Numerical modelling of lubricated foil rolling

A model of lubricated cold strip rolling (1, 2) is extended to the thin foil regime. The model considers the evolution of asperity geometry and lubricant pressure through the bite, treating the strip using a conventional slab model. The elastic deflections of the rolls are coupled into the problem using an elastic finite element model. Friction between the roll and the asperities on the strip is modelled using the Coulomb and Tresca friction factor approaches. The shear stress in the Coulomb friction model is limited to the shear yield stress of the strip. A novel modification to these standard friction laws is used to mimic slipping friction in the reduction regions and sticking friction in a central neutral zone. The model is able to reproduce the sticking and slipping zones predicted by Fleck et al. (3). The variation of rolling load, lubricant film thickness and asperity contact area with rolling speed is examined, for conditions typical of rolling aluminium foil from a thickness of 50 to 25 μm. T he contact area and hence friction rises as the speed drops, leading to a large increase in rolling load. This increase is considerably more marked using Coulomb friction as compared with the friction factor approach. Forward slip increases markedly as the speed falls and a significant sticking region develops.

Influence of the state of the inlet endwall boundary layer on the interaction between pressure surface separation and endwall flows

This paper describes the effect of the state of the inlet boundary layer (laminar or turbulent) on the structure of the endwall flow on two different profiles of low-pressure (LP) turbine blades (solid thin and hollow thick). At present the state of the endwall boundary layer at the inlet of a real LP turbine is not known. The intention of this paper is to show that, for different designs of LP turbine, the state of the inlet boundary layer affects the performance of the blade in very different ways. The testing was completed at low speed in a linear cascade using area traversing, flow visualization and static pressure measurements. The paper shows that, for a laminar inlet boundary layer, the two profiles have a similar loss distribution and structure of endwall flow. However, for a turbulent inlet boundary layer the two profiles are shown to differ significantly in both the total loss and endwall flow structure. The pressure side separation bubble on the solid thin profile is shown to interact with the passage vortex, causing a higher endwall loss than that measured on the hollow thick profile.