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

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

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.

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, 319-321 (1878)

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

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

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

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)

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

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

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):

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

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

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

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

Technical Specs Independent of Acoustic Amplitude Differential Sensitivity: “Invariant”: 0.459 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).

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.

Les Questions?

Additional Slides

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 .

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

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).

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.

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

Indirect Run (losing acoustics)

Direct Heating

Direct Heating

Graphite Capsules

Graphite Experiment

Graphite Expt

Early Indirect Run

Acceptable Indirect Run

Experiments at INL Detecting different gases

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

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: http://www.lanl.gov/thermoacoustics/DeltaEC.html)

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

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

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)

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

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

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

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

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).

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).

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).

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

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: 0735400652) (2002).

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): .

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