Nuclear Safety Parameters
of TRIGA Reactor
The purpose of this presentation is physical explanation of most important nuclear safety parameters:
·power peaking factors
· temperature and void reactivity coefficient.
Results are directly applicable to TRIGA reactor operation and safety analysis.
More detailed explanation is found in the following references:
1. M. Ravnik, Nuclear safety parameters of mixed TRIGA cores, Workshop on reactor physics calculations, 12 February to 13 March 1990, ICTP, Trieste, Proceedings: p. 399-421, World Scientific,1991.
2. M. Ravnik, PWR Core design calculations, Workshop on reactor physics calculations, 17 February to 21 March 1986, ICTP, Trieste, Proceedings: p. 157-186, World Scientific,1986.
1. Power peaking factors
Fuel power density must be limited due to temperature, thermal-hydraulics and mechanical design limitations. In TRIGA, temperature limitation (11000C) is imposed by internal hydrogen pressure due to temperature dissociation of Zirconium-hydride.
Power density distribution in a realistic reactor is neither continuos nor smooth, due to
- leakage and reflector effects
- differences in fuel composition, uranium concentration, enrichment, burnable absorbers, burn-up, control rod effect,…
- non-fuel parts of the core: empty positions, water gaps, irradiation channels, control rods
fuel rod heterogeneity
1.1. Leakage and reflector effects
Even if the core is homogeneous and compact the flux and power density is affected at the core/reflector boundary (Fig. 1)
flux distribution is continuos
function of position in the reactor
power density distribution, proportional to product of flux and macroscopic fission cross-section, is not continuos
Inherent effect due to leakage in finite reactor systems:
Flux distribution in radialdirection normally peaked in the center with radial power peaking factor typically 1.65 (in TRIGA)
Theoretical radial distribution for homogeneous bare cylinder: Bessel function
Flux distribution in axial direction also peaked in the center with axial power peaking factor typically 1.3 (in TRIGA)
Theoretical axial distribution for homogeneous bare cylinder: cosine
1.2. Core composition
Core is normally loaded with fuel elements that are (practically) identical in
but may significantly differ in
burnable poison concentration.
These design features are normally applied to reduce power density variations induced by leakage (e.g. by using more enriched fuel elements at the core periphery, 'Low Leakage Loading Pattern'). However, if they are not properly used, the effect may be opposite.
Radial power peaking factor in mixed core normally increased compared to uniform core (Fig. 4)
Effect of burn-up and burnable poison is similar but normally not so strong as effect of design variations in enrichment or uranium concentration.
1.3. Non-fuel parts of the core
Influence of irradiation channel on power density in nearest fuel elements is illustrated in Fig. 4 and Fig. 5.
1.4. Power distribution inside fuel rod
Particularly important for pulsing, when fuel temperature immediately after the pulse proportional to power distribution due to too short time for heat diffusion.
Relative radial power distribution in TRIGA fuel rod is presented in Fig.6.
Total power peaking factor is conservatively product of several partial peaking factors, depending on conditions
radial x axial x irradiation channel x inside fuel rod x … = total
For pulsing with compact uniform TRIGA core with Standard 20% enriched fuel containing one irradiation channel:
1.6 x 1.3 x 1.17 x 1.20 = 2.92
Maximum power density is approximately three times bigger than the average
For pulsing with mixed TRIGA core with 20% and 70% enriched fuel containing one empty (water filled) position:
2.0 x 1.3 x 1.45 x 1.50 = 5.65
Maximum power density is almost two times bigger than in uniform core without empty positions
Obviously: To reduce power density peaking avoid
mixed core (use one type of fuel elements)
water gaps, empty positions, irradiation channels (use compact core configuration).
2. Fuel temperature reactivity coefficient
Two main effects contribute to fuel temperature reactivity effect:
thermal spectrum shift (spectrum hardening).
Doppler effect is result of increased resonance capture reaction rate in U-238 due to resonance broadening (the same effect as in low enriched uranium power reactors). In TRIGA Doppler effect contributes less than half to total fuel temperature reactivity effect.
Spectrum hardening is dominating effect in TRIGA. The effect is as follows:
Increasing of fuel temperature results in shift to higher energy and deformation of Maxwellian spectrum in fuel. Spectrum in water is only slightly affected due to smaller increase in water temperature. Fission reaction rate in fuel is reduced due to harder spectrum in fuel, absorption reaction rate (sum of absorption in fuel and water) is less reduced. Ratio of fission reaction rate and absorption reaction rate (p.d. equal to multiplication factor) is reduced. Reactivity effect is negative.
Temperature reactivity coefficient af in TRIGA reactors is sensitive to neutron spectrum due to spectrum hardening effect.
For this reason af depends on
enrichment (also affects Doppler effect, directly through U-238 concentration)
Examples for two fuel types with different enrichment and different uranium concentration are presented in Fig. 7 and 8 in dependence of burn-up and temperature.
3. Void reactivity coefficient
Reducing effective water density in reactor by
temperature expansion (temperature increase) or
void (steam or air bubbles, void irradiation channels)
directly affects moderation in water. This may affect reactivity in negative or positive way, depending on fuel/water volume ratio (reactor overmoderated or undermoderated). TRIGA reactors are designed as undermoderated. Decreasing water/fuel ratio normally results in reducing reactivity. However, effect depends also on the position of void in the reactor:
void in fuel region inside core reduces reactivity
void in water gap between core and reflector may increase reactivity.
Negative void effect of the core is prevailing considering water density changes due to heating or cooling. Water temperature reactivity coefficient is for this reason negative.
4. Power reactivity coefficient, which is a "superposition" of fuel temperature reactivity and water temperature reactivity coefficient is also negative. Prevailing contribution is fuel temperature reactivity effect, because Doppler and spectrum hardening contribute more to negative reactivity than reduced moderation density in water.
Power peaking factors and temperature reactivity coefficients are the most important reactor parameters for normal operation and transient safety analysis in research as well as in power reactors. They form the basis for technical specifications and limitations for reactor operation such as loading pattern limitations for pulse operation (in TRIGA).
Fig. 1. Flux and power radial distribution in mixed TRIGA core
Fig. 2. Radial flux distribution in uniform TRIGA core
Fig. 3. Axial flux distribution in uniform TRIGA core
Fig. 4. Thermal flux distribution in mixed TRIGA core (70% enriched FLIP fuel mixed with 20% enriched Standard fuel).
Fig. 5. Radial power density distribution around a core position not containing fuel rod
Fig. 6. Relative radial power density distribution in fuel rod for different types of TRIGA fuel
Fig. 7. Fuel temperature reactivity coefficient in pcm/0C as a function of fuel temperature and burn up for standard, 20% enriched TRIGA fuel containing 12wt% uranium
Fig. 8. Fuel temperature reactivity coefficient in pcm/0C as a function of fuel temperature and burn up for FLIP, 70% enriched TRIGA fuel containing 8.5wt% uranium