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Development characteristics of fluctuating velocity field of drag-reducing surfactant solution flow in a duct

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Abstract

Development behavior of the fluctuating velocity of surfactant solution in a duct has been studied experimentally. The concentration of surfactants was kept constant at 1,000 ppm, mean velocity at 0.78 m/s and fluid temperature at 15 °C. Using laser Doppler velocimetry, the fluctuating streamwise velocity distributions at six cross sections, which ranged from 14 to 112 times of hydraulic diameter of the duct, were measured. From the results, the fluctuating structures of surfactant solution flow are observed to have structures different from that of turbulent water flow in the developing field. The wavelet analysis reveals that the high-level fluctuation of surfactant solution flow is characterized by periodicity rather than irregularity around the position where the fluctuation intensity takes a peak value and that the period and the scale of periodic flow structures are related to the relaxation times of the fluid. This indicates that the high-level fluctuation is deeply related to the elastic instability and has a different generation mechanism from that of turbulence observed in a Newtonian turbulent flow.

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Abbreviations

A1, A2:

Coefficients for time constant fitting (–)

a, b:

Scale and translation parameter of wavelet analysis (s)

B :

Breadth of the test duct (m)

D H :

Hydraulic diameter (m)

DR:

Drag reduction rate (%)

f :

Friction coefficient of surfactant solution flow (–)

f w :

Friction coefficient of water flow (–)

g :

Frequency (Hz)

H :

Width of the test duct (m)

Re:

Reynolds number (=UmDH/ν)

T :

Variable in a mother wavelet

t :

Time (s)

t x :

Relaxation time (s)

tx1, tx2:

Relaxation time for double-time constant fitting (s)

U :

Time mean velocity (m/s)

U m :

Bulk mean velocity (m/s)

U + :

Maximum velocity normalized with friction velocity (–)

u τ :

Friction velocity (m/s)

u′:

Fluctuation velocity intensity (m/s)

u′max:

Maximum value of fluctuation intensity (m/s)

W:

Wavelet coefficient

W max :

Maximum value of each wavelet analysis

W rms :

Root mean square value of wavelet coefficient

x, y:

Coordinates (m)

y p :

Normal position taking maxium fluctuation intensity (m)

η:

Solution viscosity (Pa s)

ν:

Water kinematic viscosity (m2/s)

ρ:

Density (kg/m3)

τ:

Shear stress (Pa)

φ:

Mother wavelet of wavelet analysis

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Authors and Affiliations

  1. Graduate School of Science and Technology, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan

    Hiroshi Suzuki, Hong-Phuc Nguyen & Tomoe Nakayama

  2. Department of Chemical Engineering and Science, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan

    Hiromoto Usui

Authors
  1. Hiroshi Suzuki
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  2. Hong-Phuc Nguyen
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  3. Tomoe Nakayama
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  4. Hiromoto Usui
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Correspondence to Hiroshi Suzuki.

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Suzuki, H., Nguyen, HP., Nakayama, T. et al. Development characteristics of fluctuating velocity field of drag-reducing surfactant solution flow in a duct. Rheol Acta 44, 457–464 (2005). https://doi.org/10.1007/s00397-004-0425-0

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  • DOI: https://doi.org/10.1007/s00397-004-0425-0

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