# Models and Stability Analysis of Boiling Water Reactors

## Abstract

We have studied the nuclear-coupled thermal-hydraulic stability of boiling water reactors (BWRs) using a model that includes: space-time modal neutron kinetics based on spatial w-modes; single- and two-phase flow in parallel boiling channels; fuel rod heat conduction dynamics; and a simple model of the recirculation loop. The BR model is represented by a set of time-dependent nonlinear ordinary differential equations, and is studied as a dynamical system using the modern bifurcation theory and nonlinear dynamical systems analysis. We first determine the stability boundary (SB) - or Hopf bifurcation set- in the most relevant parameter plane, the inlet-subcooling-number/external-pressure-drop plane, for a fixed control rod induced external reactivity equal to the 100% rod line value; then we transform the SB to the practical power-flow map used by BWR operating engineers and regulatory agencies. Using this SB, we show that the normal operating point at 100% power is very stable, that stability of points on the 100% rod line decreases as the flow rate is reduced, and that operating points in the low-flow/high-power region are least stable. We also determine the SB that results when the modal kinetics is replaced by simple point reactor kinetics, and we thereby show that the first harmonicmore »

- Authors:

- Publication Date:

- Research Org.:
- University of Virginia (US)

- Sponsoring Org.:
- (US)

- OSTI Identifier:
- 793688

- Report Number(s):
- DOE/ID/13650

TRN: US0201040

- DOE Contract Number:
- FG07-98ID13650

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 15 Apr 2002

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; BWR TYPE REACTORS; CONTROL ELEMENTS; DIFFERENTIAL EQUATIONS; FLOW RATE; FUEL RODS; REACTOR KINETICS; STABILITY; SYSTEMS ANALYSIS; TWO-PHASE FLOW; THERMODYNAMICS; HYDRAULICS; MATHEMATICAL MODELS

### Citation Formats

```
John Dorning.
```*Models and Stability Analysis of Boiling Water Reactors*. United States: N. p., 2002.
Web. doi:10.2172/793688.

```
John Dorning.
```*Models and Stability Analysis of Boiling Water Reactors*. United States. doi:10.2172/793688.

```
John Dorning. Mon .
"Models and Stability Analysis of Boiling Water Reactors". United States. doi:10.2172/793688. https://www.osti.gov/servlets/purl/793688.
```

```
@article{osti_793688,
```

title = {Models and Stability Analysis of Boiling Water Reactors},

author = {John Dorning},

abstractNote = {We have studied the nuclear-coupled thermal-hydraulic stability of boiling water reactors (BWRs) using a model that includes: space-time modal neutron kinetics based on spatial w-modes; single- and two-phase flow in parallel boiling channels; fuel rod heat conduction dynamics; and a simple model of the recirculation loop. The BR model is represented by a set of time-dependent nonlinear ordinary differential equations, and is studied as a dynamical system using the modern bifurcation theory and nonlinear dynamical systems analysis. We first determine the stability boundary (SB) - or Hopf bifurcation set- in the most relevant parameter plane, the inlet-subcooling-number/external-pressure-drop plane, for a fixed control rod induced external reactivity equal to the 100% rod line value; then we transform the SB to the practical power-flow map used by BWR operating engineers and regulatory agencies. Using this SB, we show that the normal operating point at 100% power is very stable, that stability of points on the 100% rod line decreases as the flow rate is reduced, and that operating points in the low-flow/high-power region are least stable. We also determine the SB that results when the modal kinetics is replaced by simple point reactor kinetics, and we thereby show that the first harmonic mode does not have a significant effect on the SB. However, we later show that it nevertheless has a significant effect on stability because it affects the basin of attraction of stable operating points. Using numerical simulations we show that, in the important low-flow/high-power region, the Hopf bifurcation that occurs as the SB is crossed is subcritical; hence, growing oscillations can result following small finite perturbations of stable steady-states on the 100% rod line at points in the low-flow/high-power region. Numerical simulations are also performed to calculate the decay ratios (DRs) and frequencies of oscillations for various points on the 100% rod line. It is determined that the U.S. NRC requirement of DR is not rigorously satisfied in the low-flow/high-power region; hence, this region should be avoided during normal startup and shutdown operations. The frequency of oscillation is shown to decrease as the flow rate is reduced. Moreover, the simulation frequency of 0.5Hz determined in the low-flow/high-power region is consistent with those observed during actual instability incidents. Additional numerical simulations show that in the low-flow/high-power region, for the same initial conditions, the use of point kinetics leads to damped oscillations, whereas the model that includes the modal neutron kinetics equations results in growing nonlinear oscillations.},

doi = {10.2172/793688},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Apr 15 00:00:00 EDT 2002},

month = {Mon Apr 15 00:00:00 EDT 2002}

}