Flow past a line of cylinders at intermediate gap ratio: Three-dimensionality influence

• Demonstrate influence of three dimensionality on hydrodynamics of flow past a line of cylinders. • The onset of three dimensionality within a line of cylinders occurs at Reynolds number of 175 for the intermediate gap ratio. • The critical Reynolds number of 175 appears to be independent of the total number of cylinders within the line. Three dimensionality of flow past a line of obstacles is responsible for mixing in many practical systems, which in turn, for example, enhances the nutrient uptake and sediment transport within aquatic vegetation, increases the yield of turbine farms and improve the efficiency of heat exchangers. However, the system was often modelled by two-dimensional (2-D) numerical simulations, which remove the three-dimensional (3-D) flow features. This paper presents, for the first time, results from 3-D direct numerical simulations that have been undertaken to examine the influence of three dimensionality on flow past a line of cylinders (obstacles) for Reynolds number up to 200 ( Re d = U ∞ d / υ , U ∞ is the velocity upstream of the cylinder, d is the cylinder diameter, and υ is the fluid viscosity) at a representative intermediate gap ratio ( G / d = 4.5, G is the centre-to-centre distance between adjacent cylinders). It is demonstrated that the flow past the line of cylinders displays very strong 3-D hydrodynamic features for Re d = 200, which leads to large distinctions in instantaneous and time-mean flow and force characteristics from 2-D results. With increasing Re d from 175 to 200, a transition is observed from ordered mode A structure forming throughout a line of cylinders to an intermittent regime characterised by alternating between a state with coexisting mode A and mode B structures and a state with disordered 3-D flow structures in the wakes of the first two cylinders followed downstream by chaotic 3-D flow structures within the line. The onset of three dimensionality for a line of cylinders occurs at Re d ≈ 175. This critical Reynolds number appears to be independent of the total number of cylinders within a line as mode A instability always initiates within the wake of the first cylinder. It is therefore recommended to use 3-D numerical simulations to investigate flow past a line of cylinders for Re d ≳ 175 at intermediate gap ratio.