Skip to main content
SpringerLink
Log in

An investigation of the scales in transitional boundary layers under high free-stream turbulence conditions

  • Originals
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

The scales in a transitional boundary layer subject to high (initially 8%) free-stream turbulence and strong acceleration (K as high as 9×10−6) were investigated using wavelet spectral analysis and conditional sampling of experimental data. The boundary layer shows considerable evolution through transition, with a general shift from the lower frequencies induced by the free-stream unsteadiness to higher frequencies associated with near-wall-generated turbulence. Within the non-turbulent zone of the intermittent flow, there is considerable self-similarity in the spectra from the beginning of transition to the end, with the dominant frequencies in the boundary layer remaining constant at about the dominant frequency of the free-stream. The frequencies of the energy-containing scales in the turbulent zone change with streamwise location and are significantly higher than in the non-turbulent zone. When normalized on the local viscous length scale and velocity, however, the turbulent zone spectra also show good self-similarity throughout transition. Turbulence dissipation occurs almost exclusively in the turbulent zone. The velocity fluctuations associated with dissipation are isotropic, and their normalized spectra at upstream and downstream stations are nearly identical. The distinct differences between the turbulent and non-turbulent zones suggest the potential utility of intermittency based transition models in which these zones are treated separately. The self-similarity noted in both energy containing and dissipation scales in both zones suggests possibilities for simplifying the modeling for each zone.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Notes

  1. Results based on the turbulent zone wavelet spectra agreed well with those of Fig. 20 up to the peak, but then continued to increase monotonically at higher frequencies. Comparison of the composite flow wavelet and Fourier spectra revealed very good agreement over nearly all frequencies, including all those associated with the energy containing scales described in the sections above. Some small differences were always present in the high frequency tails of the spectra, however, with the magnitudes of the wavelet spectra always slightly higher than those of the Fourier spectra. While insignificant in terms of energy, the difference was significant in terms of dissipation. A different wavelet than the Mexican Hat may have produced better results, but since virtually all the dissipation occurs in the turbulent zone, the composite flow Fourier spectra can be normalized using the local intermittency at each station to give the time averaged turbulent zone contribution.

Abbreviations

C :

dilation factor

FSTI:

free-stream turbulence intensity

f :

frequency in Hz

f fs :

frequency in Hz of free-stream v‘ spectra peak

K :

(ν /U∞ 2)(dU∞ /dx), acceleration parameter

PSD:

power spectral density

Re x :

U∞ x/ν, Reynolds number

Re λ :

\(\overline {u^{'2} } \sqrt {15/(\nu \varepsilon )} ,\)

Re θ :

momentum thickness Reynolds number

t :

time

U ∞ :

local free-stream velocity

u :

instantaneous streamwise velocity

u ‘ :

instantaneous streamwise fluctuating velocity

u τ :

\(\sqrt {\tau _{{\rm w}} /\rho} \)

-u‘v‘:

instantaneous turbulent shear stress

v :

instantaneous wall normal velocity

v ‘ :

instantaneous wall normal fluctuating velocity

w :

wavelet function

x :

streamwise coordinate, distance from leading edge

y :

cross-stream coordinate, distance from wall

y + :

yuτ /ν, distance from wall in wall coordinates

Γ:

intermittency function

γ:

intermittency, time average of Γ (fraction flow is turbulent)

γ pk:

peak intermittency in profile

δ99.5:

99.5% boundary layer thickness

ε:

turbulence dissipation rate

ν:

kinematic viscosity

ρ:

density

τ w :

wall shear stress

θ:

momentum thickness

-:

(overbar) time average

∞:

free-stream

References

  • Blair MF (1992) Boundary layer transition in accelerating flows with intense freestream turbulence: Part 1—Disturbances upstream of transition onset; Part 2—The zone of intermittent turbulence. J Fluids Eng 114:313–332

    Google Scholar 

  • Bradshaw P (1994) Turbulence: the chief outstanding difficulty of our subject. Exp Fluids 16:203–216

    Google Scholar 

  • Breuer KS, Cohen J, Haritonidis JH (1997) The late stages of transition induced by a low-amplitude wavepacket in a laminar boundary layer. J Fluid Mech 340:395–411

    Google Scholar 

  • Farge M (1992) Wavelet transforms and their applications to turbulence. Ann Rev Fluid Mech 24:395–457

    Article  Google Scholar 

  • Higuchi H, Lewalle J, Crane P (1994) On the structure of a two-dimensional wake behind a pair of flat plates. Phys Fluids A 6:297–305

    Google Scholar 

  • Hinze JO (1975) Turbulence, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  • Hughes JD, Walker GJ (2001) Natural transition phenomena on an axial compressor blade. J Turbomach 123:392–401

    Google Scholar 

  • Jones WP, Launder BE (1972) Some properties of sink flow turbulent boundary layers. J Fluid Mech 56:337–351

    Google Scholar 

  • Kim J, Simon TW, Kestoras M (1994) Fluid mechanics and heat transfer measurements in transitional boundary layers conditionally sampled on intermittency. J Turbomach 116:405–416

    Google Scholar 

  • Kline SJ, McClintock FA (1953) Describing uncertainties in single sample experiments. Mech Eng 75:3–8

    Google Scholar 

  • Kuan CL, Wang T (1990) Investigation of the intermittent behavior of a transitional boundary layer using a conditional averaging technique. Exp Therm Fluid Sci 3:157–170

    Google Scholar 

  • Lewalle J (1995) Tutorial on continuous wavelet analysis of experimental data. Mechanical Aerospace and Manufacturing Engineering Dept., Syracuse University. World-Wide-Web: http://www.mame.syr.edu/faculty/lewalle/tutor/tutor.html

  • Lewalle J, Ashpis DE (1995) Transport in bypass transition: mapping active time scales using wavelet techniques. Proceedings of the 10th Symposium on Turbulent shear flows, University Park, PA, pp P2-37–P2-42

    Google Scholar 

  • Ligrani PM, Bradshaw P (1987) Subminiature hot-wire sensors: development and use. J Phys E: Sci Inst 20:323–332

    Google Scholar 

  • Mayle RE (1991) The role of laminar-turbulent transition in gas turbine engines. J Turbomach 113:509–537

    Google Scholar 

  • Mayle RE, Dullenkopf K, Schulz A (1998) The turbulence that matters. J Turbomach 120:402–409

    Google Scholar 

  • Moss RW, Oldfield MLG (1996) Effect of free-stream turbulence on flat-plate heat flux signals: spectra and eddy transport velocities. J Turbomach 118:461–467

    Google Scholar 

  • Praisner TJ, Clark JP (2004) Predicting transition in turbomachinery, Part 1—A review and new model development. ASME pap GT2004-54108

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

    Google Scholar 

  • Schobeiri MT, Read K, Lewalle J (2003) Effect of unsteady wake passing frequency on boundary layer transition, experimental investigation and wavelet analysis. J Fluids Eng 125:251–266

    Google Scholar 

  • Shaikh FN (1997) Investigation of transition to turbulence using white-noise excitation and local analysis techniques. J Fluid Mech 348:29–83

    Google Scholar 

  • Sohn KH, Reshotko E (1991) Experimental study of boundary layer transition with elevated freestream turbulence on a heated flat plate. NASA CR 187068

  • Solomon WJ, Walker GJ, Gostelow JP (1995) Transition length prediction for flows with rapidly changing pressure gradients. ASME pap 95-GT-241

  • Steelant J, Dick E (1996) Modelling of bypass transition with conditioned Navier–Stokes equations coupled to an intermittency transport equation. Int J Numer Methods Fluids 23:193–220

    Google Scholar 

  • Suzen YB, Huang PG (2000) Modeling of flow transition using an intermittency transport equation. J Fluids Eng 122:273–284

    Google Scholar 

  • Thole KA, Bogard DG (1996) High freestream turbulence effects on turbulent boundary layers. J Fluids Eng 118:276–284

    Google Scholar 

  • Volino RJ (1998a) Wavelet analysis of transitional flow data under high free-stream turbulence conditions. ASME pap 98-GT-289

  • Volino RJ (1998b) A new model for free-stream turbulence effects on boundary layers. J Turbomach 120:613–620

    Google Scholar 

  • Volino RJ (2002) Separated flow transition under simulated low-pressure turbine airfoil conditions: Part 2—Turbulence spectra and length scales. J Turbomach 124:656–664

    Google Scholar 

  • Volino RJ, Simon TW (2000) Spectral measurements in transitional boundary layers on a concave wall under high and low free-stream turbulence. J Turbomach 122:450–457

    Google Scholar 

  • Volino RJ, Schultz MP, Pratt, CM (2003) Conditional sampling in a transitional boundary layer under high free-stream turbulence conditions. J Fluids Eng 125:28–37

    Google Scholar 

  • Von Kármán T (1948) Progress in the statistical theory of turbulence. Proc Natl Acad Sci USA 34:530

    Google Scholar 

  • Walters DK, Leylek JH (2004) A new model for boundary layer transition using a single-point RANS approach. J Turbomach 126:193–202

    Google Scholar 

  • Wang T, Keller FJ (1999) Intermittent flow and thermal structures of accelerating transitional boundary layers, Part 1—Mean quantities; Part 2—Fluctuation quantities. J Turbomach 121:98–112

    Google Scholar 

  • Wang T, Zhou D (1998) Conditionally sampled flow and thermal behavior of a transitional boundary layer at elevated free-stream turbulence. Int J Heat Fluid Flow 19:348–357

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, United States Naval Academy, Annapolis, MD, 21402-5042

    Ralph J. Volino

Authors
  1. Ralph J. Volino
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ralph J. Volino.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Volino, R.J. An investigation of the scales in transitional boundary layers under high free-stream turbulence conditions. Exp Fluids 38, 516–533 (2005). https://doi.org/10.1007/s00348-005-0945-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-005-0945-0

Keywords

Search

Navigation