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.