Modelling the foil rolling process

A review of the main rolling models is conducted to assess their suitability for modelling the foil rolling process. Two such models are Fleck and Johnson's Hertzian model and Fleck, Johnson, Mear and Zhang's Influence Function model. Both of these models are approximated through the use of perturbation methods. Decrease in the computation time resulted when compared with the numerical solution. The Hertzian model was approximated using the ratio of the yield stress of the strip to the plane-strain Young's Modulus of the rolls as the small perturbation parameter. The Influence Function model approximation takes advantage of the solution of the well-known Aerofoil Integral Equation to gain an insight into how the choice of interior boundary points affects the stability of numerical solution of the model's equations. These approximations require less computation than their full models and, in the case of the Hertzian approximation, only introduces a small error in the predictions of roll force roll torque. Hence the Hertzian approximate method is suitable for on-line control. The predictions from the Influence Function approximation underestimates the predictions from the numerical results. Better approximation of the pressure in the plastic reduction regions is the main source of this error.

Study of industrially relevant boundary layer and axisymmetric flows, including swirl and turbulence

Micropolar and RNG-based modelling of industrially relevant boundary layer and recirculating swirling flows is described. Both models contain a number of adjustable parameters and auxiliary conditions that must be either modelled or experimentally determined, and the effects of varying these on the resulting flow solutions is quantified. To these ends, the behaviour of the micropolar model for self-similar flow over a surface that is both stretching and transpiring is explored in depth. The simplified governing equations permit both analytic and numerical approaches to be adopted, and a number of closed form solutions (both exact and approximate) are obtained using perturbation and order of magnitude analyses. Results are compared with the corresponding Newtonian flow solution in order to highlight the differences between the micropolar and classical models, and significant new insights into the behaviour of the micropolar model are revealed for this flow. The behaviour of the RNG-bas based models for swirling flow with vortex breakdown zones is explored in depth via computational modelling of two experimental data sets and an idealised breakdown flow configuration. Meticulous modeling of upstream auxillary conditions is required to correctly assess the behavior of the models studied in this work. The novel concept of using the results to infer the role of turbulence in the onset and topology of the breakdown zone is employed.