Characterization of Turbulent Flow in a Flume with Surfactant

Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division January 13, 2003; revised manuscript received July 27, 2004. Review conducted by: M. Plesniak. Drag reduction in turbulent flow, by low concentrations of polymers, is well known since the publication on the phenomenon by Toms 1. Recently, biodegradable surface active agents (surfactants) have become a more appropriate choice as drag reducing additives. These surfactants are environmental friendly and, in addition, they are less susceptible to mechanical degradation 2. The influence on turbulent flow characteristics could be spectacular with only few parts per million of surfactant solution, added to the solvent 34. The general belief is that surfactants, like other additives, act directly on the small turbulent scales (456 and references therein). The drag reduction effect is due to the modification of the turbulence structure. A significant decrease of the Reynolds stresses was observed 7, however without a substantial reduction of the rms values of the velocity fluctuations. In addition, the turbulent kinetic energy production, and the dissipation, were measured and found to be strongly reduced in the drag reduced flow 8. Most researchers have reported an increase of anisotropy for surfactant solution flows, characterized by a considerable suppression of the wall-normal velocity fluctuations. The common agreement is that the decorrelation of the streamwise u and wall-normal v components is the main manifestation of the drag reduction effect, which leads to the reduction of Reynolds stresses 6. Theoretical models of drag reduction flows concern the stretching of the polymers by the turbulent flow in certain areas, and consequential the local viscosity changes, as the major mechanisms of drag reduction (see review in 4). Recently, the influence of the additives was investigated experimentally by using motion pictures of dye injection 9, real-time hologram interferometry 10, and dye visualization 11. The researchers found an increase in the spanwise spacing of low-speed streaks and decrease of “bursting events” in drag reduced flows. In the present research, we investigated experimentally the influence of the nonionic, biodegradable, nontoxic surfactants, on the turbulent flow in a flume, by means of particle image velocimetry (PIV) 19. Similar experimental studies with PIV were recently performed by Warholic et al. 12 and White et al. 13, and in both studies polymers were used as drag reducing additives. The drag reduction in surfactant solution flows exceed Virk’s maximum drag reduction limit 14 for polymers, for relatively low concentrations 15. Therefore, these nontoxic and biodegradable materials that are also shown to be good drag reducers, have a great potential for many engineering and industrial applications. The experiments were performed in a flume with dimensions of 4.9×0.32×0.1m, shown in Fig. 1. The entrance and the following part of the flume, up to 2.8 m downstream, were made of glass. All necessary precautions were taken: the eddies and recirculating currents were dampened by means of narrow slits in the inlet tank (as presented by dotted lines in the Fig. 1), baffles were installed in the pipe portion of the tank, the inlet to the channel was a converging channel in order to have a smooth entrance, the 0.75 HP, 60 RPM centrifugal pump was isolated from the system by means of rubber joints fitted to the intake and discharge pipes. A flowmeter, with an accuracy of 0.5% of the measured flow rate, continuously recorded the flow rate. In order to make the measurement area long enough and to avoid a flow-depth decrease at the end of the flume, flow restrictors (in the form of an array of cylinders) were placed at the outlet portion. The working fluid was treated and filtered tap water. A detailed description of the flume is given in 16. In the present study we used the dilute solution of Agnique PG 264-U surfactant (also known as Agrimul PG 2062), which is clustered under the alkyl polyglycosides family. The surfactant is based on plant-derived chemicals (carbohydrate molecular structure), it is readily biodegradable, nontoxic, nonionic, and does not add to the Earth’s CO2 burden. It has a density of 1070kg/m3 and a dynamic viscosity of 17 kg/m s at 25°C. The surfactant molecules consist of a hydrophobic and a hydrophilic part. In water these molecules tend to assemble to aggregates called micelles. Above a certain value of concentration, defined as the critical micelle concentration, globular micelles are usually formed, resulting in drag reduction 4. The critical micelle concentration value for the Agnique PG 264-U is 20 ppm. A semidilute surfactant solution was prepared by mixing of Agnique PG 264-U with 500 mL of water, heated up to 80°C and stirred for 30 min, then added to the outlet water tank. The PIV system included a double pulsed Nd:YAG laser (170 mJ/pulse, 15 Hz) operating at 532 nm, sheet forming optics, and 8 bit, 1024×1024pixels, 30 frames-per-second charge-coupled device camera. The camera was located 0.2 m under the flume, with imaging axis normal to the laser light sheet, as shown in Fig. 2. The velocity fields were measured in the streamwise-spanwise plane. The laser sheet was located 0.01 m above the bottom, which is equivalent to y+=80 (the friction velocity was estimated in the streamwise-wall normal plane by 17). The time separation between the two laser pulses was adjusted according to the mean streamwise velocity value and was equal to 2 ×10−3s. Hollow glass spherical particles with an average diameter of 11.7 μm and a density of 1100kg/m3, were used for seeding. The calibration procedure and the PIV cross-correlation analysis were performed by using INSIGHT 5.10 software 18. In all the cases an interrogation area of 32×32pixels with 50% overlapping was used. The spatial resolution of the camera was 80 μm per pixel, and the field of view was approximately 80mm×80mm. The analysis produced about 3000 vectors per map, filtered by using standard median and global outlier filters. About 5% of the erroneous vectors were removed during the post-processing analysis. The statistical analysis was based on 50 image pairs, resulting in 50 two-component velocity vector fields for each experimental case. The acquisition time of each experiment was 50/15≈3.3s.The influence of the surfactant solution on the turbulent flow field is demonstrated by means of the comparative results for water and drag reduced flow. The results were compared for the same flow-rate velocity Uq=Q/A, where Q is the flow rate and A is the cross-sectional area of the flow. All the experiments were conducted for a constant flow rate of 5.8×10−3m3/s, which is equivalent to Uq=0.2m/s and Reh=Uqh/ν=20,000, where h is the water height, and ν is the kinematic viscosity of the water. Figure 3 presents the two fluctuating velocity fields: of water flow (left) and of the flow with surfactant (right). The flow direction is from top to bottom, and the coordinates in the streamwise and the spanwise directions are normalized with the water height, h. Arrows represent the two-component fluctuating velocity vector field, u′−w′. The colors emphasize the high- and low-speed regions: The blue stands for fluctuating streamwise velocity which is higher than the ensemble averaged velocity field, and red is for the low speed regions. A negative value corresponds to a high speed region, since the positive x is defined from left to right and the positive z direction is from the bottom to the top. The effect of surfactant is shown qualitatively in Fig. 3, where one can observe weaker streamwise velocity fluctuations, than in the solvent counterpart. The average root-mean-square value of the streamwise velocity fluctuations, calculated as urms′=〈u′2〉, is shown as the probability density function in Fig. 4. The rms of the streamwise fluctuations of the surfactant flow is reduced, as compared to that of water. This result shows the effect of the surfactant, which suppresses the turbulent activity. This result is in a good agreement with the literature (e.g., 6 and references therein). Note that the rms values are compared as they are normalized by means of the flow-rate velocity Uq, which is the constant quantity in this experiment. Since the profile is altered as a part of the drag reducing effect, the mean streamwise velocity 〈U〉, calculated as the ensemble average of the PIV realizations at some constant wall normal location y, is not appropriate for the normalization. The spatial characteristics are shown through two-point spatial correlation functions. The autocorrelation function of the streamwise velocity fluctuations along the streamwise axis is defined as Ruux=〈ux,z⊗ux+Δx,z〉 and along the spanwise coordinate Ruuz=〈ux,z⊗ux,z+Δz〉. The autocorrelation function Ruux, shown in Fig. 5, clearly demonstrates that the surfactant additive does not change the longitudinal length scale. In contrast, the spanwise correlation, statistically demonstrates the effect of the modification of the spanwise structure. In the case of water flow, the transversal correlation Ruuwz crosses the zero axis, corresponding to the anticorrelation of the positive and negative velocity fluctuation values. In contrast, the function Ruusz in the case of flow of surfactant solution, shows that the distance between high- and low-speed regions increases. This result is in good agreement with the experimental results of Warholic et al. 12 and Oldaker and Tiederman 11. It is known that polymers, in addition to the scale modification effect, strongly decrease the one-point correlations between the streamwise and the wall-normal fluctuating velocities. In the present study we present comparative experimental results of the Reynolds stress component −〈u′w′〉, summarized in Table 1. The first two rows in the Table 1 demonstrate the so-called “decorrelation” effect of u′ and w′ velocity components. The magnitude of the Reynolds stress more often approaches zero: The average value is the one order of magnitude smaller, and the distribution of values is less (e.g., standard deviation). In addition, the distribution for water flow includes larger values of the Reynolds stress (normalized by the square of the flow-rate velocity), shown by maximum values: i.e., 0.05 for water and only 0.03 for surfactant solution. The most important difference between water and surfactant solution flows is apparently the skewness factor, that emphasizes the fact of the decorrelation. This is consistent with the PIV results obtained by Kawaguchi et al. 20, in which the influence of surfactants was investigated in the streamwise-wall normal plane in a channel flow. Since the strong suppression of the Reynolds stress takes place without substantial reduction of the turbulent fluctuations (e.g., Fig. 4), we might conclude that the reduction is, for the most part, due to the decorrelation of the velocity components, which is in agreement with the previous results (6 and references therein). Table 2 presents the turbulent energy production term in the kinetic energy balance equation, −〈u′w′〉Suw. The effect of the surfactant on this quantity is even more pronounced, as production reaches lower values, compared to water flow, and the skewness factor changes the sign from the positive (i.e., productive) to the negative sign. The result implies that in addition to the decorrelation between the velocity fluctuations, the surfactant reduces the momentum transfer and the kinetic energy production. Similar results are presented by Wei and Willmarth 21, in which the LDV measurements were performed in a channel flow with polymer additives. They showed a dramatic reduction of the turbulent kinetic energy production in the x−y plane, in a wall region between 40<y+<200. The mean rate-of-strain component in the streamwise-spanwise plane is defined as Suw=〈∂u/∂z+∂w/∂x〉 and in the production it represents the energy contribution of the large scale motions. This leads to the conclusion that the significant decrease of the turbulent energy production is not solely due to the decrease of the Reynolds stress, neither due to the decrease of the rate-of-strain component itself, but it is associated with an additional decorrelation effect. This effect was previously reported, but only by DNS results of den Toonder et al. 22, where the effect of polymer additives was investigated by using the “dumb-bell” model. The drag reducing effect of a surfactant additive from the alkyl polyglycosides family was investigated experimentally. In the present study, PIV measurements were done to investigate the turbulent flow in the streamwise-spanwise plane of a flume at y+=80, in the buffer zone, where about 80% of the energy production takes place. The influence of the surfactant solution on the turbulent flow and its structure is presented by means of the correlation and the probability density functions. The biodegradable surfactant was shown to be an efficient drag reducing solution. The results support the explanation of the mechanisms responsible for the drag reduction, reviewed by 6. The qualitative and quantitative results, that demonstrate the effect of the surfactant are summed up as follows: x,y,z= Streamwise, wall normal, and spanwise coordinate, respectively, m u,v,w= Instantaneous streamwise, wall normal, and spanwise velocity components, respectively, m/s U,V,W= Ensemble average velocity components, m/s u′,v′,w′= Fluctuating velocity components, m/s urms′= Root-mean-square (rms) value of the fluctuating streamwise velocity, m/s Q= Flow rate, m3/sUq= “Flow-rate” velocity per unit length, the ratio of the flow-rate and the cross-sectional area, m/s h= Water level, m Suw= Mean stress tensor component in the streamwise-spanwise plane, 1/s 〈⋅〉 = Ensemble averaging operator