Repair sensitivity study for compressor inlet labyrinth seal using Computational Fluid Dynamics
Allan Thomson & David Anderton, APM Team, Wood Group Light Industrial Turbine Ltd.

This study examines the potential to relax the repair limits for an industrial gas turbine compressor inlet labyrinth seal through numerical analysis, in order to minimize unnecessary, costly and timely rework. The study demonstrates that for steady-state running conditions there is considerable potential to relax repair limits without sacrificing seal performance. It recommends that these results should be discussed for implementation and highlights areas for further work.

During the overhaul of a 6.4MW industrial gas turbine, Wood Group Light Industrial Turbines Ltd (WGLIT) adopt a standard practice of restoring compressor labyrinth seal fins and abradable liners as new design clearances. Repair of the rotating knife-edge seals requires the compressor rotor to be disassembled which itself incurs considerable further rework and repair cycle time that would otherwise not necessarily be required. It therefore follows that if the relationship between seal clearance, bearing chamber sealing efficiency and compressor delivery pressure losses could be quantified, then the setting of acceptable overhaul limits for the labyrinth seal clearances would result in reduced overhaul cost and turn times whilst delivering the required quality and performance for the intended service duration.

Objectives
The objectives of this study were twofold:

1. To quantify the effects of compressor inlet bearing abradable labyrinth seal clearances on;
   • Bearing chamber to compressor annulus sealing
     
   • Compressor delivery pressure
     
2. To examine acceptable overhaul limits for the above mentioned labyrinth seals.

Methodology
Computational Fluid Dynamics: Analysis with Air Only
One eighth (45 degrees) of the complete labyrinth seal was modeled with axi-symmetric boundaries, Figure 1. Four models were built comprising 755,000 hexahedral computational cells. The labyrinth seal was modeled as a solid wall and the rotating fins did not cut into the seal. The oil drain in the seal was neglected. The rotor speed was taken to be 11,000 rev/min. The clearance between the fin the seal varied from 0.05 mm to 0.250 mm in steps of 0.050 mm.

The flow was assumed to be steady state, compressible and turbulent. Turbulence was modeled using the two equation k - ε turbulence model with hybrid wall functions. This approach was chosen as the value of non-dimensional wall distance, Y+, can range from about 1 to 250 and the wall treatment function method would still be valid. Second order differencing was used for momentum to ensure accuracy and first order differencing on turbulence and enthalpy.

he pressure drop across the seal was unknown therefore two pressure drops were chosen to be representative: 2.28 bar – no throttling had taken place after the sealing air had been bled off from the 8th compressor stage and 1 bar – some degree of throttling had taken place.

At a later stage one of the seal fins was removed, the downstream fin closest to the inlet pipe, and an analysis was carried out at clearances of 0.05 mm, 0.10 mm and 0.15 mm. A run was also completed, assuming the fin had cut into the abradable seal with a clearance of 0.05 mm between the fin and the non-abradable surface.

Extended Model (droplets - two phase flow):
The initial model was extended (1,038,000 computational cells) to include the chamber with the inlet journal bearing, Figure 2.

Morgan (1) proposed that an efficient way to simulate oil flow through an inlet labyrinth seal was to use a transient Lagrangian droplet model coupled with a liquid film analysis. Similar types of analyses have been carried out on crankshaft bearings in internal combustion engines. Due to time constraints and computing resource it
was decided not to include the liquid film analysis, as the end result would be still be relatively correct. The rotational speed was kept at 11,000 rev/min and the time step
0.5 degrees.

Inlet Bearing Leakage:
A generic spreadsheet was adapted to determine the static load on inlet bearing and since the geometry and oil type (Shell Turbo Oils Type T46) were known, an analysis was carried out by Harrison (2) to determine the oil leakage from the bearing. He found it was 0.4 m3/s for the bearing. In order that a fine mist of oil was produced 80 injection points were defined, and the particle diameter was chosen to be 0.05 mm. The injection rate was then found to be 4.33 x 106 droplets/s at a temperature of 50°C. Using the above calculations at a maximum bearing clearance of 0.124 mm, the velocity of the oil droplets was found to be 13.5 m/s.

Results and Discussion:
A plot of air leakage against clearance is shown in Figure 3. It can be seen that with all the seal fins present, a worst case pressure drop of 2.18 bar across the seal and a clearance of 0.25 mm, the leakage across the seal was just over 0.07 kg/s (less than 0.5% of the total air mass flow rate through the engine), compared to 0.014
kg/s when the clearance was 0.05 mm. At 1 bar pressure drop across the seal, at a clearance of 0.25 mm the airflow was just over 0.04 kg/s compared to 0.008 kg/s
when the clearance was 0.05 mm. The peak Mach number across the seal fins was approximately 1 when the pressure drop was 2.18 bar, i.e. the flow was almost
choked at all seal clearances. At 1 bar the peak Mach number was approximately 0.7. When one fin was removed (first fin downstream of the inlet pipe in the direction
of the compressor exit) then the increase in airflow across the seal remained roughly constant at about 7% at both pressure drops, at each fin clearance, Figure 3.

Comparison of the straight through loss at a fin clearance of 0.05 mm and the loss incurred when the fins had cut into the seal shows that a reduction in loss of about
5% at both pressure drops when the fins had cut into the seal, Figure 3. Due to time constraints and computer limitations only two models were run with oil injection from
the inlet bearing:

1. At a clearance of 0.25 mm and a pressure drop of 2.18 Bar.
   
2. At a clearance of 0.25 mm and the inlet flow pipe blocked.

Two phase Lagrangian modeling can only be simulated when the second fluid phase occupies less than 40% by volume of the computational cell. If this was exceeded
the model would become unstable, and fail. Due to the positioning of the oil injection points, the flow boundaries and its nature, only about 4 revolutions of the engine
were possible before the instability mentioned above occurred. However this was enough time to show that in model 1 (Figure 5) no oil passed across the seal even though oil had passed the lip on the rotor. Model 2 (Figure 7) showed oil passing through the seal, which would very quickly enter the compressor. The models show
progression of oil particles through the seal. Figures 4 and 6 show the centerline velocities, to the same scale 0 m/s to 60 m/s. In model 1 the maximum velocity was
60 m/s whilst in model 2 the maximum velocity was found to be 310 m/s.

Conclusion
It has been shown that for the clearances considered here (Figure 3) under steady state conditions there will be negligible reduction in compressor delivery pressure and flow rate. For the worst case (0.25mm clearance at a pressure drop of 2.18 Bar) 70 g/s seal air leaked across the seal (less than 0.5% of the total air mass flow rate). For the largest clearance considered there was sufficient mass flow across the seal to prevent oil ingress to the seal and hence compressor. Oil is most likely to enter the compressor via the lab seal when the seal airflow rate is at a minimum, i.e. if the air pipe is blocked.

Recommendations
Based on the analysis conducted in this study the compressor inlet labyrinth seal repair tolerance should be reviewed with the intent of implementing relaxed
clearances.

Further studies
Transient effects, which were considered to be secondary, such as thermal growth and start up / shut down effects, were not considered in this study.