relationship that contributes to rotor whirlingexcitation with respect to the rotor eccentric phase, thereby contributing to rotor instability vibration.
In addition, highly detailed pressure distributions inside the seal cavity and near the seal fins wereobtained, which are data that can be used for comparison with the results of CFD analysis.

Figure 8Comparison of pressure sensitive paint and pressure sensor

Mitsubishi Heavy Industries Technical Review Vol. 60 No. 1 (March 2023)
6Figure 9

Phase averaging method

Figure 10

Measurement result after phase averaging|4. CFD analysis and consideration
4.1

CFD analysis

To verify the accuracy of CFD analysis, which is used as a prediction method for seal
excitation force, a CFD analysis was used to reproduce and analyze the excitation force
measurement test. For the CFD analysis, a steady-state analysis method called the whirling rotor
method was used, in which the SST k-ω RANS model was used as the turbulence model, theeccentricity of the rotor was given as the steady eccentricity, and the relative velocity due to rotor
rotation speed and whirling excitation was given as the wall surface velocity. Figure 11 shows theanalysis domain. The analysis domain simulates only the rotor disk on one side of the rotational
test equipment. The cavities between the disks, the nozzle to simulate swirling flow, and theexhaust channel are modeled with the same dimensions as those of the test equipment. Table 1shows the CFD analysis setting.

Mitsubishi Heavy Industries Technical Review Vol. 60 No. 1 (March 2023)
7

Figure 11CFD analysis domain
Table 1

CFD analysis setting

Solution typeCalculation method
Analysis solver
Fluid
Turbulent condition

Physical property
Density change
Specific heat, viscosity,heat transfer coefficient
Turbulence model
Inlet turbulence condition

Wall model
Eccentricity
Inlet boundary condition
Bypass flow boundary condition
Outlet boundary condition

4.2

Analysis setting
Steady-state calculation(Whirling rotor method)
Three-dimensionalpressure-velocity coupling
Air
Ideal gas
Set as a function of temperature
RANS SST k-ω
5%Adiabatic boundary, smooth surface
10% of seal clearanceMass flow rate
Static pressure condition
Static pressure condition (open toatmosphere)

Comparison of CFD analysis result and test result

Figure 12 shows the result of CFD analysis and the result of measurement using pressure
sensitive paint. First, the trends of the pressure distribution inside the seal cavity are in good
agreement between the two. In the result of CFD analysis, the isobars of the pressure distribution
tend to bend strongly at the flow separation points, but in the result of measurement using pressure
sensitive paint, this tendency is not noticeable. This is thought to reflect the fact that the actualseparation is different from that of CFD given that the measurement using pressure sensitive paintalso has sufficient spatial resolution. Figure 13 compares the values of the added stiffness andadded damping coefficient values of the seal excitation force calculated from the result ofmeasurement using pressure sensitive paint and those calculated from the result of CFD analysis.
Although the trends of the two results are consistent, differences are observed when the levels ofadded stiffness and added damping coefficient for each seal cavity are compared. The difference
between the result of CFD analysis and the result of measurement using pressure sensitive paint is
considered to be caused by the reproduction accuracy for flow separation as described above, and it
is considered that the accuracy can be improved by optimizing the turbulence model to be used.

Mitsubishi Heavy Industries Technical Review Vol. 60 No. 1 (March 2023)
8Figure 12 Comparison of result of measurement using PSP (upper) and resultof CFD analysis (lower)

Figure 13 Comparison of excitation force coefficients between
result of measurement using PSP and result of CFD analysis|5. Conclusion
To visualize unsteady pressure in narrow sections of rotating machinery, we developed amethod of measurement from the back surface using unsteady pressure sensitive paint, andsucceeded in measuring unsteady pressure distribution with high accuracy and high definition.
Comparing the measurement result with the CFD analysis result, it was found that the globalpressure distribution characteristics of the two were in agreement, but the aspects of flow
separation points were not. Based on these detailed measurement results, it is possible to realize
more accurate CFD analysis, which will be useful for further improving the reliability of rotatingmachinery in the future. This method can be applied to the visualization of unsteady pressure inother rotating machinery and internal flows, and is expected to contribute to the elucidation of thegeneration mechanism of fluid excitation forces in various products and to the enhancement ofCFD analysis methods.

References(1)

Nishida, S. et al., Visualization of Destabilization Force of Labyrinth Gas Seal Using Fast-Responding
Pressure Sensitive Paint, ASME Turbo Expo, GT2021-58893