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

Simultaneous measurements of the velocity (u and v 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, -v⁺θ⁺, was depressed throughout the measured range. The depression of -v⁺θ⁺ was due to a cause similar to that of the depression of the Reynolds shear stress -u⁺v⁺, i.e., in addition to the decrease of v'⁺, decorrelation between the two variables occurred. The decrease of -v⁺θ⁺ resulted in HTR, which was similar to that of the decrease of -u⁺v⁺ resulted in DR for the drag-reducing flow by additives. The turbulence production terms, -u⁺v⁺(∂U⁺/∂y⁺) and 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.