**RSICC CODE PACKAGE PSR-492**

**1. NAME AND TITLE**

QUARK: Code System for 2-Group, 3D Neutronic Kinetics Calculations Coupled
to Core Thermal Hydraulics.

**2. CONTRIBUTORS**

Synthesis Srl, Milano, Italy and ENEL SpA, Milano, Italy through the
NEA Data Bank Issy-les-Moulineaux, France.

**3. CODING LANGUAGE AND COMPUTER**

Fortran 77; Pentium (P00492PC58600).

**4. NATURE OF PROBLEM SOLVED**

QUARK is a combined computer program comprising a revised version of
the QUANDRY three-dimensional, two-group neutron kinetics code and an upgraded
version of the COBRA transient core analysis code (COBRA-EN). Starting
from either a critical steady-state (k-effective or critical dilute Boron
problem) or a subcritical steady-state (fixed source problem) in a PWR
plant, the code allows one to simulate the neutronic and thermal-hydraulic
core transient response to reactivity accidents initiated both inside the
vessel (such as a control rod ejection) and outside the vessel (such as
the sudden change of the Boron concentration in the coolant). QUARK output
can be used as input to PSR-470/NORMA-FP to perform a subchannel analysis
from converged coarse-mesh nodal solutions.

**5. METHOD OF SOLUTION**

The thermal-hydraulic model is based on three partial differential equations that describe the conservation of mass, energy and momentum for the water liquid/vapor mixture and the interaction of the two-phase coolant with the system structures. Optionally, a fourth equation can be added which tracks the vapor mass separately and which, along with the correlations for vapor generation and slip ratio, replaces the subcooled quality and quality/void fraction correlations, needed by the homogeneous model.

In each coolant channel, the one-dimensional (z) fluid dynamics equations in the vertical direction, as well as the one-dimensional (r) equation in the horizontal direction that models the heat transfer in solid structures, are approximated by finite differences. The resulting equations for hydrodynamic phenomena form a system of coupled nonlinear equations that are solved by the original upflow scheme (when no reverse flow is predicted) or by a Newton-Raphson iteration procedure. The heat-transfer equations in the solid structures are treated implicitly. Moreover, a full boiling curve is provided, comprising the basic heat-transfer regimes, each represented by a set of optional correlations for the heat-transfer coefficient between a solid surface and the coolant bulk.

The neutronic module is based on the Analytical Nodal Method (ANM) for two-group neutron diffusion equation in three-dimensional cartesian geometry, developed by A. F. Henry and his coworkers at MIT, which approximates the diffusion equation by analytical formulae that are exact in one dimension and solves the resulting nodal equations for node-averaged fluxes and directional leakages by a triple level of iteration.

The cross-sections and the discontinuity factors correcting for homogenization
errors are updated for thermal (fuel temperature) and thermal-hydraulic
feedback (coolant temperature and density) and also for dilute Boron effect,
either by applying temperature and density coefficients (quadratic at the
most) or by interpolating in input multiple-entry libraries of reference
values.

**6. RESTRICTIONS OR LIMITATIONS**

The data-dependent arrays are contained in the named common block BLANK
whose standard length of 10106 bytes can be changed by modifying a PARAMETER
statement in an include file (see the Installation Directions).

**7. TYPICAL RUNNING TIME**

Sample problem 1 with 360 assembly-sized (20 cm) cubic nodes and 60
time steps (each 1 s long) requires only 3 min of CP time on a PC-486/100
but typical problems concerning actual large LWR cores may require some
thousands of nodes and some hundred or thousand time steps. Therefore,
the CP times can range from a few to some tens of minutes for a steady-state
and rise to some hours for a transient.

**8. COMPUTER HARDWARE REQUIREMENTS**

QUARK runs on a Personal Computer with 486 or Pentium processor and
at least 16 Mb of RAM.

**9. COMPUTER SOFTWARE REQUIREMENTS**

The software runs under DOS or WINDOWS, and the included executable
was created with MS FORTRAN Power Station Compiler Version 1.0 and was
tested at RSICC in a DOS window of Windows95.

**10. REFERENCES**

E. Salina, G. Alloggio, E. Brega, "QUARK: a Computer Code for the Neutronic
and Thermal-Hydraulic Space- and Time-Dependent Analysis of Light Water
Reactor Cores by Advanced Nodal Techniques," Synthesis Srl Rep. 1034/1
(September 1994).

**11. CONTENTS OF CODE PACKAGE**

Included on the CD-ROM are the referenced document in electronic PDF
format and a compressed, self-extracting DOS file which contains the source,
executable, test cases and data files.

**12. DATE OF ABSTRACT**

May 2000.

**KEYWORDS:** PWR; REACTOR SAFETY; THERMAL HYDRAULICS