7.1 NATURAL CONVECTION IN NUCLEAR PLANTS

Following the immersion of a heated surface in a fluid, molecular heat conduction raises local temperatures and thereby reduces fluid densities [208,209]. Buoyancy forces then lift these localized lighter fluid packets to induce a continuous laminar or turbulent flow called natural circulation or natural convection. Industrial research on natural con­vection began in the 1930s but largely stalled in the mid 1950s because the enhanced heat transfer rates with forced convection (i. e., pumps) enable more compact and therefore more cost-effective plant designs.1 After the Three Mile Island incident in 1979, natural circulation research restarted to develop passive safety systems [108] that would function even after a total loss of emergency power. An IAEA Conference [298] in 1991 noted that passive safety systems based on natural circulation are a desirable method of enhancing the

1 Even domestic central-heating boilers now have forced circulation on both flue and water sides. [105] simplification and reliability of essential safety functions. Though some new innovative designs for small integrated reactors (< 100 MWe) now propose natural circulation as a means of core cooling during normal operation, these have yet to gain formal compliance with European Utility Requirements [59,109].

The principal advantage of natural circulation systems lies in the elimination of active power supplies and pumps, so simplifying plant architecture, maintenance and operation. It also eliminates certain accident scenarios in nuclear power plants, and an increase in channel power intrinsically increases its mass flow rate. On the other hand with a stable forced convective channel an active control system is required to increase its mass flow rate with input power. Specifically, momentum conservation in a vertical channel gives the steady-state pressure gradient [117]

— dp = PS + D (GG/2p) + dZ (G[106]/p) (7.1)

where

p — density; g — gravitational acceleration; G — mass flux (kg/m2s) D — hydraulic diameter; f — Fanning friction factor

Local density and dynamic viscosity m for a two-phase flow may be calculated as a function of steam quality x from the saturated values as

1/p = x/pG + (1 — x)/pL and 1/m = x/mG + (1 — x)/pL (7.2)

and for clean2 reactor or boiler channels with single or two-phase flow

1/f = -4log1o(1.25/Re f (7.3)

where

Re = GD/m — Reynolds Number

The driving pressure from modern pumps is only weakly dependent on flow rate, so for present purposes it can be assumed constant. An increase in channel power clearly decreases local density which accord­ing to equation (7.1) then increases local pressure gradients. Thus to preserve a constant overall driving pressure, a channel’s mass flux must suffer an inappropriate decrease. For this reason boiler feed water flow in conventional forced convective stations is controlled by cascaded throttle valves whose opening increases with demanded output[107] power.

The principal disadvantage of heat removal by natural circulation is that the driving forces from density disparities and gravity are relatively small. Their increase necessitates increases in loop heights and decreases in loop resistances to achieve prescribed heat transfer rates. Because 60 to 70% of the capital costs for nuclear stations reside in civil engineering, the economic viability of plants of order 1 GWe appears questionable. Also larger reactor cores with their smaller bucklings [58] are more susceptible to a spatially unstable neutron flux, and the thermal-hydraulic problems associated with boiling channels are also exacerbated under natural circulation. Specifically, flow stability at economic output powers (exit steam quality) requires the insertion of inlet ferrules to increase the liquid-phase pressure drop as described in Section 3.2. However, this artifice patently reduces the circulating mass flow rate unless loop heights are increased with the penalty of higher construction costs. Moreover, lower mass fluxes and higher steam qualities in two-phase flows encourage a radical reduction in heat transfer that occurs when the liquid phase can no longer “wet” fuel pin surfaces. Under these burn-out[108] or critical heat flux conditions[109] the pressurized fission product gases can locally puncture the fuel cladding whose creep strength [96] progressively weakens with increas­ing temperature. It is concluded here that heat removal by natural circulation is most cost-effective and reliable for single-phase liquid flows in safety systems removing just the decay heat in Grid-sized reactors (>100MWe). To meet the United Kingdom’s present peak demand of circa 60 GW, economic and environmental considerations favor large stations of around 1 GWe due to the limited availability of suitable sites (Section 4.4) and the existing form of transmission network.

A pioneering paper by Lorenz in 1881 analyzed natural convection heat transfer from a uniformly heated vertical plate in terms of molecular conduction to the neighboring fluid whose reduced density results in its buoyant upward laminar flow [219]. His formula for the corresponding heat transfer coefficient has the form

Nu = Function of Gr(Pr)1 (7.4)

where

Nu — Nusselt Number; Gr — Grasshof Number; Pr — Prandtl Number

l — a constant

Later in 1902, Bourinesq showed that when viscosity is negligible (as in very many turbulent flows) the above index l equals 2. Further investigations [219,303,305] during the twentieth century still generally relate to flat plates or the outsides of horizontal tubes. The earlier experiments reveal that natural circulation can become turbulent with an enhanced heat transfer rate, and this is encouraged in reactor fuel pin bundles by diagrids [268,304]. Heat transfer and pressure drop in tube bundles also depend on their pitch-diameter ratio so the relevant correlations are very much design-specific. Because the gas-side heat — transfer resistance in AGR steam generators is a significant part of the overall primary to secondary-side thermal resistance, specific correla­tions are necessary for sufficiently accurate predictions of steady-state and dynamic performances [117]. Likewise by virtue of the lower mass fluxes in natural circulation, pertinent experimental heat transfer and pressure drop data are necessary to underwrite proposed safety system designs: especially if the stability of a two-phase channel flow is in question. Thermo-hydraulic transitions in natural circulation are a tractable numerical problem and they can be negotiated like those found under forced convection [64,117]. However, stratified cold sections can be potentially created prior to ECCS operation and these would block decay heat removal by natural circulation, as would an accumulation of nitrogen or hydrogen in the upper U-bend of a steam generator (a loop seal) [306]. Thus the operation of heat removal systems by natural convection must be unequivocally confirmed by experimental rigs. Because full-scale whole plant replicas are impractical, one adopted approach is to adjudge representative cross-sectional sizes and to replicate exactly the differential heights between components so as to preserve gravitational driving forces. A superbly engineered rig relying on this principle has been constructed for example at CEN Grenoble, but the APEX and MASLWR rigs in the United States also scale differential heights by 1/4 or 1/3, respec­tively [109].

Though natural circulation is proposed for the on-load cooling of Generation IV water reactors [109,298,302], it is installed in presently operational plants only for decay heat removal in potential Severe Accidents. In this context, the separate steam generators of existing PWRs have an important safety role [59,65]. If the primary recircu­lation pumps in Figure 1.3 were to fail and the system were depres — surized,[110] then sufficient coolant injected into the secondary-side boiler inlets is seen to encourage natural circulation in the original flow direction of the reactor circuit. Deaerator or emergency tanks are presently available for this purpose. Moreover, the intrinsic water inventory and that of the ECCS ensure that fuel degradation is a progressive process [66,93,213] so time is available to secure civilian fire engines [65], or to reconfigure the plant to use its steam turbine condensers as heat sinks [59].

An alternative scenario to MFCIs during a Severe Accident in PWRs is a progressively increasing mass of corium on its lower core support structures and at the bottom of its pressure vessel, whose creep strengths [96] are diminished by heat transfer. At high pressures the vessel itself fails first,[111] whereas at lower pressures the supports fail some computed 15 min before the vessel [65]. Steam, fission products and hydrogen from oxidation of the fuel cladding would then be discharged into the reinforced concrete containment building, whose hydrogen content would further increase from a rapidly developing corium-concrete interaction [65]. A major concern is then a potential rupture of the building from a hydrogen explosion with the consequential atmospheric release of radioactive isotopes. Ejected steam, air and gaseous fission products diminish the likelihood of the initial 7 to 16% by volume of hydrogen [307] to detonate: as do igniters and catalytic recombiners which innocuously dissipate locally concentrated pockets. However, the ejected hot material also threatens the normally well-sealed building by over-pressurization. To restrict the excess pressure to well below its ultimate strength of 5 bar, elevated rings of chemically doped[112] sprays are automatically activated at around 2 bar [66,307]. These produce fine droplets with Sauter diameters of 448 to 544 mm [308], and their large surface area to aggregate volume effects a rapid condensation of steam and ambient cooling, whilst evidently increasing the volumetric concen­trations of hydrogen. Herein lies a trade-off problem between spray cooling to counter over-pressurization and the increased risk of a sig­nificant hydrogen explosion. It evidently demands serious investigation.

Spray cooling within a reactor containment building creates multi­dimensional natural circulation flows which to a greater or lesser extent are complicated by

i. Interactive heat transfer between all solid, liquid and gaseous components.

ii. Permanent gases which inhibit steam condensation [219,311]. Also they increase the fugacity [3] of the contents which alters thermodynamic state equations from those of the pure sub­stance [210].

iii. Multicomponent two-phase turbulent flows.

iv. Thermal disequilibrium at liquid-vapor interfaces; see Section 5.5.

v. Dissolved fission products decreasing the vapor pressure of water (boiling point increases)—a fugacity effect.

vi. The efficiency of sump screens in removing core debris from water to be recirculated [310].

Due to the daunting physical and mathematical complexity of a containment’s spray cooling process, a combined step-by-step exper­imental and computer simulation investigation is first necessary to identify the most significant phenomena and then their pertinent interactions. The TOSQAN program is a European initiative along these lines. However, unlike the replica scaling described in Chapter 6, Zuber’s time-preserving Hierarchical Two Tiered Scaling Method [307,309] is adopted for this far more complex problem. Though the TOSQAN experiments are not necessarily dynamically similar to reactor-scale processes, the above step-by-step creation of validated computer models eventually results in a reliable simulation for safety assessments at reactor-scale [312,313].