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# Reactor

## Reactor

(OP)
Hello,

I am a mechanical engineer. While my knowledge about archaeology is more than nuclear sciences I appreciate your guidance for solving following problem:

How can I calculate?

1-Mass of fuel UO2 in reactor, kg
2-Total heat release rate in fuel, MW
3-Average fuel power density, kW/kg
4-Average core power density MW/m3
5-Average fuel rod heat flux kW/m2
6-Thermal power output based on coolant flow rate, MW

With below characteristics for a reactor:

Number of fuel assemblies in reactor    157
Number of fuel rods per assembly    264 (17X17 array)
Fuel rod outside diameter        9.5 mm
Fuel rod lattice pitch            12.6mm
Fuel rod effective length        3.658m
Fuel pellet diameter            8.19mm
Equivalent reactor core diameter    3.040m
Average U-235 enrichment        2.8%
Effective U-235 fission cross section    360 barns
Uranium dioxide density            10400kg/m3
Average neutron flux        4.5x10e13 neutron/cm2s
Energy per fission            32pJ
Reactor coolant inlet temperature    286C
Reactor coolant outlet temperature    325C
Coolant flow rate through reactor core    12600kg/s
Coolant pressure            15.5Mpa
and 1 barn=10e-28 m2

### RE: Reactor

Is this a homework problem?

### RE: Reactor

(OP)
No! that's a personal study.

### RE: Reactor

If it is a power reactor, I would think that most of the "average" values can be derived from the turbine cycle diagram or process heat and mass balance diagram.

### RE: Reactor

(OP)
The problem is, actually I could not find any equation in available sources in the internet for:

Heat release rate in fuel, MW
Fuel rod heat flux kW/m2
Average fuel power density, kW/kg

### RE: Reactor

That's some pretty specific information you have about the reactor.  I'd probably go to the source for that information to find the missing values.  Unless that's what you're supposed to be solving (i.e., it's homework, even if "for personal study.")

In that case, you probably need to go buy a nuclear engineering textbook.  I'm not sure of the exact title of the one I have (as it's at home) but it was something like "Principles of Nuclear Engineering."

Patricia Lougheed

******

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### RE: Reactor

Well, how sophisticated (accurate) do your answers need to be?  Given the coolant inlet & outlet temperatures and pressures, you can look up the enthalpies.  Don't have inlet & outlet pressures? - recognize that the small variation in pressure doesn't affect the enthalpy much.  Multiply core enthalpy rise with flow rate to get power generated.

Now, when you  ask for 'heat release in fuel' do you mean, 'exclusive of heat generated in structure or coolant'?  You see, some of the fission energy appears as gamma heating outside the fuel itself.  If you are aware of this and wish to account for it, see vpl's post above ('get a nuclear engineering book').  If you are simply looking for the 'core power' then the (flow)x(enthalpy rise) above will be OK.

I notice you list 'reactor' inlet/outlet temperature.  Do you mean 'vessel' inlet/outlet or 'core' inlet outlet?  They are not necessarily identical, as there is usually a 'core bypass' flow that isn't heated by passing through the core.  I ask because your flow rate is called 'core' flow.  The enthalpy rise calc mentioned above must be done with the vessel temps & the vessel flow; or with the core temps and the core flow - if you mix these up you will get the wrong answer.

Once you have this total power, the other parameters are derived by dividing by total fuel length, surface area, mass etc.

### RE: Reactor

Hmmm, this looks oddly like something I had to do while in school... *shrugs*

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