Qi, ZX; Eames, I; Johnson, ER; (2014) Force acting on a square cylinder fixed in a free surface channel flow. Journal of Fluid Mechanics , 756 pp. 716-727. 10.1017/jfm.2014.455.

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Abstract

We describe an experimental study of the forces acting on a square cylinder (width b), which occupies 10 to 40% of a channel (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 Fr1 (depth h1), which sets the downstream Froude number, Fr2 (depth h2). When Fr1 < Fr1c, where Fr1c is a critical Froude number, the flow is subcritical upstream and downstream of the obstacle. The effect of drag tends to decrease/increase the water depth downstream/upstream of the obstacle. The force is form drag caused by an attached wake and scales as FD ≃ CD bu2 1h1/2, where CD is a drag coefficient and u1 is the upstream flow speed. The empirically determined drag coefficient is strongly influenced by blocking and its variation follows the trend CD = CD0(1 + CD0b/2w)2, where CD0 = 1.9 corresponds to the drag coefficient of a square cylinder in an unblocked turbulent flow. The RMS lift force is about 10-40% of the mean drag force and is generated by vortex shedding from the obstacle. When Fr1 = Fr1c(< 1), the flow is choked and adjusts by generating a hydraulic jump downstream of the obstacle. The drag force scales as FD ≃ CK bg(h2 1 − h2 2)/2, where experimentally, we find CK ≃ 1. The RMS lift force is significantly smaller than the mean drag force. A consistent model is developed to explain the transitional behaviour by using a semiempirical form of the drag force that combines form and hydrostatic components. The mean drag force scales as FD ≃ bg1/3u4/3 1 h4/3 1 , where is a function of b/w and Fr1. For a choked flow, = c is a function of blocking (b/w). For small blocking fractions c = CD0/2. In the choked flow regime, the largest contribution to the total drag force comes from the form drag component.

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