Numerical investigation of static flow instability in a low-pressure subcooled boiling channel

A three-dimensional two-fluid model to predict subcooled boiling flow at low pressure is presented. The model is adopted to investigate the two-phase flow and heat transfer characteristics in a heated channel. The presence of bubbles as a consequence of heating flow through a vertical rectangular channel has a significant effect on the overall pressure drop along the channel. Numerical results were compared against a series experimental data performed at various conditions – mass flux, heat flux, inlet temperature and exit pressure. Good agreement on the overall pressure drop was achieved. The onset of flow instability velocity was also accurately determined when compared against measurements. Predicted results of void fraction provided useful information towards a more fundamental understanding of the occurrence of onset of nucleate boiling, onset of significant voiding and onset of flow instability. The phenomenon of boiling onset oscillations was also predicted through the use of the two-fluid model.     

Thermal hydraulic modeling of a natural circulation loop

 The experiment was carried out on the test loop HRTL-5, which simulates the geometry and system design of a 5 MW nuclear heating reactor. The analysis was based on a one-dimensional two-phase flow drift model with conservation equations for mass, steam, energy and momentum. Clausius–Clapeyron equation was used for the calculation of flashing front in the riser. A set of ordinary equations, which describes the behavior of two-phase flow in the natural circulation system, was derived through integration of the above conservation equations for the subcooled boiling region, bulk boiling region in the heated section and for the riser. The method of time-domain was used for the calculation. Both static and dynamic results are presented. System pressure, inlet subcooling and heat flux are varied as input parameters. The results show that subcooled boiling in the heated section and void flashing in the riser have significant influence on the distribution of the void fraction, mass flow rate and flow instability of the system, especially at low pressure. The response of mass flow rate, after a small disturbance in the heat flux is shown, and based on it the instability map of the system is given through experiment and calculation. There exists three regions in the instability map of the investigated natural circulation system, namely, the stable two-phase flow region, the unstable bulk and subcooled boiling flow region and the stable subcooled boiling and single phase flow region. The mechanism of two-phase flow oscillation is interpreted. Received on 24 January 2000     

Effects of dynamic load on flow and heat transfer of two-phase boiling water in a horizontal pipe

An experimental investigation was performed to obtain the flow and heat transfer characteristics of single-phase water flow and two-phase pipe boiling water flow under high gravity (Hi-G) in present work. The experiments were conducted on a rotating platform, and boiling two-phase flow state was obtained by means of electric heating. The data were collected specifically in the test section, which was a lucite pipe with inner diameter of 20 mm and length of 400 mm. By changing the parameters, such as rotation speed, inlet temperature, flow rate, and etc., and analyzing the fluid resistance, effective heat and heat transfer coefficient of the experimental data, the effects of dynamic load on the flow and heat transfer characteristics of single phase water and two-phase boiling water flow were investigated and obtained. The two-phase flow patterns under Hi-G condition were obtained with a video camera. The results show that the dynamic load significantly influences the flow characteristic and boiling heat transfer of the two-phase pipe flow. As the direction of the dynamic load and the flow direction are opposite, the greater the dynamic load, the higher the outlet pressure and the flow resistance, and the lower the flow rate, the void fraction, the wall inner surface temperature and the heat transfer capability. Therefore, the dynamic load will block the fluid flow, enhance heat dissipation toward the ambient environment and reduce the heat transfer to the two-phase boiling flow.     

Multivariate hydrodynamic analysis of boiling channel flow stability from inherent noise measurements

Perturbations in the inlet flow, temperature, channel power, pressure drop and exit void fraction were monitored on a test channel for a range of power levels up to flow stability threshold. Multivariate spectral analysis methods are used to determine the significant frequency response relationships between the measured variables, and the significant cross-spectral density estimates are compared with those obtained from a distributed frequency domain model whose subcooled boiling, two-phase slip and friction correlations are optimised using a special parameter estimation procedure. The optimised model gives the physical mechanisms (perturbed pressure drop components) which tend to drive the channel unstable. The spectral analysis and modelling techniques are generally applicable to performance and diagnostic studies in commercial heat transfer plant where traditional methods of superimposing test signals are impractical during normal operation.     

The effect of internal surface modification on flow instabilities in forced convection boiling in a horizontal tube

This paper presents the experimental result of a study on the effects of heat transfer enhancement on two-phase flow instabilities in a horizontal in-tube flow boiling system. Five different heat transfer surface configurations and five different inlet temperatures are used to observe the effect of heat transfer enhancement and inlet subcooling. All experiments are carried out at constant heat input, system pressure and exit restriction. Dynamic instabilities, namely pressure-drop type, density-wave type and thermal oscillations are found to occur for all the investigated temperatures and enhancement configurations, and the boundaries for the appearance of these oscillations are found. The effect of the enhancement configurations on the characteristics of the boiling flow dynamic instabilities is studied in detail. The comparison between the bare tube and the enhanced tube configurations are made on the basis of boiling flow instabilities. Differences among the enhanced configurations are also determined to observe which of them is the most stable and unstable one. The amplitudes and periods of pressure-drop type oscillations and density-wave type oscillations for tubes with enhanced surfaces are found to be higher than those of the bare tube. The bare tube is found to be the most stable configuration, while tube with internal springs having bigger pitch is found to be the most unstable one among the tested tubes. It is found that system stability increases with decreasing equivalent diameter for the same type heater tube configurations; however, on the basis of effective diameter there is no single result such as stability increase/decrease with increasing/decreasing effective diameter.     

Experimental investigation of flow boiling characteristics in a cross-linked microchannel heat sink

This paper experimentally investigates flow boiling characteristics in a cross-linked microchannel heat sink at low mass fluxes and high heat fluxes. The heat sink consists of 45 straight microchannels each with a hydraulic diameter of 248 μm and heated length of 16 mm. Three cross-links, of width 500 μm, are introduced in the present microchannel heat sink to achieve better temperature uniformity and to avoid flow mal-distribution. Flow visualization, flow instability, two-phase pressure drop, and two-phase heat transfer measurements are conducted using the dielectric coolant FC-72 over a range of heat flux from 7.2 to 104.2 kW/m², mass flux from 99 to 290 kg/m² s, and exit quality from 0.01 to 0.71. Thermochromic liquid crystals are used in the present study as full-field surface temperature sensors to map the temperature distribution on the heat sink surface. Flow visualization studies indicate that the observed flow regime is primarily slug. Visual observations of flow patterns in the cross-links demonstrate that bubbles nucleate and grow rapidly on the surface of the cross-links and in the tangential direction at the microchannels’ entrance due to the effect of circulations generated in those regions. The two-phase pressure drop strongly increases with the exit quality, at x_e,o < 0.3, and the two-phase frictional pressure drop increases by a factor of 1.6–2 compared to the straight microchannel heat sink. The flow boiling heat transfer coefficient increases with increasing exit quality at a constant mass flux, which is caused by the dominance of the nucleation boiling mechanism in the cross-link region.     

Analysis of forced-convection boiling flow instabilities in a single-channel upflow system

A numerical model is developed to predict the steady-state and transient behaviour of forced-convection boiling two-phase flow in a single channel. The model is based on the assumption of homogeneous two-phase flow and thermodynamic equilibrium of the phases. Compressibility effects in the two-phase region, motion of the bulk boiling interface and the thermal capacity of the heater wall have been included in the analysis. The model is used to study the effects of heat input, inlet subcooling and flow rate on the system behaviour. For comparison purposes, an experimental investigation was conducted using a single-channel, electrically heated, forced-convection upflow system. Steady-state operating characteristics, and stable and unstable regions, are determined as a function of heat flux, inlet subcooling and mass flow rate. Different modes of oscillation and their characteristics have been investigated. The model's predictions are in good agreement with the experimental results.     

Freon R141b flow boiling in silicon microchannel heat sinks: experimental investigation

This paper presents experimental investigations on Freon R141b flow boiling in rectangular microchannel heat sinks. The main aim is to provide an appropriate working fluid for microchannel flow boiling to meet the cooling demand of high power electronic devices. The microchannel heat sink used in this work contains 50 parallel channels, with a 60 × 200 (W × H) μm cross-section. The flow boiling heat transfer experiments are performed with R141b over mass velocities ranging from 400 to 980 kg/(m² s) and heat flux from 40 to 700 kW/m², and the outlet pressure satisfying the atmospheric condition. The fluid flow-rate, fluid inlet/outlet temperature, wall temperature, and pressure drop are measured. The results indicate that the mean heat transfer coefficient of R141b flow boiling in present microchannel heat sinks depends heavily on mass velocity and heat flux and can be predicted by Kandlikar’s correlation (Heat Transf Eng 25(3):86–93, 2004). The two-phase pressure drop keeps increasing as mass velocity and exit vapor quality rise.     

Two-phase flow instabilities in a silicon microchannels heat sink

Two-phase flow instabilities are highly undesirable in microchannels-based heat sinks as they can lead to temperature oscillations with high amplitudes, premature critical heat flux and mechanical vibrations. This work is an experimental study of boiling instabilities in a microchannel silicon heat sink with 40 parallel rectangular microchannels, having a length of 15 mm and a hydraulic diameter of 194 μm. A series of experiments have been carried out to investigate pressure and temperature oscillations during the flow boiling instabilities under uniform heating, using water as a cooling liquid. Thin nickel film thermometers, integrated on the back side of a heat sink with microchannels, were used in order to obtain a better insight related to temperature fluctuations caused by two-phase flow instabilities. Flow regime maps are presented for two inlet water temperatures, showing stable and unstable flow regimes. It was observed that boiling leads to asymmetrical flow distribution within microchannels that result in high temperature non-uniformity and the simultaneously existence of different flow regimes along the transverse direction. Two types of two-phase flow instabilities with appreciable pressure and temperature fluctuations were observed, that depended on the heat to mass flux ratio and inlet water temperature. These were high amplitude/low frequency and low amplitude/high frequency instabilities. High speed camera imaging, performed simultaneously with pressure and temperature measurements, showed that inlet/outlet pressure and the temperature fluctuations existed due to alternation between liquid/two-phase/vapour flows. It was also determined that the inlet water subcooling condition affects the magnitudes of the temperature oscillations in two-phase flow instabilities and flow distribution within the microchannels.     

Theoretical analysis of pressure-drop type instabilities in an upflow boiling system with an exit restriction

 In this work, two-phase flow pressure-drop type instabilities in an upflow boiling system are studied theoretically. Dynamic simulations of the pressure-drop type instabilities require the knowledge of the steady state characteristics of the system in terms of the pressure drop versus the mass flow rate. In a boiling system with an exit restriction at the outlet of the boiling channel, the pressure drop through the system concentrates at the exit restriction. Therefore, the correlation of the pressure drop of the two-phase mixture flowing through the exit restriction (i.e. a sharp-edged orifice) is essential in the calculation of the total pressure drop of the system. A model for the exit restriction is developed and compared with the experimental results covering a wide range of vapor quality with different heat inputs and inlet subcoolings. The drift-flux model is adopted to predict the steady state characteristics of the boiling system. The dynamic oscillations of the quasi-static pressure-drop type instabilities in the boiling system are simulated and good predictions of the system stability boundary and oscillatory characteristics are obtained when compared with the experimental results. Received on 4 May 2000     

Two-phase flow instabilities in a horizontal single boiling channel

A study of the stability of an electrically heated single channel, forced convection horizontal system was conducted by using Freon-11 as the test fluid. Two major modes of oscillations, namely, density-wave type (high frequency) and pressure-drop type (low frequency) oscillations have been observed. The steady-state operating characteristics and stable and unstable regions are determined as a function of heat flux, exit orifice diameter and mass flow rate. Different modes of oscillations and their characteristics have been investigated. The effect of the exit restriction on the system stability has also been studied.A mathematical model has been developed to predict the transient behavior of boiling two-phase systems. The model is based on homogenous flow assumption and thermodynamic equilibrium between the liquid and vapor phases. The transient characteristics of boiling two-phase flow horizontal system are obtained for various heat inputs, flow rates and exit orifice diameters by perturbing the governing equations around a steady state. Theoretical and experimental results have been compared.     

An experimental investigation of thermally induced flow instabilities in a convective boiling upflow system

The two-phase flow instabilities in a single channel, forced convection, open loop, up-flow system have been investigated experimentally using R-11 as the working fluid. The effects of mass flow rate, heat input, inlet liquid temperature and upstream compressible volume on two-phase flow instabilities have been investigated. Two heater surfaces were tested at five different heat inputs with constant inlet temperature, and four different inlet temperatures with constant heat input. For each case, the mass flow rate was varied over a wide range covering the entire scope for boiling two-phase flows. Experiments were also conducted at different compressible volumes, with constant heat input, inlet fluid temperature, and average mass flow rate. The oscillations of inlet mass flow rate, heater inlet pressure, and heater wall temperature were recorded. The effects of mass flow rate, inlet liquid temperature and heat input on the amplitudes and periods of inlet pressure and thermal oscillations are presented in tabular and graphical forms.

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Experimentelle Untersuchung der thermisch bedingten Strömungsinstabilitäten bei konvektiven Sieden in einer Aufwärtsströmung

Zusammenfassung Mit R-11 als Arbeitsfluid werden Zweiphasen-Strömungsinstabilitäten im Einzelkanal bei erzwungener Aufwärtsströmung ohne Rückführung experimentell untersucht, und zwar besonders im Hinblick auf den Einfluß der Massenstromdichte, der Wärmezufuhr, der Eintrittstemperatur und des in Strömungsrichtung zunehmenden kompressiblen Volumenanteils. Zwei Heizflächen wurden einmal mit fünf verschiedenen Heizflächenbelastungen und konstanter Eintrittstemperatur getestet und dann bei vier verschiedenen Wärmeeinträgen und konstanter Eintrittstemperatur. In jedem der Fälle erfolgte die Variation der Massenstromdichte in einem so weiten Bereich, daß das gesamte Feld der Zweiphasen-Siedeströmungen durchfahren werden konnte. Es wurden auch Experimente mit verschiedenen kompressiblen Volumenanteilen bei konstanter Wärmezufuhr, Fluideintrittstemperatur und mittlerer Massenstromdichte durchgeführt. Die Oszillationen der Massenstromdichte und des Druckes am Eintritt in die Heizstrecke sowie deren Wandtemperatur wurden aufgezeichnet. Die Enflüsse der Massenstromdichte, der Fluideintrittstemperatur und der Wärmezufuhr auf Amplituden und Perioden der Druck- und Temperaturoszillationen sind tabellarisch und in Diagrammform dargestellt.

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Dedicated to Prof. Dr.-Ing. F. Mayinger's 60th birthday     

The prediction of two-phase mixture level and hydrodynamically-controlled dryout under low flow conditions

A theory is given for the thermal-hydraulic phenomena during uncovery of a flow channel. This is relevant to a reactor core under typical small break or operational transient conditions. A distinct equivalent collapsed liquid level and a two-phase-mixture level are defined in the model. The former represents the liquid inventory in the channel, while the latter characterizes the heat transfer regimes. The definition of these levels are coupled through the mass and energy conservation equations, and the constitutive relations for void fraction and net vapor generation location.Analytical solutions are obtained for the transient variation of both the collapsed liquid and the two-phase mixture levels.The analyses have been compared with existing single-tube data with uniform heat flux, and rod bundle experiments with an axial power profile and inlet feedwater flow. The results demonstrate the potential of the present model for application to reactor conditions.     

Microgravity flow regime data and analysis

To utilize the advantageous properties of two-phase flow in microgravity applications, the knowledge base of two-phase flow phenomena must be extended to include the effects of gravity. In the experiment described, data regarding the behavior of two-phase flow in a conduit under microgravity conditions (essentially zero gravity) are explored. Of particular interest, knowledge of the void fraction of the gas and liquid in a conduit is necessary to develop models for heat and mass transfer, pressure drop, and wall shear. An experiment was conducted under reduced gravity conditions to collect data by means of a capacitance void fraction sensor and high speed visual imagery. Independent parameters were varied to map the flow regime regions. These independent parameters include gas and liquid volumetric flow rates and saturation pressures. Void fraction measurements were taken at a rate of 100 Hz with six sensors at two locations along the conduit. Further, statistical parameters were developed from the void fraction measurements. Statistical parameters such as variance, signal-to-noise ratio, half height value, and linear area difference were calculated and found to have characteristics allowing flow regime identification.     

Correlations of flow maldistribution parameters in an air cooled heat exchanger

The present paper provides correlations of flow maldistribution parameters in air‐cooled heat exchangers. The flow field in the inlet header was obtained through the numerical solution of the governing partial differential equations including the conservation equations of mass and momentum in addition to the equations of the turbulence model. The results were obtained for different number of nozzles of 2–4, different inlet flow velocities of 1–2.5m/s and different nozzle geometries in addition to incorporation of a second header. The results are presented in terms of mass flow rate distributions in the tubes of the heat exchanger and their standard deviations. The results indicate that the inlet flow velocity has insignificant influence on maldistribution while the nozzle geometry shape has a slight effect. Also, the results indicate that reducing the nozzle diameter results in an increase in the flow maldistribution. A 25% increase is obtained in the standard deviation as a result of decreasing the diameter by 25%. Increasing the number of nozzles has a significant influence on the maldistribution. A reduction of 62.5% in the standard deviation of the mass flow rate inside the tubes is achieved by increasing the number of nozzles from 2 to 4. The results indicate that incorporating a second header results in a significant reduction in the flow maldistribution. A 50% decrease in the standard deviation is achieved as a result of incorporation of a second header of seven holes. It is also found that the hole‐diameter distribution at the exit of the second header has a slight influence on the flow maldistribution. Correlations of the flow maldistribution in terms of the investigated parameters are presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Flow boiling heat transfer in a vertical spirally internally ribbed tube

 Experiments of flow boiling heat transfer and two-phase flow frictional pressure drop in a spirally internally ribbed tube (φ22×5.5 mm) and a smooth tube (φ19×2 mm) were conducted, respectively, under the condition of 6×10⁵ Pa (absolute atmosphere pressure). The available heated length of the test sections was 2500 mm. The mass fluxes were selected, respectively, at 410, 610 and 810 kg/m² s. The maximum heat flux was controlled according to exit quality, which was no more than 0.3 in each test run. The experimental results in the spirally internally ribbed tube were compared with that in the smooth tube. It shows that flow boiling heat transfer coefficients in the spirally internally ribbed tube are 1.4–2 times that in the smooth tube, and the flow boiling heat transfer under the condition of smaller temperature differences can be achieved in the spirally internally ribbed tube. Also, the two-phase flow frictional pressure drop in the spirally internally ribbed tube increases a factor of 1.6–2 as compared with that in the smooth tube. The effects of mass flux and pressure on the flow boiling heat transfer were presented. The effect of diameters on flow boiling heat transfer in smooth tubes was analyzed. Based on the fits of the experimental data, correlations of flow boiling heat transfer coefficient and two-phase flow frictional factor were proposed, respectively. The mechanisms of enhanced flow boiling heat transfer in the spirally internally ribbed tube were analyzed. Received on 1 December 1999     

Prediction of refrigerant void fraction in horizontal tubes using probabilistic flow regime maps

A state of the art review of two-phase void fraction models in smooth horizontal tubes is provided and a probabilistic two-phase flow regime map void fraction model is developed for refrigerants under condensation, adiabatic, and evaporation conditions in smooth, horizontal tubes. Time fraction information from a generalized probabilistic two-phase flow map is used to provide a physically based weighting of void fraction models for different flow regimes. The present model and void fraction models in the literature are compared to data from multiple sources including R11, R12, R134a, R22, R410A refrigerants, 4.26–9.58 mm diameter tubes, mass fluxes from 70 to 900 kg/m² s, and a full quality range. The present model has a mean absolute deviation of 3.5% when compared to the collected database.     

Algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow

The study considers algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow, focusing in particular on momentum and heat transfer (so-called ‘convective boiling’) through the annular liquid film. In contrast with single-phase wall-bounded flow theory, shear-driven annular liquid films are assumed here to behave as fluid-bounded flows, mostly interacting with the shearing gas-entrained droplets core flow. Besides providing velocity and temperature profiles through the liquid film, the turbulence model proposed here predicts key parameters such as the average liquid film thickness, the void fraction and the convective boiling heat transfer coefficient with accuracies comparable or better than those of leading design correlations. This turbulence model is part of a unified annular flow modeling suite that includes methods to predict the entrained liquid fraction and the axial frictional pressure gradient. The underlying heat transfer database covers nine fluids (water, two hydrocarbons and six refrigerants) for vertical and horizontal tubes of 1.03-14.4 mm diameter and pressures of 0.1-7.2 MPa. Importantly, this study shows that there appears to be no macro-to-microscale transition when it comes to annular flow. Simply better physical modeling is required to span this range.     

Periodic flow boiling in a non-uniformly heated microchannel heat sink

Hydrodynamic and thermal characteristics of flow boiling in a non-uniformly heated microchannel were studied. Experiments were performed with a single microchannel and a series of microheaters to study the microscale boiling of water under axially non-uniform heat input conditions. A simultaneous real time visualization of the flow pattern was performed with the measurement of experimental parameters. Tests were performed over a mass flux of 309.8 kg/m² s, and heat flux of 200–600 kW/m². Test results showed different fluctuations of heated wall temperature, pressure drop, and mass flux with variations of the heat input along the flow direction. The unique periodic flow boiling in a single microchannel was observed at all heat flux conditions except for the increasing heat input distribution case which is the nearly uniform effective heat input distribution condition. The instability is correlated with flow pattern transition. For the nearly uniform effective heating condition, no fluctuation of the wall temperature, pressure drop, or mass flux was observed. We can relieve the instability by increasing total heat input along the flow direction and predict the instability using the transition criteria and flow pattern map.     

Explosive boiling of water in parallel micro-channels

The objective of this study is to visualize the flow pattern and to measure heat transfer coefficient during explosive boiling of water in parallel triangular micro-channels. Tests were performed in the range of inlet Reynolds number 25–60, mass flux 95–340 kg/m²s, and heat flux 80–330 kW/m².The flow visualization showed that the behavior of long vapor bubbles, occurring in a micro-channel at low Reynolds numbers, was not similar to annular flow with interposed intermitted slugs of liquid between two long vapor trains. This process may be regarded as explosive boiling with periodic wetting and dryout.In the presence of two-phase liquid–vapor flow in the micro-channel, there are pressure drop oscillations, which increase with increasing vapor quality.This study shows strong dependence of the heat transfer coefficient on the vapor quality. The time when liquid wets the heated surface decreases with increasing heat flux. Dryout occurs immediately after venting of the elongated bubble.