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Rewetting of a hot vertical surface by liquid sprays
Experimental Thermal and Fluid Science 29 (2005) 885–891 www.elsevier.com/locate/etfs
Rewetting of a hot vertical surface by liquid sprays M. Casamirra a, F. Castiglia a,*, M. Giardina a, C. Lombardo a, G.P. Celata b, A. Mariani b, L. Saraceno b b
a Department of Nuclear Engineering, University of Palermo, Viale delle Scienze 90128 Palermo, Italy Institute of Energetic Thermal-Fluid Dynamics (Casaccia Center) of ENEA, Via Anguillarese 301, 00060 S. Maria di Galeria, Roma, Italy
Abstract Hot surfaces rewetting interests several technological fields. A very important application is in nuclear reactors technology, where it governs the cooling of overheated fuel elements during hypothesized loss of coolant accidents (LOCAs). This phenomenon is also important in many normal processes and accidental situations taking place in conventional processes. For example when the integrity of metallic containers, filled by toxic or dangerous substances, is endangered by a hypothetical fire. The rewetting consists in the re-establishment of coolant in contact with metallic surfaces become dried due to high temperature. To this end cold liquid is injected on these surfaces via sprays or other means. The knowledge of the heat transfer phenomenology between the metallic wall and cooling fluid is very important for safe accident management and containment. Recently, about this topic, at the Institute of Energetic Thermal-Fluid Dynamics of ENEA (the Italian National research body for Energy and Ambient, at Casaccia), experimental tests on the cooling of a hot vertical surface have been carried out, by using spraying devices of various configuration, to supply subcooled water at the top. The reference situation was a tank surface subjected to a fire. In the framework of a research collaboration between the Department of Nuclear Engineering (DIN) of the University of Palermo and the above mentioned Institute, a model set up at DIN has been tested as regards its capability to describe the ENEA experimental data. The results of this activity seem quite satisfactory, as weÕll show in the present paper. 2005 Elsevier Inc. All rights reserved.
1. Introduction Hot surfaces rewetting interests many industrial normal or abnormal processes in several technological fields. For example, it occurs in metallurgical quenching, in cryogenic processes, in spacecraft systems and electronic systems thermal control, and so on. Moreover, in nuclear reactors, it governs the cooling of overheated fuel elements during a hypothesized loss of coolant accident (LOCA). This phenomenon can also play an important role in case of a hypothetical fire involving the integrity of
*
Corresponding author. Tel.: +39 091232252; fax: +39 091232215. E-mail addresses: [email protected] (F. Castiglia), celata@ casaccia.enea.it (G.P. Celata). 0894-1777/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2005.03.014
metallic containers filled by toxic or dangerous substances. In all cases the knowledge of the heat transfer phenomenology between the metallic walls and the cooling fluids is very important for the project of an effective process or, in case of accidental situations, for the accident management and containment in terms of safety of authorized personnel, as well as of the people who accidentally gets involved. In the last decades a large amount of experimental works about the subject of the rewetting was done [1,2,4–7] and several models for the description of the relevant phenomenology have been set up [2,3,8–11]. Recently, at the Institute of Energetic Thermal-Fluid Dynamics of ENEA, with reference to a situation in which the wall of a tank containing dangerous substances is subjected to the flames of a fire, an experimental
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M. Casamirra et al. / Experimental Thermal and Fluid Science 29 (2005) 885–891
Nomenclature a = 1.057/D, b = 1.322/D dimensionless model parameters B Biot number, he/k c solid specific heat, J kg1 C1 G flow rate, kg s1 h heat transfer coefficient, W m2 C1 k solid thermal conductivity, W m1 C1 T temperature, C T0 sputtering temperature, C DT = T0 Ts incremental temperature, C Ts saturation temperature, C Tw initial wall temperature, C TLeid Leidenfrost temperature, C
campaign of rewetting tests at atmospheric pressure has been carried out. The rewetting was accomplished by using liquid spraying devices of various configuration to supply subcooled water at the top of a vertical surface, in form of very small drops of uniform diameter. Referring to [12,13] for the description of the experimental apparatus and of the performed tests, we confine to remember that, following the drops impact, and when somewhere the surface temperature achieves values below the so called ‘‘rewetting temperature’’, T0, a falling liquid film forms, whose edge goes down governed by the rapidity by which the heat is transferred by conduction, from the dried region of the surface to the rewetted one (conduction controlled rewetting). The present paper refers to the activity performed in the framework of a research collaboration between the Department of Nuclear Engineering of University of Palermo (for a long time now engaged in theoretical studies on the rewetting phenomenology) and the above mentioned Institute, with the aim to correlate the ENEA experimental data, in terms of the most important parameters that are thought to govern the rewetting phenomenon.
2. Rewetting models The most basic model adopted to describe the falling film rewetting is the two-region one, with a step change in the heat transfer coefficient. It considers an infinitely extended vertical slab, with the back face thermally insulated and the front face associated with a heat transfer coefficient undergoing an abrupt change, from a constant value to zero, in correspondence of the moving film front. Such a model has received much attention and for it, besides the one-dimensional solution [2], approximate and exact two-dimensional solutions have been presented [8–11,14]. In particular the two-
u v
dimensionless rewetting velocity, qcve/k rewetting velocity, m s1
Greek symbols D dimensionless parameter numerically coincident with DT e slab thickness, m h0 dimensionless rewetting temperature, (T0 Ts)/(Tw Ts) q solid density, kg m3 /0 dimensionless critical heat flux, Bh0 u0 critical heat flux, W m2
dimensional solution presented in [11,14] furnishes the dimensionless temperature distribution in the entire slab in terms of two series, one for the wet region and the other for the dry one. Whereas, the dimensionless rewetting temperature h0, is put in the form of an infinite product, the factor of which are function of the dimensionless rewetting velocity, u, and of the Biot number, B (for the symbols, see the nomenclature). As in practical applications it is more convenient to handle an explicit expression of the dimensionless rewetting velocity, u, in terms of B and h0, a simple and very accurate correlation which accomplishes the inversion of the exact expression in approximate manner (rms error less than 3%) has been introduced [15]. Owing to this very good agreement, in the following we will refer to this correlation as to the model solution for the rewetting velocity. In general, the theoretical models proposed for the study of a given phenomenon allow to connect, in terms of either tables or formulas, the main involved physical parameters. In particular, for the rewetting phenomenology these parameters are the wet front velocity v, the rewetting (or sputtering) temperature T0, and the heat transfer coefficient h. Consequently, in order to predict the wet front velocity, the knowledge of both T0 and h is a prerequisite. As unfortunately, the direct measurement of these parameters presents acute experimental difficulties, one can to attempt to draw them as matching parameters between the experimental data and the theoretical model, on the basis of a suitable connecting procedure. It should be noted that, at least in principle, the parameters values obtained in such a way are valid only in the framework of the particular adopted model and, consequently, no definite physical meaning can be assigned to them. A procedure of this kind has been presented in [16] and will be summarized, a little modified, in the next section.
M. Casamirra et al. / Experimental Thermal and Fluid Science 29 (2005) 885–891
Here we confine ourselves to observe that the activities developed to correlate the experimental data with the above mentioned model, in order to better understand the fundamental mechanism involved in the phenomenon, have only partially succeeded because, whereas it is possible to reproduce very accurately, both in magnitude and in trend, the values of the rewetting velocities measured in most rewetting experiments, this is obtained at the cost of too large values for the parameter h, not consistent with those encountered in boiling phenomena. Therefore, these values have to be regarded as correlating parameters only. In a more recent work, to which the reader is referred for the details [17], reconsidering the results obtained in the previous activities devoted to the correlation of a significant number of experimental data with the above model, we have suitably rearranged the model solution, in such a manner that it suggested nucleate boiling crisis conditions as the prevailing heat transfer mechanism taking place at the rewetting front, as claimed by most authors [18]. Owing to this, we proposed an empirical touch up to the model expression for the rewetting velocity, as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffi /0 h0 u ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1Þ a þ bh0 1 h0 where a and b are model dimensionless parameters and /0 = Bh0, is the dimensionless heat flux at the film front. We notice that subsequently, considering of some interest searching for a justification of such a relationship, it has been formally identified as the solution of a semitheoretical, one-dimensional model, based on a form of boundary layer analysis [19].
ð3Þ
where Ts is the saturation temperature, DT is an incremental temperature, hypothesized as constant, and h(G) is the heat transfer coefficient thought as function of the flow rate G. In order to determine DT and h(G), the experimental data points, that is the couples (Twi, vi) of the measured values of the initial wall temperature and of the corresponding rewetting front velocity, are first grouped in sets, each characterized by a single value of the flow rate. Then the following steps are in succession performed: (i) A hypothetical reasonable value of T0 is used in the dimensional form of the Eq. (1) solved with respect to h, to calculate tables of estimated h(G) for each couple of each set. (ii) The mean value of the estimated h(G)Õs in each set is considered as the heat transfer coefficient for the set and is used in the dimensional form of (1), to calculate the model estimates of the rewetting velocity in correspondence to each value Twi of the set. And so forth for the other sets.All sets run out, the following variable is computed, by using the measured, vi, and the estimated, vi,theor, values of the rewetting velocities: " # 2 X 1 X ðvi vi;theor Þ 2 v ¼ ð4Þ N all sets all data points of the set vi;theor where N is the total number of the utilized experimental data.One recognizes in (4) a normalized form of the chi-square variable of the statistics. (iii) the steps (i) and (ii) are repeated for a range of T0 values, and finally, the best estimate of T0 is chosen as the one giving the lowest value of v2. At the same time, a table of estimates of h(G) one for each set, is obtained. Subsequently a suitable correlation for h(G) is searched for.
3. Procedure for correlating experimental results with theoretical models The following procedure closely recalls the one presented in [16,20], slightly modified however, to fit the kind of experiments performed at ENEA. It applies to results of rewetting experiments performed at a given pressure, which for given values of coolant flow rate (G) and initial wall temperature (Twi), furnish measured values of the rewetting front velocity (vi). The aim is to find explicit values or expressions for the rewetting temperature, as well for the heat transfer coefficient, compatible with the relationship (1) of the rewetting velocity. As the ENEA experiments were performed at a single pressure (the atmospheric one), after a preliminary analysis of the experimental data, we thought to cast the unknown parameters, T0 and h, in the following forms: T 0 ¼ T s þ DT
h ¼ hðGÞ
887
ð2Þ
4. Processing of rewetting experiments on the light of the correlating procedure A suitable version of the above depicted procedure has been already applied to the rewetting experiments by Bennett et al. [1], Elliott and Rose [4,5], and Yu [6]. These Authors used, as coolant, water in steam environment at various pressures, flow rates and different stainless steel or inconel vertical tubes as test sections. As in these experiments the coolant flow rate showed a not significant influence on the heat transfer coefficient, the experimental data were processed as a whole, irrespective of the coolant flow rate. Here we confine ourselves to report, in Figs. 1 and 2, only the results obtained in
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1.E-01
Table 1 Nozzle injectors characteristics
χ2
1.E-02 1.E-03
Number of hole
Hole diameter [mm]
36 9 4 1
0.15 0.30 0.45 0.90
1.E-04 1.E-05 T0 [ ºC] 1.E-06 150
170
190
210
230
250
270
290
2
Fig. 1. v versus hypothesized values of the rewetting temperatures for Yu et al. experiments at atmospheric pressure.
v[m/s]
1
0.1
0.01
Tw[º C] 0.001 150
250
350
450
550
650
750
850
Fig. 2. Model reproduction (curve) of the experimental data (points) performed at atmospheric pressure by Yu et al.
the case of Yu et al. experiments, performed at atmospheric pressure. Fig. 1, where v2 versus some hypothesized rewetting temperatures is reported, shows that there is a sharp absolute minimum value of this variable at T0 = 200 C. Therefore this is the value to assume for the rewetting temperature, on the basis of the proposed procedure. On the other hand, Fig. 2 shows how well the model reproduces the experimental data. It is noticeable that the value provided by Eq. (1) for the heat flux at the wet front is u0 = 1.37 · 106 W m2, very close to the one reported for the heat flux at the saturated pool boiling crisis. All this completely agrees with that is generally recognized by most authors: in top rewetting ‘‘the rewetting temperature corresponds to the critical heatflux temperature’’ [18]. We now turn our attention to the experiments performed at ENEA. As above said, the research was carried out to investigate the rewetting of a hot surface cooled with droplet impingement at the top, the reference situation being the external surface of a tank which,
subjected to the flames of a fire, is cooled by subcooled water provided by suitable spray devices. The spraying system consisted of various multihole nozzle injectors, able to generate droplets with a mostly uniform diameter, based on the principle of jet varicose breakup (Rayleigh–Weber instability). Nozzles total flow area is constant, independent of the number of holes, in order to have the same flow rate for the same liquid velocity. Nozzle injectors characteristics are reported in Table 1, whereas the adopted drops velocities ranged from 2 m s1 to 7 m s1. The test section consisted of a vertical stainless steel plate, 0.14 m (heated only 0.1 m) height, 0.01 m width, and 0.005 m thickness, heated at different initial surface temperatures (from 100 C to 700 C) by Joule effect. Several rewetting experiments have been performed changing droplets size and velocity at each test [12,13]. Before presenting the results obtained in applying to the ENEA experiments, Eq. (1) in conjunction with the above depicted correlating procedure, it is worth to mention that a further test has been performed at ENEA, consisting in placing the heated wall in horizontal position, heating it step by step at different increasing temperatures, and injecting on it at each step a single water droplet. This, to gain an estimate of the Leidenfrost temperature, defined as the one at which the drop, after impacting, contracts and bounces back. As a result, TLeid = 265 C was measured.
5. Obtained results on the ENEA experiments Applying the proposed correlation procedure to some of the ENEA experiments, we obtained the results reported in Figs. 3–10. Fig. 3, where v2 versus a selected number of hypothesized rewetting temperature values is reported, shows that up to about T0 = 200 C the v2 variable decreases very rapidly, attaining at this temperature a relative minimum value. Subsequently it decreases very slowly up to about T0 = 265 C, where it attains, once more, a minimum value. After, the v2 variable steadily increases. One recognizes, anyway, that between the T0 = 200 C and 265 C a substantially flat region of minima is exhibited. Referring to the end of this section for some consideration about such a region of minima, for the moment we present the results obtained by
0.1
1
χ2
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v[m/s]
M. Casamirra et al. / Experimental Thermal and Fluid Science 29 (2005) 885–891
Experiments T0 =200ºC T0 =265ºC
0.1
0.01 0.01
T0 [ºC]
0.001 175
200
225
250
275
300
Tw[º C] 0.001 150
250
350
450
550
650
750
850
2
Fig. 6. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.001908 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
1
h[W/m2 ºC]
70000 60000 50000
h(G) (T0 = 200ºC) h(G) (T0 = 265ºC)
v[m/s]
Fig. 3. v versus hypothesized values of rewetting temperature for the ENEA experiments.
Experiments T0 =200ºC T0 =265ºC
0.1
40000 30000 0.01 20000 10000
Tw[ºC]
G[kg/s] 0
0.001
0.002
0.003
0.004
0.005
Fig. 4. Estimated heat transfer coefficients, as function of the water flow rate, in correspondence of the two values hypothesized for the rewetting temperature.
v [m/s]
Experiments T0 =200ºC T0 =265ºC
0.1
250
350
450
550
650
750
850
Fig. 7. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.002544 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
1
1
Experiments T0 =200ºC T0 =265ºC
0.1
0.01
0.01
Tw [ºC] 0.001 150
0.001 150
v[m/s]
0
250
350
450
550
650
750
850
Tw[º C] 0.001 150
250
350
450
550
650
750
850
Fig. 5. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.001272 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
Fig. 8. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.00318 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
assuming, in turn, T0 = 200 C and 265 C as rewetting temperatures. It is worth to note that, for both these assumptions the model in conjunction with the correlat-
ing procedure, gives estimated values for the heat fluxes at the film front ranging between about 1.2 · 106 W m2 and about 6.0 · 106 W m2, then consistent with those
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v[m/s]
1 Experiments T0 =200ºC T0 =265ºC
0.1
0.01
Tw[ºC] 0.001 150
250
350
450
550
650
750
850
Fig. 9. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.003816 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
v[m/s]
1 Experimental T0 =200ºC T0 =265ºC
0.1
wall temperature. Moreover, one easily realizes that the same should happen, whatever T0 would be chosen in the near flat region of the v2 minima in Fig. 3. At this point, as on the other hand previously observed regarding this figure, the procedure criterium for deducing from the v2 behaviour the rewetting temperature T0, would need to be more precisely stated. This, obviously, should be made on physical ground. Intending to deepening this subject in future works for the sake of brevity, for the moment we confine to only observe that if the rewetting temperature is to be thought as the temperature at which liquid can still touch the solid wall without being immediately turned into vapour [22], among the temperatures comprised between 200 C and 265 C, the first temperature (or one quite close to it) might fulfil such a requirement rather than the higher ones. Therefore it seems useful to provisionally reformulate the above quoted criterium of individuation of T0 as follows: the rewetting temperature is found as the one in correspondence to which the v2 variable attains, for the first time, a minimum value.
6. Conclusion 0.01
Tw [ºC] 0.001 150
250
350
450
550
650
750
850
Fig. 10. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.004452 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
reported for subcooled thermal crisis in pool boiling [21]. Finally, we point out that, contrary to the rewetting experiments by Yu et al., in the present ones, performed by injecting subcooled instead of saturated water, the values of the flow rates exert a not negligible influence as, however, recognized by many authors [6]. This is shown in Fig. 4, which reports for both the alternative hypotheses about T0, the deduced values of the heat transfer coefficient, as function of the applied water flow rates (points). We see that suitable correlations for h(G) are quadratic functions, which have been preliminarily utilized in Eq. (1), to trace by continuous curves the model predictions in Figs. 5–10. From the inspection of the obtained results one recognizes, in the first place, that, irrespective of the two employed values for the rewetting temperature, the model predictions of the ENEA experimental rewetting velocities result quite good and almost coincident in practice but, obviously, at the lower values of the initial
A number of experimental data on top rewetting, performed at the Institute of Energetic Thermal-Fluid Dynamics of ENEA by using subcooled water sprays, have been correlated with a theoretical model previously set up at the Department of Nuclear Engineering of the University of Palermo (DIN). Such a correlation has been carried out by means of a suitable procedure, also this set up at the DIN, aimed at deducing from experimental data, acceptable values for the parameters involved in the rewetting phenomenon, i.e., the rewetting temperature and the heat transfer coefficient at the wet front. The obtained results prove very appreciable, in fact they show that the model in conjunction with the correlating procedure is capable to attain in noteworthy manner this objective.
Acknowledgement Work supported by Ministero dellÕUniversita` e della Ricerca Scientifica e Tecnologica (MIUR): Piani di Potenziamento della Rete Scientifica e Tecnologica, Progetto no. 23 ISR1.
References [1] A.W. Bennet, G.F. Hewitt, H.A. Kearsey, R.K.F. Keys, The wetting of hot surfaces by water in a steam environment at high pressure, Report AERE-R5 146, UKAEA, Winfrith, 1966.
M. Casamirra et al. / Experimental Thermal and Fluid Science 29 (2005) 885–891 [2] A. Yamanouchi, Effect of core spray cooling in transient state after loss of coolant accident, Journal of Nuclear Science and Technology 5 (1968) 547–558. [3] E. Elias, Yadigarouglu, A general one-dimensional model for conduction-controlled rewetting of a surface, Nuclear Engineering and Design 42 (1977) 185–194. [4] D.F. Elliott, P.W. Rose, The quenching of a heated surface by a film of water in a steam environment at pressure up to 35 bar, AEEW-M 976, 1970. [5] D.F. Elliott, P.W. Rose, The quenching of a heated zircaloy surface by a film of water in a steam environment at pressure up to 35 bar, AEEW-M 1027, 1971. [6] S.K.W. Yu, The rewetting of hot surfaces by a falling water film— the effects of pressure, subcooling and flow rate, CERL Report RD/L/N20/75 (SGHW/HTWG/P(75) 79), 1975. [7] R.B. Duffey, D.T.C. Porthouse, Experiments on the cooling of high temperature surfaces by water jets and drops, Central Electricity Generating Board (1972). [8] R.B. Duffey, D.T.C. Porthouse, The physics of rewetting in water reactor emergency core cooling, Nuclear Engineering and Design 25 (1973) 379–394. [9] J.M. Blair, An analytical solution to a two-dimensional model of the rewetting of a hot dry rod, Nuclear Engineering and Design 32 (1975) 159–170. [10] T.S. Thompson, An analysis of the wet-side heat transfer coefficient during rewetting of a hot dry patch, Nuclear Engineering and Design 22 (1972) 212–224. [11] F. Castiglia, E. Oliveri, S. Taibi, G. Vella, Exact solution to the two-dimensional approach of the rewetting by falling film, in: Proceedings of the Eighth International Heat Transfer Conference, San Francisco, vol. 3, 1983–1986, 1986. [12] G.P. Celata, M. Cumo, A. Mariani, Rewetting of hot surfaces by droplet impingement, in: 40th European Two-Phase Flow Group Meeting, Stockholm, 11–13, Giugno, 2001, 2002.
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[13] G.P. Celata, M. Cumo, C. Lombardo, A. Mariani, L. Saraceno, Experimental result on rewetting of hot surfaces by droplet impingement, in: 3rd European-Japanese Two-Phase Flow Group Meeting, Certosa di Pontignano, 21–27 September 2003, 2003. [14] F. Castiglia, E. Oliveri, S. Taibi, G. Vella, Exact solution to the two-dimensional approach of the rewetting of a rod by a falling film, International Journal of Engineering Fluid Mechanics 2 (1989) 267–276. [15] F. Castiglia, E. Oliveri, S. Taibi, G. Vella, A correlation for the quench front velocity in the rewetting of a rod by falling film, 6Congresso Internazionale sulla Trasmissione Del Calore, Bari, 1988. [16] F. Castiglia, E. Oliveri, S. Taibi, G. Vella, Procedure for correlating experimental and theoretical results in the rewetting of hot surfaces, Heat and Technology 5 (3–4) (1987). [17] G. Bonanno, F. Castiglia, M. Giardina, Correlation of experimental data on quench front velocity, ATI—50Congresso Nazionale, 11–15 September, St Vincent, 1995. [18] J.J. Carbajo, A study on the rewetting temperature, Nuclear Engineering and Design 84 (1985) 21–22. [19] F. Castiglia, M. Giardina, E. Oliveri, The heat transfer mechanisms at the quench front, in: 4th International Symposium on Heat Transfer, 7–11 October, Beijing, China, 1996. [20] F. Castiglia, E. Oliveri, S. Taibi, G. Vella, Correlating the experimental data in the rewetting of hot surfaces by liquid falling film, in: 7th Eurotherm Seminar on Thermal Non-Equilibrium in Two-Phase Flow, Rome , March 23–24, 1989. [21] G. Hetsroni, Handbook of multiphase systems, 1982 (Chapter 6, Section 6-44). [22] V. Gerweck, G. Yadigaroglu, A local equation of state for a fluid in the presence of a wall and its application to rewetting, International Journal Heat Mass Transfer 35 (7) (1992) 1823– 1832.
Rewetting of a hot vertical surface by liquid sprays M. Casamirra a, F. Castiglia a,*, M. Giardina a, C. Lombardo a, G.P. Celata b, A. Mariani b, L. Saraceno b b
a Department of Nuclear Engineering, University of Palermo, Viale delle Scienze 90128 Palermo, Italy Institute of Energetic Thermal-Fluid Dynamics (Casaccia Center) of ENEA, Via Anguillarese 301, 00060 S. Maria di Galeria, Roma, Italy
Abstract Hot surfaces rewetting interests several technological fields. A very important application is in nuclear reactors technology, where it governs the cooling of overheated fuel elements during hypothesized loss of coolant accidents (LOCAs). This phenomenon is also important in many normal processes and accidental situations taking place in conventional processes. For example when the integrity of metallic containers, filled by toxic or dangerous substances, is endangered by a hypothetical fire. The rewetting consists in the re-establishment of coolant in contact with metallic surfaces become dried due to high temperature. To this end cold liquid is injected on these surfaces via sprays or other means. The knowledge of the heat transfer phenomenology between the metallic wall and cooling fluid is very important for safe accident management and containment. Recently, about this topic, at the Institute of Energetic Thermal-Fluid Dynamics of ENEA (the Italian National research body for Energy and Ambient, at Casaccia), experimental tests on the cooling of a hot vertical surface have been carried out, by using spraying devices of various configuration, to supply subcooled water at the top. The reference situation was a tank surface subjected to a fire. In the framework of a research collaboration between the Department of Nuclear Engineering (DIN) of the University of Palermo and the above mentioned Institute, a model set up at DIN has been tested as regards its capability to describe the ENEA experimental data. The results of this activity seem quite satisfactory, as weÕll show in the present paper. 2005 Elsevier Inc. All rights reserved.
1. Introduction Hot surfaces rewetting interests many industrial normal or abnormal processes in several technological fields. For example, it occurs in metallurgical quenching, in cryogenic processes, in spacecraft systems and electronic systems thermal control, and so on. Moreover, in nuclear reactors, it governs the cooling of overheated fuel elements during a hypothesized loss of coolant accident (LOCA). This phenomenon can also play an important role in case of a hypothetical fire involving the integrity of
*
Corresponding author. Tel.: +39 091232252; fax: +39 091232215. E-mail addresses: [email protected] (F. Castiglia), celata@ casaccia.enea.it (G.P. Celata). 0894-1777/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2005.03.014
metallic containers filled by toxic or dangerous substances. In all cases the knowledge of the heat transfer phenomenology between the metallic walls and the cooling fluids is very important for the project of an effective process or, in case of accidental situations, for the accident management and containment in terms of safety of authorized personnel, as well as of the people who accidentally gets involved. In the last decades a large amount of experimental works about the subject of the rewetting was done [1,2,4–7] and several models for the description of the relevant phenomenology have been set up [2,3,8–11]. Recently, at the Institute of Energetic Thermal-Fluid Dynamics of ENEA, with reference to a situation in which the wall of a tank containing dangerous substances is subjected to the flames of a fire, an experimental
886
M. Casamirra et al. / Experimental Thermal and Fluid Science 29 (2005) 885–891
Nomenclature a = 1.057/D, b = 1.322/D dimensionless model parameters B Biot number, he/k c solid specific heat, J kg1 C1 G flow rate, kg s1 h heat transfer coefficient, W m2 C1 k solid thermal conductivity, W m1 C1 T temperature, C T0 sputtering temperature, C DT = T0 Ts incremental temperature, C Ts saturation temperature, C Tw initial wall temperature, C TLeid Leidenfrost temperature, C
campaign of rewetting tests at atmospheric pressure has been carried out. The rewetting was accomplished by using liquid spraying devices of various configuration to supply subcooled water at the top of a vertical surface, in form of very small drops of uniform diameter. Referring to [12,13] for the description of the experimental apparatus and of the performed tests, we confine to remember that, following the drops impact, and when somewhere the surface temperature achieves values below the so called ‘‘rewetting temperature’’, T0, a falling liquid film forms, whose edge goes down governed by the rapidity by which the heat is transferred by conduction, from the dried region of the surface to the rewetted one (conduction controlled rewetting). The present paper refers to the activity performed in the framework of a research collaboration between the Department of Nuclear Engineering of University of Palermo (for a long time now engaged in theoretical studies on the rewetting phenomenology) and the above mentioned Institute, with the aim to correlate the ENEA experimental data, in terms of the most important parameters that are thought to govern the rewetting phenomenon.
2. Rewetting models The most basic model adopted to describe the falling film rewetting is the two-region one, with a step change in the heat transfer coefficient. It considers an infinitely extended vertical slab, with the back face thermally insulated and the front face associated with a heat transfer coefficient undergoing an abrupt change, from a constant value to zero, in correspondence of the moving film front. Such a model has received much attention and for it, besides the one-dimensional solution [2], approximate and exact two-dimensional solutions have been presented [8–11,14]. In particular the two-
u v
dimensionless rewetting velocity, qcve/k rewetting velocity, m s1
Greek symbols D dimensionless parameter numerically coincident with DT e slab thickness, m h0 dimensionless rewetting temperature, (T0 Ts)/(Tw Ts) q solid density, kg m3 /0 dimensionless critical heat flux, Bh0 u0 critical heat flux, W m2
dimensional solution presented in [11,14] furnishes the dimensionless temperature distribution in the entire slab in terms of two series, one for the wet region and the other for the dry one. Whereas, the dimensionless rewetting temperature h0, is put in the form of an infinite product, the factor of which are function of the dimensionless rewetting velocity, u, and of the Biot number, B (for the symbols, see the nomenclature). As in practical applications it is more convenient to handle an explicit expression of the dimensionless rewetting velocity, u, in terms of B and h0, a simple and very accurate correlation which accomplishes the inversion of the exact expression in approximate manner (rms error less than 3%) has been introduced [15]. Owing to this very good agreement, in the following we will refer to this correlation as to the model solution for the rewetting velocity. In general, the theoretical models proposed for the study of a given phenomenon allow to connect, in terms of either tables or formulas, the main involved physical parameters. In particular, for the rewetting phenomenology these parameters are the wet front velocity v, the rewetting (or sputtering) temperature T0, and the heat transfer coefficient h. Consequently, in order to predict the wet front velocity, the knowledge of both T0 and h is a prerequisite. As unfortunately, the direct measurement of these parameters presents acute experimental difficulties, one can to attempt to draw them as matching parameters between the experimental data and the theoretical model, on the basis of a suitable connecting procedure. It should be noted that, at least in principle, the parameters values obtained in such a way are valid only in the framework of the particular adopted model and, consequently, no definite physical meaning can be assigned to them. A procedure of this kind has been presented in [16] and will be summarized, a little modified, in the next section.
M. Casamirra et al. / Experimental Thermal and Fluid Science 29 (2005) 885–891
Here we confine ourselves to observe that the activities developed to correlate the experimental data with the above mentioned model, in order to better understand the fundamental mechanism involved in the phenomenon, have only partially succeeded because, whereas it is possible to reproduce very accurately, both in magnitude and in trend, the values of the rewetting velocities measured in most rewetting experiments, this is obtained at the cost of too large values for the parameter h, not consistent with those encountered in boiling phenomena. Therefore, these values have to be regarded as correlating parameters only. In a more recent work, to which the reader is referred for the details [17], reconsidering the results obtained in the previous activities devoted to the correlation of a significant number of experimental data with the above model, we have suitably rearranged the model solution, in such a manner that it suggested nucleate boiling crisis conditions as the prevailing heat transfer mechanism taking place at the rewetting front, as claimed by most authors [18]. Owing to this, we proposed an empirical touch up to the model expression for the rewetting velocity, as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffi /0 h0 u ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1Þ a þ bh0 1 h0 where a and b are model dimensionless parameters and /0 = Bh0, is the dimensionless heat flux at the film front. We notice that subsequently, considering of some interest searching for a justification of such a relationship, it has been formally identified as the solution of a semitheoretical, one-dimensional model, based on a form of boundary layer analysis [19].
ð3Þ
where Ts is the saturation temperature, DT is an incremental temperature, hypothesized as constant, and h(G) is the heat transfer coefficient thought as function of the flow rate G. In order to determine DT and h(G), the experimental data points, that is the couples (Twi, vi) of the measured values of the initial wall temperature and of the corresponding rewetting front velocity, are first grouped in sets, each characterized by a single value of the flow rate. Then the following steps are in succession performed: (i) A hypothetical reasonable value of T0 is used in the dimensional form of the Eq. (1) solved with respect to h, to calculate tables of estimated h(G) for each couple of each set. (ii) The mean value of the estimated h(G)Õs in each set is considered as the heat transfer coefficient for the set and is used in the dimensional form of (1), to calculate the model estimates of the rewetting velocity in correspondence to each value Twi of the set. And so forth for the other sets.All sets run out, the following variable is computed, by using the measured, vi, and the estimated, vi,theor, values of the rewetting velocities: " # 2 X 1 X ðvi vi;theor Þ 2 v ¼ ð4Þ N all sets all data points of the set vi;theor where N is the total number of the utilized experimental data.One recognizes in (4) a normalized form of the chi-square variable of the statistics. (iii) the steps (i) and (ii) are repeated for a range of T0 values, and finally, the best estimate of T0 is chosen as the one giving the lowest value of v2. At the same time, a table of estimates of h(G) one for each set, is obtained. Subsequently a suitable correlation for h(G) is searched for.
3. Procedure for correlating experimental results with theoretical models The following procedure closely recalls the one presented in [16,20], slightly modified however, to fit the kind of experiments performed at ENEA. It applies to results of rewetting experiments performed at a given pressure, which for given values of coolant flow rate (G) and initial wall temperature (Twi), furnish measured values of the rewetting front velocity (vi). The aim is to find explicit values or expressions for the rewetting temperature, as well for the heat transfer coefficient, compatible with the relationship (1) of the rewetting velocity. As the ENEA experiments were performed at a single pressure (the atmospheric one), after a preliminary analysis of the experimental data, we thought to cast the unknown parameters, T0 and h, in the following forms: T 0 ¼ T s þ DT
h ¼ hðGÞ
887
ð2Þ
4. Processing of rewetting experiments on the light of the correlating procedure A suitable version of the above depicted procedure has been already applied to the rewetting experiments by Bennett et al. [1], Elliott and Rose [4,5], and Yu [6]. These Authors used, as coolant, water in steam environment at various pressures, flow rates and different stainless steel or inconel vertical tubes as test sections. As in these experiments the coolant flow rate showed a not significant influence on the heat transfer coefficient, the experimental data were processed as a whole, irrespective of the coolant flow rate. Here we confine ourselves to report, in Figs. 1 and 2, only the results obtained in
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1.E-01
Table 1 Nozzle injectors characteristics
χ2
1.E-02 1.E-03
Number of hole
Hole diameter [mm]
36 9 4 1
0.15 0.30 0.45 0.90
1.E-04 1.E-05 T0 [ ºC] 1.E-06 150
170
190
210
230
250
270
290
2
Fig. 1. v versus hypothesized values of the rewetting temperatures for Yu et al. experiments at atmospheric pressure.
v[m/s]
1
0.1
0.01
Tw[º C] 0.001 150
250
350
450
550
650
750
850
Fig. 2. Model reproduction (curve) of the experimental data (points) performed at atmospheric pressure by Yu et al.
the case of Yu et al. experiments, performed at atmospheric pressure. Fig. 1, where v2 versus some hypothesized rewetting temperatures is reported, shows that there is a sharp absolute minimum value of this variable at T0 = 200 C. Therefore this is the value to assume for the rewetting temperature, on the basis of the proposed procedure. On the other hand, Fig. 2 shows how well the model reproduces the experimental data. It is noticeable that the value provided by Eq. (1) for the heat flux at the wet front is u0 = 1.37 · 106 W m2, very close to the one reported for the heat flux at the saturated pool boiling crisis. All this completely agrees with that is generally recognized by most authors: in top rewetting ‘‘the rewetting temperature corresponds to the critical heatflux temperature’’ [18]. We now turn our attention to the experiments performed at ENEA. As above said, the research was carried out to investigate the rewetting of a hot surface cooled with droplet impingement at the top, the reference situation being the external surface of a tank which,
subjected to the flames of a fire, is cooled by subcooled water provided by suitable spray devices. The spraying system consisted of various multihole nozzle injectors, able to generate droplets with a mostly uniform diameter, based on the principle of jet varicose breakup (Rayleigh–Weber instability). Nozzles total flow area is constant, independent of the number of holes, in order to have the same flow rate for the same liquid velocity. Nozzle injectors characteristics are reported in Table 1, whereas the adopted drops velocities ranged from 2 m s1 to 7 m s1. The test section consisted of a vertical stainless steel plate, 0.14 m (heated only 0.1 m) height, 0.01 m width, and 0.005 m thickness, heated at different initial surface temperatures (from 100 C to 700 C) by Joule effect. Several rewetting experiments have been performed changing droplets size and velocity at each test [12,13]. Before presenting the results obtained in applying to the ENEA experiments, Eq. (1) in conjunction with the above depicted correlating procedure, it is worth to mention that a further test has been performed at ENEA, consisting in placing the heated wall in horizontal position, heating it step by step at different increasing temperatures, and injecting on it at each step a single water droplet. This, to gain an estimate of the Leidenfrost temperature, defined as the one at which the drop, after impacting, contracts and bounces back. As a result, TLeid = 265 C was measured.
5. Obtained results on the ENEA experiments Applying the proposed correlation procedure to some of the ENEA experiments, we obtained the results reported in Figs. 3–10. Fig. 3, where v2 versus a selected number of hypothesized rewetting temperature values is reported, shows that up to about T0 = 200 C the v2 variable decreases very rapidly, attaining at this temperature a relative minimum value. Subsequently it decreases very slowly up to about T0 = 265 C, where it attains, once more, a minimum value. After, the v2 variable steadily increases. One recognizes, anyway, that between the T0 = 200 C and 265 C a substantially flat region of minima is exhibited. Referring to the end of this section for some consideration about such a region of minima, for the moment we present the results obtained by
0.1
1
χ2
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v[m/s]
M. Casamirra et al. / Experimental Thermal and Fluid Science 29 (2005) 885–891
Experiments T0 =200ºC T0 =265ºC
0.1
0.01 0.01
T0 [ºC]
0.001 175
200
225
250
275
300
Tw[º C] 0.001 150
250
350
450
550
650
750
850
2
Fig. 6. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.001908 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
1
h[W/m2 ºC]
70000 60000 50000
h(G) (T0 = 200ºC) h(G) (T0 = 265ºC)
v[m/s]
Fig. 3. v versus hypothesized values of rewetting temperature for the ENEA experiments.
Experiments T0 =200ºC T0 =265ºC
0.1
40000 30000 0.01 20000 10000
Tw[ºC]
G[kg/s] 0
0.001
0.002
0.003
0.004
0.005
Fig. 4. Estimated heat transfer coefficients, as function of the water flow rate, in correspondence of the two values hypothesized for the rewetting temperature.
v [m/s]
Experiments T0 =200ºC T0 =265ºC
0.1
250
350
450
550
650
750
850
Fig. 7. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.002544 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
1
1
Experiments T0 =200ºC T0 =265ºC
0.1
0.01
0.01
Tw [ºC] 0.001 150
0.001 150
v[m/s]
0
250
350
450
550
650
750
850
Tw[º C] 0.001 150
250
350
450
550
650
750
850
Fig. 5. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.001272 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
Fig. 8. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.00318 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
assuming, in turn, T0 = 200 C and 265 C as rewetting temperatures. It is worth to note that, for both these assumptions the model in conjunction with the correlat-
ing procedure, gives estimated values for the heat fluxes at the film front ranging between about 1.2 · 106 W m2 and about 6.0 · 106 W m2, then consistent with those
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v[m/s]
1 Experiments T0 =200ºC T0 =265ºC
0.1
0.01
Tw[ºC] 0.001 150
250
350
450
550
650
750
850
Fig. 9. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.003816 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
v[m/s]
1 Experimental T0 =200ºC T0 =265ºC
0.1
wall temperature. Moreover, one easily realizes that the same should happen, whatever T0 would be chosen in the near flat region of the v2 minima in Fig. 3. At this point, as on the other hand previously observed regarding this figure, the procedure criterium for deducing from the v2 behaviour the rewetting temperature T0, would need to be more precisely stated. This, obviously, should be made on physical ground. Intending to deepening this subject in future works for the sake of brevity, for the moment we confine to only observe that if the rewetting temperature is to be thought as the temperature at which liquid can still touch the solid wall without being immediately turned into vapour [22], among the temperatures comprised between 200 C and 265 C, the first temperature (or one quite close to it) might fulfil such a requirement rather than the higher ones. Therefore it seems useful to provisionally reformulate the above quoted criterium of individuation of T0 as follows: the rewetting temperature is found as the one in correspondence to which the v2 variable attains, for the first time, a minimum value.
6. Conclusion 0.01
Tw [ºC] 0.001 150
250
350
450
550
650
750
850
Fig. 10. Predicted rewetting velocities as function of wall temperature for the flow rate G = 0.004452 kg s1 and in correspondence of the two hypothesized values for rewetting temperature.
reported for subcooled thermal crisis in pool boiling [21]. Finally, we point out that, contrary to the rewetting experiments by Yu et al., in the present ones, performed by injecting subcooled instead of saturated water, the values of the flow rates exert a not negligible influence as, however, recognized by many authors [6]. This is shown in Fig. 4, which reports for both the alternative hypotheses about T0, the deduced values of the heat transfer coefficient, as function of the applied water flow rates (points). We see that suitable correlations for h(G) are quadratic functions, which have been preliminarily utilized in Eq. (1), to trace by continuous curves the model predictions in Figs. 5–10. From the inspection of the obtained results one recognizes, in the first place, that, irrespective of the two employed values for the rewetting temperature, the model predictions of the ENEA experimental rewetting velocities result quite good and almost coincident in practice but, obviously, at the lower values of the initial
A number of experimental data on top rewetting, performed at the Institute of Energetic Thermal-Fluid Dynamics of ENEA by using subcooled water sprays, have been correlated with a theoretical model previously set up at the Department of Nuclear Engineering of the University of Palermo (DIN). Such a correlation has been carried out by means of a suitable procedure, also this set up at the DIN, aimed at deducing from experimental data, acceptable values for the parameters involved in the rewetting phenomenon, i.e., the rewetting temperature and the heat transfer coefficient at the wet front. The obtained results prove very appreciable, in fact they show that the model in conjunction with the correlating procedure is capable to attain in noteworthy manner this objective.
Acknowledgement Work supported by Ministero dellÕUniversita` e della Ricerca Scientifica e Tecnologica (MIUR): Piani di Potenziamento della Rete Scientifica e Tecnologica, Progetto no. 23 ISR1.
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