9.132. There is often confusion regarding what is meant by the terms natural circulation and free convection. If we have a fluid being heated in a vertical tube, its density will decrease. Now, if the system is closed, that is, consists of a “loop” and the fluid is cooled before returning to our heated tube, we would have flow induced by the so-called chimney effect, which causes a pressure differential, or “driving pressure,” in the heated tube which would be resisted by frictional effects. Flow can be either laminar or turbulent, depending on the flow velocity achieved. This effect is known as natural circulation and can be analyzed by application of the mechanical energy equation (§9.111) to determine the flow rate. We would have the same effect, but less pronounced, if our heated tube was in a reservoir of fluid, as we have in a fireplace chimney.

Example 9.10. As an introduction to the role of the chimney in a natural circulation boiling-water reactor (§15.25), estimate the driving pres­sure resulting from a 10-m-high chimney above a boiling core that has an exit quality of 15 percent. At the dome pressure of 7.2 MPa, the specific volumes are 0.00136 m3/kg for the saturated liquid and 0.0265 m3/kg for the saturated vapor. Figure 9.18 shows the circulation path schematically. For purposes of this estimate, assume that the system is isothermal and that friction outside the core is negligible. Feedwater replaces the steam produced.

Specific volume of two-phase mixture = (0.85)(0.00136) + (0.15)(0.0265)

= 0.00513 m3/kg; p2_i — 195 kg/m3; p2_3 = 735 kg/m3;

then

p3 — px = 10(735 — 195)(9.8) = 53 kPa.

This compares with a core pressure loss in the SBWR of 44 kPa.

9.133. The terms free convection or natural convection normally apply to fluid motion caused by buoyancy effects when we have a heated surface immersed in a surrounding fluid. Under such conditions we have a so — called boundary layer problem rather than a chimney effect.

9.134. In designing reactor core cooling systems, it is very desirable to make the geometry and pressure losses such that there will be significant natural circulation cooling after shutdown in the event that the circulating pumps fail. Natural circulation cooling considerations are also important in the design of water-filled storage pools for spent-fuel assemblies (§11.34).