# A DIGITAL COMPUTER SOLUTION FOR SPACE-DEPENDENT NEUTRON KINETICS EQUATIONS

## Abstract

A set of one-group space-dependent neutron kinetics equations for reactor cores with spatially variable moderator density is developed. The solution to this set of differential equations is obtained numerically using an IBM-7094 digital computer. Employing the variational technique of von Neumann, a numerical stability criterion for space-dependent neutron kinetics equations is established. The analysis is useful in the determination of the core open-loop response as well as the reactor system transient behavior. The open-loop response of a typical boiling-water reactor core for several values of step change in reactivity was determined using the analysis. These are shown to be in agreement with the results of the classical space-independent neutron kinetics equations. The open-loop characteristic of the reactor core due to a step change in density distribution is also presented. The main distinguishing feature of the present study is the ability to determine the open-loop response due to disturbances (such as a series of successive step changes in density distribution) for which the classical space-independent approach provides no solution. Characteristics of this type are necessary in the dynamic analysis of boiling-water reactors where the system density distribution varies in time and space. A simple approximate method for the solution of themore »

- Authors:

- Publication Date:

- Research Org.:
- Westinghouse Electric Corp., Pittsburgh

- OSTI Identifier:
- 4069009

- NSA Number:
- NSA-18-015439

- Resource Type:
- Journal Article

- Journal Name:
- Nuclear Science and Engineering (U.S.)

- Additional Journal Information:
- Journal Volume: Vol: 18; Other Information: Orig. Receipt Date: 31-DEC-64

- Country of Publication:
- Country unknown/Code not available

- Language:
- English

- Subject:
- REACTOR TECHNOLOGY; COMPUTERS; DENSITY; DIFFERENTIAL EQUATIONS; DIGITAL SYSTEMS; DISTRIBUTION; EQUATIONS; IBM 7094; MODERATORS; NEUTRONS; NUCLEATE BOILING; NUMERICALS; REACTIVITY; REACTOR CORE; REACTORS; STABILITY; TRANSIENTS; VARIATIONS; ZONES

### Citation Formats

```
Nahavandi, A.N., and Von Hollen, R.F.
```*A DIGITAL COMPUTER SOLUTION FOR SPACE-DEPENDENT NEUTRON KINETICS EQUATIONS*. Country unknown/Code not available: N. p., 1964.
Web.

```
Nahavandi, A.N., & Von Hollen, R.F.
```*A DIGITAL COMPUTER SOLUTION FOR SPACE-DEPENDENT NEUTRON KINETICS EQUATIONS*. Country unknown/Code not available.

```
Nahavandi, A.N., and Von Hollen, R.F. Sun .
"A DIGITAL COMPUTER SOLUTION FOR SPACE-DEPENDENT NEUTRON KINETICS EQUATIONS". Country unknown/Code not available.
```

```
@article{osti_4069009,
```

title = {A DIGITAL COMPUTER SOLUTION FOR SPACE-DEPENDENT NEUTRON KINETICS EQUATIONS},

author = {Nahavandi, A.N. and Von Hollen, R.F.},

abstractNote = {A set of one-group space-dependent neutron kinetics equations for reactor cores with spatially variable moderator density is developed. The solution to this set of differential equations is obtained numerically using an IBM-7094 digital computer. Employing the variational technique of von Neumann, a numerical stability criterion for space-dependent neutron kinetics equations is established. The analysis is useful in the determination of the core open-loop response as well as the reactor system transient behavior. The open-loop response of a typical boiling-water reactor core for several values of step change in reactivity was determined using the analysis. These are shown to be in agreement with the results of the classical space-independent neutron kinetics equations. The open-loop characteristic of the reactor core due to a step change in density distribution is also presented. The main distinguishing feature of the present study is the ability to determine the open-loop response due to disturbances (such as a series of successive step changes in density distribution) for which the classical space-independent approach provides no solution. Characteristics of this type are necessary in the dynamic analysis of boiling-water reactors where the system density distribution varies in time and space. A simple approximate method for the solution of the space-dependent neutron kinetics equations is also presented. (auth)},

doi = {},

journal = {Nuclear Science and Engineering (U.S.)},

number = ,

volume = Vol: 18,

place = {Country unknown/Code not available},

year = {1964},

month = {3}

}