Post on 30-Mar-2015
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