Research Papers

On the Influence of the Entrance Section on the Rotordynamic Performance of a Pump Seal With Uniform Clearance: A Sharp Edge Versus A Round Inlet

[+] Author and Article Information
Jing Yang

Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843
e-mail: yangjing@tamu.edu

Luis San Andrés

Mast-Childs Chair Professor
Fellow ASME
Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843
e-mail: lsanandres@tamu.edu

Manuscript received June 25, 2018; final manuscript received June 28, 2018; published online December 4, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(3), 031029 (Dec 04, 2018) (9 pages) Paper No: GTP-18-1343; doi: 10.1115/1.4040742 History: Received June 25, 2018; Revised June 28, 2018

Secondary flows through annular seals in pumps must be minimized to improve their mechanical efficiency. Annular seals, in particular balance piston seals, also produce rotordynamic force coefficients, which easily control the placement of rotor critical speeds and determine system stability. A uniform clearance annular seal produces a direct (centering) static stiffness as a result of the sudden entrance pressure drop at its inlet plane when the fluid flow accelerates from an upstream (stagnant) flow region into a narrow film land. This so-called Lomakin effect equates the entrance pressure drop to the dynamic flow head through an empirical entrance pressure loss coefficient. Most seal designs regard the inlet as a sharp edge or square corner. In actuality, a customary manufacturing process could produce a rounded corner at the seal inlet. Furthermore, after a long period of operation, a sharp corner may wear out into a round section. Notice that to this date, bulk-flow model (BFM) analyses rely on a hitherto unknown entrance pressure coefficient to deliver accurate predictions for seal force coefficients. This paper establishes the ground to quantify the influence of an inlet round corner on the performance of a water lubricated seal reproducing a configuration tested by Marquette et al. (1997). The smooth surface seal has clearance Cr = 0.11 mm, length L = 35 mm, and diameter D = 76 mm (L/D = 0.46). The test case considers design operation at 10.2 krpm and 6.9 MPa pressure drop. Computational fluid dynamics (CFD) simulations apply to a seal with either a sharp edge or an inlet section with curvature rc varying from ¼Cr to 5Cr. Note the largest radius (rc) is just 1.6% of the overall seal length L. Going from a sharp edge inlet plane to one with a small curvature rc = ¼Cr produces a ∼20% decrease on the inlet pressure loss coefficient (ξ). A further reduction occurs with a larger circular corner; ξ drops from 0.43 to 0.17. That is, the entrance pressure loss will be lesser in a seal with a curved inlet. This can occur easily if the inlet edge wears due to solid particles eroding the seal inlet section. Further CFD simulations show that operating conditions in rotor speed and pressure drop do not affect the inlet loss coefficient, while the inlet circumferential swirl velocity does. In addition, further CFD results for a shorter (half) length seal produce a very similar entrance loss coefficient, whereas an enlarged (double) clearance seal leads to an increase in the entrance pressure loss parameter as the inlet section becomes less round. CFD predictions for most rotordynamic coefficients are within 10% relative to published test data, except for the direct damping coefficient C. For the seal with a rounded edge (rc = 5 Cr) at the inlet plane, both the direct stiffness K and direct damping C decrease about 10% compared against the coefficients for the seal with a sharp inlet edge. The other force coefficients, namely cross-coupled stiffness and added mass, are unaffected by the inlet edge geometry. The same result holds for seal leakage, as expected. A BFM incorporates the CFD derived entrance pressure loss coefficients and produces rotordynamic coefficients for the same operating conditions. The CFD and BFM predictions are in good agreement, though there is still ∼10% discrepancy for the direct stiffnesses delivered by the two methods. In the end, the analysis of the CFD results quantifies the pressure loss coefficient as a function of the inlet geometry for ready use in engineering BFM tools.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Childs, D. W. , 2013, Turbomachinery Rotordynamics With Case Studies, 1st ed., Minter Spring Pubs., College Station, TX, Chap. 7.
Hirs, G. G. , 1973, “ A Bulk-Flow Theory for Turbulence in Lubricant Films,” ASME J. Lubrication Tech. 95(2), pp. 137–145. [CrossRef]
San Andrés, L. , 1991, “ Analysis of Variable Fluid Properties, Turbulent Annular Seals,” ASME J. Tribol., 113(4), pp. 694–702. [CrossRef]
Marquette, O. R. , Childs, D. W. , and San Andrés, L. , 1997, “ Eccentricity Effects on the Rotordynamic Coefficients of Plain Annular Seals: Theory Versus Experiment,” ASME J. Tribol., 119(3), pp. 443–447. [CrossRef]
Al-Qutub, A. M. , Elrod, D. , and Coleman, H. W. , 2000, “ A New Friction Factor Model and Entrance Loss Coefficient for Honeycomb Annular Gas Seals,” ASME J. Tribol., 122(3), pp. 622–627. [CrossRef]
Benedict, R. P. , Carlucci, N. A. , and Swetz, S. D. , 1966, “ Flow Losses in Abrupt Enlargements and Contractions,” J. Eng. Power, 88(1), pp. 73–80. [CrossRef]
Bullen, P. R. , Cheeseman, D. J. , Hussain, L. A. , and Ruffell, A. E. , 1987, “ The Determination of Pipe Contraction Pressure Loss Coefficients for Incompressible Turbulent Flow,” Int. J. Heat Fluid Flow, 8(2), pp. 111–118. [CrossRef]
Constantinescu, V. N. , and Galetuse, S. , 1976, “ Pressure Drop Due to Inertia Forces in Step Bearings,” J. Lubr. Technol., 98(1), pp. 167–174. [CrossRef]
San Andrés, L. , and Velthuis, J. F. M. , 1992, “ Laminar Flow in a Recess of a Hydrostatic Bearing,” Tribol. Trans., 35(4), pp. 738–744. [CrossRef]
Ha, T. W. , and Choe, B. C. , 2012, “ Numerical Simulation of Rotordynamic Coefficients for Eccentric Annular-Type-Plain-Pump Seal Using CFD Analysis,” J. Mech. Sci. Technol., 26(4), pp. 1043–1048. [CrossRef]
Arghir, M. , and Frene, J. , 2004, “ A Bulk-Flow Analysis of Static and Dynamic Characteristics of Eccentric Circumferentially Grooved Liquid Annular Seals,” ASME J. Tribol., 126(2), pp. 316–325. [CrossRef]
Migliorini, P. J. , Untaroiu, A. , Wood, H. G. , and Allaire, P. E. , 2013, “ A Computational Fluid Dynamics/Bulk-Flow Hybrid Method for Determining Rotordynamic Coefficients of Annular Gas Seals,” ASME J. Tribol., 134(2), p. 022202. [CrossRef]
San Andrés, L. , Wu, T. , Maeda, H. , and Ono, T. , 2018, “ A Computational Fluid Dynamics Modified Bulk Flow Analysis for Circumferentially Shallow Grooved Liquid Seals,” ASME J. Eng. Gas Turbines Power, 140(1), p. 012504. [CrossRef]
Grigoriev, B. , Schmied, J. , Fedorov, A. , and Lupuleac, S. , 2006, “ Consideration of the Pressure Entrance Loss for the Analysis of Rotordynamic Gas Seal Forces,” Seventh IFTOMM Conference on Rotor Dynamics, Vienna, Austria, Sept. 25–28, Paper No. 245. http://www.delta-js.ch/file/356/Seal_IFToMM.pdf
Elrod, D. A. , Childs, D. W. , and Nelson, C. C. , “ CAn Annular Gas Seal Analysis Using Empirical Entrance and Exit Region Friction Factors,” ASME J. Tribol., 112(2), pp. 196–204. [CrossRef]
ANSYS, 2013, ANSYS Fluent Usereedx.doi.org/, ANSYS Inc., Canonsburg, PA.
San Andrés, L. , 2010, “ Annular Pressure (Damper) Seals: Modern Lubrication Theory,” Notes 12(a), Texas A&M University Digital Libraries, College Station, TX, accessed Oct. 11, 2017, http://oaktrust.library.tamu.edu/handle/1969.1/93197


Grahic Jump Location
Fig. 1

Geometry of an annular pressure seal and coordinate system

Grahic Jump Location
Fig. 2

Schematic diagram of seal inlet plane with either a square or a round corner (not to scale)

Grahic Jump Location
Fig. 3

View of mesh for two-dimensional flow in an annular pressure seal. Seal with an inlet round corner (rc = ½Cr). Upstream flow section with length and width Lu = wu = ¼ L shown. Inset showcases mesh density at inlet section of seal land.

Grahic Jump Location
Fig. 4

Predicted static pressure (MPa) on rotor surface versus axial direction z (m), for annular seal with a square corner or a round corner (rc = ¼Cr and 5Cr): (a) distribution from upstream section to seal exit plane; (b) distribution around seal entrance plane. Water annular seal (L/D = 0.46, Cr = 0.11 mm): 6.89 MPa pressure drop and rotor speed of 10,200 rpm.

Grahic Jump Location
Fig. 5

Pressure contours (MPa) around seal entrance with (a) a square corner or (b) a round corner (rc = Cr). Water annular seal (L/D = 0.46, Cr = 0.11 mm): 6.89 MPa pressure drop and rotor speed 10.2 krpm.

Grahic Jump Location
Fig. 6

Streamlines near seal entrance plane with (a) a sharp edge or (b) a circular corner (rc = Cr). Water annular seal (L/D = 0.46, Cr = 0.11 mm): 6.89 MPa pressure drop and rotor speed 10.2 krpm.

Grahic Jump Location
Fig. 7

CFD-derived entrance pressure loss coefficient (ξ) versus corner radius for a nominal length seal (L), a seal with length Ls = ½L, a seal with inlet swirl ratio equaling to 1.0 or −0.5, a seal with rotor speed Ω1 or Ω2, and seal with a twofold clearance

Grahic Jump Location
Fig. 8

Schematic view of rotor spinning with angular speed Ω and orbiting about its center with orbit amplitude r and whirl frequency ω (not to scale). Fixed coordinates (X,Y) and rotating coordinates (X¯,Y¯).

Grahic Jump Location
Fig. 9

Components of seal reaction force (radial and tangential) (FX¯,FY¯)/r versus excitation frequency ω. Effect of inlet corner shape (sharp to round). Water annular seal (L/D = 0.46, Cr = 0.11 mm): 6.89 MPa pressure drop and rotor speed of 10.2 krpm. Test data from Ref. [4].

Grahic Jump Location
Fig. 10

Predicted seal rotordynamic force coefficients versus inlet corner radius (rc/Cr): (a) direct stiffness, K; (b) cross-coupled stiffness, k; (c) direct damping, C; (d) cross-coupled damping, c; (e) inertia, M; (f) WFR. Water annular seal (L/D = 0.46 and Ls/D = 0.23, Cr = 0.11 mm): 6.89 MPa pressure drop and rotor speed of 10,200 rpm. Test data from Ref. [4].

Grahic Jump Location
Fig. 11

Predicted seal inlet loss coefficient ratio (1 + ξ)/ (1 + ξ1 L) versus ratio of upstream flow length Lu (= width wu = Lu) and seal length L. Water lubricated seal (L/D = 0.46, Cr = 0.11 mm): ΔP = 6.89 MPa and 10.2 krpm rotor speed.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In