## 1 Introduction  
Sewers as indispensable infrastructures in urban development, are located in all corners of the city, which undertake the sewage conveyance, water pollution control, flood control, storm drainage, and other significant functions. After the heavy rainfall flood, the sewers may be full at one place due to the large increase of flow. When the sewers break or collapse somewhere, it may cause pollutants to enter the sewers, and then spread in sewers. The mixing, migration, and degradation of pollutants in sewers are significant reasons for pipeline corrosion [1] and the expansion of the pollution scope [2; 3], resulting in point source pollution. The study of turbulent mixing characteristics in sewers is critical for inspecting the pipeline damage and identifying sources of pollution, including the determination of a single source of pollution for a water supply network. Turbulent mixing in a T-junction system [4] is similar to the jet in crossflow (JIC) [5; 6], which has received widespread attention because of its importance in many different engineering applications [7; 8], including mixing fluid flows with different species, temperatures, velocities, densities, or concentrations. Simultaneously, the examination of turbulent mixing characteristics in a T-junction system can provide important significances for that in the sewers. Earlier investigations in T-junctions had been carried out by [PERSON] et al. [9], who experimentally investigated T-junctions near a rectangular duct entry with various angles. The reasonable agreement between laser Doppler velocimetry measurements and numerical results with the numerical results under predicting was obtained. The fluid mixing in T-junction configurations experimentally and numerically was presented by [PERSON] et al. [10]. They concluded the pipe length required to achieve 95% mixing in a T-junction was a function of the velocity ratio (Vr) of the branch pipe flow to the main pipe. The optimized mixing in such pipelines to the mixing in pipelines with a T-junction was conducted by [PERSON] [11] through numerical and experimental investigations. These investigations showed the angle of jet had a significant effect on mixing length and mixing depended on the flow patterns created by the jet impingement. The thermal mixing and reverse flow characteristics in a T-junction was investigated by [PERSON] et al. [12] to study the effects of different flow rates in the branch/main pipe qualitatively. They reported that the thermal mixing for a T-junction could be enhanced as the flow rate in the branch increases or the flow rate in the main pipe decreases, as clearly revealed in the comparison results of different flow rate ratios. A small-scaled test facility to investigate the mixing effects in a T-junction with two streams at different temperatures and flow rates in the main and branch pipes preliminarily was devised by [PERSON] et al. [13], who found that a lower main pipe flow rate led to a better mixing effect with a constant branch pipe flow rate. The T-junction with a 90\({}^{\circ}\) bend upstream mixing phenomenon experimentally was reviewed by [PERSON] et al. [14]. Results showed that a 90\({}^{\circ}\) bend had a strong effect on the fluid mixing mechanism and the momentum ratio between the main velocity and the branch velocity of the T-junction, which could be an important parameter for the classification of the fluid mixing mechanism. The thermal mixing of turbulent flow in a T-junction with hot fluid flowing in the main pipe and cold fluid in the branch by three-dimensional numerical simulations was investigated by [PERSON] et al. [15]. They concluded that the injection angles and flow rate ratios had significant influence on the reverse and secondary flow on the mixing. In the face of the advances achieved until now in the understanding of flow in T-junctions, including the study of the flow rate of a branch/main pipe and the incident angle of the branch, several questions remain open.