Two distinctly different modes of cooling high-temperature bodies in subcooled liquids

Highlights

• Rapid cooling differs principally from rewetting process

• High heat flux arises at the local liquid/solid contact area in film boiling

• Heat sink near 50 MW/m² can provide conditions for the wetted area spreading

Abstract

The paper sequentially substantiates an existence of the two distinct modes of film boiling during quenching the high-temperature bodies in subcooled liquids. Based on the vast investigations of film boiling regularities during cooling high-temperature metallic spheres in different subcooled liquids, the authors of the present paper revealed that among pure liquids, only in subcooled water there are the two distinctly different cooling regimes. According to the approximate physical model developed earlier (2018) by the authors, incipience of the micro-bubble boiling arises, if the local liquid/solid contacts occur between the surface roughness protrusions and the liquid crests of the wavy liquid/vapor interface. At such a contact, near a boundary of the three phases, a huge local heat sink (q_ev) acts. This heat sink is proportional to (σh_lg/ν) and its value explains, in particular, why the fast cooling regime occurs in subcooled water at definite subcoolings, but never in cryogens or fluorocarbons. The model quantitatively predicts influence of the properties of a coolant and a cooled body on the incipience of the fast cooling regime. However, some issues remain open. The present paper considers the results of the numerical studies of a metallic body cooling under effect of the local heat sink q_ev. These studies shed light on some of these issues. The numerical simulation determines realistic values of a heat sink, a period of its action, and a size of the cooled area at the plane surface, which provide the conditions for spreading the wetted area at the surface of a cooled body. According to the simulation, the cooling process predictably occurs more rapidly for metals with lower thermal effusivity and for low-conductive and rather thick coating at the high-conductive metal. The strong effect of very thin low-conductive coatings from Teflon and silica exceeded expectation. At q_ev= 50 MW/m² even 10-μm coating of the porous silica leads to the surface temperature drops larger 500 K during 0.01 s for the both basic metals studied. The results have confirmed that the local heat sink of high intensity, particularly at the modelled roughness protrusions, can provide the conditions of the liquid/wall contacts and spreading of the wetted area at the surface.

Introduction

An interest to the problem of rapid cooling high-temperature bodies in saturated or subcooled liquids grows nowadays. Besides a widely used technology of quenching in metallurgy and in metals treatment [1], this process is very important for cryogenics [2], [3], [4], [5], [6] and for the safety systems of nuclear power plants (NPP) [7], [8], [9], [10], [11], [12], [13]. The quenching technology has a long history from ancient times. Usually, a determined rate of cooling process provides desirable internal structure in a metal part or in its surface layer; in the most cases the maximal rate is preferable in the technology. Water jet cooling allows to achieve very high cooling rates corresponding to heat transfer coefficients (HTC) at the part surface up to 20 kW/(m²K). At the same time, heat transfer mechanisms are commonly beyond an attention of the specialists on the metal science. The authors of the monograph [1] have no doubts that an initial stage of a hot metal quenching is controlled with film boiling. However, they write on the surface rewetting at its temperature T_w =500 °C or liquid/solid contacts at T_w =800 °C, although the critical temperature of water is near 374 °C and at the higher temperature liquid water state is absolutely excluded. Extremely high heat transfer intensity during quenching has no clear explanation and sometimes [14] they say on nucleate boiling in spite of the part temperatures as high as 700-900 °C. Unfortunately, there are very seldom cases of reciprocal citation between the specialists in the quenching technology and in the unsteady heat transfer.

Cryogenics is rather young science field, its practical applications appearing only the previous century. The cooling process is intrinsic for cryogenics, because the ambient temperature of the equipment exceeds greatly the critical temperatures of the practically used cryogens. Enhancement of this process means shortening of its duration and saving of a cryogen. It was revealed long ago [15] that a low-conductivity coating of the metallic surface studied in [2,[4], [5], [6]], strongly effects on the cooling rate. This follows from the well-known solution of the thermal conductance problem that determines the temperature at the boundary of the two semi-infinite bodies with the different initial temperatures at the instance of their contact. In application to the contact of a solid and a liquid, this solution is as follows:

$$T_i=\left(T_w{\epsilon }_w+T_l{\epsilon }_l\right)/\left({\epsilon }_w+{\epsilon }_l\right).$$

This is clear that at the low values of thermal effusivity of the coating, especially at ε_w < ε_l, the surface temperature drops greatly. One can assume that several such contacts can decrease the temperature to the value that corresponds to the rewetting conditions. In the papers [2,3], the experimental results on cooling the copper plate with a flowing film of liquid nitrogen at atmospheric pressure are presented. The rewetting temperature of the surface coated with vacuum greasy is estimated as T_rw≈160 K [2], while at the bare copper surface [3], T_rw≈90 K; the cooling duration (from 190 to 78 K) decreases four times due to low-conductivity coating. This effect is much higher than influence of liquid flow velocity: almost threefold increase of film Reynolds number gave only 15% decrease of the cooling duration of the coated plate. The authors of [4] have obtained the qualitatively similar results in cryogenic cooling the stainless steel tubes of 12.7 mm outer diameter. Varying the LN₂ inlet pressure allowed to study an influence of liquid flow velocities on the cooling process. The experiments with the bare tube inner surface showed rather small effect of this parameter: at Re ≈63,000, transition from film boiling to the transient one occurred at T_w= T_tr =124 K and at Re ≈19,500, at 118 K. This temperature measured at the outside tube surface was determined on a sharp slope increase of the cooling curve (a thermogram) and was defined as the Leidenfrost temperature (Leidenfrost point, LFP). The analogous experiments were conducted on the tubes with Teflon thin layers coating; one to four layers, each of ∼15 μm in thickness being studied. Low thermal conductivity coating greatly shortened the cooling duration (from 280 K until the nitrogen saturation temperature), mainly due to increase of the LFP temperature and decrease of the time of the film boiling regime. At the highest inlet pressure (∼0.7 MPa), 4-layers coating led to shortening the duration of film boiling to 0.5 s, the LFP temperature was defined as T_Leid =263 K (for 1-layer coating the corresponding values were ∼7 s and 180 K). Low thermal conductivity coating, increasing greatly the LFP, leads simultaneously to increase of the thermal resistivity from the cooled body to the coolant. In the paper [4], it is pointed that there exists a definite optimal thickness of isolating layer, corresponding to maximal efficiency of coolant amount using.

In the papers [5,6], the metallic cylindrical rods with different coatings were cooled in LN₂ pool. An evident optimal thickness of the Teflon coating δ_c=90 μm that corresponds to the fastest cooling of the stainless steel (SS) rod, was revealed in the experiments [6], at larger thickness (up to 215 μm) the cooling duration became longer, although the T_Leid continues to grow. The other coating with the higher thermal conductivity (yttria-stabilized zirconia) manifested the monotonic shortening of the cooling duration with its thickness increase from 135 up to 500 μm. In the both papers [5] and [6], a reasonable remark is made on slight effect of a surface wettability on the quenching process in LN₂ as this coolant features with high wettability to any solid surfaces. The experiments with the aluminum alloy rod in [5] have found that the main reason of heat transfer enhancement is the low thermal conductivity of coatings. An absolute wettability and large roughness of the surface etched with HCl (hydrochloric acid) gave increase of the LFP temperature to 126 K compared with 112 K at the baseline case of polished surface, the chilldown duration being less only by 10%. Anodic aluminum oxidation (AAO) surface appears to be the most effective way of the cooling enhancement, and the low thermal conductivity of the Al₂O₃ porous layer of 15-μm thickness being the main reason of the effect. At the same time, the effective thermal conductivity of AAO coating with the open porosity, λ_eff, according to [5], practically coincides with λ_eff of raw anodic aluminum oxidation (RAAO) coating without pores opening. However, T_Leid in the latter was lower by 74 K (138 K and 212 K correspondingly). The authors’ explanation of this phenomenon by means of the “critical pinning state of liquid/vapor interface on the nanopores” at the open porosity raises doubts, because in the closed porosity the porous space is, probably, also gas filled. The factual difference of these coatings is that the outer surface of the RAAO coating is thin, but continuous one with the higher conductivity than λ_eff. Besides, in the AAO coating there exists a possibility of the direct cooling of the carcass of the porous layer. In any case, independently on actual mechanisms of the phenomenon discussed, the authors’ idea on the low thermal conductivity of the AAO coating as a main reason of the chilldown enhancement deserves a support. In its favor, the similar influence of the Teflon coating evidences: the LFP temperatures for these two cases in [5] are close, 194 and 212 K.

In nuclear energy, the safety requirements are always of the first importance. Numerous experimental studies simulated the different power-cooling mismatch accidents (PCM) have been conducted in the XX-th century [7]. The heavy accidents in 1979 (USA), 1986 (USSR), and 2011 (Japan) have shown that an extreme case of the loss-of-coolant accident (LOCA) seemed initially rather unrealistic, has to be included in scenario of design-basic accident (DBA) as very dangerous, but possible event. After the accident at Fukushima-Daiichi, the new direction of researches in the field, connected with development of accident tolerant fuels (ATF), arose. The question is the prevention of high-temperature steam-zirconium reaction with hydrogen generation at the possible accident in light water reactors [12,13]. In the papers [8], [9], [10], [11], [12], [13], the experimental results on quenching the zirconium alloys and ATF materials surfaces are presented. Since the cooling rate depends mainly on the duration of the film boiling regime, these researches focus on the increase of the LFP temperature. The authors of the papers [8,9] have obtained super-hydrophilic surface on a zirconium (Zr-702) rod or a sphere (completely wetted surface, CWS) by means of anodic oxidation and studied influence of this surface modification on quenching in saturated and subcooled water. According to [8], in subcooled water even at low subcooling ΔT_sub =15 K “direct quenching” without film boiling at the zirconium rod with CWS has been obtained at the initial rod temperature T_w = 800 °C. At the bared zirconium surface (BZS) such a cooling regime was also observed, but at the higher subcooling ΔT_sub =60 K. Two questions arise on these results. The first one concerns the absence of film boiling at T_w = 800 °C, whether the authors assume a possibility of direct liquid/solid contact at this temperature? In the paper [10] by the same scientific team, the experimental and the calculated according to Eq. (1) values of minimum film-boiling temperature T_mfb during quenching the ATF material FeCrAl and the oxidized Zry-4 were higher 500 °C, i.e. much higher than T_cr for water. However, this is strictly proved theoretically and confirmed experimentally [16] that any liquid at the temperature of homogeneous nucleation T_hom (or at the almost coincident attainable limiting temperature T_lim) transfers into vapor practically instantly, the characteristic time of the phase transition being 10⁻¹⁰-10⁻⁹ s.

The second question relates influence of wettability on the LFP. The phenomena of wettability or wickability have a physical content, if and only if a liquid phase exists. Therefore, large doubts arise, when the wickability is considered as an important factor in the quenching process. This concerns, in particular, several new studies [17], [18], [19], where the two different sub-regimes of transition boiling are discussed. This idea appeared in 1982 [20] and concerned to an ordinary boiling curve, when the wall superheat varies between ΔT_cr1 (at q= CHF) and ΔT_cr2 = T_mfb-T_s (at q_min) correspondingly. In this temperature range, liquid/solid contacts do not contradict thermodynamics, and the above sub-regimes differ with frequency and duration of the contacts. In the researches of [17,19], the liquid/surface contacts at quenching occurred at the initial T_w = 800 °C, when the superhydrophilic surface was created by coating of three layers of silica nanoparticles, in [18], at 700 °C, when the superhydrophilic surface was obtained by chemical etching in HF acid solution. The fact of these contacts does not cause any doubts, however, their probable reason is low thermal conductivity of the coating, and their local temperature at the contact points cannot exceed T_lim. We have detail discussed this problem in [21], in a special section “The Leidenfrost phenomenon and the lower boundary of film boiling”. In particular, we have cited an important statement of the Japanese colleagues [22] that the local (and instantaneous) surface temperature must be less than T_hom in order to provide the conditions for the direct liquid/solid contact, while the average surface temperature can be essentially higher during such the contacts. Factually, when one discusses an increase of the LFP, this relates to the average or to some effective parameter. It is interesting that the several authors of the papers [17], [18], [19] in the work [23] demonstrate clear understanding of this. Coating of the brass sphere surface with porous structure of CuO cones of 100-μm height gives increase of T_mfb from 250 to 600 °C in saturated water. However, this relates to the baseline sphere surface, i.e. to the temperature of the base of the cones; the authors of [23] showed that the cones top temperature was approximately equal to 330 °C, i.e. close to T_hom of water.

Nevertheless, in many cases one meets some inconsistencies in interpretation of the quenching phenomena. In paper [24], an original way of LFP temperature increase by means of electrostatic suppressing of the vapor layer was studied. Constant voltage of 65 V between a liquid drop and the solid surface caused appearing of liquid fingers protruded the vapor film toward the surface, at the higher voltage, the film deceased, and wetting occurred at T_w, higher 500 °C for water and isopropanol droplets. The authors are sure that liquid/solid contacts exist at this temperature, although this contradicts the strict thermodynamics regularities and the real task is to explain a reason of the local surface temperature decrease. This is especially so, because the electrostatic suppression of the vapor film under a droplet of dielectric liquid FC-40 does not occur; the explanation of this anomaly given in [24] seems to be unconvincing since the effect considered was observed with the other dielectric, isopropanol. In the frequently cited paper [25], the results of the previous works [26,27] are considered. The authors studied the separate effects of surface roughness, wettability, and porosity on boiling crisis and on the LFP temperature of water droplets. Two important results have to be noticed. The first one is the observed in [26] liquid filaments connecting the droplet to the hydrophilic surface with micro-posts. In this relation, the papers [25,26] demonstrate the results, similar to those in the paper [24], since in the both cases the LFP temperature was much higher than the critical one of water. However, in the paper [25], there is an essential remark that the values of LFP are “the nominal temperatures of the test surface”, while “the local temperature at which the liquid–solid contact occurs must be below the critical point”. One can add (to this second result of [24], [25], [26]) that the local temperature must be even lower than T_lim.

In the paper [11], a possibility of instantaneous liquid/solid contacts even in the saturated liquid film boiling regime is proved. The contacts become possible due to successive liquid approaches to the surface, which can decrease its local temperature below T_lim; the surface roughness protrusions or any spots with low thermal conductance present the most convenient locations for such contacts. This allows explaining the strong effect of the surface oxidation and roughness on transient boiling heat transfer of Zircaloy-4 surfaces during cooling in saturated and subcooled water. The authors of [11] have solved the 2D unsteady heat conduction problem to confirm the hypothesis; in the absence of reliable information on heat flux during liquid/solid contacts and on duration of these contacts, they have used the experimental results on water drops heat transfer at a hot surface. Certainly, this is a different process compared with the real cooling of the metallic rodlets in water, therefore, one can say only about a qualitative confirmation of the hypothesis.

Returning to the rather old paper [7], this is noteworthy that the authors point out a necessity to discriminate as distinctly different phenomena quenching and rewetting. Rewetting supposes appearing a boundary of three phases (solid, liquid, and vapor), therefore the interface temperature must be less than the attainable limiting temperature T_lim (in thermodynamics, this temperature corresponds to the spinodal). In quenching of metallic bodies, a ratio of thermal effusivities ε_w/ε_l >> 1, so that the rewetting temperature according to Eq. (1) practically coincides with T_lim, and the authors of [7] state, “For most applications, the maximum rewet temperature can be considered synonymous with the Leidenfrost temperature”. This statement fully agrees with the position of the authors of the present paper [21], where we have written that physically founded Leidenfrost temperature T_Leid≈T_lim≈T_hom. As for the quench temperature, it is defined in [7] as the surface temperature at the onset of rapid cooling; the authors note that this definition is rather arbitrary and proposed to accept a condition ∂T_w/∂t ≥ 200 K/s as the onset of rapid cooling. They inform on the quench temperature higher 1000 °C measured in the experiments on cooling the Zircaloy rods in subcooled water forced flow. As is clear from the previous analysis, namely the onset of rapid cooling is often accepted as the LFP temperature. The discussed distinction between the LFP and the quenching temperature is not only a question of the “pure theory”, but is also important from a practical view.