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Measurements of power consumption in stirred vessel flows powered by a Rushton and an hyperboloid impeller were carried out. The fluids were aqueous solutions of tylose, CMC and xanthan gum at weight concentrations ranging from 0.1% to 0.6% and also included Newtonian fluids. For the Rushton turbine flows the addition of polymer increased the Newton number by about 13–20% at Reynolds numbers in the range 1,000–3,000, whereas with the hyperboloid impeller the Newton number decreased about 13%. This decrease was especially noticeable for the CMC solutions and was absent from the 0.2% tylose solution flow. Concentrated aqueous solutions of CMC (5.2%) and XG (3.6%) were also produced to determine the characteristic impeller parameter k for the hyperboloid, following the procedure of Metzner and Otto (1957) which was found to be 48 ±16.

The analytical solution for the steady-state flow in a pipe of viscoelastic fluids obeying the complete Phan-Thien-Tanner constitutive equation with a linear stress coefficient is derived. The results include the radial profiles of all relevant stresses, of the axial velocity and of the viscosity. The pipe flow is found to be unstable when the pressure gradient exceeds a critical value determined by a maximum shear rate at the wall. Expressions are also given for the viscometric viscosity and the first and second normal stress difference coefficients, as a function of the shear rate, in steady plane shear flow. For this case, and in line with similar results for the Johnson-Segalman model, the shear stress was found not to be a monotonically increasing function of the shear rate as strong shear-thinning sets in. A new finding is that the critical condition for the maximum shear stress in the simple-shear case is related to the condition for existence of steady-state solution in the pipe flow case. While this may seem evident “a priori” since the pipe flow is a viscometric flow, it is formally demonstrated.

Accurate solutions are obtained with the numerical method of Oliveira et al (1998) for the inertialess plane flow around a confined cylinder. This numerical procedure is based on the finite-volume method in non-orthogonal block-structured meshes with a collocated arrangement of the dependent variables, and makes use of a special interpolation practice to avoid stress-velocity decoupling. Two high-resolution schemes are implemented to represent the convective terms in the constitutive equations for the upper converted Maxwell and Oldroyd-B fluids, and the resulting predictions of the drag coefficient on the cylinder are shown to be as accurate as existing finite-element method predictions based on the very accurate h-p refinement technique.

In this work, aqueous suspensions of 1% and 1.5% by weight Laponite and a blend of 0.5%/ 0.07% Laponite/ CMC are investigated in terms of their rheology and their hydrodynamic behaviour in a pipe flow. The viscometric viscosity was measured for all fluids, but due to the fluid thixotropy a flow-equilibrium procedure was adopted. All fluids were viscoplastic and the measurement of the yield stress was carried out by direct and indirect methods. The yield stress values were of 0.93, 2.13 and 3.4 Pa for the 1% Laponite, 0.5/0.07% Laponite/CMC blend and 1.5% Laponite suspensions, respectively. The oscillatory tests shows that the 1% Laponite suspension is inelastic but the other two suspensions exhibit some elasticity. All solutions exhibited drag reduction with the difference between the total and shear-thinning drag reductions (DR – DRv) of the order of 10% to 20% for both pure laponite suspensions but increasing to 25 to 30% for the laponite-polymer blend. For the pure clay suspensions, and based also on evidence from the literature, it was speculated that DR – DRv, could be due to a strong decrease of the viscosity associated with a turbulence-induced destruction of the internal structure plus a second mechanism more akin to that found with drag reducing polymer solutions.

The temperature distribution and the heat transfer coefficient for forced convection in laminar channel flow with viscous dissipation are derived for the simplified Phan-Thien–Tanner fluid with a linear stress coefficient. Fully-developed thermal and hydrodynamic conditions are assumed with a constant wall heat flux imposed on both walls. As a simplifying assumption the effect of temperature variations on the material parameters is neglected. The results show that, in all circumstances, ie for wall heating and cooling and regardless of the magnitude of viscous dissipation, an increase of fluid elasticity and/or an increase of ε results in enhanced heat transfer. As a beneficial consequence the range of temperatures inside the duct is reduced. There is also a coupling effect of viscous dissipation and fluid elasticity: heat transfer enhancement by fluid elasticity is stronger in the presence of a more intense viscous dissipation. For positive wall heat fluxes, ie wall cooling, whenever the Brinkman number exceeds a threshold value, the viscous dissipation overcomes the wall cooling effect and the fluid heats up longitudinally. Fluid elasticity delays this critical Brinkman number to higher values.

A new general finite-volume method based on an efficient collocated mesh arrangement, with the added advantage of indirect addressing, has been applied to predict the flow of UCM fluids in a 4:1 sudden planar contraction. First and second order differencing schemes were used, and the Deborah number ranged from 0 to 10 for a Reynolds number of 0.01. The predicted flow patterns showed all the flow features seen in flow visualisation and in recent numerical simulations of contraction flows, namely the corner Moffat vortex, the lip vortex, the fingering and merging of the two vortex types and single vortex growth with Deborah number. The presence of a lip vortex is detected at a Deborah number of 2 and the observations of those flow features requires very fine meshes in the vicinity of the contraction plane.

This paper reports the development of a methodology for calculating the flow of upper convected Maxwell fluids using a finite-volume based method. The algorithm was developed for a general non-orthogonal collocated grid, and the pressure-velocity-stress coupling was addressed by a special interpolation technique inspired by Rhie and Chow’s (1982) method. The differencing schemes are second order accurate and calculations were carried on for a two-dimensional entry channel flow in order to assess the performance of the method. The interpolation technique specially devised for the stresses was found to work well and the results of the simulation compared favourably with those of the literature (Eggleton et al, 1996). Convergence was attained for Deborah and Reynolds numbers identical to those reported in the literature for a similar flow problem using other numerical methods. Viscoelasticity was responsible for the development of very intense normal stresses, which were tractive in the wall region. As a consequence the viscoelastic fluid was forced to move away from the wall, in a more intense way than with Newtonian fluids, thus reducing locally the shear rates and the role of viscosity in redeveloping the flow.