Leidenfrost [204] in 1756 reported that water droplets can endure for several seconds on a sufficiently hot metal surface as a result of an intervening vapor film that inhibits heat transfer. With decreasing surface temperature the vapor film could no longer be sustained and the droplet quickly boiled away. The minimum surface temperature for the existence of a vapor film became known as the Leidenfrost Point. However, later experiments and theoretical analyses in the twentieth century showed that the Leidenfrost Point is not just a property of the liquid and surface temperature. Specifically, particulate impurities or surface roughness are found to reduce the formation energy [205] of an embryonic vapor bubble and so precipitate nucleation. Indeed with extreme liquid purity, stillness and surface purity, boiling on a wetted surface can be inhibited until temperatures are well above normal and towards the limiting homogeneous nucleation temperature [205].

The destabilization of a vapor film (triggering) to initiate an MFCI in a Severe Accident differs radically from the collapse of a Leidenfrost vapor film. First, liquid corium temperatures are orders of magnitude larger (> 3500 K) so an enormous radiant heat flux component[81] [82] enters the liquid interface. Secondly, a film would contain non-condensable hydrogen11 or fission product gases that can modify its thermodynamic states and thermal conductivity [3,210]. Finally, an explosive liquid to liquid heat transfer over m-seconds is induced by external shock waves: rather than spontaneous passive nucleation over seconds. Preliminary aluminum-water experiments at AEEW confirm the necessity of a shock wave to destabilize otherwise quiescent film boiling. These tests in Rig A repeatedly created a detonable coarse mixture like that in Figure 5.1 without an MFCI. Later, a small chemical explosive was used to initiate a weak shock wave which then consistently triggered an MFCI. On the other hand, subsequent urania-water experiments in Rig A and MFTF were consistently triggered just by the injection of melt. Accordingly, to achieve greater understanding for reactor safety assess­ments, experimental [207] and theoretical [206] research was under­taken into shock wave destabilization of vapor films.

As can be readily visualized from Figure 5.1, a realistic three­dimensional simulation of triggering is presently intractable. Never­theless by characterization of the pertinent physical processes useful insight can be gained from the one-dimensional model in Figure 5.4. Due to their widely different acoustic impedances a trigger pressure wave in the liquid propagates only weakly into the vapor. Also many reflections of this transmitted wave occur in the relatively thin vapor before the next stress wave in the liquid arrives back at the interface.[83] Consequently, as inferred from Figure 5.5, vapor pressure can be considered spatially uniform at any instant. Moreover, because thermodynamic relaxation times [211] are of order

I ns and film destabilization requires [207] some 20 ms, classical thermodynamic state variables can describe each point in a film. However, by increasing fugacity [3], permanent gases in a vapor film during a Severe Accident alter these states from those of the pure substance. For example, if the partial pressure of a permanent gas is

dPsat = (tlSAt/tGSAt) • p0

where

vLSAT, vGSAT — specific volume of saturated liquid and vapor, respectively.

Table 5.1 presents the specific volume ratio vLSAT/vGSAT and the fraction of undissociated steam as a function of pressure at 3500 K [208,209]. Because the fission product pressure for locally rupturing a fast reactor fuel pin is of order 2 MPa, the change in the saturation vapor pressure of sodium is seen to be largely negligible. Accordingly, it is inferred that all other thermodynamic states in a film mixture remain essentially those of its separate constituents. In the case of a water reactor, the corresponding specific volume ratio is seen to increase slowly enough for the permanent gases to have a negligible effect on the saturated steam pressure: especially as increasing pressure inhibits its dissociation. It is again concluded that all thermodynamic states in a film mixture are those of its separate constituents.

The extreme temperatures in a vapor film significantly affect its local thermal conductivity. Available data [209] for superheated sodium vapor appear restricted to temperatures no greater than 1500 K. Never­theless, it can be assumed to behave as a perfect gas at higher temperatures. On this basis kinetic theory [210] suggests a two-fold increase in thermal conductivity across a sodium vapor film to the obvious benefit of its stability. In the case of superheated steam, thermal conductivities in Table 5.2 exceed kinetic theory predictions by virtue of more mobile hydrogen molecules created by its partial dissociation.

Accordingly, film stability considerations should involve a distributed model of heat diffusion in the vapor, but too many mesh points would clearly aggravate numerical problems as a film collapses.

If water is in thermal equilibrium with its vapor at 60 °C, the evaporation and condensation mass fluxes derived from kinetic theory

are about 2kg/m2 — s or 6.7 x 1026 molecules/m2 — s. Despite this chaotic interchange at an interface, experiments [214,215] show that it remains plane to within 1 or 2 molecular diameters due to inter­molecular attraction. When a shock wave accelerates the liquid into its vapor, Rayleigh-Taylor waves [216,217] are suppressed so the inter­face remains locally plane. On the other hand if an interface deceler­ates close to a hot melt, these waves could conceivably distort an originally plane interface element. No analysis is apparently pub­lished that engrosses both surface tension and viscosity, but larger predicted oscillatory amplitudes would patently obtain without vis­cous damping. Assuming a uniform deceleration over half the typical 20 ms destabilization period [207] of a 100 mm vapor film by a 10 MPa trigger, then with just surface tension the fastest growing wavelength l* and its time constant t* are shown in Table 5.3 from calculations

where

€ — uniform deceleration of liquid phase

sL — surface tension of the liquid

pL, po — density of liquid and vapor, respectively

Though it appears that Rayleigh-Taylor waves could grow significantly during film destabilization, the large viscous shear forces associated with such rapid micron-sized wavelengths would (in the author’s opinion) strangle their growth. Moreover, experiments [207] confirm a later analysis that the collapse of a vapor film is hardly resisted, so it is therefore reasonable to conclude that a liquid-vapor interface remains essentially locally plane during its destabilization.

Tidal movements result from an interaction of the gravitational fields of the sun and moon with the earth’s water masses. The global potential for tidal power is an estimated [22] 6 TW, but there are just a few special locations for its economic exploitation. Specifically they have the appropriate orientation to access the Coriolis forces created by the earth’s rotation and a shape whose natural oscillatory frequency closely matches that of the tides [23]. Depending on the situation, then principally[4] tidal range or tidal stream systems are the flexible means of extracting the energy. In the former mature technology, water flows at a flood tide are trapped behind a dam or lagoons and in the process drive horizontal low-head turbines during parts of both flood and ebb tides. Suitable sites include the Severn Estuary (UK), La Rance (France), Bay of Fundy (Canada) and some others where the tidal range exceeds the necessary 7 m for an economic development [22]. Though lagoons as a means of reducing upstream ecological damage were considered for the Severn Estuary scheme, they were subse­quently rejected for the induced scouring of the interstitial seabed and their cost-effectiveness [23]. In fact there are no tidal lagoon schemes presently in the world.

Tidal stream devices extract a portion of the kinetic energy from relatively fast tidal currents as for example at the UK sites of Pentland Firth, Strangford Lough, and Alderney. Various blade designs are under development for the Kaplan-type turbines, but as yet no real choice exists with regard to efficiency and cost-effectiveness [23]. Individual units can provide up to 1 MW, so “farms” of as many as 30 are planned in order to justify the provision of substantial new Grid connections to prevent transmission “bottlenecks” that would otherwise exist between these generating units and the centers of largest electricity demand [23]. Other issues can be identified by assessing the potential of two powerful tidal steams in New Zealand to provide a material portion of its 13 GW demand [116]. These particular steams peak around 5h apart, so their combined power profile assumes the form

P = P0[2 + cos 0 + cos (0 + f)] (1.3)

where

0 = at; a = p/6 and f = 5p/6

Extreme values occur at

tan U = —b/a; b = sin f and a = 1 + b giving the ratio

Pmax : Pmin = 1.33 : 1.0 (1.4)

Granted sufficient tidal energies, equation (1.4) shows that even at minimum flow enough Kaplan turbines could meet a specific quota in any 24—h period. The excess power at higher flows could simply be rejected by de-exciting individual generators. Though apparently very promising, some 5000 of the presently largest 1 MW turbines would be required for 5 GW. Moreover, powerful tidal streams (~5 m/s) offer very restricted safe diving windows[5] and are likely to entrain amounts of grit that could erode turbine blades. Because installation, intercon­nections and maintenance do not benefit from scale only much smaller stations appear viable. In this respect the 30 MW trial at Strangford Lough should be definitive in terms of reliability, scale, and costs. In contrast the proposed 16-km-long Severn Barrage between Cardiff and Weston would have produced a material maximum output of 8.46 GW that is closer to the largest demand centers and 4.7% of UK national consumption.

Flood and ebb tides each occur twice daily and repeat about 1 h later each successive day. Also tidal ranges and stream speeds vary periodically over the 28-day lunar cycle due to the changing align­ment of the sun and moon. The electrical output of a tidal generator varies in like manner so it is frequently out of step with a grid network’s daily demand. Nevertheless tides are regular and largely predictable [24] so tidal generators can be readily incorporated into the largely predictable daily load schedule of a Grid network. Furthermore the relatively low height of a tidal barrage results in low mechanical stresses so that unforeseen outages are rare. Indeed the La Rance 240 MW plant has performed without a major incident for some 40 years since its construction in 1966. At 2006 prices, maintenance costs for the Severn scheme are estimated at £139M or $214M per year which is about 1% of total capital costs, and

Tidal barrages affect the physical, chemical and ecological features of an estuary. La Rance is the one materially sized plant in the world, but studies of its environmental impact have been limited [23]. However, insight can be gained from observations on harbor walls, jetties, bridges, or breakwaters. Though a barrage mitigates upstream flooding by tidal surges, its associated storage would regularly flood marshes used for previous centuries by wildlife, and it may also reflect tidal surges to damage downstream areas. Water management at La Rance creates the advertised “largest whirl­pool in the world” and has become a frequently videoed tourist attraction. Also changes in hydrodynamics, dissolved oxygen and salt concentrations can produce radical changes in local flora and fauna as well as to sources of public drinking water. At La Rance for example sand eels and plaice have been replaced by sea bass and cuttlefish. Sediment accumulated behind a barrage not only requires regular dredging as in a conventional hydro scheme, but the estuary’s topography and shipping channels could be altered by the modified silt deposits. A subdued water flow behind a barrage may also concentrate human and industrial effluents. The “footprint” of a tidal barrage scheme is highly significant for the densely populated United Kingdom, and that for La Rance is 9.38 hactares per installed MW.

Though La Rance was originally intended as a prototype of many tidal stations supplying a material portion of France’s electricity requirements [27], nuclear power development became the final choice. Reasons for EDF’s decision have apparently not been published [27], but the above environmental issues must have entered the argument. Whatever the truth, the nuclear choice became very profitable. After the unification of Germany in 1990 and with Chernobyl probably influenc­ing matters, the Russian RMBK reactors and heavily polluting lignite­burning generators in the DDR were decommissioned. The resulting energy gap was filled by energy from France’s largely[6] nuclear plants, which also buffer the UK’s grid network by the 2GW cross-channel ac connector. In the case of the Severn Barrage, BBC News announced on 9th February 2010 that the estuary would be “devastated” and on the 5th September the Guardian newspaper wrote that governmental support had been withdrawn.

Passive safety systems consist entirely of passive components, or use active elements in a very limited way to initiate subsequently all passive operations [108]. Manual intervention is excluded in all cases. Because they eliminate multiple pumps with their independent and redundant power supplies some proposed passive systems appear potentially more cost-effective and reliable than current active sys­tems [109]. Accordingly, the IAEA initiated in 2004 an internationally coordinated research project to investigate the performance and reliability of passive safety systems deploying natural circulation for the removal of decay heat after a successful reactor scram (a “hot shutdown”). To provide direction for this experimental and analytical program, the following four degrees of passivity were formulated [108]. The specification for the most stringent Category A passive system is as follows [113]

which are exemplified by

i. Hardened fuel cladding [300]

ii. Containments resistant to excess internal pressures, impacts or seismic activity

iii. Heat removal by thermal radiation or conduction to external structures.

Criteria 1, 2 and 3 are satisfied by Category B systems though moving working fluids are now allowed. Examples include reactor shutdown by the destabilization of hydrostatic equilibrium between its pressure vessel and an external pool of borated water, or containment building cooling by intrinsic natural convection to its internal walls. Category C systems conform to restrictions 1 and 2 but allow moving mechanical parts and fluids. An example in presently operational plants is the pre-pressurized accumulators of borated water which are connected into a reactor circuit by check valves. Under normal operation these are held closed by differential pressures, but in a LOCA the pressure differential reverses and the valves open automatically to shut down the reactor. Category D, the least degree of passivity, allows just battery or gravity — powered active components or intelligent signals to initiate their operation but in no way to control it. Examples include electro­magnetically latched scram rods, and those items listed below for decay heat removal or reactor shutdown:

i. Core make-up tanks of borated water which form part of a natural circulation loop with the reactor.

ii. Borated water injection by gravity at low reactor circuit pressures.

iii. PWR circuit cooling by natural circulation using its steam generators whose secondary circuits become large external cold water sources.

iv. A separate natural circulation heat exchanger whose secondary is a separate large external water tank.9

v. Passively cooled core-isolation condensers (BWRs only).

9 Decay heat removal in PFR was achieved by a NaK air-cooled, natural convective heat exchanger attached to each IHX circuit [314].

vi. A natural circulation loop using water collected in the contain­ment building’s sump and the hot reactor core. Any steam produced is vented into and then condensed on its walls, etc.

vii. The spray cooling system for a containment building which is described in Section 7.1.

These Category D passive safety systems and their incorporation into some Generation IV plant proposals are clearly described in Reference 108. However, they are not regarded as preferable to the active systems in presently operational plants. Also the IAEA concludes that the level of understanding and connected code capabilities of the thermal hydraulic phenomena in passive safety systems appear presently to be limited.

Flow instability in the boiling channels of fossil or nuclear plants would soon lead to boiler tube or fuel pin ruptures from the thermally induced stresses. Experiments show that channel flow oscillations with a period of 1 to 10 s can exist under constant inlet and outlet pressures. A resolution of this paradox is obtained by considering the transport delays and changes of thermodynamic phase along a boiling channel [80,117]. Qualitatively, an inlet mass flow perturbation dW 1sin vt in Figure 3.4 persists over the largely incompressible liquid-phase region to produce a simultaneous differential pressure drop of dPL sin vt. However, due to its compressibility, the average acceleration of the two-phase region and its corresponding pressure perturbation dP2f suffer a significant delay. A similar argument applies a fortiori to the steam region, whose average acceleration and differential pressure change dPs are still further delayed. The phasor diagram in Figure 3.4 reveals qualitatively that a flow oscillation can exist with no change in
the differential pressure across a boiling channel. Flow stabilization can then only be achieved by inserting inlet ferrules (gags), which increase the liquid-phase component of a differential pressure change. As can be inferred from Figure 3.4, this artifice pulls the Nyquist diagram away from the critical (—1,0) point. Though feedpump power is relatively small,[36] quite small changes (e. g., 0.1%) in station efficiency are material [80], so the ferrules must be designed to be sufficient for purpose and little more.[37] Engineering experience and comprehensive non-linear simulations are now shown to simplify a quantitative analysis of the problem.

In response to an inlet-flow perturbation vector d W 1 (t) in Figure 3.5 define

Primary inlet mass flow perturbation Primary inlet temperature perturbation Water-side inlet mass flow perturbation Water-side inlet temperature perturbation Water-side inlet pressure perturbation

Upper plenum

SP,.,„ = о

Figure 3.5 Parallel Channel Stability Model

and the incremental outlet flow vector of the boiling channel by

Primary outlet mass flow perturbation Primary outlet temperature perturbation Water-side outlet mass flow perturbation Water-side outlet temperature perturbation Water-side outlet pressure perturbation

which are related by a matrix transfer function T(s). During the observed period of flow oscillations, water-inlet temperature is effec­tively buffered by a large mass stored in the feed train [141], and inlet pressure by the feedpump circuit. Also at high subcritical pressures, heat transfer and thermodynamic states along a channel are essentially unaffected [64] by the relatively small pressure changes, and those across a ferrule simply add to the overall differential pressure pertur­bation [117]. Both inlet and outlet primary-side variables are main­tained effectively constant by virtue of their: thermal capacities, pump speed, and reactor reactivity settings.5 Accordingly the perturbed inlet mass flow vector to a channel reduces to

u = (Water-side inlet mass flow perturbation) (3.3)

Thus the outlet water-side pressure perturbation dP0 is given for practical purposes by the SISO transfer function relationship

dP0 = T53 (s)dW 1 (3.4)

5 This conclusion applies to both fossil and nuclear plants.

With large amplitude mass flows, the pressure drop across a ferrule is [304]

Pf = Pf (W2/pL; Ferrule Geometry) (3.5)

but because the density of liquid-phase water is essentially constant under all normal operating conditions, incremental pressure and mass flow changes for a ferrule are related by

dPf = —KfSWi; Kf > 0 (3.6)

where Kf is a constant specific to a ferrule’s geometry and the inlet flow Wi at the selected output power. It follows from Figure 3.5 that no change in overall differential pressure occurs when

0 = SPout = — Kf SW i + T53 (s)SW i + SPnoise (3.7)

where the noise term SPnoise arises from fluid turbulence and variations in pump speed induced by Grid-frequency fluctuations. Incremental flow stability by a choice of ferrule geometry can therefore be engi­neered from

By analogy with a SISO unity feedback system, Davis and Potter [83] originally in the context of SGHWR described —T53(s) as the “open loop” transfer function, and by analytical linearization derived transfer functions for the three different water-phase zones in Fig­ure 3.4. Suitable ferrule geometries to cope with different load factors and flow distribution in the lower plenum were then selected by Nyquist diagram techniques. As an alternative, Knowles [117,128] perturbs comprehensive non-linear simulations to achieve the same end: but on the basis of the above more rigorous state vector formulation. Nevertheless, the original simplified analysis is sound and it illustrates the considerable simplification achievable by engi­neering insight and industry specific experience. However, as with all linearized models, confirmation by a full non-linear simulation is absolutely necessary.

Severe Accidents would result with corium temperatures in the range [59] 3500 to 5000 K, for which Planck’s Black-body radiation spectra
[218,219] W(l) in Figure 5.6 has an effective waveband of 0 < l < 5 mm. Similar to neutrons, the probability of an interaction

13

between an EM wave and the atoms or molecules in a medium is found to increase with its density and thickness. Accordingly, it is reasonable to postulate that the absorption of thermal radiation in a steam film depends on the product of its pressure P and thickness L. Though Doppler broadening of absorption bands also occurs with increasing temperature, the decrease in density at constant PL can be expected to predominate. With these principles Hottel [219] successfully correlates seven different

X-ray studies [16] might have prompted the original conjecture.

independent data sets for the total emissivity (= absorptivity) of steam as a function of temperature by a family of curves indexed by constant values of PL. For example, the total absorptivity of a 100 mm thick steam film at 1 MPa is derived from his graph at T(K)as

a = -3.2 x 10—5(T — 1944)) + 0.055 (5.18)

More generally, Hottel’s correlation and data in Ref. [233] establish a largely insignificant absorption of thermal radiation in the steam film around an evolving coarse mixture. The total emissivity of a water surface is 0.96 [218], so it acts as a perfect absorber for present purposes. Over the waveband 4.58-6.47 mm the total emissivity of solid or liquid urania measures as 0.82 [220], and so it can be regarded as a gray emitter. On this basis the thermal radiation flux entering the interfacial liquid in Figure 5.4 is[84]

frad = гмs(T4MB — TLg) (5.19)

where

гм — Emissivity of UO2 = 0.82

TMB; TLB — Interfacial temperatures of melt and liquid (water), respectively

s — Stefan—Boltzmann constant = 5.67 x 10-8 W/m2 — K Because

TLB ~ TMB=10

then to a close approximation

frad = гмsT4MB = гм j W(l)dl (5.20)

0

where

W(l) — Planck’s radiation intensity function (in Figure 5.6)

The absorbed thermal radiation flux fab in a slab of incremental thickness Sz is generally specified by

A(1, Sz) — spectral absorption factor = 1 — exp (—a^Sz) al — spectral absorption coefficient

Measured values [221,222] of a(l) for water at 1 bar and 20 °C are graphed in Figure 5.7. As a result of Doppler broadening, increases in temperature of over 20-60 °C decrease the resonant amplitude at 2.95 mm by around 25% but pressure has little effect [223] because water is relatively incompressible. Table 5.4 provides values of the absorption factor A(1, Sz)for a range of wavelengths and water thick­ness (mm). In the waveband 0 to 2.5 mm, less than 5% of a radiation flux

„ 10°

T

e

Figure 5.7 The Absorption Coefficient of Water at 20 °C and 0.1 MPa

is absorbed over the first 5 mm from an interface. For corium at 3500 K over 87% of the radiated power lies in this waveband [218] with an even larger fraction at higher temperatures [59]. Though the total radiant flux at 3500 K evaluates from equation (5.20) as 7MW/m2, it follows that less than 0.3MW/m2 can be absorbed in this crucial interfacial region. By comparison, Table 5.2 reveals an average molec­ular conductivity for steam that is well in excess of 200 mW/m — K, so the corresponding heat flux across a typical 100 mm film with a temperature difference of at least 3000 K is

fconduction0200 x 10—3 x (3000/10—4) = 6 MW/m2

Furthermore, over an incremental time 8t heat absorbed at a plane surface approximately diffuses the distance [224]

d ~ V4 a8t (5.22)

For water and a typical steam film destabilization period of 20 ms

awater = 0.16 x 10—6 m2/s so d = 3.6 mm (5.23)

Consequently the radiant heat absorbed by water beyond 5 mm can hardly influence film stability. It is therefore concluded that molecular conduction across a steam film is the effective stabilizing heat — transfer process. Several published simulations [198,225,226] of steam film destabilization omit the effect of a wavelength-dependent absorption coefficient on the radiant energy absorbed by the sur­rounding water.

Monatomic and symmetric molecules, like those of sodium vapor, undergo neither vibrational nor rotational transitions. Also symmetric molecules have no electrical dipole moment, so they can neither significantly absorb nor emit radiation by vibration or rotational bands. It follows that gases of such molecules are transparent to thermal radiation at low to moderate temperatures [218]. At high temperatures, however, these gas molecules can radiate or absorb appreciably by electron bound to bound or bound-free transitions. However, the asymmetric molecules of steam have all these degrees of freedom yet still absorb negligible amounts of thermal radiation. A fortiori, the same must be true for sodium vapor. For a good electrical conductor, like liquid sodium, the effective total absorption length lab can be estimated from the skin-depth equation [227] of EM wave theory

where

kGB — thermal conductivity of interfacial sodium vapor

@T

@x GB

Wind is a costless, inexhaustible but intermittent energy source. Early twentieth century wind turbines were domestic multibladed fixed-pitch metal machines. Though aviation developments during World War I led to higher efficiency two — and three-bladed rotors [28], output powers before 1945 were generally no greater than 5 KW. A notable exception was the 1.25 MW variable-pitch machine on Grandpa’s Knob (Vermont, US), but after just 6 years in service one of its 8 ton metal blades fractured. Now lighter composite blades, power electronics and control schemes [29] result in mechanically reliable 2 to 3 MW rated machines with 20 to 30 year life expectancies. These are frequently deployed for individual factories or in “farms” of as many as 100 units to enable a cost-effective Grid network connection [30,31]. Powerful motivation for the present commercial developments of wind power emanates from the escalating costs of fossil fuels and the strident pandemic voices urging less global pollution.

An idealized fluid dynamic model [28] for the steady-state output power P of an isolated wind turbine reveals the engineering features necessary for materially sized power generation

P = CppAV 3 (1.5)

where

Cp — power coefficient; p — density of air, which at STP =1.29 kg/m3

A — area swept by blades; V1 — steady incident upstream windspeed

Because the density of air is so small[7] commercially sized power generation requires very large diameter blades. Contemporary 3 MW rated machines have 60 m diameter blades elevated to a total height of 115 m, and so are particularly visually intrusive [324]. Furthermore the 100 units of the Isle of Thanet 300 MW wind offshore wind farm [30,31] occupy 3500 hactares or about 3500 football pitches. Land shortages and therefore prices [20] in the United Kingdom dictate the construction of mainly offshore farms. In contrast, the complete nuclear reactor site at Winfrith occupied [32] about 31/2 hactares and reliably[8] generated its rated 100 MW for around 25 years. Moreover, its structure was designed to be compact, and apart from a water vapor plume all was invisible[9] from the main A352 road about 1 km away.

Equation (1.5) also shows that accessible power is proportional to the cube of the incident wind speed, so the geographical location of a wind farm is very important. As early as 1948 a UK government committee organized a survey of national onshore windspeeds [28]. Since then many countries have produced their own contour maps of annual mean wind speeds (Isovents) with coastal and offshore regions appearing to be the most economically favorable. Though Grid connections using synchronous or induction generators [35] have not encountered insurmountable difficulties [28], UK offshore wind farms now generate three-phase rectified dc current with onshore Grid-tied inverters [33,34] so as to effect an efficient and more economic Grid connection. Specifically, cable costs are determined by both the peak transmitted voltage and current, as heating by the latter reduces the breakdown voltage of its insulation. For a given cable, the ac and dc powers transmitted are

Pac = %VI cos f and Pdc = VI (1.6)

where

V, I — peak transmitted voltage and current respectively, cos f — power factor of the Grid network

(‘ 0.8 lagging for the United Kingdom)

It is seen that a wind farm with a dc cable link carries twice the power for the same installation cost.[10]

Table 1.4

Annual Wind-Power Data 2005-07

United Kingdom United States

Country Spain Denmark Germany

Capacity factor (%) 24.6 24 16 28 16-20

MCR wind power 41 4 81 5“ 105

(GW)

and the Netherlands.[11] However, if a shortfall in UK power is drawn from a continental connector, it would be at a premium price: especially in mid-winter. Furthermore, though Norway has an installed hydro­capacity [43] of about 30 GW, its peak demand in winter is around 22 GW, so this country could not offset [44] a major meteorologically induced disruption to the projected UK’s wind power generation. On the other hand, because reliable predictions of high barometric pressure zones can now be made several days in advance, UK-sited fossil and nuclear stations would be able to increase their outputs at demanded rates well within operational constraint limits.[12] Because nuclear power plants are capital-cost dominant and fossil stations are fuel-cost domi­nant, it is cost-effective for nuclear stations to supply the largely predictable daily base load, and for fossil stations to supply the more rapidly varying load excursions. For this latter purpose a number of fossil stations operate at around 80% of nameplate ratings (MCR) to provide a so-called “spinning reserve.” Sudden very rapid demands such as the unexpected disconnection of a large generating unit or a pause in a very popular TV program are also buffered by the pumped storage schemes at Dinorwic [40] (1.8 GW), Ffestiniog (0.36 GW) and Ben Cruachan (0.44 GW) but due to the very special topography required it is unlikely that other such suitable UK sites can be found. It is to be concluded that a “mix” of wind, fossil and nuclear stations has become necessary for a flexible, secure and economical UK power supply.

Total capitalization of the Isle of Thanet wind farm [31] is $1353 M or $4.5 M per installed MW. However, in addition to the loss of revenue from an inevitable shortfall of delivered power, there are the presently uncertain capital and operational costs of the necessary backup systems [52]. These depend on the future chosen “mix” of fossil and nuclear plants together with charges levied for power dispatched over the as yet unbuilt European Supergrid. Currently quoted costs for wind generation are therefore subject to considerable uncertainty, which perhaps led the Royal Dutch Shell Company to withdraw its support from renewable energy schemes [45]. On the other hand the UK Sustainable Develop­ment Commission [46] reports that “the economics of nuclear new — build are uncertain,” but this statement is contradicted by decades of worldwide practical experience—especially in the Far East. It is possibly of note that the UK’s coalition government disbanded [47] this Commission in July 2010.

Finally, the capacity factor of UK wind turbines in Table 1.4 appears heavily biased: possibly toward offshore systems. According to the UK regulator OFGEM that for the nominal 2 MW Reading city installation was just 15.4% during 2010. Even more significantly the market value of its electricity production was £0.1M, but thanks to a government subsidy, its owner Ecoelectricity received £0.13M. Under these conditions, large-scale wind power is an excellent investment for UK utility companies! Clearly, the true cost per actual MW generated, as well as environmental impacts [324] and Grid compatibility should be properly considered when deciding the future “mix” of UK generat­ing plant.

During Severe Accidents quantities of corium as a melt or slurry might slump into the lower head of the pressure vessel.[114] Its sensible and decay heat would then be transferred to the structure whose creep strength progressively decreases with temperature. To mitigate this potential cause of a catastrophic rupture, some PWRs have their lower structures submerged in water [315]. Temperature increases in the pressure vessel are clearly dependent on a debris-bed’s morphology, as voidage for example decreases molecular conduction and thereby extends the margin-to or time-to failure. The Three Mile Island incident in 1979 has created the (presently) one and only authentic water reactor debris-bed whose importance to safety assessments motivated an OECD-funded investigation into its relevant character­istics [316].

For a margin-to failure calculation data are required on the physical, metallurgical and radiochemical composition of the debris. Its density, porosity and particle-size statistics broadly characterize morphology, while its metallurgy indicates initial temperatures, melting points, cooling rates and oxidation levels. Radiochemical data completes the required information with regard to decay heat production. “Loose” debris with sizes exceeding 150 mm were found to be broadly sur­rounded by denser material with sizes less than 75 mm. Measured porosities of samples varied markedly between 5.7 to 32% with an average11 of 18 ± 11%. Chemical analyses reveal that 97% of the debris had the broad composition (U; 70%), (Zr; 13.75%) and (O; 13%) by weight of mixed uranium-zirconium oxides, which supports simula­tions having a chemically homogeneous melt pool [93,319]. Some samples of these oxide mixtures contained stratified layers of “pores” which are suggested to result from steam or metallic vapors locked in situ as the corium became more viscous prior to solidification. Debris metallurgy indicates gradual cooling rather than rapid quenching, and that single component regions solidified first. The lowest temperature for uranium to dissolve in zirconium is predicted to be around 1760 ° C, which is about 1000 °C below the melting point of urania. Metallo — graphic and scanning electron microscope examinations reveal that the maximum temperature for a well-mixed solid solution of uranium- zirconium oxides is between 2600 to 2850 °C. Accordingly, the simu­lated initial temperature of corium entering the lower head is taken as 2600 °C. Finally, chemical analyses of the debris samples enable the decay heat to be calculated as 130 W/kg and 96 W/kg after 224 and 600 min respectively.[115] [116]

If no MFCIs occur during a Severe Accident, an increasing mass of molten corium would first vaporize any residual water as it slumps into the lower head. Sensible and decay heat would then be transferred by turbulent natural convection into the pressure vessel and by thermal radiation into the degraded structure above [318]. A likely scenario is a multi component liquid pool encased in a growing solidified crust which forms on its free surface and on the vessel’s wall. Sohal et al. [315] provide a thorough assessment of available experimental corre­lations for turbulent natural convective heat transfer between molten corium and solid surfaces. With internal heat generation the recom­mended correlation takes the form

Nu = a(Ra’)b; Ra’ = gbqvL5/avk (7.5)

where Ra’ is the Internal Rayleigh Number and

g — gravitational acceleration; b — thermal expansion coefficient qv — volumetric heat generation rate; L — a “characteristic” length a — molecular thermal diffusivity; y — kinematic viscosity k-molecular thermal conductivity; a, b — parameters to match the data

Unlike turbulent flow in pipes and laminar flow aerodynamics, the characteristic length L here is open to more subjective interpretations such as

i. The radius of a pool’s top surface

ii. The maximum depth of a pool

iii. The average of 1 and 2 above

iv. The radius of a hemispherical pool equivalent to the volume of the cylindrical one

If the exponent b in equation (7.5) equals 0.2, the characteristic length exactly cancels out. Because the experimental data is best correlated with b ‘ 0.2 predicted heat transfer coefficients are quite insensitive to the actual choice. Table 7.1 depicts the recommended values of (a; b) with option 3 to give a regression within about13 ± 10% of the data from six water or Freon experiments. Though these experiments

This author’s own estimate from graphs in Ref. [315].

involve radically different fluids compared to corium, it should be noted that the burn-out margin for the SGHWR derived from a low- pressure replica-scaled Freon rig accurately matched later measure­ments derived from a prototype water-cooled rig at 62 bar [63,297]. For situations with Internal Rayleigh Numbers outside those in Table 7.1, the nearest correlation should be used.

An alternative situation to a developing homogenous melt pool is one with a purely metallic layer floating on its upper surface. No internal heat generation occurs within this superficial layer for which turbulent natural convective heat transfer is correlated by

Nu = a(Ra)b; Ra=gfi(AT )L3/av (7.6)

where Ra is the External Rayleigh Number and

AT — local temperature difference between the bulk liquid and its boundary

Table 7.2 depicts the recommended values for (a; b) with option 3 as the characteristic length. No well-tested correlation for horizontal flow is apparently available, but as the contact area with a pressure vessel is relatively small, an average of the upward and downward flow coef­ficients is suggested [315] as adequate.14

Molecular heat diffusion into the particulates of a debris bed or in the reactor pressure vessel can be characterized by the axisymmetric form of

@ T

— = a [V2T + s/k (7.7)

Two terms from equation (7.6) added together with these (a ; b)s.

where

a — thermal diffusivity; к — thermal conductivity s — volumetric heat generation rate

Flow through porous media was first quantified experimentally by Henri Darcy in 1856 in connection with aquifers that supplied the civic fountains of Dijon. Under the essentially laminar flow conditions the usually intractable Navier-Stokes equations [256,268] become analyti­cally solvable to generalize Darcy’s empirical formula as

Z

qv = — VP (7.8)

m

where

qv — volumetric flow rate (m/s); P — pressure (Pa) m — dynamic viscosity (kg/ms); Z — permeability

The corresponding flow velocity is given by

V = qv/h; h-porosity (7.9)

with the Reynolds Number

Re = pVD/m (7.10)

Here the characteristic dimension D is taken as the smallest sieve-size to allow free-passage for 30% of all particles, and equation (7.8) is valid for Re <10.

In addition to the above equations and correlations, simulations of debris-bed cooling by the SCDAP/REALP5 code [319] involve

i. The usual two-phase fluid conservation equations

ii. A range of possible debris-bed permeabilities

iii. The oxidation of intact and slumped cladding under re-flooded conditions

iv. The penetration of melted core-plate into existing porous debris, and its effect on heating up the lower head

v. The re-slumping of previously frozen fuel-cladding

vi. The up-take of oxygen and hydrogen under conditions of steam starvation or rapid changes of temperature, etc.

The “stand-alone” development of SCDAP began early in the 1970s to assess the progressive oxidation or melt-down of fuel elements and control rods. Two-phase fluid dynamics patently interacts with these processes, so in 1979 it was merged with the RELAP5 code whose own development had started previously in 1975. Thereafter evaluation and validation of the combination’s phenomenological-based modules have been ongoing. It should be recalled that the accuracy of degraded core dynamics is not the usual ± 10% for engineering design purposes, but it is required only to be demonstrably conservative and bounded. In addition to assessing the margin-to failure of a reactor’s pressure vessel, degraded core calculations bound the amount of liquid corium and water in the lower head during a Severe Accident, and thereby the yield of potential MFCIs.

Grid-connected power stations form a diverse interconnection of fossil, nuclear and renewable units whose objective is to meet the area’s power demands as safely, economically and securely as feasi­ble. On a continuous basis centralized management selects genera­tion from those available units best able to meet these objectives. Sinusoidal ac power at nominal frequencies of 50 or 60 Hz has many advantages from the viewpoints of generation, transmission and utilization [35]. Specifically, two-pole cylindrical alternators with water-cooled conductors provide the highest commercially available power generation per unit volume, but even these machines are limited to around 3000 or 3600 rpm which corresponds to 50 or 60 Hz respectively. With present units of between 100 and 660 MW this rotational speed is near optimum for steam turbine efficiency and blade reliability. Consequently a turbine and an alternator can be directly coupled together with a bolted flange to avoid the complexi­ties and inefficiencies of high-power gear trains. Electrical transmis­sion losses countrywide are reduced by the use of high voltage (e. g., 400 kV) to current ratios, but use in industrial and domestic situations requires relatively lower voltages (440 V or 230 V). For frequencies of 50 or 60 Hz, transformers provide a highly efficient (>96%) and reliable execution of this task.[38] However, as explained in the context of equation (1.62), high voltage dc is more cost-effective for cable transmission. A similar argument for dc transmission also applies to very long (~650km) overhead lines for which corona losses [147] increase with line voltage[39] and length.

Figure 1.1 illustrates the partially predictable seasonal and daily changes in the power demands on a Grid network. In addition, there are unforeseen material fluctuations induced for example by the start-up or shutdown of large industrial plant, or the substantial loss of a 400 kV Supergrid transmission line. Consequently, instantaneous electricity generation and demand cannot be identically matched by pure prediction, and thermal constraints also restrict each station’s rate of change of power.[40] As electricity cannot be stored in the required quantities, a mismatch between instantaneous Grid generation and demand must be accommodated in the short term by thermal energy stored in the coupled generating units and in the rotational energies of all Grid-connected generators and motors. Because the synchronizing torque per degree electrical of an ac machine is so large compared to its inertia [35], all directly connected ac machines can be considered for present purposes to be “locked” together at a synchronous speed V rad/s given by

Synchronous speed (V) (3.9)

= 2p x Grid frequency fG)/pole-pairs of a machine

where fG — Grid frequency (Hz).

Thus mismatches in Grid power appear throughout as a common frequency fluctuation about the nominal, and three principal reasons for its tight constraint now follow.

Firstly, each turbo-alternator is a multi-machine system of inertias linked by resilient shafts and therefore exhibit mechanical resonances at certain critical speeds [148] above and below the nominal 3000 or 3600 rpm. Unless the Grid frequency is controlled within narrow limits, these resonances could persist long enough to inflict serious damage. In practice during the Grid synchronization of a turbo-alternator these resonant speeds are accelerated through as quickly as possible.

Secondly, a large number of industrial and domestic consumers are still metered by electro-mechanical units which were installed by virtue of their good stability of calibration, wide measurement range and low cost of mass production [149]. Measurement accuracy with these single — and three-phase induction instruments depends on maintaining a 90° phase relationship between line voltage and the voltage coil’s magnetic flux. Though a degree of compensation is provided by “shaded poles,” measurement errors still occur when the frequency deviates from the calibration frequency of 50 or 60 Hz. Because the United Kingdom’s national electricity consumption is currently of the order of 350 TWh/year, even very small errors are fiscally significant.

Accordingly, UK consumers are protected by a Parliamentary Statute that requires the 24-h average deviation to be within ± 0.5 Hz, though National Grid plc self-imposes stricter limits of ± 0.2 Hz. Measure­ments [151] in 1972 characterized UK Grid fluctuations by a Normal distribution having a standard deviation of 0.05 Hz, which is consistent with the now continuously updated data on the Internet [150]. Safety trip limits for UK steam turbines impose operation between 48 and 52 Hz.

Finally, synchronous[41] or induction motors [35] are generally used to drive power station boiler feedpumps, whose pressure rise is approxi­mately proportional to the square of their rotational speed. When power demand exceeds generation, the Grid frequency and feedpump speed fall, so boiler pressures are reduced contrary to the required increased steam flow and alternator output. On the other hand, when power demand is less than generation, feedpump speed rises so boiler pressures increase, and the life expectancy of turbine blading in its low-pressure cylinder could thereby be prejudiced by a potential over­expansion of the steam [117]. A suitably controlled boiler inlet-pressure is therefore necessary, so an excess feedpump pressure must be devel­oped and the flow throttled to provide the required operating condi — tions.[42] Thermodynamics show that the steady-state power required for an incremental pump pressure change dP is

Pumping power = (W/hp)SP

where

W — mass flow rate (kg/s) h—pump efficiency p — water density (kg/m3)

The above conditions imply that a +1% frequency deviation corre­sponds to an extra pumping-power loss of about 1.6MW(e) for a 1200MW(e) station having an ac motor-driven feedpump [80].

The required control of Grid frequency is achieved by closely balancing instantaneous generated power with demand. For this pur­pose previous statistics as well as meteorological forecasts and mass entertainment data are involved to continuously predict demand so as to accommodate intrinsic plant start-up delays and thermal rate con­straints. In the United Kingdom, regional quotas are allocated on the basis of these predictions with consideration for plant outages and the overall security of supply. Accordingly, a Grid control region has more nominal capacity than historic demands. Individual stations are initially selected for operation by regional controllers in terms of a Merit Order based on fuel costs (£ per kWh) and reliability. This selection clearly favors relatively high capital but low fuel-cost nuclear stations, though these can no longer meet the minimum UK consumption. Thus contri­butions to the daily predicted load are required from fossil and renew­able plants. When wind turbines are available, they too appear as an economic option for this purpose. However, in a UK winter, extensive areas of meteorological high pressure would render a large number of turbines impotent, so that fossil-fired units are required for balancing during this season of greatest demand. As described in Section 1.7 combined cycle gas turbine (CCGT) plants have progressively replaced less thermally efficient and more polluting end-of-life coal-fired stations since 1991. Though these factors in part favor the selected operation of CCGT units, the principally coal-fired 3960 MW(e) Drax plant is usually operational by virtue of its high capacity factor (‘75%) and relatively high thermal efficiency11 (‘40%). Due to the absence of ponderous coal pulverizers and a more favorable fuel- combustion chemistry,[43] [44] CCGT generation has the additional advantage of faster dynamics for meeting major predicted and unscheduled load changes. Consequently a number of CCGT stations are operated at around 75% of full-load (a spinning reserve) or at almost zero output (hot starts) to meet these load changes. Currently the United Kingdom has access to some 650 MW(e) of auxiliary diesel or gas turbine units along with 1800 MW(e) from the Dinorwic pumped storage scheme having a 10 s access time [40], and 2000 MW(e) of rapidly disconnect — able load. With many individual stations maneuvering to effect an instantaneous Grid power balance there is clearly the problem of overall network stability to be addressed.

In this context, the energy stored in an inertia (I) rotating at V rad/s is

E = 1/2.i V2

so the rate of change of energy as it is delivered or withdrawn is

Power = E = IV (3.10)

dt

As described above, the speeds of all Grid-connected units can be considered locked together at the existing synchronous Grid frequency fG. Because Grid frequency is necessarily maintained within ±0.5 Hz about the nominal 50 or 60 Hz, equation (3.10) can be approximated by

Grid power perturbation d Power = KRTfG (3.11)

where RT is the sum of name-plate ratings for all synchronized

13

generators and motors. An allowance for some multi-pole pair units is accommodated by

0.2<K<0.4per VA of RT (3.12)

Coupled (or boiler-follows-turbine) stations buffer frequency fluctua­tions, but decoupled (or turbine-follows-boiler) stations contribute only to RT. Figure 3.6 illustrates stability considerations for a hypothetically isolated coupled controlled station. As a result of meeting physical rate constraints and a circumspect engineering design,[45] [46] its open loop frequency deviation to output-power transfer function can be approxi­mated by a SISO function H(s) which relates just the measured frequency deviation through the turbine control-valve dynamics to a release rate of stored energy in the plant. By means of comprehensive non-linear simulations, a set{H(iw) g can be derived for a representative number of load factors including synchronization. Simulations then confirm that the isolated station can deliver demanded power up to its
name plant rating, but the impact of its Grid connection on the stability of the overall network needs to be addressed as in Figure 3.7.

Intuitively it might seem that a parallel combination of individually stable isolated units would always be stable in the coupled-control mode, but theoretically this is untrue. Consider just two such stations with identical nameplate ratings R, but with different transfer functions H1(s) and H2(s). Equation (2.10) and Figure 3.7 yield the open loop Real Frequency Response of this hypothetical arrangement as

[H1(ia)+H2(ia)]/iaK2R = l/2[H1(im)/imKR + H2(im)/imKR]

If at some frequency V the individual station responses were complex conjugates of each other, then the open loop response function of their parallel combination would be

Re [H1(iv/iVKR] = Re [H2(iv)/iVKR]

I National Power Demand |

t— Hi do))

f set point

Power output change from Station К

Figure 3.7 Grid Network Stability Model

Though each station is stable in isolation under coupled control, Figure 3.8 shows they could be unstable in a parallel combination. However, the depicted situation patently cannot arise if their open loop frequency responses do not cross the negative real axis. That is, the stations are each unconditionally stable.[47] Accordingly, the sufficient Grid stability criterion [80,117] devised by Butterfield et al. [150], is

“The Nyquist Diagrams for each station in conceptual isolation must imply unconditional and adequate stability at all output powers.”

Given a stable multi-station Grid network with totalized nameplate ratings RT, there is the academic question—what if a conditionally stable station with coupled control and a nameplate rating R were then to be synchronized? After connection the modified open loop response is derived from Equation 2.10 and Figure 3.7 as

— [RT (HT (iv) / itvKRj)+ R(H(iv)/ivKR)] (3.13)

Rt + R

where:

K

Ht (iv) = Hk (iv);

k=1

Hk(iv) — transfer function for kth coupled controlled station

and

H(iv) — transfer function for the additional coupled station

Because for the United Kingdom

20GW <RT < 60GW and R < 1GW then by defining

r = R/Rt < 1

equation (3.13) approximates to

(1 — r)[HT (iv) / ivKRT ] + r[H (iv) / ivKR]

Thus the connection of an additional coupled-controlled station affects stability margins by between 12/3 to 5%, which is negligible. If a decoupled station is synchronized, the open loop response of the Grid network becomes modified to

(1 — r’)[HT (iv)/ivKRT] with Г = R/(Rt + R)

which is again negligible.

These examples so far demonstrate the value of

i. a comprehensive non-linear simulation,

ii. engineering insight and experience,

iii. the utility of Real Frequency Response functions (Nyquist diagrams) in solving complex practical problems.

Though these “working functions” evolve as more tractable SISO systems, their proper formulation is rooted in MIMO system theory.

Finally, popular UK media often comment that some particular Grid-connected wind farm can supply a certain number of homes. Such

statistics often assume that all turbines are providing their rated maximum outputs and a daily average energy consumption of about 1V2 kW per household. Table 1.4 shows that the capacity factors of wind turbines is around 20%, so the predicted number of homes should at least be reduced by a factor of 5. During intervals in globally popular events like the World Cup, a large number of homes simultaneous brew tea or coffee and a typical electric kettle alone consumes 2 kW. In fact at the end of a 1970s Miss World competition UK power demand surged at 2 GW/min. As just described Grid operation necessitates a close instantaneous match between generated and demanded powers, and not daily averaged values. Such media statistics are therefore fallacious and suggest quite unrealistic contributions from wind energy. Adopting their same argument would suggest that 2 kW electric kettles could be properly fused on the basis of a daily averaged milliampere current.

Under conditions of thermodynamic equilibrium the Maxwell- Boltzmann probability density function characterizes the velocities of ideal gas molecules. Assuming isotropic scattering [58], the mass flux of ideal gas molecules traversing one way through a conceptual plane sur­face is derived [210] on this basis from classical kinetic theory. Ignoring the significant inter-molecular attractions in the liquid and vapor states (i. e., the Joule-Kelvin effect), applications of this classical analysis to the liquid-vapor interface gives the net mass flux in the liquid as [241]

where

GB — interfacial mass flux (kg/m2 — s); R — specific gas constant PGB, TGB — interfacial vapor pressure and temperature, respectively TLB — interfacial liquid temperature s — condensation coefficient (0 < 0 < 1)

It is recommended [229] that the molecular structure function F(s) takes the form

where:

g — specific heat ratio of the vapor (Cp/Cv)

Equation (5.27) correctly implies a net mass flux of zero when saturated liquid and vapor co-exist at an interface under conditions of thermodynamic equilibrium. However, under non-equilibrium condi­tions it loses some accuracy. Specifically, apart from the omission of inter-molecular forces, vapor molecules near an interface originate as

i. Those having just emerged from the liquid

ii. Those having diffused from a higher temperature near the melt

iii. Those reflected from the liquid surface

This motley ensemble is unlikely to be characterized by a Maxwell- Boltzmann distribution as required for the validity of equation (5.27). Moreover, the rigorous definition [3] of temperature is in the context of thermal equilibrium, so with net interfacial mass transport neither TGB nor TLB strictly exists. Nevertheless there appears no alternative to equation (5.27), and for simulation purposes they are taken as extrap­olations of heat diffusion calculations in the two media. Under net evaporation or condensation equation (5.27) predicts an interfacial temperature jump (discontinuity) that is confirmed by experiments with liquid metals [230,231]. An early simulation of vapor film destabilization by Corradini [198] assumes both interfacial fluids to be saturated, but his later corrected model [226] reveals the marked effect of this discontinuity on computed transients.

A condensation coefficient is in essence the probability that a molecule impinging the interface enters the other phase. Mills and Saban [232] comprehensively review many published analytical deri­vations, but conclude that reliance is best placed on experimental data. They consider the most reliable measurements for water to be those by Nabavian [233], Berman [234] or themselves which together give

0.35 < a < 1.0 (5.29)

After reviewing 11 independent publications on the condensation coefficient for various liquid metals over the pressure range 0.001 to 1 bar, Fedorovich and Rosenhow [231] conclude that

0.1 < a < 1.0 (5.30)

Results are tightly clustered for pressures no greater than 0.1 bar, but thereafter their dispersion increases. The wide uncertainties in
equations (5.29) and (5.30) are exceptional by twentieth century standards, and might well reflect the purity of the coolant. In fact experiments with a liquid metal indicate that the condensation coefficient decreases with increasing contamination [242]. Later labo­ratory measurements show that the coefficient assumes its maximum value of unity when the water or liquid metal is exceptionally pure [255], but in Severe Accidents a reactor coolant would be heavily contaminated. Consequently, because decreased interfacial condensa­tion saps less energy from an expanding MFCI bubble, the least of the above values for a condensation coefficient should be used in safety simulations.

Permanent gas molecules in sufficient numbers can seriously reduce the mass flow rate from industrial steam condensers by restricting access to heat transfer surfaces [219]. As a preventative measure, deaerators are installed in the feed-trains of power station boilers, where they also provide emergency supplies (see Section 3.4). In Severe Accidents hydrogen or fission product gases might similarly be expected to reduce interfacial condensation rates, and thereby conserve the energy of an expanding MFCI vapor bubble. However, fast reactor tests [228] show that collapse times of sodium bubbles are largely unaffected when contaminated with Xenon concentrations representative of spent fuel. Other laboratory experiments [236,237] with steam bubbles establish that condensation rates are reduced by less than 10% with the introduction of 15% molar concentrations of nitrogen. In both cases, the authors conclude that efficient turbulent mixing must exist within a collapsing bubble. No experiments concerning the effect of permanent gases on triggered vapor — film destabilization were found in the literature. From Table 5.2 the principal effect of hydrogen is seen to increase a film’s thermal conduc­tivity and therefore to a degree its stability.15

The above discussion describes the considerable uncertainties in predicted interfacial condensation rates. Nevertheless, Section 5.8 shows that conservative interfacial condensation rates largely account for the experimentally observed reduction in MFCI energies from the idealized isentropic Hicks-Menzies yields [85]. From the viewpoint of reactor safety assessments, the identification of a physical process to justify the extension of experimental 4 to 5% MFCI efficiencies to reactor-scale tonne-quantities is highly significant.

See Section 5.6.

The global industrial revolution in the late nineteenth century originated in the United Kingdom with coal powering steam engines and iron smelting. Now in the twenty-first century electricity generation by coal is constrained by economics, carbon emission penalties and the availability of cleaner natural gas [49]. Though coal remains the planet’s largest fossil-fuel resource [55] its large-scale utilization is presently incompatible with the pursuit of low carbon emissions. As well as carbon dioxide, other environmentally damaging combustion products [55] include sulfurous oxides and fly ash which contains mercury, arsenic and radioactive uranium and thorium. In fact without fly ash capture equipment, coal-fired stations would contribute signifi­cantly to background radiation. Table 1.5 shows the estimated coal

reserves [53] of all types17 for a number of industrialized countries in 2006-07. It suggests the strong motivation [50] to develop so-called Clean Coal technology for reducing pollutants and achieving fuller combustion by pulverization. Because nitrogenous oxides are produced at combustion temperatures above 1370 °C, temperature control between 760 to 927 °C eliminates these without the need for flue­gas scrubbers [50].

When finely divided limestone is intermixed with pulverized coal, 95% of the sulfurous precursors of acid rain are absorbed: but at the expense of larger carbon dioxide emissions. Present research searches for more suitable sorbants [50] and Carbon Capture processes [54]. By measuring the ratios of stable isotopes of carbon dioxide and noble gases, recent studies of nine gas fields in North America, China and Europe have established that underground water is the principal sink and has been so for millennia [54]. These experiments could provide a basis for validating mathematical models of future storage locations and for tracing captured carbon dioxide. However, on-going capture tests require 25% of the Longannet 2.4 GW station’s output [56] so that an economically viable process has yet to be developed. A sum of £1 billion was allocated for this purpose in the October 2010-UK Spending Review, but was declined by a consortium of Scottish Power, Shell, and National Grid.

Commercial quantities of natural gas were discovered in the North Sea during 1965, and since then in many other countries. Combined cycle gas turbine plants (CCGT) [51] have subsequently had a material impact on new-build generating capacity as illustrated [57] for the United Kingdom in Figure 1.2. In these, gas first powers a gas turbine whose exhaust via a heat exchanger provides steam for a conventional steam turbine with feed water heating and reheat to enhance thermal efficiency. With the lower cost CCGT configuration, an alternator is driven by gas and steam turbines sharing a common shaft, while with the more flexible but more expensive multishaft arrangement, each has its own alternator. Typical burnt-gas and steam-inlet temperatures for CCGT and coal fired plants are

Tccgt ‘ 1000 °C and Troal ‘ 570 °C (1.7)

Anthracite, coking, lignite, and steam.

For an ambient condenser temperature of 30 °C, the corresponding Carnot Efficiencies are derived from equation (1.2) as

hCCGT ‘ 76% and hcoal ‘ 64% (1.8)

but due to thermodynamic irreversibilities, the practical efficiencies achieved are

hCCGT ‘ 50% and hcoal940% (1.9)

The preferential installation of CCGT units shown in Figure 1.2 is now clear. Because investment in a privatized market is governed by a commensurate return on capital expenditure and associated risks, and because UKelectricity prices are set by those for CCGT generation [52] and infrastructure provision, utility companies are assured a fair and timely low-risk return. During 2011 CCGT stations delivered around 44% of the UK electricity: but what of the future?

With the reduction in North Sea gas production, the United Kingdom has now become a net importer and is therefore potentially beholden to the vagaries of international markets or the political whims of some exporters. Accordingly coal-bed methane, shale and conven­tionally drilled gas production are being actively investigated to regain a self-sufficient supply. Hydraulic fracturing [323] or “fracking” is particularly successful in speeding up gas flow rates from shale or other “tight” reservoirs to render them economical. This technology

involves unconventional horizontal drilling along a promising shale strata followed by the injection of high-pressure water and chemicals. The process has transformed US gas production from next to zero in 2000 to an almost self-sufficient 13.4 billion cubic feet per day. Cuadrilla Resources plc claims to have discovered a potential 200 trillion cubic-feet shale gas reservoir in the northwest of England, and the British Geological Survey suggests a total onshore resource of some 1000 trillion cubic-feet. However, test drillings have elicited small earth tremors[13] at Blackpool and there are further concerns regarding the contamination of drinking water supplies. Consequently commercial development has been halted until the Department of Energy and Climate Change has completed a review. Even if an abundance of onshore gas becomes available, a detailed study [57] reveals that CCGT generation alone could not fill the UK energy gap within the ratified carbon emission targets [1,52], so that a nuclear component appears as the necessary reliable complement in the eventual “mix” of generating stations. To achieve an economical fuel cycle (burn-up) and the inter­vention of safety circuits nuclear stations must supply the more slowly varying and largely predictable national base load.[14] Accordingly CCGT plants with preferably Lamont boilers [117] are better able to provide the more flexible and faster responses to rapid unscheduled changes in Grid power demand.

Sizeable UK oil-fired power stations like Poole and Marchwood were decommissioned over 10 years ago, but a number of small (<10MW) units still exist to buffer unexpected peaks in national demand. These relatively low thermal efficiency, but highly responsive “peak lopping” units presently contribute around 1% of national energy consumption [49].