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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.

Copyright © 2016 by ASME
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References

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Untaroiu, A. , Untaroiu, C. D. , Wood, H. G. , and Allaire, P. E. , 2013, “ Numerical Modeling of Fluid-Induced Rotordynamic Forces in Seals With Large Aspect Ratios,” ASME J. Eng. Gas Turbines Power, 135(1), p. 012501. [CrossRef]
Migliorini, P. J. , Untaroiu, A. , Wood, H. G. , and Allaire, P. E. , 2012, “ A Computational Fluid Dynamics/Bulk-Flow Hybrid Method for Determining Rotordynamic Coefficients of Annular Gas Seals,” ASME J. Tribol., 134(2), p. 022202. [CrossRef]
Untaroiu, A. , Hayrapetian, V. , Untaroiu, C. D. , Wood, H. G. , Schiavello, B. , and McGuire, J. , 2013, “ On the Dynamic Properties of Pump Liquid Seals,” ASME J. Fluids Eng., 135(5), p. 051104. [CrossRef]
Morgan, N. R. , Untaroiu, A. , Migliorini, P. J. , and Wood, H. G. , 2014, “ Design of Experiments to Investigate Geometric Effects on Fluid Leakage Rate in a Balance Drum Seal,” ASME J. Eng. Gas Turbines Power, 137(3), p. 032501.
Morgan, N. R. , Wood, H. G. , Migliorini, P. J. , and Untaroiu, A. , 2014, “ Groove Geometry Optimization of Balance Drum Labyrinth Seal to Minimize Leakage Rate by Experimental Design,” 13th EDF/Pprime Workshop: Energy Saving in Seals, Poitier, France, Oct. 2.
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Asok, S. P. , Sankaranarayanasamy, K. , Sundararajan, T. , Rajesh, K. , and Sankar, G. , 2007, “ Neural Network and CFD-Based Optimisation of Square Cavity and Curved Cavity Static Labyrinth Seals,” Tribol. Int., 40(7), pp. 1204–1216. [CrossRef]
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Figures

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Fig. 1

Fluid flow path through seal geometry

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Fig. 2

First experimental design example and parameterization

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Fig. 3

Second experimental design example

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Fig. 4

Third experimental design example

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Fig. 5

Minimum depth, width > flat width

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Fig. 6

Minimum depth, flat width > width

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Fig. 7

Maximum depth, converging angles

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Fig. 8

Maximum depth, parallel angles

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Fig. 9

Maximum depth, diverging angles

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Fig. 10

Spacing between groove cavities, tangential to groove front

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Fig. 11

Spacing between groove cavities, horizontal between groove radii

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Fig. 12

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

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Fig. 13

Second mesh structure example, wide and shallow groove skewed left

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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. 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. 22

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

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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. 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. 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. 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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