Nuclear design Flashcards
average volumetric power of typical reactors
AGR = 3 kW/l
PHWR = 10 kW/l
RBMK = 20 kW/l
BWR = 50 kW/l
PWR = 100 kW/l
LMFR = 300 kW/l
what is the equivalent radiative heat transfer coefficent for the gap
h_irr = 4 * sigma * T_fo^3 / (1/eps_f + 1/eps_cl -1)
Thermal resistance of vod fuel
R_fuel = 1 / (4 * pi * avgK) * (void factor)
void factor = 1 - ln( (R_fo/R_fi)^2 ) / ((R_fo/R_fi)^2 -1)
hot channel coefficents
FzN = average hf hot ch / average hf average ch = 1.5 (Bessel)
FmaxN = max hf hot ch / average hf hot ch = 2.3 (cosine)
hentalpy hot ch factor
Fh = hentalpy rise in hot ch / hentalpy rise in avergae ch = 1.1
engineering safety factor
Feng = 1.05 (5%)
Robertson factor
RF = 4 / (chi^2R_fo^2) * I(chiR_fo) -1)
How can we categorize different tyoe of reactor (U, BR, cycle)
U = fuel fissioned/resource input = 0.5%(LWR) - 5% (LMFR)
BR = fission produced/atoms consumed
open or closed cycle
Burner: BR<1, open
Breeder: BR>1, open
Converter: BR<1, closed
Incinerators: BR=1
Melting temperature for fuels
Tmelt:
UO2 = 2800 °C
UN = 2300°C
Umetal = 110°C
What phenomena must be descirbed by fuel performance codes?
-Thermo-mechanical behaviour
-Neutron flux
-Fission gas and Helium
-Microstructural change (high burnup and restructuring)
-Radial temperature gradient (hourglassing, …)
-Chemical phenomena
Very different scales in space and time
Which phenomena are involved in fuel restructuring?
-Densification
-Grain growth
-Formation of columnar and equiaxed
-Formation of central void
Other related phenomena are:
-crack healing
-plutonium, hence power redistribution
Which phenomena contribute, negatively or positively, to restructuring?
- temperature caused evaporation and condensation in lenticular pores (high temperature vapours)
- diffusion due to temperature (Soret) and concentration gradients
- irradiation at EoL
- cracks increase the migration
Which are the thermal effects of restructuring?
- Better geometry
- Less porosity
- Pu redistribution increase power production towards the center
- O/M = 2 at perphery, lower at center, due to high volatility
Why a O/M ratio higher than 2 is dangerous?
High oxygen concentration can react and corrode the cladding if there is contact. For this reason pelets are always hypostoichiometric
What are the effects of plutonium redistribution?
-Reduction of melting temperature
-Increase of power production
-Reduction of thermal conductivity
What are the O/M stoichiometry effects?
-Fabrication with hypostochiometry to reduce risk of cladding corrosion so that conductivity increases during operation (pyramidal shape)
- T melting is maximum at O/M = 2
What is the effect of porosity?
It decreases fuel conductivity
fuel conductivity formula with all dependences?
K = (1/(A+BT) + CT^3 + D/T^2 * exp(-E/T) ) * (1-p)^alpha
Also it decrases asintotically with burnup
When densification and swelling are important in LWR?
Densification is dominant for Bu< 10 GWd/ton. It is due to frenkel pair created from fission. 5 MeV create 25000 Frenkel pair per each fission but only 5000 do not recombine and create densification. Interstitals are absobed and vacancies diffuse to grain boundary.
To limit densification, a limit on fuel porosity at fabrication must be respected (in LWR)
Above Bu>10 GWd/ton swelling dominate, due to fission gas
What happens in a LWR if p_gap > p_coolant ?
We have outward creep, cause Zry it’s not very resistant to creep -> the gap increase -> fuel temperature increases -> more gas are released -> p_gap increases
Also k_fuel decreases and D_hyd decreases -> T_coolant increases
What about densification in LMFR?
Densification due to restructuring is dominant respect to the one due to fission. Because of this porosity is actually wanted in FR fuel becuase it enhances restructuring
Void swelling
Happens at EoL for FR and causes both fuel and cladding to expand. The rate is almost the same.
Which are the main Pellet-Cladding interaction
Hourglassing, negligible for hollow pellets. This leades to
-high stresses in cladding
-chemical reaction between iodine and Zry (not with SS)
What is the burn up in MWd/ton?
Bu is the energy extracted per unit mass.
Bu = releases energy (MWd) / mass of uranium fuel (kg_U)
Tipically 1MWd/1.05 g_U235
We can also measure it as (released energy / mass of oxide fuel) which will be smaller of a factor 0.88.
The teoretical limit is 950’000 MWd/ton_U but in reality we reach around 50’000 - 70’000 MWd/ton_U
What is the burnup in FIMA?
FIMA = Fission per metal atom = fissions / initail metal atoms
So 1% FIMA = 9.5 MWd/kg_U
What are the effects of burnup ?
- may lead to a high burnup structure
- decrease young modulus
- decrease thermal conductivity