Theoretical comparison of performance using transfer functions for reactivity meters based on inverse kinetic method and simple feedback method

Figures & data

Figure 1. Block diagram of IPK reactivity meter.

Figure 2. Block diagram of SRE.

Table 1. Reactor kinetic parameters.

Delayed neutron fraction	0.0065
Delayed neutron precursors decay constant	0.078 sec^−1
Prompt neutron life time	0.00002 sec

Figure 3. Typical reactivity difference.

Table 2. Numerical results of the integrated square of the reactivity difference.

F	τ = 0.1 sec	τ = 0.5 sec	τ = 1.0 sec	τ = 5.0 sec	τ = 10 sec
0.01					0.014020
0.09					0.008408
0.1	0.010994	0.010346	0.009587	0.006286	0.008345
0.11					0.008327
0.12					0.008342
0.19				0.004535
0.2				0.004518
0.21				0.004516
0.22				0.004525
0.5	0.004640	0.003381	0.002241
0.9			0.001007
1	0.003040	0.001518	0.000970	0.006601	0.01053
1.1			0.000996
2		0.000491
3		0.000805
5	0.000657	0.001345	0.002682
9	0.000134
10	0.000103	0.001866	0.003087
11	0.000127
20	0.000471
50	0.000830

Figure 4. Comparison of the integrated square of the reactivity difference.

Figure 5. Reactivity response for a step reactivity input of 10 pcm τ = 0.5 sec for IPK and F = 2.0 for SRE.

Figure 6. Reactivity response for a ramp reactivity input for 0.5 pcm/sec τ = 0.5 sec for IPK and F = 2.0 for SRE.

Figure 7. Reactivity response for a sinusoidal reactivity input of 10 pcm × sin(π/20t); τ = 0.5 sec for IPK and F = .0 for SRE.

Figure 8. Comparison of Bode charts for IPK and SRE transfer functions; τ = 0.5 sec and F = 2.0.

Figure 9. Comparison of the respective reactivity difference for IPK and SRE.