Various corrections were previously proposed to account for wall roughness with the k–ω and shear stress transport (SST) models. A simplified analysis, based upon the wall region analysis, is proposed to characterize the behavior of these roughness corrections. As this analysis points out some deficiencies for each correction, two new corrections are proposed for the SST model, to reproduce different behaviors, mainly in the transition regime. The correction development is based upon a previously developed strategy. A large set of boundary layer experiments is used to compare the different roughness corrections, confirm the failures of previous proposals, and validate the present ones. Moreover, it assesses the proposed simplified analysis. It also evidences the difficulty to determine the equivalent sand grain roughness for a given surface. The Colebrook based correction is recommended while the Nikuradse based one can add information about the envelope of possible behaviors in the transition regime.
Issue Section:
Fundamental Issues and Canonical Flows
References
1.
Nikuradse
, J.
, 1933
, “Strömungsgesetze in Rauhen Rohren
,” VDI-Forschungsheft, July/August, Technical Report No. 361.2.
Nikuradse
, J.
, 1937
, “Laws of Flows in Rough Pipes
,” NACA, WA, April, Technical Memorandum 1292.3.
Bons
, J.
, Taylor
, R.
, McLain
, S.
, and Rivir
, R.
, 2001
, “The Many Faces of Turbine Surface Roughness
,” ASME J. Turbomach.
, 123
(4)
, pp. 739
–748
.10.1115/1.14001154.
Lu
, M.
, and Liou
, W.
, 2009
, “New Two-Equation Closure for Rough-Wall Turbulent Flows Using the Brinkman Equation
,” AIAA J.
, 47
(2
), pp. 386
–398
.10.2514/1.384045.
Busse
, A.
, and Sandham
, N.
, 2012
, “Parametric Forcing Approach to Rough-Wall Turbulent Channel Flow
,” J. Fluid Mech.
, 712
, pp. 169
–202
.10.1017/jfm.2012.4086.
Aupoix
, B.
, Cousteix
, J.
, Délery
, J.
, Oswald
, J.
, Reijasse
, P.
, and Thibert
, J. J.
, 1998
, “Expertise ONERA sur les Causes du Roulis du Vol Ariane 502. Examen de L'effet de la Chambre Propulsive et de la Tuyère VULCAIN
,” ONERA, Mars, Rapport Technique RT 5200/25 DMAE/Y.7.
Bons
, J.
, McClain
, S.
, Wang
, Z.
, Chi
, X.
, and Shih
, T.
, 2008
, “A Comparison of Approximate Versus Exact Representations of Roughness for CFD Calculations of Cf and St
,” ASME J. Turbomach.
, 130
(2)
, p. 021024
.10.1115/1.27521908.
Aupoix
, B.
, 1994
, “Modelling of Boundary Layers Over Rough Surfaces
,” Advances in Turbulence
, V. R.
Benzi
, ed., Fifth European Turbulence Conference
, Siena, Italy, July 5–8, Kluwer
, pp. 16
–20
.9.
Robertson
, J.
, 1961
, “Surface Resistance as a Function of the Concentration and Size of Roughness Elements
,” Ph.D. thesis, State University of Iowa, Iowa.10.
Finson
, M.
, 1982
, “A Model for Rough Wall Turbulent Heating and Skin Friction
,” AIAA
Paper No. 82-0199.11.
Coleman
, H.
, Hodge
, B.
, and Taylor
, R.
, 1983
, “Generalized Roughness Effects on Turbulent Boundary Layer Heat Transfer—A Discrete Element Predictive Approach for Turbulent Flow Over Rough Surfaces
,” Air Force Armament Laboratory, Mississippi State University, November, No. AFATL-TR-83-90.12.
McClain
, S.
, Hodge
, B.
, and Bons
, J.
, 2004
, “Predicting Skin Friction and Heat Transfer for Turbulent Flow Over Real Gas Turbine Surface Roughness Using the Discrete Element Method
,” ASME J. Turbomach.
, 126
(2)
, pp. 259
–267
.10.1115/1.174077913.
McClain
, S.
, Collins
, S.
, Hodge
, B.
, and Bons
, J.
, 2006
, “The Importance of the Mean Elevation in Predicting Skin Friction for Flow Over Closely Packed Surface Roughness
,” ASME J. Fluids Eng.
, 128
(3)
, pp. 579
–586
.10.1115/1.217516414.
Kojima
, H.
, Toda
, K.
, and Yamamoto
, M.
, 2002
, “Computation of Aerodynamic Performance of Airfoil With Surface Roughness
,” Fifth International Symposium on Engineering Turbulence Modelling and Measurements
, Mallorca, Spain, W.
Rodi
, and N.
Fueyo
, eds., Elsevier
, pp. 629
–636
.15.
Spalart
, P.
, and Allmaras
, S.
, 1992
, “A One-Equation Turbulence Model for Aerodynamic Flows
,” AIAA
Paper No. 92-0439.16.
Spalart
, P.
, and Allmaras
, S.
, 1994
, “A One-Equation Turbulence Model for Aerodynamic Flows
,” Rech. Aérosp.
, 1
, pp. 5
–21
.17.
Menter
, F.
, 1994
, “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,” AIAA J.
, 32
(8
), pp. 1598
–1605
.10.2514/3.1214918.
Perry
, A.
, Schofield
, W.
, and Joubert
, P.
, 1969
, “Rough Wall Turbulent Boundary Layers
,” J. Fluid Mech.
, 37
(2)
, pp. 383
–413.10.1017/S002211206900061919.
Schlichting
, H.
, 1936
, “Experimentelle Untersuchungen zum Rauhigkeitsproblem
,” Ing. Arch.
, VII
(1
), pp. 1
–34
.10.1007/BF0208416620.
Schlichting
, H.
, 1937
, “Experimental Investigation of the Problem of Surface Roughness
,” NACA, WA, April, Technical Memorandum 823.21.
Ligrani
, P.
, and Moffat
, R.
, 1986
, “Structure of Transitionally Rough and Fully Rough Turbulent Boundary Layers
,” J. Fluid Mech.
, 162
, pp. 69
–98
.10.1017/S002211208600193322.
Colebrook
, C.
, and White
, C.
, 1937
, “Experiments With Fluid Friction in Roughened Pipes
,” Proc. R. Soc. London, A
, 161
, pp. 367
–381
.10.1098/rspa.1937.015023.
Colebrook
, C.
, 1938–1939
, “Turbulent Flow in Pipes, With Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws
,” J. Inst. Civ. Eng.
, 21
, pp. 133
–156
.24.
Grigson
, C.
, 1992
, “Drag Losses of New Ships Caused by Hull Finish
,” J. Ship Res.
, 36
(2
), pp. 182
–196
.25.
Townsend
, A.
, 1976
, The Structure of Turbulent Shear Flow
, 2nd ed., Cambridge Monographs on Mechanics and Applied Mathematics
, Cambridge University Press, Cambridge, UK.26.
Jiménez
, J.
, 2004
, “Turbulent Flows Over Rough Walls
,” Annu. Rev. Fluid Mech.
, 36
, pp. 173
–196
.10.1146/annurev.fluid.36.050802.12210327.
Flack
, K.
, Schultz
, M.
, and Connelly
, J.
, 2007
, “Examination of a Critical Roughness Height for Outer Layer Similarity
,” Phys. Fluids
, 19
, p. 095104
.10.1063/1.275770828.
Kolmogorov
, A.
, 1942
, “Equations of Turbulent Motion of an Incompressible Fluid
,” Izv. Acad. Sci. USSR, Phys.
, 6
(1–2
), pp. 56
–58
.29.
Wilcox
, D.
, 1988
, “Reassessment of the Scale-Determining Equation for Advanced Turbulence Models
,” AIAA J.
, 26
(11
), pp. 1299
–1310
.10.2514/3.1004130.
Boussinesq
, M.
, 1877
, “Essai sur la Théorie des Eaux Courantes
,” Mémoires Présentés par Divers Savants Étrangers à l'Académie des Sciences
, Gauthier–Villars
, Paris, France
, p. 1
.31.
Menter
, F.
, 1992
, “Influence of Freestream Values on k–ω Turbulence Model Predictions
,” AIAA J.
, 30
(6
), pp. 1657
–1659
.10.2514/3.1111532.
Menter
, F.
, Kuntz
, M.
, and Langtry
, R.
, 2003
, “Ten Years of Industrial Experience With the SST Turbulence Model
,” Turbulence, Heat and Mass Transfer 4
, K.
Hanjalić
, Y.
Nagano
, and M.
Tummers
, eds., Begell House, Inc.
33.
Zheng
, X.
, Liao
, C.
, Liu
, C.
, Sung
, C.
, and Huang
, T.
, 1997
, “Multigrid Computation of Incompressible Flows Using Two-Equation Turbulence Models—Part I—Numerical Method
,” ASME J. Fluids Eng.
, 119
(4)
, pp. 893
–899
.10.1115/1.281951334.
Peng
, S.
, Davidson
, L.
, and Holmberg
, S.
, 1997
, “A Modified Low-Reynolds Number k–ω Model for Recirculating Flows
,” ASME J. Fluid Eng.
, 119
(4)
, pp. 867
–875
.10.1115/1.281951035.
Kok
, J.
, 2000
, “Resolving the Dependance on Freestream Values for the k–ω Turbulence Model
,” AIAA J.
, 38
(7
), pp. 1292
–1295
.10.2514/2.110136.
Wilcox
, D.
, 1993
, “A Two-Equation Turbulence Model for Wall-Bounded and Free-Shear Flows
,” AIAA
Paper No. 93-2905.37.
Wilcox
, D.
, 2008
, “Formulation of the k–ω Turbulence Model Revisited
,” AIAA J.
, 46
(11
), pp. 2823
–2838
.10.2514/1.3654138.
Hellsten
, A.
, and Laine
, S.
, 1998
, “Extension of the k–ω Shear-Stress Transport Turbulence Model for Rough-Wall Flows
,” AIAA J.
, 36
(9
), pp. 1728
–1729
.10.2514/2.754339.
Knopp
, T.
, Eisfeld
, B.
, and Calvo
, J.
, 2009
, “A New Extension for k–ω Turbulence Models to Account for Wall Roughness
,” Int. J. Heat Fluid Flow
, 30
(1)
, pp. 54
–65
.10.1016/j.ijheatfluidflow.2008.09.00940.
Aupoix
, B.
, and Spalart
, P.
, 2003
, “Extensions of the Spalart–Allmaras Turbulence Model to Account for Wall Roughness
,” Int. J. Heat Fluid Flows
, 24
(4)
, pp. 454
–462
.10.1016/S0142-727X(03)00043-241.
Aupoix
, B.
, 2007
, “A General Strategy to Extend Turbulence Models to Rough Surfaces—Application to Smith's k–l Model
,” ASME J. Fluid Eng.
, 129
(10
), pp. 1245
–1254
.10.1115/1.277696042.
Aupoix
, B.
, 2010
, “Couches Limites Bidimensionnelles Compressibles. Descriptif et Mode D'emploi du Code Clicet—Version 2010
,” ONERA, Octobre, Technical Report No. RT 1/117015 DMAE.43.
Hosni
, M.
, Coleman
, H.
, and Taylor
, R.
, 1989
, “Measurements and Calculation of Surface Roughness Effects on Turbulent Flow and Heat Transfer
,” Thermal & Fluid Dynamics Laboratory, Mechanical and Nuclear Engineering Department, Mississippi State University, December, Technical Report No. TFD-89-1.44.
Hosni
, M.
, Coleman
, H.
, and Taylor
, R.
, 1991
, “Measurements and Calculations of Rough-Wall Heat Transfer in the Turbulent Boundary Layer
,” Int. J. Heat Mass Transfer
, 34
(4/5
), pp. 1067
–1082
.10.1016/0017-9310(91)90017-945.
Hosni
, M.
, Coleman
, H.
, Gardner
, J.
, and Taylor
, R.
, 1993
, “Roughness Element Shape Effects on Heat Transfer and Skin Friction in Rough-Wall Turbulent Boundary Layer
,” Int. J. Heat Mass Transfer
, 36
(1
), pp. 147
–153
.10.1016/0017-9310(93)80074-546.
Grabow
, R.
, and White
, C.
, 1975
, “Surface Roughness Effects on Nosetip Ablation Characteristics
,” AIAA J.
, 13
(5
), pp. 605
–609
.10.2514/3.4977247.
Waigh
, D.
, and Kind
, R.
, 1998
, “Improved Aerodynamic Characterization of Regular Three-Dimensional Roughness
,” AIAA J.
, 36
(6
), pp. 1117
–1119
.10.2514/2.49148.
Flack
, K.
, and Schultz
, M.
, 2010
, “Review of Hydraulic Roughness Scales in the Fully Rough Regime
,” ASME J. Fluid Eng.
, 132
(4)
, p. 041203
.10.1115/1.400149249.
Acharya
, M.
, Bornstein
, J.
, and Escudier
, M.
, 1986
, “Turbulent Boundary Layers on Rough Surfaces
,” Exp. Fluids
, 4
(1
), pp. 33
–47
.10.1007/BF0031678450.
Tarada
, F.
, 1987
, “Heat Transfer to Rough Turbine Blading
,” Ph.D. thesis, University of Sussex, Brighton, England.51.
Blanchard
, A.
, 1977
, “Analyse Expérimentale et Théorique de la Structure de la Turbulence d'une Couche Limite sur Paroi Rugueuse
,” Ph.D. thesis, Université de Poitiers U.E.R.–E.N.S.M.A., Poitiers, France.52.
Coleman
, H.
, Moffat
, R.
, and Kays
, W.
, 1976
, “Momentum and Energy Transport in the Accelerated Rough Turbulent Boundary Layers
,” Stanford University, Thermosciences Division, Department of Mechanical Engineering, May, Technical Report No. HMT-24.53.
Coleman
, H.
, Moffat
, R.
, and Kays
, W.
, 1977
, “The Accelerated Fully Rough Turbulent Boundary Layer
,” J. Fluid Mech.
, 82
(3)
, pp. 507
–528
.10.1017/S0022112077000810Copyright © 2015 by ASME
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