Critical heat flux of forced convection boiling in an oscillating acceleration field — I. General trends

The influence of periodically varying acceleration on critical heat flux (CHF) of Freon-113 flowing upward in a uniformly heated vertical annular channel has been studied experimentally. The freon loop was oscillated vertically to determine the ratio of CHF in the oscillating acceleration field to the corresponding stationary value. The amplitude of inlet flow oscillation induced by variation of acceleration, which causes early CHF, is proportional to the acceleration amplitude. The dependence of inlet flow rate on the oscillating acceleration decreases with increasing inlet subcooling, and no oscillation of inlet flow is observed in the case of negative exit quality (subcooled boiling). Nevertheless the degradation of CHF is more remarkable in the low quality region. This result suggests the necessity to introduce an other mechanism of early CHF than flow oscillation.     

Critical heat flux of forced convection boiling in an oscillating acceleration field—II. Contribution of flow oscillation

Critical heat flux (CHF) with forced convection generally decreases under an oscillating acceleration condition. Contribution of flow oscillation on the decrease in CHF was investigated experimentally and theoretically. The experiments were performed with a Freon-113 boiling loop. The results showed that, in the high exit quality region deteriotation of CHF could almost wholly be attributed to the variation of inlet flow rate induced by motion. The amplitude of flow oscillation for a given acceleration variation could be predicted from a transfer function derived with linearization technique. Prediction of the transient CHF on the basis of “local-conditions hypothesis” gave conservative values.     

Two-phase flow regimes and mechanisms of critical heat flux under subcooled flow boiling conditions

A literature review of critical heat flux (CHF) experimental visualizations under subcooled flow boiling conditions was performed and systematically analyzed. Three major types of CHF flow regimes were identified (bubbly, vapor clot and slug flow regime) and a CHF flow regime map was developed, based on a dimensional analysis of the phenomena and available experimental information. It was found that for similar geometric characteristics and pressure, a Weber number (We)/thermodynamic quality (x) map can be used to predict the CHF flow regime.Based on the experimental observations and the review of the available CHF mechanistic models under subcooled flow boiling conditions, hypothetical CHF mechanisms were selected for each CHF flow regime, all based on a concept of wall dry spot overheating, rewetting prevention and subsequent dry spot spreading. Even though the selected concept has not received much attention (in term or theoretical developments and applications) as compared to other more popular DNB models, its basis have often been cited by experimental investigators and is considered by the authors as the “most-likely” mechanism based on the literature review and analysis performed in this work. The selected modeling concept has the potential to span the CHF conditions from highly subcooled bubbly flow to early stage of annular flow and has been numerically implemented and validated in bubbly flow and coupled with one- and three-dimensional (CFD) two-phase flow codes, in a companion paper. [Le Corre, J.M., Yao, S.C., Amon, C.H., in this issue. A mechanistic model of critical heat flux under subcooled flow boiling conditions for application to one and three-dimensional computer codes. Nucl. Eng. Des.].     

A mechanistic critical heat flux model for wide range of subcooled and low quality flow boiling

A mechanistic model to predict a critical heat flux (CHF) over a wide operating range in the subcooled and low quality flow boiling has been proposed based on a concept of the bubble coalescence in the wall bubbly layer. The conservation equations of mass, energy and momentum, together with appropriate constitutive relations, are solved analytically to derive the CHF formula. The model is characterized by an introduction of the drag force due to wall-attached bubbles roughness in the momentum balance, which determines the limiting transverse interchange of mass flux crossing the interface of the wall bubbly layer and core. Comparison between the predictions by the proposed model and the experimental CHF data shows good agreement over a wide range of parameters for both light water and fusion reactors operating conditions. The model correctly accounts for the effects of flow variables such as pressure, mass flux and inlet subcooling as well as geometry parameters.     

Influence of heat input waveform on transient critical heat flux of subcooled water flow boiling in a short vertical tube

The transient critical heat fluxes (CHFs) of the subcooled water flow boiling for ramp-wise heat input [Q = αt, α = 6.21 × 10⁸ to 1.63 × 10¹² W/m³ s, (q ≅ 1.08 × 10⁷ to 6.00 × 10⁷ W/m²)] and stepwise one [Q = Q_s, Q_s = 0 W/m³ at t = 0 s and Q_s = 2.95 × 10¹⁰ to 7.67 × 10¹⁰ W/m³ at t > 0 s, (q = 0 W/m² at t = 0 s and q ≅ 1.61 × 10⁷ to 3.87 × 10⁷ W/m² at t > 0 s)] with the flow velocities (u = 4.0-13.3 m/s), the inlet subcoolings (ΔT_sub,in = 86.8-153.3 K) and the inlet pressures (P_in = 742.2-1293.4 kPa) are systematically measured by an experimental water loop comprised of a pressurizer. The SUS304 tubes of inner diameters (d = 3, 6 and 9 mm), heated lengths (L = 33.15, 59.5 and 49.3 mm), L/d (=11.05, 9.92 and 5.48), and wall thickness (δ = 0.5, 0.5 and 0.3 mm) respectively with the rough finished inner surface (surface roughness, Ra = 3.18 μm) are used in this work. The experimental errors in the subcooling measure and the pressure one are ±1 K and ±1 kPa, while in the heat flux it is ±2%. The transient CHF data for the ramp-wise heat input and the stepwise one are compared with those for the exponentially increasing heat input (Q = Q₀ exp(t/τ), τ = 16.82 ms to 15.52 s) previously obtained and the dominant variables on transient CHF for heat input waveform difference are confirmed. The transient CHF data are compared with the values calculated by the steady state CHF correlations against inlet and outlet subcoolings, and the applicability of steady state CHF correlations is confirmed extending its possible validity for the reduced time, ω_p, down to 800 ms. The transient CHF data are compared with the values calculated by the transient CHF correlations against inlet and outlet subcoolings, and the influence of heat input waveform on transient CHF is clarified based on the experimental data for the ramp-wise heat input, the stepwise one and the exponentially increasing one. The dominant mechanisms of the subcooled flow boiling critical heat flux for the ramp-wise heat input, the stepwise one and the exponentially increasing one are discussed.     

Critical heat fluxes of subcooled water flow boiling in a short vertical tube at high liquid Reynolds number

The steady state critical heat fluxes (CHFs) and the heat transfer of the subcooled water flow boiling for the flow velocities (u = 17.2-42.4 m/s), the inlet subcoolings (ΔT_sub,in = 80.9-147.6 K), the inlet pressures (P_in = 812.1-1181.5 kPa) and the exponentially increasing heat input (Q₀ exp(t/τ), τ = 8.5 s) are systematically measured by the experimental water loop comprised of a new multi-stage canned-type circulation pump with high pump head. The SUS304 test tube of inner diameter (d = 6 mm), heated length (L = 59.5 mm), L/d = 9.92 and wall thickness (δ = 0.5 mm) with surface roughness (Ra = 3.18 μm) is used in this work. The steady state CHFs of the subcooled water flow boiling for the flow velocities ranging from 17.2 to 42.4 m/s are clarified. The steady state CHFs are compared with the values calculated by our transient CHF correlations against outlet and inlet subcoolings based on the experimental data for the flow velocities ranging from 4.0 to 13.3 m/s. The influence of flow velocity at high liquid Reynolds number on the subcooled flow boiling CHF is investigated in detail and the widely and precisely predictable correlations of the transient CHF correlations against outlet and inlet subcoolings in a short vertical tube are derived based on the experimental data at high liquid Reynolds number. The transient CHF correlations can describe the subcooled flow boiling CHFs for the wide range of flow velocities at high liquid Reynolds number obtained in this work within ±15% difference.     

Film boiling heat transfer from a vertical cylinder in forced flow of liquids under saturated and subcooled conditions at pressures

Forced convection film boiling heat transfer on a vertical 3-mm diameter and 180-mm length platinum test cylinder located in the center of the 40-mm inner diameter test channel was measured. Saturated water, and saturated and subcooled R113 were used as the test liquids that flowed upward along the cylinder in the test channel. Flow velocities ranged from 0 to 3 m s⁻¹, pressures from 102 to 490 kPa, and liquid subcoolings for R113 from 0 to 60 K. The heat transfer coefficients for a certain pressure and liquid subcooling are almost independent of flow velocity and of a vertical position on the cylinder for the flow velocities lower than ≈1 m s⁻¹ (the first range), and they become higher for the velocities higher than ≈1 m s⁻¹ (the second range). Slight dependence on a vertical position being nearly proportional to z^−1/4, where z is the height from the leading edge of the test cylinder, exists for the flow velocities in the second range. The heat transfer coefficients at each velocity in the first and second ranges are higher for higher pressure and liquid subcooling. Correlation for the forced convection film boiling heat transfer with radiation contribution on a vertical cylinder was derived by modifying an approximate analytical solution for a two-phase laminar boundary layer model to agree better with the experimental data. It was confirmed that the experimental data of film boiling heat transfer coefficients in water and R113 were described by the correlation within ±20% difference.     

A mechanistic model of critical heat flux under subcooled flow boiling conditions for application to one- and three-dimensional computer codes

Based on a review of visual observations at or near critical heat flux (CHF) under subcooled flow boiling conditions and consideration of CHF triggering mechanisms, presented in a companion paper [Le Corre, J.M., Yao, S.C., Amon, C.H., 2010. Two-phase flow regimes and mechanisms of critical heat flux under subcooled flow boiling conditions. Nucl. Eng. Des.], a model using a two-dimensional transient thermal analysis of the heater undergoing nucleation was developed to mechanistically predict CHF in the case of a bubbly flow regime. The model simulates the spatial and temporal heater temperature variations during nucleation at the wall, accounting for the stochastic nature of the boiling phenomena. It is postulated that a high local wall superheat occurring underneath a nucleating bubble at the time of bubble departure can prevent wall rewetting at CHF (Leidenfrost effect). The model has also the potential to evaluate the post-DNB heater temperature up to the point of heater melting.Validation of the proposed model was performed using detailed measured wall boiling parameters near CHF, thereby bypassing most needed constitutive relations. It was found that under limiting nucleation conditions; a peak wall temperature at the time of bubble departure can be reached at CHF preventing wall cooling by quenching. The simulations show that the resulting dry patch can survive the surrounding quenching events, preventing further nucleation and leading to a fast heater temperature increase. The model was applied at CHF conditions in simple geometry coupled with one-dimensional and three-dimensional (CFD) codes. It was found that, within the range where CHF occurs under bubbly flow conditions (as defined in Le Corre et al., 2010), the local wall superheat underneath nucleating bubbles is predicted to reach the Leidenfrost temperature. However, a better knowledge of statistical variations in wall boiling parameters would be necessary to correctly capture the CHF trends with mass flux (or Weber number).     

Critical heat flux of oxidized zircaloy surface in saturated water pool boiling

In the present experimental study, the critical heat flux (CHF) of an oxidized zircaloy surface and its enhancement were investigated during saturated water pool boiling at atmospheric pressure. Three kinds of zircaloy specimens, oxidized at three different temperature conditions (i.e., 300, 450, and 600 °C), were prepared with a non-treated (i.e., fresh) zircaloy surface. The surfaces of the test specimens were characterized by an energy dispersive spectroscopy analysis, scanning electron microscopy image, and water contact angle measurement. The oxidized surface (OS) specimens increased the CHF, which could be because the oxidized surface improves the surface wettability (i.e., decreases the water contact angle). The OS specimens showed the similar water contact angles, and their CHF values became almost the same. In the present experimental conditions, the water contact angle could be considered as a reasonable parameter to explain the CHF data of test specimens. The CHF enhancement of the OS specimens was about 40%, as compared with the non-treated specimen, and interestingly, it was a comparable value to that of the specially treated zircaloy surfaces of the previous report, for a similar water contact angle condition. This implies that the oxidation process used in this work can be a simple, convenient, and cost-effective way to improve the CHF of the zircaloy surface. Using the present experimental data, the previous CHF correlations were assessed and discussed. Among the correlations tested, Kandlikar model best fitted the present CHF measurement data and enhancement factors.     

Experimental investigation of local two-phase flow parameters of a subcooled boiling flow in an annulus

As a series of subcooling boiling flow tests, local two-phase flow parameters were obtained at SUBO (subcooled boiling) test facility under steam–water flow conditions. The test section is a vertical annulus of which the axial length is 4.165 m with a heater rod at the center of a channel. The inner and outer diameters of the test section and the heater rod are 35.5 mm and 9.98 mm, respectively. The test was performed by a two-stage approach. Stage-I for the measurement of local bubble parameters has been already done (Yun et al., 2009). The present work focused on the stage-II test for the measurement of local liquid parameters such as a local liquid velocity and a liquid temperature for a given flow condition of stage-I. A total of six test cases were chosen by following the test matrix of stage-I. The flow conditions are in the range of the heat flux of 370–563 kW/m², mass flux of 1110–2100 kg/(m² s) and inlet subcooling of 19–31 °C at pressure condition of 0.15–0.2 MPa. From the test, local liquid parameters were measured at 6 elevations along the test section and 11 radial locations of each elevation in addition to the previously obtained local void fraction, interfacial area concentration, Sauter mean diameter and bubble velocity. The present subcooled boiling (SUBO) data completes a data set for use as a benchmark, validation and model development of the Computational Fluid Dynamics (CFD) codes or existing safety analysis codes.     

Critical heat flux in a vertical tube at low and medium pressures. Part II — new data representation

An analysis of the physical processes taking place in a dispersed-annular flow which govern dry-out type CHFs has been carried out. The analysis has shown that the number of variables required to describe the critical phenomena can be reduced by the introduction of a new parameter: the length over which dispersed-annular flow takes place, L_dan. In this case only, for a given tube diameter, pressure and mass flux, the critical heat flux may be expressed in terms of a single variable: L_dan. A correlation which may be used to determine this length has also been developed. The representation of the CHF data obtained at low pressures in terms of the coordinate system (L_dan, q″_cr) has shown that the dispersion of the data about the regression curves is considerably reduced as compared with the traditional presentation of the critical heat flux as a function of the thermodynamic quality at the end of the heated length.     

Characteristics of the local bubble parameters of a subcooled boiling flow in an annulus

An experimental study on the subcooled boiling phenomena was carried out in the SUBO (SUbcooled BOiling) test facility under steam-water flow condition. The test section is a vertical annulus of which axial length is 4.165 m with a heater rod at the center of a channel. The inner and outer diameters of the test section and the heater rod are 35.5 mm and 9.98 mm, respectively. For the measurement of the local bubble parameters, double sensor optical fiber probes were applied at six elevations along the test channel. Among them, one is installed in the unheated region which is located downstream of the heated section for the measurement of bubble condensation. A total of six test cases was chosen for the parametric study of the heat flux of 370-563 kW/m², mass flux of 1110-2100 kg/(m² s) and inlet subcooling of 19-31 K at pressure condition of 0.15-0.2 MPa. From the test, local void fraction, interfacial area concentration, Sauter mean diameter and bubble velocity were measured at 11 radial locations at each elevation. The measured data shows well development and propagation of the bubble parameters along the test channel. The present data is expected to be suitable for a benchmark, validation and model development of the CFD codes or existing safety analysis codes.     

Critical heat flux under choking flow conditions: Part II – Maximum values of flow parameters attained under choking flow conditions

Under conditions of forced convective boiling at low pressures and high mass fluxes, beyond a certain quality, choking flow may occur at the exit of a heated channel. An experimental investigation carried out by Olekhnovitch et al. (Olekhnovitch, A., Teyssedou, A., Tye, P., Champagne, P., 2000. Critical heat flux under choking flow conditions. Part I — Outlet pressure fluctuations. Nucl. Eng. Des., this issue) has shown that the occurrence of choking flow does not radically influence the values of the critical heat flux (CHF). However, once the choking flow conditions have occurred, for a given mass flux and quality, the outlet pressure cannot be lowered below a certain value that is fixed by the flow itself. A model that allows this pressure to be determined and which must be used in conjuction with correlations for the prediction of the CHF is presented.     

Letter to the editor on “Evaluation of subcooled critical heat flux correlations for tubes with and without internal twisted tapes” by F. Inasaka and H. Nariai and “Consideration of CHF margin prediction by subcooled or low quality CHF correlations” by P. Hejzlar and N.E. Todreas

Some comments are presented concerning CHF correlations which have the property MCHFR = MCPR and on the limitations of our knowledge of how to apply such models to three dimensional situations and rapid transients.     

Reduction of heat flux on divertor plates by remote radiative cooling in doublet III

Using a single null divertor configuration, heat flux intensity and its profile on the divertor plates as a function of plasma current and density were measured with an infrared camera and thermocouples. The vertical width of the heat flux on the divertor plates 2λ is ≈ 10 cm at the lower separatrix and is ≈ 5.5 cm at the upper separatrix. A diffusion coefficient D which is obtained from the measurement of the diffusion length across the scrape-off field lines is roughly proportional to and its magnitude is on the order of Bohm diffusion. The heat flux on the plates decreases by more than a factor of 5 with increasing electron density in the main plasma and is much smaller than that on the limiters in non-diverted plasmas. Only 3% of ohmic input power goes into the divertor plates at high density of the main plasma, while ≈ 20% goes in at low density. The decrease of heat flux is in good agreement with the increase of radiation loss in the divertor region. The heat flux on the divertor plates can be reduced by remote radiative cooling in high density discharges.     

竖直矩形窄流道内过冷沸腾汽泡生长特性及对换热的影响

在一个大气压下以水为工质研究了竖直矩形窄流道内过冷沸腾的汽泡生长特性。采用Laplace数(La)和时间因子(ξ)无量纲化汽泡半径和汽泡生长时间,得到了不同工况下的无量纲汽泡生长曲线。通过分析质量流速和热流密度变化对无量纲汽泡生长的影响,发现增加质量流速会抑制汽泡生长;增加热流密度则会促进汽泡生长。汽泡的生长行为会严重影响核态沸腾换热系数hNB,从而影响总沸腾两相流动换热系数htp。采用与雷诺数(Re)相关的无量纲时间(t*)的1/3次方模型来预测无量纲汽泡生长,发现此模型能较好地预测本研究中所得到的无量纲汽泡生长数据。     

The correlation of the experimental data on critical heat loads in forced flow of water heated below the boiling temperature

At low pressures, theory predicts a simplification of the similarity-parameter equation proposed by the writer [2] on the basis of a correlation of the experimental data on critical thermal loads in forced flow of water not heated to boiling, in the pressure range 100–210 atmos.It is shown that it is possible to apply the previously proposed similarity-parameter equation over a wider range of pressures, namely 35–210 atmos.Furthermore an analysis of the published experimental data onq _cr at low pressures confirms the theoretical conclusion about a degeneration of the functional connections between the parameter to be determined and the two determining parameters at water pressures close to atmospheric pressure, owing to which the similarity-parameter equation for this case takes a considerably simpler form. A computational formula obtained on the basis of this equation is recommended for the pressure range 1–15 atmos.O. L. Peskov, N. D. Sergeev, Z. F. Deryugin, and N. A. Gushchina took part in the taking of the measurements and the analysis of the data.