b
Figure 10. Effect of pipe diameter on drag reduction in coiled pipe. (a) 40 Ib/Mgal xanthan fluid (b) 20 Ib/Mgal xanthan fluid. [33].

3.1.4 Effect of pipe diameter on drag reduction in coiled pipes for flow of polymer and surfactant solutions

The effect of diameter on the effectiveness of drag-reducing agents in curves remain unclear. For the case of polymer DRA, the effect of curvature on effectiveness of DRAs is said to be more pronounced in small diameter pipes than in larger ones [9]. Though further investigation is required, existing data show that the effectiveness of DRPs in small diameter pipes is higher than in larger ones. Coil diameter has been reported to influence the onset of drag reduction. However, for larger diameter coiled pipes the onset of drag reduction tends to a higher generalised Reynolds number [33], [88] (Fig. 10). Investigation on the effect of pipe diameter on DR by surfactant DRAs is lacking and studies in this area could throw more light on the mechanism of surfactant DR.

3.1.5. Effect of temperature on drag reduction in coiled pipes for polymer and surfactant solutions

Limited studies have been carried out to demonstrate the effect of temperature on the effectiveness of both polymer and surfactant DRAs. Reports show that the effect of temperature is more pronounced in straight pipes than in curves of equivalent length [11], [89]. Conflicting reports exist on the effect of temperature on effectiveness of DRPs. While Kamel [10] reported that DR was unaffected by temperature in coiled pipe flow, Gallego and Shah [86] stated that DR decreased with temperature. Data from the limited studies available for flow of surfactant solution, in both straight and coiled pipes, show that, the range and maximum values of drag reduction increased with temperature [23], [73]. This is linked to the increase in critical wall shear stress associated with increase in temperature. These tests were, however, conducted over a limited range of temperatures (5–20 oC) for both straight and coiled pipes. More research is required to establish the effect of a wider range of temperature for all drag reducing agents.

3.1.6 Effect of dissolved salts, starch or solids on drag reduction in coiled pipes for polymer and surfactant DRAs

It has been reported that salt concentration influenced the conformation of polymer molecules [13], [76]. For the case of high salt content (typical of randomly coiled polymers chains) the DR in straight pipes occurs only after a threshold shear stress is attained. This may be associated with the uncoiling of the polymer chains of extensional flow or polymer entanglement reaching the size of eddies [91], [92]. At low concentrations in straight pipe flows, DRPs show asymptotic DR immediately after transition from laminar to turbulent flow regime [93]. It has been reported that the presence of dissolved salts in solution reduces the effectiveness of the DRA in both straight pipes and curves [9], [94]. Also adding starch to polymers is reported to have little or no effect on the frictional losses in curved pipes [9]. There is insufficient data on the effect of salts, starch and solids on drag reduction in curved pipes and so no general conclusion could be drawn.

3.1.7 Effect of pipe roughness on drag reduction in curves for polymer and surfactant solutions

Pipe roughness is expected to have appreciate effect on DR since it is likely to affect both velocity fluctuations and degradation of polymer and surfactant DRAs. It has been reported that the mechanism that sustains turbulence in smooth and rough pipes are quite different [95]. Due to the limited studies in this area, the effect of pipe roughness on DR it remains unclear. In the case of straight pipe flow of DRPs, Karami and Mowla [93] reported increased DR with increase in pipe roughness, while in a rectangular open channel Petrie et al. [94] observed a decrease in DR with pipe roughness. This discrepancy is not entirely surprising. The increase in percentage DR with pipe roughness reported by Karami and Mowla [93] could be explained by increased velocity fluctuation and turbulent intensities with increase in pipe roughness. In smooth pipe flows increase Reynolds number is often associated with increase in velocity fluctuation and turbulent intensities. It has been reported that, below critical wall shear, percentage DR increase with Reynolds number [34], [88]. Therefore, one would expect an increase in percentage DR with increase in velocity fluctuation and turbulent intensities associated with increased pipe roughness. On the other hand, increased pipe roughness could also increase the rate of polymer degradation within the channel. The implication of this would be reduced percentage DR with increase in pipe roughness, especially for high Reynolds number flows. Since increased turbulent intensities/velocity fluctuation and increased DRA degradation could result from flow over rough surfaces, the dominant of the two would most likely determine whether there is increased or reduced DR with roughness. Gallego and Shah [86] reported that, for the flow of DRPs, the effect of pipe roughness was more pronounced in curved pipes than in straight pipes. Their plots showed that pipe roughness results in decrease in DR in coiled pipes. This might be associated with increased shear in curved pipe flow when compared to straight pipe flow which in turn results in degradation of polymer chains.

3.2 Effect of polymer and surfactant DRAs on pressure drop for single phase liquid flows in bends

Flow through bends exhibits a more complex geometry than flow in coiled pipes. This is because of entry and separation effects coupled with the idealised flow similar to that in coiled pipes. The disturbance generated at the bends, increases the downstream flow redevelopment length. The redevelopment for surfactant solutions, for example, has been reported to be slower than that of water [10]. The redevelopment is even slower at higher velocities (Fig. 11). This could be the result of higher drag and heat transfer reductions associated with higher velocities. The slower redevelopment for flow of surfactants compared to water introduces added drag which counters its drag-reducing effects on the flow [10]. This additional drag effect is linked to flow separation. It has been reported that, for flow of surfactant flow through threaded elbows there is significant drag reduction upstream and downstream (after full development) of the elbow but not in the elbow region of undeveloped flow itself [10]. The report indicates that, although there is drag reduction in the bend, the overall effect of flow redevelopment is overbearing on the drag reduction. One may deduce from the work of Gasljevic and Matthys [9] that, the difference in drag for surfactants in the elbow is linked to the effect of the surfactant on flow separation and reattachment. Thus, if the surfactant reduces turbulence, it may hinder reattachment and energy transfer to the wake. There is however insufficient data to fully explain the effect of surfactant DRAs on pressure drop in bends. At the time of this report, studies of polymer DRAs in bends could not be found in open literature. However, since only small concentrations (compared to surfactants) of DRPs are required for DR, it should be expected that flow redevelopment for DRPs solution in bends would approach that of the solvent. If this is the case, below the critical wall shear, addition of DRP is likely to yield significant DR for single phase liquid flows in bends. In addition, since surfactants undergo temporary degradation at high shear, flow rate control can be used as a means of optimising drag-reducing effects of surfactants in and around bends. Experimental investigation is currently under way by the authors to gain more insight into the effect of DRPs on flows in bends.