## 1 Introduction  
With the rapid development of bridge construction technology, in order to ensure that the construction period does not affect existing traffic, incremental launching construction technology has been widely adopted. During the incremental launching construction of long-span bridges, the spacing between main piers is large. In order to ensure construction safety, temporary piers need to be set between the main piers. When water flows through the pier columns, flow separation, vortex shedding and other phenomena will occur, which will lead to an increase in the force on the temporary piers. When the water flow speed is high, the resulting water flow force may become an important component of force on the temporary piers. The fatigue failure of the temporary piers caused by the bypass flow may also lead to instability and collapse of the bridge. In previous studies, scholars conducted relevant research on the hydraulic characteristics of engineering structures such as cofferdam structures [1, 2], bridge substructures [3]and toothed-component mixed embankment overturning [4]. The difference in the three-dimensional wake between square and circular sections was examined by [PERSON] et al. [5]. In the study of flow around cylinders [6; 7; 8; 9], through the numerical simulation of tandem double cylinders, it is found that the spacing ratio has a significant effect on the shedding flow pattern, the lift drag coefficient and the Strouhal number. [PERSON] et al. [10] carried out a cylindrical flow tank experiment, and obtained the effect of the spacing ratio on the near wall tandem double cylinders. [PERSON] et al. [11] verified the existence of critical spacing. [PERSON] et al. [12] studied the flow characteristics of tandem double corrugated cylinders. For the study of parallel double cylinders, the influence of the spacing ratio on wake vortices, cylinder hydrodynamic coefficients, double cylinder interaction effects and flow field characteristics was analyzed via numerical and experimental research [13; 14; 15; 16; 17]. [PERSON] et al. [18] obtained the energy distribution of the wake field around two parallel cylinders. [PERSON] and [PERSON] [19] pointed out the frequency of the cylinder and the flow field. [PERSON] et al. [20] and [PERSON] et al. [21] analyzed the characteristics of three series columns. [PERSON] et al. [22] studied the critical spacing of three cylinders in series. [PERSON] et al. [23] studied the vortex-induced vibration of three consecutive cylinders with different spacing ratios. In the design of temporary pier structure, according to the \"_General Code for Design of Highway Bridges and Culverts_\" [24], the flow force of a single pile column can be simply calculated. However, there is no stipulated calculation method for the flow effect of series three-column temporary pier structures, and the code does not consider the lateral force caused by vortex shedding and the lifting effect on the structure under the action of water flow. The API [25] specification in the United States uses the Morison equation to calculate water flow force. The Morison equation itself is a semi-empirical formula, which is not convenient for direct application. The value of the parameters in the Morison equation directly determines the accuracy of the calculation, and there are some limitations in the current method of parameter selection. In summary, the current research on the flow around these cylinders has reference value for us to calculate the water flow force on temporary piers. However, in practical engineering, the value of water flow force is related to various parameters of the bridge (cross section type, column spacing, etc. ), so the water flow force acting on a specific structure is worth studying. However, there is currently very little research on the water flow effect on temporary piers; the existing design specifications do not fully consider the water flow force effect of temporary piers.