S.M. Richardson

Explicit numerical simulation of time-dependent viscoelastic flow problems by a finite element/finite volume method

Abstract A combination of the finite element method and the finite volume method has been developed for time-dependent viscoelastic flow problems. The governing system of equations is decoupled provided that a reasonably small time-increment is used, which is obtained from a Courant-Friedrichs-Lewy (CFL) condition taking into account a local vorticity wave speed. The momentum equation is solved explicitly with respect to time by a finite element method. The constitutive equation for an upper-convected Maxwell model is solved implicitly by finite volume methods. Case studies have been conducted for start-up of planar Poiseuille flow and planar four-to-one contraction flow for upper-convected Maxwell and Oldroyd-B fluids. Numerical results agree with analytical solutions for shock propagation in start-up of Poiseuille flow with no upper limit on the Weissenberg number We . In planar 4:1 contraction flow, the size of the comer vortex compares well with experimental measurements and other numerical predictions. An attempt to seek a critical value of We was stopped at We = 2 because of transient behaviour of the viscoelatic flow. There are new findings: vorticity separation from a re-entrant corner and a temporary lip vortex in transient flow induced by an instantaneous increase of We .

NUMERICAL STUDY OF THE BLOCKAGE EFFECTS ON VISCOUS FLOW PAST A CIRCULAR CYLINDER

In various numerical solutions of flow around bluff bodies the unbounded physical domain is replaced by a restricted computational one whose extent depends on the size of the computational grid network. The truncation of the solution domain in the cross-flow direction reduces the computer time required for the solution, but introduces numerical blockage effects which influence considerably the values of the various flow parameters. In the present paper the finite element solution of steady and unsteady flow around a circular cylinder at Re = 106 is presented for blockage ratios of 0.05, 0.15 and 0.25. A boundary condition was tested for which the streamfunction values at the outer boundaries were those of the irrotational solution around a circular cylinder. The size of the standing vortices decreases with the blockage ratio when the flow is steady, while the spacing of the vortices decreases in both directions with increasing blockage ratio when the wake becomes unsteady. The hydrodynamic forces on the cylinder and the Strouhal number are magnified as the blockage ratio increases. The application of the streamfunction values derived from the irrotational solution at the outer boundaries reduced blockage effects only at high blockage ratio.

Extended leveque solutions for flows of power law fluids in pipes and channels

Abstract A laminar flow with fully-developed velocity profile is assumed to exist in a circular pipe or rectangular channel with constant wall temperature. The Leveque solution is the zero-order term in a power series expansion of temperature for the high Graetz number (thermal entry) flow of a Newtonian fluid. The Leveque solution is extended here in the sense that analytical expressions for the zero-, first-and second-order terms in the power series expansion of temperature are derived for the flow of a power law fluid. The effect of heat generation by viscous dissipation is included.

Fouling in Crude Oil Preheat Trains: A Systematic Solution to an Old Problem

A major cause of refinery energy inefficiency is fouling in preheat trains. This has been a most challenging problem for decades, due to limited fundamental understanding of its causes, deposition mechanisms, deposit composition, and impacts on design/operations. Current heat exchanger design methodologies mostly just allow for fouling, rather than fundamentally preventing it. To address this problem in a systematic way, a large-scale interdisciplinary research project, CROF (crude oil fouling), brought together leading experts from the University of Bath, University of Cambridge, and Imperial College London and, through IHS ESDU, industry. The research, coordinated in eight subprojects blending theory, experiments, and modeling work, tackles fouling issues across all scales, from molecular to the process unit to the overall heat exchanger network, in an integrated way. To make the outcomes of the project relevant and transferable to industry, the research team is working closely with experts from many world leading oil companies. The systematic approach of the CROF project is presented. Individual subprojects are outlined, together with how they work together. Initial results are presented, indicating that a quantum progress can be achieved from such a fundamental, integrated approach. Some preliminary indications with respect to impact on industrial practice are discussed.

The stability of inelastic non-Newtonian fluids in Couette flow between concentric cylinders: a finite-element study

Abstract The onset of axisymmetric (toroidal) vortices in flow between concentric cylinders of infinite length, the inner of which is rotating, is analysed for inelastic non-Newtonian fluids using finite-element techniques. Results are presented for thin and wide annuli of finite gap width and compared with literature values where possible. The shear-thinning behaviour of the fluid is shown to have a significant effect on both the critical Taylor number and the critical wavenumber. The former indicates the speed of rotation at which vortices appear while the latter describes the axial spacing of the vortices in terms of the number of gap widths. The effect of radial distribution of effective viscosity, present in any annulus having a finite gap width, is included. This variation is responsible for the occurrence of a maximum value of critical aspect ratio and a minimum value of critical Taylor number with respect to departure from Newtonian rheology.

Blowdown of LPG Pipelines

In order to be able properly to assess the hazards associated with the rapid depressurization or blowdown of an oil, gas or condensate pipeline, there is a need to be able to predict fluid pressure, fluid and wall temperatures and effux rate, composition and phase. Several computer programs have been developed to do this, including our program BLOWDOWN. A comparison is made here of BLOWDOWN predictions with the measurements made during eight of the tests using LPG carried out by Shell and BP on the Isle of Grain in 1985. Four of the tests were for full-bore depressurizations and four for depressurizations with orifices at the open ends of the lines. The BLOWDOWN predictions are shown to be in at least adequate, and often good, agreement with the Isle of Grain measurements.

Flow instabilities in polymer blends under shear

Abstract The effect of shear flow on the miscibility behaviour of the model polymer blend polystyrene/poly(vinyl methyl ether) has been investigated in real time by two-dimensional light scattering and optical microscopy. Under certain shear and dynamic temperature conditions large ‘waves’ have been observed which are aligned either in the direction parallel to the applied shear flow or just off it. Two-dimensional light scattering patterns from samples under the same conditions show sharp streaks aligned in the direction perpendicular to the flow. The evidence presented in this work indicates that these ‘waves’ are unlikely to be elongated phase-separated domains; instead, they could be caused by fluid instabilities.

Rapid depressurization of pressure vessels

Abstract Experiments were conducted on the rapid depressurization of large pressure vessels. Measurements taken included the pressure, temperatures at a large number of positions both within the fluid phase(s) and on the wall of the vessel, and composition, all as a function of time during the blowdown process. The systems studied included subcritical and supercritical, condensing and non-condensing. From these experiments, an understanding of the physical processes involved during blowdown was evolved. This was incorporated into a mathematical model of blowdown, and implemented in a computer program. The model correctly predicts all the major phenomena observed in the experiments, as a function of time.

High-speed visualisation of nucleate boiling in vertical annular flow

Abstract High-speed video recording was carried out of annular flow of steam–water mixtures in an internally heated annulus test section. The heated section was 0.32 m long and made of stainless steel. The equivalent diameter of the channel was 12.9 mm. The results demonstrated the interaction between disturbance waves in the liquid film and the activity of nucleation sites.

Flows of variable-viscosity fluids in ducts with heated walls

Abstract An asymptotically valid analytical solution is presented of the equations governing high Graetz number, high Pearson number, low Nahme number flows of power-law fluids in ducts with heated walls. Thus the flows are developing and the imposed difference between the wall temperature and the entry temperature of the fluid is sufficiently large to cause significant viscosity variations, but temperature differences due to heat generation by viscous dissipation are not. Three different duct geometries are considered: channels, pipes and discs. Estimates are made of the pressure drop, maximum temperature and flow-average temperature rise for flows in each of the geometries.