This thesis is concerned with the numerical prediction of the flow of liquids that display both elastic and viscous properties. Such liquids are termed visco-elastic liquids and are of considerable industrial importance. The properties of liquids are defined through a set of constitutive equations, which define a relationship between the rate of strain and extra-stress tensors. The derivation of constitutive equations that predict visco-elastic properties and are valid under all conditions of flow is a complex task that usually results in a relationship in the form of a differential or integral equation. To obtain a solution for the flow field the constitutive equation must be solved in conjunction with the equations of momentum and continuity. Because of the complexity of the equations and the flow geometries considered in this thesis a numerical method must be used. To represent the fluid an upper convected Maxwell model is taken as the constitutive relation. For the numerical method the finite element method is used with velocities, pressure, and extra-stresses as dependant variables. When using the finite element method care must be taken in the choice of shape functions for each dependant variable. An analysis is given that shows certain combinations of shape functions can give rise to a non-unique solution. The 'online' measurement of the elastic properties of a fluid is of industrial importance. The hole pressure technique for the 'on-line' measurement of the first normal stress difference is modelled. The effects of elasticity and inertia on the theoretical basis for the instrument is investigated. Flow through a 'U' shaped vessel with stirrers in the bottom corners of the vessel is modelled. The effect of elasticity and inertia on the flow field for different strengths of the stirring action is investigated.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:638661 |
| Date | January 1981 |
| Creators | Richards, G. D. |
| Publisher | Swansea University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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