1. Thermoacoustic Sensor for Nuclear Fuel Temperature Monitoring
22nd May 2013, NDCM-13, Le Mans, France
Randall Ali and Steven Garrett, Graduate Program in Acoustics,
The Pennsylvania State University, USA
James Smith and Dale Kotter, Fundamental Fuel Properties Group,
Idaho National Lab, USA

2. Fukushima Daiichi Nuclear Disaster
The research was motivated by the most powerful earthquake to hit Japan which severely damaged the Nuclear Power Plant at Fukushima Daiichi. Because they lost power to the sensors, in particular temp information, quick, informed decisions to make the situation better were difficult to implement. Is there a way to take advantage of the harsh operating conditions of the nuclear reactor?
Most powerful earthquake in Japan
Failure of Nuclear Reactors
Loss of Electrical Power to Sensors

3. A Thermoacoustic Solution?
Mass and two springs.
Porous substrate with pores that are about twice the thermal penetration depth.
Pressure gets higher at left pushing the gas out a little farther and vice versa.

4. J. W. Strutt (Lord Rayleigh)
“If heat be given to the air at the moment of greatest condensation, or be taken from it at the moment of greatest rarefaction, the vibration is encouraged.”
Nature 18, (1878)

5. Synergistic with Fuel Rods
No Heat Exchangers!
Acoustic
Streaming
Electromagnetic
Radiation
Heat source
(Nuclear Fuel)
stacks

6. The Thermoacoustic Fuel-Rod Engine
Temp Sensor
Schrader Valve
3 Type- E T/C Feedthroughs
Mic
Instrumentation Plate
Thermal Mass
(Distilled H2O))
Nitronic 60 Stainless Steel – same size as a fuel rod
Calorimeter

7. Where’s the Nuclear Fuel???
Indirect Heating
Direct Heating

8. True for ideal gases at a constant temperature.
Thermometry Basics
INVARIANT QUANTITY
c – Sound Speed (m/s)
f – Frequency (Hz)
True for ideal gases at a constant temperature.
T – Temperature (K)
We figured that since the gas on the ambient side of the resonator was the same temp. as the water, we can measure the temperature of the water.
g – Polytropic Coefficient
 – Universal Gas Constant (J/mol-K)
The nature of the thermoacoustic resonator is that it needs a temperature gradient for operation!
M – Molecular Mass of Gas (kg/mol)
L – Length of Resonator (m)

9. Thermometry Experiment
Indirect Method of heating
5 temperature measurements
Simply run at onset and correlate the frequency to temperature

10. Temperature Profile
Exponential temperature profile from the hot end of the stack to the other rigid ambient end of the resonator.

11. Transfer Matrix Solution?
Represent entire resonator with a concatenation of lumped elements.
Lacs modified according to exponential temperature profile.
Lacs and Cacs modified to accommodate the stack.
Mass (Inertance):
Spring (Compliance):

12. Setting up the Transfer Matrix
Lumped Element Segment:
1 Inertance
2 half Compliances

13. Transfer Matrix Model 31 Slice Model:
Hot Duct: 1 Slice (Avg. Temp of Nut and Hot Stack)
Stack: 10 slices (using modified L and C)
Ambient End: 20 slices.
*Density of Inertance sections calculated from the exponential temperature profile

14. T-Matrix Model and Measured Results
Middle TC Temp, TM (oC)

15. What are we measuring? Twater Teff (from Measured Frequency)
T-net (Model) TM

16. Technical Specs Independent of Acoustic Amplitude
Differential Sensitivity:
“Invariant”: mK/Hz2 (± 5%)
How well do we know the “effective” length of the resonator?
Accuracy dependent on:
How accurate we can measure the frequency?
Additional signal processing needed to extract the signal.
How well the model relates measured frequency to the temperature in the region of interest?
Range: 1200oC – 1400oC  limit for Celcor® Ceramic Stack
Can explore the use of reticulated vitreous carbon stacks (3500oC in O2 free environments)2.
2 - J. Adeff, T. Hofler, A. Atchley, and W. Moss, “Measurements with reticulated vitreous carbon stacks in thermoacoustic prime movers and refrigerators”, Journal of the Acoustical Society of America 104, 1145–1180 (1998).

17. Summing it up…
The thermoacoustic fuel rod engine requires no moving parts, no in-pile cabling and can operate without hot or cold heat exchangers.
Thermoacoustic effect can be achieved through electromagnetic radiation, hence the device will be able to operate without electrical power.
The thermoacoustic fuel rod engine measures an effective temperature within the gas of the resonator through a frequency that is radiated in the surrounding fluid. (Can be remotely monitored).
It may be possible to measure the temperature of other parts of the nuclear reactor:
Graphite fuel capsules in gas reactors.
Surrounding fluid (since in good thermal contact with gas).
Put one in an actual nuclear reactor or spent-fuel pool!
Lets put one in a reactor and evaluate its performance on a bigger scale and real operating conditions.

18. Les Questions?

19. Additional Slides

20. Heat Transfer within the Resonator and Calorimeter
Qrad : Electromagnetic Radiation from the heat source to the hot end of the stack. .
HEAT SOURCE
Qresw : Conduction from the heat source through the walls of the resonator to the water. . .
Qha : Conduction from hot end of the stack to the ambient end of the stack. .
Qrad
Qaw : Conduction from the ambient end of the stack through the gas, resonator walls and into water. .
Hot End of Stack
H2 : Total enthalpy flux flow from the hot end of the stack to the ambient end of the stuck in the presence of thermoacoustics. .
H2 - Qha . .
Qha
Qsd : Heat flow through acoustic streaming convection from the ambient end of the stack through the gas, resonator walls and into the water. . .
Qresw
Ambient End of Stack
Qhenv: Conduction and radiation from the heat source to the ambient environment. . .
Qsd .
Qwenv: Conduction from the water to the ambient environment. .
Qaw
Qhenv .
AMBIENT ENVIRONMENT
WATER
Qwenv .

21. The Enhanced Heat Transfer is proportional to the Acoustic Pressure Squared
Recall streaming velocity <u2> and total enthalpy flux H2 proportional to p12 .

22. Experiments w/out the stack
Without the stack, for some electrical powers the net heat into the water is greater than with streaming!
First law of thermodynamics satisfied (Conservation of energy).

23. What does this enhanced heat transfer all mean?
Removed stack from the resonator and established steady states at the same electrical powers
Heat is transferred into the water at a lower temperature difference between the gas and surrounding fluid when streaming is present.

24. Acoustic pressure is proportional to the temperature difference between the gas in the resonator and the surrounding fluid (Indirect heating experiment)

25. Indirect Run (losing acoustics)

26. Direct Heating

27. Direct Heating

28. Graphite Capsules

29. Graphite Experiment

30. Graphite Expt

31. Early Indirect Run

32. Acceptable Indirect Run

33. Experiments at INL
Detecting different gases

34. “The Invariant” (is varying…)
Frequency/(TM)1/2 (Hz/K1/2)
Middle TC Temp, TM (oC)
There exists some effective temperature

35. Dist. From hot end of resonator
DELTAEC1
STACK
Parameter
Value
Stack Size
1,100 cells/in2
Dist. From hot end of resonator
36.7 mm
Stack Length
10.5 mm
Stack Type
Corning Celcor®
1. W. C. Ward and G. W. Swift, “Design environment for low amplitude thermoacoustic engines”, Journal of the Acoustical Society of America 95, 3671–3672 (1994), (For latest download:

36. Transfer Matrix Model Apply boundary conditions to obtain a solution…
Find freq. when this eq’n. = 0 to
satisfy boundary condition, U2 = 0

37. Thermal Model Πelec – Electrical Heater Power Input
Rna – Thermal Resistance (without ACS)
Rac – Thermal Resistance (with ACS)
Rleak – Thermal Resistance from H2O to Air
Rsolid – Thermal Resistance from Resonator to Air

38. Heat Transfer with and without Acoustics
Total thermal resistance from gas to water decreased. Confirmation that Rac introduced during streaming.
(dependent on direction of Qleak)

39. The Remote “Killer” Linear Actuator changes boundary conditions
through opening and closing the Schrader valve

40. Simulating the Nuclear Environment
Calorimeter
Beverage Cooler
Insulated Container
Thermal Mass
(Distilled H2O))
Thermistor
Fuel Rod
Motor

41. A simple lumped element model?
Acoustic Profile in Resonator
Mass (Inertance):
Acoustic Pressure
Volume Velocity
S T A C K
Spring (Compliance):

42. Radiative Heat Transfer
Stefan-Boltzmann Law:
No Hot or Cold Heat Exchangers Needed
Hot Duct
Hot Stack
Amb. Stack
Total radiant energy emitted by a black body proportional to the fourth order of temp of radiating surface. Actual formula includes emissivities and effective areas of radiating surfaces.
Mic

43. Acoustic Streaming Convection (Qsd).
Streaming as introduced by Rayleigh2:
Axial Streaming Velocity:
PROPORTIONAL TO p12
Transverse Streaming Velocity:
2. J. W. Strutt(Lord Rayleigh), “On the circulation of air observed in Kundt’s tubes, and on some allied acoustical problems”, Philosophical Transactions of
the Royal Society 175, 1–21 (1884).

44. Modifications to Rayleigh’s Theory
Rott introduced pressure-temperature fluctuations, thermal boundary layer, variation of mean temperature with axial coordinate and dependence of viscosity and thermal conductivity on temperature3.
3. N. Rott, “The influence of heat conduction on acoustic streaming”, Journal of Applied Math and Physics 25, 417–421 (1974).

45. Thompson and Atchley’s experiments4
Used Laser Doppler Anemometry to measure the streaming velocity.
Defined “nonlinear Reynolds Number”:
Demonstrated good thermal contact with walls even at high amplitudes!
4. M. W. Thompson and A. A. Atchley, “Measurements of rayleigh streaming in high-amplitude standing waves”, Journal of the Acoustical Society of America
111, 2418 (2002).

46. Excellent Thermal Contact between the gas and surrounding fluid
Temp. at Middle of Resonator and Water Temp.
w/ and w/out 26 W
NO ACS
NO ACS TM
Twater TM

47. Total Enthalpy Flux Flow H2.
Enhanced enthalpy transport along the stack is due to the “bucket brigade” effect5 which acoustically transports heat through stack. Total power flow through stack can be calculated6:
PROPORTIONAL TO p12
THERMOACOUSTIC TERM
(This term disappears when “the killer”
suppresses acoustics)
CONDUCTION TERM
5. A. Gopinath, N. L. Tait, and S. L. Garrett, “Thermoacoustic streaming in a resonant channel: The time-averaged temperature distribution”, Journal of the Acoustical Society of America 103, 1388–1405 (1998).
6. G. W. Swift, Thermoacoustics : A unifying perspective for some engines and refrigerators (Acoustical Society of America through the American Institute of Physics, ISBN: ) (2002).

48. DELTAEC (again!) The result (@ 1300 Parms):
Use DELTAEC model to calculate the net heat with and without the thermoacoustic term.
DELTAEC outputs H2. Simple to calculate conduction term (all variables from DELTAEC) . .
A – Cross-sect area of tube
Asolid – Porous area of stack (GasA/A from DeltaEC)
κ – Thermal conductivity of gas
κsolid – Thermal conductivity of stack
dTm/dx – Temperature gradient across stack
The result 1300 Parms): .

49. Further evidence of the enhanced enthalpy transport
NO ACS
NO ACS TC