Critical review of conservation equations for two-phase flow in the U.S. NRC TRACE code

The field equations for two-phase flow in the computer code TRAC/RELAP Advanced Computational Engine or TRACE are examined to determine their validity, their capabilities and limitations in resolving nuclear reactor safety issues. TRACE was developed for the NRC to predict thermohydraulic phenomena in nuclear power plants during operational transients and postulated accidents. TRACE is based on the rigorously derived and well-established two-fluid field equations for 1-D and 3-D two-phase flow.It is shown that:

• (1) 

  The two-fluid field equations for mass conservation as implemented in TRACE are wrong because local mass balances in TRACE are in conflict with mass conservation for the whole reactor system, as shown in Section 3.1.

• (2) 

  Wrong equations of motion are used in TRACE in place of momentum balances, compromising at branch points the prediction of momentum transfer between, and the coupling of, loops in hydraulic networks by impedance (form loss and wall shear) and by inertia and thereby the simulation of reactor component interactions.

• (3) 

  Most seriously, TRACE calculation of heat transfer from fuel elements is incorrect for single and two-phase flows, because Eq. (3-4) of the TRACE Manual is wrong (see Section 5.2).

• (4) 

  Boundary conditions for momentum and energy balances in TRACE are restricted to flow regimes1 with single-phase wall contact because TRACE lacks constitutive relations for solid–fluid exchange of momentum and heat in prevailing flow regimes.

Without a quantified assessment of consequences from (3) to (4), predictions of phasic fluid velocities, fuel temperatures and important safety parameters, e.g., peak clad temperature, are questionable.Moreover, TRACE cannot predict 3-D single- or two-phase flows because:

• (5) 

  incorrectly averaged equations are used for 3-D predictions,

• (6) 

  fluid shear is ignored but needed to predict counter-current flows with the two-fluid model, and

• (7) 

  fictitious body forces and fictitious distributed mass and heat sources are used to replace contact forces at the wall, mass injection and wall heat fluxes in 3-D mass, momentum and energy equations for both phases. No modeling error estimates are given in the TRACE Manual.

• (8) 

  Imposed perfect mixing in every control volume causes artificial damping and disables TRACE to track reliably propagation of thermal and kinematic disturbances, thereby adversely affecting the prediction of nuclear fuel temperature.

• (9) 

  According to its manual, TRACE relies on numerical diffusion far greater than physical dissipation by turbulence, to solve TRACE's ill-posed field equations and to compensate for missing fluid shear. TRACE with scale-sensitive numerical diffusion is tuned to match data from small-scale experiments. TRACE is therefore not reliable for analyzing full-size power plants. Numerical diffusion could also reduce the ability of TRACE to predict the onset of instability for reactors or test facilities entering large power and flow oscillations.

Agreements of TRACE code results with experimental data from test facilities with isolated full-size components or with data from reduced-size integral-effect tests may be achieved by adjusting numerous coefficients, some of them scale-dependent (i.e., by tuning with documented non-physical coefficients in momentum balances, by spurious time-averaging (through time step adjustment) of algebraic boundary conditions, by built-in, non-physical space grid tuning in momentum balances and in mixture level predictions). Such results may not be applied reliably to full-size systems with realistic interactions between reactor components. TRACE may not be applicable to predict the outcome of postulated accidents for which validations are not possible (e.g., Anticipated Transients without Scram).New experimental techniques are needed first for closure of the two-fluid model. A new approach to TRACE modeling is needed. Recommendations are given for improved code documentation.     

Letter to the editor on the paper by D.C. Groeneveld and L.K.H. Leung, “The 1995 look-up table for critical heat flux in tubes”

This letter gives a brief critique of the new 1995 Look-Up-Table for critical heat flux (CHF). Issues on Look-Up-Table statistics, table usage and CHF values for critical flow are highlighted.     

Comment on the paper “Radiation induced by relativistic electrons propagating through random layered stacks: Numerical simulation results” by Varfolomeev et al. [Nucl. Instr. and Meth. B 256 (2007) 705]

We show that the numerical code used in the above mentioned paper does not take into account the multiple scattering effects of electromagnetic fields properly and is, therefore, incorrect.     

A second order turbulence model based on a Reynolds stress approach for two-phase boiling flow. Part 1: Application to the ASU-annular channel case

High-thermal performance PWR (pressurized water reactor) spacer grids require both low pressure loss and high critical heat flux (CHF) properties. Numerical investigations on the effect of angles and position of mixing vanes and to understand in more details the main physical phenomena (wall boiling, entrainment of bubbles in the wakes, recondensation) are required.In the field of fuel assembly analysis or design by means of CFD codes, the overwhelming majority of the studies are carried out using two-equation eddy viscosity models (EVM), especially the standard K-? model, while the use of Reynolds Stress Transport Models (RSTM) remains exceptional.But extensive testing and application over the past three decades have revealed a number of shortcomings and deficiencies in eddy viscosity models. In fact, the K-? model is totally blind to rotation effects and the swirling flows can be regarded as a special case of fluid rotation. This aspect is crucial for the simulation of a hot channel in a fuel assembly. In fact, the mixing vanes of the spacer grids generate a swirl in the coolant water, to enhance the heat transfer from the rods to the coolant in the hot channels and to limit boiling.First, we started to evaluate computational fluid dynamics results against the AGATE-mixing experiment: single-phase liquid water tests, with Laser-Doppler liquid velocity measurements upstream and downstream of mixing blades. The comparison of computed and experimental azimuthal (circular component in a horizontal plane) liquid velocity downstream of a mixing vane for the AGATE-mixing test shows that the rotating flow is qualitatively well reproduced by CFD calculations but azimuthal liquid velocity is underestimated with the K-? model.Before comparing performance of EVM and RSTM models on fuel assembly geometry, we performed calculations with a simpler geometry, the ASU-annular channel case. A wall function model dedicated to boiling flows is also proposed.     

Loose-parts monitoring: Present status of the technology, its implementation in U.S. reactors, and some recommendations for achieving improved performance

At the request of the U.S. Nuclear Regulatory Commission (NRC), an assessment of the technical development status of loose-parts monitoring systems (LPMS) and their performance record to date in commercial light-water-cooled nuclear reactor plants was made during the spring of 1977, using an on-site personal interview and equipment demonstration approach. Our study revealed that while presently demonstrated LPMS technology does indeed provide a capability for detecting the presence of those relatively massive loose parts that would likely constitute a serious operational or safety hazard to the plant, it unfortunately affords little information useful to the determination of the parts' safety significance and has not yet attained the levels of sophistication and reliability ordinarily associated with safety systems. We also found a definite need for specification of the functional requirements for LPMS, in the form of a clear and comprehensive statement of NRC policy regarding the formulation and implementation of safety-oriented, yet operationally practicable, loose-parts monitoring programs for both existing and future nuclear generating stations so that overall objectives of both the utilities and the regulatory agency might be satisfied simultaneously.

While it is our best technical judgment that loose-parts monitoring programs providing reliable detection (but not characterization) capabilities could be implemented with today's technology, the path on which the nuclear utility industry should proceed in order to meet NRC expectations is not completely clear. A Regulatory Guide entitled “Loose Part Detection Program for the Primary System of Light-Water-Cooled Reactors,” soon to be issued for public comment, constitutes a first step towards satisfying this need for guidance and goal establishment.     

Erratum to “Measurement of cross-sections for the (p, xn) reactions in natural molybdenum” [Nucl. Instr. and Meth. B 262 (2007) 171]

Using PIGE (TIARA, JAPAN) technique, we measured fluorine (F) uptake into the tooth enamel around a fluoride-containing material during caries progression using pH cycling. Class I cavities in the buccal surfaces of 6 extracted human teeth were drilled and filled with fluoride-containing material; a glass ionomer cement (Fuji IX(GC)). Three 300 μm sections through the material were obtained from each tooth. Two of these specimens were utilized to measure the F distribution in enamel adjacent to the material. A 1.7 MeV proton beam accelerated by the TIARA single-ended accelerator was delivered to a micro-beam apparatus. The beam spot size was about 1 μm with a beam current of about 100 pA. A nuclear reaction, ¹⁹F(p, αγ)¹⁶0, was used to measure the F concentration and the gamma-rays from this reaction were detected with a 4” NaI detector. X-rays induced by proton were detected with a Si(Li) detector to measure calcium concentration and the beam intensity was monitored with the X-ray yield from a copper foil for quantitative analysis. After measurement of F uptake, all specimens were polished to a thickness of 120 μm. In order to simulate daily acid challenges occurring in the oral cavity, the pH cycling (pH6.8–pH4.5) was carried out for 1, 3 and 5 weeks, separately. The duration that the solution remained below pH 5.5 was 37 min per cycle. The cycles were repeated 6 times per day with 2 h interval between cycles, and the specimens were kept in remineralizing solution for the rest of pH cycle. After pH cycling, F and calcium distribution of each specimen was evaluated using PIGE technique. The F distribution of the specimens before pH cycling clearly showed the F uptake from fluoride-containing material into enamel adjacent to the material. After pH cycling, the caries progression in all specimens was observed by the image of transverse microradiography (TMR). The depth of caries and mineral loss progressed with increasing the duration of pH cycling, although the enamel adjacent to the material remained a caries inhibition zone due to low rate of demineralization. With caries progression, fluorine accumulated in the subsurface of the caries lesion, while the outermost surface of the caries lesion gradually dissolved under increasing pH cycling. The data obtained using PIGE (TIARA, JAPAN) technique were useful to understand the fluorine benefit for preventing dental caries by means of fluoride-containing dental materials.