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

Underlying Flow Regime 3-06 © copyright ERCOFTAC 2004

Best Practice Advice

Best Practice Advice for the UFR

Key Physics

For gas flows in vertical tubes, the intense wall heating induces in the near-wall fluid a significant fluid property variation. When the Reynolds number at the inlet of the tube is low so that although the flow is initially turbulent, it may become either partially or fully laminarized as a result of being heated. Thickening of the viscous sub- layer and growth of the thermal boundary layer lead to readjustment of the flow so that fluid property variations and buoyancy can cause impairment of heat transfer.

Computational Domain and Boundary Conditions

The flow should be calculated upstream of the start of the heated section to minimize entry effects at the start of the heated section. At the model inlet, apply an isothermal fully developed flow. The outlet should be positioned downstream of the heated section. For the solution of the thermal energy equation, apply a uniform heat flux to the heated section. Upstream of the test section, the pipe should be adiabatic.

Turbulence Modelling

Low Reynolds (k, ε) models can give good predictions for these types of flows but additional terms have to be included to account for diffusion of k and production of e in the near wall region. The Launder and Sharma model performs reasonably well.

Analytic wall functions for low-Reynolds number flows in tubes with intense heating at the wall are not recommended. It must be preferred to solve the full set of equations right up to the wall.

As it is necessary to resolve the flow and temperature variation near the wall, the value of y+ for the inlet near wall node, should be no larger than 0.5 and a number of points (roughly 50) have to be located in the zone y+<30. This is an expensive approach.

Application Uncertainties

The standard (k-ε) model, using conventional wall functions, may give reasonable predictions only at fairly low heat loadings. However, this practice will under-estimate the enhancement or reduction in heat transfer compared with the equivalent forced flow.

Acknowledgements: The study reported here has been published by D.P. Mikielewicz et al. in 2002 (1), it was supported by the University of Manchester, by Nuclear Energy Research Initiative of the US department of energy and by the long term research initiative of the Idaho National Engineering and environment Laboratory.

Contributors: André Latrobe - CEA / DRN / Department de Thermohydraulique