c Allerton Press, Inc., 2015. ISSN 1068-3356, Bulletin of the Lebedev Physics Institute, 2015, Vol. 42, No. 8, pp. 233–236. c M.I. Delov, K.V. Kutsenko, A.A. Lavrukhin, M.I. Pisarevskii, V.N. Fedoseev, 2015, published in Kratkie Soobshcheniya po Fizike, 2015, Vol. 42, Original Russian Text No. 8, pp. 16–21.
Effect of Water Subcooling to the Saturation Temperature on Boiling Crisis Characteristics during a Rapid Increase in the Heat Release Power M. I. Delov, K. V. Kutsenko, A. A. Lavrukhin, M. I. Pisarevskii, and V. N. Fedoseev National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow, 115409 Russia; e-mail:
[email protected] Received May 12, 2015
Abstract—The experimental results on the effect of water subcooling to the saturation temperature and the thermal exposure time on the maximum allowed energy removed by coolant without the boiling crisis onset are presented. The boiling crisis under subcooling conditions results in cooled surface damage. The results of this study can find application to calculate cooling systems of equipment operating in pulsed mode. DOI: 10.3103/S1068335615080035
Keywords: pulsed heat input, pulse energy, boiling crisis, subcooling to the saturation temperature, water cooling. Introduction. When designing and calculating an energy device operating in pulsed mode and cooled by water (heat exchange equipment in emergency modes, active regions of water-cooled nuclear reactors during reactive accidents, cooling systems of laser mirrors, and others), two main questions arise, which require a comprehensive analysis. What is the time for reaching the cooled surface temperature resulting in its damage? What is the maximum energy which can be transferred to water in this case? It is known that the heat transfer coefficient to heat carrier in quasi-stationary processes significantly increases in passing to the bubble boiling mode; nevertheless, as the heat flux qcrl is reached, the transition to the film mode occurs (boiling crisis). This process is accompanied by a sharp decrease in the coefficient of heat transfer to coolant and an increase in the heat-releasing surface temperature. In this case, the cooled element can be damaged. The probability of such an outcome is especially high under conditions of device cooling by a liquid subcooled to the saturation (boiling) temperature Ts . As the heat release in non-stationary processes increases, the heat flux can significantly exceed qcrl without boiling crisis onset until reaching a certain time interval τcr during which the heat exchange intensity remains sufficiently high. Thus, if the thermal exposure time is shorter than τcr , there is a real possibility of cooling equipment without irreversible consequences. Experimental study. The experiments were performed with the setup [1] allowing the study of heat exchange processes under conditions of a large water volume at atmospheric pressure. As a work area, a platinum wire of the diameter d = 0.1 mm and length l = 25 − 35 mm was used. The overheating ΔT = Th − Tl of the heat-releasing surface over the liquid temperature and the generated heat flux qh on the heater surface were measured as a function of time τ after a sharp increase in the power. The study was performed for various values of the water subcooling to the saturation temperature θ = Ts − Tl . The heat flux removed from the heater surface to liquid was determined by the heat balance equation under the assumption of heater isothermality, q(τ ) = qh (τ ) −
(cρ)h · d d(ΔT (τ )) · , 4 dτ
(1)
where (cρ)h = 2.88 · 106 J/(m3 ·K) is the specific heat capacity of the platinum heater. In the general case, Eq. (1) is written as q(τ ) = qh (τ ) −
(cρ)h · V d(ΔT (τ )) · , S dτ 233
(1a)
234
DELOV et al.
Fig. 1. Experimental time dependences of the (1) generated heat flux and (2) heater overheating in the case of water subcooling to the saturation temperature θ = 10 K (q qcr1 ).
Fig. 2. Experimental time dependences of the (1) generated heat flux, (2) heater overheating, and (3) heat flux removed to liquid in the case of water subcooling to the saturation temperature θ = 10 K (q >> qcr1 ).
where V is the heater volume and S is the heat-release surface area. The absolute error in measuring the time intervals was less than 10−7 s, the total errors in determining the generated heat flux qh (τ ), overheating ΔT (τ ), and removed heat flux q(τ ) are no more than 5%, 10%, and 15%, respectively. Examples of the dependences experimentally determined at subcooling θ = 10 K are shown in Figs. 1 and 2. The dynamic curves can be divided into two types. The first type (Fig. 1) includes curves with temperature oscillations about the average value in the metastable boiling stage from the boiling time point τeb to the crisis onset time τcr corresponding to the beginning of a steady increase in the heater temperature. In this interval, the heat flux removed from the surface q can be considered as, on average, BULLETIN OF THE LEBEDEV PHYSICS INSTITUTE
Vol. 42 No. 8 2015
EFFECT OF WATER SUBCOOLING TO THE SATURATION TEMPERATURE
235
Fig. 3. Dependence of the energy removed to liquid from the wire unit area on the critical time interval: (1) experimental data for saturated water, (2) calculation by the model [1], and (3) calculation by the model [2].
equal to the heat load (q ≈ qh ). This type of curves is reached at low heat fluxes. For the second-type dynamic curves (Fig. 2) obtained at high generated heat fluxes, the heater overheating monotonically increases, and the heat flux q removed to liquid reaches maximum qcr at the time point τcr . The critical time interval τcr reaching of which results in the liquid boiling crisis is the sum of time intervals until the time of liquid boiling on the heating surface τeb and metastable boiling τmb . The first stage is described by nonstationary thermal conductivity equations in the heater and adjacent immobile liquid layer, whose solutions can be used to determine τeb . A more complex problem is the determination of the metastable boiling stage duration. Previously, the authors proposed two models [1, 2] allowing this calculation for liquid at the saturation temperature Ts . The first model [1] is constructed on the assumption that in the region of high heat loads (q qcrl ) the crisis occurs for the time τcr shorter than the time of vapor bubble departure (τd ≈ 20 ms). This model is based on the known law of vapor bubble growth. At low heat fluxes (q qcrl ), when τcr is much longer than the time of vapor bubble departure, the second model is applicable [2]. The second model is based on the heat balance equation taking into account a change in the vapor fraction in the near-wall liquid layer. It is clear that under conditions of liquid subcooling to the saturation temperature the proposed models are not physically validated, since it is difficult to estimate the vapor bubble dynamics under conditions of boiling with subcooling. Based on the available experimental data, the specific energy removed from the heat-release element surface until the boiling crisis onset was calculated as τcr (2) E = q(τ )dτ. 0
Figure 3 shows the dependence of the removed energy on the critical time interval in saturated water. We can see that experimental data are in good agreement with calculations by the models described above. It is clear that the removed energy in subcooled liquid will be always higher than under saturation conditions. Thus, the calculation by the proposed models allows the determination of the lower bound of the maximum energy removed to liquid, which is applicable to the conservative approach to the calculation of nonstationary heat processes. To consider the effect of liquid subcooling on the removed energy, the empirical dependence E(τcr , θ) should be obtained. BULLETIN OF THE LEBEDEV PHYSICS INSTITUTE
Vol. 42 No. 8
2015
236
DELOV et al.
Fig. 4. Dependence of the energy removed to liquid from the wire unit area on the critical time interval: symbols are experimental data and lines are calculations by formula (3).
Figure 4 shows the determined dependence of the removed energy on the time τcr and subcooling θ: k·θ+b , E(τcr , θ) = (A + θ α ) · τcr
(3)
where A = 243 · 103 , exponents a = 2.79, b = 0.58, and k = 0.02. The experimental data are well described by the empirical dependence in the range θ = 10 − 20 K. The obtained dependence for the energy removed to water at atmospheric pressure is universal and can be used for various heat-releasing surfaces. Conclusions. The formula for calculating the energy removed to liquid as a function of the critical time interval and subcooling to the saturation temperature was derived. In the case of pulsed heat transfer at a given pulse duration and a known liquid subcooling, the proposed relation allows the determination of the maximum energy removed to liquid without heat-releasing surface damage. REFERENCES 1. V. I. Deev, H. L. Oo, V. S. Kharitonov, et al., Int. J. Heat Mass Transfer 50, 3780 (2007). 2. V. I. Deev, K. V. Kutsenko, A. A. Lavrukhin, et al., Int. J. Heat Mass Transfer 53, 1851 (2010).
Presented at the 4th International Youth Scientific School-Conference “Current Problems of Physics and Technologies”.
BULLETIN OF THE LEBEDEV PHYSICS INSTITUTE
Vol. 42 No. 8 2015
