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.     

Critical heat flux under zero flow conditions in vertical annulus with uniformly and non-uniformly heated sections

The experimental study of water CHF (critical heat flux) under zero flow conditions has been carried out in an annulus flow channel with uniformly and non-uniformly heated sections over a pressure range of 0.52–14.96 MPa. In the present boiling system, the CHFs occur in the upper region of the heated section, in contrast to the results in the experiments for boiling tubes conducted by several investigators. The general trend of the CHF with pressure is that the CHF increases up to a medium pressure of about 6–8 MPa and decreases as the pressure is further increased. A comparison of the present data with the existing flooding CHF correlations shows that the correlations depend greatly on the effect of the heat flux distribution. When the correction terms with the density ratio and the effect of the heat flux distribution proposed in the present work are used with the CHF correlation based on the Wallis flooding correlation, it predicts the measured flooding CHF within an RMS error of 9.0%.     

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.     

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.     

Comparison of correlations for predicting critical heat flux for uniformly heated vertical porous coated tubes at low pressure

The paper includes comparison of correlations for predicting critical heat flux for uniformly heated vertical porous coated tubes at pressure between 0.1 and 0.7 MPa. In this study, a total of 1120 data points of CHF (Critical heat flux) in uniformly heated vertical porous coated tubes were used. Accuracy of correlations was estimated by calculating average and RMS error with available experimental data, and a new correlation is presented. The new correlation predicts that the CHF data are significantly better than those currently available correlations, with average error 0.69% and RMS error 10.9%.     

Numerical study on flow and heat transfer characteristics in the rod bundle channels under super critical pressure condition

In this study, the 3D flow and heat transfer characteristics in rod bundle channels of the super critical water-cooled reactor were numerically investigated using CFX codes. Different turbulent models were evaluated and the flow and heat transfer characteristics in different typical channels were obtained. The effect of pitch-to-diameter ratio (P/D) on the distributions of surface temperature and heat transfer coefficient (HTC) was analysed. For typical quadrilateral channel, it was found that HTC increases with P/D first and then decreases significantly when P/D is <1.4. There exists a “flat region” at the maximum value when P/D is 1.4. If P/D is larger than 1.4, heat transfer deterioration (HTD) occurs as main stream enthalpy is quite small. Furthermore, the HTD under low mass flow rate and the non-uniformity of circumferential temperature were also discussed.     

An experimental study of turbulent flow through a square-array rod bundle

Using laser-Doppler anemometry and calibrated Preston tubes, experiments were performed in water (80°C, 0.6 MPa) to obtain information on the distributions of wall shear stresses, mean axial velocities and turbulence intensities for fully developed adiabatic flow through a six-rod bundle at a Reynolds number of 5 × 10⁵. The rods were arranged in a square array with a pitch to a diameter ratio of 1.15 and a wall-distance to diameter ratio of 0.62. The core flow in the central subchannel appears to be similar to pipe flow, but in the gap regions much higher turbulence intensities are encountered. The skewed wall shear stress profiles together with the deformed constant-velocity lines suggest the presence of secondary flows in the corner subchannels.     

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.     

Analysis of the critical heat flux in round vertical tubes under low pressure and flow oscillation conditions. Applications of artificial neural network

Artificial neural networks (ANNs) for predicting critical heat flux (CHF) under low pressure and oscillation conditions have been trained successfully for either natural circulation or forced circulation (FC) in the present study. The input parameters of the ANN are pressure, mean mass flow rate, relative amplitude, inlet subcooling, oscillation period and the ratio of the heated length to the diameter of the tube, L/D. The output is a nondimensionalized factor F, which expresses the relative CHF under oscillation conditions. Based on the trained ANN, the influences of principal parameters on F for FC were analyzed. The parametric trends of the CHF under oscillation obtained by the trained ANN are as follows: the effects of pressure below 500 kPa are complex due to the influence of other parameters. F will increase with increasing mean mass flow rate under any conditions, and will decrease generally with an increase in relative amplitude. F will decrease initially and then increase with increasing inlet subcooling. The influence curves of mean mass flow rate on F will be almost the same when the period is shorter than 5.0 s or longer than 15 s. The influence of L/D will be negligible if L/D>200. It is found that the minimum number of neurons in the hidden layer is a product of the number of neurons in the input layer and in the output layer.     

Fully developed rod bundle flow over a large range of Reynolds number

In an investigation of the fluid mechanics of single phase reactor cores, extensive measurements of mean axial velocity, wall shear stress and all six Reynolds stresses have been made in fully developed flow through a square pitched rod bundle array with pitch to diameter ratio of 1.107. The range of Reynolds numbers, based on bulk velocity and hydraulic diameter was 22600 to 207600. The mean secondary flow velocities could not be measured at any Reynolds number, implying that they were always less than about 1% of the bulk velocity. The axial momentum integral equation is used to show that the wall shear stress distribution is determined primarily by the pressure gradient and the transverse shear stress |ovbar|uw, a result that confirms the negligible size of the mean secondary flow. The implications of the results for current engineering calculation methods are discussed.     

Prediction of critical heat flux in vertical pipe flow

A previously developed semi-empirical model for adiabatic two-phase annular flow is extended to predict the critical heat flux (CHF) in a vertical pipe. The model exhibits a sharply declining curve of CHF versus steam quality (X) at low X, and is relatively independent of the heat flux distribution. In this region, vaporization of the liquid film controls. At high X, net deposition upon the liquid film becomes important and CHF versus X flattens considerably. In this zone, CHF is dependent upon the heat flux distribution. Model predictions are compared to test data and an empirical correlation. The agreement is generally good if one employs previously reported mass transfer coefficients.     

Critical heat flux for finned and unfinned geometries under low flow and low pressure conditions

This paper presents the experiment and analysis for the critical heat flux (CHF) in a vertical annulus with finned and unfinned geometries under low flow and low pressure conditions. To consider the fin effect on CHF, the tests were performed on both finned heater and unfinned heater having same dimension as finned heater without fins. An analytical model was applied to estimate the heat flux and temperature distributions along the periphery of the finned geometry. The physical phenomena observed during the experiments are discussed and the parametric trends of the obtained data are examined to investigate the CHF characteristics for the finned geometry. A new correlation is proposed to predict the CHF for both finned and unfinned geometries at low flow and low pressure conditions. The developed correlation predicts the experimental data with an RMS error of 13.7%.     

Experimental investigation on critical heat flux in horizontal channel for low pressure low flow (LPLF) condition

Studies reported in the past on critical heat flux (CHF) are mostly limited to vertical flow, large channel diameter, high pressure and high mass flux. Only few investigations are reported in the literature for horizontal flow CHF especially under low pressure and low flow conditions. Hence, predictive methods of CHF for horizontal flow are scarce. There is a need for understanding CHF in horizontal flow under low pressure and low flow conditions because they are commonly encountered in nuclear reactor fuel channels of pressurized heavy water reactor (PHWR) under loss of coolant accidental (LOCA) conditions. The present work investigates CHF of horizontal flow for low flow rates (mass flux of 100–400 kg/m² s) at nearly atmospheric pressure conditions. Parameters covered in this study are diameter (5.5 mm, 7.5 mm and 9.5 mm), length (0.45 m and 0.8 m) and a inlet temperature of 32 °C. The first occurrence of ‘red hot’ spot on the test section is considered as the onset of critical heat flux condition in the present work. Experimental results obtained are compared with Groeneveld et al. (2007) look up table data for vertical flow after applying correction factor given by Wong et al. (1990). The deviation of experimental CHF data from those predicted using Groeneveld et al. (2007) look up table and Wong et al. (1990) correction factor is more than 50%.     

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.     

An experimental and analytical investigation of uncovered core heat transfer under high pressure, low heat flux conditions

Experimental and analytical results are reported from two series of high pressure core uncovering experiments. It was determined that the uncovered core is cooled primarily by convection and radiation to dry steam and that droplets are confined to the immediate vicinity of the mixture level. Spacer grids substantially increased heat transfer at and downstream of the grid. A simple heat transfer model is presented which accurately predicts uncovered core heat transfer at modified wall Reynolds numbers greater than 2000. Results are expected to be use in modelling small break loss of coolant accidents.     

An experimental investigation on the critical heat flux enhancement by mechanical vibration in vertical round tube

In order to gain an understanding of the relationship between critical heat flux (CHF) and flow-induced vibration (FIV), an experimental investigation was carried out with vertical round tube at the atmosphere. In the both condition of departure from nucleate boiling (DNB) and the liquid film dryout (LFD), CHF increases up to 12.6% with vibration intensity, represented by vibrational Reynolds number (Re_v). CHF enhancement by tube vibration seems to come from the reinforced flow turbulent mixing and the increment of deposition of droplet into the liquid film. Based on the experimental results, an empirical correlation is proposed for the prediction of CHF enhancement ratio. The correlation predicts the CHF enhancement ratio (E_n) with reasonable accuracy, with an average error rate of 4.5 and 26.5% for RMS. Vibration is an effective method for heat transfer enhancement as well as CHF. Nonetheless, the risk of system failure by FIV has made it very difficult to take advantage of vibration in heat transfer facilities. Therefore, it is necessary to find out optimal fuel design enhancing the CHF but preventing FIV damage in an acceptable vibration range.     

An investigation of flow characteristics and critical heat flux in vertical upward round tube

Prediction of critical heat flux （CHF） in annular flow is important for the safety of once - through steam generator and the reactor core under accident conditions. The dryout in annular flow occurs at the point where the film is depleted due to entrainment, deposition, and evaporation. The film thickness, film mass flow rate along axial distribution, and CHF are calculated in vertical upward round tube on the basis of a separated flow modcl of annular flow. The theoretical CHF values are higher than those derived from experimental data, with error being within 30%.     

Prediction of critical heat flux for water flow in vertical round tubes using support vector regression model

This paper deals with ν-support vector regression (ν-SVR) based prediction model of critical heat flux (CHF) for water flow in vertical round tubes. The dataset used in this paper is obtained from available published literature. The dataset is partitioned into two independent sets, a training data set and a test data set, to avoid overfitting problem. To train the ν-SVR models with more informative data, the training data is selected using a subtractive clustering (SC) scheme, and then the remaining data is used as test data to evaluate the performance of the ν-SVR models. Next, the parametric trends of CHF are investigated using the ν-SVR models. The results obtained from the ν-SVR models are compared with those obtained from the radial basis function (RBF) network, which is a kind of artificial neural networks (ANNs). It is found that the results of the ν-SVR models are not only in better agreement with the experimental data than those of the RBF network, but also follow the general understanding. The analysis results indicate that the ν-SVR models can be successfully applied to CHF prediction.     

An utilization of liquid sublayer dryout mechanism in predicting critical heat flux under low pressure and low velocity conditions in round tubes

From a theoretical assessment of extensive critical heat flux (CHF) data under low pressure and low velocity (LPLV) conditions, it was found out that lots of CHF data would not be well predicted by a normal annular film dryout (AFD) mechanism, although their flow patterns were identified as annular–mist flow. To predict these CHF data, a liquid sublayer dryout (LSD) mechanism has been newly utilized in developing the mechanistic CHF model based on each identified CHF mechanism. This mechanism postulates that the CHF occurrence is caused by dryout of the thin liquid sublayer resulting from the annular film separation or breaking down due to nucleate boiling in annular film or hydrodynamic fluctuation. In principle, this mechanism well supports the experimental evidence of residual film flow rate at the CHF location, which can not be explained by the AFD mechanism. For a comparative assessment of each mechanism, the CHF model based on the LSD mechanism is developed together with that based on the AFD mechanism. The validation of these models is performed on the 1406 CHF data points ranging over P=0.1–2 MPa, G=4–499 kg m⁻² s⁻¹, L/D=4–402. This model validation shows that 1055 and 231 CHF data are predicted within ±30 error bound by the LSD mechanism and the AFD mechanism, respectively. However, some CHF data whose critical qualities are <0.4 or whose tube length-to-diameter ratios are <70 are considerably overestimated by the CHF model based on the LSD mechanism. These overestimations seem to be caused by an inadequate CHF mechanism classification and an insufficient consideration of the flow instability effect on CHF. Further studies for a new classification criterion screening the CHF data affected by flow instabilities as well as a new bubble detachment model for LPLV conditions, are needed to improve the model accuracy.