Flow through a very porous obstacle in a shallow channel

Abstract

A theoretical model, informed by numerical simulations based on the shallow water equations, is developed to predict the flow passing through and around a uniform porous obstacle in a shallow channel, where background friction is important. This problem is relevant to a number of practical situations, including flow through aquatic vegetation, the performance of arrays of turbines in tidal channels and hydrodynamic forces on offshore structures. To demonstrate this relevance, the theoretical model is used to (i) reinterpret core flow velocities in existing laboratory-based data for an array of emergent cylinders in shallow water emulating aquatic vegetation and (ii) reassess the optimum arrangement of tidal turbines to generate power in a tidal channel. Comparison with laboratory-based data indicates a maximum obstacle resistance (or minimum porosity) for which the present theoretical model is valid. When the obstacle resistance is above this threshold the shallow water equations do not provide an adequate representation of the flow, and the theoretical model over-predicts the core flow passing through the obstacle. The second application of the model confirms that natural bed resistance increases the power extraction potential for a partial tidal fence in a shallow channel and alters the optimum arrangement of turbines within the fence.

Effects of blockage, arrangement, and channel dynamics on performance of turbines in a tidal array

“…For partial arrays occupying a large portion of the channel width, the array-scale flow area may be large enough to give rise to changes in the bottom drag. Gupta and Young 23 and Creed et al 22 have developed models to investigate this.…”

“…Thus, we neglect the effects of the bottom drag on the power coefficients and the effects of its variation between the core flow and bypass flow on the total drag. The influence of the bottom drag has been studied by Creed et al 22 and Gupta and Young 23 , and we will also discuss it in the last section.…”

Residence time in presence of moving defects and obstacles

“…The characterization of transport regimes in presence of obstacles and irregular patterns is a classical problem of fluid dynamics [1,2], which is also relevant to a number of biological [3] and engineering [4,5] applications. For instance, a careful design of the shape and the location of the obstacles in microfluidic channels was observed to enhance the mixing of fluid flows [6].…”

“…In Sec. 4 we study the residence time problem in presence of moving defects which follow a stochastic updating rule. The discussion of relevant applications and our conclusions are deferred to Sec.…”

Performance of two-dimensional tidal turbine arrays in free surface flow

“…However, these do not weaken the meaningful of this trend.Finally, we notice that the bed friction is neglected within array scale dynamics. For large array, the changing of friction drag may be important and the quantitative influence of friction on turbine performance has been investigated by Creed et al21 , showing an increase in power as friction enhances. The work of Creed et al21 assumes constant velocity in vertical direction.…”