###### Abstract  
One of the most common systems in engineering problems is the multi-column system in the form of an equilateral-triangular arrangement. This study used three-dimensional numerical simulations to investigate the flow around three cylinders in this arrangement at the super-critical Reynolds number \(Re=3\times 10^{6}\), concentrating on the influence on the spacing ratio (\(L/D\)) among cylinders. The instantaneous vortex structures, Strouhal numbers, fluid force coefficients, and pressure distributions are analyzed thoroughly. The present study demonstrated that fluid dynamics is sensitive to \(L/D\), by which five different flow patterns are classified, namely single bluff body flow (\(L/D\leq 1.1\)), deflected gap flow (\(1.2\leq L/D\leq 1.4\)), anti-phase flow (\(1.5\leq L/D\leq 2.3\)), in-phase flow (\(2.5\leq L/D<3.5\)), and co-shedding flow (\(L/D\geq 3.5\)). Critical bounds are identified by significant transitions in the flow structure, discontinuous drop and jump of \(St\), and force coefficients. flow interference; vortex interaction; vortex dynamics; improved delayed-detached eddy simulation (DDES) 20  
body. When 1.1-1.2 \(\leq L/D\leq\) 2-2.2, a biased flow pattern shows up. When \(L/D\geq\) 2-2.2, cylinders behave more independent and show parallel vortex streets. More details of the wake flow of two cylinders at variable \(Re\) and \(L/D\) are summarized by [PERSON] [7]. For three cylinders in tandem and side-by-side layout, the flow patterns, force coefficients, and pressure distributions have been investigated [8; 9; 10]. More complicated than a tandem or side-by-side layout is the flow past through three cylinders arranged in a triangle. [PERSON] [11] measured the drag and lift force coefficients of one of the three cylinders in triangular arrangement at \(Re=3\times 10^{6}\) and \(1.25\leq L/D\leq 5\) with various incidence angles (\(\alpha\)). Only one cylinder was measured, so the interference between the cylinders is not clear. The vortex-shedding-frequency data of three cylinders in an equilateral triangle configuration at \(Re=2.1\times 103\) and \(3.5\times 103\) at various incidence angles and \(L/D\) were obtained by [PERSON] et al. [12] using a dye-injection approach to visualize the flow. Bi-stable flow characteristics were observed at \(L/D<2.29\), \(\alpha=0^{\circ}\) and they depend on the starting conditions. The static pressures of each cylinder were individually measured by [PERSON] et al. [13]. The results show that when the spacing ratio is small, the impacts of the flow interference are obvious. By conducting wind tunnel studies, [PERSON] et al. [14] categorized the flow pattern of the three cylinders arranged in an equilateral triangle. It shows that the incidence angle has a huge influence on the pressure distribution on each cylinder and the flow patterns. Four basic levels of interference (small, transition, medium, large spacing) are identified according to the spacing ratio. Furthermore, according to the various incidence angles, the interference type can be identified as proximity effect, shear layer reattachment effect, and wake effect. [PERSON] et al. [15] carried out wind tunnel experiments with five subcritical Reynolds numbers at the incidence angle \(0^{\circ}\) (one cylinder in the upstream and others in the downstream). They showed that as \(L/D\) increases, the mean drag coefficient of all cylinders almost increases. When \(L/D=1.5\) and 2, the downstream cylinders' drag coefficients reach their lowest value since there is no vortex shedding from them. [PERSON] et al. [16] investigated the influence of the incidence angle (\(0^{\circ}\)-\(60^{\circ}\)) when the \(L/D=1.35\) and \(Re=2100\) by PIV and laser Doppler velocimetry. They found that large-scale vortexes shed at about \(5D\) downstream from the cylinders for all incidence angles. [PERSON] et al. [17] investigated the effects of \(L/D\) (2.8-5.2) and incidence angle (\(0^{\circ}\)-\(30^{\circ}\)) on the flow around an equilateral-triangular-arranged three-cylinder cluster at \(Re=8000\).