22.08.2015   Frequency Response Testing. in Nuclear Reactors

Lumped-Parameter Zero-Power Frequency Response

Подпись: (5.1.1) (5.1.2) The space-independent neutron kinetics equations are dn/dt = [{p — P)/A]n + £ ЛС;

І = 1

dCJdt = — ЛІСІ

where n is the neutron density (proportional to power level), p the reactivity, P the total delayed neutron fraction, A the neutron generation time, 2, the decay constant for ith delayed neutron precursor group, C, the concentration of the ith delayed neutron precursor, and the delayed neutron fraction for delayed neutron group i.

image249 Подпись: - 1 Подпись: (5.1.3)

The transfer function obtained from these equations is

TABLE 5.1

Delayed Neutron Yield from Thermal Fission in 233U, 225U, and 239Pu“

Isotope

Total delayed neutron fraction

Group

Index,

і

Half-life,

T; (sec)

Decay constant, X, (sec-1)

Group delayed neutron fraction

233U

0-0027

1

55.00

0.0126

0.00023

2

20.57

0.0337

0.00081

3

5.00

0.139

0.00068

4

2.13

0.325

0.00075

5

0.615

1.13

0.00014

6

0.277

2.50

0.00009

235U

0.0065

1

55.72

0.0124

0.00021

2

22.72

0.0305

0.00142

3

6.22

0.111

0.00127

4

2.30

0.301

0.00257

5

0.61

1.13

0.00075

6

0.23

3.00

0.00027

239 Pu

0.0021

1

54.28

0.0128

0.00007

2

23.04

0.0301

0.00063

3

5.60

0.124

0.00044

4

2.13

0.325

0.00068

5

0.618

1.12

0.00018

6

0.257

2.69

0.00009

From Keepin (1).

where n0 is the steady-state neutron density. The delayed-neutron parameters needed for theoretical calculations of the frequency response are shown in Table 5.1. Zero-power frequency response results for a reactor with 235U fuel are shown in Fig. 5.1.

image81

Fig. 5.1. (a)Amplitude for a 235U-fueled, zero-power reactor, (b) phase shift for a 235U — fueled, zero-power reactor.

An approximate transfer function based on a single effective group of delayed neutrons is often used. The transfer function is

Sn _ n0(s + X) dp As(s + X + p/A)

where X is the average decay constant (sO. l sec-*).