HYDRODYNAMIC BEHAVIOR OF A DRAG-REDUCING SURFACTANT IN CONSTANT-AREA FLOWMETERS
ASAD A. SALEM
FennCollege of Engineering
ClevelandStateUniversity
Cleveland, OH44115
U.S.A.
Abstract: The effects of cationic viscoelastic drag-reducing surfactant solutions in constant-area flow meters were experimentally investigated. The drag-reducing surfactant solutions produced substantially lower pressure differentials across this type of flow-meters than those of water. The amount of these pressure differentials was dependent on flow rate, ratio, and the concentration of the drag- reducing solution. In general, the dimensionless flow coefficients for the drag–reducing solutions were consistently higher than those for water. However, the nonrecoverable head loss coefficients for this of flow-meters were consistently smaller than those for water.
Key-Words:Viscoelastic surfactant, Orifice flow meter, Venturi flow meter
1
1 Introduction
Drag reduction is a flow phenomenon by which small amounts of additives can reduce the turbulent friction. This phenomenon is well documented and is used in a variety of technological applications. Long-chain-polymer molecules and surfactants are two types of additives used as drag reducers. Long-chain-polymers are effective drag reducing agents even at very low concentrations; but they are very prone to mechanical degradation when they pass through high stress regions. Unfortunately, experience has shown that this mechanical degradation is not reversible which leads to a decrease in the drag reduction level. As is the case with long chain polymers, ”degradation” of the surfactant solutions will occur and drag reduction effects will decrease if the shear stress exceeds a critical value. However, there is an important difference between polymers and surfactants in the following respect: while degradation of polymers is permanent, the degradation for surfactant solutions is thought to be linked to a temporary disruption of the large–scale micellar micro-structures which will readily regenerate when the shear is reduced below critical levels.
In spite of a large amount of experimental and simulational data, the exact mechanism of surfactant drag reduction has remained somewhat unclear. However, it is believed to be related to the subsequent configuration of rod-like micelles, which in turn, may generate larger structures of ordered micelles under optimal shear conditions. Most of the drag reducing surfactant mixtures are viscoelastic and have high extensional viscosity behaviors common to drag reducing solutions.
The most commonly used flow metering principle involves placing a constant–area flow obstruction of some type in the pipe or duct carrying the fluid. This flow obstruction causes a pressure drop which varies with the flow rate; thus measurement of the pressure drop by means of a suitable differential-pressure measurement device allows flow-rate measurement. The most common practical devices that utilize this principle are the orifice and venturi tube flow meters. The actual volumetric flow rate (Qa) for such meters is given by:
(1)
(2)
One can also group Cd and to form the dimensionless flow coefficient C:(3)
The orifice and venturi tube are the most employed flow metering elements, mainly because of their simplicity, their low cost, and the great volume of research data available for predicting their behavior. The venturi tube offers the advantages of high accuracy and small pressure drop. However, the orifice is considerably lower in cost, but it has a relatively high permanent pressure drop. The dimensionless flow coefficient C lumps all “head losses” for this kind of flow meters. Note that the “head losses” are not directly related to the viscous friction but to the dissipation of kinetic energy due to fluid acceleration and deceleration in the flow meter. In addition to friction and kinetic losses, the sharp and sudden change in flow geometry of the obstruction-type flow meters generates a swirling motion and secondary flow separation ahead of the meter throat. This swirling motion and flow separation exerts a shear stress on the fluid.
The average non-recoverable head loss coefficient, Km, for obstruction-type flow meters is expressed as a ratio of the measured head loss (hm) to the throat velocity head:
(4)
The hydrodynamics behaviors of drag reducing fluids in constant-area flow meters are not known and have not been reported. Hence the objectives of the present work are to measure the head losses in the orifice and venturi flow meter for drag-reducing fluids and to study the effect of these fluids in the dimensionless flow coefficient C. It is widely hypothesized that the shearing stresses generated as a result of fluid flow in obstruction- type flow meters are significant to cause serious mechanical degradation of drag–reducing solutions. As a result of this, the microstructure of the drag reducer will be destroyed and the polymer or surfactant solutions will completely loose their drag reducing ability.
Pak et al. [1] experimentally investigated the hydrodynamic characteristics of drag-reducing viscoelastic fluids in a sudden-expansion pipe. They measured the local pressure distribution in a sudden–expansion pipe flow. In addition they calculated the expansion loss coefficient as a function of the Reynolds number at three different concentration solutions of polyacrylamide Separan AP-273. They concluded that the expansion loss coefficient for the polyacrylamide solution was consistently smaller than that for water over a wide range of Reynolds number. Pak et al. [2] conducted a flow visualization study to investigate the hydrodynamics characteristics of aqueous solutions of polyacrylamide across a sudden-expansion step over a wide range of Reynolds number. The reattachment length for this solution was two to three times longer than those for water and gradually increased with increasing concentrations of polyacrylamide solutions.
Qi et al. [3] conducted drag reduction and heat transfer reduction and enhancement tests in a fluted tube-in-tube heat exchange for a cationic surfactant solution and a zwitterionic/anionic surfactant solution. The zwitterionic /anionic surfactant solution caused a significant heat transfer enhancement with moderate increase in pressure drop. However, the cationic surfactant caused higher pressure drops with little heat transfer enhancement. Casljevic et al. [4] experimentally explored the general features of the flow of surfactant solutions through centrifugal pumps. They determined the effect of drag-reducing surfactant on the pump performance characteristics. They also reported that full recovery of the drag reduction effectiveness of the fluid was achieved within 50 to 200 diameters distance downstream of the pump. Hameed et al. [5] used an orifice flow meter to measure flow rates in their investigation of the influence of different low molecular weight of polyethylene oxides on the flow of water in closed piping system with standard fittings. Results indicated low molecular weight polyethylene oxides exerted a reduction in the friction factor. The extend of this reduction was a function of Reynolds number and the loss coefficient of the fittings. Rose et al. [6,7] investigated the drag reduction and rheological properties of cationic viscoelastic surfactant. They pointed out that the critical wall shear stress was independent of tube diameter but it does have a close relationship with the nature, concentration, and the temperature of the cationic surfactant and the counter ions present.
2 Flow Loop and Instrumentation
A re-circulatory flow apparatus was constructed to measure the pressure drop caused by the flowmeter. A schematic of the apparatus is shown in Figure 1. The system consists of a 300-liter stainless steel reservoir, a water heater, a surge tank, a variable speed pump, a flow control valve, flow-meters, a 3-way pneumatic valve, a fluid collection apparatus for measuring flow rates, piping system, multiple differential pressure traducers, controls, and data acquisition system.
The system temperature was controlled to allow experiments to be run from room temperature to 80 oC. In order to reduce heat loss from the system, all tubes and the reservoir were thermally insulated by fiberglass. Temperatures of the test fluids were measured with E-Type thermocouples.
The flow loop was made from a 5/8-inch smooth stainless steel tube (I. D. 13.4 mm and O. D. 15.9 mm). The dimensionless hydrodynamic entry length (L/d) for drag-reducing fluids in a turbulent flow is approximately 80-100, which is substantially longer than that of Newtonian fluids. The length of hydrodynamics entry section used in this study was more than 300. An additional 110 diameter was provided to minimize the effects of downstream disturbances on the flow-meter. The flow loop was also fitted with an inter-changeable 5/16-inch smooth stainless tube (I.D = 6.2 mm) for drag reduction measurements. In addition, the flow loop was equipped with an Omega turbine flow meter to provide an accurate approximation of the flow rate circulating in the system.
A stainless steel positive displacement pump was used to circulate the test fluids. The pump speed was varied with volt-hertz motor speed controller to maintain a continuous change of flow rates. In addition the flow rates were controlled with a flow-rate control valve. To minimize the effect of pumping head fluctuations on hydrostatic pressure measurements, a 20 liters surge tank was installed between the pump and the flow rate control valve. The fluid level in the surge tank was controlled by compressed air until the flow was stable.
The pressure measurement devices become quite inaccurate below about 10 percent of its full-scale reading, and the flow rate of constant area flow-meters is proportional to (P)1/2 . Consequently, a meter of this type cannot be used accurately below about 30 percent of its maximum flow rating. To minimize the effect of this non-linearity in flow measurements four Rosemount differential pressure transducers (4-20 mA), with different calibration range, were used to measure the pressure drops across the flow-meter. The first transducer was calibrated to a range of 0-4 kPa with an uncertainty of 4.3 Pa, the second to a range of 0-25 kPa with an uncertainty of 5.5 Pa, the third 0-100 kPa with an uncertainty of 10.8 Pa, while the fourth was 0-250 kPa with an uncertainty of 47.5 Pa.
Flow rates were directly measured by weighing test fluids exiting the outlet of flow loop. During the flow rate measurement, a 60-liter container received the test fluid that was weighed with 200 kg capacity Ohaus balance and a resolution of 0.02 kg. The weigh platform was calibrated with a precision triple beam balance and connected to the data acquisition system via a RS232 bi-directional interface. A 3-way pneumatic valve (100 ms response time) was used to divert the flow to the weigh platform.
Two kinds of flow-meter were tested in this work. The first kind was a sharp-edge orifice meter (D = 13.4 mm) fitted with three interchangeable plates with ratios (/D) 0.459, 0.647, and 0.807. The thickness of each plate was 1.2 mm, edge thickness of 0.325 mm, and bevel angle of 45 o. Type-2 (D:1/2 D) pipe-wall pressure taps at D upstream and ½ D downstream were used for pressure measurement. Two venturi tube flow meters that followed the classic 21o -10 o rounded entry convergent-divergent design were tested. The ratios for these venturi meters were 0.323 and 0.402. The upstream and downstream pipe diameters were both 13.4 mm. The convergence and throat pressure taps were placed 42 mm apart.
The data acquisition system consisted of a National Instruments E- series multi- function device that provides analog I/O, digital I/O, and counter-timer functions. NIVI data logger and LabVIEW software were used to collect and analyze the data.
3 Materials
Aqueous solutions of two different concentrations of cetyltrimethlammonium salicylate (CTASal) plus 0.2wt.% sodium salicylate (NaSal) were used to investigate the effect of drag-reducing surfactants on orifice and venturi flow meters. CTASal is a viscoelastic cationic drag reducing surfactant and NaSal was used as counter ion. The drag reduction and rheological properties of CTASal plus NaSal aqueous solutions were extensively studied by Rose et al. [6,7].
4 Experimental Procedures and Data Reduction
Prior to the tests using CTASal plus 0.2 wt% NaSal aqueous solutions, system calibration runs were performed using water to examine the validity of the experimental apparatus and overall experimental procedures. The densities of CTASal plus 0.2 wt% NaSal aqueous solutions were measured with a hydrometer and found almost the same as that of water. The relative viscosities of aqueous solutions were measured with a capillary tube viscometer, and Brookfield DV-II + Programmable Viscometer to cover a wide range of shear rates. The densities and relative viscosities were tested over a temperature range of 45-60 o C of 5 o C increment and concentrations of CTASal plus 0.2 wt% NaSal .
Different concentrations of CTASal+ 0.2 wt% NaSal were tested in a 6.2- mm tube after 320 diameters entrance section to determine the optimum concentration and temperature for maximum drag reduction. Drag reduction rates of about 74 percent were achieved at 0.2 wt% CTASal + 02.wt% NaSal aqueous solution at about 51.5o0.2o C. At the same temperature, about 43 percent were achieved at 0.15 wt% CTASal + 02.wt% NaSal. The critical wall shear stresses were about 380.0 Pa at 0.2 wt% CTASal + 02. wt% NaSal aqueous solution and 176.0 Pa for 0.15 wt% CTASal + 02. wt% NaSal aqueous solution. This corresponded to a critical Reynolds number of 27.4 104 and 14.1104 based on solvent properties respectively. These results were in correlation with Rose et al. [6,7].
In light of these findings, aqueous solutions of two different concentrations of CTASal (0.15 wt% and 0.2 wt%) + 0.2 wt% NaSal at 52o0.2o C were used to investigate the effect of drag–reducing surfactants on obstruction type flow-meters, such as, orifice and venture.
Initially the 3-way valve was at the default position; whereby the testing fluid was circulated throughout the flow loop and no flow to the weighing platform. The system was adjusted to an approximated flow rate. The temperature and pressure drop data were monitored by the control/data acquisition system. When determined to be nearly constant, the control/data acquisition system simultaneously: (a) energized the 3-way valve to a fully opened position to divert the testing fluid to the weighing platform, (b) started time count, and (c) collected pressure measurements at a frequency of 1 HZ for 90 seconds. After 90 seconds the control system de-energized the 3-way valve to its default position to divert the flow away from the platform. After stabilization, the mass of the fluid that accumulated in the weighing platform was weighed and returned to the main storage tank. This sequence of operation was repeated an additional 5 times before another approximated flow rate was selected. Then all pressure and flow rate data collected during that set of measurement were averaged to obtain a single P corresponding to a single flow rate Q.
Following the sequence of operation stated above, the orifice meter with = 0.459 was calibrated using water at 52o0.2o C. This test was repeated several times to find out any inconsistencies in the system. Later, the orifice flow meter was calibrated for other ratios. Then the system was flushed, new water was added, and heated to 52o0.2o C, and the same sequence was followed to calibrate the venturi flow-meters.
Next, the system was drained, washed and dried by blowing compressed air through it. A 316 kg of fresh water was weighed with an Ohaus platform balance and poured into the system to fill the storage and surge tanks. The water was allowed to flow throughout the system while it was heated. When the temperature of the fluid reached 45o C a proper amount of CTASal and NaSal was added to make 0.15 wt% CTASal +0.2wt % NaSal aqueous solution. Next, the temperature of the system was increased to 52o0.2o C with a slower rate to avoid any excessive heating.
Prior to any measurements, the CTASal aqueous solutions were circulated in the flow loop for about 30 minutes at 52o0.2o C to ensure uniformity. Later, the sequence of operation stated earlier was followed to test the effect of 0.15 wt% CTASal +0.2 wt% NaSal aqueous solutions on orifice and venturi flow meters. Eventually, the same procedure was performed for 0.2-wt % CTASal+0.2wt.%NaSal for both meters for all ratios.
5 Results and discussion
For convenient comparison of the results between water and surfactant solutions, the Pressure Reduction “%PR” is defined as:
(5)
The experimental results of pressure drop (kPa) for water were compared with those for CTASal aqueous solutions for different meter sizes and kinds. Figure 2 presents the pressure drop for the orifice flow-meter with three different ratios. This figure represents, substantial and measurable pressure reductions were obtained at both concentrations. The amount of these pressure reductions appeared to be dependent on flow rate, ratio, and the concentration of the CTASal solution. Furthermore, Figure 3 presents the result of pressure-drop for two venturi flow meters with two different ratios. Similar trends to those of the orifice flow-meter were observed for venturi meters. However these pressure reductions were less than those of orifices but were maintained over a wider range of flow rates.
It was interesting to interpret the results of water and those of CTASal solutions in the following manner: Pressure reduction indicated that the CTASal solutions demonstrated a small pressure rise while water demonstrated a significant pressure drop. This was consistent with drag reduction phenomena commonly observed in a straight tube in turbulent flows. This drag reduction might be attributed to the presence of the super-ordered microstructure of CTASal aqueous solution. This indicated that the shear stress inside the flow meter did not cause serious mechanical degradation. As a result of that, the microstructure of the drag reducer was not completely destroyed and CTASal solutions did not completely loose their drag reducing ability. The reason for this pressure rise could be attributed to the viscoelastic nature of the CTASal solutions. Much of the energy for this pressure rise came from the kinetic energy flux from the fluid passing through the meter throat (or vena contracta). In addition, stored elastic energy resulting from work done at the throat inlet (or vena contracta) was consumed when the solution suddenly expanded, thus resulting in reducing pressure drop.