# UFR 3-07 Evaluation

# Natural and mixed convection boundary layers on vertical heated walls (B)

Underlying Flow Regime 3-07 © copyright ERCOFTAC 2004

# Evaluation

## Comparison of CFD calculations with Experiments

The predictions of heat transfer behaviour for cases in which (a) the heat flux distribution applied is irregular and (b) uniform are virtually the same (Li, 1994). Therefore most calculations have been performed with a uniform heat flux, using the mean experimental value rather than the actual slightly non-uniform distribution.

**Downward Flow**

This case is buoyancy-opposed. Simulations with the Launder-Sharma two-equation k-ε turbulence model have been undertaken to cover the range of flows from forced convection to strongly buoyancy-influenced conditions for the heated downward flow of air (Li, 1994). The predicted Nusselt number development is in particularly good agreement with the experimental data for the cases of Re<9000, when the buoyancy effects are strong. There are discrepancies between the predictions and the experimental data for the cases with relatively weak buoyancy influences but significant property variation. These are probably due to the over-response of the model to the laminarisation caused by the property variation. In these cases the model under-predicts the Nusselt number by up to 20% compared with the experimental data.

Generally, the Nusselt number for air flow in the tube decreases along the heated section, which can be explained by the decreasing turbulent viscosity with the increase of x/D. In downward flow the buoyancy forces generally increase the turbulence level, and hence cause enhancement of heat transfer.

Gerasimov (2002) describes several of the downward flow cases obtained by Li (1994), using the analytic wall function. Figure 1 shows results for a case in which the Launder-Sharma model under-predicts heat transfer by ~20% (Re=14815). The analytic wall function performs slightly better than the low-Reynolds number model solution down to the wall for this case.

Figure 2 shows another case (Re=7044), which is one for which Li (1994) shows a good prediction using the Launder-Sharma model. Results from the analytic wall function are just as good. Figure 3 shows results from cases in which the Reynolds number is low, and enhancement of heat transfer, compared with forced flow, is significant. The results are good.

Results using the analytic wall function are good, and almost independent of the size of the wall layer.

** **

**Figure 1** Downward flow of air in a heated tube, inlet Re=14815, Gr=2.128x10^{7}, Bo=0.1162, T_{w}=83.3°C, T_{a}=23.1°C, outlet T_{w}=212.0°C, T_{a}=137.1°C. Also shown are predictions for a different set of conditions. CFD predictions by Gerasimov (2002); the different y^{+} values correspond to meshes with a different wall layer size.

**Figure 2** Downward flow of air in a heated tube, inlet Re=7044, Gr=8.010x10^{7}, Bo=0.5573, T_{w}=58.3°C, T_{a}=20.5°C, outlet T_{w}=147.9°C, T_{a}=105.0°C. Also shown are predictions for a different set of conditions, inlet Re=5016, Gr=8.003x10^{7}, Bo=1.7816, T_{w}=72.7°C, T_{a}=20.9°C, outlet T_{w}=195.3°C, T_{a}=143.9°C. CFD predictions by Gerasimov (2002).

**Figure 3** Downward flow of air in a heated tube, inlet Re=4097, Gr=6.800x10^{7}, Bo=3.0268, T_{w}=71.8°C, T_{a}=20.1°C, outlet T_{w}=194.4°C, T_{a}=147.7°C. CFD predictions by Gerasimov (2002).

**Upward Flow**

This case is buoyancy-aided. The simulated results, using the Launder-Sharma low Reynolds number model, agree well with the experimental data under the conditions where the flow is laminarised and the heat transfer is severely impaired by buoyancy forces. Some discrepancies between the model predictions and the experimental data are evident for the cases of weak buoyancy influence, where the model under-predicts the experimental values by as much as 20%, as was also found in the downward flow case.

Gerasimov (2002) also describes calculations of upward flow in a heated tube, using the analytic wall function. Figure 4 shows results for a case in which there is weak buoyancy influence, i.e. one in which the low-Reynolds number model under-predicts the experimental values by ~20%. The analytic wall function model performs slightly better than the low Reynolds number model, and results are almost independent of the size of the wall layer.

**Figure 4** Upward flow of air in a heated tube, inlet Re=15023, Gr=2.163x10^{8}, Bo=0.1124, T_{w}=74.0°C, T_{a}=19.1°C, outlet T_{w}=222.4°C, T_{a}=130.4°C. Also shown are predictions for a different set of parameters. CFD predictions by Gerasimov (2002). No experimental data in (b).

© copyright ERCOFTAC 2004

Contributors: Mike Rabbitt - British Energy