SOURCE TERM DEVELOPMENT

The following two sections describe the accidents that occurred aboard the nuclear submarines and icebreaker that led to their ultimate disposal in the Kara Sea. 

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The paper summarizes eiforts started to deliver a profound chemical base for risk assessment, namely to properly take into account the physico-chemical phenomena governing the contamination source term development in time and space. One major aspect there is the substitution of conventional distribution coefficients (IQ values) for the empirical description of sorption processes by surface complexation models, in combination with other thermodynamic concepts. Thus, the framework of a Smart Kd is developed for complex scenarios with a detailed explanation of the underl3dng assumptions and theories. It helps to identify essential processes and the associated most critical parameters, easing further refinement studies. The presented case studies cover a broad spectrum of contamination cases and successfully demonstrate the applicability of the methodology. The necessity to create a mineral-specific sorption database to support the Smart IQ approach is derived and a first prototype for such a digital database introduced, combining numeric data with a knowledge base about the relevant theories, experimental methods, and structural information. 

It is user friendly and possesses a graphical user interface for developing the flow paths, ventilation system, and initial conditions. The FIRIN and CFAST modules can be bypassed and temperature, pressure, gas, release energy, mass functions of time specified. FIRAC i.s applicable to any facility (i.e., buildings, tanks, multiple rooms, etc,) with and without ventilation systems. It is applicable to multi species gas mixing or transport problems, as well as aerosol transport problems, FIRAC includes source term models for fires and limitless flow paths, except the FlRlN fire compartment limit of to no more than three... 

Blond, R., The Development Severe Reactor Source Terms 1957-1981, November 1982. Safety Goals for Nuclear Power Plant Operation May 1983. 

Typically, the interface obtained with the versions of the VOF method described above is smeared over a few grid cells, which, on sufficiently fine grids, allows one to identify uniquely the simply connected volumes belonging to the different phases. Instead of regarding the dynamic conditions of Eqs. (132)-(134) as boundary conditions, surface tension can be implemented as a volume force in those cells where c lies between 0 and 1. In the method developed by Brackbill et al. [176], a momentum source term of the form... 

Because estimates of health risk are based on the levels of radionuclides in or near the vicinity properties, the quality of the potential health risk estimates depends upon the availability of appropriate measurement data. Hence, the first steps involved the determination of the appropriate environmental pathways of exposure and developing the source term for the exposure of persons potentially at risk. For our work, the radiological source-term data was based on measurements made principally by the Oak Ridge National Laboratory and the Mound Laboratory. 

The source terms on the right-hand sides of Eqs. (25)-(29) are defined as follows. In the momentum balance, g represents gravity and p is the modified pressure. The latter is found by forcing the mean velocity field to be solenoidal (V (U) = 0). In the turbulent-kinetic-energy equation (Eq. 26), Pk is the source term due to mean shear and the final term is dissipation. In the dissipation equation (Eq. 27), the source terms are closures developed on the basis of the form of the turbulent energy spectrum (Pope, 2000). Finally, the source terms... 

The CFD model developed above is an example of a moment closure. Unfortunately, when applied to reacting scalars such as those considered in Section III, moment closures for the chemical source term are not usually accurate (Fox, 2003). An alternative approach that yields the same moments can be formulated in terms of a presumed PDF method (Fox, 1998). Here we will consider only the simplest version of a multi-environment micromixing model. Readers interested in further details on other versions of the model can consult Wang and Fox (2004). 

A theoretical framework based on the one-point, one-time joint probability density function (PDF) is developed. It is shown that all commonly employed models for turbulent reacting flows can be formulated in terms of the joint PDF of the chemical species and enthalpy. Models based on direct closures for the chemical source term as well as transported PDF methods, are covered in detail. An introduction to the theory of turbulence and turbulent scalar transport is provided for completeness. 

As discussed in Chapter 2, a fully developed turbulent flow field contains flow structures with length scales much smaller than the grid cells used in most CFD codes (Daly and Harlow 1970).29 Thus, CFD models based on moment methods do not contain the information needed to predict x, t). Indeed, only the direct numerical simulation (DNS) of (1.27)-(1.29) uses a fine enough grid to resolve completely all flow structures, and thereby avoids the need to predict x, t). In the CFD literature, the small-scale structures that control the chemical source term are called sub-grid-scale (SGS) fields, as illustrated in Fig. 1.7. 

In developing closures for the chemical source term and the PDF transport equation, we will also come across conditional moments of the derivatives of a field conditioned on the value of the field. For example, in conditional-moment closures, we must provide a functional form for the scalar dissipation rate conditioned on the mixture fraction, i.e.,... 

Owing to the sensitivity of the chemical source term to the shape of the composition PDF, the application of the second approach to model molecular mixing models in Section 6.6, a successful model for desirable properties. In addition, the Lagrangian correlation functions for each pair of scalars (( (fO fe) ) should agree with available DNS data.130 Some of these requirements (e.g., desirable property (ii)) require models that control the shape of /, and for these reasons the development of stochastic differential equations for micromixing is particularly difficult. 

For higher-order reactions, a model must be provided to close the covariance source terms. One possible approach to develop such a model is to extend the FP model to account for scalar fluctuations in each wavenumber band (instead of only accounting for fluctuations in In any case, correctly accounting for the spectral distribution of the scalar covariance chemical source term is a key requirement for extending the LSR model to reacting scalars. 

Since the supply of hydrogen in the long term depends on different technical and energy policy developments and frame conditions, such as the expansion of renewable energy sources, the development of clean coal technologies or the required reduction of C02 emissions, hydrogen production is simultaneously closely linked to the conventional energy supply system. 

So far, the Lagrangian density for a homogenous problem (no sink or source term in the diffusion equation) has been considered, subject to the requirement that the approximate trial function, ip, can be forced to satisfy the boundary conditions. In this sub-section, these limitations are removed and the Lagrangian density for the Green s function developed. The Green s functions for the forward and backward time process satisfy the equations... 

TU any of the less-understood phenomena leading to the observed fall-out distribution resulting from a nuclear explosion occur on a relatively short time scale (a few tens of seconds or less). These short term phenomena lead to an initial distribution of radioactive material referred to as the source term in a fallout study. Many predictive calculations are based on an assumed source term, which of necessity has been quite oversimplified. Two typical simplifications made for purposes of model development are (1) that the radiochemical composition of fallout is well defined and uniform (2) that the particles comprising the initial debris are uniform with respect to settling rate in the atmosphere. The latter assumption has received considerable attention elsewhere, notably in the work of Miller (2). However, the former assumption concerning the radiochemical uniformity of the debris has received far less systematic attention. 

It remains for workers to develop a method of selecting correlations based on mechanism rather than on adequacy of measurement and to attempt some interpretation of these results in terms of mechanisms of source-term formation. This paper has attempted to show only that the complexity of the phenomenology, while enough to cause trouble, is not beyond analysis. 

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