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

Development characteristics of dilute cationic surfactant solution flow have been studied through the measurements of the time characteristics of surfactant solution by birefringence experiments and of the streamwise mean velocity profiles of surfactant solution duct flow by a laser Doppler velocimetry system. For both experiments, the concentration of cationic surfactant (oleylbishydroxymethylethylammonium chloride: Ethoquad O/12) was kept constant at 1000 ppm and the molar ratio of the counter ion of sodium salicylate to the surfactants was at 1.5. From the birefringence experiments, dilute surfactant solution shows very long retardation time corresponding to micellar shear induced structure formation. This causes very slow flow development of surfactant solution in a duct. Even at the end of the test section with the distance of 112 times of hydraulic diameter form the inlet, the flow is not fully developed but still has the developing boundary layer characteristics on the duct wall. From the time characteristics and the boundary layer development, it is concluded that the entry length of 1000 to 2000 times hydraulic diameter is required for fully developed surfactant solution flow.List of abbreviations and symbols A₁, A₂ Coefficients for time constant fitting [-] - B Breadth of the test duct [m] - C₁, C₂ Coefficients for time constant fitting [-] - D Pipe diameter [m] - D_H Hydraulic diameter [m] - g Impulse response function [Pa] - H Width of the test duct [m] - n Index of Bird-Carreau model [-] - Re Reynolds number (=U_mD_H/) - Re_D Pipe Reynolds number (=U_mD/) - Re_x Streamwise distance Reynolds number (=U₀x/) - T Absolute temperature [K] - t Time [s] - t_a Retardation time [s] - t_b Build-up time [s] - t_x Relaxation time [s] - t_x1, t_x2 Relaxation time for double time constant fitting [s] - t Time constant in Bird-Carreau model [s] - U Time mean velocity [m/s] - U_m Bulk mean velocity [m/s] - U_max Maximum velocity in a pipe [m/s] - U₀ Main flow velocity [m/s] - u Friction velocity [m/s] - x, y Coordinates [m] - Shear rate [s^–1] - Mean shear rate [s^–1] - n Birefringence [-] - 99% boundary layer thickness [m] - Solution viscosity [Pa·s] - _P, _S Surfactant and solvent viscosity [Pa·s] - ₀, Zero and infinite viscosity of Bird-Carreau model [Pa·s] - Characteristic time in Maxwell model [s] - Water kinematic viscosity [m²/s] - Density [kg/m³] - Solution shear stress [Pa] - _P, _S Surfactant and solvent shear stress [Pa] - Time in convolution [s]     

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

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.     

Headgroup effect on drag reduction and rheological properties of micellar solutions of quaternary ammonium surfactants

Two sets of cationic surfactants each with essentially the same alkyl chains but different headgroup structures were studied to investigate the effects of surfactant headgroup structure on micelle microstructures, drag reduction (DR) and rheological properties at certain counterion and surfactant concentrations. Cetyldimethylethylammonium bromide (CDMEAB) was compared with alkyltrimethyl ammonium bromide (CnTAB) and benzyldimethyl(hydrogenated tallow)ammonium chloride (DMHTB) was compared with alkyltrimethylammonium chloride (CmTAC), respectively. Surfactants with larger headgroups showed lower high temperature limits for DR. CDMEAB systems have better DR abilities than CnTAB below room temperature but the opposite is true at higher temperatures. DMHTB has stronger counterion binding ability than CmTAC, giving better DR properties than CmTAC at low counterion concentration, but has a lower upper temperature limit for DR. These results provide further understanding of the self-assembly nature of threadlike micelles of cationic surfactants and guidance for design of effective surfactant structures to meet particular DR requirements.     

Experimental studies on drag reduction and rheology of mixed cationic surfactants with different alkyl chain lengths

Experimental studies of the effects of mixtures of cationic surfactants on their drag reduction and rheological behaviors are reported. Cationic alkyl trimethyl quaternary ammonium surfactants with alkyl chain lengths of C₁₂ and C₂₂ were mixed at different molar ratios (total surfactant concentrations were kept at 5 mM with 12.5 mM sodium salicylate (NaSal) as counterion). Drag reduction tests showed that by adding 10% (mol) of C₁₂, the effective drag reduction range expanded to 4–120 °C, compared with 80–130 °C with only the C₂₂ surfactant. Thus mixing cationic surfactants with different alkyl chain lengths is an effective way of tuning the drag reduction temperature range. Cryo-TEM micrographs revealed thread-like micellar networks for surfactant solutions in the drag reducing temperature range, while vesicles were the dominant microstructures at non-drag reducing temperatures. High extensional viscosity was the main rheological feature for all solutions except 50% C₁₂ (mol) solution, which also does not show strong viscoelasticity. It is not clear why this low extensional viscosity solution with relatively weak viscoelasticity is a good drag reducer. Received: 3 November 1999/Accepted: 5 January 2000     

The effects of salts on the rheological characteristics of a drag-reducing cationic surfactant solution with shear-induced micellar structures

The effect of the counterion salt sodium salicylate (Nasal) on the transient rheological properties of a drag-reducing surfactant system tris (2-hydroxyethyl) tallowalkyl ammonium acetate (TTAA) has been studied with both rheometric and rheo-optical methods. Three types of transient behavior for N₁ and viscosity were identified in 5 mM TTAA solutions depending on the counterion concentration: induction and growth (below equimolar concentration); overshoot and growth (above equimolar concentration); and overshoot then plateau (at high concentrations of Nasal). The transient flow birefringence and orientation angle show trends similar to those of the viscosity and N₁. The second type of transient behavior suggests a two-stage alignment and shear thickening process. The SIS buildup time from the quiescent state, the rebuilding time after a strong preshear, and the relaxation time were also obtained from N₁ measurements, and show a maximum around equimolar conditions. The initial N₁ and viscosity immediately after the flow startup, on the other hand, show a maximum around a ratio of 2.5 to 3 Nasal/TTAA. For solutions with a Nasal concentration in the ratio 1.5 to 3, the steady state values of N₁ and viscosity do not show much variation with Nasal concentration over the shear rate range covered, however. The effect of an addition of sodium chloride (NaCI) to an equimolar Nasal/TTAA solution on the characteristic times and steady state values was also quantified. These rheological results provide us with tools to determine the optimal concentration ratio for practical drag reduction applications.     

Aerodynamic characteristics of a square cylinder with a rod in a staggered arrangement

The aerodynamic characteristics of a square cylinder with an upstream rod in a staggered arrangement were examined. The pressure measurement was conducted in a wind tunnel at a Reynolds number of Re_D=82,000 (based on the width of the square cylinder) and the flow visualization was carried out in a water tunnel with the hydrogen bubble technique at Re_D=5,200. When the rod and the square cylinder were in tandem, the reduction of drag was mainly caused by the increase of the rear suction pressure. When the staggered angle was introduced, the shield and disturbance effect of the rod on the square cylinder diminished, which results in the increase of the cylinder drag. The side force induced by the staggered angle is small (the maximum value is 20% of the drag of the isolate square cylinder). There were six different flow modes with various staggered angles and spacing ratios, and the corresponding flow patterns are presented in present paper.