On the Stability and Flow Reversal of an Asymmetrically Heated Open Convection Loop

Experimental results are reported for a U-shaped, free convection loop. The top of the loop is open to an isothermal reservoir. The horizontal leg and one vertical leg are heated at rates Q1 and Q2, respectively. The loop is filled either with water or a watersaturated porous medium. Symmetric heating and asymmetric heating favouring the ascending leg of the loop both yield stable flows. Asymmetric heating favouring the descending leg leads to stable flows when the ratio Q1/Q2 is above a critical value. Below this critical value, the flow is observed to oscillate with increasing amplitude until the direction of flow in the loop undergoes a reversal. A steady flow follows the reversal. Analytical results include a stability analysis and time-dependent, one-dimensional numerical calculations, both of which compare favourably with experiment. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Bau, Haim H. and Kenneth E. Torrance. (1981) On the stability and flow reversal of an asymmetrically heated open convection loop. Journal of Fluid Mechanics. Vol. 109. p. 417-433. Copyright 1981 Cambridge University Press. http://dx.doi.org/10.1017/S0022112081001146 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/206 J . Fluid Mech. (1981), vol. 106, pp. 417-433 Printed in Great Britain 417 On the stability and flow reversal of an asymmetrically heated open convection loop By HAIM H. BAUT AND K. E. TORRANCE Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14863 (Received 29 April 1980 and in revised form 9 December 1980) Experimental results are reported for a U-shaped, free convection loop. The top of the loop is open to an isothermal reservoir. The horizontal leg and one vertical leg are heated at rates Q1 and On, respectively. The loop is filled either with water or a watersaturated porous medium. Symmetric heating and asymmetric heating favouring the ascending leg of the loop both yield stable flows. Asymmetric heating favouring the descending leg leads to stable flows when the ratio Ql/Qa is above a critical value. Below this critical value, the flow is observed to oscillate with increasing amplitude until the direction of flow in the loop undergoes a reversal. A steady flow follows the reversal. Analytical results include a stability analysis and time-dependent, onedimensional numerical calculations, both of which compare favourably with experiment. The disturbance amplification mechanism is explained in terms of thermal anomalies which move through the loop with the material motion of the fluid. Since the heating and buoyancy generation processes are in phase in the heated, descending leg, a thermal anomaly can amplify as it flows through that leg. As the anomaly moves through the ascending leg, it initiates a subsequent anomaly of opposite sign in the descending leg. The result is an oscillating flow which, under appropriate conditions, can amplify.