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32 4. METHODS √ ∆ = min(κy, 3 Cell volume) (4.12) y is defined as the distance form the wall to the adjacent cell centre and κ is a constant. 4.3.2. Wheel modelling In the turbine, the turbine wheel is rotating in relative to the stationary turbine house. This can be modelled by two different approaches: • The Rotating Reference Frame technique (RRF) • Moving mesh technique. In the RRF concept one uses a coordinate system that rotates with the turbine. Therefore, the Coriolis term is added to the Navier-Stokes equation. Since the housing of the turbine is not rotating, the computational domain con- tains also regions which are described in non-rotating coordinates. Hence the Coriolis terms are activated only in the region where rotation of the geometry occurs. In the moving mesh technique, also called the Sliding Mesh (SM) tech- nique, one part of the mesh is moving or rotating in relative to the stationary part. At the interface between the moving and the stationary part, the moving mesh is made to slide past the stationary part. At the sliding interface, the connectivity for cells on either side of the interface change at each time step. This is implemented in a way that there are no restrictions on the relative po- sition of the cell faces on either side of the sliding interface, i.e. cell faces across the sliding interface do not to have a one-to-one correspondence. In order to preserve flux of mass, momentum and energy across the sliding interface and to avoid introducing non-physical perturbations, the interpolation over the slid- ing interface must be done in an appropriate way. The rotational speed of the wheel and cell sizes at the sliding interface will also determine the time step; the time step must be small enough to ensure that cells on both sides of the sliding interface do not pass each other completely during one time step. 4.4. Numerical accuracy and uncertainty All numerical techniques are based on discrete approximations of the dependent variables and thereby a discrete approximation to the governing equations. The discretization steps in both the time and space introduce errors. The errors can be divided in four groups: • Errors due to modelling errors in the governing equations. • Discretization errors, due to time and space discretization and the used discretised representation of the dependent variables.PDF Image | Numerical computations of the unsteady flow in a radial turbine
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