Improved near-wall RANS modelling

Researcher: Flavien Billard

Supervisor(s): Prof. D. Laurence
Sponsor: School of MACE (University of Manchester), British Energy
Start Date: September 2006 End Date: February 2011
Keywords: RANS modelling, Elliptic Blending

Overall Research Aim

The work aims at developing a robust near-wall Reynolds Averaged Navier Stokes (RANS) model using the elliptic blending method, which proved to be a robust and accurate way of modelling non local cinematic effects induced by the presence of a wall. Work was also undertaken to improve the representation of the turbulent length-scale determining equation. A substantial proportion of work was devoted to calibration of the new model on a wide set of flows, ranging from 2D academic pressure induced separating flows to buoyancy driven boundary layers.

Research Progress

Developments of the proposed model : BL-$\overline{v^2}/k$ model

A new but well validated and truly robust version of an elliptic-blending low-Reynolds-number eddy-viscosity RANS model is derived starting from the $\overline{v^2}-f$ model (Durbin (1991)), whose original aim was to integrate higher-order RANS developments into a simpler formulation. However, early $\overline{v^2}-f$ proposals suffered from numerical stiffness, which made them impractical for everyday industrial simulations. The present work proposes to revive Durbins' original formulation and integrate experience gained over the past 20 years by $\overline{v^2}-f$ modellers. In the current proposal, the elliptic blending approach keeps the main appealing feature of the original elliptic operator. It distinguishes near-wall and low-Reynolds number effects, the former being modelled by the elliptic nature of the operator (which makes the flow feel the wall-blocking effect far beyond the mere molecular viscosity affected region). Following the previous developments done at Manchester ($\varphi-\overline{f}$ model of Uribe (2006)), wall damping is accounted for by the resolved parameter $\varphi=\overline{v^2}/k$ representing the near-wall anisotropy and the subsequent modifications are blended with a high Reynolds number model.

Rationale and validation of the model

The lack of versatility of $\overline{v^2}-f$ models in general (being tuned to reproduce at best either low or high Reynolds number flows) was the motivation of the proposed improvements. The new BL-$\overline{v^2}/k$ model integrates two new terms in the $\varepsilon$ equation. The first one accounts for dissipation rate anisotropy in the buffer layer following the idea of Launder and Sharma (1974) and is based on second derivative of the mean velocity. The second one, active only at the edge of a boundary layer, offers a better representation of turbulent transport and cures the well known turbulence overprediction returned by the standard $k-\varepsilon$ model in this region. The final form of the model has been validated in a wide range of academic flows and stands as a sounder and more robust alternative to the version adopted by commercial package developers (namely the Lien and Kalitzin version, LIE01). Comparison of the models on a flow through a constricted channel and a plane asymmetric diffuser is shown, figure 1.
Fig 1: Prediction of the skin friction coefficient in a constricted channel (left) and a plane diffuser (right).

An illustration: buoyancy induced relaminarisation

In the case of a heated vertical pipe, where the flow is driven upward, the aiding buoyancy force leads to the steepest streamwise velocity gradients being shifted towards the walls, which can yield an attenuation of turbulence and a heat transfer impairment. It is clear that models in which near-wall turbulence damping is based on the wall distance $y$, such as the $k-\omega$ SST formulation, would have little chance of predicting this impairment. Whereas all $\overline{v^2}-f$ models yield more satisfactory results, the case remains numerically challenging because of the small level of turbulence encountered. The improved robustness of the BL-$\overline{v^2}/k$ model proved to be decisive in this case (figure 2).

Fig 2: Nusselt number as a function of the buoyancy parameter in an upward flow through a vertical heated pipe for different flow regimes

Last Modification: r27 - 2011-02-02 - 14:53:06 - DominiqueLaurence

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Topic revision: r27 - 2011-02-02 - 14:53:06 - DominiqueLaurence

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