# Comparison of turbulent channel and pipe flows with varying Reynolds number

- First Online:

- Received:
- Accepted:

## Abstract

Single normal hot-wire measurements of the streamwise component of velocity were taken in fully developed turbulent channel and pipe flows for matched friction Reynolds numbers ranging from 1,000 ≤ *Re*_{τ} ≤ 3,000. A total of 27 velocity profile measurements were taken with a systematic variation in the inner-scaled hot-wire sensor length *l*^{+} and the hot-wire length-to-diameter ratio (*l*/*d*). It was observed that for constant *l*^{+} = 22 and \(l/d \gtrsim 200\), the near-wall peak in turbulence intensity rises with Reynolds number in both channels and pipes. This is in contrast to Hultmark et al. in J Fluid Mech 649:103–113, (2010), who report no growth in the near-wall peak turbulence intensity for pipe flow with *l*^{+} = 20. Further, it was found that channel and pipe flows have very similar streamwise velocity statistics and energy spectra over this range of Reynolds numbers, with the only difference observed in the outer region of the mean velocity profile. Measurements where *l*^{+} and *l*/*d* were systematically varied reveal that *l*^{+} effects are akin to spatial filtering and that increasing sensor size will lead to attenuation of an increasingly large range of small scales. In contrast, when *l*/*d* was insufficient, the measured energy is attenuated over a very broad range of scales. These findings are in agreement with similar studies in boundary layer flows and highlight the need to carefully consider sensor and anemometry parameters when comparing flows across different geometries and when drawing conclusions regarding the Reynolds number dependency of measured turbulence statistics. With an emphasis on accuracy, measurement resolution and wall proximity, these measurements are taken at comparable Reynolds numbers to currently available DNS data sets of turbulent channel/pipe flows and are intended to serve as a database for comparison between physical and numerical experiments.

### References

- Balakumar BJ, Adrian RJ (2007) Large and very-large-scale motions in channel and boundary-layer flows. Philos Trans R Soc A 365:665–681MATHCrossRefGoogle Scholar
- Bruun HH (1995) Hot-Wire anemometry: principles and signal analysis, 1st edn. Oxford University Press, New YorkGoogle Scholar
- Buschmann MH, Gad-el-Hak M (2009) Evidence of nonlogarithmic behaviour of turbulent channel and pipe flow. AIAA J 47(3):535–541CrossRefGoogle Scholar
- Buschmann MH, Gad-el-Hak M (2010) Normal and cross-flow Reynolds stresses: difference between confined and semi-confined flows. Exp Fluids 49(1):213–223CrossRefGoogle Scholar
- Chin CC, Hutchins N, Ooi ASH, Marusic I (2009) Use of DNS data to investigate spatial resolution issues in measurements of wall bounded turbulence. Meas Sci Technol 20:115401Google Scholar
- Chung D, McKeon BJ (2010) Large-eddy simulation of large-scale flow structures in long channel flow. J Fluid Mech 661:341–364MATHCrossRefGoogle Scholar
- Comte-Bellot G (1965) Ecoulement turbulent entre deux parois paralleles. Technical Report 419, Publications Scientifiques et Techniques du Ministere de l’AirGoogle Scholar
- DeGraaff DB, Eaton JK (2000) Reynolds-number scaling of the flat-plate turbulent boundary layer. J Fluid Mech 422:319–346MATHCrossRefGoogle Scholar
- del Álamo J, Jiménez J (2009) Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J Fluid Mech 640:5–26MathSciNetMATHCrossRefGoogle Scholar
- del Álamo J, Jiménez J, Zandonade P, Moser RD (2004) Scaling of energy spectra in turbulent channels. J Fluid Mech 500:135–144MATHCrossRefGoogle Scholar
- Dennis DJC, Nickels TB (2008) On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J Fluid Mech 614:197–206MathSciNetMATHCrossRefGoogle Scholar
- Durst F, Jovanovic J, Sender J (1995) LDA measurements in the near-wall region of a turbulent pipe flow. J Fluids Mech 295:305–335CrossRefGoogle Scholar
- Eggels JGM, Unger F, Weiss MH, Westerweel J, Adrian RJ, Friedrich R, Nieuwstadt FTM (1994) Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J Fluid Mech 268:175–209CrossRefGoogle Scholar
- Fernholz HH, Finley PJ (1996) The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog Aerosp Sci 32:245–311CrossRefGoogle Scholar
- Guala M, Hommema SE, Adrian RJ (2006) Large-scale and very-large-scale motions in turbulent pipe flow. J Fluid Mech 554:521–542MATHCrossRefGoogle Scholar
- Hoyas S, Jiménez J (2006) Scaling of velocity fluctuations in turbulent channel flows up to
*R**e*_{τ}= 2003. Phys Fluids 18:011702Google Scholar - Hoyas S, Jiménez J (2008) Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys Fluids 20:101511Google Scholar
- Hultmark M, Bailey SCC, Smits AJ (2010) Scaling of near-wall turbulence intensity. J Fluid Mech 649:103–113MATHCrossRefGoogle Scholar
- Hutchins N, Marusic I (2007a) Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J Fluid Mech 579:1–28MATHCrossRefGoogle Scholar
- Hutchins N, Marusic I (2007b) Large-scale influences in near-wall turbulence. Philos Trans R Soc A 365:647–664MATHCrossRefGoogle Scholar
- Hutchins N, Nickels T, Marusic I, Chong M (2009) Hot-wire spatial resolution issues in wall-bounded turbulence. J Fluid Mech 635:103–136MATHCrossRefGoogle Scholar
- Iwamoto K, Fukagata K, Kasagi N, Suzuki Y (2004) DNS of turbulent channel flow at
*R**e*_{τ}= 1160 and evaluation of feedback control at practical reynolds numbers. In: Proceedings of the fifth symposium smart control of turbulence, 29 Feb–2 MarchGoogle Scholar - Iwamoto K, Kasagi N, Suzuki Y (2005) Direct numerical simulation of turbulence channel flow at
*R**e*_{τ}= 2320. In: Proceedings of the sixth symposium smart control of turbulence, TokyoGoogle Scholar - Jiménez J (2003) Computing high-reynolds number turbulence: will simulations ever replace experiments? J Turbul 4(22). doi:10.1088/1456-5248/4/1/022
- Jiménez J, Hoyas S (2008) Turbulent fluctuations above the buffer layer of wall-bounded turbulence. J Fluid Mech 611:215–236MATHCrossRefGoogle Scholar
- Johansson AV, Alfredsson PH (1982) On the structure of turbulent channel flow. J Fluid Mech 122:295–314CrossRefGoogle Scholar
- Johansson AV, Alfredsson PH (1983) Effects of imperfect spatial resolution on measurements of wall-bounded turbulent shear flows. J Fluid Mech 137:409–421CrossRefGoogle Scholar
- Jorgensen FE (1996) The computer-controlled constant-temperature anemometer. Aspects of set-up, probe calibration, data acquisition and data conversion. Meas Sci Technol 7:1378–1387CrossRefGoogle Scholar
- Kim J, Moin P, Moser R (1987) Turbulence statistics in fully developed channel flow at a low Reynolds number. J Fluid Mech 177:133–166MATHCrossRefGoogle Scholar
- Kim KC, Adrian RJ (1999) Very large-scale motion in the outer layer. Phys Fluids 11(2):417–422MathSciNetMATHCrossRefGoogle Scholar
- Kline S, McClintock FA (1953) Describing uncertainties in single sample experiments. Mech Eng 75(1):38Google Scholar
- Kline S, Reynolds W, Shrub F, Rundstadler P (1967) The structure of turbulent boundary layers. J Fluid Mech 30:741–773CrossRefGoogle Scholar
- Laufer J (1950) Investigation of turbulent flow in a two-dimensional channel. Technical Report 1053, National Advisory Committee for AeronauticsGoogle Scholar
- Laufer J (1954) The structure of turbulence in fully developed pipe flow. Technical Report 1174, National Advisory Committee for AeronauticsGoogle Scholar
- Lawn CJ (1971) The determination of the rate of dissipation in turbulent pipe flow. J Fluid Mech 48:477–505CrossRefGoogle Scholar
- Li JD, McKeon BJ, Jiang W, Morrison JF, Smits AJ (2004) The response of hot wires in high Reynolds-number turbulent pipe flow. Meas Sci Technol 15:789–798CrossRefGoogle Scholar
- Ligrani P, Bradshaw P (1987) Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes. Exp Fluids 5:407–417CrossRefGoogle Scholar
- Marusic I, Kunkel GJ (2003) Streamwise turbulence intensity formulation for flat plat-plate boundary layers. Phys Fluids 15(8):2461–2464CrossRefGoogle Scholar
- Marusic I, Uddin AKM, Perry AE (1997) Similarity laws for the streamwise turbulence intensity in zero-pressure-gradient turbulent boundary layers. Phys Fluids 9(12):3718–3726CrossRefGoogle Scholar
- Marusic I, McKeon BJ, Monkewitz PA, Nagib HM, Smits AJ, Sreenivasan KR (2010) Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys Fluids 22:065103Google Scholar
- Mathis R, Hutchins N, Marusic I (2009a) Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J Fluid Mech 628:311–337Google Scholar
- Mathis R, Monty J, Hutchins N, Marusic I (2009b) Comparison of large-scale amplitude modulation in boundary layers, pipes and channel flows. Phys Fluids 21:111703Google Scholar
- McKeon BJ, Li J, Jiang W, Morrison JF, Smits AJ (2004) Further observations on the mean velocity distribution in fully developed pipe flow. J Fluid Mech 501:135–147MATHCrossRefGoogle Scholar
- Metzger M, Klewicki J (2001) A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys Fluids 13(3):692–701CrossRefGoogle Scholar
- Mochizuki S, Nieuwstadt FTM (1996) Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence. Exp Fluids 21:218–226CrossRefGoogle Scholar
- Moin P (2009) Revisiting Taylor’s hypothesis. Journal of Fluid Mechanics 640:1–4MathSciNetMATHCrossRefGoogle Scholar
- Monty JP (2005) Developments in smooth wall turbulent duct flows. Ph.D. thesis, The University of MelbourneGoogle Scholar
- Monty JP, Chong MS (2009) Turbulent channel flow: comparison of streamwise velocity data from experiments and direct numerical simulation. J Fluid Mech 633:461–474MATHCrossRefGoogle Scholar
- Monty JP, Stewart JA, Williams RC, Chong MS (2007) Large-scale features in turbulent pipe and channel flows. J Fluid Mech 589:147–156MATHCrossRefGoogle Scholar
- Monty JP, Hutchins N, Ng H, Marusic I, Chong MS (2009) A comparison of turbulent pipe, channel and boundary layer flows. J Fluid Mech 632:431–442MATHCrossRefGoogle Scholar
- Morrison J, McKeon B, Jiang W, Smits A (2004) Scaling of the streamwise velocity component in turbulent pipe flow. J Fluid Mech 508:99–131MATHCrossRefGoogle Scholar
- Morrison WRB, Kronauer RE (1969) Structural similarity for fully developed turbulence on smooth tubes. J Fluid Mech 39:117–141CrossRefGoogle Scholar
- Nagib HM, Chauhan K (2008) Variations of von Kármán coefficient in canonical flows. Phys Fluids 20:101518Google Scholar
- Niederschulte MA, Adrian RJ, Hanratty TJ (1990) Measurements of turbulent flow in a channel at low Reynolds numbers. Exp Fluids 9:222–230CrossRefGoogle Scholar
- Perry AE, Abell C (1975) Scaling laws for pipe-flow turbulence. J Fluid Mech 67:257–271CrossRefGoogle Scholar
- Perry AE, Henbest S, Chong MS (1986) A theoretical and experimental study of wall turbulence. J Fluid Mech 165:163–199MathSciNetMATHCrossRefGoogle Scholar
- Perry AE, Hafez S, Chong MS (2001) A possible reinterpretation of the princeton superpipe data. J Fluid Mech 439:395–401MATHCrossRefGoogle Scholar
- Taylor GI (1938) The spectrum of turbulence. Proc R Soc Lond A 164:476–490CrossRefGoogle Scholar
- den Toonder JMJ, Nieuwstadt FTM (1997) Reynolds number effects in a turbulent pipe flow for low to moderate Re. Phys Fluids 9(11):3398–3409CrossRefGoogle Scholar
- Wei T, Willmarth WW (1989) Reynolds-number effects on the structure of a turbulent channel flow. J Fluid Mech 204:57–95CrossRefGoogle Scholar
- Wu X, Moin P (2008) A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J Fluid Mech 608:81–112MATHCrossRefGoogle Scholar
- Yavuzkurt S (1984) A guide to uncertainty analysis of hot-wire data. J Fluids Eng 106:181–186CrossRefGoogle Scholar
- Zagarola M, Smits A (1998) Mean flow scaling in turbulent pipe flow. J Fluid Mech 373:33–79MATHCrossRefGoogle Scholar
- Zanoun ES, Durst F, Nagib H (2003) Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows. Phys Fluids 15(10):3079–3089CrossRefGoogle Scholar