Two-phase flow and pool boiling heat transfer in microgravity

Researches on two-phase flow and pool boiling heat transfer in microgravity, which included ground-based tests, flight experiments, and theoretical analyses, were conducted in the National Microgravity Laboratory/CAS. A semi-theoretical Weber number model was proposed to predict the slug-to-annular flow transition of two-phase gas–liquid flows in microgravity, while the influence of the initial bubble size on the bubble-to-slug flow transition was investigated numerically using the Monte Carlo method. Two-phase flow pattern maps in microgravity were obtained in the experiments both aboard the Russian space station Mir and aboard IL-76 reduced gravity airplane. Mini-scale modeling was also used to simulate the behavior of microgravity two-phase flow on the ground. Pressure drops of two-phase flow in microgravity were also measured experimentally and correlated successfully based on its characteristics. Two space experiments on pool boiling phenomena in microgravity were performed aboard the Chinese recoverable satellites. Steady pool boiling of R113 on a thin wire with a temperature-controlled heating method was studied aboard RS-22, while quasi-steady pool boiling of FC-72 on a plate was studied aboard SJ-8. Ground-based experiments were also performed both in normal gravity and in short-term microgravity in the drop tower Beijing. Only slight enhancement of heat transfer was observed in the wire case, while enhancement in low heat flux and deterioration in high heat flux were observed in the plate case. Lateral motions of vapor bubbles were observed before their departure in microgravity. The relationship between bubble behavior and heat transfer on plate was analyzed. A semi-theoretical model was also proposed for predicting the bubble departure diameter during pool boiling on wires. The results obtained here are intended to become a powerful aid for further investigation in the present discipline and development of two-phase systems for space applications.     

Physical mechanism of the destabilizing effect of damping in continuous non-conservative dissipative systems

The paper attempts to give a physical explanation of the mechanism behind the so-called destabilizing effect of small internal damping in the dynamic stability of Beck's column. Both internal (material) and external (viscous fluid) damping are considered. An energy equation is derived for the balance between the work done by the non-conservative ‘follower force’ and the energy dissipated by the internal and external damping forces. Evaluated at the critical load, where a flutter instability is initiated, this equation explicitly shows the influence of damping upon flutter frequency, phase angle, and vibration amplitude. The gradient of the phase angle, evaluated at the free end of the column, is found to be the ‘valve’, which controls how much work the follower force can do on the column during each period of oscillation. And a large change in this gradient with increasing—but still small—internal damping is found to be responsible for the destabilizing effect.     

Two-phase flow operational maps for multi-microchannel evaporators

The current paper presents new operational maps for several different multi-microchannel evaporators, with and without any inlet restrictions (micro-orifices), for the two-phase flow of refrigerants R245fa, R236fa, and R1234ze(E). The test fluids flowed in 67 parallel channels, each having a cross-sectional area of 100 × 100 μm². In order to emulate the power dissipated by active components in a 3D CMOS CPU chip, two aluminium microheaters were sputtered onto the back-side of the test section providing a 0.5 cm² each. Without any inlet restrictions in the micro-evaporator, significant parallel channel flow instabilities, vapor back flow, and flow maldistribution led to high-amplitude and high-frequency temperature and pressure oscillations. Such undesired phenomena were then prevented by placing restrictions at the inlet of each channel. High-speed flow visualization distinguished eight different operating regimes of the two-phase flow depending on the tested operating conditions. Therefore, the preferred operating regimes can be easily traced. In particular, flashing two-phase flow without back flow appeared to be the best operating regime without any flow and temperature instabilities.     

Two-phase flow regime assignment based on wavelet features of a capacitance signal

In this work, a new method is proposed to determine the two-phase flow regime based on the capacitance trace of the flow. The experimental data set contains 123 capacitance traces measured for a horizontal tube with an inner diameter of 8 mm. The tested refrigerant is R134a. The mass flux is varied between 200 and 500 kg/m² s and the vapour quality x is varied between 0 and 1. For each capacitance signal the wavelet variance is estimated based on the maximum overlap wavelet transform of the signal. The used wavelet function is a D8 wavelet of the Daubechies family. A feature space is generated based on the wavelet variance values associated with frequencies below 100 Hz. Principal component analysis and linear discriminant analysis are subsequently applied to this raw feature space, after which the Fuzzy c-means clustering algorithm is used to divide the feature space into clusters corresponding to different flow regimes. The resulting flow regime assignment shows a good agreement with a visual classification of the data set based on flow visualisations. Finally, the classification was performed based on variable training data to show the robustness of the method.     

Two-phase flow of R-134a refrigerant during flow boiling through a horizontal circular mini-channel

This research focuses on heat transfer to R-134a during flow boiling in a 1.75 mm internal diameter tube. Flow visualisation and heat transfer experiments are conducted to obtain heat transfer coefficients for different flow patterns. The measured data in each flow regime are compared with predictions from a three-zone flow boiling model. The calculations are in fair agreement with the experimental results which correspond in particular to slug flow, throat-annular flow and churn flow regimes under conditions of low heat flux.     

Surface wettability effect on flow pattern and pressure drop in adiabatic two-phase flows in rectangular microchannels with T-junction mixer

Wettability is an important parameter in micro-scale flow patterns. Previous research has usually been conducted in conventional microtubes due to limitations of visualizing flow patterns and fabricating microchannels. However, most microchannels in practical applications have rectangular shape. Furthermore, pressure drop is closely related with flow pattern. Hence, we studied water liquid and nitrogen gas flows in rectangular microchannels with different wettabilities. The rectangular glass microchannels were fabricated from photosensitive glass, whose surface is hydrophilic. The surface of one was silanized using octadecyl-trichloro-silane (OTS) to prepare a hydrophobic microchannel. The two-phase flow pattern was visualized with a high-speed camera and a long distance microscope. The frictional pressure drop in the microchannel was measured directly with embedded pressure ports. The flow pattern and pressure drop in the hydrophobic microchannel were totally different from those in the hydrophilic microchannel. Finally, the two-phase frictional pressure drop was analyzed based on the flow patterns of different wettabilities.     

Two-phase flow distribution of air–water annular flow in a parallel flow heat exchanger

The air and water flow distribution are experimentally studied for a round header – flat tube geometry simulating a parallel flow heat exchanger. The number of branch flat tube is 30. The effects of tube outlet direction, tube protrusion depth as well as mass flux, and quality are investigated. The flow at the header inlet is identified as annular. For the downward flow configuration, the water flow distribution is significantly affected by the tube protrusion depth. For flush-mounted configuration, most of the water flows through frontal part of the header. As the protrusion depth increases, more water is forced to the rear part of the header. The effect of mass flux or quality is qualitatively the same as that of the protrusion depth. Increase of the mass flux or quality forces the water to rear part of the header. For the upward flow configuration, however, most of the water flows through rear part of the header. The protrusion depth, mass flux, or quality does not significantly alter the flow pattern. Possible explanations are provided based on the flow visualization results. Negligible difference on the water flow distribution was observed between the parallel and the reverse flow configuration.     

悬臂输流管道在基础激励与脉动内流联合作用下的参激振动

首先建立了悬臂输流管道在基础激励与脉动内流联合作用下的运动方程;然后基于Galerkin法研究了该系统的非线性动力学行为,分析了系统运动状态随激励频率和相位差的变化,以及混沌百分比随频率比(基础激励频率与脉动频率之比)和相位差的变化。结果表明,无论以激励频率还是以相位差为分岔参数,系统都具有多种形式的动态响应,包括周期运动、概周期运动和混沌运动,但进入和脱离混沌的途径不同。相位差和频率比对系统的混沌百分比有重要影响:相位差为π/2时系统混沌百分比最大;频率比为1时系统混沌百分比最小,频率比较小或较大时系统混沌百分比与只有基础激励时接近。     

Two-phase flow in inclined tubes with specific reference to condensation: A review

Tilting influences the flow patterns and thus the heat transfer and pressure drop during condensation in smooth tubes. However, few studies are available on diabatic two-phase flows in inclined tubes. The purpose of the present paper is to review two-phase flow in inclined tubes, with specific reference to condensation. Firstly, the paper reviews convective condensation in horizontal tubes. Secondly, an overview is given of two-phase flow in inclined tubes. Thirdly, a review is conducted on condensation in inclined tubes. It is shown for convective condensation in inclined tubes that the inclination angle influences the heat transfer coefficient. The heat transfer coefficient can be increased or decreased depending on the experimental conditions, and especially the flow pattern. Under certain conditions, an inclination angle may exist, which leads to an optimum heat transfer coefficient. Furthermore, this paper highlights the lack of experimental studies for the prediction of the inclination angle effect on the flow pattern, the heat transfer coefficient and the pressure drop in two-phase flows during phase change.     

Two-phase refrigerant flow instability analysis and active control in transient electronics cooling systems

Two-loop refrigeration systems are being explored for two-phase cooling of ultra high power electronic components. For effective and efficient thermal management of electronic systems, active control methods are desired to suppress inherent flow instabilities especially in transient applications. This paper presents a framework for the transient analysis and active control of pressure-drop flow instabilities under varying imposed heat loads. The external effects on boiling flow characteristics and the boiling oscillatory flow responses to transient heat load changes are studied. Flow instability margins can be quantitatively predicted from an analytical two-phase flow model. In addition, the effects of wall thermal inertia on flow oscillations is systematically investigated. Based on the theoretical analysis of oscillatory flow boiling of refrigerants, a set of active control schemes are developed and studied to suppress flow oscillations and to increase the critical heat flux. With the available control devices – inlet valve and supply pump – different active control schemes are studied to improve the transient two-phase cooling performance.     

Macro-to-microchannel transition in two-phase flow: Part 1 - Two-phase flow patterns and film thickness measurements

The classification of macroscale, mesoscale and microscale channels with respect to two-phase processes is still an open question. The main objective of this study focuses on investigating the macro-to-microscale transition during flow boiling in small scale channels of three different sizes with three different refrigerants over a range of saturation conditions to investigate the effects of channel confinement on two-phase flow patterns and liquid film stratification in a single circular horizontal channel (Part 2 covers the flow boiling heat transfer and critical heat flux). This paper presents the experimental two-phase flow pattern transition data together with a top/bottom liquid film thickness comparison for refrigerants R134a, R236fa and R245fa during flow boiling in small channels of 1.03, 2.20 and 3.04 mm diameter. Based on this work, an improved flow pattern map has been proposed by determining the flow patterns transitions existing under different conditions including the transition to macroscale slug/plug flow at a confinement number of Co ≈ 0.3-0.4. From the top/bottom liquid film thickness comparison results, it was observed that the gravity forces are fully suppressed and overcome by the surface tension and shear forces when the confinement number approaches 1, Co ≈ 1. Thus, as a new approximate rule, the lower threshold of macroscale flow is Co = 0.3-0.4 while the upper threshold of symmetric microscale flow is Co ≈ 1 with a transition (or mesoscale) region in-between.     

An experimental investigation of flow boiling in an asymmetrically heated rectangular microchannel

By using unique experimental techniques and carefully constructed experimental apparatus, the characteristics of flow boiling of water in microscale were investigated using a single horizontal rectangular microchannel. A polydimethylsiloxane rectangular microchannel (D_h = 103.5 and 133 μm) was fabricated by using the replica molding technique, a kind of soft lithography. A piecewise serpentine platinum microheater array on a Pyrex substrate was fabricated with the surface micromachining MEMS technique. Real time flow visualization of the phase change phenomena inside the microchannel was performed using a high speed CCD camera with microscope. The experimental local boiling heat transfer coefficients were studied, and single bubble inception, growth, and departure, as well as elongated bubble behavior were analyzed to elucidate the microscale heat transfer mechanisms. Tests were performed for mass fluxes of 77.5, 154.9, and 309.8 kg/m² s and heat fluxes of 180–500 kW/m². The effects of mass flux, heat flux, and vapor qualities on flow boiling heat transfer in a microchannel were studied.     

A simultaneous PIV and heat transfer study of bubble interaction with free convection flow

Whole field velocity and point temperature and surface heat flux measurements were performed to characterise the interaction of a single rising ellipsoidal air bubble with the free convection flow from a heated flat surface immersed in water at different angles of inclination. Two thermocouples and a hot film sensor were used to characterise heat transfer from the surface, while a time-resolved digital particle image velocimetry technique was used to map the bubble induced flow in a plane parallel to the surface. Heat flux fluctuations, preceding and following the bubble passage, were shown to correlate with the variation in both local flow velocities and fluid temperatures. The largest increases in heat transfer were recorded when both flow and temperature effects combined to enhance the convective cooling simultaneously. Such conditions were shown to be most likely met when the block was inclined at 45°, thus forcing the bubble to slide closer to the heated surface and hence to the thermal boundary layer.     

Two-phase flow in heterogeneous porous media III: Laboratory experiments for flow parallel to a stratified system

Two-phase flow in stratified porous media is a problem of central importance in the study of oil recovery processes. In general, these flows are parallel to the stratifications, and it is this type of flow that we have investigated experimentally and theoretically in this study. The experiments were performed with a two-layer model of a stratified porous medium. The individual strata were composed of Aerolith-10, an artificial: sintered porous medium, and Berea sandstone, a natural porous medium reputed to be relatively homogeneous. Waterflooding experiments were performed in which the saturation field was measured by gamma-ray absorption. Data were obtained at 150 points distributed evenly over a flow domain of 0.1 × 0.6 m. The slabs of Aerolith-10 and Berea sandstone were of equal thickness, i.e. 5 centimeters thick. An intensive experimental study was carried out in order to accurately characterize the individual strata; however, this effort was hampered by both local heterogeneities and large-scale heterogeneities.The theoretical analysis of the waterflooding experiments was based on the method of large-scale averaging and the large-scale closure problem. The latter provides a precise method of discussing the crossflow phenomena, and it illustrates exactly how the crossflow influences the theoretical prediction of the large-scale permeability tensor. The theoretical analysis was restricted to the quasi-static theory of Quintard and Whitaker (1988), however, the dynamic effects described in Part I (Quintard and Whitaker 1990a) are discussed in terms of their influence on the crossflow.Roman Letters A interfacial area between the -region and the -region contained within V, m² - a vector that maps onto , m - b vector that maps onto , m - b vector that maps onto , m - B second order tensor that maps onto , m² - C second order tensor that maps onto , m² - E energy of the gamma emitter, keV - f fractional flow of the -phase - g gravitational vector, m/s² - h characteristic length of the large-scale averaging volume, m - H height of the stratified porous medium , m - i unit base vector in the x-direction - K local volume-averaged single-phase permeability, m² - K - {K}, large-scale spatial deviation permeability - { K} large-scale volume-averaged single-phase permeability, m² - K ^* large-scale single-phase permeability, m² - K ^** equivalent large-scale single-phase permeability, m² - K local volume-averaged -phase permeability in the -region, m² - K local volume-averaged -phase permeability in the -region, m² - K - {K } , large-scale spatial deviation for the -phase permeability, m² - K ^* large-scale permeability for the -phase, m² - l thickness of the porous medium, m - l characteristic length for the -region, m - l characteristic length for the -region, m - L length of the experimental porous medium, m - characteristic length for large-scale averaged quantities, m - n outward unit normal vector for the -region - n outward unit normal vector for the -region - n unit normal vector pointing from the -region toward the -region (n = - n ) - N number of photons - p pressure in the -phase, N/m² - p ₀ reference pressure in the -phase, N/m² - local volume-averaged intrinsic phase average pressure in the -phase, N/m² - large-scale volume-averaged pressure of the -phase, N/m² - large-scale intrinsic phase average pressure in the capillary region of the -phase, N/m² - - , large-scale spatial deviation for the -phase pressure, N/m² - p_c , capillary pressure, N/m² - p _c capillary pressure in the -region, N/m² - p capillary pressure in the -region, N/m² - {p _c } ^c large-scale capillary pressure, N/m² - q -phase velocity at the entrance of the porous medium, m/s - q -phase velocity at the entrance of the porous medium, m/s - S_wi irreducible water saturation - S /, local volume-averaged saturation for the -phase - S _i initial saturation for the -phase - S _r residual saturation for the -phase - S ^* { }^*/}^*, large-scale average saturation for the -phase - S saturation for the -phase in the -region - S saturation for the -phase in the -region - t time, s - v -phase velocity vector, m/s - v local volume-averaged phase average velocity for the -phase, m/s - {v } large-scale averaged velocity for the -phase, m/s - v local volume-averaged phase average velocity for the -phase in the -region, m/s - v local volume-averaged phase average velocity for the -phase in the -region, m/s - v -{v } , large-scale spatial deviation for the -phase velocity, m/s - v -{v } , large-scale spatial deviation for the -phase velocity in the -region, m/s - v -{v } , large-scale spatial deviation for the -phase velocity in the -region, m/s - V large-scale averaging volume, m³ - y position vector relative to the centroid of the large-scale averaging volume, m - {y}^c large-scale average of y over the capillary region, m Greek Letters local porosity - local porosity in the -region - local porosity in the -region - local volume fraction for the -phase - local volume fraction for the -phase in the -region - local volume fraction for the -phase in the -region - {}^* { }^*+{ }^*, large-scale spatial average volume fraction - { }^* large-scale spatial average volume fraction for the -phase - mass density of the -phase, kg/m³ - mass density of the -phase, kg/m³ - viscosity of the -phase, N s/m² - viscosity of the -phase, Ns/m² - V /V , volume fraction of the -region ( + =1) - V /V , volume fraction of the -region ( + =1) - attenuation coefficient to gamma-rays, m^-1 - -      

Two-phase flow in heterogeneous porous media II: Numerical experiments for flow perpendicular to a stratified system

In this work, we make use of numerical experiments to explore our original theoretical analysis of two-phase flow in heterogeneous porous media (Quintard and Whitaker, 1988). The calculations were carried out with a two-region model of a stratified system, and the parameters were chosen be consistent with practical problems associated with groundwater flows and petroleum reservoir recovery processes. The comparison between theory (the large-scaled averaged equations) and experiment (numerical solution of the local volume averaged equations) has allowed us to identify conditions for which the quasi-static theory is acceptable and conditions for which a dynamic theory must be used. Byquasi-static we mean the following: (1) The local capillary pressure,everywhere in the averaging volume, can be set equal to the large-scale capillary pressure evaluated at the centroid of the averaging volume and (2) the large-scale capillary pressure is given by the difference between the large-scale pressures in the two immiscible phases, and is therefore independent of gravitational effects, flow effects and transient effects. Bydynamic, we simply mean a significant departure from the quasi-static condition, thus dynamic effects can be associated with gravitational effects, flow effects and transient effects. To be more precise about the quasi-static condition we need to refer to the relation between the local capillary pressure and the large-scale capillary pressure derived in Part I (Quintard and Whitaker, 1990). Herep _c ¦_y represents the local capillary pressure evaluated at a positiony relative to the centroid of the large-scale averaging volume, and {p _c }¦_x represents the large-scale capillary pressure evaluated at the centroid.In addition to{p _c } ^c being evaluated at the centroid, all averaged terms on the right-hand side of Equation (1) are evaluated at the centroid. We can now write the equations describing the quasi-static condition as , , This means that the fluids within an averaging volume are distributed according to the capillary pressure-saturation relationwith the capillary pressure held constant. It also means that the large-scale capillary pressure is devoid of any dynamic effects. Both of these conditions represent approximations (see Section 6 in Part I) and one of our main objectives in this paper is to learn something about the efficacy of these approximations. As a secondary objective we want to explore the influence of dynamic effects in terms of our original theory. In that development only the first four terms on the right hand side of Equation (1) appeared in the representation for the local capillary pressure. However, those terms will provide an indication of the influence of dynamic effects on the large-scale capillary pressure and the large-scale permeability tensor, and that information provides valuable guidance for future studies based on the theory presented in Part I.Roman Letters A scalar that maps {}*/t onto - A scalar that maps {}*/t onto - A interfacial area between the -region and the -region contained within, m² - A interfacial area between the -region and the -region contained within, m² - A interfacial area between the -region and the -region contained within, m² - a vector that maps ({}*/t) onto , m - a vector that maps ({}*/t) onto , m - b vector that maps ({p}– g) onto , m - b vector that maps ({p}– g) onto , m - B second order tensor that maps ({p}– g) onto , m² - B second order tensor that maps ({p}– g) onto , m² - c vector that maps ({}*/t) onto , m - c vector that maps ({}*/t) onto , m - C second order tensor that maps ({}*/t) onto , m² - C second order tensor that maps ({}*/t) onto . m² - D third order tensor that maps ( ) onto , m - D third order tensor that maps ( ) onto , m - D second order tensor that maps ( ) onto , m² - D second order tensor that maps ( ) onto , m² - E third order tensor that maps () onto , m - E third order tensor that maps () onto , m - E second order tensor that maps () onto - E second order tensor that maps () onto - p _c =(), capillary pressure relationship in the-region - p _c =(), capillary pressure relationship in the-region - g gravitational vector, m/s² - largest of either or - - - i unit base vector in thex-direction - I unit tensor - K local volume-averaged-phase permeability, m² - K local volume-averaged-phase permeability in the-region, m² - K local volume-averaged-phase permeability in the-region, m² - {K } large-scale intrinsic phase average permeability for the-phase, m² - K –{K }, large-scale spatial deviation for the-phase permeability, m² - K –{K }, large-scale spatial deviation for the-phase permeability in the-region, m² - K –{K }, large-scale spatial deviation for the-phase permeability in the-region, m² - K ^* large-scale permeability for the-phase, m² - L characteristic length associated with local volume-averaged quantities, m - characteristic length associated with large-scale averaged quantities, m - I _i i = 1, 2, 3, lattice vectors for a unit cell, m - l characteristic length associated with the-region, m - ; characteristic length associated with the-region, m - l _H characteristic length associated with a local heterogeneity, m - - n unit normal vector pointing from the-region toward the-region (n =–n ) - n unit normal vector pointing from the-region toward the-region (n =–n ) - p pressure in the-phase, N/m² - p local volume-averaged intrinsic phase average pressure in the-phase, N/m² - {p } large-scale intrinsic phase average pressure in the capillary region of the-phase, N/m² - p local volume-averaged intrinsic phase average pressure for the-phase in the-region, N/m² - p local volume-averaged intrinsic phase average pressure for the-phase in the-region, N/m² - p –{p }, large scale spatial deviation for the-phase pressure, N/m² - p –{p }, large scale spatial deviation for the-phase pressure in the-region, N/m² - p –{p }, large scale spatial deviation for the-phase pressure in the-region, N/m² - P _c p –{p }, capillary pressure, N/m² - {p_c}^c large-scale capillary pressure, N/m² - r ₀ radius of the local averaging volume, m - R ₀ radius of the large-scale averaging volume, m - r position vector, m - , m - S /, local volume-averaged saturation for the-phase - S ^* {}*{}*, large-scale average saturation for the-phaset time, s - t time, s - u , m - U , m² - v -phase velocity vector, m/s - v local volume-averaged phase average velocity for the-phase in the-region, m/s - v local volume-averaged phase average velocity for the-phase in the-region, m/s - {v } large-scale intrinsic phase average velocity for the-phase in the capillary region of the-phase, m/s - {v } large-scale phase average velocity for the-phase in the capillary region of the-phase, m/s - v –{v }, large-scale spatial deviation for the-phase velocity, m/s - v –{v }, large-scale spatial deviation for the-phase velocity in the-region, m/s - v –{v }, large-scale spatial deviation for the-phase velocity in the-region, m/s - V local averaging volume, m³ - V volume of the-phase in, m³ - V large-scale averaging volume, m³ - V capillary region for the-phase within, m³ - V capillary region for the-phase within, m³ - V _c intersection of m³ - V volume of the-region within, m³ - V volume of the-region within, m³ - V () capillary region for the-phase within the-region, m³ - V () capillary region for the-phase within the-region, m³ - V () , region in which the-phase is trapped at the irreducible saturation, m³ - y position vector relative to the centroid of the large-scale averaging volume, m Greek Letters local volume-averaged porosity - local volume-averaged volume fraction for the-phase - local volume-averaged volume fraction for the-phase in the-region - local volume-averaged volume fraction for the-phase in the-region - local volume-averaged volume fraction for the-phase in the-region (This is directly related to the irreducible saturation.) - {} large-scale intrinsic phase average volume fraction for the-phase - {} large-scale phase average volume fraction for the-phase - {}* large-scale spatial average volume fraction for the-phase - –{}, large-scale spatial deviation for the-phase volume fraction - –{}, large-scale spatial deviation for the-phase volume fraction in the-region - –{}, large-scale spatial deviation for the-phase volume fraction in the-region - a generic local volume-averaged quantity associated with the-phase - mass density of the-phase, kg/m³ - mass density of the-phase, kg/m³ - viscosity of the-phase, N s/m² - viscosity of the-phase, N s/m² - interfacial tension of the - phase system, N/m - , N/m - , volume fraction of the-phase capillary (active) region - , volume fraction of the-phase capillary (active) region - , volume fraction of the-region ( + =1) - , volume fraction of the-region ( + =1) - {p }– g, N/m³ - {p }– g, N/m³     

Flow pattern and flow characteristics for counter-current two-phase flow in a vertical round tube with wire-coil inserts

Flow pattern, void fraction and slug rise velocity on counter-current two-phase flow in a vertical round tube with wire-coil inserts are experimentally studied. Flow pattern and slug rise velocity are measured visually with a video camera. The void fraction is measured by the quick-closing valve method. Four kinds of coils with different coil pitches and coil diameters are used as inserts. The presence of wire-coil inserts induces disturbance into gas and liquid flows so that the shape and motion of gas slug or bubbles in a wire-coil inserted tube are quite different from those observed in a smooth tube without insert. The bubbly flow occurs in the low gas superficial velocity region in the wire-coil inserted tube, while the slug or churn/annular flow only appears in the smooth tube without insert over the all test range. The measured slug rise velocity in the wire-coil inserted tube is higher than that in the smooth tube. With modified mean flow velocity calculated with core area, the slug rise velocity in wire-coil tube inserted is in good agreement with Nicklin's correlation. The void fraction in a wire-coil inserted tube is lower than that in a smooth tube in the range of high gas superficial velocities. By introducing a simple assumption on considering the effective flowing area, the measured void fractions in a wire-coil inserted tube are in relatively good agreement with the predicted result based on the drift flux model proposed by others with the correlation for slug rise velocity given by others when the coil pitch is dense.     

Two-phase flow in heterogeneous porous media: The method of large-scale averaging

The analysis of two-phase flow in porous media begins with the Stokes equations and an appropriate set of boundary conditions. Local volume averaging can then be used to produce the well known extension of Darcy's law for two-phase flow. In addition, a method of closure exists that can be used to predict the individual permeability tensors for each phase. For a heterogeneous porous medium, the local volume average closure problem becomes exceedingly complex and an alternate theoretical resolution of the problem is necessary. This is provided by the method of large-scale averaging which is used to average the Darcy-scale equations over a region that is large compared to the length scale of the heterogeneities. In this paper we present the derivation of the large-scale averaged continuity and momentum equations, and we develop a method of closure that can be used to predict the large-scale permeability tensors and the large-scale capillary pressure. The closure problem is limited by the principle of local mechanical equilibrium. This means that the local fluid distribution is determined by capillary pressure-saturation relations and is not constrained by the solution of an evolutionary transport equation. Special attention is given to the fact that both fluids can be trapped in regions where the saturation is equal to the irreducible saturation, in addition to being trapped in regions where the saturation is greater than the irreducible saturation. Theoretical results are given for stratified porous media and a two-dimensional model for a heterogeneous porous medium.     

Heat transfer measurements and correlations for air–water flow of different flow patterns in a horizontal pipe

Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the flow patterns was supplemented with photographic data, and the results were plotted on the flow regime map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.     

On a robust BEM formulation for the Dirichlet problem of exterior stokes flow

A new formulation is proposed for the solution of the Dirichlet problem of Stokes flow (resistance problem) which considerably improves the conditioning of the algebraic system associated and is meant for application in large-scale problems with iterative solvers.