https://orcid.org/0000-0002-9662-9633
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Abstract
The interface between the main channel and the floodplain of a compound channel is often populated by trees or buildings that normally remain emergent during floods. This study investigates how drag on an emergent cylinder is affected by the shear flow that develops at the interface. The experimental set-up features a circular cylinder at the interface of a straight compound channel under uniform flow conditions. The integral form of the equation of conservation of momentum was used to calculate the magnitude and direction of the time-averaged drag force per unit submerged-length of the cylinder. All terms were experimentally determined, except for those associated with fluid interaction with the cylinder. The same method was also applied to a cylinder under symmetrical flow conditions. It is concluded that the existence of the shear layer leads to an asymmetrical drag force and to a reduced drag coefficient.
Acknowledgements
This experimental work was aligned with the objectives of the FlowRes ANR Project (2015–2018), IRSTEA, towards characterization of compound-channel flow, influenced by various floodplain land-uses.
Notations
Subscript or superscript m (m = 1,2,3,4,5,6) refer to an open control-section.
Superscripts L and R refer to left-side and right-side control volumes respectively.
Subscripts mc and fp refer to main channel and floodplain respectively.
| α | = | generic time-averaged variable (–) |
| b | = | width of the fluid control-volume (m) |
| C | = | normalization quantity for forces (N) |
| Cd | = | drag coefficient (–) |
| Cl | = | lift coefficient (–) |
| d | = | diameter of circular cylinder (m) |
| F | = | Froude number (–) |
| gi | = | gravitational acceleration (m s−2) |
| h | = | height of the fluid control-volume (m) |
| hfp, hmc | = | flow depth in the floodplain and in the main channel (m) |
| hr | = | relative flow depth in the channel (–) |
| K | = | shear parameter (–) |
| l | = | length of the fluid control-volume (m) |
| l0 | = | longitudinal distance of the control volume’s boundary upstream the cylinder (m) |
| ni | = | outward pointing normal unit-vector (–) |
| P | = | time-averaged pressure of fluid (N m−2) |
| Q | = | channel discharge (l s−1) |
| Rd | = | Reynolds number based on cylinder’s diameter (–) |
| R | = | time averaged force exerted by the cylinder on the flow (N) |
| Sc | = | total surface of the boundaries of the fluid control-volume (m2) |
| Sm | = | open control-section (–) |
| S(m) | = | area of an open control-section (m2) |
| Tik | = | time-averaged viscous stress tensor (N m−2) |
| U | = | time-averaged velocity (m s−1) |
| U0 | = | mean representative velocity of the approaching flow to the cylinder (m s−1) |
| = | time-averaged Reynolds-stress tensor (m2 s−2) | |
| Vc | = | control volume (m3) |
| x, y, z | = | longitudinal, lateral and vertical distances (m) |
| θ | = | angle between the channel bottom and the horizontal plane (°) |
| λ | = | dimensionless shear (–) |
| ν | = | kinematic viscosity of fluid (m2 s−1) |
| ρ | = | density of fluid (kg m−3) |