High Inlet Subcooling Research Articles

Nonlinear Analysis of Chaotic Time Series in a Natural Circulation Boiling Loop

The present study reports chaotic flow oscillations observed in a natural circulation boiling loop. The periodic oscillations of wall temperature (thermal oscillations) initiate at a certain condition of heat flux and inlet subcooling in addition to geysering instability and pressure-drop oscillations. We observed that boiling regime changes from nucleate boiling to transition boiling as a result of decrease in inlet subcooling and increase in heat flux. The thermal oscillations are strongly coupled with pressure-drop oscillations. Nonlinear analysis of the time series of loop flow rate at various heater power and inlet subcooling have been carried out using statistical analysis, fast Fourier transform (FFT), time delay embedding for attractor reconstruction, autocorrelation, and correlation dimension. The analysis confirms that the oscillations are more chaotic at relatively low heater power and high inlet subcooling. The complexity of the oscillations strongly depends on boiling heat transfer regime. Our observations and analysis have been supported by other relevant experiments.

Lumped parameterization of boiling channel—Bifurcations during density wave oscillations

The research on density wave oscillation (DWO) in boiling channels during the last few decades has been reviewed. Model reductions through lumped parameterization of the distributed channels have been exercised to compute nonlinear DWOs. In the present article, we attempt to analyze DWOs in several boiling channels with varying lengths (Froude number) adopting moving node scheme (MNS) and fixed node scheme (FNS). Relative performances of MNS and FNS have been analyzed to evaluate the capability of the methods. The analysis suggests that MNS is highly computationally efficient and has excellent convergence compared to FNS and finite difference method. Extended numerical oscillations have been observed in FNS. The analysis also suggests that DWOs are strongly coupled with the extent of inlet subcooling (boiling boundary), pressure drop and vapor quality. At high inlet subcooling, the ratio of time period to transit time is significantly higher than 2.0 (2.5–6.0) whereas at low inlet subcooling the ratio remains around 2.0.Numerical experiments on long boiling channels (low Froude number) and short ones (high Froude number) derives a clear difference that the short channels with high Froude number has “islands of instability” in Npch–Nsub plane and undergoes both supercritical and subcritical bifurcations, whereas the boiling channel with low Froude number undergoes only supercritical bifurcations. The effect of node numbers on marginal stability boundary (MSB) has been discussed. Increased speed of convergence is observed with higher number of nodes. With finer nodalizations, the region of instability extends. Extensive validations of the nonlinear models with reference experimental data and numerical results confirm that MNS satisfactorily predicts MSB, supercritical and subcritical bifurcations. Quasi-periodic en route to chaos has been detected in the boiling channel as a result of periodic perturbation of pressure drop (Eu). The same has been confirmed by the analysis of power spectrum density (PSD) and computation of Lyapunov exponents.

Numerical research on oscillation of two-phase flow in multichannels under rolling motion

Two-phase flow instability and dynamics of a parallel multichannels system has been theoretically studied under periodic excitation induced by rolling motion in the present research. Based on the homogeneous flow model considering the rolling motion, the parallel multichannels model and system control equations are established by using the control volume integrating method. Gear method is used to solve the system control equations. The influences of the inlet, upward sections, heating power and rolling amplitudes on the flow instability under rolling motion have been analyzed. The marginal stability boundary (MSB) under the rolling motion condition is obtained. The unstable regions occur in both low and high equilibrium quality and inlet subcooling regions. The multiplied period phenomenon occurs in the high equilibrium quality region and the chaos phenomenon appears on the right of MSB. The concept of stability space is presented.

System instability of evaporative micro-channels

In parallel evaporative micro-channels, system instability may occur in terms of cyclical fluctuations at a long period. This is due to the co-existence of the liquid phase flow at high mass flux and the two-phase flow at a lower mass flux among different parallel channels under the same total pressure drop. For a system at constant flow rate pumping, with a pressure regulating tank and a constant heating pre-heater, alternations between these two states of boiling and non-boiling could happen with a period of minutes. This cyclical system instability has been modeled, where the liquid phase flow occurs at conditions of high inlet subcooling and low surface heat flux that the boiling inception is hard to initiate. The system instability criteria are established in terms of a system binary states parameter, S, and a non-dimensional surface heat flux. This model has been validated experimentally.

Recent Work on Boiling and Condensation in Microchannels

Recent work on boiling of water and condensation of steam in single and parallel microchannels is reviewed in this paper. It is found that the amplitude and frequency of fluctuations of temperature and pressure during the unstable flow-boiling mode depend greatly on the inlet/outlet configurations and the exit vapor quality. By fabricating an inlet restriction on each microchannel or the installation of a throttling valve upstream of the test section, reversed flow of vapor bubbles can be suppressed resulting in a stable flow-boiling mode. Boiling heat transfer coefficient and pressure drop in microchannels under stable flow-boiling conditions are obtained. These data at high vapor qualities are found to be substantially different from the correlations obtained for flow-boiling in macrochannels. Microbubble emission boiling phenomena, which can defer the arrival of critical heat flux, exist in a partially heated Pyrex glass microchannel at sufficiently high heat flux and high inlet subcooling conditions. For condensation in a microchannel, transition from annular flow to slug/bubbly flow is investigated. The occurrence of the injection flow is owing to the instability of the liquid/vapor interface. The location, at which the injection flow occurs, depends on the mass flux and the cooling rate of steam. Increase in steam mass flux, decrease in cooling rate, and microchannel diameter tend to enhance the instability of the condensate film on the wall, resulting in the occurrence of injection flow further downstream at increasingly high frequency. The pressure drop in the condensing flow increases with the increase in mass flux and quality or with decreasing microchannel diameter. The existing correlations for pressure drop and heat transfer of condensing flow in macrochannels overestimate the experimental data in microchannels.

Subcooled flow boiling and microbubble emission boiling phenomena in a partially heated microchannel

A simultaneous visualization and measurement study has been carried out to investigate subcooled flow boiling and microbubble emission boiling (MEB) phenomena of deionized water in a partially heated Pyrex glass microchannel, having a hydraulic diameter of 155 μm, which was integrated with a Platinum microheater. Effects of mass flux, inlet water subcooling and surface condition of the microheater on subcooled flow boiling in microchannels are investigated. It is found that MEB occurred at high inlet subcoolings and at high heat fluxes, where vapor bubbles collapsed into microbubbles after contacting with the surrounding highly subcooled liquid. In the fully-developed MEB regime where the entire microheater was covered by MEB, the mass flux, the inlet water subcooling and the heater surface condition have only small effects on the boiling curves. The occurrence of MEB in microchannel can remove a large amount of heat flux, as high as 14.41 MW/m 2 at a mass flux of 883.8 kg/m 2 s, with only a moderate rise in wall temperature. Therefore, MEB is a very promising method for cooling of microelectronic chips. Heat transfer in the fully-developed MEB in the microchannel is presented, which is compared with existing subcooled flow boiling heat transfer correlations for macrochannels.

Subcooled flow boiling of R-134a in vertical channels of small diameter

Subcooled flow boiling heat transfer for refrigerant R-134a in vertical cylindrical tubes with 0.83, 1.22 and 1.70 mm internal diameter was experimentally investigated. The effects of the heat flux, q″ = 1–26 kW/m 2, mass flux, G = 300–700 kg/m 2 s, inlet subcooling, Δ T sub, i = 5–15 °C, system pressure, P = 7.70–10.17 bar, and channel diameter, D, on the subcooled boiling heat transfer were explored in detail. The results are presented in the form of boiling curves and heat transfer coefficients. The boiling curves evidenced the existence of hysteresis when increasing the heat flux until the onset of nucleate boiling, ONB. The wall superheat at ONB was found to be essentially higher than that predicted with correlations for larger tubes. An increase of the mass flux leads, for early subcooled boiling, to an increase in the heat transfer coefficient. However, for fully developed subcooled boiling, increases of the mass flux only result in a slight improvement of the heat transfer. Higher inlet subcooling, higher system pressure and smaller channel diameter lead to better boiling heat transfer. Experimental heat transfer coefficients are compared to predictions from classical correlations available in the literature. None of them predicts the experimental data for all tested conditions.

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.

An experimental study on the critical heat flux for low flow of water in a non-uniformly heated vertical rod bundle over a wide range of pressure conditions

An experimental study of the critical heat flux (CHF) has been performed for a water flow in a non-uniformly heated vertical 3 × 3 rod bundle under low flow and a wide range of pressure conditions. The experiment was especially focused on the parametric trends of the CHF and the applicability of the conventional CHF correlations to a return-to-power conditions of a main steam line break accident whose conditions might be a low mass flux, intermediate pressure, and a high inlet subcooling. The effects of the mass flux and pressure on the CHF are relatively large and complicated in the low pressure conditions. At a high mass flux or a low critical quality, the local heat flux at the CHF location sharply decreases with an increasing local critical quality. However, at a low mass flux or a high critical quality, the local heat flux at the CHF location shows a nearly constant value regardless of the increase of the critical quality. The CHF data at the very low mass flux conditions are correlated well by the churn-to-annular flow transition criterion or the flow reversal phenomena. Several conventional CHF correlations predict the present return-to-power CHF data with reasonable accuracies. However, the prediction capabilities become worse in a very low mass flux of below about 100 kg/(m 2 s).

Nonlinear analysis for a nuclear-coupled two-phase natural circulation loop

The objective of this paper is to develop a nonlinear numerical model to investigate the stability and nonlinear dynamics of a nuclear-coupled two-phase natural circulation loop. Some stability maps, parametric effects and transient characteristics of this natural circulation loop have been studied. Results indicate that the system indeed has two instability regions, the type-I and type-II instabilities, as is well known for a natural circulation loop. Parameters may induce different effects on the system stability in type-I and type-II unstable regions. In particular, the void-reactivity feedback destabilizes the system in both regions of low and high operating powers. Moreover, by strengthening nuclear feedback effect, period-doubled bifurcation may prevail in the system at relatively high inlet subcoolings and eventually a chaotic attractor appears with a fractal dimension of 1.79 ± 0.01 and an embedding dimension of 5.

Transport Mechanism of Thermohydraulic Instability in Natural Circulation Boiling Water Reactors during Startup

This paper presents experimental study on transport mechanism of thermohydraulic instability, which may occur in natural circulation boiling water reactor during startup. The research was carried out using a natural circulation experimental loop featuring twin parallel boiling channels with chimney assembly. The experiments were performed with the pressure range of 0.1 to 0.7MPa and maximum heat flux of 577kW/m2. The objective of the study is to formulate thermohydraulic stability maps required for determining rational startup procedure of the reactor, in which the instability could be prevented. The study clarified that the flow modes during startup consist of the following sequence: (1) single-phase flow, (2) geysering, (3) oscillation due to hydrostatic head fluctuation, (4) density wave oscillation, (5) transition oscillation, and (6) stable two-phase flow. The main findings of the experiments are as follows: First, low amplitude geysering still occurs at 0.7 MPa under lower heat flux and high inlet subcooling. Second, stable two-phase natural circulation is achieved with system pressure as low as 0.2 MPa, under medium heat flux, and subcooling lower than 5 K. Third, oscillation due to hydrostatic head fluctuation only occurs under atmospheric condition. Finally, thermohydraulic stability maps and rational startup procedure are formulated.

Inlet throttling effect on the boiling two-phase flow stability in a natural circulation loop with a chimney

Experiments have been conducted to investigate an effect of inlet restriction on the thermal-hydraulic stability. A Test facility used in this study was designed and constructed to have non-dimensional values that are nearly equal to those of natural circulation BWR. Experimental results showed that driving force of the natural circulation at the stability boundary was described as a function of heat flux and inlet subcooling independent of inlet restriction. In order to extend experimental database regarding thermal-hydraulic stability to different inlet restriction, numerical analysis was carried out based on the homogeneous flow model. Stability maps in reference to the core inlet subcooling and heat flux were presented for various inlet restrictions using the above-mentioned function. Instability region during the inlet subcooling shifted to the higher inlet subcooling with increasing inlet restriction and became larger with increasing heat flux.

A delay theory for boiling flow stability analysis

An analysis of density-wave instabilities in boiling channels based on delay equations is presented. A two-dimensional mapping is derived from the flow conservation equations by assuming constant transport delays along the different parts of the channel. The simplicity of the final equation allows the fully analytical treatment of the system dynamics, both linear and non-linear, valid for high inlet subcoolings. Hopf bifurcations, subcritical and supercritical, could be identified and treated using perturbation methods. The derivation of a fully analytical criterion for Hopf bifurcation transcription was applied to determine the amplitude of limit cycles and the maximum allowed perturbations necessary to break the system stability.

Experimental Study of Two-Phase Flow Oscillation in Natural Circulation

The experiment was performed on the test loop HRTL-5, which simulates the geometry and system design of the 5-MW nuclear heating reactor developed by the Institute of Nuclear Energy Technology, Tsinghua University. The flow behavior for a wide range of inlet subcoolings, in which the flow experience varies from single- to two-phase, is described in a natural circulation system at different pressures (p = 0.1, 0.24, and 1.5 MPa). Several kinds of flow instability are investigated, including geysering, flashing-related flow instability, and high-frequency flow oscillation at p = 0.1 and 0.24 MPa, as well as low steam quality density wave oscillation at p = 1.5 MPa. The mechanisms of geysering, which has new features, and flashing-related flow instability, which has never been studied well enough in this field, are particularly interpreted. The experimental results show the following: First, for a low-pressure natural circulation system, the two-phase flow is unstable in most inlet subcooling conditions, and the two-phase stable flow can be reached only with very low inlet subcoolings. Second, at high inlet subcoolings, the flow instability is dominated by subcooling boiling in the heated section, and at intermediate inlet subcoolings, it is dominated by void flashing in the adiabatic long riser. Third, in the two-phase stable flow region, the conditions for boiling out of the core, namely, single-phase flow in the heated section and two-phase flow in the riser due to vapor flashing, can be realized. The experimental results are of significance for the design and accident analysis of vessel and swimming pool–type natural circulation nuclear heating reactors.

Modeling of thermal hydraulic instabilities in single heated channel loop during startup transients

A thermal hydraulics computer code was developed to simulate the geysering instability in a natural circulation system starting from subcooled conditions and to assess the impact of the system pressure and channel inlet subcooling on the inception of instability. The formulation of thermal hydraulics is inherently general and accounts for both single-phase liquid flow and nonhomogeneous, nonequilibrium two-phase flow. The computer code is based on momentum integral method where the current practice of basing fluid properties on the system averaged pressure has been relaxed and the local properties are based on local pressures estimated using the shape of steady-state pressure distribution, thereby, improving the predictions while preserving the computation speed, one of the important strength of the integral methods. This is an important modeling feature since the local vapor generation rate depends on local saturation temperature The methodology has been validated with the experiments conducted to investigate the instabilities in a low pressure natural circulation loop at low powers and high inlet subcoolings. The numerical simulations predicted periodic channel flow reversal, which is one of the feature of condensation-induced geysering. Basing local properties on local pressures instead of system average pressure led to decrease in the discrepancy in the prediction of the positive side amplitude from 40% to 6% and in the frequency from −15% to 5%. In addition, it was observed that the start-up instability can be avoided by increasing system pressure or by decreasing channel inlet subcooling. This study showed that the integral method coupled with local pressure variation for the vapor generation model is suitable to predict startup or geysering transients.

Nonlinear dynamics of a nuclear-coupled boiling channel with forced flows

The nonlinear dynamics of a nuclear-coupled boiling channel with forced flows was explored on the basis of the Galerkin nodal approximation method for the channel fluid flow and point kinetics for the neutron field dynamics. The marginal stability boundary (MSB) for a Freon boiling channel predicted by the model agreed well with experimental data from previous available literature, thereby verifying the model accuracy. A strip of limit cycle oscillation on the unstable side of the boundary was found to be system dependent. The marginal stability boundaries for boiling water channels with/without nuclear-coupled effects were also obtained. Moreover, the characteristics of limit cycle oscillations on the boundary were investigated. Routes from limit cycle oscillation to chaotic oscillation were identified under high inlet subcooling conditions. The strange attractor found in this study was characterized by a correlation dimension of 1.69±0.01.

Periodic flow excursion in an open two-phase natural circulation loop

Flow excursion instability in an open two-phase natural circulation loop was studied both experimentally and analytically. At high inlet subcooling, stable mode (continuous circulation) does not exist; instead, three different circulation modes such as periodic circulation (A), multimode circulation, and periodic circulation (B) appear at different heat flux conditions. The multimode circulation is represented by the combination of periodic circulations A and B and it is termed here as “periodic flow excursion”. The decrease in the inlet restriction and/or the increase in the exit restriction broadened the region of the flow excursion, and these aspects were summarized on the instability map of the heat flux vs. inlet subcooling. In addition, with the one-dimensional two-phase homogeneous equilibrium assumption, the region of flow excursion was obtained analytically, which fairly agrees with the experimental results.

Chaotic oscillations in a low pressure two-phase natural circulation loop under low power and high inlet subcooling conditions

The oscillation characteristics of a low pressure two-phase natural circulation loop have been investigated experimentally in this study. Experimental results indicate that the characteristics of the thermal hydraulic oscillations can be periodic, with 2–5 fundamental frequencies, or chaotic, depending on the heating power and inlet subcooling. The number of fundamental frequencies of oscillation increases if the inlet subcooling is increased at a given heating power or the heating power is decreased at a given inlet subcooling; chaotic oscillations appear if the inlet subcooling is further increased and/or the heating power is further decreased. A map of the oscillation characteristics is thus established. The change in oscillation characteristics is evident from the time evolution and power spectrum of a thermal hydraulic parameter and the phase portraits of two thermal hydraulic parameters. These results reveal that a strange attractor exists in a low pressure two-phase natural circulation loop with low power and very high inlet subcooling.

A correlation to predict chf in subcooled flow boiling

The present paper provides a discussion of the thermal-hydraulics requirements in fusion reactor components, with particular reference to the removal of high heat flux from plasma facing components and the critical heat flux (CHF) limit. Available experimental data on CHF of subcooled flow boiling in water, in the ranges of interest of fusion reactors thermal-hydraulic conditions, i.e. high inlet subcooling and velocity, and small channel diameter and length, are analyzed to discuss the influence of these parameters on CHF. The reference data-set (1887 experimental points) covers a wide range of operating conditions in the frame of present interest (0.1 < p < 8.4 MPa; 0.3 < D < 25.4 mm; 0.25 < L < 61 cm; 900 < G < 90000 kg/m 2·s; 0.3 < T in < 242.7°C). The aim of the research was to identify a new correlation based on a structure representing the relation of heat balance and using a non-linear regression analysis of the available data-set. A preliminary correlation (DINCE-92), based on 544 data points, had been developed providing a sensible improvement in predictions with respect to available predictive tools. Now, a new correlation (DINCE-93), based on the same structure of the above one and characterized by a very good statistics using a total of 1887 experimental points (88% of predictions are within ±20%) and by an R.M.S. error of 14.2%, has been identified and analyzed.

Effects of double-humped axial heat flux variation on the stability of two-phase flow in heated channels

Stability analysis of two-phase flow in heated channels with double-humped axial heat flux variation, relevant to boiling water nuclear reactors, has been carried out. Single-phase and two-phase flow equations are linearized about the steady-state solution, and the stability of the fixed points is studied in frequency domain. Effects of symmetric and asymmetric double-humped axial heat flux variation on stability has been determined. Results are presented as stability boundaries in parameter space and as bifurcation diagrams. It is found that whether a channel with single-humped heat flux variation becomes more or less stable as the heat flux is replaced by an equivalent double-humped profile, actually depends upon other system parameters, such as the channel inlet subcooling. For example, for low inlet subcooling, a channel with symmetric double-humped heat flux variation is less stable than another channel with single-humped heat flux variation (same total heat flux), whereas, the trend is reversed for high inlet subcooling.