Investigation on the characteristics of turbulence transport for momentum and heat in a drag-reducing surfactant solution flow

Abstract

Simultaneous measurements of the velocity (u and ν in the streamwise and wall-normal directions, respectively) and temperature fluctuations (θ) in the thermal boundary layer were carried out for a heated drag-reducing surfactant solution flow in a two-dimensional channel by means of a two-component laser Doppler velocimetry and a fine-wire thermocouple probe. The drag-reducing fluid tested was a dilute aqueous solution of a cationic surfactant, cetyltrimethylammonium chloride (CTAC), with 30 ppm concentration. Measurements were performed for CTAC solution flows at an inlet temperature of 31 °C and at three Reynolds numbers of 3.5×104, 2.5×104, and 1.5×104, respectively, and for water flow at the Reynolds number of 2.5×104. Drag reduction (DR) and heat transfer reduction (HTR) for the three CTAC solution flows were DR(HTR)=33.0(20.2), 70.0(77.3), and 65.1(77.0) percentage, respectively. At a high HTR level, a large temperature gradient appeared when y+<50 in the measured range (the superscript “+” denotes normalization with inner variables). Temperature fluctuation intensity, θ′+, and the streamwise turbulent heat flux, u+θ+¯, were enhanced in the layer with large temperature gradient for the drag-reducing flow, whereas the wall-normal turbulent heat flux, −ν+θ+¯, was depressed throughout the measured range. The depression of −ν+θ+¯ was due to a cause similar to that of the depression of the Reynolds shear stress −u+ν+¯, i.e., in addition to the decrease of ν′+, decorrelation between the two variables occurred. The decrease of −ν+θ+¯ resulted in HTR, which was similar to that of the decrease of −u+ν+¯ resulted in DR for the drag-reducing flow by additives. The turbulence production terms, −u+ν+¯(∂U+/∂y+) and −ν+θ+¯(∂Θ+/∂y+) where U and Θ are mean velocity and temperature, were reduced in the drag-reducing CTAC solution flows. The estimated power spectra of temperature fluctuations implied that the drag-reducing surfactant additive depressed the turbulence at high frequencies or at small scales, whereas it increased the turbulent energy at low frequencies or at large scales. The profiles of the eddy diffusivities for momentum and heat in the CTAC solution flows were both decreased. The turbulent Prandtl number deviated from that of the water flow near the heated wall with a value close to the molecular Prandtl number of the solvent.