Two other important dimensions, the height of the core and the spa­cing between the fuel elements, are determined mainly, although not completely, by the coolant. The flow of coolant through the core is subject to limitations on temperature rise, pressure drop, and velocity, none of which can be too high.

If the height of the core is H, so that the power output from the highest rated fuel element is qmax fzH, then

qmax fzH = AvmaxPc^Tc^ (3.5)

where p and c are the density and specific heat capacity of the coolant, ATc is the temperature rise of the coolant as it passes through the core, and vmax is the mean velocity of the coolant associated with the highest rated element. A is the coolant flow area per fuel element and depends on the spacing of the fuel elements.

The temperature rise ATc is the difference between the coolant temperatures at the core outlet and inlet. The outlet temperature is fixed by the need for adequate strength and resistance to creep in the cladding and structural materials, whereas the inlet temperature is determined by the design of the steam plant and by the need for adequate resistance to thermal shock in the event of a sudden change such as a turbine trip (see section 4.2.4).

The maximum coolant velocity vmax is limited by considerations of erosion, vibration and pressure drop. For sodium it cannot exceed about 10 ms-1, partly because of the risk of erosion of steel cladding, and partly because vibration of fuel elements and structural compon­ents is much more difficult to control at higher velocities. For lead, with its much higher density, the limit is much lower and is usually set at 3 ms-1 or less.

As explained later (section 3.4.1) it is normal to restrict the coolant flow to less highly rated fuel elements so that the temperature rise is uniform across the core. The pressure drop is therefore determined by the most highly rated fuel. It is convenient to think of it as being given by an expression of the form

APc = C (1/2Pviax) (4H/Dh), (3.6)

where Dh is the hydraulic diameter of the coolant channels (which depends on the separation of the fuel elements) and C is a constant with the nature of a friction factor. Equation 3.6 is useful as an illus­tration but in reality the situation is not so simple because the value of C depends on the details of the design of the coolant channels and especially on the nature of the fuel element supports.

If the radius of the fuel elements is fixed then A in equation 3.5 and Dh in equation 3.6 are determined by the fuel element spacing. Consequently these two equations can be used to determine vmax and APc as functions of H and the spacing. Typical results for a 1 m high

core (H = 1) cooled with sodium are shown in Figure 3.1. The fuel elements are taken to be arranged in a triangular array the shape of which is determined by the ratio of pitch to diameter P/D, and the power is taken to be 2500 MW (heat). P/D determines the coolant flow area associated with each fuel element and, because the total number of fuel elements is fixed by the total power output and the linear rating, the overall diameter of the core.

The choices open to the designer can now be seen. If for example APc is required to be no greater than 0.3 MPa, P/D must be greater than about 1.3 and the core diameter something more than 2 m. If the core is lower (H > 1m) the pressure drop and coolant velocity are lower so P/ D can be reduced, but at the cost of making the core diameter greater. This is undesirable becauseit forces the entire reactor structure to be larger and increases the capital cost of the plant. Higher

values of APc are possible, but if it exceeds about 700 kPa cavitation and the generation of noise may be important.

Figures 3.2 and 3.3 illustrate the choices available with different coolants. If lead is used its high density requires a much higher pressure drop, and this and the more stringent limitation on velocity to avoid damaging erosion force a considerably larger value of PID, typically at least 1.5, and with it a larger core diameter. Velocities are much greater if the coolant is a gas, of course, and even with the relatively high density of supercritical CO2 at a pressure of 20 MPa, to which Figure 3.3 refers, they are of the order of 50 ms-1, but the pressure drop is not unduly high and PID < 1.4 is possible.

There are many other choices to be made because other paramet­ers, such as the maximum linear rating and the core temperature rise, can be varied. The ultimate choice depends on the criteria used for optimisation, including safety (see Chapter 5) and economics.