Contents
1.0 Introduction3
2.0 Drag reduction in curved pipes4
2.1 Drag-reducing Agents (DRAs)7
2.1.1 Polymer DRAs7
2.1.2 Surfactant DRAs9
2.1.3 Micro-bubbles DRAs10
3.0 Effect of polymer and surfactant DRAs on pressure drop and friction factor for single phase flows in curved pipes and channels10
3.1 Effect of polymer and surfactant DRAs on pressure drop for single phase liquid flows in coiled pipes10
3.1.1 Effect of varying polymer and surfactant DRA concentration on drag reduction in coiled pipes12
3.1.2 Effect of fluid velocity/Reynolds number on the drag reduction in coiled pipes for polymer and surfactant DRA13
3.1.3 Effect of coil curvature ratio on the effectiveness of polymer and surfactant DRA13
3.1.4 Effect of pipe diameter on drag reduction in coiled pipes for flow of polymer and surfactant solutions14
3.1.5. Effect of temperature on drag reduction in coiled pipes for polymer and surfactant solutions15
3.1.6 Effect of dissolved salts, starch or solids on drag reduction in coiled pipes for polymer and surfactant DRAs15
3.1.7 Effect of pipe roughness on drag reduction in curves for polymer and surfactant solutions16
3.2 Effect of polymer and surfactant DRAs on pressure drop for single phase liquid flows in bends16
3.2.1 Effect of DRAs concentration on pressure drop in bends for polymer and surfactant solutions17
3.2.2 Effect of curvature on effectiveness of DRAs in bends for flow of polymer and surfactant solutions17
3.3 Effect of micro-bubble injection on pressure drop for single phase liquid flows in coiled pipes18
3.3.1 Effect of curvature ratio on micro-bubble drag reduction in coiled pipes18
3.3.2 Effect of air micro-bubble fraction on drag reduction in curved pipes18
3.3.3 Effect of flow rate on micro-bubble drag reduction in curved pipes19
3.3.4 Effect of micro-bubble size on drag reduction in curves and bends19
3.4 Effect of polymer and surfactant DRAs on fluid flux in curved pipes19
3.5 Secondary flow in bends and curves20
3.5.1 Effect of DRAs on secondary flow for single phase flows in curves20
3.5.2 Effect of DRAs on secondary flow in bends21
3.6 Flow transition and critical Reynolds number in bends and curves of circular cross-section21
3.6.1 Effect of DRAs on flow transition and critical Reynolds number22
3.7 Friction factor correlations for single phase flow in curved pipes22
3.8 Flux models for non-Newtonian fluids24
3.9Two phase liquid-liquid flow and the effect of drag-reducing agents on two-phase (gas-liquid and liquid-liquid) flow in curved pipes
3.9.1 Effect of drag-reducing agents on gas-liquid flows in curved pipes25
4.0Knowledge gap
4.1 Single phase flow in curved pipes26
4.2 Two-phase flows in curved pipes27
5.0Conclusion