High order scheme for thermally driven flows in an open channel

摘要

The paper presents a high order numerical scheme for solving thermally driven hows in an open duct. More precisely, this approach deals with flows at large Rayleigh number and large aspect ratio of channel (length much greater than spacing). For such flows we propose an appropriate set of boundary conditions which is devoted to approach the part played by the return how 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 how 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 hows 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 how 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%. (C) 1998 Elsevier Science Ltd. All rights reserved. [References: 36]