# Roots blower with three-lobed

## Roots blower with three-lobed

This paper studies a roots blower with three-lobed rotors mounted on parallel shafts that rotate in opposite directions to transfer air as working fluid. The physical model is shown in Figure 1. The suction and discharge pipes connect to the inlet and outlet domains respectively. The air passes into the roots blower through the inlet and fills into the suction chamber formed by the casing and rotor. The female rotor rotates clockwise, and the reference crank angle when the female rotor is vertical is defined as 0°. Three types of gaps are recognised in the roots blower, namely the tip gap, the interlobe gap and the axial gap between the side of the lobes and the casing. The main dimensions are shown in Table 1.

Stationary fluid domains of the inlet and outlet chambers can be extracted from a CAD model of the roots blower. For the transient simulation, rotor domains move and deform with the rotation of rotors. Figure 2 shows the fluid domain and the generated grids of rotors and ports. The moving rotor grids (left in Figure 2) were generated by in-house grid generation software SCORG. The rotor to casing non-conformal mesh was generated using algebraic transfinite interpolation and numerical smoothing. This preserves the shape of the tip and side steps on the lobes (see Figure 1). To check the grid independence, four levels of rotor grids were generated. Different grid levels used for calculations are shown in Table 2. The angular divisions for one chamber are 180, which means that there are 180 angular positions for single interlobe rotation. For the two-lobe Roots blower, the gird files were generated with the angle interval of 1°. And the time step was calculated out u sing the following equation.

where Z is the number of lobes, and n is the rotation speed (rpm). Inversely, the angular divisions can be calculated out when the simulation time step is given. As shown in the right of Figure 2, the stationary grids consist of inlet grids, outlet girds and axial-gap grids which have six layers of grids in each axial gap. The lengths of suction pipe and discharge pipe are three and nine times of the pipe diameter. Hexahedral grids with 889405 nodes for the stationary grids were generated in ANSYS- Mesh and used in all cases. The rotor grids and the stationary grids are combined and connected with interfaces. 