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.     

Transition flow boiling heat transfer to water in a vertical annulus

Transition boiling heat transfer coefficients for water at 25–30 psia flowing upward at low velocities have been obtained Hot mercury, flowing on the inside of a tube with a 0.54 in. o.d. served as the heat source. Water flowed in the annular space between the heat source and an outer glass tube having a 1 in. dia. Thermocouples placed at several elevations within the mercury stream allowed the rate of heat transfer to be determined. The heat transfer coefficients appear consistent with other transition boiling data providing an appropriate allowance is made for the reduction in critical heat flux at high void fractions.     

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.     

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。     

A flow boiling critical heat flux correlation for water and Freon-12 at low mass fluxes

An empirical correlation has been developed for calculating critical heat flux (CHF) at low mass fluxes for vertical upflow in uniformly heated tubes. The correlation is based upon dimensionless groups. It compares favourably with experimental CHF data for both Freon-12 and pressurized water. When solved iteratively in conjunction with the heat balance equation, an overall mean ratio of predicted to experimental CHF of 0.986 was obtained with a root means square (r.m.s.) error of 7.0%, for the 233 low flow rate data sets examined.The boundary between the high flow rate correlation developed in earlier work and the proposed low flow rate correlation can be specified by a dimensionless factor δ₁. For values of δ₁ greater than 0.07, the low flow correlation is valid whereas for values less than 0.07 the high flow correlation applies.Development of this correlation and a means of defining its range of validity enables the prediction of CHF levels to be made over an increased range of coolant flow conditions. This is important in the analysis of postulated loss-of-coolant accidents in water-cooled nuclear reactors.     

Critical heat flux data in a vertical tube at low and medium pressures

AECL Research and École Polytechnique have been cooperating on the validation of the critical heat flux (CHF) look-up table (D.C. Groeneveld et al., Heat Transfer Eng. 7(1–2) (1986) 46–62). For low and medium pressures the values in the table have been obtained by extrapolation and curve fitting; therefore, errors could be expected. To reduce these possible extrapolation errors, CHF experiments are being carried out in water cooled 8 mm internal diameter (ID) tubes, at conditions where the data are scarce. This paper presents some of the experimental CHF data obtained for vertical up flow in an 8 mm ID test section, for a wide range of exit qualities (5–70%) and the exit pressure ranging from 5 to 30 bar. The experiments were carried out for heated lengths of 0.75, 1, 1.4 and 1.8 m. In general, the collected data show parametric trends similar to those described in the open literature. However, it was observed that for low pressure conditions CHF depends on the heated length; this dependence begins to disappear for exit pressure of about 30 bar. The CHF data have also been compared with predictions of well-known correlations (L. Biasi et al., Energia Nucl. 14(9) (1967) 530–536; R. Bowring, Br. Report AEEW-R789, Winfrith, UK, 1972; Y. Khatto and H. Ohno, Int. J. Heat Mass Transfer 27 (1984) 1641–1648) and those of the look-up table given by Groeneveld et al. For low pressures and low mass fluxes the look-up table seems to yield better predictions of the CHF than the correlations. However, for medium pressures and mass fluxes the correlations perform better than the look-up table; among those tested, Katto and Ohno's correlation gives the best results.     

An integral equation model for critical heat flux at subcooled and low quality flow boiling

A new theoretical model of critical heat flux (CHF) is developed for the flow boiling condition from bubble-detached to low quality range. The CHF condition is postulated to occur when the superheated liquid layer on the heated wall, which is formed under the bubbly layer from the point of the onset of significant void generation, is depleted due to the evaporation along the heated length. The model shows a very promising agreement with the uniformly heated round tube data for both water and refrigerants by simply applying well-known constitutive relationships without any tuning constant for the CHF data. The significance of the proposed model in unifying the existing models is also discussed.     

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.].     

Subcooled boiling heat transfer in a short vertical SUS304-tube at liquid Reynolds number range 5.19 × 10 to 7.43 × 10

The subcooled boiling heat transfer and the steady-state critical heat fluxes (CHFs) in a short vertical SUS304-tube for the flow velocities (u = 17.28-40.20 m/s), the inlet liquid temperatures (T_in = 293.30-362.49 K), the inlet pressures (P_in = 842.90-1467.93 kPa) and the exponentially increasing heat input (Q = Q₀ exp(t/τ), τ = 8.5 s) are systematically measured by the experimental water loop comprised of a multistage canned-type circulation pump with high pump head. The SUS304 test tubes of inner diameters (d = 3 and 6 mm), heated lengths (L  =  33 and 59.5 mm), effective lengths (L_eff = 23.3 and 49.1 mm), L/d (=11 and 9.92), L_eff/d (=7.77 and 8.18), and wall thickness (δ = 0.5 mm) with average surface roughness (Ra = 3.18 μm) are used in this work. The inner surface temperature and the heat flux from non-boiling to CHF are clarified. The subcooled boiling heat transfer for SUS304 test tube is compared with our Platinum test tube data and the values calculated by other workers’ correlations for the subcooled boiling heat transfer. The influence of flow velocity on the subcooled boiling heat transfer and the CHF is investigated into details and the widely and precisely predictable correlation of the subcooled boiling heat transfer for turbulent flow of water in a short vertical SUS304-tube is given based on the experimental data. The correlation can describe the subcooled boiling heat transfer obtained in this work within 15% difference. Nucleate boiling surface superheats for the SUS304 test tube become very high. Those at the high flow velocity are close to the lower limit of Heterogeneous Spontaneous Nucleation Temperature. The dominant mechanisms of the flow boiling CHF in a short vertical SUS304-tube are discussed.     

Low-quality and subcooled film boiling of water at elevated pressures

Stable film boiling heat transfer data have been obtained in an 8.9 mm ID tube at pressures from 2 to 9 MPa. These data were obtained at low-quality and subcooled conditions, over a mass flux range of 0.11 to 2.75 Mg m⁻² s⁻¹. Excessive film boiling surface temperatures were avoided by using the hot patch technique. Contrary to the high-quality data, the low-quality data showed a decrease in heat transfer coefficient with an increase in quality. The film boiling data were compared with existing film boiling correlations. None of these were found to be satisfactory.     

Critical heat flux of water in vertical round tubes at low pressure and low flow conditions

An experimental study on critical heat flux (CHF) has been performed for water flow in vertical round tubes under low pressure and low flow (LPLF) conditions to provide a systematic data base and to investigate parametric trends. Totally 513 experimental data have been obtained with Inconel-625 tube test sections in the following conditions: diameter of 6, 8, 10 and 12 mm; heated length of 0.31.77 m; pressure of 106951 kPa; mass flux of 20277 kg m⁻² s⁻¹; and inlet subcooling of 50654 kJ kg⁻¹, thermodynamic equilibrium critical quality of 0.3231.251 and CHF of 1081598 kW m⁻². Flow regime analysis based on Mishima & Ishii’s flow regime map indicates that most of the CHF occurred due to liquid film dryout in annular-mist and annular flow regimes. Parametric trends are examined from two different points of view: fixed inlet conditions and fixed exit conditions. The parametric trends are generally consistent with previous understandings except for the complex effects of system pressure and tube diameter. Finally, several prediction models are assessed with the measured data; the typical mechanistic liquid film dryout model and empirical correlations of (Shah, M.M., 1987. Heat Fluid Flow 8 (4), 326–335; Baek, W.P., Kim, H.G., Chang, S.H., 1997. KAIST critical heat flux correlation for water flow in vertical round tubes, NUTHOS-5, Paper No. AA5) show good predictions. The measured CHF data are listed in Appendix B for future reference.     

Critical heat flux of forced convection boiling in an oscillating acceleration field — III. Reduction mechanism of CHF in subcooled flow boiling

To investigate the effect of variation in acceleration on the critical heat flux (CHF) in subcooled flow boiling, a photographic study was made. The test section was an internally heated vertical annulus with a glass shroud, in which Freon-113 flowed upwardly. The observation was made at a pressure of 3 bar, a mass flux of 920 kg/m²s, an inlet subcooling 45 K and a slightly lower heat flux level than steady CHF. The vertical acceleration was oscillated with amplitude of 0.3g_e and a period of 6 s.At low apparent gravitational acceleration, bubbles generated on the heated surface moved longer along the surface without detachment and coalesced with other bubbles to form large vapor slugs. This causes early CHF, the mechanism of which is dry-out of the liquid film existing between the heated surface and vapor slugs.     

Actual flow calibration of a feedwater flowmeter using a high Reynolds number facility at NMIJ

The results of calibration tests of the feedwater flowrate of ultrasonic flowmeters used in a nuclear power plant for variety of upstream conditions obtained using the new high Reynolds number calibration facility at NMIJ are described. In this examination, the measurements are performed for five pattern pipe layouts with one or two elbows. The flow conditioners installed upstream of the flowmeter are the tube bundle type and the Mitsubishi, which are normally used in nuclear power plants. The calibration result for each flowmeter are largely different for each flow conditioner and each upstream pipe layout, except in some special cases. Moreover, the trend of the correction factor with Reynolds number is not uniform for each case. Furthermore, some differences were observed for individual flowmeters. It is recommended that the feedwater flowmeter, especially when used to perform measurement uncertainty recapture, is calibrated based on the actual pipe layout and the Reynolds number corresponding to the actual nuclear power plant conditions.     

Bubble rise characteristics after the departure from a nucleation site in vertical upflow boiling of subcooled water

Rise characteristics of vapor bubbles after the departure from a nucleation site in forced convective subcooled flow boiling were studied visually using two synchronized high speed video cameras. The test section was a transparent glass tube of 20 mm in inside diameter, filtrated and deionized tap water was used as a working fluid, and the flow direction adopted was vertical upward. The outer surface of test section tube was electrically heated to generate vapor bubbles inside of the tube. In the present experiments, the mass flux and liquid subcooling were varied within 94–1435 kg/m² s and 2.2–10 K, respectively. Since the observations were performed at low heat fluxes to avoid the significant increase in the number of active nucleation sites, the obtained bubble images were clear enough to carry out the detailed image analysis for the rise characteristics of individual bubbles. The following three different bubble rise paths were observed after the departure from nucleation sites: some bubbles slid upward the vertical wall for long distance, while other bubbles were detached from the wall after sliding for several millimeters and then migrated toward the bulk liquid; after the migration, some of the detached bubbles were collapsed in subcooled liquid but others remained close to the wall and were reattached to the wall. The results of detailed image analyses suggested that the variation in bubble shape from flattened to more rounded was of primary importance for the occurrence of bubble detachment from the wall.     

Influence of subcooled boiling on out-of-phase oscillations in boiling water reactors

In this paper, we develop a reduced order model with modal kinetics for the study of the dynamic behavior of boiling water reactors. This model includes the subcooled boiling in the lower part of the reactor channels. New additional equations have been obtained for the following dynamics magnitudes: the effective inception length for subcooled boiling, the average void fraction in the subcooled boiling region, the average void fraction in the bulk-boiling region, the mass fluxes at the boiling boundary and the channel exit, respectively, and so on. Each channel has three nodes, one of liquid, one with subcooled boiling, and one with bulk boiling. The reduced order model includes also a modal kinetics with the fundamental mode and the first subcritical one, and two channels representing both halves of the reactor core. Also, in this paper, we perform a detailed study of the way to calculate the feedback reactivity parameters. The model displays out-of-phase oscillations when enough feedback gain is provided. The feedback gain that is necessary to self-sustain these oscillations is approximately one-half the gain that is needed when the subcooled boiling node is not included.