# UFR 3-11 Evaluation

# Pipe expansion (with heat transfer)

Underlying Flow Regime 3-11 © copyright ERCOFTAC 2004

# Evaluation

## Comparison of CFD calculations with Experiments

As noted in Section 2, comparisons of velocity and turbulence results are not given in this document as the findings will be very similar to those for the 2D backward-facing step (UFR 3-15). Instead, attention is directed at the heat transfer results. Comparisons of the results of the analyses by Craft et al. (1999) with the experiments of Yap (1987) are shown in Figures 2 to 4. These show the Nusselt number profiles along the pipe wall downstream of the expansion. The Nusselt number is plotted as the ratio Nu/Nu_{DB}, where Nu_{DB} is the Nusselt number calculated using the standard Dittus-Boelter correlation, and distances from the step are plotted as the ratio of the distance to the step height (X/H).

As a baseline, in Figure 2 the Nusselt number variations are shown for a Reynolds number of 40000 for linear and non-linear eddy viscosity models and with the correction proposed by Yap (1987). It can be seen that in the region of flow separation, both models over-estimate wall heat transfer.

In Figure 3, results using the standard algebraic Yap correction are compared with those obtained using a differential form of the correction, and a modified differential form in which the need to prescribe the wall distance is removed.

As shown in Figure 3, the modified differential Yap correction improves the prediction of heat transfer in the recovery region, downstream of the reattachment point, using both the linear and non-linear eddy viscosity models. However, the non-linear model still somewhat over-predicts the peak heat transfer levels.

Some results for different Reynolds numbers with the linear and non-linear eddy viscosity models are presented in Figure 4.

The experiments, in common with those of Baughn et al. (1984) indicate that heat transfer relative to that for fully-developed pipe flow should be enhanced as the Reynolds number is reduced. From Figure 4, this is not seen to be the case either with the non-linear eddy viscosity model with the modified differential correction term, or with the linear model with the standard Yap correction. It was concluded by Craft et al. that to address this, low Reynolds number models should not be dependent on length-scale correction terms, and should in particular avoid using the wall distance.

Some results from the calculations of Vieser et al. (2002) and Esch et al. (2003) in comparison with the measurements of Baughn et al. (1984) are shown in Figure 5. The normalised Nusselt number and distance from the expansion are the same as used by Craft et al. (1999). In this figure, wall heat transfer results from the SST model are compared with those produced by k-ε and k-ω models. The latter overpredict the peak Nusselt number by about 20%, whereas the SST results are within 5% of the measured values but show a slightly broader distribution near the maximum Nusselt number.

Figure 5: Comparison of Solutions for the Non-Dimensional Nusselt Number Along the Outer Pipe Diameter (From Vieser et al. (2002), with permission from ANSYS-CFX)

Another comparison of the results using different near-wall models is provided in Figure 6. Here, results from the SST and k-ε models are compared with those from a two-layer turbulence model in which the ε equation is only solved in the outer part of the boundary layer, with the inner portion and viscous sub-layer being treated by a mixing length formulation. It can be seen that this results in a significant underestimation of the heat transfer.

Figure 6: Comparison of the Two-Layer, SST and k-ε Model for the Non-Dimensional Nusselt Number Distribution Along the Outer Pipe Diameter (From Vieser et al. (2002), with permission from ANSYS-CFX)

© copyright ERCOFTAC 2004

Contributors: Jeremy Noyce - Magnox Electric