The distribution of dag force inside the inlet region of a canopy model

Drag is the force needed to hold an object in its place and is often measured by a force probe. Such a measurement provides the overall force that is applied by the whole object leaving the spatial distribution of drag per unit mass unknown. Though the overall force is nice to have it is not useful when it comes to modeling the three dimensional flow-field inside obstructed regions such as aquatic vegetation, forests and urban canopies. The research presented here focuses on the internal drag distribution of a canopy laboratory model made of randomly distributed thin glass plates.

Three closure models are needed when using the double average momentum equation for canopy flows; a model for the Reynolds stresses, a model for the dispersive stresses and a model for drag. Two years ago, at the 30th AMS Conference on Agricultural and Forest Meteorology in Boston, we demonstrated that dispersive stresses at the canopy inlet are highly significant (Moltchanov et al., 2011) and proposed a closure model that links these stresses to the mean velocity square (Moltchanov and Shavit, 2013). A recording of this talk can be found in the following link: https://ams.confex.com/ams/30AgFBioGeo/flvgateway.cgi/id/21139?recordingid=21139.

This time, at the 31st meeting in Portland, we will present our results of measuring the drag distribution along the inlet region of the same canopy model.

The study is unique as it presents measured distributions of drag per unit mass. This is different from measuring the drag force of a whole tree, parts of a tree or even the use of sensors to reveal the drag that develops along the tree surfaces. Moltchanov (2013) calculated the drag coefficient inside the canopy model by using a complete mapping of the velocity field by Particle Image Velocimetry (PIV). It was shown that the drag coefficient varies with location and flow rate. As the flow enters the leading edge of the canopy, the drag coefficient increases to a very large peak value, followed by a decrease to a final value downstream. In the fully developed flow section, the drag coefficient was found to increase with depth. Note, that a similar pattern was found for the fully developed flow region by Coceal et al., (2007), however their results were based on numerical solutions and not on measurements.

In complementary experiments we validated Molchanov's (2013) result by directly measuring the drag force on isolated sections of the canopy and found a good agreement between the two experiments. The conclusions are that a constant drag force coefficient is an inadequate modeling parameter and that more detailed mapping of the velocity field and the geometrical properties are paramount when dealing with such an inhomogeneous environment.

In the talk we will present the results of Molchanov's (2013), compare them with the results of the direct measurement and analyze the unique behavior of the drag coefficient at the inlet to the canopy.

References:

Coceal, O., T. G. Thomas, and S. E. Belcher (2007), Spatial variability of flow statistics within regular building arrays, Boundary Layer Meteorol., 125, 537–552, doi:10.1007/s10546-007-9206-5.

Moltchanov, S., Y. Bohbot-Raviv, and U. Shavit (2011), Dispersive stresses at the canopy upstream edge, Boundary Layer Meteorol., 139, 333–351

Moltchanov, S. (2013), Dispersive stresses in canopy flows, PhD thesis, 156 pp., Technion IIT, Haifa, Israel.

Moltchanov, S., and U. Shavit (2013), A phenomenological closure model of the normal dispersive stresses, Water Resour. Res., 49, doi:10.1002/2013WR014488.