ARTICLE IN PRESS
Fire Safety Journal 42 (2007) 161–166 www.elsevier.com/locate/firesaf
Measuring incident radiant heat flux using the plate thermometer Haukur Ingason, Ulf Wickstro¨m SP Swedish National Testing and Research Institute, Department of Chemistry and Fire Technology, PO Box 857, 50115 Boras, Sweden Received 6 February 2006; received in revised form 24 July 2006; accepted 30 August 2006
Abstract This paper shows that the plate thermometer as described in the fire resistance test standards ISO 834-1 and EN 1363-1 can be used for measuring incident radiant flux under ambient conditions as an alternative to water cooled total flux heat metres (HFMs). Measurements with a plate thermometer mounted in the cone calorimeter and exposed to different heat flux levels were analysed as well as simultaneous measurements with total HFMs and plate thermometers in large scale tests. It is shown how the incident radiant flux to a target can be derived from measurements with total HFMs and plate thermometers, respectively, and how well these two methods match. The plate thermometer is therefore deemed to be a practical alternative for measuring thermal conditions including incident radiant heat flux particularly under field conditions. It is, however, recommended that the plate thermometer should be modified when used under ambient conditions to reduce errors. r 2006 Elsevier Ltd. All rights reserved. Keywords: Plate thermometer; Total heat flux metre; Radiation; Convection
1. Introduction The plate thermometer (PT) was developed by Wickstro¨m [1,2] in the 1980s for controlling fire resistance furnaces to get harmonized test results. At that time, the PT was not thought to be a heat flux metre (HFM) but to measure an ‘effective temperature’ assuring the same heat transfer to specimens in various types of fire resistance furnaces [3]. The PT has since then been specified in the relevant international (ISO 834) and European (EN 1363-1) standards. The PT consists of a stainless steel plate, 100 mm 100 mm and 0.7 mm thick, with a 10 mm thick insulation pad on the back side. A thermocouple is welded to the centre of the plate, see Fig. 1. HFM such as Gardon gauges or Schmidt–Boelter (SB) metres are used routinely in fire tests to measure total heat flux by radiation and convection. In fact, they measure total heat flux to a water cooled small surface. When the cooling water temperature is kept near the ambient gas temperature, the heat transfer by convection will be reduced to negligible levels and the probe will measure Abbreviations: HFM, heat flux metre; PT, plate thermometer; SB, Schmidt–Boelter Corresponding author. Fax: +46 33 13 55 02. E-mail address:
[email protected] (U. Wickstro¨m). 0379-7112/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.firesaf.2006.08.008
very close to incident radiant heat flux. HFMs are relatively easy to use under laboratory conditions. However, under field conditions such as fire tests in tunnels, it may be difficult and cumbersome to arrange cooling of the water. Therefore, it is of great interest to explore the possibility of using the much simpler PTs for monitoring thermal conditions as an alternative or a complement. Below it is shown theoretically how incident radiant flux to a target can be derived from HFM and PT measurements and comparisons are then made between experimental data derived from the two types of instruments when placed in air at ambient temperature. 2. Heat transfer theory The analysis below is aimed at deriving the incident heat flux by radiation, q_ inc , for HFMs and PTs, respectively. It is based on theory outlined by Wickstro¨m [3]. The radiation is assumed to be grey, i.e. the emissivity is independent of wavelength. 2.1. Radiation The incident heat flux by radiation to a surface from flames, hot gas layers, surrounding structures, etc. will be
ARTICLE IN PRESS H. Ingason, U. Wickstro¨m / Fire Safety Journal 42 (2007) 161–166
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Nomenclature C c g Gr h kg K cond L m Nu Ra Pr q_ conv q_ cond q_ emi q_ inc q_ rad q_ stor q_ tot
empirical constant in Eq. (7) (dimensionless) specific heat capacity (J/kg K) acceleration of gravity (kg/s2 m) Grashof number (dimensionless) convective heat transfer coefficient (W/m2 K) conductivity of fluid (W/m K) conduction correction factor (W/m2 K) characteristic length (m) empirical constant in Eq. (7) (dimensionless) Nusselt number (dimensionless) Rayleigh number (dimensionless) Prandtl number (dimensionless) convective heat flux (W/m2) conductive heat flux (W/m2) emitted heat flux by radiation (W/m2) incident heat flux by radiation (W/m2) net heat flux by radiation (W/m2) rate of storage of heat (W/m2) total heat flux by radiation and convection (W/ m 2)
partly absorbed by the surface and partly be reflected, see e.g. [4]. The absorbed heat can be expressed as q_ abs ¼ q_ inc ,
(1)
as the emissivity is equal to the absorptivity according to Kirchhoff’s identity. The reflected heat may be written as q_ ref ¼ ð1 Þq_ inc .
(2)
The surface emits heat as well, which according to the SB law may be expressed as q_ emi ¼ sT 4s ,
(3)
where Ts is the surface temperature. The net heat flux by radiation, q_ rad , entering the surface will then be q_ rad ¼ q_ inc q_ emi q_ ref ¼ ðq_ inc sT 4s Þ.
(4)
2.2. Convection Heat transfer by convection occurs when a fluid flows over a solid surface at different temperature. It depends on the temperature gradient near the surface and the thermal conductivity of the fluid and can be written as q_ conv ¼ hðT fluid T s Þ,
(5)
where h is identified as the convective heat transfer coefficient and Tfluid is the main stream temperature of the gas or fluid in the vicinity of the surface. The convective heat transfer coefficient depends on the flow situation near the surface and on the geometry of the target body. It can
T Tf Tfluid Tw t
temperature (K) film temperature (K) temperature of gas or fluid (K) cooling water temperature (K) time (s)
Greek symbols thermal expansion coefficient 1/T (K1) surface emissivity (dimensionless) thickness of steel plate (m) Stefan–Boltzmann constant (W/m2 K4) kinematic viscosity (m2/s) density (kg/m3)
b d s n r Index ins s st 1
insulation surface steel ambient
be obtained from the dimensionless Nusselt number Nu ¼
hL , kg
(6)
where kg is the conductivity of the fluid and L the characteristic length of the surface. For free or natural convection the Nusselt number can be determined from Eq. (7) [5], see also [4,6]. Nu ¼ C Ram ,
(7)
where C and m are empirical constants determined according to the position and the flow situation. Ra is the dimensionless Rayleigh number, a product of two other dimensionless numbers, the Prandtl number (Pr) and the Grashof number (Gr): gbðT s T 1 ÞL3 , (8) n2 where b is the thermal expansion coefficient equal to the reciprocal of the gas temperature, T 1 is the ambient gas temperature and n the kinematic viscosity (m2/s). Pr can be approximated as 0.7 for air. The properties of air kg and nas well as b are determined at the film temperature of the gas defined as
Gr ¼
Ts þ T1 . (9) 2 The conductivity kg and the kinematic viscosity n of air depend on the film temperature and can be approximated in the temperature range considered as [7,8] Tf ¼
kg ¼ 13:75 105 T 0:92 f
(10)
ARTICLE IN PRESS H. Ingason, U. Wickstro¨m / Fire Safety Journal 42 (2007) 161–166
Note that the convective heat transfer coefficient in this case depends weakly on temperature difference and characteristic length, raised to a power of 1/4, and even more weakly on the temperature level, raised to a power of 0.16. Therefore, a constant value of hPT 10 W=m2 K is used here for PTs with a characteristic length of L ¼ 0.1 m. This value applies both in horizontal positions (when cooled by convection phasing upwards, or vice versa) and in vertical positions.
0.7 mm steel plate
insulation Thermocouple welded on backside of plate
(a)
163
Plate thermometer with insulation pad on its back side
2.3. Total heat transfer The total heat transfer q_ tot is the sum of the net heat transfer by radiation and by convection, i.e.
Thermocouple connected to data logger
q_ tot ¼ q_ rad þ q_ conv ,
Not to scale
(13)
or by inserting Eqs.(4) and (5) q_ tot ¼ ðq_ inc sT 4s Þ þ hðT 1 T s Þ.
(14)
Supporting and protecting tube
2.4. Heat balance of the plate thermometer The incident heat flux by radiation to a PT can be obtained from the heat balance at the measuring point at the centre of the PT:
Plate Thermometer Radiation
q_ tot ¼ q_ stor þ q_ cond ,
where the first term, q_ stor , represents the heat stored in the PT. The second term, q_ cond , is a combination of heat losses due to two-dimensional conduction in the plane of the plate away from the thermocouple welding point in the centre to the edges, and the heat losses by conduction through the insulation to the back side of the PT. The last term of Eq. (15) is defined as
Specimen
Furnace
(b)
q_ cond ¼ K cond ðT PT T 1 Þ,
Plate thermometer placed in a fire resistance furnace
Fig. 1. The plate thermometer according to ISO 834 and EN 1363-1: (a) plate thermometer with insulation pad on its back side, (b) plate thermometer placed in a fire resistance furnace.
and 5=3
(11)
respectively. Combining Eqs. (6)–(11) and assuming C ¼ 0:54 and m ¼ 1=4 for 105oRao107 [9,10] (see also e.g. [4,6]), for a horizontal plate exposed to natural convection (hot surface up or cold surface down) yields the following expression for the average convective heat transfer coefficient: ðT s T 1 Þ 1=4 h ¼ 4:0 ðT s þ T 1 Þ0:16 . L
(12)
(16)
where the conduction correction factor K cond is determined experimentally in the applications shown below. The rate at which heat is stored in the steel plate per unit area q_ stor can be approximated from measurements as q_ stor ¼ rst cst d
n ¼ 1:13 109 T f
(15)
DT PT , Dt
(17)
where rst and cst are the density and the specific heat capacity, respectively, and d the thickness of the steel plate of the PT. In the calculations presented later in this paper the heat capacitivity cst is assumed to be constant, 460 J/ kg K. The accuracy of the final results does not justify assuming it to vary with temperature. The thickness d of the steel plate is 0.7 mm, and the density rst of steel was assumed to be 8100 kg/m3. DT PT is the temperature difference between two consecutive temperature recordings with an interval Dt.
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Thus from Eqs. (14)–(17) the incident heat flux by radiation can be derived from the PT temperature as q_ inc
PT sT 4PT þ ðhPT þ K cond ÞðT PT T 1 Þ þ rst cst d DT PT =Dt ¼ PT
When the PT was put under the cone, the temperature reached a steady-state value within 2–3 min. The storage term in Eq. (17) can then be neglected and the incident radiation q_ inc can be obtained as :
(18)
When the cooling water temperature is close to ambient temperature, the heat transfer by convection to the sensing point of the HFM is negligible [11] and the incident heat flux may be written as q_ inc ¼ q_ HFM þ sT 4w ,
(19)
where q_ HFM is the heat flux received by the HFM and Tw is its cooling water temperature. It is here assumed that the HFM responds directly to the heating changes, i.e. has a negligible time constant and that the HFM was calibrated according to the international standard under development ISO/FDIS 14934—Fire tests—Calibration and use of heat flux metres—Part 2: primary calibration methods. 3. Test results In the following, we will present comparisons of incident radiant heat flux using PTs and HFMs under three different heating conditions, i.e. steady-state conditions in a cone calorimeter, nearly steady-state conditions close to a pool fire, and transient conditions from a growing fire. These conditions deviate from the conditions in a fire resistance furnace where the PT is exposed to high gas temperatures and corresponding radiation levels from all sides. In the test presented here the PTs are exposed to high levels of incident heat flux by radiation while the surrounding air is at room temperature. Therefore convective heat transfer losses become considerable in these cases when the temperature of the exposed side of the PTs rises due to incident radiation. 3.1. Steady-state measurements in the cone calorimeter A PT was mounted horizontally 25 mm under the edge of the radiation heater in a cone calorimeter (ISO, 5660) and exposed to constant incident radiant heat flux levels, q_ inc . The radiation levels were controlled with a SB total HFM with a small body diameter of 12.5 mm. The actual incident heat flux by radiation from the cone is calculated according to Eq. (19) as the cooling water temperature is close to the ambient temperature.
(20)
Tests data for comparisons were available at heat flux levels of 10, 15, 20, 25 and 45 kW/m2 measured with a SB total HFM. Assuming natural convection for a horizontal plate in a quiescent atmosphere, the convective heat transfer coefficient h for the PT can be estimated according to Eq. (12). In Fig. 2, a comparison is shown between the calculated incident heat flux, q_ inc , based on PT measurements when neglecting and when considering, respectively, heat losses by conduction represented by the correction term according to Eq. (16). A correction factor K cond of 5 W/m2 K gave in this case the best fit to the experimental data. As can be seen in Fig. 2, there is a very good agreement (linear regression coefficient R ¼ 0:999) between the calculated value based on PT measurements corrected for conduction losses and the values measured with the SB total HFM.
3.2. Measurements on pool and spray fire tests at nearly steady state conditions Arvidson and Ingason [12] measured total heat flux from pool and spray fires using both PTs and SB total HFMs. The instruments were positioned 1 m above the floor 2 and 4 m, respectively, from the fire. The PTs were mounted vertically close to the SB total HFM as shown in Fig. 3. The PTs used in this study were modified with an additional steel sheet on the backside to protect its insulation pad from being wetted by sprinkler water. Comparison Cone Calorimeterand PT 50
2
2.5. Heat balance of water cooled flux metres
q_ inc
Incident radiation PT (kW/m )
Note that the conduction correction factor K cond could be substantially reduced by designing the PT alternatively. Thus conduction losses could be reduced by avoiding direct metal contact at the edges between the front and back sides of the PT and by using thicker and more effective insulation pads. Similarly the inertia term could be reduced by using thinner steel plates.
PT sT 4PT þ ðh þ K cond ÞðT PT T 1 Þ ¼ . PT
no correction with correction
40
30
20
10
0 0
10
20
30
40
50
Nominal incident radiation cone (kW / m2) Fig. 2. Comparison of calculated incident radiation based on PT measurements and SB measurements in the cone calorimeter with and without correction for conduction losses.
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SB - PT - 4 m 10
Incident Radiation (kW/m2)
SB
6
4
2
0
Fig. 3. A Schmidt–Boelter heat flux meter (SB) and a plate thermometer (PT) mounted at the same location.
PT
8
0
2
6 4 Time [min]
8
10
Fig. 5. Comparison of calculated incident radiation q_ inc obtained from Schmidt–Boelter and plate thermometer measurements (including the storage term, q_ stor ), respectively, at a distance of 4 m from a 3.5 MW pool fire.
SB - PT - 2 m
Incident Radiation (kW/m2)
50
were recorded when the heat flux was stable, usually about 1 min after ignition. The diagram includes free burning pool fires of nominal sizes 1, 2, 3.5 and 6 MW and spray fires of nominal sizes 1, 2 and 3.5 MW. We deem the correlation between the two methods of measuring radiant heat flux under these variable conditions to be very good and quite acceptable for most fire test applications. The best fit between all the tests in the Arvidson and Ingason study [12] was obtained for conduction correction factor Kcond ¼ 22 W/m2 K. In this open configuration, where the PT is cooled on the backside, the cooling is much greater than in the corresponding cone calorimeter configuration.
SB PT - with qstor PT - no qstor
40
30
20
10
0
0
2
4 6 Time [min]
8
10
Fig. 4. Comparison of calculated incident radiation q_ inc obtained from Schmidt–Boelter and plate thermometer measurements, respectively, at a distance of 2 m from a 3.5 MW pool fire.
Figs. 4 and 5 show comparisons of measurements of incident radiation q_ inc from a 3.5 MW pool fire based on SB total HFM measurements (Eq. (19)) and PT measurements (Eq. (18)), respectively. The effect of inertia for the PT measurements is demonstrated in Fig. 5 by comparing the line with q_ stor with the line no q_ stor . It is also obvious that the PT due to its inertia smoothes out the measurements which may be important when fast thermal changes need to be monitored. The inertia is taken into account in the PT curve of Fig. 5. Even at the low flux levels shown in this figure, the two measurements match well although the uncertainties of the conduction and convection terms could be expected to be relatively high at these levels. Fig. 6 shows a comparison between the average value of q_ inc over time obtained by SB and PT measurements, respectively, in the Arvidson and Ingason study. The values
3.3. Transient measurements on tests with cartons Lo¨nnermark and Ingason [13] measured radiation from free burning tests of goods consisting of paper cartons. They used both SB total HFMs and PTs in a similar manner as Arvidson and Ingason [12]. In Fig. 7, a comparison is shown of the calculated q_ inc for a test where the measuring devices were located 2 m from the fire. This fire test is highly transient as can be seen in Fig. 7. 4. Discussion and conclusions It is shown in this paper that incident radiant heat flux can be obtained indirectly from plate thermometer measurements. The PT was, however, designed for monitoring temperature in fire resistance furnaces and not for measuring incident radiant heat flux in air at ambient temperature as discussed here. Corrections are therefore needed as is outlined in this paper to compensate for conduction and convective errors. Alternative designs of the PT could, however, minimize these corrections. The
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Average values over test period2 m
Average values over test period 4 m 14 Incident radiation PT (kW / m2)
Incident radiation PT (kW / m2)
50
40
30
20
10
0
0
10
20
30
40
50
Incident radiation SB (kW/m2)
12 10 8 6 4 2 0
0
2
4
6
8
10
12
14
Incident radiation SB (kW/m2)
Fig. 6. The time average value of q_ inc for the time period when the heat flux level is stable. The graph on the left is for 2 m distance and on the right for 4 m distance. Both graphs include free burning pool fires of sizes 1, 2, 3.5 and 6 MW and spray fires of sizes 1, 2 and 3.5 MW.
on temperature measurements, compensating for thermal inertia and conduction losses. His device has, however, a relatively thick exposed plate, 5.0 mm, and will therefore have a slow time response making it mainly suitable for monitoring steady state conditions.
SB - PT - transient 25
Incident Radiation (kW / m2)
SB PT -withqstor
20
PT - no qstor 15
References
10
5
0
0
1
2
3
4
5
6
7
8
Time [min] Fig. 7. A comparison q_ inc obtained with a SB total heat flux meter and with a PT, respectively. In the latter case q_ inc is calculated when neglecting and when considering, respectively, the storage term q_ stor .
conduction losses could be substantially reduced by avoiding direct metal contact at the edges between the front and back sides of the PT and by using thicker and more effective insulation pads. The inertia could also be considerably reduced by using thinner steel plates and thereby getting much faster responses to thermal changes. Such modifications of the PT design for use in ambient air are possible and work with this objective has recently started at SP. The PT does not normally need to be as robust when used in ambient air as when used in fire resistance furnaces. For measuring total heat flux from the ignition source in the full-scale Room/Corner test according to ISO 9704, Dillon [14] developed a special steel plate assembly with several thermocouples. He shows with similar expressions to those used here how heat fluxes can be calculated based
[1] Wickstro¨m U. The plate thermometer—a simple instrument for reaching harmonized fire resistance rests, SP REPORT 1989:03, SP Swedish National Testing and Research Institute, Bora˚s, Sweden, 1989. [2] Wickstro¨m U. The plate thermometer—a simple instrument for reaching harmonized fire resistance tests. Fire Technol Second Quart 1994:195–208. [3] Wickstro¨m U. Short communication: heat transfer by radiation and convection in fire testing. Fire Mater 2004;28:411–5. [4] Holman JP. Heat transfer, 7th ed. Singapore: McGraw-Hill; 1992. [5] McAdams WH. Heat transmission. 3rd ed. New York: McGraw-Hill; 1954. [6] Atreya A. Convection heat transfer. In: DiNenno PJ, editor, SFPE handbook of ire protection engineering, NFPA and SFPE, 1995. p. 130 to 1-64. [7] Wickstro¨m U. ASEF-2—A computer program for temperature analysis of structures exposed to fire. Report no. 79-2, Lund Institute of Technology, 1979. [8] Hadvig S. Sto¨kiometri og Stofverdier (Stochiometry and material properties). Danmarks Tekniske Ho¨jskole, 1972 [in Danish]. [9] Fujii T, Imura H. Natural convection heat transfer from a plate with arbitrary inclination. J Heat Mass Transfer 1972;15:755. [10] Lloyd JR, Moran WR. Natural convection adjacent to horizontal surface of various planforms. ASME Paper 74-WA/HT-66, 1974. [11] Persson B, Wetterlund I. Tentative guidelines for calibration and use of heat flux meters, sp swedish national testing and research institute. SP Rep 1997;33:1997. [12] Arvidson M, Ingason H. Measurement of the efficiency of a water spray system against diesel oil pool and spray fires’’, SP Swedish national testing and research institute. SP Rep 2005;33:2005. [13] Lo¨nnermark A, Ingason H. Fire spread in large industrial premises and warehouses, SP Swedish national testing and research institute. SP Rep 2005;21:2005. [14] Dillon SE. Analysis of the ISO 9705 room/corner test: simulations, correlations and heat flux measurements, NIST-GCR-98-756, 1998.