Two-phase Flow Instability Research Articles

Active control of flow and heat transfer in silicon microchannels

Boiling heat transfer in silicon microchannels needs high walls and liquid superheats for bubble nucleation, leading to a strong thermal non-equilibrium between vapor and liquid phases, which not only damages the heat transfer device at the start-up stage, but also causes two-phase flow instabilities. In this paper, the seed bubble technique is used as an active control strategy to improve the flow and heat transfer in silicon microchannels. Seed bubbles are miniature bubbles of micron size, which are produced on a set of microheaters upstream of microchannels driven by pulse voltage signal. They flow downstream of microchannels after they depart from microheaters to decrease and control the thermal non-equilibrium between vapor and liquid phases in microchannels. The working fluid was methanol and the hydraulic diameter of the microchannels was 100 µm. The demand curves of pressure drops versus mass fluxes were examined with and without active control. Four regions (I, II, III and IV) of demand curves were identified. For the flow without active control, the four regions were the subcooled liquid flow, the superheated liquid flow, the unstable boiling flow and the vapor flow at high-vapor-mass qualities. Alternatively, for the flow with active control, the four regions were the subcooled liquid flow, the seed-bubble-triggered boiling flow, the seed-bubble-stabilized boiling flow and the vapor flow at high-vapor-mass qualities. The linear part of the demand curves is shortened when the seed bubble technique is used. The points at which the demand curves deviate from the linear part coincide into one point at different seed bubble frequencies. The seed bubbles have no influence on the subcooled liquid flow (region I) and the vapor flow at high-vapor-mass qualities (region IV). However, seed bubbles not only convert a superheated liquid flow into a quasi-stable boiling flow in region II, but also convert an unstable boiling flow into a quasi-stable boiling flow in region III. Besides, heat transfer coefficients with active control are several times those without active control in regions II and III. The higher the seed bubble frequencies, the more the heater surface temperatures decrease.

Heat transfer, flow regime and instability of a nano- and micro-porous structure evaporator in a two-phase thermosyphon loop

Two-phase flow instabilities which may occur at low and high heat loads were studied for a thermosyphon loop with R134a as refrigerant. The heat transfer surface of the evaporator was enhanced with a copper nano- and micro-porous structure. The heat transfer of the enhanced evaporator was compared to a smooth surface evaporator. Finally, the influence of the liquid level and the inside diameter of the riser on the instability of the system have been investigated. It was found that the enhanced structure surface decreased the oscillations at the entire range of heat fluxes and enhanced the heat transfer coefficient. Three flow regimes were observed: Bubbly flow with nucleate boiling heat transfer mechanism, confined bubbly/churn flow with backflow and finally churn flow at high heat fluxes.

Interfacial instability of turbulent two-phase stratified flow: Pressure-driven flow and non-Newtonian layers

We derive a flat-interface model to describe the flow of two horizontal, stably stratified fluids, where the bottom layer exhibits non-Newtonian rheology. The model takes into account the yield stress and power-law nature of the bottom fluid. In the light of the large viscosity contrast assumed to exist across the fluid interface, and for large pressure drops in the streamwise direction, the possibility for the upper Newtonian layer to display fully developed turbulence must be considered, and is described in our model. We develop a linear-stability analysis to predict the conditions under which the flat-interface state becomes unstable, and pay particular attention to characterizing the influence of the non-Newtonian rheology on the instability. Increasing the yield stress (up to the point where unyielded regions form in the bottom layer) is destabilizing; increasing the flow index, while bringing a broader spectrum of modes into play, is stabilizing. In addition, a second mode of instability is found, which depends on conditions in the bottom layer. For shear-thinning fluids, this second mode becomes more unstable, and yet more bottom-layer modes can become unstable for a suitable reduction in the flow index. One further difference between the Newtonian and non-Newtonian cases is the development of unyielded regions in the bottom layer, as the linear wave on the interface grows in time. These unyielded regions form in the trough of the wave, and can be observed in the linear analysis for a suitable parameter choice.

Analysis of Flow Instability for OTSG Using Frequency Domain Control Theory

Two-phase flow instability in parallel channels of a once-through steam generator (OTSG) is systematically analyzed by the modern frequency domain method. The mathematical expressions of heat transfer and flow for an OTSG are proposed, and the transfer function of the closed-loop system is deduced by the use of linearization and Laplace transfer. The OTSG’s stability is judged according to the Nyquist Stability Criterion. The instability of OTSG in two cases (single-channel model and multichannel model) is researched, respectively, for a numerical example. The result shows the classical frequency domain method can be commonly used when the coupling effects in the system are negligible, and it is only a special case of the multivariable method. Furthermore, the stability sensitivity to the operating parameters is analyzed for the OTSG in this paper. The predicted results are in agreement with the experimental results given in the literature.

Analysis of convective two-phase flow instabilities in vertical and horizontal in-tube boiling systems

In this work, analysis of two-phase flow boiling instabilities in vertical and horizontal systems is presented. The steady-state system pressure-drop characteristics are determined by a numerical solution of the governing equations as derived from the Drift-Flux model. The transient characteristics of the two-phase flow are obtained for various parameters and the results are presented in graphical and tabular forms. The numerical solutions are determined using an explicit finite difference scheme. The results of numerical solutions are verified by the experimental findings. A satisfactory agreement between the theory and experiments is obtained.

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 research on two-phase flow instability in parallel channels

Two-phase flow instability of two-channel system has been theoretically studied in the present study. Based on the homogeneous flow model, the parallel channels 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 marginal stability boundary (MSB) at different system pressure conditions is obtained. The typical MSB shape is usually a classical inclination “L” at some operation condition (i.e. the system pressure is low and the inlet resistance coefficient is small). The three-dimensional instability spaces (or instability reefs) with different inlet resistance coefficients are obtained. The three coordinates consists of phase change number ( N pch ), subcooling number ( N sub ) and nondimensional pressure ( P +). The lower part of the instability space is larger than the upper one. Increasing the system pressure or inlet resistance coefficient can strengthen the system stability. However, increasing the heating power destabilize the system stability. The influence of inlet subcooling on the system stability is multi-valued.

Experimental investigation of boiling two-phase flow instability of nitrogen in a vertical tube

Boiling flow instability of nitrogen in a vertical tube is experimentally investigated in the present study. The experiments reveal that pressure has a significant effect on the characteristics of the heat flux—mass flux type boiling flow instability. First, the pressure has strong effects on both the developing time and the fluctuation amplitude. Especially increasing pressure leads to decrease the fluctuating amplitude of mass flux. Then, the mass flux evolving curves under different pressures feature out a shape like a leaf. The characteristics of the heat flux—mass flux type boiling flow instability under lower pressure are very complicated, however, with increasing pressure, this type of instability is gradually suppressed.

Correction for Bakhtar et al. , Instability in two-phase flows of steam

Correction for ‘Instability in two-phase flows of steam’ by F. Bakhtar, S. R. Otto, M. Y. Zamri and M. Sarkies (Proc. R. Soc. A 464 , 537–553. (doi: 10.1098/rspa.2007.0087 )). The following equation contains typographical errors that has no consequence for any other equation or result in the above paper.

Experimental study on two-phase flow instability of natural circulation under rolling motion condition

Two-phase flow instability of natural circulation under a rolling motion condition is experimentally studied. The experimental results show the rolling motion induces a fluid flow fluctuation. At the trough point of the flow fluctuation, rolling motion can cause the early occurrence of natural circulation two-phase flow instability, and this case is defined as trough-type flow oscillation. The system stability decreases with increasing rolling amplitude and effect of rolling frequency is nonlinear. The complex overlap effect of trough-type flow oscillation and density wave oscillation can enhance the system coolant fluctuation; this case is defined as complex flow oscillation. Complex flow oscillation may be divided into two types: regular and irregular complex flow oscillations. Irregular complex flow oscillation is a transition type from trough-type flow oscillation to regular complex flow oscillation. Under the same thermal hydraulic conditions, the marginal stability boundary (MSB) of regular complex flow oscillation is similar to that of density wave oscillation without rolling motion, and the influences of rolling parameters on the MSB are slight.

The influence of ocean conditions on two-phase flow instability in a parallel multi-channel system

In this paper, the two-phase flow instability between multi-channels (FIBM) operating under ocean conditions is studied theoretically. The physical and mathematical model of the multi-channel system which is based on Lee and Pan [Lee, J.D., Pan, C., 1999. Dynamics of multiple parallel boiling channel systems with forced flows. Nuclear Engineering and Design 192, 31–44], is extended to analyze the influence of ocean conditions. The influence of ocean conditions on the FIBM is analyzed, particularly with respect to the periodic total mass flow rate and rolling motion. Furthermore, the instability oscillation trajectories of the multi-channel system are obtained on the phase plane of the inlet velocity and boiling boundary. Some of the trajectories show chaotic characteristic. The instability zone of a nine-channel system under rolling motion is then obtained.

Instability in two-phase flows of steam

In two-phase flows of steam, when the velocity is between the equilibrium and frozen speeds of sound, the system is fundamentally unstable. Because any disturbance of the system, e.g. imposition of a small supercooling on the fluid, will cause condensation, the resulting heat release will accelerate the flow and increase the supercooling and thus move the system further from thermodynamic equilibrium. But in high-speed flows of a two-phase mixture, dynamic changes affect the thermodynamic equilibrium within the fluid, leading to phase change, and the heat release resulting from condensation disturbs the flow further and can also cause the disturbances to be amplified at other Mach numbers. To investigate the existence of instabilities in such flows, the behaviour of small perturbations of the system has been examined using stability theory. It is found that, although the amplification rate is highest between the equilibrium and frozen speeds of sound, such flows are temporally unstable at all Mach numbers.

A first assessment of the NEPTUNE_CFD code: Instabilities in a stratified flow comparison between the VOF method and a two-field approach

This paper presents some results concerning a first benchmark for the new European research code for thermal hydraulics computations: NEPTUNE_CFD. This benchmark relies on the Thorpe experiment to model the occurrence of instabilities in a stratified two-phase flow. The first part of this work is to create a numerical trial case with the VOF approach. The results, in terms of time of onset of the instability, critical wave-number or wave phase speed, are rather good compared to linear inviscid theory and experimental data. Additional numerical tests showed the effect of the surface tension and density ratio on the growing dynamics of the instability and the structure of the waves. In the second part, a code to code (VOF/multi-field) comparison is performed for a case with zero surface tension. The results showed some discrepancies in terms of wave amplitudes, growing rates and a time shifting in the global dynamics. Afterward, two surface tension formulations are proposed in the multi-field approach. Both formulations provided similar results. The time for onset of the instability, the most amplified wave-number and its amplitude were in rather good agreement with the linear analysis and VOF results. However, the time-shifted dynamics was still observed.

Flow boiling of liquid nitrogen in micro-tubes: Part I – The onset of nucleate boiling, two-phase flow instability and two-phase flow pressure drop

This paper is the first portion of a two-part study concerning the flow boiling of liquid nitrogen in the micro-tubes with the diameters of 0.531, 0.834, 1.042 and 1.931 mm. The contents mainly include the onset of nucleate boiling (ONB), two-phase flow instability and two-phase flow pressure drop. At ONB, mass flux drops suddenly while pressure drop increases, and apparent wall temperature hysteresis in the range of 1.0–5.0 K occurs. Modified Thom model can predict the wall superheat and heat flux at ONB. Moreover, stable long-period (50–60 s) and large-amplitude oscillations of mass flux, pressure drop and wall temperatures are observed at ONB for the 1.042 and 1.931 mm micro-tubes. Block phenomenon at ONB is also observed in the cases of high mass flux. The regions for the oscillations, block and stable flow boiling are classified. A physical model of vapor patch coalesced at the outlet is proposed to explain the ONB oscillations and block. Vapor generation caused by the flash evaporation is so large that it should be taken into account to precisely depict the variation of mass quality along the micro-tube. The adiabatic and diabatic two-phase flow pressure drop characteristics in micro-tubes are investigated and compared with four models including homogeneous model and three classical separated flow models. Contrary to the conventional channels, homogeneous model yields better prediction than three separated flow models. It can be explained by the fact that the density ratio of liquid to vapor for nitrogen is comparatively small, and the liquid and vapor phases may mix well in micro-tube at high mass flux due to small viscosity of liquid nitrogen, which leads to a more homogeneous flow. Part II of this study will focus on the heat transfer characteristics and critical heat flux (CHF) of flow boiling of liquid nitrogen in micro-tubes.

Theoretical investigations on two-phase flow instability in parallel multichannel system

In this paper, the behavior of multichannel system two-phase flow instability is studied theoretically. A physics model that includes the entrance section, heater section and riser section is built. The subcooled boiling is also included. The results of twin-channel system are compared with the twin-channel experiment. Then the model is extended to the multichannel systems that have more channels. The two-phase flow instability between multichannels (FIBM) is studied under different system pressures, different inlet resistance coefficients and asymmetric heating. The instability boundaries of the multichannel system are obtained in the parameter plane of the subcooling and phase change numbers. A concept of instability space or instability reef is brought forward. Finally, the influence of inlet and riser sections on the FIBM is analyzed.

Two-phase flow instability for boiling in a microchannel heat sink

The present study explores experimentally the two-phase flow instability in a microchannel heat sink with 15 parallel microchannels. The hydraulic diameter for each channel is 86.3 μm. Flow boiling in the present microchannel heat sink demonstrates significantly different two-phase flow patterns under stable or unstable conditions. For the stable cases bubble nucleation, slug flow and slug or annular flows appear sequentially in the flow direction. On the other hand, forward or reversed slug/annular flows appear alternatively in every channel. Moreover, the length of bubble slug may oscillate for unstable cases with reversed flow demonstrating the suppressing effect of pressure field for bubble growth. It is found that the magnitude of pressure drop oscillations may be used as an index for the appearance of reversed flow. A stability map on the plane of inlet subcooling number versus phase change number is established. A very narrow region for stable two-phase flow or mild two-phase flow oscillations is present near the line of zero exit quality.

B38 熱水系不安定振動による定量的banded tremorモデル(火山の物理(2),日本火山学会2006年秋季大会)

B38 熱水系不安定振動による定量的banded tremorモデル(火山の物理(2),日本火山学会2006年秋季大会)

Review on two-phase flow instabilities in narrow spaces

Instabilities in two-phase flow have been studied since the 1950s. These phenomena may appear in power generation and heat transfer systems where two-phase flow is involved. Because of thermal management in small size systems, micro-fluidics plays an important role. Typical processes must be considered when the channel hydraulic diameter becomes very small. In this paper, a brief review of two-phase flow instabilities encountered in channels having hydraulic diameters greater than 10 mm are presented. The main instability types are discussed according to the existing experimental results and models. The second part of the paper examines two-phase flow instabilities in narrow spaces. Pool and flow boiling cases are considered. Experiments as well as theoretical models existing in the literature are examined. It was found that several experimental works evidenced these instabilities meanwhile only limited theoretical developments exist in the literature. In the last part of the paper an interpretation of the two-phase flow instabilities linked to narrow spaces are presented. This approach is based on characteristic time scales of the two-phase flow and bubble growth in the capillaries.

Pressure drop and flow boiling instabilities in silicon microchannel heat sinks

A simultaneous visualization and measurement experiment has been performed to study pressure drop and flow instabilities at various mass fluxes and heat fluxes during flow boiling of deionized water in a silicon microchannel heat sink. The silicon micro heat sink consisted of eight parallel microchannels 60 mm long, having a trapezoidal cross section with a hydraulic diameter of 72.7 µm. It is found that (1) the onset of nucleate boiling (ONB) depends on both the amount of heat flux and mass flux. The mass flux, at which the onset of nucleate boiling occurs, increases as the heat flux is increased; (2) the difference in mass fluxes between the ONB and the onset of flow instability (OFI) decreases as the heat flux is increased; (3) both oscillation amplitude and oscillation period of various measurements near the OFI are small; (4) as the mass flux is decreased further from the OFI while keeping the heat flux constant, the following boiling instability flow modes occurred sequentially: the liquid/two-phase alternating flow (LTAF) and the liquid/two-phase/vapor alternating flow (LTVAF); (5) the occurrence of LTAF and LTVAF, as well as their induced large-amplitude/long-period oscillations of various measurements, are owing to the reversed flow of vapor core because of the limited expansion space in the microchannels; (6) the appearance of the reversed flow of the vapor core in parallel microchannels is not in phase due to the flow or nucleation nonuniformity. The results presented in this paper help us to better understand the two-phase flow instabilities occurring in the silicon-based micro heat sinks.

Limiting Factors for External Reactor Vessel Cooling

The method of external reactor vessel cooling (ERVC) that involves flooding of the reactor cavity during a severe accident has been considered a viable means for in-vessel retention (IVR). For high-power reactors, however, there are some limiting factors that might adversely affect the feasibility of using ERVC as a means for IVR. In this paper, the key limiting factors for ERVC have been identified and critically discussed. These factors include the choking limit for steam venting (CLSV) through the bottleneck of the vessel/insulation structure, the critical heat flux (CHF) for downward-facing boiling on the vessel outer surface, and the two-phase flow instabilities in the natural circulation loop within the flooded cavity. To enhance ERVC, it is necessary to eliminate or relax these limiting factors. Accordingly, methods to enhance ERVC and thus improve margins for IVR have been proposed and demonstrated, using the APR1400 as an example. The strategy is based on using two distinctly different methods to enhance ERVC. One involves the use of an enhanced vessel/insulation design to facilitate steam venting through the bottleneck of the annular channel. The other involves the use of an appropriate vessel coating to promote downward-facing boiling. It is found that the use of an enhanced vessel/insulation design with bottleneck enlargement could greatly facilitate the process of steam venting through the bottleneck region as well as streamline the resulting two-phase motions in the annular channel. By selecting a suitable enhanced vessel/insulation design, not only the CLSV but also the CHF limits could be significantly increased. In addition, the problem associated with two-phase flow instabilities and flow-induced mechanical vibration could be minimized. It is also found that the use of vessel coatings made of microporous metallic layers could greatly facilitate downward-facing boiling on the vessel outer surface. With vessel coatings, the local CHF limits at different angular locations of the vessel outer surface could be enhanced by ~1.2 to 2 times the CHF compared with a plain vessel without coatings. The CHF enhancement could be attributed to the structure of the porous coating itself and the capillary action it induced. The matrix of cavities and voids within the coating effectively trap vapor, which serve as active nucleation sites. These sites in turn are fed with liquid flowing through the interconnected channels. The pores on the surface of the porous coating serve as flow inlets for liquid supply to the heating surface, leading to appreciable enhancement in downward-facing boiling heat transfer and the local CHF limits. Results of the present study suggest that by utilizing an enhanced vessel/insulation design with vessel coating, it is possible to significantly enhance the CLSV and the CHF limits as well as minimize the two-phase flow instability problems, thus substantially increasing the margin for IVR.