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Characterizing developing adverse pressure gradient flows subject to surface roughness

Abstract

An experimental study was conducted to examine the effects of surface roughness and adverse pressure gradient (APG) on the development of a turbulent boundary layer. Hot-wire anemometry measurements were carried out using single and X-wire probes in all regions of a developing APG flow in an open return wind tunnel test section. The same experimental conditions (i.e., T U ref, and C p) were maintained for smooth, k + = 0, and rough, k + = 41–60, surfaces with Reynolds number based on momentum thickness, 3,000 < Re θ < 40,000. The experiment was carefully designed such that the x-dependence in the flow field was known. Despite this fact, only a very small region of the boundary layer showed a balance of the various terms in the integrated boundary layer equation. The skin friction computed from this technique showed up to a 58% increase due to the surface roughness. Various equilibrium parameters were studied and the effect of roughness was investigated. The generated flow was not in equilibrium according to the Clauser (J Aero Sci 21:91–108, 1954) definition due to its developing nature. After a development region, the flow reached the equilibrium condition as defined by Castillo and George (2001), where Λ = const, is the pressure gradient parameter. Moreover, it was found that this equilibrium condition can be used to classify developing APG flows. Furthermore, the Zagarola and Smits (J Fluid Mech 373:33–79, 1998a) scaling of the mean velocity deficit, U δ*/δ, can also be used as a criteria to classify developing APG flows which supports the equilibrium condition of Castillo and George (2001). With this information a ‘full APG region’ was defined.

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References

  • Akinlade OG, Bergstrom DJ, Tachie MF, Castillo L (2004) Outer flow scaling of smooth and rough wall turbulent boundary layers. Exp Fluids 37:604–612

    Article  Google Scholar 

  • Anderson C, Turan ÖF, Brzek B, Castillo L (2004) Adverse pressure gradient turbulent boundary layer flows, Part 1: flow development. AFMC, Sydney, NSW. AFMC15-259

  • Antonia RA, Krogstad PÅ (2001) Turbulence structure in boundary layers over different types of surface roughness. Fluid Dyn Res 28:139–157

    Article  Google Scholar 

  • Aubertine CD, Eaton JK (2005) Turbulence development in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient. J Fluid Mech 532:345–364

    MATH  Article  Google Scholar 

  • Bergstrom DJ, Kotey NA, Tachie MF (2002) The effects of surface roughness on the mean velocity profiles in turbulent boundary layer. J Fluids Eng 124:664–670

    Article  Google Scholar 

  • Bradshaw P (1966) The turbulence structure of equilibrium boundary Layers. NPL Aero Rep 1184, Tabulated data reproduced in ‘Proceedings Computation of Turbulent Boundary Layers-1968 AFOSR-IFP-Stanford Conference’ as ‘Flow 2500’ (Kline et al. 1968)

  • Bradshaw P (1967) The response of a constant pressure turbulent boundary layer to a sudden application of an adverse pressure gradient. NPL Aero Rep 1219. Tabulated data reproduced in ‘Proceedings Computation of Turbulent Boundary Layers-1968 AFOSR-IFP-Stanford Conference’ as ‘Flow 3300’ (Kline et al. 1968)

  • Bradshaw P (2000) A note on “critical roughness height” and transitional roughness. Phys Fluids 12:1611–1614

    MATH  Article  MathSciNet  Google Scholar 

  • Brzek B (2004) Development and characterization of an increasing adverse pressure gradient turbulent boundary layer. Master’s thesis, Rensselaer Polytechnic Institute

  • Brzek B (2007) The effect of external conditions in turbulent boundary layers. PhD dissertation, Rensselaer Polytechnic Institute, Troy, NY

  • Brzek B, Anderson C, Turan ÖF, Castillo L (2004) Adverse pressure gradient turbulent boundary layer flows, Part 2: scaling of Reynolds stresses. AFMC, Sydney, NSW. AFMC15-260

  • Brzek B, Cal RB, Johansson G, Castillo L (2007) Inner and outer scalings in rough surface turbulent boundary layers. Phys Fluids 19:065101

    Article  Google Scholar 

  • Brzek B, Cal RB, Johansson G, Castillo L (2008) Transitionally rough zero pressure gradient Turbulent boundary layers. Exp Fluids 44(1):115–145

    Article  Google Scholar 

  • Cal RB, Castillo L (2008) Similarity analysis of favorable pressure gradient turbulent boundary layers with eventual quasi-laminarization. Phys Fluids 20:105106

    Article  Google Scholar 

  • Cal RB, Brzek B, Johansson G, Castillo L (2008) Influence of the external conditions on transitionally rough favorable pressure gradient turbulent boundary layers. J Turbul 8(38):1–22

    Google Scholar 

  • Cal RB, Brzek B, Johansson G, Castillo L (2009) The rough favorable pressure gradient turbulent boundary layer. J Fluid Mech (in press)

  • Castillo L (2000) Application of Zagarola/Smits scaling in turbulent boundary layers with pressure gradient. Adv Fluid Mech 3, Canada

  • Castillo L, George WK (2001) Similarity analysis for turbulent boundary layer with pressure gradient: outer flow. AIAA J 39(1):41–47

    Article  Google Scholar 

  • Castillo L, Johansson G (2002) The effects of the upstream conditions on a low Reynolds number turbulent boundary layer with zero pressure gradient. J Turbul 3:031

    Article  Google Scholar 

  • Castillo L, Seo J, Hangan H, Antonia RA (2004) Smooth and rough turbulent boundary layers at high Reynolds number. Exp Fluids 36:759–774

    Article  Google Scholar 

  • Castillo L, Wang X, George WK (2004) Similarity analysis for nonequilibrium turbulent boundary layers. J Fluids Eng 126:827–834

    Article  Google Scholar 

  • Castillo L, Walker D (2002) The effects of the upstream conditions on the outer flow of turbulent boundary layers. AIAA J 40(7):1292–1299

    Article  Google Scholar 

  • Castillo L, Wang X (2004) Similarity analysis for nonequilibrium boundary layers. J Fluids Eng 126:825–837

    Google Scholar 

  • Castro IP (2007) Rough wall boundary layers—mean flow Universality. J Fluid Mech 585:469–485

    MATH  Article  Google Scholar 

  • Chao D (2007) Effect of roughness in the development of an adverse pressure gradient turbulent boundary layer. MS thesis, Rensselaer Polytechnic Institute

  • Clauser FH (1954) Turbulent boundary layers in adverse pressure gradients. J Aero Sci 21(2):91–108. Tabulated data of two 1954 experiments reproduced in ‘Proceedings Computation of Turbulent Boundary Layers-1968 AFOSR-IFP-Stanford Conference’ as ‘Flow 2200’ and ‘Flow 2300’ (Kline et al. 1968)

    Google Scholar 

  • Coles DE (1962) The turbulent boundary layers in a compressible fluid. RAND Corp Rept R-403-PR

  • DeGraaff DB, Eaton JK (2000) Reynolds-number scaling of the flat-plate turbulent boundary layer. J Fluid Mech 422:319–346

    MATH  Article  Google Scholar 

  • Elsberry K, Loeffler J, Zhou M, Wygnanski I (2000) An experimental study of a boundary layer that is maintained on the verge of separation. J Fluid Mech 423:227–262

    MATH  Article  Google Scholar 

  • George WK, Castillo L (1997) Zero-pressure gradient turbulent boundary layer. Appl Mech Rev 50:689–729

    Article  Google Scholar 

  • Herring HJ, Norbury JF (1967) Some experiments on equilibrium turbulent boundary layers in favourable pressure gradients. J Fluid Mech 127:541–549

    Article  Google Scholar 

  • Indinger T, Buschmann MH, Gad-el-Hak M (2006) Mean velocity profile of turbulent boundary layers approaching separation. AIAA J 44(11):2465–2474

    Article  Google Scholar 

  • Jiménez J (2004) Turbulent flows over rough walls. Annu Rev Fluid Mech 36:173–196

    Article  Google Scholar 

  • Kline et al (1968) Proceedings computation of turbulent boundary layers-1968 AFOSR-IFP-Stanford Conference

  • Krogstad PÅ, Antonia RA, Browne LWB (1992) Rough- and smooth-wall turbulent boundary layers. J Fluid Mech 245:599–617

    Article  Google Scholar 

  • Krogstad P-Å, Antonia RA (1999) Surface roughness effects in turbulent boundary layers. Exp Fluids 27:450–460

    Article  Google Scholar 

  • Krogstad PÅ, Skåre PE (1995) Influence of a strong adverse pressure gradient on the turbulent structure in a boundary layer. Phys Fluids 7(8):2014–2024

    Article  Google Scholar 

  • Ligrani P, Moffat R (1986) Structure of transitionally rough and fully rough turbulent boundary layers. J Fluid Mech 162:69–98

    Article  MathSciNet  Google Scholar 

  • Ludwieg H, Tillmann W (1950) Investigations of the wall shearing stress in turbulent boundary layers. NACA TM, No. 1285

  • Lueptow RM (1988) Computer-aided calibration of X-probes using a look-up table. Exp Fluids 6:115–118

    Google Scholar 

  • Maciel Y, Rossignol KS, Lemay J (2006) Self-similarity in the outer region of adverse pressure-gradient turbulent boundary layers. AIAA J 44(11):2450–2464

    Article  Google Scholar 

  • Nagib H, Chauhan K, Monkewitz P (2005) Scaling of high Reynolds number turbulent boundary layers. 4th AIAA Theoretical fluid Mechanics Meeting, AIAA-2005-4810, Toronto, Canada

  • Nikuradse J (1933) Gesetzmäß igkeit der turbulenten Strömung in glatten Rohren. Forsch. Arb. Ing.-Wes.H. 356

  • Newman BG. Somce contributions to the study of the turbulent boundary near separation. Austr Dept Supply Rep ACA-53, 1951 Tabulated data reproduced in ‘Proceedings Computation of Turbulent Boundary Layers −1968 AFOSR-IFP-Stanford Conference’ as ‘Flow 3500’ (Kline et al. 1968)

  • Österlund J (1999) Experimental studies of zero pressure-gradient turbulent boundary layer flow. PhD thesis, KTH, Stockholm

  • Pailhaus G, Touvet Y, Auxpoix B (2008) Effects of Reynolds number and adverse pressure gradient on a turbulent boundary layer developing on a rough surface. J Turbul 9(43):1–24

    Google Scholar 

  • Perry AE (1966) Turbulent boundary layers in decreasing adverse pressure gradients. J Fluid Mech 26(3):481–506

    Article  Google Scholar 

  • Perry AE, Schofield WH, Jourbert PN (1969) Rough-wall turbulent boundary layer. J Fluid Mech 37:383–413

    Article  Google Scholar 

  • Perry AE, Li JD (1990) Experimental support for the attached-eddy hypothesis in zero-pressure-gradient turbulent boundary layers. J Fluid Mech 218:405–438

    Article  Google Scholar 

  • Perry AE, Marusic I, Jones MB (2002) On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J Fluid Mech 461:61–91

    MATH  Article  MathSciNet  Google Scholar 

  • Samuel AE, Joubert PN (1974) A boundary layer developing in an increasingly adverse pressure gradient. J Fluid Mech 66:481–505. Tabulated data reproduced in ‘Proceedings Computation of Turbulent Boundary Layers-1980 AFOSR-IFP-Stanford Conference’ as ‘Flow 141’

    Article  Google Scholar 

  • Schlichting H (1979) Boundary-layer theory. 7th edn. McGraw-Hill, New York

    MATH  Google Scholar 

  • Schubauer GB, Klebanoff PS (1951) Investigation of separation of the turbulent boundary layer. NACA Report 1030, NACA Technical Note 2133

  • Schultz MP, Flack KA (2005) Outer layer similarity in fully rough turbulent boundary layer. Exp Fluids 38:324–340

    Article  Google Scholar 

  • Schultz MP, Flack KA (2007) The rough wall turbulent boundary layer from the hydraulically smooth to the fully rough regime. J Fluid Mech 580:381–405

    MATH  Article  Google Scholar 

  • Skåre PE, Krogstad PÅ (1994) A turbulent equilibrium boundary layer near separation. J Fluid Mech 272:319–348

    Article  Google Scholar 

  • Smith RW (1994) Effect of Reynolds number on the structure of turbulent boundary layer. PhD thesis, Princeton University

  • Stratford BS (1959) An experimental flow with zero skin friction throughout its region of pressure rise. J Fluid Mech 8:143–155

    MathSciNet  Google Scholar 

  • Tachie MF (2007) PIV study of turbulent flow over transverse square ribs in asymmetric diffuser. Phys Fluids 19:6

    Article  Google Scholar 

  • Tachie MF, Bergstrom DJ, Balachandar R (2000) Rough wall turbulent boundary layers in shallow open channel flow. J Fluids Eng 122:533–541

    Article  Google Scholar 

  • Tachie MF, Bergstrom DJ, Balachandar R (2003) Roughness effects in a low-Re θ open channel turbulent boundary layer. Exps Fluids 35:338–346

    Article  Google Scholar 

  • Thomas LC, Hasani SMF (1992) Equilibrium boundary layers—a new wall/outer variable perspective. J Fluids Eng 114:152–154

    Article  Google Scholar 

  • Townsend AA (1976) The structure of turbulent shear flow. Cambridge University Press, Cambridge, pp 150–158

    MATH  Google Scholar 

  • Walker D, Castillo L (2002) The effects of the upstream conditions on turbulent boundary layers. AIAA J 40(12):2540–2542

    Article  Google Scholar 

  • Zagarola M, Smits A (1998a) Mean-flow scaling of turbulent pipe flow. J Fluid Mech 373:33–79

    MATH  Article  Google Scholar 

  • Zagarola M, Smits A (1998b) A new mean velocity scaling for turbulent boundary layers. Proceedings of FEDSM’98, Washington, DC

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Acknowledgments

A special thanks to Victoria University and Dr. Turan for the use of their facility and Dr. Roosevelt Johnson from NSF-AGEP for making this international collaboration possible. And finally to Dr. Ronald Joslin from the Office of Naval Research for continuously funding this project.

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Correspondence to Luciano Castillo.

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Brzek, B., Chao, D., Turan, Ö. et al. Characterizing developing adverse pressure gradient flows subject to surface roughness. Exp Fluids 48, 663–677 (2010). https://doi.org/10.1007/s00348-009-0759-6

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  • DOI: https://doi.org/10.1007/s00348-009-0759-6

Keywords

  • Wall Shear Stress
  • Skin Friction
  • Reynolds Stress
  • Turbulent Boundary Layer
  • Reynolds Shear Stress