Natural circulation loops (thermosyphons) are flow systems heated from below and cooled from above, such that the heat sink is higher than the heat source. This specific configuration creates a density gradient which generates the driving force. Thermosyphons appear in geophysical and geothermal systems and have been used in many applications in diverse energy conversion systems, such as solar heating devices, absorption refrigerators, reboilers in chemical industries and cooling of various engines. One of the most important uses of thermosyphons is in emergency core cooling of nuclear reactors. This subject gained more interest following the recovery of the reactor after the *Three Mile Island* (TMI) *accident* in 1979, when it was demonstrated that natural circulation was the only effective way to remove the decay heat.

Natural circulation flows are often divided into single- and two-phase loops. Reviews on thermosyphons were written by Zvirin (1981) and Greif (1988). Summaries of recent advances appear in D'Auria and Vigni (1990) and Knaani and Zvirin (1993).

Theoretical methods have been developed in order to simulate various loops, derive scaling laws for experiments and explain physical phenomena including stability characteristics. The mathematical models are based on the coupled conservation equations, rendering the problem nonlinear. The continuity equation in one-dimensional models yields the result that the velocity, v, is a function of time only (and an unknown constant for steady state). The temperature distribution, T, is obtained in terms of v by solving the energy equation. For two-phase loop sections the quality, x, is obtained and for double-diffusive loops the salinity, S, is found from the diffusion equation. The momentum equation is integrated along the closed loop, to yield v. Analytical solutions exist for simple loops. Numerical methods are needed for more complex ones and for transient calculations. Stability features have been obtained by linear stability analysis as well as by finite amplitude methods; numerical solutions are used for both. (See also Instability, Two-phase.)

Data on natural circulation exist in the literature for the whole range of scales, from large working systems to laboratory experiments. The former include nuclear reactors, (e.g., post-accident TMI and many tests on others), solar energy systems and reboilers. The latter are usually simple geometry loops to study various phenomena and to validate computer codes.

The experimental and theoretical investigations have produced the information needed to understand, predict and simulate the behavior of thermosyphons. The interaction of the participating physical forces is complex and nonlinear; gravity, friction and inertia depend on heat and mass transfer characteristics. This leads to several interesting features of the convective flows.

In general, steady state loop flows (SF) are established for a certain range of Rayleigh Numbers, Ra, above some thresholds and below critical instability limits. These flows can be reached either from a perturbation of a rest state (conductive solution) or by coast-down from forced flow. For two-phase thermosyphons, the curve of flow rate vs. loop inventory exhibits a local maximum. Transients leading to SF can be monotonic or oscillatory. For a range of Ra, the SFs are unstable (growing oscillations). This can lead to bifurcation (multiple SFs), long term periodic flow and chaotic behavior. These phenomena have also been observed in systems with parallel loops and thermosyphons with throughflows.

Finally, there does not yet exist a general set of heat transfer and friction correlations for natural circulation loops, and in theoretical and numerical studies forced flow correlations are often used, with some loss of accuracy. Other approximations have also been made in cases where there is a lack of more accurate information, such as linear profiles of void fraction.

#### REFERENCES

D'Auria, F. and Vigni, P., (Eds.) (1990) Proc. Eurothem Seminar Nr. 16: Natural Circulation in Industrial Applications, Pisa, Italy.

Greif, R. (1988) Natural Circulation Loops. *J. Heat Transfer*. Vol. 110, 1243–1258.

Knaani, A. and Zvirin, Y. (1993) Bifurcation Phenomena in Two-Phase Natural Circulation Loops. Int. J. Multiphase Flow. Vol. 19, 1129–1151 DOI: 10.1016/0301-9322(93)90081-5.

Zvirin, Y. (1981) A Review of Natural Circulation Loops in Pressurized Water Reactors and other Systems. *Nucl. Engng. & Des.*, Vol. 67, 203–225. DOI: 10.1016/0029-5493(82)90142-X