Pressure Drops and Dryout Heat Fluxes of Packed Beds with Cylindrical Particles

Abstract

Motivated by reducing the uncertainties in coolability analysis of a debris bed formed in severe accident of nuclear reactors, the pressure drops of single-/two-phase flow and dryout heat fluxes of the packed beds with non-spherical particles are investigated in the present study. Both adiabatic single-/two-phase flow tests and boiling tests are performed on a particulate porous bed packed with cylindrical particles separately, the pressure drops and dryout heat fluxes under different conditions are measured to identify and validate the debris coolability analysis models. The results show that for a particulate bed packed with non-spherical particles such as cylinders, the effective particle diameter can be represented by the equivalent diameter of the particles, which is the product of Sauter mean diameter and the shape factor. Given this diameter, the measured pressure drops and the dryout heat fluxes are comparable with the predictions of Reed model. Comparing with the cooling scheme of top-flooding case, the bottom injection improves the dryout heat flux significantly.     

Dryout analysis of overloaded microscale capillary-driven two-phase heat transfer devices

Dryout occurrence at high heat input is one of the detrimental factors that limit the thermal efficiency of a phase-change heat transfer device. In this work, we demonstrate that by employing visualization method, the dryout occurrence of an elongated liquid droplet in a transparent evacuated microscale two-phase flow device can be scrutinized. The circulation of liquid from the condenser to the evaporator is driven by the capillary action which is the primary limitation that governs the maximum heat transport capability of the device. When the evaporation rate exceeds the circulation rate of condensate, dryout will take place in the evaporator end. The propagation of dryout lengths can be accurately determined directly from visualization and a more accurate evaluation of the dryout length compared to the conventional method by measuring the axial temperatures has been developed. By quantifying the performance indicators of the cooling device over a wide range of operating conditions, including the underloaded and overloaded operations, the observation of dryout occurrence in this study correlates highly with the anticipated heat transfer characteristics of a phase-change heat transfer device. This study provides essential insights, particularly on the overloaded conditions, to the design of a microscale two-phase heat transfer device.     

CHF in a Circumferentially Nonuniformly Heated Tube Under Low-Pressure and Low-Mass-Flux Condition (Influence of Inclined Angles Under High-Heat-Flux Condition)

Critical heat flux (CHF) is an important design factor for boiling two-phase flow equipment, such as boilers and others. In actual boiling systems, the water tube suffers from the nonuniform heating and/or tube inclinations. The objective of this investigation is to understand the influence of tube inclination on CHF characteristics under such high-heat-flux conditions. The experimental investigation was conducted with a forced convective boiling system by using a uniformly heated tube and a nonuniformly heated tube set at arbitrary inclination angles ?. The obtained CHF was strongly influenced by the circumferential location of local maximum heat flux point and tube inclination. In the case of the normal tube, the CHF always occurred by the liquid film dryout at the top of the tube. In the case of the nonuniformly heated tube, the influence of the inclination on the CHF characteristics strongly depended on the circumferential heat flux distribution. When the the heat flux at the bottom was higher than that at the top, two types of CHF mechanism, namely, low-quality CHF upstream of the test section under high-mass-flux condition, and liquid film dryout at the tube exit under low-mass-flux condition, were observed. When the heat flux at the top was higher than that at the bottom, intermittent dryout was observed as the dryout mechanism. These CHF characteristics could be categorized by using the CHF ratio against the value of the vertical upward flow with the modified Froude number, which corresponded to the influence factor of disturbance wave.     

Forced flow evaporative cooling of a volumetrically heated porous layer

In this paper, the temperature rise and pressure drop experienced by an evaporating coolant flowing through a volumetrically heated porous layer have been studied experimentally. Experimental data for the temperature distribution and the two-phase pressure drop along the direction of flow is obtained for water flowing through layers of inductively heated steel particles. Spherical steel particles varying in size from 590 to 4763 μm are used to form porous layers in 5 and 10 cm dia. glass jars. In these experiments the data are obtained for layer depths varying from 9 to 81 cm, volumetric heat generation rate varying from 1.44 to 44.0 W/cm³ and the mass flow rate of water varying from 510 to 18200 kg/m² h.A theoretical model for the temperature profile in the liquid region and the two phase region has been made and is found to compare well with the measurements. Vapor channels are observed to form in porous layers of particle diameter less than 1600 μm. Separate semi-theoretical models have been developed for the two phase pressure drop in particles with diameter less than and greater than 1600 μm.     

Study on water transport in PEM of a direct methanol fuel cell

Water transport phenomenon in PEM and the mechanism of occurrence and development of a two-phase countercurrent flow with corresponding transport phenomenon in the PEM are analyzed. A one-dimensional steady state model of heat and mass transfer in porous media system with internal volumetric ohmic heating is developed and simulated numerically. The results show that two dimensionless parameters D and N, which reflect the liquid water flow rate and inner heat source in the PEM, respectively, are the most important factors for the water fraction and thermal balance in the PEM. The saturation profiles within the two-phase region at various operating modes are obtained. Smaller mass flow rate of liquid water and high current density are the major contributions to the membrane dehydration.     

Liquid film behavior in annular two-phase flow under flow oscillation conditions

Experiments were carried out to investigate the effects of sinusoidal forced oscillation of the inlet flow rate on the time variations of local liquid film thickness and the frequencies of large wave’s passing in steam–water annular two-phase flows. The liquid film thickness oscillated with the same period as the inlet flow rate. The mean film thickness in the thin film regions decreased and approached to an asymptotic value with an increase in the oscillation period of the inlet flow rate. This result was consistent with the experimental results of the occurrence of liquid film dryout under flow oscillation conditions reported in the literature. It was hence considered that the axial liquid transport from the thick to thin film regions mitigates the reduction of the critical heat flux caused by the flow oscillation. It was also found that the wave frequency in the thin film region increased with a decrease in the oscillation period. This observation suggested that the disturbance waves contribute to the enhancements of the liquid transport and consequently the critical heat flux associated with the liquid film dryout under flow oscillation conditions.     

The effect on pressure drop across horizontal pipe and control valve for air/palm oil two-phase flow

Studies on operating characteristics of control valves with two-phase flow have not been given much attention in the literature despite its industrial importance during design and selection as well as during plant operation. However, literature shows considerable work with two-phase flow through pipes and different geometrical shapes of flow ducts. The present work attempts to study experimentally the effect of two-phase flow on pressure drop across the control valve for different volume fractions of the fluids. A typical fluid system of palm oil (liquid phase) and air (gas phase) has been used for the studies. The pressure drop in a horizontal straight pipe upstream of the valve is also considered to test the correlations from the literature on two-phase pressure drop. The same is extended to represent the pressure drop across the valve. The operating characteristics are obtained from the pressure drop relationship and valve opening. It is found that Lockhart-Martini (L-M) parameter and the quality (fraction of liquid) are found to correlate well with the two-phase multiplier defined based on pressure drop with gas phase. The installed characteristics of the valve for varying pressure drop and quality is presented.     

Pressure drop and heat transfer characteristics of air-rockbed thermal storage systems

Experiments were conducted to determine the pressure drop and heat transfer characteristics of rockbeds with air as the heat transfer medium. Both the pressure drop and the coefficient of volumetric heat transfer between the air and the rockbeds were found to depend upon the rock size and the air flow rate. In addition, the pressure drop also exhibited dependence on the rockbed porosity. The data, however; did not suggest any influence of rockbed porosity and inlet air and initial rockbed temperatures on the volumetric heat transfer coefficient. Relationships are proposed to estimate the pressure drop and volumetric heat transfer coefficients in rockbeds for the range of variables encountered in low temperature storage applications.     

基于格子Boltzmann方法的饱和土壤渗流与传热数值模拟

本文利用随机多孔介质生成算法重构了与真实土壤外貌相近的多孔介质几何结构。通过引入不可压耦合双分布格子Boltzmann模型（lattice Boltzmann model ,LBM）对孔隙尺度下单相饱和土壤渗流和传热进行了模拟。着重讨论了不同渗流压差、孔隙率、土壤固体颗粒尺寸分布对流动与传热的影响。结果表明：土壤渗流速度与渗流压差呈线性单调递增关系,平均温度随渗流压差增加而增大,但温升速率逐渐减缓;当孔隙率增大时,渗流速度增加,且当孔隙率大于0.58时,对流换热作用迅速增强,土壤温升速率显著加快;对于相同孔隙率,当土壤固相颗粒尺寸较大时,流动出现典型优先流效应;随着土壤固相颗粒尺寸减小,土壤温度变化逐渐趋于平缓,平均温度降低。     

气液两相流相空间复杂网络非线性动力学特性分析

气液两相流动作为一个具有混沌特征的非线性动力学系统,其流型演化动力学特性尚未取得清楚的认识。以垂直上升管内空气-水两相流为研究对象,在实验获取气液两相流流型压差波动时间序列的基础上,将空气-水两相流的压差波动时间序列映射到流型相空间复杂网络对其非线性动力学特性进行了分析。通过分析发现在相空间不稳定周期轨的吸引特性作用下,不同流型的相空间复杂网络现呈出明显不同的网络结构,并且网络密度的演化趋势与流型的转化过程相吻合,较好地反映了垂直上升管内空气-水两相流的非线性动力学特性。     

Liquid film dryout in a boiling channel under flow oscillation conditions

A simple theory was developed to elucidate the influence of sinusoidal oscillation of the inlet flow rate on the occurrence of liquid film dryout in an annular two-phase flow regime in a boiling channel. The theory assumes that the critical heat flux (CHF) under an oscillatory condition can be calculated from values in steady states provided that the effect of axial mixing of the liquid film is appropriately considered. The trends of CHFs calculated using a one-dimensional three-fluid model and those experimentally measured under atmospheric pressure were in reasonable agreement with the proposed theory. However, the CHF values measured under oscillatory conditions were usually higher in the experiment than in the numerical simulation, which indicated that axial liquid transport induced by disturbance waves might enhance axial mixing of the liquid film.     

Analysis of staggered tube bundle heat transfer to vertical foam flow

In general heat transfer intensity between solid surface and coolant (fluid) depends on three main parameters: heat transfer coefficient, size of heat exchange surface and temperature difference between surface and fluid. Sometimes the last two parameters (surface size and temperature difference) are strictly limited due to the process or technological requirements, and only increase of heat transfer coefficient is allowed. Simplest way offering sufficient increase in heat transfer rate (heat transfer coefficient as well) is to go from the laminar fluid flow regime to the turbulent one by increasing flow velocity. In many cases it helps despite such disadvantages like more complicated fluid supply system, rise of fluid flow mass rate and growth of energy usage for pumping. But in some cases, for example, in space application, in nuclear engineering, etc. there is not allowed to use high flow velocity of coolant – gas (due to vibration danger) or to apply high mass rate of coolant – liquid (due to limitation concerning weight or mass). One of the possible solutions of that problem could be the usage of two-phase flow as a coolant. An idea to use such two-phase coolant for heat removal from the solid surface is not new. Boiling liquid (water especially), gas flow with liquid droplets and other two-phase systems are widely used for heat and mass transfer purposes in various industries like food, chemical, oil, etc. An application of such two-phase coolants has lot advantages; high value of heat transfer coefficient is one of the most important. Unfortunately nothing is ideal on the Earth. Restrictions on vibration, on coolant weight (or mass rate); necessity to generate two-phase flow separately from the heat removal place; requirements on very low coolant velocities and other constraints do not allow using such type of two-phase coolant for purposes which were mentioned above (space application especially). As a possible way out can be usage of the statically stable foam flow produced from gas (air) and surfactant solutions in liquid (water). Our previous investigations [J. Gylys, Hydrodynamics and Heat Transfer under the Cellular Foam Systems, Technologija, Kaunas, 1998] showed the solid advantages of that type of two-phase coolant, including high values of heat transfer coefficient (up to 1000 W/m² K and more), low flow velocities (less than 1.0 m/s), small coolant density (less than 4 kg/m³), possibility to generate foam flow apart from the heat removal place, etc.This article is devoted to the experimental investigation of the staggered tube bundle heat transfer to the vertical upward and downward statically stable foam flow. The investigations were provided within the laminar regime of foam flow. The dependency of the tube bundle heat transfer on the foam flow velocity, flow direction and volumetric void fraction were analyzed. In addition to this, the influence of tube position in the bundle was investigated also. Investigation shows that the regularities of the tube bundle heat transfer to the vertical foam flow differ from the one-phase (gas or liquid) flow heat transfer peculiarities. It was showed that the heat transfer intensity of the staggered tube bundle to the foam flow is much higher (from 25 to 100 times) than that for the one-phase airflow under the same conditions (flow velocity). The results of the investigations were generalized using criterion equations, which can be applied for the calculation and design of the statically stable foam heat exchangers with the staggered tube bundles.     

Effects of jet pattern on two-phase performance of hybrid micro-channel/micro-circular-jet-impingement thermal management scheme

This paper explores the two-phase cooling performance of a hybrid cooling scheme in which a linear array of micro-jets deposits liquid gradually along each channel of a micro-channel heat sink. The study also examines the benefits of utilizing differently sized jets along the micro-channel. Three micro-jet patterns, decreasing-jet-size (relative to center of channel), equal-jet-size and increasing-jet-size, were tested using HFE 7100 as working fluid. It is shown feeding subcooled coolant into the micro-channel in a gradual manner greatly reduces vapor growth along the micro-channel. Void fraction increased between jets but decreased sharply beneath each jet, creating a repeated pattern of growth followed by coalesce, and netting only a mild overall increase in void fraction along the flow direction with predominantly liquid flow at outlet. Unlike most flow boiling situations, where pressure drop increases with increasing heat flux, pressure drop in the hybrid configurations actually decreased and reached a minimum just before CHF. This behavior is closely related to the low void fraction and predominantly liquid flow. Pressure drop in the two-phase region is highest for the equal-jet-size pattern, followed by the decreasing-jet-size and increasing-jet-size patterns, respectively. Low void fraction increased the effectiveness of the hybrid cooling schemes in utilizing bulk liquid subcooling and therefore helped achieve high CHF values. The decreasing-jet-size pattern, which had the highest outlet subcooling, achieved the highest CHF. A single correlation was constructed for the three jet patterns, which relates the two-phase heat transfer coefficient to heat flux and wall superheat.     

Determination of the void fraction and drift velocity in a two-phase flow with a boiling solar collector

This paper presents an approach to determine the void fraction and the drift velocity in a two-phase flow with a boiling solar collector using easily obtained experimental data. The solar collector operates in a thermal siphon circuit, where the working fluid absorbs solar radiation mostly while boiling. The vapor bubbles release their latent heat in a condenser, while heating up a flow of water–glycol. Two numerical procedures are developed to calculate the void fraction because its experimental values cannot be easily measured. The use of a flow meter causes an additional pressure drop in the thermal siphon circuit and, consequently, changes the circulated mass flow rate. The first numerical procedure is based on a force balance in the thermal siphon loop and is used to estimate the total mass flow rate and the void fraction in the circuit. The second uses a drift flux correlation to estimate the void fraction and the drift velocity. Both procedures use the experimental values for the vapor mass flow rate, which is determined by an energy balance in the condenser. The volumetric flow rate of the water–glycol mixture and its temperature difference across the condenser are experimentally measured. The pipe length of the two-phase flow in the solar collector is experimentally determined using 44 thermocouples attached to the back of flow channels in the absorber plate. The results show that the two numerical models compare well and that either one can be used to estimate the void fraction in the two-phase flow solar circuit.     

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.     

Liquid-solid separation phenomena of two-phase turbulent flow in curved pipes

The present study is to contribute some knowledge of phase separation phenomena of liquid-solid two-phase turbulent flow in curved pipes and provide a basis for the invention and development of a new type of curved pipe separator. Firstly, the solid-liquid two-phase flows in two-dimensional (2D) curved channels were numerically simulated using a two-way coupling Euler-Lagrangian scheme. Phase distribution characteristics of 2D curved channel two-phase flow were examined under conditions of different particle size, liquid flowrate and coil curvature. Based on the numerical results, the dynamic effects and contributions to phase separation of particle-subjected forces, including centrifugal force, drag force, pressure gradient force, gravity force, buoyancy force, virtual mass force and lift force, were exposed by kinematic and dynamic analysis along particle trajectories. Secondly, measurement of particle size and concentration profiles in helically coiled tube two-phase flow was conducted using a nonintrusive Malvern 2600 particle sizer based on laser diffraction. Particle size and concentration distribution characteristics of helically coiled tube two-phase flow and the effect of secondary flow on phase separation were analyzed based on experimental data.     

燃油喷嘴气液两相流雾化特性研究

以空气,水为工质,利用马尔文粒度分析仪对气液两相流雾化器喷嘴的雾化特性进行了详细的实验研究。测量了气,液两相流不同入口压力比条件下通过喷嘴后形成的液体雾化粒子的粒径分布,详细讨论分析了气,液两相压力及进气,进液方式对喷雾效果的影响,得出了喷嘴雾化过程中气液两相流量与气液两相压力之间的规律和 化原则,并对喷嘴的雾化机理进行了探讨。     

Interfacial heat transfer of condensing bubble in subcooled boiling flow at low pressure

The interfacial heat transfer coefficient is an important parameter for the analysis of multi-phase flow. In subcooled boiling flow, bubbles condense through the interface of phases and the interfacial heat transfer determines the condensation rate which affects the two-phase parameters such as void fraction and local liquid temperature. Thus, the present experiments are conducted to correlate the interfacial heat transfer coefficient at low pressure in the subcooled boiling flow. The local liquid temperature is measured by microthermocouple and the bubble condensation rate is estimated by orthogonal, two-image processing. The condensate Nusselt number, which is a function of bubble Reynolds number, local liquid Prandtl number, and local Jacob number, is obtained from the experimental results. The bubble history is derived from the newly proposed correlation and the condensate Nusselt number is compared with the previous models.     

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.     

An experimental investigation on heat transfer characteristics of multi-walled CNT-heat transfer oil nanofluid flow inside flattened tubes under uniform wall temperature condition

An experimental investigation on heat transfer characteristics of MWCNT-heat transfer oil nanofluid flow inside horizontal flattened tubes has been carried out under uniform wall temperature condition. Nanoparticle weight fractions were 0%, 0.1%, 0.2%, and 0.4%. The copper tubes of 14.5 mm I.D. were flattened and used as the test section of oblong shape with inside heights of 13.4 mm, 11.7 mm, 10.6 mm, and 8.6 mm. The nanofluid flowing inside the tube was heated inside a steam chamber to keep the temperature of the tube wall constant. The required data were acquired for laminar hydrodynamically fully developed regime. The effects of different parameters such as volumetric flow rate, nanoparticle weight fraction, and hydraulic diameter on the heat transfer behavior of the tested systems have been investigated experimentally. For a given flattened tube at a constant nanoparticle weight fraction, increasing volumetric flow rate results in heat transfer enhancement. In addition, as the tube profile becomes more flattened and the hydraulic diameter decreases, the heat transfer coefficient goes up at constant volumetric flow rate. Utilizing nanofluids instead of the base fluid, the heat transfer rate enhances remarkably. The higher the nanoparticles weight fraction, the more the rate of heat transfer enhancement. Finally, the results show that the amount of increase in heat transfer coefficient caused by employing nanofluid instead of the base fluid is comparable to what caused by flattening the tube.