Thermocouple Response inFires, Part 2: Validation ofVirtual Thermocouple Modelfor Fire CodesAARON L. BRUNDAGE, A. BURL DONALDSON, WALT GILL,SEAN P. KEARNEY AND VERN F. NICOLETTE

Fire Sciences and Technologies, Sandia National Laboratories, Albuquerque, NM87123, USA

NADIR YILMAZ*Department of Mechanical Engineering, New Mexico Institute of Mining andTechnology, Socorro, NM 87801, USA

(Received March 28, 2010)

ABSTRACT: A virtual thermocouple model for high fidelity multiphysicscomputer simulation is introduced in this article. Detailed thermocouple and gastemperature (Coherent Anti-Stokes Raman Scattering) measurements wereperformed using a well-controlled, adiabatic, flat-flame Hencken burner, whichprovided data for validating the thermocouple model in a Sandia NationalLaboratories fire code. Comparison of simulation results to test data indicated amean error of 6% between the thermocouple reading and predicted temperature.

KEY WORDS: virtual thermocouple model, thermocouple heat balance, firecode development, fire temperature measurements.

*Author to whom correspondence should be addressed. E-mail: yilmaznadir@yahoo.comFigures 2–8 appear in color online: http://jfs.sagepub.com

JOURNAL OF FIRE SCIENCES, VOL. 29 – May 2011 213

0734-9041/11/03 0213–14 $10.00/0 DOI: 10.1177/0734904110386188� The Author(s), 2010. Reprints and permissions:http://www.sagepub.co.uk/journalsPermissions.nav

INTRODUCTION

INTERPRETATION OF A thermocouple reading made in a fire must be inaccordance with an appropriate energy model [1,2]. In the past, thismodel was treated as a correction that would convert the reading to thetemperature of interest (e.g., the local gas temperature). Thesecorrections are well understood and have been discussed at length byvarious researchers [3–6]. The weakness in this approach for fireapplication is that the correction model often requires parameters fromthe flame environment that are not available to the experimentalist.However, with the advent of high fidelity multiphysics computersimulations (fire codes), all necessary parameters are calculable andthus potentially available for the experimentalist to correct the readings.

Nevertheless, we propose an alternative approach where the thermo-couple model is inserted into the fire code as a virtual instrument, andthat now the experimental thermocouple reading becomes a tie point tothe fire environment that is revealed in its entirety via the code output.The quality of this approach depends on the ability of the thermocouplemodel in the fire code to adequately capture the dominating physics.Evidence of adequacy is determined by validating model predictionsagainst experimental results.

The dominating physics for the thermocouple model have beendetermined in Brundage et al. [7], and in what follows, a model will beput forth, which was implemented in a fire code VULCAN. Predictionsfrom VULCAN are then compared with experimental results todemonstrate validation.

THERMOCOUPLE MODEL

Physical Description

In full-scale fire experimentation, the use of relatively large diameter(1.5 mm) sheathed thermocouple assemblies is the norm. Mineral-insulated metal-sheathed (MIMS) thermocouples are usually usedbecause of high reliability and low cost. Figure 1 shows a schematic ofcross section of an ungrounded MIMS thermocouple probe.

This type of thermocouple construction is most widely used forhigh-temperature applications and is issued in accordance with theASTM standard specification for Compacted Mineral-Insulated, Metal-Sheathed, Noble Metal Thermocouples and Thermocouple Cable(E 2181/E 2181M). The thermocouple wires and ungrounded measuring

214 A. L. BRUNDAGE ET AL.

junction are surrounded by a magnesium oxide (MgO) mineralinsulation, and the entire assembly is encased in an Inconel 600sheath [8].

Based upon other available data for oxidized Inconel 600 [9], the totalhemispherical emissivity could be as high as 0.9, and the resulting rangeof emissivities, from 0.67 to 0.90, will be accounted for in an uncertaintyanalysis.

A thermal model of a MIMS thermocouple with geometry representa-tive of an actual thermocouple to determine the bead temperature wasreported by Nakos [10]. This model included the air gap around thesheath, assumed lumped masses for the bead and sheath, and consideredradiation and conduction as the only (dominant) modes of heat transfer.The results showed that the sheath acted as a radiation shield andreduced the heat transfer to the bead. Hence, we include the presenceand behavior of the sheath in our virtual thermocouple model.

Virtual Thermocouple Model

The thermocouple model that has been implemented into VULCANestimates the temperature that a thermocouple would register if it werein a thermal environment at a specified location. In the model, only aone-way coupling exists, such that the thermocouple temperature iscalculated after the surrounding gas temperature field is predicted.Hence, the local gas temperature and incident thermal radiation fieldare known for the time step of interest. The virtual thermocouples aremodeled as hemispheres attached to cylinders that are exposed to fires.Both the temperature of the metal sheath and the temperature of thethermocouple bead need to be considered, as they both change with time.An equation for the sheath temperature is formulated equatingradiation, convection, and one-dimensional radial conduction through

Sheath Insulation

Sheath outside diameter Thermoelement

End closure

CB

A

E

D

F

Figure 1. Cross section of an ungrounded MIMS thermocouple probe (ASTME 2181/E 2181M).

Validation of Virtual Thermocouple Model for Fire Codes 215

the thermocouple sheath. The equation is essentially given by thefollowing:

k

rTsheath � Tbeadð Þ ¼ h Tgas � Tsheath

� �þ � qrad � �T4

sheath

� �, ð1Þ

where k is an effective thermal conductivity for the thermocouple, r isthe radius of the thermocouple, Tsheath is the sheath or surfacetemperature (assumed to be uniform throughout the sheath), Tbead isthe thermocouple bead temperature, h is the convective heat transfercoefficient, Tgas is the temperature near the thermocouple (which isknown for the present time step), � is the absorptivity of the sheath, qrad

is the incident thermal radiation from the surroundings (also known forthe present time step), and � is the Stefan-Boltzmann constant.

The second equation that needs to be considered represents thetransient heating of the thermocouple (sheath plus bead plus insulatingmaterials, etc.). The heat conducted through the sheath must give rise tothe transient heat of the thermocouple and is given by the followingequation:

k

rTsheath � Tbeadð Þ ¼ �C�

�T

�t

Volume

SurfaceArea, ð2Þ

where � and Cp are the effective density and specific heat of thethermocouple, respectively, �T is the change in the bead temperaturewith time, and �t is the time step. An iterative technique is used to solvethese two equations until consistent values of Tsheath and Tbead areobtained.

Thermal properties of the virtual thermocouple, which represent anaverage of the insulation and sheath properties of a MIMS thermo-couple, are provided in Table 1. Although radial conduction at the probe

Table 1. Parameters and typical values for VULCAN virtual thermocouple model.

Parameter Value

Emissivity 0.67–0.9Length (cm) 15Diameter (mm) 1.0, 1.6Density (kg/m3) 5880Thermal conductivity (W/mK) 1.7Specific heat (J/kgK) 696

216 A. L. BRUNDAGE ET AL.

tip is included in the analysis, axial conduction along the axis of thecylindrical portions of the probe (including the Inconel sheath, leadwires, and insulation) are ignored. Furthermore, the material propertiesand thermal capacitances of the bead, insulation, and sheath arelumped.

COMPUTATIONAL SETUP

The fire code VULCAN solves the governing equations for mass,momentum, energy, species, and thermal radiation using a finite-difference field model on a grid. Its computational capabilities includethermal radiation, turbulence, combustion, and soot. It has beenvalidated for numerous fire scenarios [11,12]. Here, we apply the codeto a flat-flame Hencken burner (Figure 2) with confidence that is basedon the previous experience with the simulation.

Given the adiabatic flame temperature, equilibrium species (fuel andair) composition, and approximate gas velocity, a VULCAN [13]simulation of this product plume was constructed, with specific valuesof these initial conditions provided in Table 2 along with thecomputational domain shown in Figure 3. The product plume is modeledas a hot gas jet with the equilibrium species composition emanating from

Thermocouple

Flame

Air co-flow

Hypodermic tubing(Methane gas outflow)

Burner casing

Figure 2. Flat-flame Hencken burner used to explore the thermocouple model. Thephotograph shows a thermocouple extending across and beyond the full width of theflame for investigating the effect of sheath conduction.

Validation of Virtual Thermocouple Model for Fire Codes 217

the 25 cm2 orifice. The turbulence parameters in Table 2 arecommiserating with this type of flow. A virtual thermocouple cell isplaced approximately 12 mm above the orifice. Combustion chemistrywas not modeled. Instead, gases were injected at the equilibriumtemperature. The surface of the Hencken burner is slightly elevatedabove room temperature and is captured in the simulation by assumingit to be a highly transmitting surface. The other boundaries are blackand held at room temperature. These assumptions are consideredadequate for the purpose of evaluating the thermocouple model.

A structured computational grid with hexahedral bricks was used inthe simulation. This computational grid for the lowest resolution case of40,432 cells (N1) is shown in Figure 4. Other grid resolutions of 181,656(N2) and 295,704 cells (N3) were explored as part of a grid resolutionstudy. Results from a grid resolution study are presented in Figure 5.From the coarse to fine grid, the temperature was found to increase

Pressure boundary (5 surfaces)

Wall boundary

Velocity inlet(5cm × 5cm)

1m

1m

1m

Figure 3. Measured flame temperature from CARS and MIMS thermocouples.

Table 2. Initial conditions of [13] fire simulation.

Parameter Value

w-velocity, W (m/s) 8.19Turbulent kinetic energy (J/kg) 0.135Turbulent dissipation (J/kg-s) 0.815Temperature, T (K) 2220

218 A. L. BRUNDAGE ET AL.

Figure 4. Computational domain of simulation.

1400

1410

1420

1430

1440

1450

0 100000 200000 300000

Cell count (N)

Pre

dict

ed te

mpe

ratu

re (

K)

Figure 5. Coarse computational grid of simulation (40,432 cells).

Validation of Virtual Thermocouple Model for Fire Codes 219

by 5 K. Given the trade-off in CPU time versus accuracy, all results arereported at the lowest resolution (40,432 cells).

EXPERIMENTAL SETUP

Hencken flat-flame burners produce a laminar, premixed flame that isuniform, steady, nearly adiabatic, and are widely used to calibratethermocouples and other physical probes [14]. In our setup, toexperimentally achieve a stoichiometric flame, i.e. an equivalence ratioof unity, 40 SLPM of air, and 3.2 SLPM of methane were passed throughthe burner to achieve a stoichiometric mass flow rate of 0.0026 kg/s.Using the NASA CEA chemical equilibrium code [15] for an air/fuelmixture initially at 298 K and 0.82 atm, the adiabatic flame temperaturewas 2220 K and the density of the air–fuel mixture was 0.1239 kg/m3.Given the cross-sectional area of the flat-flame burner (25 cm2) and thedensity of the air–fuel mixture, the gas velocity was estimated at 8.2 m/s.

Flame temperatures were measured at specific locations in the flameacross a wide range of equivalence ratios (where the equivalence ratio isdefined as the ratio of the actual fuel–oxidant ratio to the stoichiometricfuel–oxidant ratio). Coherent Anti-Stokes Raman Scattering (CARS) ofthe nitrogen molecule was used to measure flame temperature [16]. Inaddition, readings were observed from 1.0 to 1.6 mm MIMS thermo-couple probes inserted in the combustion-product plume.

CARS-measured flame temperatures were found to be within 50 K ofthe adiabatic flame temperature, as shown in Figure 6. Hence, the flameof the Hencken burner is proved to be nearly adiabatic, as designed.

1200

1400

1600

1800

2000

2200

2400

0.9 1 1.1 1.2 1.3 1.4

EquilibriumCARS

62 MIL TC40 MIL TC

Tem

pera

ture

(K

)

Equivalence ratio

Figure 6. Grid resolution study.

220 A. L. BRUNDAGE ET AL.

The thermocouple data tracked the trends of the CARS measurementsas the equivalence ratio is varied from lean to rich. Also to be noted is areasonably consistent suppression of thermocouple indicated tempera-ture below gas temperature. The thermocouple data indicate muchlower temperatures (�900 K) than the CARS–measured temperaturepresumably because of radiant heat loss from the ‘white-hot’ (visible)thermocouple surface to the cold surroundings.

COMPUTATIONAL RESULTS AND VALIDATION

The predicted steady-state velocity and temperature results for thestoichiometric case are shown in Figure 7. These results are reflective ofthe modeling intent – to compare the output of the thermocouple model,to experiment and to achieve a large region of uniform temperaturesurrounding the thermocouple

There is remarkable agreement between the thermocouple tempera-ture prediction and observed thermocouple response, as demonstrated inFigure 8, with the peak error in the prediction being approximately 6%(or about 90 K) and mean error of approximately 4% (60 K). Because theemissivity of the oxidized Inconel sheath is not quantified in theexperiments, the uncertainty is propagated through the numericalresults based upon the published total hemispherical emissivity ofvarious Inconel alloys. The upper and lower bounds shown (error bars)on the simulation results partly reflect the different values ofthermocouple emissivity used in the simulations. Note that the

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0 Plane: Y= –0.50Plane: Y= –0.50

W (m/s)(Projected) (Projected)

Temperature (K)

Max

7.520

6.262

5.004

8.778

3.747

2.489

1.231

–0.027Min

Max2220.0

2000.0

1800.0

1600.0

1500.0

1300.0

1200.0

1150.0

1100.0

900.0

750.0

600.0

290.0

293.0Min

Time=48.157 X (m)

–0.4 –0.2 0.0 0.2 0.4

Time=48.157 X (m)

–0.4 –0.2 0.0 0.2 0.4

Z (

m)

Z (

m)

Figure 7. Predicted steady-state velocity and temperature of Hencken burnerproduct plume.

Validation of Virtual Thermocouple Model for Fire Codes 221

simulation values represented by the red triangles in Figure 8 (and theresults shown in Figure 5) were calculated using the temperature-dependent emissivity [7].

The actual diameters of the thermocouple probes were not measured,and the uncertainty in diameter is also propagated through thenumerical results. Hence, the 95% confidence simulation uncertaintyassociated with the emissivity and probe diameter does not fully accountfor the error between measurement and prediction. The overpredictionof the bead (junction) temperature is also consistent with the neglect ofaxial conduction and the lumping of thermal properties in thethermocouple model. Although the bead temperatures are overpre-dicted, the diameter effects (trends) are well reproduced, with the 50 Kdifference in temperature between the 1.0 and 1.6 mm diameter probesbeing nearly identical to the measured difference.

CONCLUSIONS

Flame temperature measurements were conducted using a well-controlled, sophisticated flat-flame burner that produces a laminar,premixed flame that is uniform, steady, and nearly adiabatic.Experimental temperature measurements were gathered using ahighly sophisticated and reliable method CARS, and MIMS thermo-couples of 1–1.6 mm diameters.

CARS-measured flame temperatures were found to be within 50 K ofthe adiabatic flame temperature, proving that the flame of the Henckenburner is nearly adiabatic as designed. Although the thermocouplemeasurements for two diameters had similar trends with CEA adiabaticflame temperature calculations and CARS measurements, actual values

1300

1350

1400

1450

1500

1550

1600

1650

0 0.5 1 1.5 2Thermocouple diameter (mm)

The

rmoc

oupl

e te

mpe

ratu

re (

K)

Prediction

Experiment

Figure 8. Comparison of VULCAN prediction and measured thermocoupletemperatures as functions of thermocouple diameter for the stoichiometric flame.

222 A. L. BRUNDAGE ET AL.

indicated much lower temperatures (�900 K) than the CARS-measuredtemperature because of radiant heat loss from the thermocouple surfaceto the cold surroundings.

As part of the modeling effort, a virtual thermocouple model in aSandia fire code was used for validation purposes and better under-standing of the thermocouple behavior in fires. Comparison of CFDresults to experimental data indicated the peak error in the predictionbeing approximately 6% (or about 90 K), and mean error of approxi-mately 4% (60 K) between the thermocouple reading and the predictedtemperature. This error included the combined effects of axialconduction and thermocouple sheath oxidation uncertainty.

Due to the excellent agreement between the virtual thermocouplemodel and experimental data for clean flames, it is recommendedto conduct experiments for Inconel-sheathed thermocouples innonadiabatic, soot-producing flames for further validation of themodel.

ACKNOWLEDGEMENTS

Sandia is a multiprogram laboratory operated by Sandia Corporation, aLockheed Martin Company, for the United States Department of Energy’sNational Nuclear Security Administration under contract DE-AC04-94AL85000. The virtual thermocouple model discussed in this article wasdeveloped in collaboration with Jens Holen of Statoil, Norway (formerly ofthe Division of Applied Thermodynamics, SINTEF/NTH, Norway).

REFERENCES

1. Yilmaz, N., Donaldson, A.B. and Lucero, R.E. (2008). Experimental Study ofDiffusion Flame Oscillations and Empirical Correlations, Energy Conversionand Management, 49(11): 3287–3291.

2. Yilmaz, N., Gill, W., Donaldson, A.B. and Lucero, R.E. (2008). ProblemsEncountered in Fluctuating Flame Temperature Measurements byThermocouple, Sensors Journal, 8(12): 7882–7893.

3. Jones, J.C. (2000). A Combustion Scientist’s View of ThermocoupleTemperature Measurement, IEE Colloquium, 80: 53–56.

4. Pitts, W.M., Braun, E., Peacock, R.D., Mitler, H.E., Johnsson, E.L., Reneke, P.A.and Blevins, L.G. (2002). Temperature Uncertainty for Bare-Bead and AspiratedThermocouple Measurements in Fire Environments, In: Gritzo, L.A. andAlvares, N.J. (eds), ASTM Special Technical Publication 1427, ASTMInternational, West Conshohocken, PA, pp. 3–15.

Validation of Virtual Thermocouple Model for Fire Codes 223

5. Segall, A. (2001). Solutions for the Correction of TemperatureMeasurements Based on Beaded Thermocouples, International Journal ofHeat and Mass Transfer, 44(15): 2801–2808.

6. Farrow, R.L., Mattern, P.L. and Rahn, L.A. (1982). Comparison BetweenCARS and Corrected Thermocouple Temperature Measurements in aDiffusion Flame, Applied Optics, 21(17): 3119–3125.

7. Brundage, A.L., Donaldson, A.B., Gill, W., Kearney, S.P., Nicolette, V.F. andYilmaz, N. (2010). Thermocouple Response in Fires, Part 1: Considerationsin Flame Temperature Measurements by a Thermocouple, Journal of FireSciences, DOI: 10.1177/0734904110386187.

8. Special Metals Corporation (2004). Inconel alloy 600, Publication NumberSMC-027, Special Metals Corporation, New York, USA.

9. O’Sullivan Jr, W.J. and Wade, W.R. (1957). Theory and Apparatus forMeasurement of Emissivity for Radioactive Coating of Hypersonic Aircraftwith Data for Inconel and Inconel X, NACA Tech Note 4121, superseded byNASA TR R-90.

10. Nakos, J.T. (2002). The Systematic Error of a Mineral-Insulated, MetalSheathed (MIMS) Thermocouple Attached to a Heated Flat Surface,Thermal Measurements: The Foundation of Fire Standards, In: Gritzo,L.A. and Alvares, N.J. (eds), ASTM STP 1427, American Society for Testingand Materials, West Conshohocken, PA.

11. Black, A.R. (2005). Numerical Predictions and Experimental Results for a1m Methane Fire, American Society of Mechanical Engineers, Heat TransferDivision, (Publication) HTD, 376(1): 429–435.

12. Brown, A.L. and Blanchat, T.K. (2003). A Validation Quality Heat FluxDataset for Large Pool Fires, In: Proceedings of the ASME Summer HeatTransfer Conference, Las Vegas, NV, USA, pp. 71–78.

13. Holen, J., Brostrom, M. and Magnussen, B.F. (1990). Finite DifferenceCalculation of Pool Fires, In: Twenty-Third Symposium (International) onCombustion, The Combustion Institute, Orleans, France, pp. 1677–1683.

14. Hancock, R.D., Bertagnolli, K.E. and Lucht, R.P. (1997). Nitrogen andHydrogen CARS Temperature Measurements in a Hydrogen/Air FlameUsing a Near-Adiabatic Flat-Flame Burner, Combustion and Flame, 109(3):323–331.

15. Gordon, S. and McBride, B.J. (1994). Computer Program for Calculation ofComplex Chemical Equilibrium Compositions and Applications I. Analysis,NASA RP-1311, National Aeronautics and Space Administration,Washington, D.C.

16. Antcliff, R.R. and Jarrett, O. (1984). Comparison CARS CombustionTemperatures With Standard Techniques, Progress in Astronautics andAeronautics, 92: 45–57.

224 A. L. BRUNDAGE ET AL.

BIOGRAPHIES

Aaron L. Brundage

Dr Aaron Brundage received his PhD in Mechanical Engineering fromPurdue University in 2004. He is a staff member in Fire Sciencesdepartment at Sandia National Laboratories.

A. Burl Donaldson

Dr Burl Donaldson received a MS degree in Chemical Engineeringfrom the University of Utah in 1965 and PhD in MechanicalEngineering from New Mexico State University in 1969, where heteaches now. He worked at Sandia National Laboratories-Albuquerquefor 12 years, and with a venture company seeking to commercializedirect contact steam generators for heavy oil recovery for 8 years. Hemaintains part time employment at Sandia with an emphasis on heattransfer in solid and liquid rocket propellant fires, but also works withIC and EC engines with a focus on emissions and alternate fuels.

Walt Gill

Dr Walt Gill received his Bachelor of Science in 1969, Master ofScience in 1971 and PhD in 1979, in Mechanical Engineering from NewMexico State University. Dr Gill has served in several technical positionsincluding his current position as a Member of Senior Staff at SandiaNational Laboratories where he is involved in various thermalmeasurements; principally with measurements and characterization ofthe thermal environments in fires. Specific environments of interest arelarge hydrocarbon pool fires and solid propellant fires.

Sean P. Kearney

Dr Sean Kearney received the BS degree from Clarkson University,Potsdam, NY in 1992 and the MS and PhD degrees from the Universityof Illinois at Urbana-Champaign in 1995 and 1999, respectively, all inmechanical engineering. He joined the Engineering Sciences Center atSandia National Laboratories, Albuquerque, NM in 1999 and iscurrently a Principal Member of the Technical Staff at Sandia.His research is focused on the application of laser-based diagnosticsto a variety of problems in fluid mechanics, combustion, and heattransfer.

Validation of Virtual Thermocouple Model for Fire Codes 225

Vern F. Nicolette

Dr Vern Nicolette received his PhD in Mechanical Engineering fromNotre Dame and Master of Science in Nuclear Engineering from UCBerkeley. He is a principal member of technical staff in Fire and AerosolSciences Department at Sandia National Laboratories with 25 years ofexperience in analysis, modeling, and simulation of fires and thermaleffects, with particular expertise related to nuclear weapon effects andsafety. He is WESC Nuclear Weapons Effects Fire Subgroup Co-Chair(DoD, DOE, AWE partners), designated ‘‘Founding Father’’ of SNL FireScience and Technology program and a primary developer of the SNLVulcan fire code.

Nadir Yilmaz

Dr Nadir Yilmaz received his Bachelor of Science in MechanicalEngineering from Istanbul Technical University in 1999, Master ofScience in Mechanical Engineering from Bradley University in 2001,and PhD in Mechanical Engineering from New Mexico State Universityin 2005. After obtaining his PhD, he worked as an Assistant Professor atNew Mexico State University until 2006. He works as an AssistantProfessor in Mechanical Engineering at New Mexico Institute of Miningand Technology since 2006. His research interests are computationalfluid dynamics, combustion, chemical kinetics, renewable energy, andinternal combustion engines. He serves as the editor-in-chief for SAEInternational Journal of Fuels and Lubricants.

226 A. L. BRUNDAGE ET AL.