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Research Papers: Gas Turbines: Structures and Dynamics

Design of Experiments to Investigate Geometric Effects on Fluid Leakage Rate in a Balance Drum Seal

[+] Author and Article Information
Neal R. Morgan

Rotating Machinery and Controls (ROMAC) Laboratory,
Department of Mechanical
and Aerospace Engineering,
University of Virginia,
122 Engineer's Way,
Charlottesville, VA 22904-4746
e-mail: nrm6dr@virginia.edu

Houston G. Wood

Rotating Machinery and Controls (ROMAC) Laboratory,
Department of Mechanical
and Aerospace Engineering,
University of Virginia,
122 Engineer's Way,
Charlottesville, VA 22904-4746
e-mail: hgw9p@virginia.edu

Alexandrina Untaroiu

Laboratory for Turbomachinery and Components,
Department of Biomedical Engineering
and Mechanics,
Virginia Polytechnic Institute and State University,
495 Old Turner Street,
Blacksburg, VA 24061
e-mail: alexu@vt.edu

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received September 10, 2015; final manuscript received December 13, 2015; published online February 17, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(7), 072506 (Feb 17, 2016) (12 pages) Paper No: GTP-15-1443; doi: 10.1115/1.4032416 History: Received September 10, 2015; Revised December 13, 2015

Grove configuration has a direct influence on the performance of the labyrinth seal. In this study, the geometry of the groove cavities in a water balance drum labyrinth seal was varied to investigate the effects on fluid leakage. A design of experiments (DOEs) study varied the groove cavity cross section through various trapezoidal shapes with one or both internal base angles obtuse. The grooves are parameterized by the groove width connected to the jet-flow region, the internal entrance and exit angles, the flat width inside the groove, and the depth. The corners inside the groove cavity are filleted with equal radii. As with the baseline model, the grooves are evenly spaced along the seal length and identical copies of each other. The flow path starting at the rear of the pump impeller and proceeding through the seal was created as a 5-deg sector computational fluid dynamics (CFD) model in ansys cfx. Three five-level factorial designs were selected for the cases where the entrance angle is obtuse and the exit angle is acute, the exit angle obtuse and entrance angle acute, and both angles were obtuse. The feasible geometries from each factorial design were selected based on the nonlinear geometric constraints, and CFD simulation experiments were performed in ansys cfx. The leakage results from these simulation experiments were then analyzed by multifactor linear regression to create prediction equations relating the geometric design variables to leakage and enable geometric optimization for minimum leakage. Streamline plots along the seal cross section were then used to visualize the flow and understand regression trends. This study investigates the effect of groove cavities with obtuse internal entrance and exit angles on vortex size and position and subsequent seal leakage.

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References

Figures

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Fig. 1

Fluid flow path through seal geometry

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Fig. 13

Second mesh structure example, wide and shallow groove skewed left

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Fig. 12

First mesh structure example, wide groove with both internal angles obtuse

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Fig. 7

Maximum depth, converging angles

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Fig. 6

Minimum depth, flat width > width

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Fig. 5

Minimum depth, width > flat width

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Fig. 4

Third experimental design example

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Fig. 3

Second experimental design example

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Fig. 2

First experimental design example and parameterization

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Fig. 23

Experimental design 3: geometry of predicted optimum leakage versus baseline geometry

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Fig. 24

Experimental design 3: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of groove width and flat width

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Fig. 27

Experimental design 3: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of groove width and depth

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Fig. 28

Overlap comparison of the optimal groove geometries for each design space

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Fig. 29

Experimental design 1: a groove geometry optimized for minimum leakage (w = 4.13, f = 4.34, d = 0.35, α = 169.55, and β = 77.20)

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Fig. 14

Experimental design 1: geometry of predicted optimum leakage versus baseline geometry

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Fig. 15

Experimental design 1: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of groove width and flat width

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Fig. 16

Experimental design 1: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of the groove entrance and exit angles

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Fig. 17

Experimental design 1: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of groove width and depth

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Fig. 22

Experimental design 2: geometry of predicted optimum leakage versus baseline geometry

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Fig. 25

Experimental design 3: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of groove width and entrance angle

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Fig. 26

Experimental design 3: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of groove depth and exit angle

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Fig. 11

Spacing between groove cavities, horizontal between groove radii

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Fig. 10

Spacing between groove cavities, tangential to groove front

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Fig. 9

Maximum depth, diverging angles

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Fig. 8

Maximum depth, parallel angles

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Fig. 18

Experimental design 2: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of groove width and flat width

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Fig. 19

Experimental design 2: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of groove width and entrance angle

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Fig. 20

Experimental design 2: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of groove width and exit angle

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Fig. 21

Experimental design 2: cubic regression model response surface of leakage rate sensitivity near the predicted optimal design point, in terms of groove width and depth

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Fig. 30

Experimental design 2: a groove geometry optimized for minimum leakage (w = 4.46, f = 4.27, d = 0.48, α = 77.34, and β = 165.80)

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Fig. 31

Experimental design 3: a groove geometry optimized for minimum leakage (w = 4.40, f = 4.29, d = 0.58, α = 163.76, and β = 100.80)

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