Viscous flow past an upstream inline forced oscillating circular cylinder with a stationary cylinder downstream at Reynolds number of 100 is investigated using a CIP model. The model is established in a Cartesian coordinate system using a highorder difference method to discretise the NavierStokes equations. The fluidstructure interaction is treated as a multiphase flow with fluid and solid phases solved simultaneously. An immersed boundary method is used to deal with the fluidbody coupling. The CFD model is firstly applied to the computation of flow past a fixed circular cylinder for its validation; then flow over two stationary tandem cylinders is investigated and good agreements are obtained comparing with existing ones. Computations are then performed with flow past two tandem cylinders with an upstream inline oscillating cylinder with a small spacing
Flow over multiple bluff bodies is one of the classical issues in fluid mechanics. It is of great importance in engineering applications, such as heat exchangers, adjacent tall buildings, and piles of offshore platforms. The interaction between the multiple bodies and the wake is much more complicated than that of flow past a single body.
The tandem arrangement is one of the simplest configurations of the multiple bluff bodies. Extensive experimental and numerical studies have been reported about flow past two stationary tandem circular cylinders. Zdravkovich (1977) [
The study concerning oscillating circular cylinders in tandem arrangement is relatively rare. Direct numerical simulation was carried out by Li et al. (1992) [
One of the greatest challenges in the simulation of flow around oscillating cylinders is to deal with moving solid boundaries in complex geometries, especially for large amplitude body motions. The ALE (Arbitrary LagrangianEulerian) method has been used in some studies. This means that the domain should be remeshed at every time interval; it is timeconsuming. Hence, a numerical method should be proposed without aforementioned restrictions. In this paper, an Immersed Boundary Method [
To date, few studies considering the flow past two tandem circular cylinders with the upstream one forced to oscillate streamwise to the flow could be found. The objective of the present study is to extend the CIPbased method for this gap. In this paper, the Reynolds number remains at 100, oscillating amplitude is
The basic equations governing the incompressible fluid flow are the mass conservation equation and the NavierStokes momentum equations written as
The numerical model considers the fluidbody interaction as a multiphase problem that includes fluid and structure. A fixed Cartesian grid that covers the whole computation domain is used. A volume function (or color function)
Following Zhao and Hu (2012) [
To model the body motions, the fluidstructure interaction is coupled by using the Fractional Area Volume Obstacle Representation (FAVOR) method. The FAVOR was shown to be one of the most efficient methods to treat the immersed solid bodies. The effect of a moving solid body on the flow is considered by imposing the velocity field of the solid body into the flow at the solid edge. The following equation is introduced to update the local information of the fluid domain covered by the body:
Convergence study has first been performed for flow past a stationary circular cylinder at low Reynolds number (
Comparison of mean drag coefficient (
Data  Min size of mesh  Number of meshes 



Mesh 1 
0.01 
307800  1.38  0.166 
Mesh 2  0.02 
92800  1.34  0.166 
Mesh 3  0.04 
32175  1.28  0.166 
Exp. (1959) [ 
1.26  
Exp. (1988) [ 
0.164  
Herfjord (1996) [ 
1.36  0.168  
Calhoun (2002) [ 
1.33  0.175  
Linnick and Fasel (2005) [ 
1.34  0.166  
Berthelsen and Faltinsen (2008) [ 
1.38  0.169  
Rajani et al. (2009) [ 
1.34  0.157 
Generally, the flow patterns of flow past two stationary tandem cylinders can be divided into two regimes by the critical spacing
In this section, flow past two stationary cylinders in tandem at
Sketch of the computational domain for flow past two tandem circular cylinders.
The computational mesh for flow past two tandem circular cylinders and local mesh near the cylinders with
Figure
Variation of coefficients with spacing ratio
Vorticity contours of flow past two stationary tandem circular cylinders: (a)
In this section, flow past a streamwise oscillating circular cylinder with a stationary cylinder downstream in tandem with the spacing ratio
Figure
Spectrum analysis of the lift force for flow around upstream oscillating cylinder and downstream fixed cylinder: (a) upstream cylinder; (b) downstream cylinder.
Vortex contours of flow around upstream oscillating cylinder and downstream fixed cylinder: (a)
Vortex contours in one period: (a)
Phase portrait plot at
A CIPZJU model is utilized to simulate the viscous flow past one and two circular cylinders in this paper. The model is established in a Cartesian coordinate system, using a CIP method as the base flow solver to discretise the NS equations. The fluidstructure interaction is treated as a multiphase flow with fluid and solid phases solved simultaneously. An Immersed Boundary Method was used to deal with the fluidbody coupling.
Flow past a stationary circular cylinder at
Flow around an upstream inline oscillating cylinder and a stationary cylinder in tandem with spacing ratio
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by National Natural Science Foundation of China (51209184 and 51479175), Open Research Foundation of State Key Laboratory of HydrologyWater Resources and Hydraulic Engineering (2013490211), Specialized Research Fund for the Doctoral Program of Higher Education (20120101120150), and Key Laboratory of WaterSediment Sciences and Water Disaster Prevention of Hunan Province (Grant no. 2013SS03).