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—.,,–— Sandla is a multiprogram laboratory o~i%d-by Sandia Corporation,

a Lockheed-Martin Company, for the_iJiilfed States Department of—-Energy under Contract DE-AC04-9m85000.

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Approved for public-release; fi”rther dissemination unlimited.—

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SAND2000-111 1Unlimited ReleasePrinted May 2000

Sandia Heat Flux GaugeThermal Response and Uncertainty Models

T. K. Blanchat and L. L. HumphriesNuclear Safety Testing Department

W. GillReactive Processes Department

Sandia National LaboratoriesP.O. Box 5800

Albuquerque, NM 87185-1139

ABSTRACT

The San&a Heat Flux Gauge (HFG) was developed as a rugged, cost-effectivetechnique for performing steady state heat flux measurements in the pool fireenvironment. The technique involves reducing the time-temperature history of a thinmetal plate to an incident heat flux via a dynamic thermal model, even though thegauge is intended for use at steady state. In this report, the construction of the gaugeis reviewed. The thermal model that describes the dynamic response of the gauge tothe f~e environment is then advanced and it is shown how the heat flux is determinedfrom the temperature readings. This response model is based on first principles, withno empirically adjusted constants. A validation experiment is presented where thegauge was exposed to a step input of radiant heat flux. Comparison of the incidentflux, determined from the thermal response model, with the known flux input showsthat the gauge exhibits an noticeable time lag. The uncertainty of the measurement isanalyzed, and an uncertainty model is put forth using the data obtained from “theexperiment. The uncertainty model contains contributions from seventeen separatesources loosely categorized as being either from uncontrolled variability, missingphysics, or simplifying assumptions. As part of the missing physics, an empiricalconstant is found that compensates for the gauge time lag. Because thiscompensation is incorporated into the uncertainty model instead of the responsemodel, this information can be used to advantage in analyzing pool fire data bycausing large uncertainties in non-steady state situations. A short general discussionon the uncertainty of the instrument is presented along with some suggested designchanges that would facilitate the determination and reduction of the measurementuncertainty.

3

‘a

This page intentionally left blank

.

4

CONTENTS

mTRoDucTIoN ...........................................................................................................................7THE ~G .........................................................................................................................................8THERMAL MoDEL .......................................................................................................................9

Re-radiation Loss Term - q~~d............................................................................................... 10

Convective Loss Term - qCO.v/a............................................................................................ 10

Storage Loss Term - q~W1/a.................................................................................................. 11Insulation Loss Term - qiJ~ ................................................................................................ 11

Data Reduction - q~u~tJ ...................................................................................................... 15MODEL VALIDATION ............................................................................................................... 16

Experimental Setup and O~ration ....................................................................................... 16Correction for Convective Heat Transfer ............................................................................. 17Radiant Heat Flux Step Jnput ............................................................................................... 19

HFG Response ..........~.....~....................................................................................................2OUNCERTAINTY ...........................................................................................................................22

Uncertainty Model ................................................................................................................23

Uncontrolled Vtiability .......................................................................................................23Missing Physics ....................................................................................................................25

Simpli&ng Assumptions .....................................................................................................29

Application to Validation Experiment ..................................................................................3lEffect of Sampling Frequency on Calculated Error .............................................................33

CLOSU~ .....................................................................................................................................35REFERENCES ..............................................................................................................................36

APPENDIX A SNL Hemispherical Heat Flux Gauge Assembly and Construction Details ........37

5

FIGURES

Figurel. Exmpleofa measurement ad~sociated uncetitinty using the~Gin apoolfire. Notethe uncetitinty lititsmay notdways conttin themeasurement ................7

Figure 2. The Sandia HFG . ..........................................................................................................9Figure 3. The 1-D thermal model of the HFG. ................................................-.........................lOFigure 4. A 20 Node Nodalization . ............................................................................................l3

Figure5. Themdconductivity of Kaowool@ atvwious b14etdensities . ..............................l4Figure6. Specific heatof Kaolin . ..............................................................................................l4Figure 7. Experiment setup for realizing a step increase of radiant heat flux to the HFG. .......16Figure 8. Operation of the experimental setup showing the heat up of the cavity and the

step input of heat flux as recorded by the Garden gauge. ..........................................17Figure 9. An assumed convection cell in the test cavity results in convective heat transfer

from the air to the gauges located in the mouth of the cavity. ...................................18Figure 10. Estimated convective heat transfer coefficient for a surface facing up into the

cavity as a function of surface temperature (air temperature = 1000”C). ..................18Figure 11. Step input of radiant heat flux to the HFG . ................................................................ 19

Figure 12. Measured versus calculated incident heat flux ...........................................................2oFigure 13. Calculated temperature profile in Kaowool@ insulation. ...........................................21Figure 14. Long-term insulation heat loss . ..................................................................................21Figure 15. Estimate of the uncertainty of measurement of the step input. ..................................22Figure 16. The thermocouple lags the actuaI plate temperature. The Iag can be corrected

with a first order model. .............................................................................................26Figure 17. Experimental determination of the time constant for the first order correction to

the thermocouple reading . ..........................................................................................26

Figure 18. The normal emittance of Pyromark as a function of source temperature [6]. ............30Figure 19. Relative importance of the different sources of uncertainty during a step input

of 100 kW/m2 . ............................................................................................................32

Figure 20. Heat flux calculated for various sampling frequencies . .............................................33Figure 21. Heat flux error range calculated for various sampling frequencies ............................34

TABLES

Table 1. Uncontrolled Variability as Uncertainty Sources .......................................................24Table 2. Uncontrolled Variability as Uncertainty Sources from the Systematic Error

Term ...........................................................................................................................28Table 3. Simplifying Assumptions as Uncertainty Sources .....................................................3l

●

●

6

INTRODUCTION

Over the past several years, hydrocarbon fueled pool fire experiments have been performed bothat Sandia National Laboratories’ (SNL) Lurance Canyon Burn Facility and the Navy’s ChinaLake Large Scale Pool Fire Facility where measurements of radiative heat fluxes were madeusing the Sandia Heat Flux Gauge (HFG). HFGs were developed by SNL as a rugged, cost-effective technique for performing heat flux measurements in the pool fire environment. Thetechnique involves reducing the time-temperature history of a fire exposed surface as measuredby a thermocouple, to a time resolved heat flux via a thermal model that is valid during times ofsteady-state within the fire environment. Three issues have arisen with respect to the technique.First, the original thermal model which incorporates empirically derived time constants did notperform well in a recent calibration experiment. Second, the original thermal model is notamenable to the formulation of an uncertainty statement that should accompany heat fluxmeasurements in application. And third, it is not always clear from the data as to when steady-state is achieved and the measurement is valid. To address these issues, we herein put forth analternative thermal model that avoids the use of time constants by allocating, in part, their effectto the uncertainty of the measurement. The uncertainty becomes coupled to the dynamicbehavior of the gauge with large values of uncertainty signaling when the gauge is not inequilibrium with the fire environment. We believe this approach results in an improved datareduction technique that is of use in reducing the data collected from previous fires.

Figure 1 shows a typical time-temperature history from an HFG reduced to the incident heat flux.Also in the figure, the uncertainty of the measurement is shown as error bars for each data point.

80 , -10001 ! 1 $ 1

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HFG Sensor Plate : . ; I

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850

800

750

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300 350 400 450 500 550 600

Time (see)

Example of a measurement and associated uncertainty using the HFG in a pool fire.Note the uncertainty limits may not always contain the measurement.

7

The heat flux was determined by applying the proposed thermal model, and the uncertainty wasfound from the accompanying uncertainty model. It is worth noting the uncertainty is largeduring times of dynamic change and can be used to assess the existence of steady state. Thethermal model is based on first principles, with no empirically adjusted constants. Theuncertainty model contains contributions from seventeen separate sources loosely categorized asbeing either from uncontrolled variability, missing physics, and simplifying assumptions. Theuncontrolled variability and simplifying assumptions are the major contributors to theuncertainty during times of steady-state operation, and the missing physics are responsible forthe large increase in uncertainty during dynamic changes.

In what follows, the gauge construction is first reviewed. It will be seen that the gauge isessentially a thin metal plate that responds to heating from the fire environment. A thermalmodel that describes the response is then advanced and it is shown how to determine the heatflux from the fire environment via the time-temperature history of the thin metal plate. Avalidation experiment is presented where the gauge was exposed to a step input of radiant heatflux. Comparison of the incident flux determined from the thermal model with the known fluxinput shows that the gauge exhibits a noticeable time lag. The uncertainty of the measurement isanalyzed, and an uncertainty model is put forth using the data obtained from the experiment. Anempirical constant is found that compensates for the gauge time lag. This compensation isincorporated into the uncertain y model instead of the response model, and it is shown how thisinformation can be used to advantage in analyzing pool fire data. Finally, a short generaldiscussion on the uncertainty of the instrument is presented along with some suggested designchanges to the HFG that would facilitate the determination and reduction of the measurementuncertainty associated with the HFG.

THE HFG

The HFG is intended to function by exposing one side of a thin metal plate to the fireenvironment and observing the temperature response. Ideally, the plate is perfectly isolated, i.e.,the unexposed side and the edges of the plate are thermally insulated. Furthermore, if the plate isassumed to be thermally thin, gradients through the plate and along the lateral direction can beignored. These assumptions allow interpreting the temperature measured at a single point on theunexposed surface as the one-dimensional response of a heated composite wall.

To meet the requirements of a one-dimensional response, the gauge shown in Figure 2 wasdeveloped. The assembly is essentially a hollow cylinder filled with thermal insulation that isfitted with sensor plates on each end. The body of the HFG is a 10-cm long cylinder of 10.2-cmdiameter schedule 40 steel pipe. The body is filled with Cerablanket@ ceramic fiber insulation tominimize heat transfer inside the HFG. The entire assembly is held together with four 14-cmstainless steel bolts. See Appendix A for construction drawings and fabrication details.

The sensor plates are 10.2-cm squares of 0.025-cm thick 304 stainless steel shim-stock. Theplates are held in place on the cylindrical body by endplates that are 10.2-cm square by 0.32-cmthick 304 stainless steel with a centered 5.O-cm hole. The sensor surfaces are thermally isolated

b

.

8

1- Front Plate-Thermocoudea

1

J

Figure 2. The Sandia HFG.

from the remainder of the HFG by two layers of Lytherm@ ceramic fiber insulation. The frontsides of the sensor surfaces are coated with Pyromark@ paint to achieve a diffbse gray surface. AO.16-cm diameter Inconel-sheathed type-K thermocouple is used as the sensor thermocouple.The sensor thermocouple is attached to the sensor surface with O.01-cm thick retainer straps thatare spot-welded to the back of the sensor surface.

For most of the data taken to date, the gauge has been constructed with only one sensor plate.Only one end was exposed to the fire, and the sensor plate on the other end was replaced with aflat plate (304 stainless steel, 10.2-cm square, 0.32-cm thick).

THERMAL MODEL

The heat bakmce on the heated surface of an idealized one-dimensional heat flux gauge(Figure 3) can be summarized in the following equation,

~q,u~(t)= e.q,=.(t)+q c...(t) +qs~eel(t)+qimtil~t)

where q~u~t) is the heat flux incident to the heated surface, qrd(t) represents the heat re-radiatedfrom the sensor surface, qconv(t)is the convective heat loss at the sensor surface, q,reel(t) is the

●

sensible heat stored in the thin 304 stainless steel sensor plate, and qimul(t) represents the heatconducted into the insulated backing. Absorptivity and emissivity of the steel surface are

. represented by a and S, respectively.

9

%&4

q SLXI = %ad + %mvJu + qsteelh + %sul Icf

Figure 3. The 1-D thermal model of the HFG.

To implement this model in a data reduction scheme, each one of the loss terms is related to theinstantaneous temperature of the sensor plate. Since the data is normally acquired digitally, andtemperatures other than the observed sensor plate have to be considered, the following

nomenclature is adopted. ~.Nis the temperature at the end of the l@ time step (corresponding to

the time tJ at the ir~location. The sensor plate corresponds to i=l, and increasing values of i are

in-depth positions within the thermal insulation. Thus, TIN is the observed temperature of the

sensor plate at time step N. In what follows, the loss terms are calculated in terms of TINand

added to provide a “reading” of the heat flux, q(t~), on the surface from the fme environment.

Re-radiation Loss Term - q~=d

The re-radiation term is based on the Stefan-Boltzmann law

qrad(tN )= O.(TIN )4

with o = 5.67 x 10-11kW/m2 K4.

Convective Loss Term - qconJ~

The convection term is modeled as

%w(tN) ‘(TN‘Zrnb)=a a

where the heat transfer coefficient h must be determined from knowledge of the gaugeinstallation, the temperature of the ambient fluid in contact with the sensor face Tati, and flowconditions over the surface.

10

Storage Loss Term - q.te~{~

The heat flux absorbed into the thin steel sensor plate is calculated using the surface plate

● thermocouple temperature derivative using a central difference, i.e.,

q,,,,l(tjv ) P- C,(TIN )*L dT,N PCP(T,N )*L (–TIN” +8. TIN” -8. TIN-’+.TIN-2)=a a dt=a” 12”(tN+1–tN)

.The 304 stainless steel sensor plate density and specific heat properties are temperaturedependent and can be calculated using the following equation (temperature in K) [1].

p“Cp(T) = 1215.769 +14.969 .T-0.029. T2 –2.991e-5. T3 –1.472e-8. T4

+ 2.818e-12. T5 [ti/ms/K]

L, the thin steel HFG sensor plate thickness is 0.0254 cm.

Insulation Loss Term - qi.~a

The relation between the sensor plate temperature and the heat loss into the insulation is obtainedby considering the response of the surface of a thick wall subject to a time varying temperatureon one surface and perfect insulation on the other surface. An algorithm for calculating the heatflux into the insulated backing given the thermocouple response at the surface has been derivedby numerically modeling the transient thermal response of the insulating material. The one-dimensional heat conduction equation with no internal heat generation and temperaturedependent properties is written as:

where k, p, and CP are functions of the temperature field. This equation can be cast in finitedifference form as follows (time is designated as superscript N and location as subscript i):

-’y-[2+aN+’+%’”T.N+l– TN ki_1,2P,cpi ‘ ~t ‘ =

dzi_l

s Note that thewhile density

conductivity is evaluated at the average mid-point temperature between nodesand specific heat are evaluated at the nodal temperature for the preceding time

step. This equation 1s implicit since the heat flux (right hand side of the equation)is evaluated at.

the advanced time step N+l. This equation results in the following linear system of equations.

11

%,x + %2T2 = d]

= d,C2~~ +C22TZ + C2 ~TB

C3,2T2 + c3,3T3 + c3,4T4

. . .

. . .

c,_1,,_2~_2+ cl_,,l_,~_, + c,_,,,~

cf,l_lq_, -+C,,Iq

= d,

= di

= dl_l

= dl

In these equations, the coefficients c are functions of material properties (and time step along thediagonal), the values of d are functions of material property, time step, and the temperature at thepreceding time step, and the vector T is the temperature field at the end of the time step. Thissystem is a tri-diagonal set of equations, which can be solved by Gaussian elimination. Theresulting algorithm can then be summarized with the following set of equations.

ci,i+lTi+l

‘= Y’- pi

, j=z–1,~–z,...,l

/p,= c,,, Y,= “ fll

pi =Cii -ci’i~~ , i=2,3,...,IJ

di – Ci,i-lyi-lYi =

Pi

, i=2,3,..., I

.

The nodalization is chosen such that node spacing is much finer near the heated surface thanthrough the bulk of the insulation. This objective is achieved by prescribing a geometricallyincreasing node spacing, i.e.,

dzi = d.zi_lri .

●

✎

For 20 nodes, and r = 1.2, and 7.62 cm Kaowool@ insulation thickness, the nodalization is shownin Figure 4.

12

1

0.5

0 [

Note

II

that the

0.01 0.02 0.03 0,04 0,05 0.06 0.07 0.0813istencefrom Heated Surface, m

Figure 4. A 20 Node Nodalization.

number of nodes and the geometric ratio, r, can be varied to optimize thenodalization. When the number of nodes is very large, care should be taken in selecting the ratior, since a large ratio will result in very large nodes through the bulk of the insulation. When r =1, the nodalization collapses to the uniform case.

Thermal properties are evaluated from polynomial curve fits to the manufacturer’s data. For 128kg/m3 (8 lb/ft3) Kaowool@ blanket (typically used interchangeably with Cerablanket@ in the SNLHFG),

/c(T) = –6.05.10-3 +6.98 .10’5T+1.0410-7T2 [kw/nz/K] and

pcp (T)= 128 ~(739.72733 +.2483608T) [.m?d /K]

as plotted in Figure 5 and Figure 6. Note that Kaolin is the raw, mineral material melted to formthe fibers of both the Kaowool@ and Cerablanket@ insulation. Because temperatures at thesurface of the heat flux gauge can vary widely in a fire test and thermal properties, such asthermal conductivity in particular, are strongly dependent on temperature, it is important to usetemperature-dependent properties in this evaluation.

For data reduction, this algorithm is implemented in a computer subroutine, which calculates thetemperature field in the insulation at the end of a time step for a prescribed temperature boundarycondition on the heated surface. The instantaneous thermocouple reading is used as the surfaceboundary condition to the insulation. Since the insulation is assumed to be thick, an adiabaticboundary condition is chosen for the opposite side. For the single sided gauge, this surface islocated at a distance equal to the total length of the gauge. For the double sided gauge, thissurface is located at a distance equal to half the length of the actual gauge.

13

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1 1 1

— 69 kg/mN3 (4 lb/ftA3) density

— 96 kg/mA3 (6 lb/ftA3) density

— 128 kg/mA3 (8 lb/ftA3) density

— 160 kg/mA3 (1Oib/ftA3) density

— 192 kg/mA3 (12 lb/ftA33) density

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200

Figure

1200

1100

Q 1000

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8 900

800

700

400 600 800 1000 1200 1400

Mean Temperature (K)

5. Thermal conductivity of Kaowool” at various blanket densities.

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200 400 600 800 1000 1200 1400

Temperature (K)

Figure 6. Specific heat of Kaolin.

14

●

.

The heat flux to the insulation is then calculated from the derived temperature field by taking thederivative of the temperature gradient at the surface, i.e.,

~im (tNl _ ‘(Lfl/2) . (TN ‘T2N)

a–a dzl “

Data Reduction - q.u#tN)

Summing the losses for any time, t~, results in:

() h “ (TINq,w#N)=o-T1N4+

- ‘mb )

a

p“cp(zy)”L (–~~+~+g.~~+1–g.~~-1+~~-z)+

a 12-(tN+l –tN)

where TIN is the thermocouple reading in K at the ~h time step. Tl~l,~ and TZNare determined

by running the thick wall subroutine using ~.N-* as the initial values.

Microsoft” Visual Basic macros have been written to perform heat flux gauge analysis for data

in MS Excel” spreadsheets. The subroutine hjhm calculates the various heat flux terms found inthe energy balance to arrive at a total incident heat flux. Time and temperature arrays are passedto this subroutine as real arrays in the argument list, and the incident heat flux is returned as areal array. The dimension of the arrays is calculated within hflux and variable array sizes areallowed.

Currently there are certain assumptions or specifications inherent in these macros that may bepeculiar to the specific heat flux gauges tested, i.e.,

e The stainless steel sensor plate is .0254 cm thick. The ernissivity, &,of the sensor plate is .85

. pcP for the sensor plate is specified for 304 stainless steel

@ Convection is modeled with a specific expression (discussed below) that is not applicable ina general sense

e The insulation is a 7.62 cm thick Kaowool@ blanket.

Heat losses to the insulation are calculated in the subroutine insul as described in the preceding

section. Currently the insulation is modeled as 7.62 cm thick Kaowool” blanket material andtransverse heat losses are ignored, i.e., one-dimensional heat transfer. The model has 20 nodesthat are geometrically spaced with a ratio of 1.2.

15

MODEL VALIDATION

Experimental Setup and Operation

To validate the model, we chose to subject the gauge to a step input of’radiant heat flux to a levelcommensurate with that found in typical fire experimentation. Response to a step input isparticularly desirable in that shortcomings in the data reduction technique are revealed, andglobal characteristics of interest such as instrument order and response time are directlyobservable.

To accomplish the step input, the HFG was placed below and facing up into a heated cavitywhose walls are maintained at a constant temperature (Figure 7). The cavity, 1 m in diameter by1.3 m deep, is formed from a cylindrically-shaped Inconel shroud with heat lamps directedtoward the outside of the shroud to control the temperature of the cavity. A cover is placed overthe HFG while the cavity is brought to the desired temperature (typically 1000 C). The stepinput to the HFG is initiated by removing the cover. A Garden gauge is positioned next to theHFG to observe the same flux and provide a standard for comparison.

Figure 8 shows the average temperature of the shroud and the response of the Garden gauge as afunction of time. In that figure, heating of the cavity began at about 3 minutes and steady state at1000”C was achieved at about 7 minutes. At that time, the gauges were uncovered resulting in astep change in heat flux from O to about 110 kW/m2. This flux level was held constant for a 30minute period, at which time the gauges were covered and the power to the heat lamps turnedoff. Further details on the setup and operation of this system are given in [2].

+1.----+

[-:- ““: ““1

/ I\ ‘“/

GardenRemovable GaugeCover

16

L

H+-- r).sm

Figure 7. Experiment setup for realizing a step increase of radiant heat flux to the HFG.

.

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----4 I

---— - —

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: Garden Gauge Response \ ~

1 1 1

— Nominal Shroud Temperature :, 1

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f_--l---

–--+----

J“+-&I

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10 20 30 40

Time (rein)

Figure8. Operation of theexperimentd setup showing theheat upofthe cavity mdthe stepinput of heat flux as recorded by the Garden gauge.

Correction for Convective Heat Transfer

For comparing the Garden reading to the HFG response, the convection heat transfer betweenthe ambient air in the cavity and the Garden gauge must be taken into account. To do this, it isassumed that a convection cell forms in the cavity as shown in Figure 9.

The general correlation shown in Figure 9 has been developed for vertical surfaces, but isdirectly applicable to an upward facing surface that is being heated by the flow [3]. Evaluatingthe general correlation for an air temperature of 1000”C and a surface size of 0.3 m (nominal sizeof the pedestal holding the gauges) gives results shown in Figure 10.

17

100 ! , I

2 -w !–––––+–––*_––____:____~,W

1.00E+05 1.00E+08 1.00E+07 1.00E+08 1.00E+09

Gr

~U~=0825+ 0.387(Gr.Pr)~8

[H]

9=

~+ 0.492 E

Pr

Churchill-Chu General CorrelationFlat Plate Free Convection

Figure 9. An assumed convection cell in the test cavity results in convective heat transfer fromthe air to the gauges located in the mouth of the cavity.

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1 1

1

I 1

1 I

1

1

1 1 1

1 I 1 1

200

-7

I-~

- ,

~

– ,

‘/-!

I-i--l

400 600 800 1000 1200 1400

.

.

Plate Temperature (K)

Figure 10. Estimated convective heattiasfer coefficient forastiace facing upinto the cavity

as a function of surface temperature (air temperature= 1000”C).

18

For purposes in this experimentation, it is convenient to fit the results to a curve:

~ (21.02 -0.002144 T dn(T))~ kW ~or Tin ~=1000 m2. K

It is worth pointing out, this curve is valid only for the experimental setup, and is not intendedfor use in application of the HFG in other flow situations.

Radiant Heat Flux Step Input

Figure 10 indicates that the Garden response in the experiment can be corrected for theconvective contribution by subtracting 4 kW/m2, since the Garden gauge is water cooled andoperated at about 400 K. Because the Garden gauge is calibrated using a purely radiative sourceto provide a measurement of incident flux, the Garden gauge surface absorptance (s0.85) has tobe applied to the correction value (4/0.85 = 4.7). The uncertainty in this correction value is about50% [4]. Thus, the radiant heat flux step input to the HFG is taken to be

(Garden Response - 4.7) &2.4 kW/m2

and a plot of it is shown in Figure 11.

120

100

80

“g Go

x

z

40

20

0

I 1 1 1 1 i 1

I 1 1 ! I 1 t

! I I 1 1 I I

I

I

t---- -— --— -- —-- ,-------- ~______ - —, --------, -— —— --- :_______ ——I

---—-

-----

-----

--—- ———

1

1

1

1

I

1

L–

I

t

!

I

I

I

r–

I

!

I

1

!

!

1

1

I

1

1

I

I__

0 5

---

---

---

.-— —

1 I 1 I ! 1

1 1 I I 1 1

1 1 I 1 1 1

1 1 I 1 1 1

1 1 { 1 1 1

-l-–– – - – - –! -------- 4------ –4 ----- __ J_______ -l.-

1 ! I 1 I !

I ! 1 I I $

1 I 1 1 I I

I 1 1 1 I

1 1 1 1 !

1 1 I 1 1 1

l––– – ----1 ----- - l-–––––– 7----- -– i-------i-

1 I 1 1 I I

! t 1 1 I 1

I 1 1 1 1 1

I 1 1 I 1 I

1 I 1 I 1 1

_; ——— —— —--;- ---- ___; —— —_—— ——~-- -— -- —;—- ---- -;-

! I 1 I ( !

! 1 1 I 1 I

i ! [ I I 1

1 i I 1 ! 1

1 1 I 1 I I

–i––------l----.–––l–––– –--J--–––--J--–-––– 1–1

I

1

I

i I t I

! 1 I $ I ; WI 1

f

I 1 I 1 I

10 15 20 25 30 35 40

Time (rein)

Figure 11. Step input of radiant heat flux to the HFG.

19

HFG Response

The incident heat flux for the heat flux gauge test, as determined by the Garden gauge and HFG,

is plotted in Figure 12. The vaious heat losses to the insulation (~Ju), the sensible heat stored

in the sensor plate (q~t&l/et), heat re-radiated from the steel cover (q~d), and convective heat

losses (qCOnv/cx)for the SNL HFG are also plotted in Figure 12.

Temperature profiles calculated in the insulation for the calibration test are plotted in Figure 13.Note that for this insulation thickness, saturation has not occurred even at 1700 seconds. Thenumerical technique described in this paper provides a convenient means of modeling heat lossesto the insulating material yielding improved agreement between measured and imposed heatflux. As seen in Figure 14, heat losses to the insulation are significant at times long after thestorage term (sensible heat of the steel cover) has become negligible. By modeling heat losses tothe insulation, the time response of the heat flux gauge is greatly improved. It is believed thatthe difference between the Garden Gauge response and the HFG response early on (< 40 see) isdue to the thermocouple attachment to the HFG sensor plate since this is a known source of timelag and has not been accounted for in the model.

120

100

80

n 60‘g3$5. 40

x

~ 20

0

-20

-40

, I ,

1 1 1 7I I

I 1 I

------ .-— —

1

,---- ————_—_ ---- —~-.. — — Qinsui/alpha ----

,l--------------- ..(----- -— -.:

1

---- --- ;---- ----—_ —---- -: ---

––—-l-— ——– —— --– ---—-–1———––——— ––––––—4–————– —– —------~

/1 I i

( )

t

1 I 1

--------––––––- l--------------- ––1–––––––––--––– –– 4 ----------- -– --:

I 1

1 1 1

I , 1

1 I 1

I I 1

Time (see)

Figure 12. Measured versus calculated incident heat flux.

20

1200

4

.

1100

1000

500

400

300

--, -_ ——-- --

_———---7

tt

–-:. -––-__ –;___ ______

–l---––– –--– –---– –– -----– –

--—— —— -- ———

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Distance From Heated Surface (m)

Figure 13. Calculated temperature profile in Kaowool” insulation.

Tr99 -

8e; -

60 --

I , , , !

1 1 I

)

! 1 1

I 1 I

I

I 1 1

1 I 1 I t

1–-__—–—–

I I ( 1

1 1 I

!

_——--- — ;–--–-––;__---___:_ ___—Qinsul/alpha

1 1 !

! 1 1 —Qsteel/alphaI I 1

1 I 1

--––---L ----- -–A––––-.-A– ––- — Qrad! I 1I I 1

1 1 1 —Qconv/alpha1 I I_———--—; —--- _——;---- -_——;—--- —Gardon GaugeI I I

I I 1

1 I I 1 —HFG -Energy Balance--L––--–––4-- ––––-4--––-–-4 -––-----1––----–-1-- ––---–L-----–– ,

/

o

2e+---;-------; ------- ;------- +-------{------- ;-------- \--------I

1 1 1 I I 1

I I 1 ! 1 I

!

I

I

[ 1 I I I I !

J<g I 1 I ! 1 I i I!

1_]

_—_<~

I

_— -i

Time (see)

Figure 14. Long-term insulation heatless.

UNCERTAINTY

The uncertainty has been found to be a function of the flux level, rate of change of flux level,time, and heating history. Thus, it is not appropriate to report the uncertainty as a singlepercentage value, rather, itisrequired torepoti itpoint bypoint asmobsemationd e~orbm. Asan example, our estimate of the uncertainty of the measurement realized with the flux step inputis shown in Figure 15. The measurement as determined from the response of the thermocouplevia the response model is indicated with a solid blue line in that figure. The upper and lowerbounds of the uncertainty are indicated with horizontal tick marks. These bounds weredetermined from the uncertainty model that is developed in the following sections. Forcomparison purposes, the input incident heat flux as recorded by the Garden Gauge is alsoshown in Figure 15.

In application, the slow response of the gauge means the heat flux measurement is likely to beunreliable during and after fluctuations in flux. Nearly one minute is required before themeasured flux approaches the steady state value of the step input. However, it can be seen theuncertainty is relatively large during the early times of the response to the step input, andapproaches a constant value as the gauge comes to equilibrium with the step input. This can beused to advantage in assessing heat flux measurements in actual fires. Figure 1 shows a five-minute segment of a measurement made in a 5 m outdoor pool fire with a HFG facing upwardand located near the fuel pool surface. The heat flux varied with time during this test,presumably because of wind shifts, and is typical of most fire data. The error bars shown arecalculated from the uncertainty ‘model and their variation with the flux level, rate of change offlux level, time, and heating history are evident. Times of near constant uncertainty signal theattainment of steady-state where the measurement can be assumed valid.

140

120

100

~-$$ 80

~ 60

E

40

20

0

I I

1

1:I

(

Garden Gauge !-1.————---- __L-—----- —--——1-..--——---,, _———___

.

I1/

\i;----- . . . -- ; .-. - .. - . _---__:___ _________ ~--- ---- ---- -

I

,

-.. -_ HEG_;._________ .-[_________________________--!

II 1

-- -. L__–-––__l––_l - _–––-. _––--:_– ___ --—— ---

1 II I

0 20 40 60 80 100

Time (see)

Figure 15. Estimate of the uncertainty of measurement of the step input.

22

Uncertainty Model

Uncertainty in the heat flux measurement arises from: (1) uncontrolled variability in the gauge

acharacteristics, (2) missing physics in the model, (3) and simplifying assumptions taken on informulating the instrument response model. The uncontrolled variability includes materialthermal properties, geometrical dimensions, data acquisition system hardware, thermocouple

, uncertainty, etc. Examples include the specific heat and thickness of the stainless steel sensorplate. Estimating uncertainty from this source is relatively straightforward, requiring onlyknowledge of the variability of the properties and dimensions. As for the missing physics, thesephenomena are commonly buried under empirical constants that are created to bring the modeledinstrument response into agreement with the observed experimental response to a known input.An example of this would be the empirically determined time constant derived to account for thethermocouple attachment to the HFG sensor plate. Simplifying assumptions include either sub-scale phenomena or phenomena believed to be of secondary importance. An example of theformer is the assumption of no temperature gradient through the sensor plate; and of the latter,the assumption of negligible lateral conduction in the gauge. Uncertainties arising from thissource are usually set to zero and justified by appealing to more complicated models orexperimental evidence. Here, we adopt the same approach for theattempt to account for the effect of making the 1-D assumption.

Uncontrolled Variability

The uncontrolled variability includes material thermal properties

sensor plate, however, we do

and geometrical dimensions.Estimating uncertainty from these sources is straightforward by evaluating:

%urfwhere the first seven sources S., the sensitivities —, and the source uncertainties

as,identified in Table 1 (the other seven sources are identified in a following sectionMissing Physics).

C$Seare

entitled

The sensitivity terms in the table are obtained by performing the indicated partial differentiationson the data reduction expression

~ -C, (T,N) L (–TIN+’ +8 .TIN+l –8 .TIN-’ + TIN-’)qsu~ (~iv) =CP(Tl~y+k+

G? a 12 “(tN+l – tN )

The source term uncertainties for the f~st four sources are simply fixed percentages of thepertinent term. For example, the uncertainty in the sensor plate thickness L is taken to 20%, the

uncertainty in p, CP is 5%, and so on.

23

Table 1Uncontrolled Variability as Uncertainty Sources

e Source Sensitivity Source Uncertainty&e

%@se as=

1 L P “C,(T,N ) dT,N 0.20 L

a dt2 pep L dTIN 0.05p- CP( TIN)——

a dt3 a P. CP(TIN). LdT,N o.05a

az dt4 T, 40(T1N )3 0.05. TIN

5 dTIN /Y CP(T,N). L

dt a 0’0=

6 qin.s 1.0 0.03. q,uti

a

7 qcon, 1.0 0.03. q,uti

Q!

derivative,dTIN—, is due to random noise introduced to the recorded

temperature time history via the data acquisition system. The noise is constant at 0.1 “Creg~dless of the temperature reading. Its impact on &e uncertainty of time derivative is foundfrom

12

)(~)dt .0.1 =

0.1470

aT~ 12. (tN+, –tN)

J

-.

24

*

qinsFor the uncertainty of the term, — the data reduction model was n-m with 20% changes in thea’

thermal properties of the insulating material and it was found the maximum effect on thecalculated heat flux was less than 3%; hence the uncertainty level has been conservatively set atthe 3% value.

The uncertainty due to convection is more difficult to evaluate as it is dependant on the actualinstallation of the gauge in use. The flow conditions and local gas temperatures (which inpractice are not known) contribute to this uncertainty. VULCAN calculations have indicated ingeneral convective fluxes in fires are about 3% of the radiant flux [4] although this can vary withlocation. Therefore, the value of 3% of the radiant flux has been adopted for the uncertaintyvalue.

Missing Physics

These phenomena are commonly buried under empirical constants that are created to bring themodeled instrument response into agreement with the observed experimental response to aknown input. An example of this would be the empirically determined time constant derived toaccount for the thermocouple attachment to the HFG sensor plate.

It is known the thermocouple lags the sensor plate temperature due to the thermal mass of thethermocouple and the thermal resistance between the thermocouple and the plate. Anexperimental evaluation of the lag was accomplished by attaching an intrinsic junctionthermocouple next to the existing thermocouple and exposing the HFG to a step input. Theresults are shown in Figure 16. In that figure, the temperature measured b y the intrinsic junctionis assumed to be the sensor plate temperature. It can be seen the differencethermocouple reading and the plate approaches 200°C.

Thermocouple lag is commonly corrected via a first order model that incorporatestime constant.

The value of the time constant is found by plotting the

between the

an empirical

difference between the plate andthermocouple versus the time rate of change of the thermocouple reading. This is shown inFigure 17 where it can be seen the value of r is just over 5 seconds. The correction is thenapplied to the thermocouple reading and shown in Figure 16.

The correction can be implemented into the data reduction scheme by substitution

25

900

800

700

g 500

200

100

0

-.. ————

---- ---

1 1 I I

HFGPlate ~--- _____ ~!. -----.! . .: _________---- .-—I

I

$

1 1

I 1

I I.— -—,—- .-— — —— __ ____ ~ –<–––_– –__’ *_--—_—.

1 ,

1

(

I

1 I

1

1

1

,

---— — ---- - --—— —— -- 1 ---- ---- 1--- ---— —j— --- ---—i I

(

)

~

First Order Correction ~

.-!---- ––– –-1-- ------ .+------- -& -------

---- IL---! Thermocouple ~1

1 1 I

---- L------ -1 ---- ---- -- J-------–L.–- ----

, 1 I 1

1 I I

[iii:

- - - - - - - -,- - - - - .- - - . - -- . . . _ ‘r--------l ----- --- ,----’-.-’-.-:_ ------

- - . - - - - - A - - - - - - - - I_ - - - - . - - -1- _ _ _ - . - - 1 - - - - - - _ _ 1- - - - - - - _

.r

Figure 16.

F?-----------—--____

---- -

Ef=+i4 I

280

Figure 17.

1 ! I

290 300 310 320 330 340 350

I

-’

Time (see)

Thethermocouple lags theactual plate temperature. The lag canbe corrected

Q

1

-------!----250

-------!----2(3(3

-------~----l-w

I

---- ---,---- w

---- ---- ---- 50,I

7) -;0

- -5G

first order model.

1 I I ) 1 I1 1 1 I1

1 I 1 1 A

---–––; –– –___I 1 1 I

I I 1

1 1 1

1 1

I I 1

I 1 1

1 I

1 I

(

I

1

1

I

--- .“--–-4-. -..----. -. L- -.-. --. -.-. L.-. -... -.---I-- ------

L1 1 I I 1

–J–__ -----l ---- --- !--------L-- ----. _l.-______–1 1 I 1 11 1 1 11 1 I ! II [ I 1 1 II 1 f I 1 -

dT/dt (C/see)

Experimental determination of the time constant for the first order correction to the

●

thermocouple reading.

26

.

dTNwhich after rearranging and assuming that p. CP ( TIN+ __#. )= p.cP(TIN ) gives

qSuti(lN) =~-(~N~+&+ P”CP(~N)”L”d~N ; q,~a a dt a

+—

+(7”

p. Cp(~N)Zz d2~N

[

d~N

[ .1dTIN ‘._+~. 4“.(7p’)3.z .—+(j. (q’’’)+? ~

a dt2 dt

which is seen to be the original response model plus a systematic correction for the thermocoupleinstallation.

Normally, the systematic correction would be included in the response model. Here, we chooseto put the correction in the uncertainty because it is based on ~, an empirical constant that coversthe missing physics for the thermocouple installation. Therefore, a systematic error term for themissing physics is defined:

The uncontrolled variance of the different sources enter into the totrd uncertainty via this errorterm as well. Table 2 shows the sources, sensitivities, and source term uncertainties as theremaining six entries for the total uncontrolled uncertain y expression.

The sensitivities and source uncertainties are, as before, with only the time constant and thesecond derivative being new terms. The second derivative is app~oximatedcentral difference scheme as:

& d2T1N _ – T1N+2+ 16- T,N+’– 30. TIN+ 16- TIN-’– TIN-2— _dt 12. (tN+l– tN )2

from a five-point

which allows the source term uncertainty to be calculated as explained in the previous section.

27

Table 2Uncontrolled Variability as Uncertainty Sources

from the Systematic Error Term

e Source Sensitivity Source UncertaintyBe

%urfse ase

8 L P“CP(T; ).z d2T1N 0.20 L.—

a dt’9 p“cp L ~ d2T1N 0.05p “CP( TIN). ..—

a dt’10 T]

[ 1 0.05 “TINO- 12. (T1N)2w. ~

+~12T:’’[)+’’’[11 dTIN

dt [a. 4.(<N)3-r+ 12. (~N~-r2-; 1 ““l=zz+~1’T:’’[%J+’~[

12 ‘r

~+oF(’N)3+a‘50”rP$(~N).L d2~N

+~;(~”)’w’l‘012TT”’2-[~J+4

13 d 2TIN P. CP(T; ).LZ

dt’ a “o=

14 a 0.05-(2!P. CP(TIN )-L. Z d2T1N— .—a’ dt’

28

Simplifying Assumptions

Simplifying assumptions include eitiersub-scde phenomena orphenomena believed to beefsecondary importance. Three assumptions have been adopted in formulating the gauge thermalresponse model: (1) negligible temperature gradient through the sensor plate, (2) the sensor plate

surface emissivity and absorptivity are the same, i.e. ~ =2, and (3) the heat conduction withina

the gauge is adequately modeled as l-D. Uncertainties arising from these sources are usually setto zero and justified by appealing to more complicated models or experimental evidence. Here,we adopt this same approach for the sensor plate gradient, however, we do attempt to account forthe effect of equating & and a, and for making the 1-D assumption.

The effect of assuming the sensor is a lumped thermal mass is found by analyzing the dynamicresponse of a semi-infinite wall [5]. For 13iot numbers less than 0.1, all temperatures through thethickness of the plate will be within a percentage~percent of the sensor plate temperature

where

f=50Biot%ofT~

and

and k, is the thermal conductivity of the sensor plate. This leads to

4W. (T; +273)3. L %f(T:)=50

k,,

being the uncertainty of T; due to the lumped mass assumption. To evaluate the expression, k,

is set to 0.03 kW/m K (nominal value for stainless steel) and L to 0.000254 m. For the worst

case condition, T; = 1000”C, f(T; ) = 0.2910,and there is no appreciable contribution to the

uncertainty from the assumption of no temperature gradient through the sensor plate.

The assumption of equal& and a is evaluated from;

%.$(t) =:.qmd(t)+qconv(t)+ qswel( t ~+ qinsul ( t J

Gt

A where the sensitivity is found to be:

w

29

()The uncertainty in the ratio, b ~ , is estimated from

ernittance of Pyromark Blackshows that data, and it can be

measurements made on the normal

[6], the coatingon the fire side of the sensor plate. Figure 18seen that the uncertainty in the ratio (i.e. hot source/cold surface or

cold source/hot surface) is about 4fZ0.

The systematic correction for the missing physics

simplifying assumptions uncertain y due to the ratio

summary of the total uncertainty shown in Table 3.

also generates an additional term to the

~. This additional term is included in thea

To investigate the third assumption, time histories of two thermocouples installed in theinsulation along the centerline of the gauge were recorded in the validation experiment. Incomparing their response to the step input, it was noted that a 2-D conduction model gave bettercomparisons. However, the resulting flux from the front sensor plate was at most 5% higher thanthe flux determined from the 1-D model.

0.86

0.85

0.82

0.81

0

I , 1 I 1

6 1 ! I 1

1’ 1 I 1 I

I 1 1 ! 1

1 1

1

1

(–––-_–--_T–-

1

---{;

1 1 I 1

I 1 I t

I I I 1

--–;–-–––-––––L- __–_____;_____ ___–;-– –--.____-;_________1 i I I

1 1 ! !

i I I I

1 1 I 1

1 1

1’111--—---T––-–––--––l–- --- – ----?---- -–--.–-i-––--–– - – -,--- –----–

–––--––-+ –---– – ----l ---------- t – ---- – -- –+------- ––-l--– –----–

1 1 1 I 1

I { [ 1

200 400 600 800 1000 1200

Source Temperature (C)

Figure 18. The normal emittance of Pyromark as a function of source temperature [6].

.

30

4

*

Table 3Simplifying Assumptions as Uncertainty Sources

e Source Sensitivity SourceUncertainty

kti a’.se as,

(1

15 &— o “(TIN~

u0.04. ~

a

(1 [

16 ~—a

[’w]] 0.04.;]m“ 4.(T1N)3”~ .--#+ (T1N)2)z2z2. —

+~”h’”’30’+’4”F:17 1-D 1.0 0.05 “q,u$

In the interest of parsimony, it was decided to maintain the 1-D model and add 5% to theuncertainty to account for the assumption. Thus, the total uncertainty for the simplifyingassumptions becomes:

&J~=$’(-”m)2 .,=,, ase e

Application to Validation Experiment

The expression for the total uncertainty is given as

where:

2ZJMP=p“CP(~N)”L .~ d2~N

[

d~N

[ H

d~N 2-—+~. 4.(Tl~)3.z ._+6. (TIN)?#. ~

a dt2 dt

31

and

and

The relative importance of each source varies with time and are shown in Figure 19. In thatfigure, it can be seen at early times, the uncertainty due to the missing physics of thermocoupleinstallation and the variability in the thickness of the sensor plate dominate. At later times whensteady state is reached, the error due to the simplifying assumptions and the uncontrolledvariability are most important. Referring back to Figure 15, it is of interest to see that during fastrise of the thermocouple, the uncertainty bars do not capture the reported “measured value.” Thesame effect can also be seen in Figure 1. It can be deduced that this behavior is due to thecorrection term from the missing physics uncertainty.

50

40

-lo

-20

IPI~I

Missing Physics1i I

/!.— .- 7-- -—-- -—.7 ——-- .——l---— -. --—- —-—:----- -- __ ; _________1 I1 1

: Uncontrolled Variability ~ 1I

I 1 I.--—

--s

_———.__——=___——-- .—-)- --——--—. - ~–––-_ –––.;––___–––-1 4 I

! 1 il/t 1 1 ! I

h1

Simplifying Assumptions ------ -; -----‘Fiji: ------ --; ---” , I[bi_——- -_——.._— —--- —---

r- i~----– ---— ~--- ——-.-—! i ‘---1

Time (see)

Figure 19. Relative importance of the different sources of uncertainty during a step input of 100kWlm2.

32

Effect of

The heat

Sampling Frequency on Calculated Error

flux was calculated for the model validation experiment at three different sampling*

frequencies. Theresults, plotted in FiWre20 mdFigme 21in&cate thatthe calculated heat fluxand the associated error are dependent on the sampling frequency. The sampling frequency

4 exercises effect in two ways. First, before the step change in heat flux, the 4-second and 6-second sampling curves predict heat fluxes in advance of the Garden gauge. This is because thetime derivative uses data subsequent to the step change in heat flux in determining thetemperature derivative. This ‘prediction’ in the model is observed in the calculated uncertaintyfor these curves. The second effect appears later in time. As temperatures rise from the imposedheat flux, the 2-second sampling curve shows much larger oscillations in the calculated heat flux.This is reflected as increased uncertainty during the temperature rise. Both effects disappear atsteady state; aJl three curves show agreement and the uncertainty becomes independent of thesampling rate.

120

100

20

0

I I 1

I I 1

1 I I

, ,

!

-.

I

I

k

1

--—— A––-- . . .. L.--._.._ ‘L. –– –--..

-. —-, .— —---,-- ---- ~ ------------ –

—2 second sampling --:-------

I

-.. ,-- ---- — ---- ---- ---, - ---- ---- --

0 20 40 60 80 100 1000 1050 1100

Time, sec

Figure 20. Heat flux calculated for various sampling frequencies.

.

33

) ,1 !

? 1

----- -- L-—-- ---L. _______

l-------- i-----– --,--------’, ---- - 1-----------

—k--— —— -.-k -—-——--,-—— —————,—.—–— —--,-—————- -:---

—--- --—_ I---- --—_ I____ ____ I---- -— __ I____ ____ ____

I I 1 ! 1

/ i i i----i

--------——----b -- ---- _ ~ - ___ ---;--- ----- ;-.--_--__,__ _

o 20 40 60 80 100 120 140

Time, sec

Figure 21. Heat flux error range calculated for various sampling frequencies.

The source of the uncertainty associated with sampling rate during high rates of change is theuncertainty contribution from the time derivative. This can be seen by considering a simple 3point central difference equation for the time derivative of temperature,

~ = (Tv+l–TN-1)dt (tlv+l– ~Af)

The equation for the associated uncertainty would be given by:

I

Note that as the sampling frequency increases, (or tN.1 – tN decreases), the uncertainty in the timederivative also increases. The equation for the derivative is based on differences from discretelymeasured values of temperatures, each with statistical uncertainty that does not depend on thetime step size. Therefore the noise associated with thermocouple measurement can result inexcessive error in the derivative term for small time steps.

34

To reduce some of this error, the raw data can be filtered. In fact, the five-point centraldifference expression for computing the derivative used in this model represents such an errorreduction technique. The error associated with the 5-point central difference equation,

is 33% less than the three-point

C@zi= 12”(tN+1 –tN) ‘

central difference equation. However, the price for smoothing isan increase in the “prediction” source, as the 5 point central difference will anticipate changes inrise rate.

In the final analysis, the sampling rate should be commensurate with the expected temperaturerise rate and the end use of the time derivative. This is to say, the data sampling rate is animportant parameter in the design and use of these heat flux gauges and merits special attentionprior to incorporating them in any experiment.

CLOSURE

It has been seen that the HFG is essentially a thin metal plate that responds to heating from thefire environment. A thermal model that describes the response has been advanced and it wasshown how to determine the heat flux from the fire environment via the time-temperature historyof the thin metal plate. A validation experiment was presented where the gauge was exposed to astep input of radiant heat flux. Comparison of the incident flux determined from the thermalmodel with the known flux input showed the gauge exhibited a noticeable time lag. Theuncertainty of the measurement was analyzed, and an uncertainty model was put forth using thedata obtained from the experiment. An empirical constant was found that compensated for thegauge time lag. This compensation was incorporated into the uncertainty model instead of theresponse model. As a result, the uncertain y does not capture the measurement at certain timesdue to the systematic error created by the missing physics.

We believe the missing physics model is incomplete and are not willing to include it in theresponse model. The out-of-bounds response is a signal to the user that the measurement islikely to be wrong because of the thermocouple installation. An example can be seen inFigure 1. There are alternating periods of rapidly changing heat flux and periods of steady heatflux. The uncertainty bars clearly show when it would be appropriate to use the data and when itwould be better to ignore it.

If it were desirable to reduce the uncertainty, clearly the missing physics needs to be corrected.We do not believe that complicating the model with a detailed heat transfer analysis of thethermocouple installation is appropriate. The HFG should be modified so it physically meets theassumptions in the model. The obvious first step would be to replace the existing thermocouplewith a fine wire intrinsic junction.

35

It is also felt that the early time discrepancy maybe due in part to inadequate thermal propertiesof the insulation. These properties were developed from steady state measurements where smalltemperature differences are imposed across a known thickness. It is not known if propertiesdetermined this way are appropriate in dynamic heating situations with high gradients. A ~different insulation material may be more appropriate. Experiments, similar to the modelvalidation step input test, will be required to verify improved response using the suggesteddesign modifications and to revise the uncertainty model. *

1.

2.

3.4.

5.6.

REFERENCES

Incropera, F., and D. DeWitt, Fundamentals of Heat and Mass Transfer, John Wiley & Sons,tic., New York, 1995.Vemer, D., and T.K. Blanchat, Sandia Heat Flux Gage Calibration Experiment, SandiaNational Laboratories, Albuquerque, NM 87185, August 1998.White, F. M., Heat and Mass Transfer, Addison Wesley, New York, 1988.Nicolette, V., Private Communication, Org. 9116, Sandia National Laboratories,Albuquerque, NM.Kreith, F., Principles of Heat Transfer, Intext Educational Publishers, New York, 1976.Longenbaugh, R. S., L.C. Sanchez, and A.R. Mahoney, Thermal Response of a Small Cask-Like Test Article to Three Di#erent High Temperature Environments, SAND88-0661, SandiaNational Laboratories, Albuquerque, NM, 1988.

36

APPENDIX ASNL Hemispherical Heat Flux Gauge Assembly and Construction Details

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44

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