Presentation on theme: "Thermoacoustic Sensor for Nuclear Fuel Temperature Monitoring Randall Ali and Steven Garrett, Graduate Program in Acoustics, The Pennsylvania State University,"— Presentation transcript:
Thermoacoustic Sensor for Nuclear Fuel Temperature Monitoring Randall Ali and Steven Garrett, Graduate Program in Acoustics, The Pennsylvania State University, USA 22 nd 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, (1878)
Synergistic with Fuel Rods stacks Heat source (Nuclear Fuel) Electromagnetic Radiation 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 H 2 O) ) Calorimeter
Wheres 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) – 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. L acs modified according to exponential temperature profile. L acs and C acs 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, T M ( o C)
What are we measuring? T-net (Model) T eff (from Measured Frequency) TMTM T water
Technical Specs Independent of Acoustic Amplitude Differential Sensitivity: Invariant: mK/Hz 2 (± 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: 1200 o C – 1400 o C limit for Celcor® Ceramic Stack – Can explore the use of reticulated vitreous carbon stacks (3500 o C in O 2 free environments) 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!
Heat Transfer within the Resonator and Calorimeter WATER Ambient End of Stack HEAT SOURCE AMBIENT ENVIRONMENT Q aw Hot End of Stack Q resw Q ha... Q sd. Q ha : Conduction from hot end of the stack to the ambient end of the stack.. Q resw : Conduction from the heat source through the walls of the resonator to the water.. Q aw : Conduction from the ambient end of the stack through the gas, resonator walls and into water.. Q sd : Heat flow through acoustic streaming convection from the ambient end of the stack through the gas, resonator walls and into the water.. Q henv : Conduction and radiation from the heat source to the ambient environment.. H 2 : Total enthalpy flux flow from the hot end of the stack to the ambient end of the stuck in the presence of thermoacoustics.. Q wenv. Q henv. Q wenv : Conduction from the water to the ambient environment.. Q rad. Q rad : Electromagnetic Radiation from the heat source to the hot end of the stack... H 2 - Q ha..
The Enhanced Heat Transfer is proportional to the Acoustic Pressure Squared Recall streaming velocity and total enthalpy flux H 2 proportional to p 1 2.
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)
Early Indirect Run
Acceptable Indirect Run
Experiments at INL Detecting different gases
The Invariant (is varying…) There exists some effective temperature Frequency/(T M ) 1/2 (Hz/K 1/2 ) Middle TC Temp, T M ( o C)
D ELTA EC 1 STACK ParameterValue Stack Size1,100 cells/in 2 Dist. From hot end of resonator 36.7 mm Stack Length10.5 mm Stack TypeCorning 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:
Transfer Matrix Model (U 1 = 0) Find freq. when this eqn. = 0 to satisfy boundary condition, U 2 = 0 Apply boundary conditions to obtain a solution…
Π elec – Electrical Heater Power InputR na – Thermal Resistance (without ACS) R ac – Thermal Resistance (with ACS)R leak – Thermal Resistance from H 2 O to Air R solid – Thermal Resistance from Resonator to Air Thermal Model
Heat Transfer with and without Acoustics (dependent on direction of Q leak ) Total thermal resistance from gas to water decreased. Confirmation that R ac introduced during streaming.
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 H 2 O) ) Thermistor Fuel Rod Motor
A simple lumped element model? Acoustic Pressure Volume Velocity Acoustic Profile in Resonator S T A C K Mass (Inertance): Spring (Compliance):
Radiative Heat Transfer Stefan-Boltzmann Law: No Hot or Cold Heat Exchangers Needed Hot Duct Hot Stack Amb. Stack Mic
Streaming as introduced by Rayleigh 2 : Acoustic Streaming Convection (Q sd ) 2. J. W. Strutt(Lord Rayleigh), On the circulation of air observed in Kundts tubes, and on some allied acoustical problems, Philosophical Transactions of the Royal Society 175, 1–21 (1884). Axial Streaming Velocity: Transverse Streaming Velocity: PROPORTIONAL TO p 1 2.
Modifications to Rayleighs Theory Rott introduced pressure-temperature fluctuations, thermal boundary layer, variation of mean temperature with axial coordinate and dependence of viscosity and thermal conductivity on temperature N. Rott, The influence of heat conduction on acoustic streaming, Journal of Applied Math and Physics 25, 417–421 (1974).
Thompson and Atchleys experiments 4 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 NO ACS Temp. at Middle of Resonator and Water Temp. w/ and w/out 26 W TMTM TMTM T water
PROPORTIONAL TO p 1 2 Total Enthalpy Flux Flow H 2 Enhanced enthalpy transport along the stack is due to the bucket brigade effect 5 which acoustically transports heat through stack. Total power flow through stack can be calculated 6 : 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). THERMOACOUSTIC TERM (This term disappears when the killer suppresses acoustics) CONDUCTION TERM.
Use D ELTA EC model to calculate the net heat with and without the thermoacoustic term. D ELTA EC outputs H 2. Simple to calculate conduction term (all variables from D ELTA EC) D ELTA EC (again!) A – Cross-sect area of tube A solid – Porous area of stack (GasA/A from DeltaEC) κ – Thermal conductivity of gas κ solid – Thermal conductivity of stack dT m /dx – Temperature gradient across stack The result 1300 Pa rms ):...
Further evidence of the enhanced enthalpy transport NO ACS TCTC