On the oscillatory instability of a differentially heated fluid loop

Abstract

A theoretical discussion is given of the motion of a fluid contained in a tube forming a closed loop that is heated from below and cooled from above. The fluid is assumed to have uniform temperature over each cross-section, and the heat transfer is assumed proportional to the difference between the local temperatures of the fluid and the tube. The latter temperature is prescribed. The system has one steady solution with warm fluid rising in one branch and cold fluid sinking in the other. This solution may, however, become unstable in an oscillatory manner. A weak instability takes the form of pulsations, the motion being always of one sign, while a strong instability takes the form of oscillations with zero mean motion. These oscillations are irregular and do not repeat themselves even over very long times.These unstable motions are associated with thermal anomalies in the fluid that are advected materially around the loop. The anomalies amplify through the correlated variations in flow rate. A warm pocket of fluid creates maximum flow rate going through the upper part and minimum flow rate going through the lower part of the loop. Accordingly it passes quicker through the heat sink than through the heat source, and the latter becomes more effective. Similarly, the heat sink acts more effectively on a cold pocket of fluid.The curve of neutral stability is worked out as a function of the two parameters of the problem, a non-dimensional gravity and a non-dimensional friction coefficient. The instability has also been studied by direct numerical time integration of the model equations.It is suggested that the mechanism of instability found for this model operates also in more complicated systems, and can explain the pulsative type of motions observed recently in certain convection experiments.

Detailed Loop Model (DLM) analysis of liquid solar thermosiphons with heat exchangers

“…They predicted oscillatory modes which could be long-lived during periods of high hot water draw from the tank--i.e., during periods when the system was significantly perturbed by the hot water draw. Furthermore, there have been numerous theoretical predi ions and experimental observations of fluid flow oscillations in non-solar natural convection systems [46][47][48][49][50][51][52][53] An indication of the effect of heat exchanger on system perforrnance is given by Fi • 7(a) and 7(b). In Fig.…”

Rotations and cessations of the large-scale circulation in turbulent Rayleigh–Bénard convection

“…All of these cases are two-dimensional models where only cessations with ∆θ = 1/2 revolution are possible, although in principle the models could be extended to three dimensions. Cessation also occurs in convection loops (a thin circular vertically oriented loop filled with fluid heated in the lower and cooled in the upper half) where because of the two-dimensional nature again only cessations with ∆θ = 1/2 revolution are possible [Keller(1966), Welander (1967), Creveling et al (1975), Gorman et al(1984)]. …”

Predicting flow reversals in chaotic natural convection using data assimilation

“…Following previous experiments that examined the periodic (Keller, 1966) and chaotic (Welander, 1967;Creveling et al, 1975;Gorman and Widmann, 1984;Gorman et al, 1986;Ehrhard and Mu¨ller, 1990;Yuen and Bau, 1999;Jiang and Shoji, 2003;Burroughs et al, 2005;Desrayaud et al, 2006;Yang et al, 2006;Ridouane et al, 2009) behaviour of toroidal thermosyphons, we also consider a circular thermosyphon geometry. Picture a vertically oriented hula hoop, as shown in Fig.…”

“…The first explanation of the mechanism responsible for flow reversals was presented by Welander (1967) and repeated by Creveling et al (1975). Welander, who was also the first to discover that thermosyphons exhibit aperiodic oscillatory behaviour, explained the instability of steady convecting flow by considering a thermal anomaly or 'warm pocket' of fluid.…”