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

Abstract

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, Fr1 (depth h1), which sets the downstream Froude number, Fr2 (depth h2). When Fr1 < 1), the flow is choked and adjusts by generating a hydraulic jump downstream of the obstacle. The drag force scales as F¯D ≃ CKρbg(h21 - h22)/2, where experimentally we find CK ≃ 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 FD¯ ≃ λρbg1/3u4/31 h4/31, where λ is a function of b/w and Fr1. For a choked flow, λ=λc is a function of blocking (b/w). For small blocking fractions, λc = CD0/2. In the choked flow regime, the largest contribution to the total drag force comes from the form-drag component.