Numerical Methods and Boundary Conditions

The computational grid of the compressor is divided to 33 blocks and the number of the computational cells is 618,496. The surface grid of the com­pressor is shown in Fig. 3. Every second grid line is visible. Tip clearance is not modeled. The topology of the grid has been made in such way that the all blocks except the ones in the volute and exit cone contain clustering near to the walls (Fig. 4).

The infbw boundary conditions for the numerical simulation are given at beginning of the inlet pipe, which is located 1.05 meters above the impeller leading edge. Total enthalpy, mass flow and flow direction at the inlet are defined. The pressure is extrapolated from the fbw field and the density is iterated with the help of the total enthalpy and the pressure. The velocity dis­tribution is uniform and the intensity of the turbulence and the dimensionless turbulent viscosity are defined at the inlet plane. The distributions of the veloc­ity and the quantities of the turbulence start to develop before the leading edge of the impeller since the inlet pipe is long. The outflow boundary conditions are given at the end of the outlet pipe 1.60 meters downstream of the end of the volute. The static pressure is given at the outlet to define the pressure level of the solution.

The numerical solver Finfb has been used to carry out the simulations. Finfb is a Navier-Stokes solver developed at Helsinki University of Technol­ogy. The Reynolds averaged Navier-Stokes equations are solved by a Finite – Volume method. The code utilizes Roe’s Flux-difference splitting, and con­vergence is accelerated by a multigrid method. More details can be found in Refs. [7] and [8]. The parallelization of the code is based on the Message Passing Interface (MPI) standard [9]. The computational domain is divided into groups of blocks and the boundaries between the groups are updated us­ing MPI. The number of cells in the groups should be equal in order to get the

best benefit from the parallelization. On the other hand, the different groups can contain different amounts of block, which makes it easy to assign the same number of grid cells to each processor to ensure an equal division of the com­putational workload. [10]. Time-accurate simulation is based on a three-level fully implicit second order time-integration method. This method is described in [11]. The inner iterations are made at every time step. The number of the inner iterations is chosen to get convergence for each time step. In our case, 25 seems to be enough. In this case, the time step is 1^s, which has been found to be small enough to get a solution. The rotor of the compressor is rotated 0.13 ° at every time step. The connection between the stationary and the rotating part of the mesh is handled by using a sliding mesh technique. The grid lines be­tween the impeller blocks and the stator block are discontinuous, thus a mass conserving interpolation is made at every time step.