Effect of pressure on critical heat flux in uniformly heated vertical annulus under low flow conditions

Critical heat flux (CHF) experiments have been carried out in a wide range of pressure for an internally heated vertical annulus. The experimental conditions covered a range of pressure from 0.57 to 15.01 MPa, mass fluxes of 0 kg m⁻² s⁻¹ and from 200 to 650 kg m⁻² s⁻¹, and inlet subcoolings from 85 to 413 kJ kg⁻¹. Most of the CHFs were identified to the dryout of the liquid film in the annular-mist flow. For the mass fluxes of 550 and 650 kg m⁻² s⁻¹, the CHFs had a maximum value at a pressure of 2–3 MPa, and the pressure at the maximum CHF values had a trend moving toward the pressure at the peak value of pool boiling CHF as the mass flux decreased. The CHF data under a zero mass flux condition indicate that both the effects of pressure and inlet subcooling on the CHF were smaller, compared with those for the CHF with a net water upflow. The Doerffer correlation using the 1995 CHF look-up table and the Bowring correlation show a good prediction capability for the present CHF data.     

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.     

A study of the performance of void fraction correlations used in the context of drift-flux two-phase flow models

Drift-flux models have traditionally been and are currently used in thermal-hydraulic analysis codes in the nuclear and other industries to analyze the behavior of systems during a wide variety of transient conditions. Their simplicity and closeness to experimental data, compared to two-fluid models, and their robustness, make them a cost-effective and efficient choice, although these models are generally limited to co-current flow. The drift-flux models are based on correlations to compute the void fraction distribution and slip in two-phase flow needed to obtain the relative velocity between the phases. Thus, the accuracy of the correlations has a decisive role in determining the correct transport of vapor along the system and, subsequently, in the prediction of the correct response of nuclear or industrial systems. This paper presents the results of an evaluation of the accuracy of a range of widely used void fraction correlations based on the Findlay–Zuber drift-flux model. The 13 correlations presented in this paper, a sub-set of all considered, can loosely be termed as ‘wide range void correlations’, since, as shown in this paper, they are those able to perform reasonably well for the wide range of experimental conditions used in the assessment. The size of the experimental database allowed a detailed statistically based comparison of the performance of all the correlations assessed. The void fraction data is taken from rod bundle, level swell and boil-off experiments performed within the last 10–15 years at 9 experimental facilities in France, Japan, Switzerland, the UK and the USA. The pressure and mass fluxes of the analyzed experiments range from 0.1 to 15 MPa and from 1 to 2000 kg m⁻² s⁻¹, respectively. Finally, the assessment of a widely used correlation against experimental transient void fraction data has been performed. The selected correlation is that of Chexal–Lellouche, currently used in the system codes RETRAN-3D and RELAP-5. The results show the performance of the correlation when used in the context of a system code and two different drift-flux model approaches, namely, an algebraic slip calculation and the calculation of the slip velocity based on the solution of a differential slip equation. The accuracy of the predictions shows that it is possible to use a drift-flux approach even for the analysis of rapid transients.     

A flow boiling burnout correlation for water and Freon-12

An empirical correlation has been developed for calculating critical heat flux (CHF) for vertical upflow in uniformly heated tubes. The correlation is based on parameter groups derived from a dimensional analysis and has been compared with experimental CHF data for Freon-12 and for water. Except for coolant conditions in which (i) mass fluxes are less than 300 kg s⁻¹ m⁻², (ii) dryout qualities are below 10%, or (iii) water pressures are outside the range 3.5 to 12 MPa, the correlation agrees very favourably with the experimental data. The overall mean ratio of calculated to experimental CHF values for 1760 sets of Freon-12 data is 0.992 and the r.m.s. error 3.3%; the corresponding values for 2063 sets of water data are 0.982 and 5.8%. This provides a basis for predicting CHF levels over a wide range of coolant conditions, as required in the analysis of hypothetical loss-of-coolant accidents in water-cooled nuclear reactors.     

Three-dimensional time-averaged void fraction distribution measurement technique for BWR thermal hydraulic conditions using an X-ray CT system

We have developed a void fraction distribution measurement technique using the three-dimensional (3D) time-averaged X-ray computed tomography (CT) system to understand two-phase flow behavior inside a fuel bundle for boiling water reactor (BWR) thermal hydraulic conditions of 7.2 MPa and 288 °C. As a first step, we measured the 3D void fraction distribution in a vertical square (5?×?5) rod array that simulated a BWR fuel bundle in the air–water test. A comparison of the volume-averaged void fractions evaluated by the developed X-ray CT system with those evaluated by a differential pressure transducer showed satisfactory agreement within a difference of 0.03. Thus, we confirmed that the developed system could be used to get 3D imaging of the vertical square rod array used in the test under the BWR operating pressure condition. In the next step, we did a verification test using the vertical pipe (11.3 mm ID) for BWR thermal hydraulic conditions. A comparison of the cross-sectional-averaged void fractions evaluated by the X-ray CT system with those evaluated by the drift-flux model showed good agreement within a difference of 0.05. We confirmed that the evaluated void fraction distribution forms in the horizontal cross section changed with the quality in response to the flow regime transition.     

Flow structure and bubble characteristics of steam–water two-phase flow in a large-diameter pipe

The flow structure and bubble characteristics of steam–water two-phase upward flow were observed in a vertical pipe 155 mm in inner diameter. Experiments were conducted under volumetric flux conditions of J_G<0.25 m s⁻¹ and J_L<0.6 m s⁻¹, and three different inlet boundary conditions to investigate the developing state of the flow. The radial distributions of flow structure, such as void fraction, bubble chord length and gas velocity, were obtained by horizontally traversing optical dual void probes through the pipe. The spectra of bubble chord length and gas velocity were also obtained to study the characteristics of bubbles in detail. Overall, an empirical database of the multi-dimensional flow structure of two-phase flow in a large-diameter pipe was obtained. The void profiles converged to a so-called core-shaped distribution and the flow reached a quasi-developed state within a relatively short height-to-diameter aspect ratio of about H/D=4 compared to a small-diameter pipe flow. The PDF histogram profiles of bubble chord length and gas velocity could be approximated fairly well by a model function using a gamma distribution and log–normal distribution, respectively. Finally, the correlation of Sauter mean bubble diameter was derived as a function of local void fraction, pressure, surface tension and density. With this correlation, cross sectional averaged bubble diameter was predicted with high accuracy compared to the existing constitutive equation mainly being used in best-estimate codes.     

Vapour void fraction in subcooled flow boiling

Experimental data on steam void fraction and axial temperature distribution in an annular boiling channel for low mass-flux forced and natural circulation flow of water with inlet subcooling have been obtained. The ranges of variables covered are: mass flux = 1.4 × 10⁴−1.0 × 10⁵ kg/hr m²; heat flux = 4.5 × 10³−7.5 × 10⁴ kcal/hr m²; and inlet subcooling = 10–70°C. The present and literature data match well with the theoretical void predictions using a four-step method similar to that suggested by Zuber and co-workers.     

Void fraction under high pressure, low flow conditions in rod bundle geometry

Void-fraction data are reported from a series of high pressure, low heat and mass flux experiments. Testing was performed in a heated vertical rod bundle with internal dimensions similar to a PWR fuel bundle. The results are of interest in analyses of small break loss of coolant accidents. The experiments showed that, at a given pressure, void-fraction data could be fitted to a drift-flux equation with a constant drift-velocity. The drift-velocity was observed to decrease with increasing pressure and was independent of void fraction; a characteristic normally associated with churn-turbulent flow. However, relevant drift-flux correlations found in the literature gave relatively poor predictions of void fraction. The best predictions were obtained from an empirical correlation based on dimensional analysis.     

An investigation of transient heat transfer in the region of flow boiling dryout with freon-12 in a heated tube

Power transient experiments using vertical round tube test sections have provided information on the heat transfer characteristics associated with a change from pre-dryout to post-dryout flow boiling conditions. The test sections were heated by passing electric current along the tube wall, and cooled internally by Freon-12 flowing upwards through the tube.Seven steel tubes of various sizes were used (internal diameters in the range 7.1–26.6 mm, wall thicknesses 0.9–2.0 mm, and lengths of 0.9–3.9 m). Data were obtained for coolant mass fluxes in the range 150–3270 kg m⁻² s⁻¹, at a nominal pressure of 1.0 MPa, with exit qualities in the range 0.3–1.0. The transients were initiated by small increases in power input to the test section. Heat transfer characteristics were determined by calculating wall temperature responses as functions of time and comparing these with the corresponding temperature traces recorded in the experiments.In relation to the temperature responses of the tube wall under these transient conditions, the results show that transition boiling has only a slight effect and that film boiling has very significant effects.     

Gas–liquid two-phase flow in narrow horizontal annuli

Experimental data associated with the two-phase flow regimes, void fraction and pressure drop in horizontal, narrow, concentric annuli are presented. Two transparent test sections, one with inner and outer diameters of 6.6 and 8.6 mm, and an overall length of 46.0 cm; the other with 33.2 and 35.2 mm diameters and 43.0 cm length, respectively, were used. Near-atmospheric air and water constituted the gas and liquid phases, respectively. The gas and liquid superficial velocities were varied in the 0.02–57 and 0.1–6.1 m s⁻¹ ranges, respectively. The major two-phase flow patterns observed included bubbly, slug/plug, churn, stratified, and annular. Transitional regimes, where the characteristics of two distinct flow regimes could be observed in the test sections, included bubbly-plug, stratified-slug and annular-slug. The obtained flow regime maps were different than flow regime maps typical of large horizontal channels and microchannels with circular cross-sections. They were also different from the flow regimes in rectangular thin channels. The measured average void fractions for the two test sections were compared with predictions of several empirical correlations. Overall, a correlation proposed by Butterworth [Butterworth, D., 1975. A comparison of some void fraction relationships for co-current gas–liquid flow. Int. J. Multiphase Flow 1, 845–850] based on the results of Lockhart and Martinelli (1949) provided the most accurate prediction of the measured void fractions. The measured pressure drops were compared with predictions of several empirical correlations. The correlation of Friedel [Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. 3R Int. 18, 485–492] was found to provide the best overall agreement with the data.     

An experimental and analytical study of the effect of axial power profile on CHF

The effect of axial heat flux distribution (AFD) on the critical heat flux (CHF) was investigated. CHF measurements were obtained with HFC-134a cooled vertical tubes having four non-uniform and one uniform AFD profiles. The HFC-134a test conditions covered a pressure range from 1.6 to 2.4 MPa, a mass-flux range from 2.8 to 4.7 Mg m⁻² s⁻¹, and an inlet-quality range from −0.9 to 0. The water-equivalent pressure and mass-flux ranges are 10–14 MPa and 4–6.5 Mg m⁻² s⁻¹, respectively.In general, the observed AFD effect on critical power is small at high inlet subcoolings. At low inlet subcoolings, the critical power for the inlet-peak profile is up to 15% higher than that for the outlet-peak profile. A local conditions analysis showed that the AFD has the strongest effect on CHF at high dryout qualities. CHF values for non-uniform AFDs could be 50% lower than those for the uniform AFD. The AFD effect on CHF becomes diminished with decreasing dryout quality.Four different approaches to account for the effect of AFD on CHF were assessed against the experimental values from the current experiment. The boiling-length-average heat-flux approach with the boiling-length starting point at the onset of annular flow (OAF) provided the best prediction of the critical power and the CHF location.     

Critical heat flux at high velocity channel flow with high subcooling

A quantitative analysis of critical heat flux (CHF) in heated channels under high mass flux with high subcooling was successfully carried out by applying a new flow model to the existing CHF model of a macro-water-sublayer on the heated wall and steam blankets over it. The CHF correlation proposed could correctly predict the existing experimental data for circular tubes of 0.33–4 mm in diameter with mass flux of 124–90 000 kg (m² s)⁻¹ and inlet water subcooling of 35–210 K at 0.1–7.1 MPa, resulting in CHF of 4.2–224 MW m⁻², and for rectangular channels of 3–20 mm gap with a mass flux of 940–27 000 kg (m² s)⁻¹ and inlet water subcooling of 13–166 K at 0.1–3.0 MPa, resulting in CHF of 2.0–62 MW m⁻². An error of the CHF correlation has also been estimated.     

Visualization and measurement of two-phase flow by using neutron radiography

To apply neutron radiography (NR) technique to fluid research, high frame-rate NR with a steady thermal neutron beam has been developed in the present research program by assembling up-to-date technologies for neutron source, scintillator, high-speed video and image intensifier. This imaging system has many advantages such as a long recording time (up to 21 min), high-frame-rate (up to 1000 frames s⁻¹) imaging and no need for triggering signal. Visualization of air-water two-phase flow in a metallic duct was performed at the recording speeds of 250, 500 and 1000 frames s⁻¹. The qualities of those consecutive images were good enough to observe and measure the flow structure and the characteristics. It was demonstrated also that some characteristics of two-phase flow could be measured by using the present imaging system. Image processing technique enabled measurements of various flow characteristics in two ways. By utilizing geometrical information extracted from NR images, data on flow regime, rising velocity of bubbles, and wave height and interfacial area in annular flow were obtained. By utilizing attenuation characteristics of neutrons in materials, measurements of void profile and average void fraction were performed. It was confirmed that this new technique may have significant advantages both in visualizing and measuring high-speed fluid phenomena when the other methods such as an optical method and X-ray radiography cannot be applicable.     

Some problems for bundle CHF prediction based on CHF measurements in simple flow geometries

A comparison of critical heat flux (CHF) fuel bundles data with CHF data obtained in simple flow geometries was made. The base for the comparison was primary experimental data obtained in annular, circular, rectangular, triangular, and dumb-bell shaped channels cooled with water and R-134a. The investigated range of flow parameters (pressure, mass flux, and critical quality) in R-134a was chosen to be equivalent to modern nuclear reactor water flow conditions (p=7 and 10 MPa, G=350–5000 kg (m² s)⁻¹, x_cr=−0.1–1). The proper scaling laws were applied to convert the data from water to R-134a equivalent conditions and vise versa. The effects of flow parameters (p, G, x_cr) and the effects of geometric parameters (D, L) were evaluated during comparison. The comparison showed that no one simple flow geometry can be used for accurate and reliable bundle CHF prediction in wide range of flow parameters based on local (critical) conditions approach. The comparison also showed that the limiting critical quality phenomenon is unique characteristic for each flow geometry which depends on many factors: flow conditions (pressure and mass flux), geometrical parameters (diameter or surface curvature, gap size, etc.), flow obstructions (spacers, appendages, turbulizers, etc.) and others.     

Axial static pressure variations in inner and side subchannels of a 61-tube wire-wrap bundle

Measurements of axial distribution of the static pressure in an inner and side subchannel of a 61 wire-wrap tube bundle obtained with water at atmospheric conditions are presented. The wire wrap configuration is different from those used by previous workers and more representative of a bundle for the blanket of a Gas Cooled Fast Reactor. The data display axial static pressure variations which are attributed to the interchannel cross flow induced by the wire-wrap configuration. The static pressure drop over one wire pitch agrees well with the bundle pressure drop based on a bundle average Reynolds number and a friction factor f = 0.436 Re^−0.263 (Re > 2000). The experimental data obtained with water provide a useful benchmark to model and check the accuracy of thermal-hydraulic codes used for the analysis of subchannel flow distribution and pressure drop in wire wrap tube bundle cooled with one-phase fluid.The nodal subchannel code COBRA-IV was modeled by adjusting the forced cross-flow function to match the measured axial static pressure distribution in an inner and side subchannel. Some discrepancy remained in the static pressure profile in the side channel attributed to the flow distortion at the bundle exit.     

Investigation of pre- and post-dryout heat transfer of steam-water two-phase flow in a rod bundle

Pre- and post-dryout heat transfer experiments were performed for steam-water two-phase flow in a 5 × 5 rod bundle under conditions of total mass fluxes from 80 to 320 kg/m²s, inlet qualities from 0.1 to 0.8, heat fluxes from 3 to 26 W/cm² and a pressure of 3 MPa. Heater rod surface temperatures or heat transfer coefficients predicted by several correlations were compared with experimental data with emphasis on the applicability of the correlations to the present experimental conditions which were pertinent to thermal-hydraulic conditions during a LOCA in a nuclear reactor. The Chen and Biorge et al. correlations underestimated heat transfer coefficients in the pre-dryout region. The Varone-Rohsenow prediction which accounted for the thermal nonequilibrium effect, calculated heater rod surface temperatures relatively well in the post-dryout region over the whole region of the present experimental conditions. The Dittus-Boelter and Groeneveld correlations predicted heater rod surface temperatures relatively well in the post-dryout region under high total mass flux conditions, but underestimated considerably under low total mass flux conditions.     

Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow

Double sensor probe and hotfilm anemometry methods were developed for measuring local flow characteristics in bubbly flow. The formulation for the interfacial area concentration measurement was obtained by improving the formulation derived by Kataoka and Ishii. The assumptions used in the derivation of the equation were verified experimentally. The interfacial area concentration measured by the double sensor probe agreed well with one by the photographic method. The filter to validate the hotfilm anemometry for measuring the liquid velocity and turbulent intensity in bubbly flow was developed based on removing the signal due to the passing bubbles. The local void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter, liquid velocity, and turbulent intensity of vertical upward air–water flow in a round tube with an inner diameter of 50.8 mm were measured by using these methods. A total of 54 data sets were acquired consisting of three superficial gas flow rates, 0.015–0.076 m s⁻¹, and three superficial liquid flow rates, 0.600, 1.00, and 1.30 m s⁻¹. The measurements were performed at the three locations: L/D=2, 32, and 62. This data is expected to be used for the development of reliable constitutive relations which reflect the true transfer mechanisms in two-phase flow.     

Experimental investigation on heat transfer from a heated rod with a helically wrapped wire inside a square vertical channel to water at supercritical pressures

A supercritical water heat transfer test section has been built at Xi’an Jiaotong University to study the heat transfer from a 10 mm rod inside a square vertical channel with a wire-wrapped helically around it as a spacer. The test section is 1.5 m long and the wire pitch 200 mm. Experimental conditions included pressures of 23–25 MPa, mass fluxes of 500–1200 kg/m² s, heat fluxes of 200–800 kW/m², and inlet temperatures of 300–400 °C. Wall temperatures were measured with thermocouples at various positions near the rod surface. The experimental Nusselt numbers were compared with those calculated by empirical correlations for smooth tubes. The Jackson correlation showed better agreement with the test data compared with the Dittus-Boelter correlation but overpredicted the Nusselt numbers almost within the whole range of experimental conditions. Both correlations cannot predict the heat transfer accurately when deterioration occurred at low mass flux and relatively high heat flux in the pseudocritical region. Comparison of experimental data at two different supercritical pressures showed that the heat transfer was more enhanced at the lower supercritical pressure but the deterioration was more likely to occur at the higher pressure, meaning increased safety. Based on a comparison with an identical channel without the helical wrapped wire, it was found that the wire spacer does not enhance the heat transfer significantly under normal heat transfer conditions, but it contributes to the improvement of the heat transfer in the pseudocritical region and to a downstream shift of the onset of the deterioration. The Jackson buoyancy criterion is found to be valid and works well in predicting the onset of heat transfer deterioration occurring in the experiments without wire.     

Analysis of the conjugation effect during convective flow film boiling conditions in an eccentric annular test section

The objective of this investigation was to present a technique for estimating the conjugation effect on post-dryout heat transfer. To this aim, an experimental study was conducted to measure the conjugation effect on the post-dryout heat transfer using an internally heated eccentric annular test section (outside diameter (O.D.), 13.51 mm; inside diameter (I.D.), 11.54 mm). The experiments were carried out at 7 and 9 MPa with the mass flux varying from 2.0 to 5.0 Mg m⁻² s⁻¹ and the inlet vapour quality from 0.01 to 0.20. Five different minimum gap sizes between 0.06 and 1.92 mm were tested. The two-dimensional well temperature distribution on the inside surface of the heated tube was measured using a unique sliding thermocouple technique. A data reduction method was developed to determine the radial heat flux variation on the boiling surface from the temperature measurements. A numerical smoothing procedure was used to minimize the effect of the random temperature measurement error of the sliding thermocouple on the estimated radial heat flux variation. The results show that the conjugation effect can cause the local radial heat flux to deviate by as much as 17% from the average value.     

A power perturbation technique for the measurement of fuel-to-coolant heat transfer coefficients in fast reactors

This technique provides a method of obtaining average fuel to coolant heat transfer coefficients for individual fuel subassemblies in fast reactors. A series of experiments on the UK prototype fast reactor (PFR) over the period 1977–1979 have demonstrated that the technique is simple, requires no special instrumentation other than thermocouples to monitor coolant outlet temperatures, and the measurement can be made during normal reactor operation. Thus it is possible to determine how heat transfer coefficients change with operating conditions and with the degree of burn-up in the fuel.The analysis of a single experiment is presented to illustrate the technique. This was conducted at a single reduced power level of 200 thermal megawatts for two different primary coolant flow rates, both steady fractions of the maximum (0.88 and 0.47). Cyclic and single-step perturbations of about 10% amplitude were impressed on the steady power and the delayed coolant temperature response at subassembly outlets was monitored. Burn-ups in the subassemblies ranged between 1.0% and 4.7%. From the measured delays at the two flows it was possible to determine the fuel time-constant and hence the fuel-to-coolant heat transfer coefficient. It was also shown that a simple, lumped-element, heat transfer model can be used to obtain sufficiently accurate estimates from measurements at just one coolant flow.Fuel surface-to-coolant thermal conductances (i.e. gap conductances) were subsequently derived from the heat transfer coefficients. These ranged between 2.4 kW m⁻² K⁻¹ and 3.3 kW m⁻² K⁻¹ with the smaller conductances being obtained for those fuel elements with the larger degree of burn-up. These values are lower than expected but consistent with a higher than expected value for the negative power coefficient of reactivity feedback which has been observed at reduced power.