The investigation presented in this work concerned one-dimensional modelling of transient flow in an axial turbine stage. Because of the compound motion in the rotor-blade channels, the model of this flow path element was considered the most difficult to solve. The basic modelling approaches and the usefulness of the Euler and Lagrange methods for mathematical description are discussed. Relevant applied model based on the Lagrange method is described. Results of a successful numerical simulation of transient flow in a turbine stage are presented. This success opens the opportunity to build and solve one-dimensional models of dynamic flows in turbine cascades and entire flow paths.

A particle-level simulation technique has been developed for modelling fibre suspension flow in a converging channel of a papermachine headbox. The fibre model is represented by a chain of elements connected together. The model was verified by the simulation of rigid fibre dynamics in a simple shear flow. The period of rotation was found to be in a very good agreement with theory and reference data. The model was then employed to simulate fibre motion in a converging channel of a papermachine headbox. Fibre suspension motion was resolved using two-step procedure. Velocity field was calculated by means of a commercial CFD code ANSYS Fluent with RSM turbulence model applied and used as an input to the in-house code allowing to simulate fibre dynamics. Results of the calculations were used to construct the fibre orientation probability distribution (FOPD) which was found to be consistent with available experimental data.