High order scheme for thermally driven flows in an open channel

• Published in: Computers & fluids 1998-02, Vol.27 (2), p.273-290
• Main Authors: Bade, François, Haldenwang, Pierre
• Format: Article
• Language: English
• Subjects: Applied sciences; Aspect ratio; Boundary conditions; Devices using thermal energy; Energy; Energy. Thermal use of fuels; Exact sciences and technology; Finite difference method; Heat exchangers (included heat transformers, condensers, cooling towers); Heat flux; Heat transfer
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/S0045-7930(97)00030-3

The paper presents a high order numerical scheme for solving thermally driven flows in an open duct. More precisely, this approach deals with flows at large Rayleigh number and large aspect ratio of channel (length≫spacing). For such flows we propose an appropriate set of boundary conditions which is devoted to approach the part played by the return flow that reconnects outlet to inlet in experiments and consequently that allows us to focus on the channel itself. Additional effort has been made for implementing a high order scheme in order to achieve accuracy. A 2-D mixed scheme is presented: Chebyshev collocation method in the direction transverse to the flow and fourth order finite difference schemes in the streamwise direction, i.e. parallel to the vertical plates. The scheme accuracy is shortly checked vs an elliptic problem and with respect to a classical benchmark for numerical studies of free convection: the thermally driven cavity. Afterwards, we consider the set of boundary conditions that leads to fulfil a satisfactory comparison with two experiments of free convective flows in a vertical open channel. Both cases correspond to well-documented experiments of natural convection in thermosiphon. The first comparison considers the thermal transfer due to the flow induced by symmetrical wall heating at uniform heat flux. Our scheme predicts it with 2% accuracy on a large range of parameters. Secondly, we present a successful numerical attempt concerning the phenomenon of flow reversal which appears in the case of non-symmetrical heating. The computed threshold of its onset differs from experimental observations by about 10%.