Enhancing Heat Transfer of Drag-Reducing Surfactant Solution by an HEV Static Mixer with Low Pressure Drop

Abstract

A novel high-efficiency vortex (HEV) static mixer was used to locally enhance the heat transfer coefficient of a drag-reducing fluid, Ethoquad O/12 (EO12) (3 mM) with sodium salicylate (NaSal) (5 mM). Significant enhancement of heat transfer coefficients was observed. The Nusselt numbers were three to five times those of normal drag-reducing flow without mixer and were close to those of water at high Reynolds number with only modest energy penalty. In contrast, a Helix static mixer increased Nusselt number slightly with very high pressure loss. A performance number was used for comparisons among the HEV static mixer, the Helix static mixer, and water without mixer. The HEV static mixer had a performance number comparable to that of water. The enhanced heat transfer by the HEV static mixer resulted from streamwise vortices generated by the inclined tabs, which increased the convective heat transfer in the radial direction.

1. Introduction

Many solutions of polymers [1, 2] or surfactants [3] show reduced pressure loss compared with water at the same Reynolds number (based on water or solvent). This reduction in pressure loss, known as turbulent drag reduction (DR), can be utilized to reduce energy requirements for pumping the fluids. Polymer drag reducing agents (DRAs) have been utilized in the Trans-Alaska crude oil pipeline [4, 5] and in fire fighting [6] and have been studied for many other applications [7]. However, polymeric DRAs lose drag reducing effectiveness in pumping because their relatively long molecules are degraded in high shear stress regions of piping systems [8]. Therefore, to maintain their drag reduction effectiveness, polymeric DRAs have to be replenished after each pumping station. Surfactant drag reducing solutions, on the other hand, retain their drag reduction ability even in recirculation systems without the constant addition of surfactant DRAs, because the surfactant wormlike micelles, which are essential to induce drag reduction [3, 9–11] can reassemble after being temporarily broken up by high shear stress [3, 12]. Thus, surfactant DRAs are promising for use in recirculation systems such as district heating or cooling systems (DHCS) [3, 13, 14].

However, drag reduction is accompanied by heat transfer reduction for both polymeric [15–19] and surfactant [12, 20–23] DRAs. Heat transfer reduction is found to be always greater than drag reduction for a given Reynolds number [17, 24, 25]. Aguilar et al. [26] examined the coupling issue between drag reduction and heat transfer reduction (HTR) for both polymer and surfactant DRAs. They found the ratio between the heat transfer reduction and drag reduction was nearly constant from the onset of DR to the departure from the asymptotic regime. They [27] also determined the ratio of the maximum heat transfer reduction asymptote to the maximum drag reduction asymptote to be 1.06 for Re>20,000.

The mechanism of the reduced heat transfer has been investigated. Sellin et al. [28] found the viscous sublayer region in drag-reducing surfactant solutions was significantly thicker than that in Newtonian fluids. This thicker viscous sublayer provides greater thermal resistance between the bulk drag-reducing fluid and the wall of the heat exchanger, and therefore decreases the heat transfer ability of the solution [29]. At the same time, the velocity fluctuations in the radial direction in turbulent flow are also greatly suppressed [30, 31], resulting in reduced heat transfer in the radial direction [29]. A few other characteristics of Newtonian turbulent flow were observed to be different in drag reducing flow. With the aid of particle imaging velocimetry, the disappearance of strong vorticity fluctuation [32] and reduced strength and inhibited frequency of turbulent bursts [33, 34] were observed. And reduced wall-normal (radial) turbulence intensity was also observed by Laser Doppler velocimetry [35, 36]. In short, the reduced heat transfer is due to the thickened viscous sublayer and the inhibited radial turbulence, which are caused by wormlike micelles in surfactant drag reducing solutions.

This reduced heat transfer ability is a serious drawback in applying DR surfactant solutions to DHCS. So it is necessary to enhance the heat transfer ability locally in heat exchangers of DHCS without incurring a major energy penalty. Many devices have been studied to temporarily enhance the heat transfer ability of surfactant drag-reducing solutions either by destroying the wormlike micelles or by disturbing the flow to enhance turbulence. To break the wormlike micelle structures of surfactant solutions, ultrasonic energy [21] was used, and heat transfer was enhanced slightly, but this method was not economical in energy cost. Other methods such as fluted tube heat exchanger [20], wire meshes [37], static mixers [12], and impinging jets [38] were aimed to temporarily break the wormlike micelles; they actually also disturbed the flow, but their relative contributions to enhanced heat transfer are not clear. To disturb the flow, still other methods employed were contracted channel [39], grooved tubes [40], wire coils [41], helical pipes [42], and vortex generators [43].

However, the secondary flow and vortices generated by these methods are randomly directed, which means there exists mixing in the flow direction as well as in the direction normal to the flow. Since heat transfer in heat exchangers is essentially in the normal direction, the mixing in the flow direction does not help enhance heat transfer. Therefore, the brute and unorganized disturbance by the above devices costs unnecessary energy losses by inducing unnecessary mixing in the flow direction. A novel static mixer [44], commonly called a high-efficiency vortex (HEV) static mixer, has been designed to generate organized streamwise vortices, which promote mixing in the direction normal to the flow. This static mixer consists of arrays of tabs inclining from the conduit wall in the flow direction at a certain angle, so that streamwise and counter-rotating vortices interconnecting neighboring ones can be naturally generated at the tab tips. These special vortices are designed to enhance the mixing process and heat transfer between the conduit wall and the bulk fluid. The turbulent flow structure modified by an HEV static mixer has been studied. Both intensified and inhomogeneous or anisotropic turbulent structures were observed [45]. Counter-rotating vortices behind the tabs were shown both by experiments and simulations [46–48]. An HEV static mixer enhanced heat transfer and mixing in chemical reactions in integrated chemical reactor-heat exchangers [46, 49, 50].

Due to the organized streamwise vortices, which enhance radial convective transfer, HEV static mixers cost significantly lower pressure drop or energy loss than other conventional mixers to achieve equivalent performance in various applications [51]. Fasano [52] reported that an HEV static mixer required only one twelfth to one third of the pressure drop of other conventional mixers to achieve the equivalent blending performance and thermal mixing efficiency. In some emulsification processes, an HEV static mixer was 1000 times more energy efficient than other mixers [45, 53]. It was also energetically efficient in enhancing heat transfer between two immiscible liquid phases in turbulent flow [54].

Surprisingly, HEV has not received attention in enhancing heat transfer in drag reducing flows despite its energetically economical applications in mixing and heat transfer. In this paper, the effect of an HEV static mixer on the heat transfer of a drag reducing surfactant solution, namely, EO12/NaSal (3 mM/7.5 mM), was studied experimentally and compared with a common inline static mixer. The rheological properties and drag reduction ability of the surfactant solution were also measured.

2. Experimental

2.1. Materials

The surfactant studied, EO12 (Ethoquad O/12 PG, donated by AkzoNobel), is a mixture of oleyl bis(2-hydroxyethyl)methyl ammonium chlorides (75 wt%) and propylene glycol (25 wt%). NaSal (sodium salicylate, purity > 99.8%) was purchased from Fisher Scientific. Surfactant/counterion solutions were prepared for drag reduction and heat transfer experiments by stirring in a container for 8 hours at room temperature by a high shear disperser (Janke & Hunkel IKA Ultra-Turrax SD-45), followed by overnight storage at rest. Smaller solutions were prepared using magnetic stirrers in a beaker before rheological measurements.

The inner diameter of the tube-in-tube heat exchanger is 10.2 mm. Since the commercially available HEV static mixers from Chemineer, Inc. are 2 inches in diameter or larger, a small HEV static mixer was fabricated. Tabs were first shaped by cutting the wall of a stainless steel tube with a 10 mm outer diameter and 9 mm inner diameter (purchased from McMaster-Carr), and then were pushed inwards and they formed a 30° angle with the tube wall. As shown in Figure 1(a), the isosceles trapezoidal tabs are 5 mm high and 5 mm and 3 mm in the wall base and the end base, respectively. A group of three tabs are evenly distributed around the circle of one cross section of the tube. (Figure 1(b) is the cross section view of a Tab group). 32 such groups are evenly spaced at 28 mm intervals along the tube. The distance between the wall base of the first tab group and the downstream end of the HEV tube is 868 mm, illustrated in Figure 2(a). Figure 2(b) is the overall view of the 1009 mm long HEV static mixer tube, which was inserted inside the tube-in-tube heat exchanger.

Figure 1:

(a) Tab dimensions, (b) cross section view of a group of three tabs.

Figure 2:

(a) HEV static mixer tab locations, (b) partial view (left) and overview (right) of the HEV static mixer tube, (c) an original 12-element Helix static mixer.

The plastic Helix static mixer, purchased from Cole-Parmer, had 10 helix elements, each element twisted in the opposite helical direction to the neighboring elements. Each element is 10 mm long and has an outer diameter of 10 mm (Figure 2(c)). This Helix static mixer was mounted inside the entrance of the tube-in-tube heat exchanger in some of the experiments.

2.2. Rheological Measurements

The first normal stress difference (N₁) and viscosity of the micellar solutions as functions of shear-rate were measured on an ARES rheometer (TA instruments) using a 50 mm cone-and-plate geometry (0.02 rad cone angle). The measured N₁ readings were corrected for inertial effects according to the following relation [55]:

N_{1}^{corrected} = N_{1}^{measured} + 0.15 {ρ ω}^{2} R^{2},

(1)

where ρ is the density of the solution, ω is the angular velocity, and R is the radius of the cone.

2.3. Recirculation System

Figure 3 shows a schematic of the recirculation system for drag reduction and heat-transfer experiments. This recirculation loop consists of a centrifugal pump (PROCON), a reservoir tank, an electric heater (TrueHeat 1500 W), two heat exchangers, and a magnetic flow meter (TOSHIBA LF404) connected by smooth stainless steel tubes of 10.2 mm inner diameter (ID) and 12.7 mm outer diameter (OD). The recirculation loop has a total length of about 25 m and can hold up to 16 L of liquid. The reservoir tank has a volume of 14 L.

Figure 3:

Schematic of apparatus for drag reduction and heat transfer experiments.

The pump rotation rate can be controlled in the range of 0 to 1969 rpm by a motor controller (BALDOR Adjustable Speed Drive). The flow rate (0.04 to 0.35 L/s) is monitored by the magnetic flow meter. The electric heater maintains the main loop temperature from room temperature up to ≾60°C. A chiller (Bay Voltex) in the annulus loop of the fluted tube-in-tube heat exchanger (with a coolant of 50% ethylene glycol and 50% water) cools and maintains the temperature of the main loop as low as 0°C. The inner tube of the 0.914 m long tube-in-tube heat exchanger is 10.2 mm and 12.7 mm in ID and OD, respectively. The ID of the outer shell is 50 mm. Heat transfer measurements are taken on this tube-in-tube heat exchanger. The temperature of the shell side of this tube-in-tube heat exchanger is mediated by the circulators (NESLAB RTE-111 and VWR 1160) connected in series and can be varied from 0° to 90°C. The flow rate in the shell side of the tube-in-tube heat exchanger is preset for each experiment to keep the heat transfer resistance on the shell side constant.

All the tubes, pipes, and heat exchangers are insulated with Nomaco K-Flex polyolefin to minimize heat exchange with the environment. Temperatures at all locations are measured by T-type thermocouples (T1 through T4 and T9 through T12). The differential pressures of straight pipe sections are measured by the pressure transmitters (P₁ through P₁₀) (OMEGA PX2300 series). Transmitters P₁ through P₉ measure consecutive sections of straight pipe. P₁ measures the pressure difference across a section of 50 pipe diameters. P₂ measures the differential pressure across a pipe section of 180 diameters, including the tube-in-tube heat exchanger. P₃ through P₉ each measures differential pressures across 80 diameters length downstream of the tube-in-tube heat exchanger. All the thermocouples, pressure transmitters and flow meters are connected to the data acquisition system described by Ge [56].

2.4. Drag Reduction and Heat Transfer Measurement

To obtain %DR, pressure drops were measured in a range of flow rates at fixed temperatures. The friction factor was calculated according to the following equation:

f = \frac{Δ P D}{2 ρ L V^{2}},

(2)

where f is the friction factor, ΔP is the pressure drop across the test section, D is the inner diameter of the pipe, ρ is the density of the solution, L is the length of the test section, and V is the mean flow velocity. Since ρ was essentially identical for the solutions and the solvent (water), the extent of DR (relative to water) could be calculated according to the following equation:

%DR = \frac{f_{water} - f}{f_{water}} \times 100 %,

(3)

where %DR is percent drag reduction and f_water is the friction factor of water. For direct comparison, f_water andf were taken at the same solvent Reynolds number (Re), based on the viscosity of water.

Heat loss per unit time in the annulus and heat gain per unit time in the inner tube were measured to ensure they were balanced. The difference was generally less than 5% and was mostly less than 3%. The average of these two quantities was used to calculate heat transfer coefficients. The inlet temperature (T3) was controlled at 10 ± 0.3°C, and the log-mean temperature difference between the annulus and tube was controlled at 25 ± 0.1°C. Thermocouple (T4) at the exit of the tube-in-tube heat exchanger was placed at the center of the flow to measure the mean temperature of the fluid. To avoid the radial temperature gradient established in the fluid once it got heated by the inner wall of the heat exchanger, a 6-element Helix static mixer was placed just upstream of T4 so that the fluid was well-mixed before reaching that point. This 6-element Helix static mixer was in position for all heat transfer measurements of drag-reducing solutions with and without any static mixer. Good heat balances could then be obtained under approximately steady-state conditions. The modified Wilson-plot method was used to calculate the heat transfer coefficient and Nusselt number (Nu) of the solution [29]. Heat-transfer reduction (relative to water) was then calculated by the following equation:

%HTR = \frac{{Nu}_{water} - Nu}{{Nu}_{water}} \times 100 %,

(4)

where %HTR is percent heat transfer reduction and Nu_water is the Nusselt number of water. Nu_water and Nu were taken at the same solvent Re.

The physical properties of water were used to calculate Re and Nu values. For the calculation of Nu for the HEV static mixer, the sum of heat transfer resistances of the heat exchanger wall and the HEV tube was used. Since the HEV tube was tightly fitted against the inner wall of the heat exchanger, the total wall thickness was assumed to be 3.5 mm and the effect of holes that tabs left behind in the HEV tube and the wall-wall interface were ignored.

3. Results and Discussions

3.1. Water Baselines

To validate the drag reduction and heat transfer measurements, baselines of water were obtained and were compared with existing correlations. The f_water was measured and the data were in agreement with the von Karman Equation for water flowing in smooth circular pipes (5) at Re>10,000 (Figure 4(a)). Therefore, this equation was used to calculate subsequent f_water and %DR,

\frac{1}{\sqrt{f_{water}}} = 4.0 \log (Re \cdot \sqrt{f_{water}}) - 0.4 .

(5)

Figure 4:

(a) Experimental Fanning friction factor (°) compared with von Karman Equation (—). (b) Experimental Nusselt number (°) compared with Dittus-Boelter Equation (—).

Experimental results for Nu versus Re for water at 10°C for Re>10,000 were also in good agreement with the Dittus-Boelter equation (6) for water heated in a smooth tube (Figure 4(b)). Therefore, this equation was used to calculate subsequent Nu_water and %HTR,

Nu = 0.023 {Re}^{0.8} {Pr}^{0.4},

(6)

where Pr is the Prandtl number, defined as the ratio of viscous diffusion rate to thermal diffusion rate.

3.2. Viscoelasticity and Drag Reduction of EO12/NaSal (3 mM/7.5 mM)

Drag-reducing surfactant solutions are usually shear thinning and show viscoelastic behavior [3] such as first normal stress differences (N₁). Figure 5(a) shows the shear viscosity, η, of EO12/NaSal (3 mM/7.5 mM). This solution showed shear thinning behavior in the shear rate range of 50 s⁻¹ to 1000 s⁻¹ for 10 and 20°C. η at 20°C was slightly lower than that at 10°C, but it was significantly lower at 30°C, where a shear-induced structure in viscosity was observed near 100 s⁻¹. The N₁ of EO12/NaSal (3 mM/7.5 mM) is shown in Figure 5(b). N₁ values at 10 and 20°C increased above 100 s⁻¹ with higher values at 10°C. At 30°C N₁ was essentially zero (data not shown here), in the range of shear rates we could measure (0.1 to 1,000 s⁻¹), a surprising result in view of Qi et al.'s observation [57] that N₁ increased at shear rates near those at which shear-induced structure was observed.

Figure 5:

(a) Shear viscosity of EO12/NaSal (3 mM/7.5 mM) at 10°C (∆), 20°C (□), and 30°C (°). (b) N₁ of EO12/NaSal (3 mM/7.5 mM) at 10°C (∆) and 20°C (□).

Figure 6 shows the good drag reduction of EO12/NaSal (3 mM/7.5 mM) from 10°C to 60°C. Drag reduction increased rapidly at solvent Reynolds number of 20,000 for all temperatures and leveled off near 80%. Thus, this solution has a wide range of effective drag reducing temperatures.

Figure 6:

Drag reduction of EO12/NaSal (3 mM/7.5 mM) at 10°C (∆), 20°C (□), 30°C (°), 40°C (×), 50°C (◊), and 60°C (*).

3.3. Heat Transfer Reduction of EO12/NaSal (3 mM/7.5 mM)

Figures 7(a) and 7(b) show the Nusselt number and %HTR of the EO12/NaSal (3 mM/7.5 mM) solution with no mixer, Helix static mixer, and HEV static mixer, and Figure 7(a) also shows water with and without HEV static mixer. In the tube-in-tube heat exchanger without any mixer, this solution had very low Nusselt numbers, ranging from 12.3 to 27.9 in the Reynolds number range of 2,300 to 22,000. Therefore, the heat transfer reduction for this solution was high, starting from 55% at Re=2,300 and increasing to 83% at Re=22,000. Compared with %DR at 10°C, %HTR is slightly greater, confirming that the reduction in heat transfer is larger than that of drag.

Figure 7:

(a) Nusselt number of EO12/NaSal (3 mM/7.5 mM) with Helix mixer (+), no mixer (●), HEV (♦) and water with no mixer (°) and HEV (◊). (b) %HTR of EO12/NaSal (3 mM/7.5 mM) with Helix mixer (+), no mixer (●) and HEV (♦).

Figure 8 shows the ratio of %HTR to %DR of EO12/NaSal (3 mM/7.5 mM) at 10°C. Because heat transfer and drag reduction experiments were not carried out simultaneously, the %HTR and %DR were not at the same Reynolds number, so %DR was obtained by interpolation to calculate the ratio. This ratio decreased from 3.0 at Re=6,300 and approached 1.1 as the Reynolds number increased to 22,000. This result is in agreement with the result reported by Aguilar et al. [27].

Figure 8:

Ratio of %HTR to %DR of EO12/NaSal (3 mM/7.5 mM) at 10°C.

The Helix static mixer slightly increased the rate of heat transfer of the solution (Figure 7(a)). The maximum Nusselt number it reached was 39 at Re=17,000, which was approximately 1.6 times that without any mixer. The %HTR was still high near 70% for Re>12,600. This Helix static mixer had opposite helical elements. As the fluid passed by, it was first divided and followed the twist of the first element in one direction. When it came to the second element, the fluid was divided again and was forced to follow the twist in the opposite direction. The constant dividing and alternately changing of twisting direction generated disturbances and extra shear stress in the flow. The disturbances should enhance the momentum and mass transfer in the radial direction and thus enhance heat transfer. And, if the shear stress was high enough, the wormlike micelles would be broken, and the solution should become water like and have higher heat transfer ability. While the heat transfer in the Helix mixer region may be enhanced, the enhancement over the whole heat exchanger was not significant. Heat transfer reduction was apparently restored shortly downstream of this mixer. A Helix mixer as long as the tube-in-tube heat exchanger could be used to enhance the overall heat transfer throughout the heat exchanger but this would result in extremely high pressure drop across the long Helix static mixer. The pressure drop penalty of this Helix static mixer will be discussed in the following section.

The HEV static mixer with water enhanced the Nusselt numbers, compared with water without the HEV static mixer, especially at the Re>15,000 (Figure 7(a)). The HEV static mixer with drag reducing solution had Nusselt numbers close to those of water at Re┼10,000. At Re=20,000, it again approached the Nusselt number of water (Figure 7(a)). The Nusselt number with HEV static mixer with drag reducing solution ranged from three to five times that of the solution without mixer. This significant enhancement of heat transfer was due to the HEV static mixer's disturbance to the drag reducing flow. As discussed in the introduction section, tabs in the HEV static mixer cause intensified turbulence and streamwise counter-rotating vortices behind the tabs near the wall [45–48]. The streamwise counter-rotating vortices bring the heated fluid near the wall to the axis of the flow, and at the same time, the wall region is replenished with cold fluid from the center of the bulk flow to receive heat from the wall. Thus, the radial mixing and heat transfer were significantly enhanced. In this HEV static mixer, there were three tabs in each group at one cross section. The three tabs generate three pairs of vortices, that is, three streams of fluid flowing from the bulk to the wall and three streams flowing from the wall to the bulk. As the fluid flows downstream, the streamwise vortices also move and become weaker. But when this portion of fluid hits the next group of tabs, new vortices are generated, enhancing radial mixing and heat transfer. This mechanism also explains the higher Nusselt number of water with HEV static mixer.

The high Nusselt number in the low Reynolds number range was unexpected. This might have resulted from the inaccuracy of temperature measurement because of the inhomogeneous temperature distribution of the viscoelastic solution flowing very slowly. The steep increase in the high Reynolds number range might be due in part to the breakup of wormlike micelles at high shear stress, as a high shear zone was observed at the top of HEV tab tips [45].

3.4. Pressure Drop Penalty

Pressure drops across the heat exchanger with mixers installed and an additional section downstream were measured by P₂ (refer to Figure 3). The total length of this section was 180ID (1836 mm). Figure 9 shows that the pressure drop for the 10-element Helix static mixer was three times that of the HEV static mixer, although this Helix mixer was only 100 mm long. If a Helix static mixer as long as the heat exchanger (914 mm) was used, the pressure drop would be extremely high. So the Helix static mixer was not energetically effective. In contrast, the HEV static mixer had a smaller pressure drop, while it enhanced the heat transfer much more. The pressure drop of the DR solution was also slightly lower than that of water with HEV static mixer. Without any mixer, both water and the solution had very low pressure drop. Figure 9 also shows that the maximum Reynolds number that water achieved at the maximum pump rate was 22,700 and 20,100 for no mixer and HEV static mixer, respectively. Although the pressure drop at P₂ for solution with HEV static mixer was higher than that of water without mixer, the solution could be pumped at a maximum flow rate of 0.26 L/s (Re=25,000) compared with 0.24 L/s (Re=22,700) for water.

Figure 9:

Pressure drops at P₂ for EO12/NaSal (3 mM/7.5 mM) with Helix mixer (+), no mixer (●), HEV (♦) and water with no mixer (°) and HEV (◊).

To facilitate the comparison between the solution with HEV static mixer and water without mixer, a performance number, p, was defined by (7). It represents the heat transfer performance per unit pressure drop for a defined section of the heat exchanger region. Based on the same idea, a similar “Hydrodynamic Performance Ratio” was defined [58] to evaluate the combined thermo hydrodynamic performances,

p = \frac{Nu}{2 \sum_{i = 3}^{8} {Δ P}_{i} + Δ P_{2}},

(7)

where ΔP₂ is the pressure drop across the heat exchanger and ∑_i=3⁸ΔP_i is the total pressure drop of the 400ID (4080 mm) section downstream of P₂. This pressure drop was doubled to include the pressure drop of the 400ID section upstream of the heat exchanger. Since the total length of the recirculation loop is more than 20 m, this estimation is conservative.

Figure 10 shows that as the Reynolds number increased, p for water without mixer decreased to 1.39×10^{− 3} Pa^{− 1}, while p for solution with HEV is roughly constant at about 1.39×10^{− 3} Pa^{− 1}. This means that for a tube-in-tube heat exchanger with 400ID sections upstream and downstream, the performance of the HEV static mixer was comparable to water without mixer for Re>20,000. If the distance between neighboring tube-in-tube heat exchangers is larger than 800ID, the solution with HEV would have less energy consumption than water without the HEV static mixer to achieve the same Nusselt number for Re>20,000 at 10°C Thus, in longer flow systems, the HEV static mixer with solution will have a larger p than water without mixers. In short, the HEV static mixer enhanced the heat transfer of the drag-reducing surfactant solution with a relatively lower energy penalty. The tabs of the HEV static mixer generate streamwise vortices, which enhance heat transfer in the radial direction. Few vortices in other directions, which would not be effective in enhancing heat transfer, are generated in the HEV static mixer and therefore, energy is not wasted in generating ineffective vortices, and the energy consumed is mainly used to generate streamwise vortices effective in enhancing heat transfer.

Figure 10:

Performance number of solution with HEV static mixer (■) and water without mixer (♦).

4. Conclusions

(1) The surfactant solution showed viscoelastic behavior at 10 and 20°C and had excellent drag-reducing ability, up to 80%, from 10°C to 60°C. The heat transfer ability of this solution was, however, reduced significantly. The ratio of %HTR to %DR decreased with Reynolds number and approached 1.1.

(2) The HEV static mixer mounted in the tube-in-tube heat exchanger enhanced the heat transfer of EO12/NaSal (3 mM/7.5 mM) significantly throughout the range of Reynolds numbers tested. At high Reynolds number, the Nusselt number was close to that of water without any mixer. The heat transfer enhancement was due to the streamwise vortices generated by the HEV static mixer. The relatively low pressure drop was because the vortices were mainly streamwise. Pressure loss vortices in other directions, which could not enhance the radial heat transfer, were not generated. The HEV static mixer's ability to break up the micelles was not clear in our study, as it was not possible to observe the structures of the micelles in the turbulent flow in the heat exchanger. However, because of the relatively small pressure penalty, we believe micelle destruction was not the major contributor to improvement in heat transfer by the HEV static mixer.

(3) A Helix static mixer was also used to enhance the Nusselt number of EO12/NaSal (3 mM/7.5 mM) by destroying the wormlike micelle structures. This mixer may enhance the heat transfer in the mixer region, but did not enhance the overall heat transfer significantly. The extremely high pressure drop was due to the brutal disturbance to the flow and generation of vortices that did not improve heat transfer in the radial direction.

(4) A performance number was used to evaluate the heat transfer ability at the price of pressure loss. Under assumed conditions, the HEV static mixer performance number nearly matched that of water without mixer. If the neighboring tube-in-tube heat exchangers were spaced further apart than the assumed distance (800ID), the drag-reducing solution with HEV static mixer should have less energy consumption than water without mixer to achieve the same Nusselt number for Re>20,000 at 10°C.

(5) By adjusting the design parameters, such as the tab angle, the tab group distance, and the tab size, an even better performance number might be achieved.

Footnotes

Acknowledgments

The authors would like to thank Professor R. S. Brodkey in the Department of Chemical Engineering at The Ohio State University for discussion and advice. Thanks also go to Paul Green for his dedication and skill in making the HEV static mixer. The authors greatly appreciate Leigh Evrard's technical support and maintenance of the recirculation system.

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