The aim of this paper is to present a turbulence model that allows turbulent flows between smooth and/or rough walls to be dealt with. After analyzing available literature data, an improvement of the Elrod, Ng, and Pan turbulence model is proposed, taking into account the effect of wall asperities. This model is then applied to a hydrostatic mechanical seal that is rough on one face, operating in nonlaminar flow. The roughness is due to particle deposits occurring during the seal operation. As expected, the wall roughness leads to a decrease in leakage rate.
Issue Section:
Other (Seals, Manufacturing)
1.
Childs
, D. A.
, 1993, Turbomachinery Rotordynamics—Phenomena, Modeling & Analysis
, Wiley
, New York
.2.
Brunetiere
, N.
, and Tournerie
, B.
, 2006, “Influence of Inertia in Radial Flows—Application to Hydrostatic Seals
,” ASME J. Tribol.
0742-4787, 128
(3
), pp. 566
–574
.3.
Bassani
, R.
, Ciulli
, E.
, Piccigallo
, B.
, Pirozzi
, M.
, and Staffilano
, U.
, 2006, “Hydrostatic Lubrication With Cryogenic Fluids
,” Tribol. Int.
0301-679X, 39
(8
), pp. 827
–832
.4.
Schlichting
, H.
, 1960, Boundary Layer Theory
, 4th ed., McGraw-Hill
, New York
.5.
Childs
, D. W.
, and Kim
, C. -H.
, 1985, “Analysis and Testing for Rotordynamic Coefficients of Turbulent Annular Seals With Different, Directionally-Homogeneous Surface-Roughness Treatment for Rotor and Stator Elements
,” ASME J. Tribol.
0742-4787, 107
(3
), pp. 296
–306
.6.
Hashimoto
, H.
, and Wada
, S.
, 1989, “Theoretical Approach to Turbulent Lubrication Problems Including Surface Roughness Effects
,” ASME J. Tribol.
0742-4787, 111
(1
), pp. 17
–22
.7.
Nelson
, C. C.
, and Nguyen
, D. T.
, 1987, “Comparison of Hirs’ Equation With Moody’s Equation for Determining Rotordynamic Coefficients of Annular Pressure Seals
,” ASME J. Tribol.
0742-4787, 109
(1
), pp. 144
–148
.8.
San Andres
, L. A.
, 1992, “Analysis of Turbulent Hydrostatic Bearings With a Barotropic Cryogenic Fluid
,” ASME J. Tribol.
0742-4787, 114
(4
), pp. 755
–765
.9.
Colebrook
, C. F.
, 1939, “Turbulent Flow in Pipes, With Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws
,” J. Inst. Civ. Eng.
, 11
(4
), pp. 133
–156
. 0368-245510.
Lucas
, V.
, Danaila
, S.
, Bonneau
, O.
, and Frêne
, J.
, 1994, “Roughness Influence on Turbulent Flow Through Annular Seals
,” ASME J. Tribol.
0742-4787, 116
(2
), pp. 321
–329
.11.
Arghir
, M.
, and Frêne
, J.
, 1997, “Inclusion of Roughness Effects in Perturbed Navier-Stokes Rotordynamic Methods
,” ASME J. Tribol.
0742-4787, 119
(2
), pp. 358
–360
.12.
Ferziger
, J. H.
, and Peric
, M.
, 2002, Computational Methods for Fluid Dynamics
, 3rd ed., Springer
, Berlin
, Chap. 9.13.
Ng
, C. W.
, 1964, “Fluid Dynamic Foundation of Turbulent Lubrication Theory
,” ASLE Trans.
0569-8197, 7
, pp. 311
–321
.14.
Ng
, C. W.
, and Pan
, C. H. T.
, 1965, “A Linearized Turbulent Lubrication Theory
,” ASME J. Basic Eng.
0021-9223, 87
, pp. 675
–688
.15.
Elrod
, H. G.
, and Ng
, C. W.
, 1967, “A Theory for Turbulent Films and Its Application to Bearings
,” ASME J. Lubr. Technol.
0022-2305, 89
, pp. 346
–362
.16.
Metz
, J.
, Pierre-Danos
, I.
, Cailleaux
, J. -P.
, and Randrianarivo
, L.
, 2003, “Hydrostatic Seal Operation in Reactor Coolant Pumps of French Pressurized Water Reactor Nuclear Power Plant
,” Proceedings of High Performance Rotary Shaft Seals Workshop
, Poitiers
, France
, pp. C1
–C10
.17.
Bech
, K.
, Tillmark
, N.
, Alfredsson
, P.
, and Andersson
, H.
, 1995, “An Investigation of Turbulent Plane Couette Flow
,” J. Fluid Mech.
0022-1120, 286
, pp. 291
–325
.18.
Kitoh
, O.
, Nakabyashi
, K.
, and Nishimura
, F.
, 2005, “Experimental Study on Mean Velocity and Turbulence Characteristics of Plane Couette Flow: Low-Reynolds-Number Effects and Longitudinal Vortical Structure
,” J. Fluid Mech.
0022-1120, 539
, pp. 199
–227
.19.
Niederschulte
, M.
, Adrian
, R.
, and Hanratty
, T.
, 1990, “Measurements of Turbulent Flow at Low Reynolds Numbers
,” Exp. Fluids
0723-4864, 9
, pp. 222
–230
.20.
Günther
, A.
, Papavassiliou
, D.
, Warholic
, M.
, and Hanratty
, T.
, 1998, “Turbulent Flow in a Channel at Low Reynolds Number
,” Exp. Fluids
0723-4864, 25
, pp. 503
–511
.21.
Aydin
, E.
, and Leutheusser
, H.
, 1991, “Plane-Couette Flow Between Smooth and Rough Walls
,” Exp. Fluids
0723-4864, 11
, pp. 302
–312
.22.
Tsukahara
, T.
, Kawamura
, H.
, and Shingai
, K.
, 2006, “DNS of Turbulent Couette Flow With Emphasis on the Large-Scale Structure in the Core Region
,” J. Turbul.
1468-5248, 7
(19
), pp. 1
–16
.23.
Dean
, R.
, 1974, “Reynolds Number Dependence of Skin Friction and Other Bulk Flow Variables in Two-Dimensional Duct Flow
,” ASME J. Fluids Eng.
0098-2202, 100
, pp. 215
–223
.24.
Bakken
, O.
, Krogstad
, P.
, Ashrafian
, A.
, and Andersson
, H.
, 2005, “Reynolds Number Effects in the Outer Layer of the Turbulent Flow in a Channel With Rough Walls
,” Phys. Fluids
1070-6631, 17
, p. 065101
.25.
Eckelmann
, H.
, 1974, “The Structure of the Viscous Sublayer and the Adjacent Wall Region in a Turbulent Channel Flow
,” J. Fluid Mech.
0022-1120, 65
, pp. 439
–459
.26.
El Telbany
, M.
, and Reynolds
, A.
, 1980, “Velocity Distributions in Plane Turbulent Channel Flows
,” J. Fluid Mech.
0022-1120, 100
, pp. 1
–29
.27.
Johansson
, A.
, and Alfredsson
, P.
, 1982, “On the Structure of Turbulent Channel Flow
,” J. Fluid Mech.
0022-1120, 122
, pp. 295
–314
.28.
Kim
, J.
, Moin
, P.
, and Moser
, R.
, 1987, “Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number
,” J. Fluid Mech.
0022-1120, 177
, pp. 133
–166
.29.
Papavassiliou
, D.
, and Hanratty
, T.
, 1997, “Interpretation of Large-Scale Structures Observed in a Turbulent Plane Couette Flow
,” Int. J. Heat Fluid Flow
0142-727X, 18
, pp. 55
–69
.30.
Patel
, V. C.
, and Head
, M. R.
, 1969, “Some Observations on Skin Friction and Velocity Profiles in Fully Developed Pipe and Channel Flows
,” J. Fluid Mech.
0022-1120, 38
, pp. 181
–201
.31.
Robertson
, J.
, 1959, “On Turbulent Plane-Couette Flow
,” Proceedings of the Sixth Midwestern Conference on Fluid Mechanics
, pp. 169
–182
.32.
Wei
, T.
, and Willmarth
, W.
, 1989, “Reynolds Number Effects on the Structure of a Turbulent Channel Flow
,” J. Fluid Mech.
0022-1120, 204
, pp. 57
–95
.33.
Moody
, L. F.
, 1944, “Friction Factors for Pipe Flow
,” Trans. ASME
0097-6822, 66
, pp. 671
–684
.34.
Brunetière
, N.
, 2005, “A Modified Turbulence Model for Low Reynolds Number—Application to Hydrostatic Seals
,” ASME J. Tribol.
0742-4787, 127
(1
), pp. 130
–140
.35.
Leonardi
, S.
, Orlandi
, P.
, Djenidi
, L.
, and Antonia
, R. A.
, 2004, “Structure of Turbulent Channel Flow Square Bars on One Wall
,” Int. J. Heat Fluid Flow
0142-727X, 25
, pp. 384
–392
.36.
Becker
, K. M.
, 1963, “Measurement of Convective Heat Transfer From a Horizontal Cylinder Rotating in a Tank of Water
,” Int. J. Heat Mass Transfer
0017-9310, 6
, pp. 1053
–1062
.37.
Brunetiere
, N.
, Tournerie
, B.
, and Frêne
, J.
, 2002, “Influence of Fluid Flow Regime on Performances of Non-Contacting Liquid Face Seals
,” ASME J. Tribol.
0742-4787, 124
(3
), pp. 515
–523
.38.
Brunetiere
, N.
, Tournerie
, B.
, and Frêne
, J.
, 2003, “TEHD Lubrication of Mechanical Face Seals in Stable Tracking Mode—Part 2: Parametric Study
,” ASME J. Tribol.
0742-4787, 125
(3
), pp. 617
–627
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