Thermoacoustic Sensor for Nuclear Fuel Temperature Monitoring

Randall Ali and Steven Garrett, Graduate Program in Acoustics, The Pennsylvania State University, USA

22nd May 2013, NDCM-13, Le Mans, France

James Smith and Dale Kotter, Fundamental Fuel Properties Group, Idaho National Lab, USA

Fukushima Daiichi Nuclear Disaster

• Most powerful earthquake in Japan

• Failure of Nuclear Reactors

• Loss of Electrical Power to Sensors

A Thermoacoustic Solution?

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

stacksHeat source

(Nuclear Fuel)

ElectromagneticRadiation

No Heat Exchangers!

Acoustic Streaming

The Thermoacoustic Fuel-Rod Engine

Temp Sensor

3 Type- E T/C Feedthroughs

Mic

Schrader Valve

Instrumentation Plate

Thermal Mass (Distilled H2O))

Calorimeter

Where’s the Nuclear Fuel???

Direct Heating

Indirect Heating

Thermometry Basics

INVARIANT QUANTITY

True for ideal gases at a constant temperature.

c – Sound Speed (m/s)f – Frequency (Hz)T – Temperature (K) g – Polytropic Coefficient

M – Molecular Mass of Gas (kg/mol) – Universal Gas Constant (J/mol-K)

L – Length of Resonator (m)

The nature of the thermoacoustic resonator is that it needs a temperature

gradient for operation!

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?

T-net (Model)Teff (from Measured Frequency)

TM

Twater

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).

21.0 /

T TK Hz

f f

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!

Les Questions?

Additional Slides

Heat Transfer within the Resonator and Calorimeter

WATER

Ambient End of Stack

HEAT SOURCE

AMBIENT ENVIRONMENT

Qaw

Hot End of Stack

Qresw

Qha

.

.

.Qsd

.

Qha : Conduction from hot end of the stack to the ambient end of the stack.

.Qresw : Conduction from the heat source through the

walls of the resonator to the water.

.

Qaw : Conduction from the ambient end of the stack through the gas, resonator walls and into water.

.

Qsd : Heat flow through acoustic streaming convection from the ambient end of the stack through the gas, resonator walls and into the water.

.

Qhenv: Conduction and radiation from the heat source to the ambient environment.

.

H2 : Total enthalpy flux flow from the hot end of the stack to the ambient end of the stuck in the presence of thermoacoustics.

.

Qwenv

.

Qhenv

.

Qwenv: Conduction from the water to the ambient environment.

.

Qrad

.

Qrad : Electromagnetic Radiation from the heat source to the hot end of

the stack..

.

H2 - Qha

. .

The Enhanced Heat Transfer is proportional to the Acoustic Pressure Squared

Recall streaming velocity <u2> and total enthalpy flux H2 proportional to p12

.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2

4

6

8

10

12

14

16

Acoustic Pressure Squared (Pa2rms/106)

Stre

amin

g D

riven

Con

vecti

onN

et H

eat I

ncre

ase

(%)

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)

13500 15500 17500 19500 21500 23500 25500 275000

100

200

300

400

500

600

0

50

100

150

200

250

300

350

Hot Stack, Ambient Stack, DT and ACS Pressure

Hot Stack Amb Stack

dT Acs Pressure

Time (secs)

Tem

pera

ture

(oC)

Pres

sure

(Pa)

Direct Heating

Direct Heating

Graphite Capsules

Graphite Experiment

Graphite Expt

350 450 550 650 750 850 950 105015

17

19

21

23

25

27 Freq-Temp Invariant and Model

Temperature (K)

Freq

/(Te

mp)

1/2

Early Indirect Run

0.5 1 1.5 2 2.5 3 3.5 4 4.5150

155

160

165

170

175

180

185

190

195

200

Time (hr)

DC

Pres

sure

/Am

bien

t Sta

ck T

emp

(Pa/

K)

Acceptable Indirect Run

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5100

150

200

250

300

350

400

Time (hr)

DC

Pres

sure

/Am

bien

t Sta

ck T

emp

(Pa/

K)

Experiments at INL

• Detecting different gases

“The Invariant” (is varying…)

There exists some effective temperature

Freq

uenc

y/(T

M)1/

2 (H

z/K1/

2 )

Middle TC Temp, TM (oC)

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

(U1 = 0)

Find freq. when this eq’n. = 0 to satisfy boundary condition, U2 = 0

Apply boundary conditions to obtain a solution…

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

Thermal Model

Heat Transfer with and without Acoustics

(dependent on direction of Qleak)

Total thermal resistance from gas to water

decreased. Confirmation that Rac introduced during streaming.

The Remote “Killer”

Linear Actuator changes boundary conditions

through opening and closing the Schrader valve

Simulating the Nuclear EnvironmentCalorimeterBeverage Cooler

Insulated Container Thermal Mass

(Distilled H2O))

Thermistor

Fuel Rod

Motor

A simple lumped element model?

Acoustic Pressure

Volume Velocity

Acoustic Profile in ResonatorS

T

A

C K

Mass (Inertance):

Spring (Compliance):

Radiative Heat TransferStefan-Boltzmann Law: No Hot or Cold Heat

Exchangers Needed

Hot DuctHot Stack

Amb. Stack

0.0 0.5 1.0 1.5 2.0 2.5 3.00

100

200

300

400

500

600

700

800

0

200

400

600

800

1000

1200

1400Hot DuctHot StackdT across stackAcoustic PressureAmb Stack

Time (hr)

Tem

pera

ture

(oC)

Acou

stic

Pres

sure

(Pa)

Mic

4 4b end stackE T T

Streaming as introduced by Rayleigh2:

Acoustic Streaming Convection (Qsd)

2. J. W. Strutt(Lord Rayleigh), “On the circulation of air observed in Kundt’s tubes, and on some allied acoustical problems”, Philosophical Transactions ofthe Royal Society 175, 1–21 (1884).

Axial Streaming Velocity:

Transverse Streaming Velocity:PROPORTIONAL TO p1

2

.

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 America111, 2418 (2002).

Excellent Thermal Contact between the gas and surrounding fluid

NO ACS

NO ACS

Temp. at Middle of Resonator and Water Temp.w/ and w/out ACS @ 26 W

TM

TM

Twater

PROPORTIONAL TO p12

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:

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).

THERMOACOUSTIC TERM(This term disappears when “the killer”

suppresses acoustics)

CONDUCTION TERM

.

• 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)

DELTAEC (again!)

A – Cross-sect area of tubeAsolid – Porous area of stack (GasA/A from DeltaEC)κ – Thermal conductivity of gasκsolid – Thermal conductivity of stackdTm/dx – Temperature gradient across stack

The result (@ 1300 Parms):

.

.

.

Further evidence of the enhanced enthalpy transport

0 1 2 3 4 5 6 7 8 9 10230

240

250

260

270

280

290

300

Ambient End of Stack w/ and w/out ACS @ 26W

Time (hr)

Tem

pera

ture

(oC) NO ACS

NO ACS

TC