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 Post subject: Change in power with time and temperaturePosted: Aug 12, 2009 10:27 pm

Joined: May 14, 2009 12:21 am
Posts: 41
Location: southwest corner of the US of A
I wondered how stable our LFTR design might be and I quickly exceeded my knowledge. We have some thermal-reactivity coefficients. ondrejch wrote:Feedback -9.53 pcm/K. That means dk/dT is -95.3*10-6/K to me. That is the ratio of neutrons from one generation to another.

If we knew the time from one generation to the next, the equivalent neutron lifetime, then we could calculate the rate of power change if our LFTR were one degree K above equilibrium;
power change per second= k^(1/apparent neutron lifetime)

Does anyone have a good number for the apparent neutron lifetime when used for control calculations? I know the real calculation has to include multiple neutron energy groups and delayed neutrons. The "apparent neutron lifetime" is only an affine approximation. I'm assuming the design is thermal and carbon moderated with the fuel/moderator ratio selected to maximize k.

Rob

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 Post subject: Re: Change in power with time and temperaturePosted: Aug 12, 2009 10:38 pm

Joined: Jul 28, 2008 10:44 pm
Posts: 3065
The french reactor (no graphite somewhat fast spectrum) 8.5uSec.
A thermal reactor will be much slower (tenths to tens of seconds).

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 Post subject: Re: Change in power with time and temperaturePosted: Aug 13, 2009 5:09 am

Joined: Oct 29, 2007 6:27 pm
Posts: 277
Not really...

you need to use your neutron kinetics equations...1-D normally suffices for core averaged effects. In this equations the reactivity is an input and that one is normall 0 when you operate in critical conditions. If you raise your temperature 1K your reactivity takes a jump to -95.3 E-6 and you have a transient which you can deduce from those equations...

Your type of calculation is totally inadequate as you can't predict possible overshoot in power/temperature...furthermore the reactivity change equals 1/k dk/dT

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 Post subject: Re: Change in power with time and temperaturePosted: Aug 13, 2009 3:41 pm

Joined: May 14, 2009 12:21 am
Posts: 41
Location: southwest corner of the US of A
I was inaccurate with my terms. Reactivity is 0 (zero) for steady state and the effective multiplication factor, k, k=r+1 by definition.

Therefore the reactivity, r, becomes -95.3*10-6 for a degree temperature rise. The size of the next neutron generation, N(i+1)=N(i)*k. In a departure from steady state, if the temperature increases by a degree then k becomes 1-95.3*10-6, slightly less than one. I don't think this is physics, but simply a matter of definitions.

I'd still like to know a good approximation for the neutron lifetime in a well moderated thermal carbon reactor.

Rob

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 Post subject: Re: Change in power with time and temperaturePosted: Aug 13, 2009 4:47 pm

Joined: Dec 03, 2008 5:23 pm
Posts: 137
Location: Oak Ridge, TN
I would suggest that you google or look up in an intro to nuclear engineering book "point kinetics equations". These are the equations that describe the kinetics of a reactor in a spatially independent manner. These equations explicitly take into account the delayed neutrons, for which six groups are typically used. For a simple study you can use one delayed neutron group. The equations are a system of linear ODEs that are pretty straight forward to solve (refer to NE text book). You can add an additional equation for the reactivity as a function of temperature based on a first order temperature coefficient (dk/dT). Remember that you will need to reduce the delayed neutron fraction to account for the delayed neutrons that are emitted outside of the core. You can probably find some of the key parameters (prompt neutron lifetime, effective delayed neutron fraction, delayed neutron loss) for a typical MSR in the old ORNL reports. Also note that reactivity is actually related to k-eff by rho = (k-1)/k. For k ~ 1, your equation holds, so rho(T) = dk/dT*(T-Tcrit).

The prompt neutron lifetime for a well moderated graphite system in on the order of 1 millisecond, of course this does not take into account delayed neutrons, which are treated explicitly in the point kinetics equations.

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 Post subject: Re: Change in power with time and temperaturePosted: Aug 13, 2009 7:48 pm

Joined: Nov 30, 2006 3:30 pm
Posts: 3721
Location: Alabama
Here's a java code I wrote several years ago to integrate the point-kinetics equations (using a Runge-Kutta 4th order method) for a nuclear engineering class I took:
Attachment:
PointKinetics.java [2.96 KiB]

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