Laminar,transitional and turbulent annular flow of drag-reducing polymer solutions

Mean and rms axial velocity-profile data obtained using laser Doppler anemometry are presented together with pressure-drop data for the flow through a concentric annulus (radius ratio κ = 0.506) of a Newtonian (a glycerine–water mixture) and non-Newtonian fluids—a semi-rigid shear-thinning polymer (a xanthan gum) and a polymer known to exhibit a yield stress (carbopol). A wider range of Reynolds numbers for the transitional flow regime is observed for the more shear-thinning fluids. In marked contrast to the Newtonian fluid, the higher shear stress on the inner wall compared to the outer wall does not lead to earlier transition for the non-Newtonian fluids where more turbulent activity is observed in the outer wall region. The mean axial velocity profiles show a slight shift (～5%) of the location of the maximum velocity towards the outer pipe wall within the transitional regime only for the Newtonian fluid.     

Turbulent pipe flow of a drag-reducing rigid “rod-like” polymer solution

Fully developed turbulent pipe flow of an aqueous solution of a rigid “rod-like” polymer, scleroglucan, at concentrations of 0.005% (w/w) and 0.01% (w/w) has been investigated experimentally. Fanning friction factors were determined from pressure-drop measurements for the Newtonian solvent (water) and the polymer solutions and so levels of drag reduction for the latter. Mean axial velocity u and complete Reynolds normal stress data, i.e. u′, v′ and w′, were measured by means of a laser Doppler anemometer at three different Reynolds numbers for each fluid. The measurements indicate that the effectiveness of scleroglucan as a drag-reducing agent is only mildly dependent on Reynolds number. The turbulence structure essentially resembles that of flexible polymer solutions which also lead to low levels of drag reduction.     

Effect of drag reducing polymer on air–water annular flow in an inclined pipe

Drag reduction (DR) for air and water flowing in an inclined 0.0127 m diameter pipe was investigated experimentally. The fluids had an annular configuration and the pipe is inclined upward. The injection of drag reducing polymer (DRP) solution produced drag reductions as high as 71% with concentration of 100 ppm in the pipeline. A maximum drag reduction that is accompanied (in most cases) by a change to a stratified or annular-stratified pattern. The drag reduction is sensitive to the gas and liquid superficial velocities and the pipe inclination. Maximum drag reduction was achieved in the case of pipe inclination of 1.28° at the lowest superficial gas velocity and the highest superficial liquid velocity. For the first time in literature, the drag reduction variations with the square root of the superficial velocities ration for flows with the same final flow patterns have self-similar behaviors.     

On pipe diameter effects in surfactant drag-reducing pipe flows

Remarkable power saving in a fluid transport system is possible if the surfactant drag reduction technology is used. Application of surfactant drag reduction to district heating and cooling systems has been investigated in the past. The establishment of the scale-up law in drag-reducing pipe flows is one of the most important problems in this application. Main purpose of this study is aimed to develop a reliable scale-up law in surfactant drag-reducing flows. As the basic data of surfactant solutions, both non-Newtonian viscosity and viscoelasticity were experimentally determined. A turbulent eddy diffusivity model based on the Maxwell model was employed to estimate the drag reduction of surfactant solutions. The predictions by the turbulence model developed in this study with proper rheological characteristics of surfactant solutions has resulted in a reliable estimation of the pipe diameter effect in surfactant drag-reducing flows over the pipe diameter range from 11 to 150mm. Received: 30 June 1997 Accepted: 29 December 1997     

Pool boiling of drag-reducing polymer solutions

The effect of drag-reducing polymeric additives on the critical heat flux and minimum film boiling temperature in subcooled pool boiling of water has been experimentally examined. Three water-soluble polymers, viz. a polyethylene oxide (Aldrich No. 18946-4), a polyacrylamide (Separan AP-30), and a galactomannan polysaccharide (Galactasol-211) have been examined at concentrations of 10, 50, and 100 wppm. The experiment is performed by quenching a hot brass sphere in an isothermal pool of the fluid to be examined and obtaining the corresponding boiling curve. The experiments have been conducted at atmospheric pressure with a pool temperature of 90°C. The results show that the critical heat flux increases by more than 50% while the minimum film boiling temperature increases by more than 110°C when concentrations of 100 wppm of polyox or guar gum are used. For separan solutions, the critical heat flux and minimum film boiling temperature are lower than those for water and go through a minimum at a concentration of ～10 wppm; the maximum reductions are about 73% and 34°C respectively.     

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]     

A Reynolds stress model for turbulent flow of homogeneous polymer solutions

Using a priori analyses of direct numerical simulation (DNS) data, a Reynolds stress model (RSM) is developed to account for the influence of polymer additives on turbulent flow over a wide range of flow conditions. The Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) rheological constitutive model is utilized to evaluate the polymer contribution to the stress tensor. Thirteen DNS data sets are used to analyze the budgets of elastic stress–velocity gradient correlations as well as Reynolds stress and dissipation transport. Closures are developed in the framework of the RSM model for all the required unknown and non-linear terms. The polymer stresses, velocity profiles, turbulent flow statistics and the percentage of friction drag reduction predicted by the RSM model are in good agreement with present and those obtained from independent DNS data over a wide range of rheological and flow parameters.     

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.     

Degradation of homogeneous polymer solutions in high shear turbulent pipe flow

This study quantifies degradation of polyethylene oxide (PEO) and polyacrylamide (PAM) polymer solutions in large diameter (2.72 cm) turbulent pipe flow at Reynolds numbers to 3 × 10⁵ and shear rates greater than 10⁵ 1/s. The present results support a universal scaling law for polymer chain scission reported by Vanapalli et al. (2006) that predicts the maximum chain drag force to be proportional to Re ^3/2, validating this scaling law at higher Reynolds numbers than prior studies. Use of this scaling gives estimated backbone bond strengths from PEO and PAM of 3.2 and 3.8 nN, respectively. Additionally, with the use of synthetic seawater as a solvent the onset of drag reduction occurred at higher shear rates relative to the pure water solvent solutions, but had little influence on the extent of degradation at higher shear rates. These results are significant for large diameter pipe flow applications that use polymers to reduce drag.     

Steady and dynamic shear properties of non-aqueous drag-reducing polymer solutions

The steady and dynamic shear properties of two non-aqueous drag-reducers (a medium molecular weight polyisobutylene and a commercial organic drag-reducer) in kerosene solutions over a wide range of temperature and concentration were presented. The intrinsic and zero-shear viscosity results were used to identify the concentrate regimes of these solutions. A characteristic time constant λ₀, which was based on the spring-bead model for dilute solutions, was employed as the scaling parameter for both steady-shear and dynamic data over a wide range of concentration and temperature. The inadequacy of the Graessley reduced-variable method in the dilute region was illustrated. The shear-thinning behaviour of these polymer solutions could be described by the Carreau model. The dynamic data followed the Zimm and Rouse-like behaviour in the low and high frequency limits. The Cox-Merz rule was obeyed in the low shear rate and frequency regions. The Carreau and the zero-frequency Maxwell time constants appeared to be related to λ₀ by a constant factor over a wide range of polymer concentrations. The finding provides a method for extrapolating viscoelastic information into the drag reduction regime, and could be useful for interpretation of drag reduction results.     

Friction and heat transfer in drag-reducing surfactant solution flow through curved pipes and elbows

A study of drag-reducing flow in curved pipes was conducted. In contrast to earlier studies we show that if we use a modified definition of drag reduction that includes only the turbulence effects, we observe indeed the same level of drag reduction in both coiled and straight pipes. More complex results showing reduced drag reduction compared to curved pipes were achieved with elbows. Two elbows of different size and type were tested in turbulent flow of both water and drag-reducing surfactant solution. A more elaborate analysis was conducted for a half-inch threaded elbow with a ratio of curvature radius to diameter of 1.2. The pressure drop and heat transfer were measured in a section downstream from the elbow over a distance of x/D = 130 in order to investigate the hydrodynamic and thermal developments of the flow. The pressure drop coefficient of the elbow was calculated for water and a surfactant solution, based on the total increase in pressure drop in the system due to the presence of the elbow. For a larger welded elbow of 6″ diameter some drag reduction was measured for the surfactant solution.     

Effect of pipe inclination on holdups/velocity ratios of oil-water flow without and with addition of drag-reducing polymer

In petroleum industries, the demand for effective design and operation of the oil-water transport systems is very high, and holdup of each phase is one of the important hydrodynamic parameters needed for such design and operation. This parameter can be affected by several factors one of which is the presence of the drag-reducing polymers in the oil-water flow. Therefore, the focus of this experimental study is on the effect of the drag-reducing polymer on the holdups and by extension, velocity ratios of the oil-water flow. Specifically, the investigation of the holdups and velocity ratios of the oil-water flow before and after the addition of the drag-reducing polymer was carried out in horizontal (0^ᴼ) and different inclined (−5^ᴼ, +5^ᴼ and +10^ᴼ) acrylic pipe with 30.6-mm ID. The investigation was conducted using flow conditions of 0.4, 0.8 and 1.6 m/s mixture velocities and 0.1–0.9 input oil volume fractions at each inclination. In each experimental run, the holdup of each phase was measured after steady flow was achieved using quick closing valves. Thereafter, the master solution of the polymer which was prepared at 2000 ppm water was injected at controlled flow rates to provide 40 ppm of the polymer in the water phase and the measurement was repeated. It was found generally that the water holdups and hence, the velocity ratios were increased after the addition of the polymer particularly in water-dominated flow regions. The velocity ratios also increased with the increase in the mixture velocities at these same flow regions. Finally, water was found to flow faster for separated flow at 0.4 m/s while for the dispersed flow regions at higher mixture velocities, the dispersed phase was in general the faster flowing phase.     

Drag of a sphere in dilute polymer solutions in high Reynolds number range

We have measured by means of four ultrasonic transducers the fall velocity of a sphere at high Reynolds number range in dilute polyacrylamide solutions which have viscoelastic effects. The polymer solutions were 5, 20 and 50ppm in the concentration. Basset-Bousinessq-Oseen equation for the falling sphere was analyzed numerically on Newtonian fluids in order to compare with the fall velocity of a sphere in the polymer solutions, and the experimental data of the fall velocity in tap water is in agreement with the range of no effect of the test tank wall. In polymer solutions, it was shown that the fall velocity is larger than that in Newtonian fluids within the critical Reynolds number range such that the drag reduction occurs and is smaller than that of Newtonian fluids over the range. The experimental data for the drag reduction ratio of polymer solutions is arranged by Weissenberg number calculating the experimental data of the first normal stress differences. It was shown that the maximum drag reduction ratio in the polymer solutions lies in the range of We=3∼10. Received: 15 October 1997 Accepted: 12 May 1998     

Scale effects in polymer solution pipe flow

Satisfactory scaling from laboratory-scale pipe-flow data to large industrial pipelines is an area of practical concern in the utilization of drag-reducing polymer solutions. From experimental data for pipes 0.0254 m in diameter and above, it is shown that accurate scaling can be obtained using a simple, pocket-calculator method. However, pipes of say, 0.005 m and smaller provide much less accurate scaling data for larger pipes. A detailed study of the velocity profiles in drag-reducing flow indicates a total lack of similarity of the profiles of the very small pipes compared with the larger.     

Drag reduction by polymer solutions in a riblet-lined pipe

The flow of 3 to 100 wppm aqueous solutions of a polyethyleneoxide polymer,M _w=6.2×;10⁶, was studied in a 10.2 mm i.d. pipe lined with 0.15 mm V-groove riblets, at diametral Reynolds numbers from 300 to 150000. Measurements in the riblet pipe were accompanied by simultaneous measurements in a smooth pipe of the same diameter placed in tandem. The chosen conditions provided turbulent drag reductions from zero to the asymptotic maximum possible. The onset of polymer-induced drag reduction in the riblet pipe occurred at the same wall shear stress, * _w =0.65 N/m², as that in the smooth pipe. After onset, the polymer solutions in the riblet pipe initially exhibited linear segments on Prandtl-Karman coordinates, akin to those seen in the smooth pipe, with specific slope increment . The maximum drag reduction observed in the riblet pipe was independent of polymer concentration and well below the asymptotic maximum drag reduction observed in the smooth pipe. Polymer solution flows in the riblet pipe exhibited three regimes: (i) Hydraulically smooth, in which riblets induced no drag reduction, amid varying, and considerable, polymer-induced drag reduction; this regime extended to non-dimensional riblet heightsh ⁺<5 in solvent andh ⁺<10 in polymer solutions. (ii) Riblet drag reduction, in which riblet-induced flow enhancementR>0; this regime extended from 5<h ⁺<22 in solvent and from 10<h ⁺<30 in the 3 wppm polymer solution, with respective maximaR=0.6 ath ⁺=14 andR=1.6 ath ⁺=21. Riblet drag reduction decreased with increasing polymer concentration and increasing polymer-induced flow enhancement S. (iii) Riblet drag enhancement, whereinR<0; this regime extended for 22<h ⁺<110 in solvent, withR;–2 forh ⁺>70, and was observed in all polymer solutions at highh ⁺, the more so as polymer-induced drag reduction increased, withR<0 for allS>8. The greatest drag enhancement in polymer solutions,R=–7±1 ath ⁺=55 whereS=20, considerably exceeded that in solvent. Three-dimensional representations of riblet- and polymer-induced drag reductions versus turbulent flow parameters revealed a hitherto unknown dome region, 8<h ⁺<31, 0<S<10, 0<R<1.5, containing a broad maximum at (h ⁺,S,R) = (18, 5, 1.5). The existence of a dome was physically interpreted to suggest that riblets and polymers reduce drag by separate mechanisms.     

Drag reduction change of polyethyleneoxide solutions in pipe flow

Change of drag reduction (DR) along a tube (D=2 mm, L=4 m) was experimentally investigated. To attain turbulent flow with Re=8 × 10⁴, a tank operated under high pressure up to 16 MPa. Solutions of different brands of polyethyleneoxide (PEO) with concentrations from 1 ppm to 100 ppm were tested. The results indicate that DR is not a constant value but depends on the time and intensity of interaction between the polymer and the turbulent flow. There are three regions with different behaviors of DR: growth, maximum, and slope down. Maximum DR coincides with the Virk ultimate DR and can be described by the suggested simple formula . A decrease in the DR maximum has not been found even for high shear stresses τ _p < 800 Pa. DR dynamics for four brands of PEO with different molecular weight was studied. Direct experimentally determined DR may be greater than the Virk ultimate value if the change in velocity profile is not taken into account. The corrected DR never exceeds the ultimate DR. Received: 10 April 2000/Accepted: 24 May 2001     

Measurement of laminar,transitional and turbulent pipe flow using Stereoscopic-PIV

Stereoscopic particle image velocimetry (SPIV) is applied to measure the instantaneous three component velocity field of pipe flow over the full circular cross-section of the pipe. The light sheet is oriented perpendicular to the main flow direction, and therefore the flow structures are advected through the measurement plane by the mean flow. Applying Taylor’s hypothesis, the 3D flow field is reconstructed from the sequence of recorded vector fields. The large out-of-plane motion in this configuration puts a strong constraint on the recorded particle displacements, which limits the measurement accuracy. The light sheet thickness becomes an important parameter that determines the balance between the spatial resolution and signal to noise ratio. It is further demonstrated that so-called registration errors, which result from a small misalignment between the laser light sheet and the calibration target, easily become the predominant error in SPIV measurements. Measurements in laminar and turbulent pipe flow are compared to well established direct numerical simulations, and the accuracy of the instantaneous velocity vectors is found to be better than 1% of the mean axial velocity. This is sufficient to resolve the secondary flow patterns in transitional pipe flow, which are an order of magnitude smaller than the mean flow.     

Flow of drag-reducing surfactant solutions in rough pipes

The paper reports the results of experimental study of the flow of hexadecyltrimethylammonium chloride (CTAC) solutions with addition of sodium salicylate (NaSal) in the rough pipes. Measurements were performed in the range of the surfactant concentration from 200 to 400 ppm at a constant molar ratio CTAC/NaSal of 1:2. Five pipes of the relative roughness k/D varying from 1.2 × 10^?2 to 5.6 × 10^?2, obtained by the covering of inner surface of the pipes with glued silicon carbide particles of different size, were studied. The roughness was observed to increase the drag of flow of CTAC/NaSal solutions already at Reynolds numbers higher than 800. With increasing relative roughness k/D, the critical value of Reynolds number, at which the drag reduction disappears, was found to decrease. However, no influence of the roughness on the critical shear stress was noted. The ratio of the critical Reynolds number for rough pipes to that of hydraulically smooth pipes was independent of the surfactant concentration. The degree of drag reduction by the flow of surfactants was greater in rough pipes than in smooth pipes.