SAFPWR home page

SAFPWR: PWR transients and safety analysis program general description.

Modelling features

The SAFPWR computer program aims at assessing SAFety and protections for Westinghouse-type nuclear Pressurized Water Reactors

The simulated domain includes the core itself and all the pwr system components which interact with it.

The program model makes use of a spatial kinetics representation of the core, in direct coupling with all the components of the heat removal and protection systems which may have a potential impact on its transient behaviour.

SAFPWR belongs to the "evaluation" family of programs (as opposed to a "best-estimate", such as RELAP) which allow a strict consistency with the conservative bounding methodology of licensing safety evaluations.

By simulating a standard set of transients, it makes it possible to assess reactor safety directly in terms of margin between the extreme value reached by each safety-related variable and its limiting value prescribed by plant licensing cases.
Thus, the direct coupling approach alleviates the shortcomings of the formal "uncoupled" methodology, which consists in checking the value of each relevant key-parameters (reactivity coefficients, power form factors, ....), calculated in the course of the "static" nuclear design, against its licensing bound.

Main modelling assumptions.

SAFPWR does not need to cover large depressurization accidents, such as loss-of-coolant, where the core remains anyway sub-critical and at low power.

For the type of transients of interest here, the primary coolant water remains sub-cooled or moderately boiling. This authorizes retaining the so-called "global pressure approximation" which amounts to evaluating local water massic volume vm(h,p) from its local enthalpy h, but from a single uniform system global pressure p. This approximation has the effect of "erasing" pressure waves, of relieving numerical stiffness and allowing larger time-steps.
The second major simplifying assumption consists, in the fluid nodal energy balance equations, in dropping the kinetic energy (mv2/2) and gravity (g z/vm) terms. Actually, this amounts to assigning a higher than actual value to the fluid temperature, since the neglected contributions will actually be converted in thermal energy. It will be shown that the resulting effect on the heat rate exchanged by the fluid is acceptable.
In the course of the transients, the axial shape of the power distribution may deform rapidly, which has a major impact on the safety margins. Thus this effect needs to be explicitly modeled.
By comparison, the radial shape of the power distribution in each of the axial slices delimited by the control rods insertion or core compositions, does not markedly depart from its stationary shape, for the same radially averaged values of water density, boron and effective fuel temperature. In other words, the departure of the radial shape from its steady state should have a weak effect on the core reactivity and axial shape.
This allows conceiving the spatial kinetics representation of the core as resulting from a formal axial collapsing of the general 3D model.
As the radial power distribution is not explicitly calculated, a "hot channel" must be attached to the core in order to evaluate conservative values of peak power density, fuel temperature, departure of nucleate boiling, ...
It should be stressed that the approximation resulting from this axial collapsing is actually less limiting than that of the traditional synthesis model.
At the occasion of 3D kinetic benchmarks it will indeed be shown that our axial collapsing model reproduces surprisingly well the results obtained by reference 3D kinetics codes.

This simplified model considerably lessens the burden imposed upon the computer resources.

Let us again stress that the goal of the program is not to reach "best estimate", but rather "conservative" values for the safety-related variables, in conformity with the "licensing" approach.
Except for the above simplifications, the SAFPWR mathematical model is basically the same as in the conventional system programs: conservation equations of 1D mass, energy and kinetic momentum on homogenous nodes.

Computational requirements

For the sake of maximum portability, SAFPWR was totally programmed in modern FORTRAN95 language. Systematic recourse to features such as modules, structures, dynamic allocation..., allows an object-oriented approach for the programming.

The computational requirements are modest: the program is currently executed as a console mode application under Windows98SE on a PC equipped with a 760Mhz PentiumII processor, 128MB rom, 10GB hard disk, but it has been tested on more recent machines and can be optimized, for more recent processors.
As the source code complies strictly to the fortan95 standards, without resorting to any fortran language extension or WINDOWS-related features, it could as well be compiled for LINUX, main frame and possibly Unix machines.

SAFPWR was not conceived as a single, stand-alone program, but rather as a "tool box" of individual program procedures and options which are assembled, at input time, by means of an execution management procedure made of a set of keywords sequences.
A keyword may represent either:
a constitutive physical component of the PWR system to be simulated (ex: "bottom", "core"),
or an operating option (ex: "read" for reading, "ini" for initialization, "step" for time-stepping, "plot" for plotting variables,...)

Stability and conservation requirements imposed to the field equations solving methods

The field equations integration method (for water mass, enthalpy, boron, kinetic momentum, for internal energy of metallic parts and for neutron density, delayed neutron precursor density, residual heat fission products density...) aims at solving exactly the original set of those highly non linear constitutive equations.
Numerical stability is achieved by resorting whenever feasible, to totally implicit (hence stable) schemes, where feedback effects are applied at end-of-step.

The solution scheme also guarantees strict conservation of all extensive (mass, energy, volume, neutron density,...) original field values, even for large time-steps. This makes it possible program debugging by simply checking that all local and global balances are rigorously closed.

This is of course a necessary, but not sufficient condition: it must in addition be demonstrated that the time integration of the field equation is correct.
This can be verified by refining the time stepping and by comparing to theoretical and benchmark solutions.
In addition the strongly implicit scheme alleviates the "Courant stability limitation" which, in some system codes, necessitates reducing node volumes when reducing time-step duration.

Initialization.

The feature is of great practical interest. It allows setting up a stable, steady-state initial (neutronic and thermal hydraulic), state condition for the whole PWR system, by simply entering basic geometric and operational data (power, pressures, pump heads, rod positions,...).
This is achieved by means of back-solving the field equations and adjusting multipliers for some parameters such as friction factors and heat-transfer coefficients and setting up local reactiviy correction in the core.

This approach allows a strict consistency with the static core and design methods and conceiving the SAFPWR as an a natural extension to the time domain, with minimal modelling rupture.

Special new developments

A non-equilibrium, Lagrangian, pressu model has been developed for making it possible simulation of pressu and expansion line voiding.
A rigorous "Lagrangian" solution scheme for water transport and heat-exchange in the primary loops and down-comer was developed with the purpose of quantifying the effect of "forward numerical diffusion " encountered in the classical eulerian scheme, on the response of overpower and over-temperature protections devices installed on the primary branches of steam-generator.

Last program expansions

Solving initial core eigen value problems

The above described back-solving procedure for obtaining the initial critical condition was intended for insuring maximum consistency with static core design results.
It is, however, not very practical, especially for a tutorial use of the program, because the neutronic distributions, solutions of initial core eigenvalue problem are not readily available.

Therefore, the program capability was recently expanded for covering as well the resolution of this initial eigenvalue core problem, starting directly from the set of core configuration neutronic data obtained from the core static design.

This was possible, thanks to the safpwr capability of supplying, at each time step, an accurate estimation of current core static reactivity.

It will make clear, along with the detailed description of the SAFPW neutronic transient model, that one of its important feature is the rehabilitation of reactivity as the dominant variable driving the transients.
The dominant role of reactivity is fully established in point kinetics, but is somewhat lost in classical multi group transient approach

In SAFPWR model, explicit use of local reactivity allows, for example, treating, at fine mesh level, the approach and crossing prompt criticality by means of an iterated feedback effect process, rather than by just lowering time-steps duration.
Global core static reactivity is also edited for interpreting transient behavior but is not explicitly used in the solving process.

But the availability of global core reactivity allows in addition to readily obtain the solution of the initial core eigenvalue problem by simply installing in the transient model an additional ad hoc "numerical" feedback process fed by the current core reactivity.
This procedure of solving a stationary eigenvalue problem by means of a transient program may seem peculiar but performs perfectly well.

Justification for a web presentation for the project.

Gaining maximum audience but, more importantly, seeking feedback contributions from the users.
Transients response is indeed sensitive to the choice of some empirical correlation's (for heat-exchange, fluid discharge, departure from nucleate boiling, ...) which may be proprietary or need to be specially adapted to each particular application.
A set of well established correlation's has been incorporated by default, but the user has also the ability to enter its own correlations by means of polynomial tabulations.


The best way for learning and evaluating the program is by running applications.
For facilicitating the user 's task, numerous applications examples have been included on this site.

Although the primary goal the program of educational nature, it should also be able, if fed by proper system and neutronic data derived from static design, to be used as well for practical safety evaluations.

Thanks to its rapidity, simplicity and flexibility SAFPWR may contribute allowing the user, by running numerous applications, to build up his deep insight into the core and protection response to transients.
Most of applications take at most a few sec of computer time. Simulation of the most complex steam line break transient of 1 hour duration takes less than 1 min. (20 s on Pentium4 machine) .

Prerequisites

A basic knowledge of PWR plant and reactor kinetics is required for a knowledgeable use of the program. Normally, reading the overview chapter should be sufficient for running applications.

The math model description chapter is more intended for supporting program validation and getting a deeper understanding of the program possibilities and limitations. The reactor kinetics part is more detailed. It is intended for allowing the reactor neutronic designer to build the SAFPWR neutronic tabulation as a by product of the static neutronic calculations.