Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T20:45:40.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical study of turbulent separation bubbles with varying pressure gradient and Reynolds number

Published online by Cambridge University Press:  17 May 2018

G. N. Coleman Open the ORCID record for G. N. Coleman [Opens in a new window] ,
C. L. Rumsey  and
P. R. Spalart Open the ORCID record for P. R. Spalart [Opens in a new window]
G. N. Coleman*
Affiliation:
Computational AeroSciences, NASA Langley Research Center, Hampton, VA 23681, USA
C. L. Rumsey
Affiliation:
Computational AeroSciences, NASA Langley Research Center, Hampton, VA 23681, USA
P. R. Spalart
Affiliation:
Boeing Commercial Airplanes, Seattle, WA 98124, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A family of cases each containing a small separation bubble is treated by direct numerical simulation (DNS), varying two parameters: the severity of the pressure gradients, generated by suction and blowing across the opposite boundary, and the Reynolds number. Each flow contains a well-developed entry region with essentially zero pressure gradient, and all are adjusted to have the same value for the momentum thickness, extrapolated from the entry region to the centre of the separation bubble. Combined with fully defined boundary conditions this will make comparisons with other simulations and turbulence models rigorous; we present results for a set of eight Reynolds-averaged Navier–Stokes turbulence models. Even though the largest Reynolds number is approximately 5.5 times higher than in a similar DNS study we presented in 1997, the models have difficulties matching the DNS skin friction very closely even in the zero pressure gradient, which complicates their assessment. In the rest of the domain, the separation location per se is not particularly difficult to predict, and the most definite disagreement between DNS and models is near reattachment. Curiously, the better models tend to cluster together in their predictions of pressure and skin friction even when they deviate from the DNS, although their eddy-viscosity levels are widely different in the outer region near the bubble (or they do not rely on an eddy viscosity). Stratford’s square-root law is satisfied by the velocity profiles, both at separation and reattachment. The Reynolds-number range covers a factor of two, with the Reynolds number based on the extrapolated momentum thickness equal to approximately 1500 and 3000. This allows tentative estimates of the improvements that even higher values will bring to the model comparisons. The solutions are used to assess models through pressure, skin friction and other measures; the flow fields are also used to produce effective eddy-viscosity targets for the models, thus guiding turbulence-modelling work in each region of the flow.

JFM classification

Boundary Layers: Boundary layer separation Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , pp. 28 - 70
Check for updates
Copyright
© Cambridge University Press 2018. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abe, H. 2017 Reynolds-number dependence of wall-pressure fluctuations in a pressure-induced turbulent separation bubble. J. Fluid Mech. 833, 563–598.CrossRefGoogle Scholar
Abe, H., Mizobuchi, Y., Matsuo, Y. & Spalart, P. R. 2012 DNS and modeling of a turbulent boundary layer with separation and reattachment over a range of Reynolds numbers. In CTR Annual Research Briefs, pp. 311–322. Stanford University, Center for Turbulence Research.Google Scholar
Abid, R. 1993 Evaluation of two-equation turbulence models for predicting transitional flows. Intl J. Engng Sci. 31 (6), 831–840.Google Scholar
Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28.Google Scholar
Alfredsson, P. H., Segalini, A. & Örlü, R. 2011 A new scaling for the streamwise turbulence intensity in wall-bounded turbulent flows and what it tells us about the ‘outer’ peak. Phys. Fluids 23, 041702.Google Scholar
Bachalo, W. D. & Johnson, D. A. 1986 Transonic, turbulent boundary-layer separation generated on an axisymmetric flow model. AIAA J. 24 (3), 437–443.Google Scholar
Baldwin, B. S. & Lomax, H.1978 Thin-layer approximation and algebraic model for separated turbulent flows. AIAA Paper 78-257.Google Scholar
Bentaleb, Y., Lardeau, S. & Leschziner, M. A. 2012 Large-eddy simulation of turbulent boundary layer separation from a rounded step. J. Turbul. 13 (4), 1–28.Google Scholar
Bradshaw, P. 1988 Effects of extra rates of strain: review. In Zoran Zaric Mem. Seminar, Dubrovnik. Hemisphere.Google Scholar
Bradshaw, P., Ferris, D. H. & Atwell, N. P. 1967 Calculation of boundary-layer development using the turbulent energy equation. J. Fluid Mech. 28 (3), 593–616.Google Scholar
Castro, I. P. 2015 Turbulence intensity in wall-bounded and wall-free flows. J. Fluid Mech. 770, 289–304.Google Scholar
Castro, I. P. & Epik, E. 1998 Boundary layer development after a separated region. J. Fluid Mech. 374, 91–116.Google Scholar
Castro, I. P. & Haque, A. 1987 The structure of a turbulent shear layer bounding a separation. J. Fluid Mech. 179, 439–468.Google Scholar
Castro, I. P. & Robins, A. G. 1977 The flow around a surface-mounted cube in uniform and turbulent streams. J. Fluid Mech. 79 (2), 307–335.CrossRefGoogle Scholar
Cebeci, T. & Bradshaw, P. 1977 Momentum Transfer in Boundary Layers, p. 197. McGraw-Hill.Google Scholar
Cheng, W., Pullin, D. I. & Samtaney, R. 2015 Large-eddy simulation of separation and reattachment of a flat plate turbulent boundary layer. J. Fluid Mech. 785, 78–108.Google Scholar
Coleman, G. N., Garbaruk, A. & Spalart, P. R. 2015 Direct numerical simulation, theories and modelling of wall turbulence with a range of pressure gradients. Flow Turbul. Combust. 95, 261–276.CrossRefGoogle Scholar
Coleman, G. N., Kim, J. & Spalart, P. R. 2003 Direct numerical simulation of a decelerated wall-bounded turbulent shear flow. J. Fluid Mech. 495, 1–18.Google Scholar
Coleman, G. N., Pirozzoli, S., Quadrio, M. & Spalart, P. R. 2017 Direct numerical simulation and theory of a wall-bounded flow with zero skin friction. Flow Turbul. Combust. 99, 553–564.CrossRefGoogle ScholarPubMed
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1 (2), 191–226.Google Scholar
Coles, D. E.1962 The turbulent boundary layer in a compressible fluid. Rand Rep. R403-PR, ARC 24473: Appendix A: a manual of experimental practice for low-speed flow.Google Scholar
Dianat, M. & Castro, I. P. 1989 Measurements in separating boundary layers. AIAA J. 27 (6), 719–724.Google Scholar
Dianat, M. & Castro, I. P. 1991 Turbulence in a separated boundary layer. J. Fluid Mech. 226, 91–123.CrossRefGoogle Scholar
Driver, D. M.1991 Reynolds shear stress measurements in a separated boundary layer flow. AIAA Paper 91-1787.Google Scholar
Driver, D. M. & Johnston, J. P.1990 Experimental study of a three-dimensional shear-driven boundary layer with streamwise adverse pressure gradient. NASA TM-102211. Available from NASA Technical Reports Server (https://ntrs.nasa.gov).Google Scholar
Driver, D. M. & Seegmiller, H. L. 1985 Features of reattaching turbulent shear layer in divergent channel flow. AIAA J. 23 (2), 163–171.CrossRefGoogle Scholar
Drózdz, A., Elsner, W. & Drobniak, S. 2015 Scaling of streamwise Reynolds stress for turbulent boundary layers with pressure gradient. Eur. J. Mech. (B/Fluids) 49, 137–145.Google Scholar
Eisfeld, B., Rumsey, C. & Togiti, V. 2016 Verification and validation of a second-moment-closure model. AIAA J. 54 (5), 1524–1541; Erratum: AIAA J. 54 (9), 2926.Google Scholar
Galbraith, R. A. McD. & Head, M. R. 1975 Eddy viscosity and mixing length from measured boundary layer developments. Aeronaut. Q. 26, 133–154.Google Scholar
Galbraith, R. A. McD., Sjolander, S. & Head, M. R. 1977 Mixing length in the wall region of turbulent boundary layers. Aeronaut. Q. 27, 229–242.Google Scholar
Hunt, J. C. R., Wray, A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. In Studying Turbulence Using Numerical Simulation Databases, I: Proceedings of the 1988 Summer Program. Stanford University, Center for Turbulence Research.Google Scholar
Johnstone, R., Coleman, G. N. & Spalart, P. R. 2010 The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation. J. Fluid Mech. 643, 163–175.Google Scholar
Kline, S. J., Bardina, J. G. & Strawn, R. C. 1983 Correlations of the detachment of two-dimensional turbulent boundary layers. AIAA J. 21 (1), 68–73.Google Scholar
Krist, S. L., Biedron, R. T. & Rumsey, C. L.1998 CFL3D User’s Manual (Version 5.0), NASA TM-1998-208444. Available from NASA Technical Reports Server (https://ntrs.nasa.gov).Google Scholar
Le, H., Moin, P. & Kim, J. 1997 Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–374.Google Scholar
Lighthill, M. J. 1963 Introduction: Boundary layer theory. In Laminar Boundary Layers (ed. Rosenhead, L.), chap. II, p. 687. Oxford University Press.Google Scholar
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.Google Scholar
Menter, F. R. 1994 Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32 (8), 1598–1605.Google Scholar
Mohammed-Taifour, A.2017 Instationnarités dans une bulle de décollement turbulente: étude expérimental. PhD thesis, École de Technologie Supérieure, University of Quebec, Canada.Google Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539–578.Google Scholar
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379–405.Google Scholar
Naughton, J. W., Viken, S. A. & Greenblatt, D. 2006 Skin-friction measurements on the NASA hump model. AIAA J. 44 (6), 1255–1265.Google Scholar
Raiesi, H., Piomelli, U. & Pollard, A. 2011 Evaluation of turbulence models using direct numerical and large-eddy simulation data. Trans. ASME J. Fluids Engng 133, 021203.Google Scholar
Rodriguez, I., Lehmkuhl, O., Chiva, J., Borrell, R. & Oliva, A. 2014 On the wake transition in the flow past a circular cylinder at critical Reynolds numbers. In Proceedings of 11th World Congress on Computational Mechanics (WCCM XI); 5th European Conference on Computational Mechanics (ECCM V); 6th European Conference on Computational Fluid Dynamics (ECFD VI) (ed. Oñate, E., Oliver, J. & Huerta, A.).Google Scholar
Roe, P. L. 1981 Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43, 357–372.Google Scholar
Sandborn, V. A. & Kline, S. J. 1961 Flow models in boundary-layer stall inception. Trans. ASME J. Basic Engng 83 (3), 317–327.Google Scholar
Sandham, N. D. 2002 Introduction to direct numerical simulation. In Closure Strategies for Turbulent and Transitional Flows (ed. Launder, B. E. & Sandham, N. D.), chap. 7, p. 854. Cambridge University Press.Google Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.Google Scholar
Sciberras, M. A. & Coleman, G. N. 2007 Testing of Reynolds-stress-transport closures by comparison with DNS of an idealized adverse-pressure-gradient boundary layer. Eur. J. Mech. (B/Fluids) 26, 551–582.Google Scholar
Shur, M. L., Strelets, M. K., Travin, A. K. & Spalart, P. R. 2000 Turbulence modeling in rotating and curved channels: assessing the Spalart–Shur correction. AIAA J. 38 (5), 784–792.Google Scholar
Simpson, R. L. 1989 Turbulent boundary-layer separation. Annu. Rev. Fluid Mech. 21, 205–234.Google Scholar
Skote, M. & Henningson, D. S. 2002 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 471, 107–136.Google Scholar
Skote, M. & Wallin, S. 2016 Near-wall damping in model predictions of separated flows. Intl J. Comput. Fluid Dyn. 30, 218–230.Google Scholar
Slotnick, J., Khodadoust, A., Alanso, J., Darmofal, D., Gropp, W., Lurie, E. & Mavriplis, D.2014 CFD Vision 2030 Study: a path to revolutionary computational aerosciences. NASA CR 2014-218178. Available from NASA Technical Reports Server (https://ntrs.nasa.gov).Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R 𝜃 = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Spalart, P. R. & Allmaras, S. R. 1994 A one-equation turbulence model for aerodynamic flows. Rech. Aerosp. 1, 5–21.Google Scholar
Spalart, P. R. & Coleman, G. N. 1997 Numerical study of a separation bubble with heat transfer. Eur. J. Mech. (B/Fluids) 16, 169–189 (referred to herein as SC97).Google Scholar
Spalart, P. R., Coleman, G. N. & Johnstone, R. 2009 Retraction: ‘Direct numerical simulation of the Ekman layer: a step in Reynolds number, and cautious support for a log law with a shifted origin’. Phys. Fluids 21, 109901.Google Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral solvers for the Navier–Stokes equations with two periodic and one infinite direction. J. Comput. Phys. 96, 297–324.Google Scholar
Spalart, P. R. & Strelets, M. Kh. 2000 Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329–349.Google Scholar
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337–371.Google Scholar
Stratford, B. S. 1959 The prediction of separation of the turbulent boundary layer. J. Fluid Mech. 5, 1–16.Google Scholar
Uzun, A. & Malik, M. R.2017 Wall-resolved large-eddy simulation of flow separation over NASA wall-mounted hump. AIAA Paper 2017-0538.Google Scholar
Vinuesa, R., Bobke, A., Örlü, R. & Schlatter, P. 2016 On determining characteristic length scales in pressure-gradient boundary layers. Phys. Fluids 28, 055101.Google Scholar
Weiss, J., Mohammed-Taifour, A. & Schwaab, Q. 2015 Unsteady behavior of a pressure-induced turbulent separation bubble. AIAA J. 53 (9), 2634–2645.CrossRefGoogle Scholar
Yakhot, A., Anor, T., Liu, H. & Nikitin, N. 2006 Direct numerical simulation of turbulent flow around a wall-mounted cube: spatio-temporal evolution of large-scale vortices. J. Fluid Mech. 566, 1–9.Google Scholar
Yorke, C. P. & Coleman, G. N. 2004 Assessment of common turbulence models for an idealised adverse pressure gradient flow. Eur. J. Mech. (B/Fluids) 23, 319–337.Google Scholar