Force acting on a square cylinder fixed in a free-surface channel flow

We describe an experimental study of the forces acting on a square cylinder (of width b) which occupies 10-40% of a channel (of width w), fixed in a free-surface channel flow. The force experienced by the obstacle depends critically on the Froude number upstream of the obstacle, Fr-1 (depth h(1)), which sets the downstream Froude number, Fr-2 (depth h(2)). When Fr-1 < Fr-1c, where Fr-1c is a critical Froude number, the flow is subcritical upstream and downstream of the obstacle. The drag effect tends to decrease or increase the water depth downstream or upstream of the obstacle, respectively. The force is form drag caused by an attached wake and scales as <(F)over bar>(D) similar or equal to C-D rho rho bu(1)(2)h(1)/2, where C-D is a drag coefficient and u(1) is the upstream flow speed. The empirically determined drag coefficient is strongly influenced by blocking, and its variation follows the trend C-D = C-D0(1 + C(D0)b/2w)(2), where C-D0 = 1.9 corresponds to the drag coefficient of a square cylinder in an unblocked turbulent flow. The r.m.s. lift force is approximately 10-40% of the mean drag force and is generated by vortex shedding from the obstacle. When Fr-1 =Fr-1c (< 1 ), the flow is choked and adjusts by generating a hydraulic jump downstream of the obstacle. The drag force scales as <(F)over bar>(D) similar or equal to C-K rho bg(h(1)(2) - h(2)(2))/2, where experimentally we find C-K similar or equal to 1. The r.m.s. lift force is significantly smaller than the mean drag force. A consistent model is developed to explain the transitional behaviour by using a semi-empirical form of the drag force that combines form and hydrostatic components. The mean drag force scales as (F) over bar (D) similar or equal to lambda rho bg(1/3)u(1)(4/3)h(1)(4/3), where lambda is a function of b/w and Fr-1. For a choked flow, lambda = lambda(c) is a function of blocking (b/w). For small blocking fractions, lambda(c) = C-D0/2. In the choked flow regime, the largest contribution to the total drag force comes from the form-drag component.