## 2 Introduction  
The impeller and the worm casing, as the two essential components of the centrifugal pump, can cause the uneven flow of the internal fluid due to the dynamic coupling between them, which may intensify the pressure pulsation in the pump, and this is often one of the factors that induce noise and vibration in the centrifugal pump; to alleviate this situation, it is urgent to investigate the spiral case structure of the centrifugal pump in depth [1]. [PERSON] et al. [2] targeted a centrifugal pump with a guide vane and conducted numerical simulations of the flow field of a centrifugal pump under stall conditions and found that when the guide vane outlet is aligned with the centrifugal pump worm housing tongue, the corresponding head is the highest and the pressure fluctuation is the smallest. [PERSON] et al. [3] investigated the effect of the number of vanes on the impeller-worm gear interaction and flow instability of a centrifugal pump. The results showed that the number of vanes affects performance parameters and local pressure fluctuations differently. [PERSON] [4] designed impellers using corrosive and non-corrosive materials to improve the reliability and efficiency of centrifugal pump impellers. [PERSON] et al. [5] studied a double-suction double worm gear five-stage centrifugal pump with different baffles installed at the double worm casing. The comparison revealed that installing baffles enhanced the head and efficiency of the pump. [PERSON] et al. [6] built an experimental rig including an actual impeller to observe the flow in the back sidewall gap by optical methods and to evaluate the axial thrust and torque, introducing a new flow pattern diagram. [PERSON] et al. [7] used a multi-objective genetic algorithm to find the optimal design point to optimize the input power of a centrifugal pump by varying the impeller vane exit angle. [PERSON] et al. [8] studied the effect of impeller blade hydraulic abrasive wear on the centrifugal pump head and the wear of centrifugal pump components under natural conditions and gave the dependence of wear on its characteristic dimensions and operating duration. [PERSON] et al. [9] validated CFD models of two pump impellers and performed a numerical simulation study of the variation of the slip coefficient during the dressing process, obtaining equations describing the relationship between the slip coefficient and the dressing rate of the studied pumps. In this paper, the design of a single-tongue worm casing structure was changed to a double-tongue worm casing structure by changing the tongue type, and the spacing value between the worm casing base circle and the tongue was used as the study object to investigate the effect of different spacing values on the performance of plastic centrifugal pumps. This paper takes a plastic centrifugal pump as the research object, creates the centrifugal pump computational domain model by using UG, completes the mesh division and irrelevance verification based on ICEM, determines the mesh quantity of the centrifugal pump models with five worm casing structures, and uses FLUENT to calculate the five worm casing pump models with constant, analyzes and compares the difference between single-tongue volute centrifugal pump and double-tongue volute centrifugal pump from four perspectives, such as static pressure, velocity, turbulent kinetic energy, and impeller radial force under different working conditions. The difference between the centrifugal pump with single-tongue volute and the centrifugal pump with double-tongue volute is analyzed and compared, and the difference between the centrifugal pumps with different pitch values of the volute base circle and the tongue is analyzed. It is concluded that the double-tongue volute structure can improve the static pressure gradient distribution and velocity gradient distribution of the middle section of the centrifugal pump, reduce the turbulent kinetic energy value at the tongue, and balance part of the radial force.