Hot Channel Analysis of Small PWR core

[Syed Alam]

I am currently working on thermal-hydraulics of a small PWR.

The configurations are:
Thermal power (MWth) 333
Core height is 1.8 m
Pressure (MPa) 15.5
Total rod diameter (mm) 9.50
pin pitch (mm) 12.65
Pitch/diameter ratio 1.33
Flow Area (m2) 8.92E-05
Intlet mass flow/area (kg/m2/s) 3384.46
Radial peaking factor 1.64
Axial peaking factor 1.57
Composite peaking factor 2.57
Total fuel mass (tonne) 18.05
Power density (MW/m3) 61.6
Average linear rating (kW/m) 9.90
Peak linear rating (kW/m) 27.00

1. * I have performed hot channel analysis on COBRA-EN code and got Pressure Drop of 30 KPa.
2. * But for high power density, I have changed fuel rod diameter to 11 mm with (constant pin pitch) and I have got Pressure Drop of 70 KPa

a. What is the highest and acceptable limit of "Pressure Drop" ?

b. In "constant mass flow", MDNBR is improving with the increase in fuel rod diameter. Why is it increasing?

c. In "constant mass flux", MDNBR is decreasing with the increase in fuel rod diameter. Why is it decreasing?

d. Why fuel centerline temperature is decreasing with increase in fuel rod diameter?

e. It seems that tighter fuel lattices (constant pin pitch) have improved effect in DNBR (same mass flow) and fuel and cladding surface temperature. The only problem is that "Pressure Drop" is increasing. Except the increase in "Pressure Drop" , are there any thermal-hydraulic problems that we can expect?



Thank you very much!

 

[QuantumPion]

a) depends on your pumps
b) larger heated surface area
c) if you hold mass flux constant and decrease flow area, you have less flow.
d) you have lower power density due to having more fuel
e) The reason why you are seeing improved DNBR is due to lower power density. You will also have other problems on the core physics side of things such as being way undermoderated and needing higher enrichment.

 

[Syed Alam]

I don't understand your question. Having a tighter fuel lattice and a constant pin pitch are mutually exclusive.

If I keep the pin pitch same and increase the fuel rod diameter, it can be observed

"improved effect in DNBR (same mass flow) and fuel and cladding surface temperature. The only problem is that "Pressure Drop" is increasing. Except the increase in "Pressure Drop" , are there any thermal-hydraulic problems that we can expect?


My another question is that, how can I increase the "power density"? Can I increase it only by "keeping the pin pitch same and increase the fuel rod diameter" or decreasing the pin pitch and increasing the fuel rod diameter (small Pitch-to-diameter ratio)? Which one is the correct way?

 

[QuantumPion]

Yes I figured out what you meant by tighter fuel lattice above.

Power density is an input to your analysis, not an output. You can make the reactor power whatever you want. The reason why increasing rod diameter with the same pitch decreases power density is because you are keeping MW/m^3 constant but increasing the fuel volume (and decreasing the moderator volume). You can increase your MW/m^3 and kw/m in your input to maintain the same power density but this will result in an increase in total core power because the core volume is presumably constant.

 

[Astronuc]

Those parameters look similar to a normal PWR, particularly a 17x17 design using 9.5 mm OD cladding.

If one increases the fuel diameter, but keeps the LHGR constant, then the power density in the fuel (UO₂) decreases, and the heat flux through the cladding decreases, which is good for DNBR. Furthermore, increasing the fuel rod diameter while keeping the pitch constant will reduce the moderation and harden the spectrum, and increase the coolant velocity if the mass flux is kept constant.

An 11 mm cladding diameter is more like a 15x15 or 16x16 design.

I think the pressure drop across the core is a bit low.

For improved thermal performance (maximum margin to DNB), one wants a lower heat flux and higher coolant velocity. On the other hand, to minimize the energy consumed by pumps, one wants to minimize flow velocity.

One could try natural convection, but then if the flow rate is too low, one gets a fair amount of nucleate boiling, which can be a concern with respect to cladding corrosion and crud deposition. With low flow, one can approach pool boiling regimes, which are somewhat more complicated than forced convection.

Flow velocity is a concern for flow-induced vibration (FIV) and grid-to-rod fretting (GTRF). Also, since maximum deflection in a seismic event would tend to occur at the core mid-plane, the fuel assembly would need a spacer grid at the mid-plane. For a 1.8 m core, one would employ 5 grids giving 4 spans of ~0.45 m. For conventional (3.66 m) cores, the spans are typically on the order of 0.52 m.

 

[Syed Alam]

Those parameters look similar to a normal PWR, particularly a 17x17 design using 9.5 mm OD cladding.

If one increases the fuel diameter, but keeps the LHGR constant, then the power density in the fuel (UO₂) decreases, and the heat flux through the cladding decreases, which is good for DNBR. Furthermore, increasing the fuel rod diameter while keeping the pitch constant will reduce the moderation and harden the spectrum, and increase the coolant velocity if the mass flux is kept constant.

An 11 mm cladding diameter is more like a 15x15 or 16x16 design.

I think the pressure drop across the core is a bit low.

For improved thermal performance (maximum margin to DNB), one wants a lower heat flux and higher coolant velocity. On the other hand, to minimize the energy consumed by pumps, one wants to minimize flow velocity.

One could try natural convection, but then if the flow rate is too low, one gets a fair amount of nucleate boiling, which can be a concern with respect to cladding corrosion and crud deposition. With low flow, one can approach pool boiling regimes, which are somewhat more complicated than forced convection.

Flow velocity is a concern for flow-induced vibration (FIV) and grid-to-rod fretting (GTRF). Also, since maximum deflection in a seismic event would tend to occur at the core mid-plane, the fuel assembly would need a spacer grid at the mid-plane. For a 1.8 m core, one would employ 5 grids giving 4 spans of ~0.45 m. For conventional (3.66 m) cores, the spans are typically on the order of 0.52 m.

Thanks a lot. I want to ask a question based on your reply.
Generally, I calculate Power Density by

= Power/(Total Assemblies* Core Height* Area of Assembly)
In my case for
Core Power of 333 MWth, 13x13 design with 12.65 mm pitch,
Area of assembly=(Assembly side length)^2 =(12.65*13)^2 =16.45 mm
Total Assemblies=112
Core Heigt=1.79 m
so, Power Density= 333 MW/(112*16.45*1.79)= 63 MW/m^3

So, from the calculation above, Power density is dependent on pin pitch. It pitch is reduced, power density is reduced as well.

But how does the increase in fuel diameter decrease the Power Density of the core for my calculation mentioned above?If one increases the fuel diameter while keeping the pitch constant but does not keep the LHGR constant, will the core power density decrease?

If one increases the fuel diameter while reducing the pitch, will the power density be increased?

 

[Astronuc]

It would be helpful to differentiate between the volumetric power density of the core, which includes both moderator and fuel, and the fuel power density where one only considers the power generation in the fuel proper, i.e., the fuel meat (UO₂ or MOX or whatever). One also must remember that power density and LHGR are spatially dependent, and assemblies on the periphery of the core will have a lower power density than those in the interior. It is important to design a core to minimize power peaking and maintain margins to thermal and thermo-mechanical limits.

The fuel rod diameter and pitch determine the fuel to moderator ratio, which can be optimized in lattice calculations. One may wish to look at existing fuel assembly lattice designs for conventional PWRs. Conventional square lattices vary from 14x14 to 18x18. Typically the 14x14 and 15x15 designs use similar fuel rod diameters, 16x16 designs vary depending on the supplier (AREVA (formerly Siemens/KWU) or Westinghouse (formerly CE or W 16x16 designs), and 17x17 and 18x18 use similar fuel rod diameters (typically 9.5 mm), although there is a population of 17x17 fuel which uses 9.14 mm OD on the cladding. The 17x17 population is the majority of PWR fuel in the world, and a pin pitch of 12.63 mm is common.

One could also look at BWR fuel designs, which are smaller. Current BWR fuel lattices are typically 10x10, but AREVA is offering an 11x11 design.

Of course, one could consider a hexagonal lattice similar to that used in VVER systems.If one increases the fuel diameter while keeping the pitch constant but does not keep the LHGR constant, will the core power density decrease?
If one increases the fuel diameter with constant pitch, the core power density would remain the same, but the power density in the fuel would decrease assuming the total power is fixed. The fuel to moderator ratio would decrease, because the fuel would displace moderator/coolant in the cell. The core would shift toward being undermoderated and the neutron spectrum would be harder.

If one increases the fuel diameter while reducing the pitch, will the power density be increased?
One would probably not want to do that. Less moderation and less coolant.

One has to balance the nuclear design and the thermal hydraulic design. The moderator/coolant has to carry heat from the fuel rods. One has to be concerned with the enthalpy rise along/up the coolant channel, since toward the top of the fuel assembly/rods, the coolant temperature necessarily increases, and the margin to critical heat flux decreases.

The core size/volume is determined by the number of assemblies and the size of each assembly. The rod diameter affects the internal dimensions of the assembly, more so than the envelope of the assembly.

 

[Syed Alam]

It would be helpful to differentiate between the volumetric power density of the core, which includes both moderator and fuel, and the fuel power density where one only considers the power generation in the fuel proper, i.e., the fuel meat (UO₂ or MOX or whatever). One also must remember that power density and LHGR are spatially dependent, and assemblies on the periphery of the core will have a lower power density than those in the interior. It is important to design a core to minimize power peaking and maintain margins to thermal and thermo-mechanical limits.

The fuel rod diameter and pitch determine the fuel to moderator ratio, which can be optimized in lattice calculations. One may wish to look at existing fuel assembly lattice designs for conventional PWRs. Conventional square lattices vary from 14x14 to 18x18. Typically the 14x14 and 15x15 designs use similar fuel rod diameters, 16x16 designs vary depending on the supplier (AREVA (formerly Siemens/KWU) or Westinghouse (formerly CE or W 16x16 designs), and 17x17 and 18x18 use similar fuel rod diameters (typically 9.5 mm), although there is a population of 17x17 fuel which uses 9.14 mm OD on the cladding. The 17x17 population is the majority of PWR fuel in the world, and a pin pitch of 12.63 mm is common.

One could also look at BWR fuel designs, which are smaller. Current BWR fuel lattices are typically 10x10, but AREVA is offering an 11x11 design.

Of course, one could consider a hexagonal lattice similar to that used in VVER systems.If one increases the fuel diameter while keeping the pitch constant but does not keep the LHGR constant, will the core power density decrease?
If one increases the fuel diameter with constant pitch, the core power density would remain the same, but the power density in the fuel would decrease assuming the total power is fixed. The fuel to moderator ratio would decrease, because the fuel would displace moderator/coolant in the cell. The core would shift toward being undermoderated and the neutron spectrum would be harder.

If one increases the fuel diameter while reducing the pitch, will the power density be increased?
One would probably not want to do that. Less moderation and less coolant.

One has to balance the nuclear design and the thermal hydraulic design. The moderator/coolant has to carry heat from the fuel rods. One has to be concerned with the enthalpy rise along/up the coolant channel, since toward the top of the fuel assembly/rods, the coolant temperature necessarily increases, and the margin to critical heat flux decreases.

The core size/volume is determined by the number of assemblies and the size of each assembly. The rod diameter affects the internal dimensions of the assembly, more so than the envelope of the assembly.

Dear Astronuc,
I don't know how to thank you fro your great explanation. I really had vague idea about power density concept. Now it is crystal clear. Massive thanks. Your answers are really a great support for my conception and PhD. That means a lot for me.
However, I will ask some more questions to you in this thread regarding this topic :)

 

[Astronuc]

For a PWR, one would also want to look at the number of guide tube locations in the assembly, and the number of assemblies under control rods in the core.

PWR fuel assemblies normally allow for insertion of control rods in the assembly as opposed to cruciform control rods inserted between assemblies as is the case for BWRs. There were however some notable exceptions, e.g., Yankee Row and Palisades, which did indeed use cruciform control rods among assemblies. They also required unique fuel assembly lattice designs. The guide tubes may also accept removable primary and secondary neutron source assembly, as well as burnable poison assemblies, and empty guide tubes do provide some moderation.

This book Nuclear Reactor Design may provide some useful information. It would be worth purchasing since it gives some good background and some history.