STUDY OF THE INFLUENCE OF CONVECTIVE EFFECTS IN INCIDENT RADIATIVE HEAT FLUX DENSITY MEASUREMENT UNCERTAINTY

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1 XIX IMEKO World Congre Fundamental and Applied Metrology September 6, 009, Libon, Portugal SUDY OF HE INFLUENCE OF CONVECIVE EFFECS IN INCIDEN RADIAIVE HEA FLUX DENSIY MEASUREMEN UNCERAINY L. Lage Martin, A. Silva Ribeiro and C. Pina do Santo Laboratório Nacional de Engenharia Civil, Libon, Portugal Abtract hi tudy decribe the meaurement uncertainty propagation of the incident radiative heat flux denity quantity aociated with different expoure ition of the heat flux meter, taking into account the convective effect in reaction to fire tet. o accomplih thi aim, conidering the complexity and non-linearity of the applied mathematical model to perform the indirect meaurement of the above mentioned quantity, the Monte Carlo method wa applied. he ue of thi numerical approach allow to etimate the quality of the meaurement within a high accuracy level and to evaluate deviation related with the GUM method ince it provide an approximate olution for thi pecific metrological problem. he experimental example preented concern to the reaction to fire teting (the room-corner tet and the flooring radiant panel tet) with different expoure ition of the heat flux meter ued, being the applied mathematical model decribed on each cae and a enitivity analyi of the input uncertainty contribution preented. Keyword: incident radiative heat flux denity; meaurement uncertainty; Monte Carlo method.. INRODUCION he meaurand incident radiative heat flux denity ha an important role in reaction to fire teting being applied in the room-corner tet [] and in the flooring radiant panel tet [], where it i the mot ignificant heat tranfer mode that occur in a fire. In thee tet, the etimate of thi phyical quantity allow the evaluation of the teted material contribution to fire deflagration and propagation. In the mentioned reaction to fire tet, thi thermal quantity i indirectly meaured uing an appropriate mathematical model derived from the energy balance performed at the urface of the heat flux meter ued []. he focu of thi tudy wa on the Schmidt-Boelter heat flux meter performance, one of the mot common ued in reaction to fire teting laboratorie, uch a the Laboratório de Enaio de Reacção ao Fogo at the Laboratório Nacional de Engenharia Civil (LNEC/LERF) which upported the experimental work. he equipment ued i unable to perform direct meaurement of the incident radiative heat flux denity component, due to the combined effect of radiation and convection, depite ome attempt to reduce the convective effect. One of thee attempt conited in the ue of gla window connected to the heat flux meter, conidered inappropriate due to the output meaurement uncertainty increae related with additional uncertainty contribution of the optical propertie []. Conidering the non-linear mathematical model ued to obtain the incident radiative heat flux denity by an indirect meaurement and the need to account for the convective effect, the tudy carried out intended to evaluate the propagation of the meaurement uncertainty uing the Monte Carlo method (MCM) [5] pecially uited to thi type of problem. In order to dicu thi approach, two experimental ition were tudied: the room-corner fire tet, in which the heat flux meter enor head (with a cylindrical hape) i totally expoed to the air flow (figure.a); and the radiant panel fire tet, in which only the top enor urface i expoed to the air flow (figure.b). Since the air flow over the top urface of the enor depend on the expoure ition, the convective heat tranfer will alo be different and, therefore, it hould be accounted for in the mathematical model preented in ection. Air flow a) b) Air flow Figure. Different expoure ition of the heat flux meter enor head. For both tudied ition, the MCM approach provide information to perform a meaurement uncertainty enitivity analyi, obtained by introducing independent incremental change on each input meaurement uncertainty and evaluating the correponding output meaurement uncertainty variation. he applied increment i defined in order to produce an output variation with a higher magnitude than the computational accuracy level of the performed numerical imulation.

2 . INCIDEN RADIAIVE HEA FLUX DENSIY MEASUREMEN MODEL he etablihment of the incident radiative heat flux denity meaurement model implie performing an energy balance of the different heat tranfer mode at the urface of the heat flux meter enor head. Figure repreent the urface and the control volume in which it i poible to identify the following heat tranfer mode and correponding heat flux denitie: - incident radiation, ϕ, generated by high temperature of the urrounding element due to the reaction to fire tet; - reflected and emitted radiation by the urface of the heat flux meter enor head, ϕ and ϕ, repectively; - convection on the enor urface, ϕ, generated conv by the air flow with temperature and velocity u ; - uction, ϕ, from the warm external urface to the cooled inner core. conv Senor head Air flow Figure. Diagram of energy flux tranfer at the enor head and meaurement influence quantitie. Auming a teady-tate ition, the energy balance can be expreed by the following mathematical model (the output quantity i the incident radiative heat flux denity): ϕ = ϕ + ϕ + ϕ + ϕ. () In the evaluation of the other radiative term, the urface of the enor head i conidered diffue and grey, i.e, the urface aborptivity and emiivity are taken a independent from the radiation direction and wavelength. hi aumption allow to etablih an equivalence between the urface emiivity, ε, and aborptivity, α, being the reflected radiation heat flux denity given by ( ) ϕ conv ϕ = ε, () and the emitted radiation heat flux denity ϕ = ε σ, () where σ i the Stefan-Boltzmann contant and i the urface temperature of the heat flux meter enor head. he evaluation of the uction heat flux denity etimate i obtained uing expreion () being baed on the heat flux meter calibration. he LNEC/LERF heat flux meter i calibrated by the pherical black-body cavity method, according with ISO 9- (006). hi method etablihe a procedure of decreaing the convective effect on the heat flux meter to a minimum in uch a way that it can be conidered neglectable. In thi ition, the energy balance can be given by the following expreion ϕ = ϕ + ϕ + ϕ. () he calibration provide data that can be ued to determine a linear relation between the incident radiative heat flux denity and the heat flux meter output electric tenion, V, ϕ = C V, (5) where C i the calibration contant. Applying the previou expreion together with expreion () and () to the energy balance, expreion (5) allow to write the uction heat flux denity a ϕ ( C V σ ) = ε, (6), cal in which correpond to enor head urface, cal temperature during calibration. he convective term preented in expreion () can be expreed in general a ( ) ϕ = h, (7) conv where h i the average convection heat tranfer coefficient, being dependent on everal parameter uch a the urface geometry, the nature of the air flow (laminar or turbulent) and it thermophyical propertie. For both expoure ition tudied (diplayed on figure ), laminar air flow wa conidered and the thermophyical propertie of the air flow refer to the film temperature (average temperature between the air flow temperature and the urface temperature of the heat flux meter enor head). However, the urface geometry i different in each cae, requiring the ue of adequate convection coefficient. According to [], a reaonable coefficient etimate for the firt expoure ition correpond to 0, u h = k, (8) ν d where k and ν are the air flow thermal uctivity and the cinematic vicoity at film temperature, repectively, and d i the enor head diameter. For the e expoure ition, the flat plate approach wa conidered and, according to [6], the average convection heat tranfer coefficient in a laminar flow i given by 6 Re Pr k h =, (9) d being Re the Reynold number and Pr the Prandtl number. hi expreion i valid only for Pr 50.

3 Introducing the previou deducted expreion of the heat flux denity term into expreion (), the incident radiative heat flux denity meaurement model for the firt expoure ition become 0, u k φ = ( ) + ε σ( ) + ε CV, (0) rad,inc, cal ε ν d and for the e expoure ition 6Re Pr k φ = ( ) + ε σ( ) + ε CV. () rad,inc, cal ε d. EVALUAION OF HE MEASUREMEN UNCERAINY. Probabilitic framework and calculation method he above mathematical model (0) and () hare almot all of the input quantitie. In fact, the only exception i the Prandtl number, applied only in (), conidering that the Reynold number can be obtained a a function of u, d and ν. herefore, both model can be illutrated by the ame functional diagram exhibited in following figure. Figure. Functional diagram for the two expoure ition. Regarding the expoition ition related with the room-corner tet (figure.a), the probabilitic framework of the input quantitie ued in the MCM imulation (able ) i imilar to the one adopted in [] which follow the conventional GUM approach. he ue of the ame probabilitic aumption allow a direct comparion between the evaluated meaurement uncertaintie obtained uing both method. Several input etimate related with the heat flux meter output electric tenion were tudied in order to know the behaviour of the output quantity meaurement uncertainty incident radiative heat flux denity conidering the nominal meauring interval of, approx., kw m - to 0 kw m -. hi interval comprehend the incident radiative heat flux etimate uually obtained in the room-corner tet. he tudy of convective effect influence wa developed uing different etimate for the air flow temperature (from 89 K to 7 K) and for the air flow velocity (from 0, m - to, m - ). Again, the ame ition adopted in [] were conidered, namely, the probability denity function (PDF) are all gauian and the meaurement uncertaintie of d, k, ν and σ are aumed to be neglectable within thi framework. able. Probabilitic framework related with the input quantitie in the room-corner tet []. Input quantity Etimate PDF Relative tandard uncertainty ε 6 ± % C 5 ± % (W m - mv - ) V (mv) ; ;,0;,0;,0 ± % (K) 95 gauian ± %, cal (K) 97 ± % u (m - ) 0,; ; ;, ±0 % (K) 89; 0; 7 ±0 % d (m) k (W m - K - )* 6, x ν (m - )* 5,89 x σ (W m - K - ) 5,670 x * Etimate for a film temperature equal to 00 K. For the expoition ition related with the radiant panel tet (figure.b), the input data wa the one available at LNEC/LERF regarding the heat flux meter ued (pecially, the technical pecification and the calibration certificate) and the reult obtained from the following experimental tet: urface temperature the ue of a non-contact infrared thermometer ha revealed that the urface temperature etimate on the heat flux meter enor head (at the everal reference poition and after etablihing a teady-tate ition) can change from 90 K to 80 K; the meaurement uncertainty wa etimated to be within ± K (baed on technical pecification); air flow velocity everal attempt were made in order to meaure the air flow velocity inide the tet chamber (with the ventilation ytem activated and in the abence of combution, ince available meaurement intrument uch a the hot wire anemometer or the turbine anemometer can not withtand high temperature); the obtained etimate were equal to zero for all reference meauring poition, conidering a intrument reolution equal to 0, m - ; with the preence of combution at the radiant panel it i expected that, due to the temperature gradient and, conequently, the air denity gradient, free convection will occur and the air flow velocity will not be equal to zero; due to the lack of conitent experimental data, the probabilitic formulation for thi quantity i conidered to be identical to the one mentioned for the room-corner tet (ee table ) in [];

4 air flow temperature the LNEC/LERF tet chamber ha a thermocouple at it upper part intended to meaure air temperature inide the chamber; experimental data related with thi meaurand how that the air temperature in thi region can rie up to 00 K ( 7 ºC) with a experimental tandard deviation of ±8 K; ince the meaurement of heat flux denity i performed at the lower part of the tet chamber, cloe to the air inlet (uually the ambient temperature i near 00 K, i.e., 7 ºC), it i conidered that the input temperature etimate can change between 00 K and 00 K and that the meaurement uncertainty i given by the above experimental tandard deviation. aking into account the etimate of and, the film temperature can change between 50 K and 50 K and the thermophyical propertie of the air flow will change accordingly. For thi reaon, the probabilitic formulation of k, Pr and ν i baed on uniform PDF in which all thermophyical propertie value [6] between 50 K and 50 K are conidered equally probable. able ummarize the probabilitic information of the everal accounted input variable ued in the development of MCM calculation tage. able. Probabilitic decription of the input quantitie in the flooring radiant panel tet. Input quantity Etimate PDF Standard uncertainty ε 5 uniform ± 0 C 55,5 ± % (W m - mv - ) V (mv) ; ; 6 ± 0, cal (K)* 95 ± (K) 90; 50; 80 gauian ± u (m - ) 0,; ; ± 0 % (K) 00; 50; 00 ± 8 d (m) 5 00 ± 00 0 k (W m - K - ),9 x 0 - ±, x 0 - ν (m - ) 6,7 x 0-6 ±, x 0-6 Pr 9 uniform ± 0 σ (W m - K - )** 5,670 x 0-8 gauian ± x 0 - * A mentioned in []. ** A mentioned in [7]. MCM accuracy i trongly dependent on the quality of the tool ued to perform the computational work. For the preent tudie the Merenne witer peudo-random generator [8] wa ued, being able to generate numerical equence with a dimenion of 0 6 element, and validated algorithm to perform the probability ditribution converion and the output orting were ued in accordance with [9]. he computational accuracy level of the numerical imulation wa achieved uing [0].. Achieved reult and enitivity analyi he following reult preented were obtained from everal tudie carried out regarding the room-corner tet and the radiant panel tet, conidering the two expoure ition (diplayed on figure ). Numerical imulation baed on MCM were developed in order to obtain meaurement uncertaintie etimate. he firt et of reult i related with the room-corner tet, obtained conidering that a gauian PDF decribe the probabilitic behaviour of incident radiative heat flux denity. Figure to 6 preent the 95 % expanded meaurement uncertainty with a computational accuracy level lower than ± kw m -. U 95 % (φ ) (kw/m ),5,0,5,0 Electric tenion (mv), Velocity (m/) 0, Figure. Expanded meaurement uncertaintie (95 %) for = 89 K. U 95 % (φ ) (kw/m ),5,0,5,0 Electric tenion (mv), Velocity (m/) 0, Figure 5. Expanded meaurement uncertaintie (95 %) for = 0 K. U 95 % (φ ) (kw/m ),5,0,5,0 Electric tenion (mv), Velocity (m/) 0, Figure 6. Expanded meaurement uncertaintie (95 %) for = 7 K.

5 he reult obtained how that the expanded meaurement uncertainty of the incident radiative heat flux denity quantity can change between ± kw m - to ±,0 kw m - for the meauring interval of kw m - to 0 kw m - (being the highet value obtained for etimate cloe to 0 kw m - ). In term of convective effect, it i poible to etablih a direct relation between the meaurement uncertainty and the air flow velocity in the tudied meauring interval. he ame effect can be oberved for the air flow temperature but with a lower magnitude. he ame probabilitic information a in [] alo provide a comparion between the two uncertainty calculation method. According with the reference above mentioned... an etimated relative uncertainty of 7 % - 5 % when the total heat flux i above 5 kw m -. Near flahover ition, 0 kw m -, the relative uncertainty i etimated to be 7 % - 8 %.. he MCM reult are ummarized in table. able. Relative tandard meaurement uncertaintie obtained uing the MCM. Incident radiative heat flux denity level Relative tandard meaurement uncertainty 5 kw m - 9 % to 6 % 0 kw m - 5 % to % 5 kw m - % to 0 % 0 kw m - % to 8 % he relative uncertainty interval predicted by [] i in good agreement with the reult obtained by the MCM for a 5 kw m - level. For the remaining level up to 5 kw m -, the relative meaurement uncertainty tend to be lower than the olution provided by the GUM method. he ame obervation can be made for the 0 kw m - level, in particular, when conidering the lowet etimate for the air flow velocity and temperature. Figure 7 preent the enitivity analyi reult regarding the expanded meaurement uncertainty of the incident radiative heat flux denity quantity (for an etimate cloe to 0 kw m - ) conidering independent increae in input quantity uncertainty contribution. U 95%(φ ) (%) 9,0 8,0 7,0 6,0 5,0,0,0,0 %,8 %,6 % 0, % Input quantity,0 % 0, % ε C V Τ, cal Τ u Figure 7. Reult of the meaurement uncertainty enitivity analyi (expoure ition.a). he reult obtained how that air flow temperature i the mot ignificant contribution to the radiative heat flux denity meaurement uncertainty. It i followed by the calibration contant, the temperature of the heat flux meter enor head and the output electric tenion. he remaining 8, % input quantitie have neglectable influence on the output meaurement uncertainty. hee reult are, again, in agreement with the trend found in [] baed on the GUM approach. Figure 8 to 0 repreent the expanded meaurement uncertainty (in a 95 % confidence interval) obtained uing the MCM for the radiant panel tet expoition ition. he hape of the incident radiative heat flux quantity PDF i conidered a gauian for all the input etimate, and the computational accuracy level i below ± kw m -. U 95% (φ ) (kw/m ),5,0 Electric tenion (mv) 6 Velocity (m/) 0, Figure 8. Expanded meaurement uncertaintie (95 %) for = 00 K. U 95% (φ ) (kw/m ),5,0 Electric tenion (mv) 6 Velocity Velocity (m/) 0, Figure 9. Expanded meaurement uncertaintie (95 %) for = 50 K. U 95% (φ rad,inc ) (kw/m ),5,0 Electric tenion (mv) 6 Velocity (m/) 0, Figure 0. Expanded meaurement uncertaintie (95 %) for = 00 K.

6 Although having it own probabilitic framework and mathematical model, the reult obtained for the expoure ition in the radiant panel tet are imilar to the reult of the firt tudied ition. he expanded meaurement uncertainty of the incident radiative heat flux denity quantity change between ± kw m - and ±, kw m -, conidering a meauring interval of kw m - to 0 kw m - (the highet meaurement uncertainty occur when etimate are cloer to 0 kw m - ). A oberved before, the increae of the meaurement uncertainty occur when air flow velocity and temperature are higher, although, in the lat cae, having lower magnitude. Figure preent the enitivity analyi reult for the expanded meaurement uncertainty variation of the incident radiative heat flux denity quantity (for an etimate cloe to 6 kw m - ) obtained uing a meaurement uncertainty increae on influential input quantitie. U 95% (φ ) (%) 5,0,5,0,5,0,5,0 % % ε C % V %, %, %,8 %, % % % % Τ, cal Τ u d k ν Pr Input quantity Figure. Reult of the meaurement uncertainty enitivity analyi (expoure ition.b). he previou figure how that the air flow velocity ha the mot ignificant contribution to the output meaurement uncertainty, followed by air thermal uctivity, air flow temperature, cinematic vicoity and temperature of the heat flux meter enor head. he remaining input quantitie have neglectable impact on the output meaurement uncertainty.. CONCLUSIONS AND FINAL REMARKS he tudie carried out howed how the MCM can provide the incident radiative heat flux denity etimate and it meaurement uncertainty in reaction to fire tet, taking into account the convective effect created by the heat flux enor head expoure to the urrounding environmental ition. Following the aim preented, the reult allow to conclude that, for the expoure ition related with the room-corner tet and a meauring range of,0 kw m - up to kw m -, the expanded meaurement uncertainty found i between ± kw m - and ±,0 kw m -. Regarding the cae of the expoure ition in the radiant panel tet and a meauring range of,0 kw m - up to kw m -, the expanded meaurement uncertainty admit value from ± kw m - up to ±, kw m -. he comparion of reult related with the firt tudied expoure ition, although obtained uing two different approache (GUM and MCM), gave imilar value, neverthele, the ue of non-linear model make the ue of the MCM more accurate [5] and le complex to implement. Certain input quantitie ued had phyical contrain that were taken into account on the MCM imulation, a wa the cae of the air flow velocity (with a large concentration of the PDF near the phyical limit of zero) or the urface emiivity (with etimate that can not aume value higher than one). For thee cae, alternative approache, like Bayeian Inference, would be more accurate to apply to thi type of probabilitic ition. he enitivity analyi how how different input quantitie affect the output accuracy, allowing that the experimental etup can be developed in order to achieve a higher accuracy level. herefore, improvement to reduce the meaurement uncertainty related with the air flow temperature, the calibration contant and the urface temperature in the room-corner tet would be the mot required. In a imilar way, regarding the radiant panel tet, improvement would be adviable to reduce meaurement uncertainty related with air flow velocity, air flow temperature, urface temperature poitively affecting the air thermophyical propertie. REFERENCES [] ISO 9705 Fire tet Full-cale room tet for urface product, International Organization for Standardization (ISO), Genève, 99. [] EN ISO 99- Reaction to fire tet for flooring Part : Determination of the burnimg behaviour uing a radiant heat ource, Comité Européen de Normaliation (CEN), Bruxelle, 00. []. E. Diller, Heat Flux, he Meaurement, Intrumentation and Senor Handbook, CRC Pre, Boca Raton, 999. [] R. Bryant, C. Womeldorf, E. Johnon and. Ohlemiller, Radiative heat flux meaurement uncertainty, Fire and Material, vol. 7, pp. 09, 00. [5] Evaluation of meaurement data Supplement to the Guide to the expreion of uncertainty in meaurement Propagation of ditribution uing a Monte Carlo method, JCGM, 008. [6] F. P. Incropera and D. P. DeWitt, Fundamental of Heat and Ma ranfer, 5 th edition, John Wiley & Son, New York, 00. [7] P. J. Mohr, B. N. aylor and D. B. Newel, he 006 CODAA Recommended Value of the Fundamental Phyical Contant, web verion 5., developed by J. Bakeer, M. Douma and S. Kotochigova, National Intitute of Standard and echnology (NIS), Gaitherburg, MD (USA), available at [009, March 9]. [8] M. Matumoto and. Nihimura, Merenne witer: a 6-dimenionally equiditributed uniform peudorandom number generator, ACM ranaction on Modelling and Computer Simulation, vol. 8, nº, pp. -0, January 998. [9] W. H. Pre. B. P. Flannery, S. A. eukolky and W.. Vetterling, Numerical recipe the art of cientific computing, Cambridge Univerity Pre, 986. [0] M. G. Cox, M. P. Dainton and P. M. Harri, Software pecification for uncertainty calculation and aociated tatitical analyi, National Phyical Laboratory (NPL) report CMSC 0/0, NPL, eddington, March 00.