The high Reynolds number form of the k-ε model is extended and tested by application to fully developed pipe flow. It is established that the model is valid throughout the fully turbulent, semilaminar and laminar regions of the flow. Unlike many previously proposed forms of the k-ε model, the present form does not have to be used in conjunction with empirical wall function formulas and does not include additional terms in the k and ε equations. Comparison between predicted and measured dissipation rate in the important wall region is also possible.

No abstract

Large-eddy simulation is used to predict heat transfer in the separated and reattached flow regions downstream of a backward-facing step. Simulations were carried out at a Reynolds number of 28 000 (based on the step height and the upstream centreline velocity) with a channel expansion ratio of 1.25. The Prandtl number was 0.71. Two subgrid-scale models were tested, namely the dynamic eddy-viscosity, eddy-diffusivity model and the dynamic mixed model. Both models showed good overall agreement with available experimental data. The simulations indicated that the peak in heattransfer coefficient occurs slightly upstream of the mean reattachment location, in agreement with experimental data. The results of these simulations have been analysed to discover the mechanisms that cause this phenomenon. The peak in heat-transfer coefficient shows a direct correlation with the peak in wall shearstress fluctuations. It is conjectured that the peak in these fluctuations is caused by an impingement mechanism, in which large eddies, originating in the shear layer, impact the wall just upstream of the mean reattachment location. These eddies cause a 'downwash', which increases the local heat-transfer coefficient by bringing cold fluid from above the shear layer towards the wall.

Direct numerical simulation (DNS) is used to investigate turbulent Taylor–Couette (TC) flow. A simulation was run for a Reynolds number of 3200 in an apparatus with a radius ratio of η = 0.617 and an aspect ratio of 4.58, which assumed a vortex pair wavelength of 2.29. Results reported include the mean velocity, velocity fluctuation intensities, Reynolds stress budgets, and visualizations of the instantaneous velocity fluctuation field. Secondary near-wall vortex pairs are observed near to the cylinder in addition to the Taylor vortex (TV) motion. Weaker evidence of secondary vortices is found at the outer cylinder where a banded structure has been identified. The azimuthal wall shear stress component shows large peaks and valleys at stagnation points on the surface of both cylinders where flow from neighbouring vortices impacts on the respective wall. These stagnation points correspond to locations where the secondary vortices have been identified. The effect of the mean TV motion is reflected in the Reynolds stress budgets which are similar to but more complex than those of two-dimensional boundary layers. Visualization of the turbulent velocity fluctuations reveals near-wall streaks at the inner cylinder.

No abstract