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PostPosted: Mar 18, 2012 4:55 pm 
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ORNL-4812 wrote:
Frequency Response and Reactor Stability

The dynamic behaviour of a multiple loop system, such as the MSRE or the reference MSBR, depends of course on the properties of all parts of the system and on the way the parts are linked to form the system. Neutronic characteristics are important, but so are power densities and heat capacities, heat transfer coefficients, salt circulation rates, etc. The short-term time-dependence of reactor parameters such as neutron flux or core-outlet salt temperature will depend at short times (or high frequencies) primarily on the characteristics of the reactor itself , while at longer times (and at lower frequencies) the influence of other parts of the system will, be felt.

A study of the inherent dynamic behavior of a system in the absence of any supervisory controls can reveal the extent to which the system tends to be self-controlling, can help to identify behavioral characteristics of the system that might require the intervention of the control system, and can help to establish requirements for the control system such as the necessary response times.

In studies of the dynamic characteristics of the MSRE and of prospective molten-salt power reactors, several complementary techniques have been used [11], including analysis of frequency response and of transient response to various perturbations. Stability has been studied by several standard techniques and sensitivity studies have explored the effects on stability of variations in important properties of the systems.

All of these studies have shown the MSRE and MSBR designs to be stable, tractable systems, with stability typically increasing (induced oscillations more strongly damped) with increasing power level over the ranges studied (generally 0-100% of design power).

In order to test the validity of these models, an extensive series of dynamic tests was carried out at the MSRE, with both 235U and 233U fuel [12). The tests, like the theoretical studies, included transient response and frequency response characteristics. Comparisons of test results with theoretical predictions have been very satisfactory. As an example, we show in Fig. 4.4 the measured and predicted frequency response of the MSRE at 7 MW(th) with 233U fuel, As is typical of all the frequency response curves obtained for the MSRE and for MSBR’s, this one is rather smooth and featureless, with a broad hump in the gain curve between the high-frequency roll-off due to delayed neutrons arid the falling gain at low frequencies due to the negative temperature coefficients. The small feature in the neighborhood of 0.25 rads/sec is associated with the circulation time of the fuel salt in the primary loop (25 sec). In the experiments, this feature has in all cases been somewhat less pronounced than in the calculations, indicating more mixing in the outlet plenum, piping, and heat exchanger than is included in the theoretical models tested.

Except at very low power levels, the gain curves form a monotonic sequence, falling below the zero power (open loop) curve with diminishing gain as power level increases. This, together with the absence of any structure in the curves other than the circulation effect noted above, is indicative of stable behavior and the absence of any significant resonances in the system response. The good agreement between measured and theoretical curves is evidence of the reliability of the computational models employed.

Extract from ORNL-4812, p 85-87

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PostPosted: Mar 18, 2012 7:20 pm 
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Jaro, thank you for your earlier post. I'm not entirely sure that you and I are talking about the same thing so I'm keen to check that we have a common understanding of the potential issue. When you say ringing, I think mechanical resonance, when you strike a bell with a hammer that creates an impulse at the point of impact, energy is transferred to the bell which tends to vibrate at its natural frequency with some harmonics of that natural frequency.

I presume that the specific concern is a mechanical resonance that appears within the core globally or locally where a disturbance to the system is likely to create a resonant response that continues for a a time, not unlike the ringing bell. Does that accurately describe phenomena that you are concerned about for MCFR's?


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PostPosted: Mar 18, 2012 9:05 pm 
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Thanks Lindsay.
Lindsay wrote:
ORNL-4812 wrote:
All of these studies have shown the MSRE and MSBR designs to be stable, tractable systems, with stability typically increasing (induced oscillations more strongly damped) with increasing power level over the ranges studied (generally 0-100% of design power).

Yes, I'm not surprised that the MSRE and MSBR designs were found to be stable, tractable systems: they both have hundreds of well-defined fuel channels in a graphite core, confining any disturbances to small local regions.
Its not at all like all-salt reactors, such as the MCFR.


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PostPosted: Mar 18, 2012 9:31 pm 
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Lindsay wrote:
I presume that the specific concern is a mechanical resonance that appears within the core globally or locally where a disturbance to the system is likely to create a resonant response that continues for a a time, not unlike the ringing bell. Does that accurately describe phenomena that you are concerned about for MCFR's?

OK, I'm not sure if "resonance" is the appropriate term.
I prefer the word "oscillation", which is probably more generic.
Basically, I'm just talking about pressure waves bouncing around within the confines (walls) of the reactor vessel.

For example, back in the 1950's, there was a proposal for a direct conversion reactor, that would use a long sealed tube filled with fissile gas, and which would generate an oscillating shockwave between the two ends, as compression of the gas induces a supercritical power burst, when the shock hits & compresses the gas at the sealed end, and drives another shock back to the other end (etc., etc....)
Passage of the partially ionised gas would then induce a current in induction coils wrapped around the middle section.

Aside from the question of whether such a system could in fact be made to work in a practical generating plant, the point is that oscillations in nuclear systems are definitely possible.
The curious thing is that when folks come up with concepts that are intended to operate without oscillations, they claim that oscillations are not possible.
When they WANT oscillations, then all of a sudden they work like a charm.
Call me a skeptic, but I think that oscillations can easily sneak into concepts that aren't supposed to have them.
And I don't think its surprizing that we don't see anything about this in textbooks: there is very little about molten salt reactors in general, and what little there is, doesn't include anything at all about graphite-free, all-salt reactors and potential challenges with such systems.
That, in a funny way, works in favour of people who conduct paper studies of these things: everything looks just great, when you only look at the static cases, and ignore the dynamics.
Caveat emptor to anyone who is thinking of actually building those things !!


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PostPosted: Mar 20, 2012 4:08 am 
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Thanks Jaro that helps me understand your perspective a little better. One thing that I would say in defence of fluid fuelled reactors is that liquids, especially those at conditions far from boiling, are more or less incompressible, exerting the same pressure everywhere at the same time (neglecting hydrostatic head). If we were dealing with fissile vapour, that would be compressible, that would certainly add some additional dynamics including the potential for compressible shock waves whci could do some very interesting and potentially unwanted things.

An interesting thing to model is the insertion of a supercritical cold slug into a fast core, which I have tried to do and it was really surprising, there's a horrendous power spike in the slug but within the time-frame of the speed of sound in molten salt allowing salt to leave the core, the temperature rise in the supercritical slug was remarkably modest, but enough to dismantle the excess reactivity. That's not necessary relevant to this issue, but an interesting thing to do.

>Call me a skeptic, but I think that oscillations can easily sneak into concepts that aren't supposed to have them.
I would call that healthy scepticism and encourage you to hang on to it.

There is a lot that we don't know about the dynamic behaviour of these systems, one piece of good news from a real MSR, during ARE they had evidence of a fuel rich slug circulating through the core creating a power spike each time that it passed. On each pass the influence of the slug diminished as it became mixed, but it did not precipitate any ringing or resonant response, rather it was a nicely decaying disturbance with good damping. That actually doesn't mean a lot on its own, but it is always nice to see a nicely damped response in a reactor when someone is poking it with a sharp stick, like a slug of excess reactivity that passes in and out of the running core.


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PostPosted: Mar 20, 2012 7:18 am 
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Lindsay wrote:
One thing that I would say in defence of fluid fuelled reactors is that liquids, especially those at conditions far from boiling, are more or less incompressible, exerting the same pressure everywhere at the same time (neglecting hydrostatic head). If we were dealing with fissile vapour, that would be compressible, that would certainly add some additional dynamics including the potential for compressible shock waves whci could do some very interesting and potentially unwanted things.

Right.... gas is certainly more apt to do this than liquids or solids.

But it may also be possible in liquids and solids, since only small density changes are sufficient to cause significant reactivity effects -- like the cold slug you mention.

The effect may also be augmented, if we are circulating helium bubbles through the MCFR to help remove volatile fission products (and even if not, those volatile fission products will continue to circulate as small bubbles in the system anyway).
Pressure waves will tend to collapse the bubbles, increasing the density of the bulk fluid.


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PostPosted: Mar 20, 2012 12:27 pm 
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jaro wrote:
Thanks Lindsay.
Lindsay wrote:
ORNL-4812 wrote:
All of these studies have shown the MSRE and MSBR designs to be stable, tractable systems, with stability typically increasing (induced oscillations more strongly damped) with increasing power level over the ranges studied (generally 0-100% of design power).

Yes, I'm not surprised that the MSRE and MSBR designs were found to be stable, tractable systems: they both have hundreds of well-defined fuel channels in a graphite core, confining any disturbances to small local regions.
Its not at all like all-salt reactors, such as the MCFR.


Interesting, does this apply to an unmoderated liquid fluoride MSR, too, for example a graphite free tube in tube LeBlanc's configuration ?
If it's so, I don't understand why the French group is trying to pursue their graphite free version


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PostPosted: Mar 20, 2012 3:32 pm 
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Alex P wrote:
I don't understand why the French group is trying to pursue their graphite free version

I think that by sticking to relatively small power, compact fluoride reactors (with conventional, short cylinder geometry, for minimal fissile loading), the French are minimising the risk of instability.
Long tube LFTRs are very unlikely to behave in a stable manner, IMO: Reactors are not sausages, and should not be designed as such.


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PostPosted: Mar 20, 2012 5:46 pm 
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I think this is where we may have difficulty agreeing.

It seems possible to me that for a MCFR there could be a combination of fluid dynamics in the fuel, mechanical vibration in the vessel or other parts of the system, gas bubbles and the neutronics of the core that combine/interact to cause unwanted power fluctuations under certain conditions when a disturbance is injected. But if that is possible for MCFR then it must also be possible for all other fluid fuelled reactors, I can't see any basis for saying that fast reactors might have a problem, but thermal ones can't, that seems highly improbable. The same fundamental issues apply to both, while the natural frequencies of the individual parts of the system are different in fast and thermal systems it is how the different natural frequencies interact that will create oscillations or not.


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PostPosted: Mar 20, 2012 6:20 pm 
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Lindsay wrote:
I can't see any basis for saying that fast reactors might have a problem, but thermal ones can't, that seems highly improbable.

The problem tends to be worse for MCFR than LFTR because of the different neutron spectrum and bulk density: minimum critical size is generally much smaller for fast reactors than thermal ones (the latter include a great deal of moderator, and the best moderators are light-atom, low-density materials like graphite, water, and beryllium).
Consequently, if you build a large LFTR and a similar-size MCFR, the latter is far more likely to be unstable, because it contains many more critical "unit volumes" (and a far larger fissile load), than the thermal neutron version.

Consider an extreme example, as a way to gain insight: a reactor made of a fissile gas (say UF6) surrounded by a thick wall of BeO moderator: due to the very low density of the reactor, it will need to be very large to achieve criticality - likely several meters minimum.
By contrast, a solid U-metal sphere will be critical at a small fraction of a meter, due to the high density and, consequently, low neutron leakage probability.

Now if you make both low- and high-density reactors the same size, because of heat transfer requirements, to generate the same amount of power, then the fast spectrum high-density version will be far more overloaded with fissile, than the thermal spectrum one.
Do you still maintain that there isn't any difference ?


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PostPosted: Mar 21, 2012 6:39 pm 
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I think that I get your point, but your analogy (or my understanding of it) is somewhat different to a MSR where there are a number of strong to very strong self-regulating factors that provide negative feedback to the system:
- The first being Doppler broadening of fertile material that is usually in the core as part of a homogeneous fuel mix, which increases neutron absorptions in fertile;
- The second being reduced atomic density at higher temperatures; and
- The big hammer being the fuel salt expansion moving fissile out of the critical geometry of the core into non-critical geometry.

>Do you still maintain that there isn't any difference ?
I would say that there are significant differences between fast and thermal spectrum MSR's and their expected behaviour as far as the numbers and details are concerned. In terms of possible unintended consequences I agree with your point about the possibility of vibrations and power fluctuations in a MCFR core, but I'm extending that idea to say that I don't think that thermal MSR's are so different that this possibility can be ignored. I would expect the risk of a bad outcome to be lower with a thermal design and we have operating data from two different cores that shows they had a very stable response to disturbances and changing conditions, but ORNL did enough modelling during the design phase to try and predict the likely response of the system to disturbances which is absolutely the right thing to do IMO.

I'd be happy to lay out more of my reasoning for I believe that potential for interactive resonances need to be carefully considered in all MSR designs based on my limited understanding of the physics involved, but the trump card is I believe that if it was good enough for ORNL to take the issue seriously, then it should be good enough for anyone who chooses to take up their work and that applies to thermal and fast cores alike IMO. I would also say that it entirely appropriate to examine those risks in fast cores more carefully and with a heightened sense of caution.


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PostPosted: Mar 21, 2012 6:58 pm 
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Not much argument there, Lindsay.
Lindsay wrote:
....we have operating data from two different cores that shows they had a very stable response to disturbances and changing conditions, but ORNL did enough modelling during the design phase to try and predict the likely response of the system to disturbances....
Again, I would just caution that ORNL's designs are irrelevant to any discussion of all-salt reactors - be they thermal or fast neutron spectrum.

The exception is the Fireball reactor, which was never operated, despite coming close to completion of construction.
THe core was very small though, and roughly spherical in shape (minimum critical configuration), so I would expect it to be quite stable as well.


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PostPosted: Mar 22, 2012 9:40 am 
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jaro wrote:
Alex P wrote:
I don't understand why the French group is trying to pursue their graphite free version

I think that by sticking to relatively small power, compact fluoride reactors (with conventional, short cylinder geometry, for minimal fissile loading), the French are minimising the risk of instability........

On the description page for MURE, the code the French group developed used for some of their simulation work
NEA wrote:
......MURE also provides coupling of the neutronics (with or without fuel burn-up) and thermal-hydraulics using a sub-channel 3D code, COBRA-EN.....
Which suggests they were interested in checking the dynamics / stability, though they may not have gone into it in great depth.


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PostPosted: Mar 22, 2012 9:53 am 
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Thanks Luke,
Luke wrote:
On the description page for MURE, the code the French group developed used for some of their simulation work
NEA wrote:
......MURE also provides coupling of the neutronics (with or without fuel burn-up) and thermal-hydraulics using a sub-channel 3D code, COBRA-EN.....
Which suggests they were interested in checking the dynamics / stability, though they may not have gone into it in great depth.
I'm a bit puzzled by the quote from the French study: does "coupling" neutronics with thermal-hydraulics necessarily mean dynamics / stability simulation ?
....and if it does, what sort of time resolution is their simulation capable of ? ....does it cover transients shorter than a second, as one would expect for pressure wave oscillations ?


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PostPosted: Mar 22, 2012 12:31 pm 
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Lindsay wrote:
I think that I get your point, but your analogy (or my understanding of it) is somewhat different to a MSR where there are a number of strong to very strong self-regulating factors that provide negative feedback to the system:
- The first being Doppler broadening of fertile material that is usually in the core as part of a homogeneous fuel mix, which increases neutron absorptions in fertile;
- The second being reduced atomic density at higher temperatures; and
- The big hammer being the fuel salt expansion moving fissile out of the critical geometry of the core into non-critical geometry.


Negative feedbacks are not enough to prove that a reactor is stable.

For example, consider a standard BWR with negative doppler coefficient and negative coolant void fraction coefficient. Assume a fission rate increase, which increases local temperature immediately, thereby reducing reactivity fission rate. On a longer timescale the heat is transferred to the coolant, so that the void fraction increases. The increased void fraction decreases reactivity further, which reducese the fission rate, which reduces fuel temperature. The reduced fuel temperature then increases reactivity and fission rate and the cycle continues. If the time scales and reactivity coefficients happen to be bad the cyclic behavior might not be damped but allow the oscillations to grow in magnitude.

And I think they had such oscillations described above in Swedish BWRs, so it is not only theoretical.

Therefore, negative coefficients: good, but only a starting point to dynamic studies.


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