Figure 4.13 shows the temperatures of the coolants of a 3600 MW (heat) reactor with once-through steam generators. Steam is supplied to the turbine at 18.5 MPa and 490 °C at a rate of 1650 kg s-1. The final feed temperature is 240 °C. The total secondary sodium flow rate is 15330 kg s-1 and the primary sodium flow rate is 18935 kg s-1.

The choices available in designing the steam generators can be illustrated in a simplified way as follows. Suppose there are N tubes each of length L and diameter D. Then we have

Q ~ UATmNnDL, (4.4)

where ATm is the logarithmic mean temperature difference, Q is the total heat transfer rate, and U is the mean heat transfer coefficient which depends on the steam-side conditions. If the total mass flow­rate in the evaporators is M, then clearly M = mN.

A once-through steam generator can be thought of as consisting of three regions as far as heat transfer is concerned: the inlet region where the tube is filled with single-phase water, the boiling region with a two-phase mixture of water and steam, and the superheating region of steam in the vapour phase. The heat transfer coefficient in the superheating region is considerably lower than those in the regions where liquid water is present. Values for the heat transfer coefficients for the three regions are given for example by Collier (1972), and can be used to find U, which depends on m and therefore on N, but not very strongly.

D has to be at least 15-20 mm for ease of manufacture. For a 20 mm tube, m = 1kg s-1 makes the mean speed of the two-phase mixture in the centre of the steam generator about 12 m s. If m is much greater than this the problems of vibration and erosion are significant. If D is taken to be about 20 mm the product LN is limited by equation 4.4 and the main choice is between large L (long tubes) or large N (many tubes).

Figure 4.14 shows the sodium, steam/water and tube mid-wall tem­peratures in a steam generator of the reactor described in Figure 4.13, with D = 20 mm and m = 1kgs-1. This choice of m implies that there would be 1650 tubes each about 64 m long. Clearly this rules out straight tubes, but it is reasonable for reasonably compact bundles

of helical tubes. An alternative design might select larger diameter tubes. D = 28 mm would give m = 0.5 kg s-1 and N = 3300. In this case, allowing for the slightly lower values of U, the tubes would be 30 m long and could possibly be arranged in six separate straight-tube steam generator units each with 550 tubes.

The discontinuities in the mid-wall temperature shown in Figure 4.14 mark the beginning and end of the two-phase region. Because of the turbulence caused by the formation of vapour heat transfer in this region is better than in the pure liquid region and much better than in the vapour region. An important consequence is a marked step in the tube temperature at the “dry-out” point — the last point where the surface of the tube is wetted. The dry-out point is not fixed but moves up and down the tube both as operating conditions change and at random due to the turbulent nature of the two-phase flow. Thermal stresses are associated with the temperature step, and as they fluctuate there is a possibility of fatigue damage to the tube material. (The extent of these stresses is limited, however, because whatever the heat transfer conditions the tube temperature is constrained to lie between the sodium and steam temperatures that, because of the good heat transfer on the sodium side, are relatively close. In a fossil-fuelled plant where the tube would be heated by a flame at a very much higher temperature the potential is for wider stress fluctuations and therefore greater fatigue damage.)