An abrupt release of pressurized Argon from the MFTF charge con­tainer and a record of the cover gas pressure transient were made as part of rig commissioning. Various one-dimensional fluid dynamics models proved unsuccessful in calculating this transient despite their use in other MFCI simulations.27 A spatially higher dimensional model is therefore necessary for authenticity. In fact a sufficiently accurate reproduction of this MFTF commissioning test became the first step in the validation of the MFCI dynamics code BUBEX. Because reactors and MFTF have a fair degree of axial symmetry, two-dimensional spherical coolant dynamics appear promising. In fact the two-dimen­sional code SEURBNUK had been extensively validated by the earlier WINCON experiments [276] that used scaled models of the fast reactor geometry in Figure 5.10 and contrived low brisance chemical explo­sives. Accordingly, the comprehensive MFCI model BUBEX was developed to replace SEURBNUK’s far simpler representation of a chemical explosion.28 Salient features of BUBEX are next outlined along with its application to the urania-sodium MFTF experiment in Figure 5.11, which presents just a single interaction.

Inviscid fluid dynamics can be described in general by the Eulerian conservation equations [256]

dp

+ V. p" = 0 (mass) (5.65)

See Refs. [249-254].

28 Essentially the expansion of a perfect gas.

Figure 5.11 Cover Gas Pressure Transient after an MFCI in the SUS01 Urania-Sodium Experiment

——Ь V. pIu + PV. u = 0 (energy) (5.67)

SEURBNUK solves the above equations using the Mark and Cell Method [257] assuming adiabatic flow and with boundary conditions corresponding to a cover gas space, internal structures and a chemical explosion. As illustrated by Figure 5.12 for the test in Figure 5.11, the interaction of a bubble with internal structures creates an irregular geometry so that calculations of the condensation mass flux and heat transfer to a surrounding coolant would be formidable. However, the simplifying approximation of a spherical bubble having the same instantaneous volume minimizes both the condensing and external heat transfer surfaces and thereby maximizes the computed MFCI yield. Provided that corresponding predictions evolve as small enough, the approximation is sufficient for reactor safety assessments.

Bubble growth in MFTF experiments occurs over some 20 ms, whereas vapor film destabilization in Figure 5-11 occupies just 10 ms. The linearized dynamics of equation (5.17) imply that longer time­scales allow the development of slower and longer wavelength

Figure 5.12 SEURBNUK Bubble Geometry in the Urania-Sodium Experiment of Figure 5.11. The Condensation Coefficient is 0.3

Rayleigh-Taylor instabilities for which viscosity is evidently less stifling. Experiments using ethanol-air [258] or liquid-vapor [259­261] systems show that planar interfacial decelerations create highly distended interacting “spikes” that eventually detach. Corradini [254] correlated liquid entrainment into vapor bubbles for scale-model tests at the Stanford Research Institute [264] and Purdue University [265] by

CrT = 11-6Рі[аь/(рь — Pg)]1/4€ for € > 0

(5.68)

0 otherwise

where

sL — surface tension of the liquid; € — a largely planar acceleration

However, its accuracy for MFCI simulations is compromised by the one-dimensional planar accelerations and the absence of developmental dynamics. Significantly, a lengthy numerical solution [263] of the non-linear R-T equations [262] for a spherical interface between

inviscid fluids indicates an entrained mass flux some 5 to 10-times less than equation (5.68) when radial deceleration R replaces €. In the absence of a real alternative, R-T entrainment mass flux GRT is represented in BUBEX by

t(t)GRT + GRT — Crt

where CRT is specified by equation (5.68), R replaces €,

(5.70)

and t*(t) is defined by equation (5.17). With decreasing deceleration t*(t) becomes ever larger, and to prevent numerical overflow t(t) is artificially restricted to 10 s. However, there are no adverse conse­quences as the durations of MFTF transients are markedly shorter (< 1 / 10s). Once an interfacial liquid accelerates into its vapor, the interface restablizes but no information on this behavior appears available. Under these conditions, BUBEX arbitrarily assigns the time constant of 1 ms. The above uncertainties dictate that MFCI simulations should be scoped with 5 to 10 factor scalings of the above mss flux GRT. In this respect, Severe Accident calculations are only required to be conservative rather than to meet the ±10% accuracy for engineering design.

Liquid entrainment into an MFCI bubble also occurs as the inter­face is scoured by turbulent vapor [236] or as it brushes around damaged internal structures [71]. There is a paucity of data on entrained droplet sizes, but aerosol experts [171,266] suggest a range of 1 to 100 mm. By virtue of their large surface area to mass ratio, entrained droplets are potentially efficient removers of released fission products by dissolution or adhesion [104,171,266,267]. Asymptotic values for the dominant thermal time constants of the suggested size range are obtained from equation (5.54) as

0.15 ms < t < 1s for water 0.53 ms < t < 3.6 ms for sodium

so smaller droplets are likely to be vaporized within a turbulent bubble. Their radioactive burdens would then be precipitated as larger

Table 5.5 Ratio of Expectations in Equation (5.72) for a	<< b
Probability	Falling	Symmetric	Rising
Density	Triangular	Triangular	Triangular	Uniform
£(D2)/£(D3)	1.67/b	1.56/b	1.25/b	1.33/b

agglomerates. Those larger than about 10 mm would rapidly settle-out under gravity to be trapped in the turbulent coolant. The expected area

29

of a mass MD of entrained droplets is readily derived as

£(A) = 6MDpL [£(D2)/£(D3)] (5.72)

where

D — a droplet diameter; £ — statistical expectation (mean)

If the probability density function of D has lower and upper bounds a and b with a < b, the above ratio of expectations for various rudimen­tary distributions closely approximates those in Table 5.5. Granted a wide size-spectrum the area available for aerosol scrubbing is seen to be largely dictated by the largest droplets: and not by the population’s detailed statistics. This fact should simplify experiments to provide a sounder basis for aerosol scrubbing simulations like those in BERTA [25] and BUBEX.[93] [94] The FAUST experiments [267] concerned liquid entrainment by permanent gas bubbles, so that droplet longevity was not foreshortened by evaporation or encounters with fuel fragments. Accordingly the observed highly efficient aerosol scrubbing process in FAUST might not be replicated in a reactor situation. Realistic lifetimes and heat-transfer data for entrained droplets are clearly essential pre-requisites for specifying the radiological source term in a safety assessment. In the absence of such data, BUBEX preferentially evaporates Rayleigh-Taylor droplets before those of the surrounding coolant, so as to provide a conservative assessment.

Experiments establish that the collapse rate of steam bubbles is reduced by just 10% with the presence of a 15% molar concentration of permanent gas. With the inhibiting effect of permanent gases on power station condensers[95] borne in mind [219], researchers [236,267] have concluded that violent turbulence must exist within an MFCI bubble. Also it is reasonable to conjecture that similar turbulence develops in its surrounding liquid, but an apposite correlation for heat transfer from the liquid interface was not available during BUBEX development. Previ­ously cited MFCI models adopt quite speculative heat transfer relation­ships or none. However, in order to discard Hicks-Menzies efficiencies in favor of the some six times smaller 4 to 5% experimental values for reactor safety assessments, a patently conservative representation of heat transfer from a liquid interface is required. If this heat transfer process were to be inefficient, then a weakened condensation mass flux would be less effective in sapping energy from a simulated MFCI bubble.

Turbulent fluid flow around a body results in an attached laminar flowing boundary layer whose periphery is scoured by eddies induced by viscous shear [219,268]. Steady-state heat transfer is then often represented by molecular conduction across the boundary layer augmented by a dynamic diffusion process associated with the eddies. Formally

f = -(k + p CpEff) — (5.73)

where beside the usual nomenclature,

EH = Eddy diffusivity of heat y — perpendicular distance outwards from the body

Due to their low molecular conductivities, steady-state heat transfer to turbulent water or steam is totally dominated by eddy diffusivity so experimental correlations [64,117,143,219] involve only Reynolds Number terms. On the other hand, correlations for highly conductive liquid metals involve a sum of k and EH terms [64,117]. To provide conservative predictions of MFCI yield, BUBEX models heat transfer

Table 5.7 Comparison of Bubble Expansion Parameters Experiment BUBEX Lossless Peak cover gas pressure (bar) 2.7 9.3 82 Work done on cover gas (kJ) 24 72 243

Table 5.7 compares the peak cover-gas pressurizations and correspond­ing work done on the cover gas for experiment SUS01 with this BUBEX calculation and a lossless bubble expansion (a = 0.0). The BUBEX simulation actually accounts for 78% of the energy dissipation relative to the lossless case. It is concluded that Hicks-Menzies efficiencies are indeed over-predictions and that sound reasons exist for using the some 6 times lower 4 to 5% experimental values at reactor scale.