Subcooled Region Research Articles

A heat transfer model for condensation accounting for non-equilibrium effects

A heat transfer model is proposed in this paper for condensation of annular and stratified flow in horizontal smooth round tubes accounting for the non-equilibrium effects. The model is based on a non-equilibrium flow regime map and void fraction correlation that is developed from diabatic flow visualization and film thickness measurement. The model unifies single-phase and two-phase heat transfer models into one continuous function throughout the superheated, condensing-superheated, two-phase, condensing-subcooled and subcooled regions with seamless transition in between. Film heat transfer coefficient based on the interfacial temperature of the flow is used as a tool for the modeling in the presence of two-phase flow, which is later converted back to heat transfer coefficient based on the bulk temperature of the flow. The two-phase flow model is developed for the annular and stratified flow. The effects of interfacial waviness, liquid entrainment, wall subcooling, gravity, tube diameter as well as non-equilibrium are discussed in separated sections. Data obtained from different refrigerants and working conditions are used for the validation of the model.

Modeling the full-range thermal-hydraulic characteristics and post-dryout deviation from thermodynamic equilibrium in once-through steam generators

The once-through steam generator designed by Babcock & Wilcox is used as the prototype. The two-fluid three-flow-field mathematical model is introduced and the wall heat transfer conditions are re-partitioned in present work. The model is used to calculate the flow and heat transfer involving the single-phase subcooled water region, nucleate boiling region, dryout phenomenon, post-dryout region, and single-phase superheated steam region, i.e., the “full range” of the process. The results show that the proposed model could accurately predict full-range thermal-hydraulic characteristics and post-dryout deviation from thermodynamic equilibrium. The heat transfer type in the nucleate boiling region was mainly evaporation heat transfer, accompanied with liquid heat convection and quenching heat transfer. Furthermore, the heat transfer coefficient decreased and the wall temperature rose sharply at the dryout position with the heat transfer type turning into steam heat convection in the post-dryout region. Investigation of the level of deviation from thermodynamic equilibrium in the post-dryout region was conducted by defining a new parameter post-dl, with the results showing that the level of deviation decreased gradually with the development of flow and heat transfer in the post-dryout region, and the average deviation was about 42% when the once-through steam generator ran at full load.

Nucleate boiling inside small evaporating droplets: An experimental and numerical study

Evaporating and boiling of droplets on heated surfaces are widely involved in many industrial applications. In this work, the phase change characteristics inside the small droplets in the nucleate boiling regime are studied experimentally and numerically. Confined by the free surface of the droplet, the bubble dynamics in the small evaporating droplet is found experimentally to be greatly different from those observed in pool boiling. After the droplet is deposited on the heated surface, nucleate bubbles generate immediately on the droplet bottom, and then they grow fast and coalesce into large bubbles. However, unlike pool boiling, once the bubbles grow to a specific size, they stop growing and always attach to the heated surface until the droplet evaporates to a thin liquid film, subsequently the bubbles start shrinking, collapsing and finally disappearing due to the confined effects induced by the thin film free surface. With such bubble dynamics, the heat transfer rates of the fast initial bubble nucleation stage and the last thin film evaporation stage are almost four times as large as the middle stable bubble stage. A numerical model is proposed to understand the confined boiling mechanisms with flow and temperature details. The results show that the confined boiling can be attributed to either the evaporation-condensation competition, or the jetting flows induced by the Marangoni convection inside the droplet. The bubble bottom evaporates while the top condensate when its top enters the droplet subcooled region; thus, the bubble seems to stop growing. The jetting flow due to the Marangoni flows further inhibits the bubble growing by pumping the cooled liquids from the top of the droplet onto the bubble surface. For hydrophobic surfaces, the Marangoni effect dominates the bubble dynamics within the evaporating droplet. For hydrophilic surface, the evaporation-condensation competition dominates the bubble dynamics inside the evaporating droplet.

Dynamic behavior and transfer function of collector field in once-through DSG solar trough power plants

Dynamic modeling and analysis for once-through direct steam generation (DSG) solar trough are difficult because of the phase changes of the fluid and the discontinuity of fluid properties. This work develops a Collector Field Dynamic Model (CFDM) for the collector field of once-through DSG solar trough. Dynamic behaviors of fluid parameters are analyzed when there are disturbances in either full or partial small Direct Irradiance (DNI), inlet mass flow rate, and spray water flow rate. Transfer functions of outlet fluid temperature and mass flow rate are derived using the CFDM. Key results are concluded: (1) DNI disturbances closer to the subcooled water region have the largest impact on fluid parameters. (2) In initial period, the outlet temperature and mass flow rate are mainly influenced by the DNI disturbance closer to the field outlet and on the mid-section of the collector loop, respectively. (3) When the field inlet mass flow rate increases slightly, the outlet fluid temperature and mass flow rate will change significantly and take a long time to achieve new balances. (4) The outlet fluid temperature and mass flow rate change quickly and noticeably with the change in spray flow rate, and converge rapidly to new balance levels.

垂直下降流の限界熱流束予測モデル

Critical heat flux is one of the most important keys for various systems involving two-phase flow and heat transfer, such as nuclear reactors and boilers. But under downward flow condition, it is very difficult to predict critical heat flux because of complex flow caused by buoyancy. In series studies, obtained critical heat flux for downward flow were classified into four modes, however there are still not enough information about critical heat flux on stagnant region. In this investigation, critical heat flux experiment was carried out on a forced convective boiling system with a stainless steel tube of 15 mm in inner diameter and 200 mm in heating length. As the results, in the stagnant region, critical heat flux occurred in intermittent flow region, and the critical heat flux value was evaluated by a critical heat flux model taking into account of Kelvin-Helmholtz instability. In the high mass flux region, critical heat flux was observed in subcooled region. The obtained critical heat flux could be estimated by a departure from nucleate boiling model with modified departing bubble diameter correlation.

Boiling pressure drop and local heat transfer distribution of helical coils with water at low pressure

The objective of the present work is to study the influence of curvature on local boiling heat transfer coefficient and two-phase pressure drop in helically coiled tubes with water as the working medium. In helically coiled tubes, the geometric parameters like pipe diameter and coil diameter vary the curvature and hence secondary flow which affects the heat transfer distribution and pressure drop. The present work investigates the characteristics of flow boiling in helically coiled tubes. Very less information is available on the influence of curvature on flow boiling system. The local wall temperature is measured not only in the axial direction (along the length of coil) but also in the circumferential direction using thermal imaging technique. Experiments are performed with six helically coiled test sections made of SS 304 tubes having inner diameters varying from 6 to 10 mm. The coil diameter to the tube diameter ratio ranges from 14 to 58 and coil pitch is 50 mm. The effect of geometric and operating parameters like tube diameter, coil diameter, heat flux and mass flux on local boiling heat transfer coefficient and two-phase pressure drop is analysed. In the subcooled region and in a low quality region, boiling heat transfer coefficient in helical coils is much higher (12%–100%) than in straight tubes. However, in a high quality region, the boiling heat transfer coefficient in helical coils is same as in straight tubes. A correlation is suggested for two-phase pressure drop in helical coils.

Real-time dynamic analysis for complete loop of direct steam generation solar trough collector

Direct steam generation is a potential approach to further reduce the levelized electricity cost of solar trough. Dynamic modeling of the collector loop is essential for operation and control of direct steam generation solar trough. However, the dynamic behavior of fluid based on direct steam generation is complex because of the two-phase flow in the pipeline. In this work, a nonlinear distribution parameter model has been developed to model the dynamic behaviors of direct steam generation parabolic trough collector loops under either full or partial solar irradiance disturbance. Compared with available dynamic model, the proposed model possesses two advantages: (1) real-time local values of heat transfer coefficient and friction resistance coefficient, and (2) considering of the complete loop of collectors, including subcooled water region, two-phase flow region and superheated steam region. The proposed model has shown superior performance, particularly in case of sensitivity study of fluid parameters when the pipe is partially shaded. The proposed model has been validated using experimental data from Solar Thermal Energy Laboratory of University of New South Wales, with an outlet fluid temperature relative error of only 1.91%. The validation results show that: (1) The proposed model successfully outperforms two reference models in predicting the behavior of direct steam generation solar trough. (2) The model theoretically predicts that, during solar irradiance disturbance, the discontinuities of fluid physical property parameters and the moving back and forth of two-phase flow ending location are the reasons that result in the high-frequency chattering of outlet fluid flow. (3) The model validates that the solar irradiance disturbance at subcooled water region would generates larger fluctuation of fluid parameters than two-phase flow region or superheated steam region.

Effect of Transient Heat Transfer of a Condenser on a Cascade Heat Pump Performance

Transient heat transfer characteristics of a condenser of a cascade heat pump are investigated by comparing the experimental result and the prediction from a mathematical model. In the experiment part, the cascade heat pump consists of the low-temperature refrigeration cycle using R22 and the high-temperature heat pump cycle using R134a.The transient effect is presented by circulating water to receive the rejection heat from the condensing refrigerant of the cascade heat pump causing the rise of the hot water temperature. On the other hand, a mathematic model of the condensation heat consisting of the heat transfer models in the two-phase mixture region and the superheated vapor region is developed to compare the results. The effect of the hot water flow rate on the hot water temperature and the heat transfer rate is examined. The result indicates that the hot water temperature continuously increases with time. The condensation heat rapidly increases at the beginning and gradually increases with time. The result obtained from the model prediction of the condensation heat is similar to the experimental result except the initial and final period. The discrepancy between these two results is because of the transient behavior at beginning and the existent of the subcooled region.

Boiling pressure drop and local heat transfer distribution of water in horizontal straight tubes at low pressure

The objective of the present work is to investigate the heat transfer and pressure drop in flow boiling at low pressure with water as the working medium. The effect of pipe diameter, heat flux and mass flux on boiling pressure drop and local heat transfer coefficient is studied. In the present work, the available correlations are revisited for low pressure flow boiling. Comparison of local heat transfer coefficient with the existing correlation is carried out to identify an appropriate correlation which performs well in complete flow boiling range (subcooled regions and saturated regions) for water at low system pressure.Experiments are performed with eight test sections made of thin walled stainless steel (SS 304) tubes having inner diameters from 5.5 mm to 12 mm and length varying from 550 mm to 1000 mm. The system pressure is varying form 1 bar to 3 bar. No change in slope of heat transfer curve is found for subcooled regions. Heat transfer in all the three regions of subcooled boiling namely partial subcooled boiling, fully developed subcooled and net vapour generation are predicted by a single correlation. Tube diameter has no effect on boiling heat transfer distribution. However, tube diameter affects two phase pressure drop. Increase in mass flux increases the convective heat transfer coefficient. However, mass flux has no influence on subcooled and nucleate boiling heat transfer coefficient. Heat flux increases the boiling heat transfer coefficient. Increase in tube diameter and mass flux decreases the two-phase pressure drop. Most of all the correlations in the subcooled region predict heat transfer coefficient with reasonable accuracy. Kandlikar and Shah correlations perform well in the low pressure saturated boiling i.e. nucleate and convective. None of the available two-phase pressure drop correlations are able to predict the pressure drop in a low pressure system. A correlation is developed to predict two-phase pressure drop in low pressure flow boiling system with a reasonably good accuracy.

Study on the Structure Optimization and the Operation Scheme Design of a Double-Tube Once-Through Steam Generator

A double-tube once-through steam generator (DOTSG) consisting of an outer straight tube and an inner helical tube is studied in this work. First, the structure of the DOTSG is optimized by considering two different objective functions. The tube length and the total pressure drop are considered as the first and second objective functions, respectively. Because the DOTSG is divided into the subcooled, boiling, and superheated sections according to the different secondary fluid states, the pitches in the three sections are defined as the optimization variables. A multi-objective optimization model is established and solved by particle swarm optimization. The optimization pitch is small in the subcooled region and superheated region, and large in the boiling region. Considering the availability of the optimum structure at power levels below 100% full power, we propose a new operating scheme that can fix the boundaries between the three heat-transfer sections. The operation scheme is proposed on the basis of data for full power, and the operation parameters are calculated at low power level. The primary inlet and outlet temperatures, as well as flow rate and secondary outlet temperature are changed according to the operation procedure.

Solidification characteristics of water based graphene nanofluid PCM in a spherical capsule for cool thermal energy storage applications

This study aimed to investigate the solidification behavior of water dispersed with graphene nanoplatelets (GNPs) in a spherical container during solidification. The nanofluid phase change materials (NFPCMs) with GNP mass concentrations of 0.3%, 0.6%, 0.9% and 1.2% were prepared and their corresponding thermal conductivity was measured both in liquid and solid states. The thermal conductivity data showed the linear and nonlinear enhancement in liquid and solid state, respectively. The addition of GNPs resulted to an appreciable reduction in the subcooling of water from −7 °C to −2.5 °C along with reduction of 25% in solidification time owing to its high thermal conductivity and larger specific surface area. The onset of solidification got advanced in the case of NFPCM due to higher cooling rate in the subcooling region for any given driving potential. The accelerated mode of energy charging occurred during 78% of total solidification time.

An experimental study on characteristics of post-CHF heat transfer in the high subcritical pressure region near to the critical pressure

Supercritical pressurized water cooled reactor (SCWR), which has a once-through water cooled reactor for supplying supercritical pressure steam at high temperature to a turbine system, is one of the next generation reactors for the purpose of improving economic efficiency and safety. In the SCWR system, water pressure passes through the critical pressure during startup, shutdown and in case of loss of coolant accident (LOCA). Similarly, in fossil-fired power plants, once-through boilers of sliding pressure type operate at supercritical pressure during nominal load, but they work near the critical pressure during partial load. In the high subcritical pressure region slightly below the critical pressure, critical heat flux (CHF) phenomenon readily occurs at relatively low heat flux and in a high subcooled region, and then it causes serious damages to fuel rods or boiler tubes due to the abrupt temperature rise in the rod or tube. In this study, experiments on post-CHF heat transfer in such the high subcritical pressure region near the critical pressure (reduced pressure range of 0.924 up to 0.992) in the range of mass flux 400-1000 kg/(m(2).s) with a circular tube of 4.4 mm ID in vertical upward flow. HCFC22 and HFC134a were used as the test fluids. Based on the obtained data, characteristics of the post-CHF heat transfer were examined and found to be classified into two distinctive types mainly according to flow rate conditions. The influences of pressure, flow rate and heat flux on the characteristics were also clarified.

Numerical study on CTF code to predict void fraction in PWR sub channel conditions

CTF is a version of the widely used COBRA-TF code with capability of 3D simulation for core sub channel thermal hydraulics behavior. Recently, CTF is reviewed and the consideration of CTF to predict void fraction in PWR sub channel conditions such as subcooled region still need more investigation. Due to the fact that the Chen’s correlation of heat transfer coefficient is developed for relatively low pressure and high quality conditions associated with forced convection vaporization, and is not strictly valid for PWR operation conditions, so that, in this study, some runs of single channel in the benchmark based on NUPEC PWR Sub channel and Bundle Tests (PSBT) are used to investigate void fraction prediction by CTF in subcooled region and also to verify some remarkable notice of CTF from other authors. The goal of the study is to evaluate deviation for CTF void fraction prediction in PWR sub channel conditions.

Thermal–hydraulic design and analysis code development for steam generator of CFR600

China Fast Reactor (CFR) with 600MW electric power is under development in China. Lots of efforts are being made to its Research and Development (R&D). The CFR600 steam generator with straight tubes consists of the evaporator and the superheater. Phase change exists in the water/steam side and the thermal–hydraulic behavior is difficult to predict. It is challenging to design such a steam generator. Therefore, a suitable thermal–hydraulic code is necessary to assist its design and analysis. A steady-state thermal–hydraulic model is derived based on the mass, energy and momentum equations. The characteristic tube is divided into four regions: subcooled region, nucleate boiling region, film boiling region and superheated region. Equal node enthalpy increment in a region is applied to enhance the numerical accuracy. The model is verified with the design results of design code SG-33 and CEFR. It is proven that the code developed can be used to design and analyze the thermal–hydraulic behavior. Sensitivity analysis is performed to investigate the influence on the heat transfer from key parameters. A preliminary design of CFR600 steam generator is presented using the developed code and reasonable results are obtained.

The optimum design and arrangement of a steam generator in an integral pressurized water reactor

This paper presents a double-tube once-through steam generator (DOTSG), whose tube unit includes an outer straight tube and an inner helical tube, in an integral pressurized water reactor (IPWR). To obtain the optimum structure of the inner helical tube and the arrangement of DOTSGs in the reactor pressure vessel, a two-level optimization method is used, aiming at the lower pumping power needed, and a smaller reactor pressure vessel volume is used. The pitch of inner helical tubes and the central distance of outer tubes are considered design parameters when minimizing the pumping power with the genetic algorithm in the bottom level, while the number of tube units in a single DOTSG and the number of DOTSGs in the reactor pressure vessel (RPV) are optimized to obtain the minimum volume of the IPWR, which is conducted in the top level. The optimum pitch of the helical tube varies in the sub-cooled region, boiling region and superheated region. The results show that the smaller pitch brings a shorter tube length and a higher pressure drop, and the effects are strong in the sub-cooled region and the superheated region but weak in the boiling region. In this way, the optimal structure of the inner helical tube is a small pitch in the single-phase region and a large pitch in the boiling region. According to the bottom level results, the optimum arrangement of DOTSGs in the pressure vessel is determined.

The Behavior of IAPWS-95 from 250 to 300 K and Pressures up to 400 MPa: Evaluation Based on Recently Derived Property Data

Over the past several years, considerable scientific and technical interest has been focused on accurate thermodynamic properties of fluid water covering part of the subcooled (metastable) region and the stable liquid from the melting line up to about 300 K and pressures up to several hundred MPa. Between 2000 and 2010, experimental density data were published whose accuracy was not completely clear. The scientific standard equation of state for fluid water, the IAPWS-95 formulation, was developed on the basis of experimental data for thermodynamic properties that were available by 1995. In this work, it is examined how IAPWS-95 behaves with respect to the experimental data published after 1995. This investigation is carried out for temperatures from 250 to 300 K and pressures up to 400 MPa. The starting point is the assessment of the current data situation. This was mainly performed on the basis of data for the density, expansivity, compressibility, and isobaric heat capacity, which were derived in 2015 from very accurate speed-of-sound data. Apart from experimental data and these derived data, property values calculated from the recently published equation of state for this region of Holten et al. (2014) were also used. As a result, the unclear data situation could be clarified, and uncertainty values could be estimated for the investigated properties. In the region described above, detailed comparisons show that IAPWS-95 is able to represent the latest experimental data for the density, expansivity, compressibility, speed of sound, and isobaric heat capacity to within the uncertainties given in the release on IAPWS-95. Since the release does not contain uncertainty estimates for expansivities and compressibilities, the statement relates to the error propagation of the given uncertainty in density. Due to the lack of experimental data for the isobaric heat capacity for pressures above 100 MPa, no uncertainty estimates are given in the release for this pressure range. Results of the investigation of IAPWS-95 concerning its behavior with regard to the isobaric heat capacity in the high-pressure low-temperature region are also presented. Comparisons with very accurate speed-of-sound data published in 2012 showed that the uncertainty estimates of IAPWS-95 in speed of sound could be decreased for temperatures from 283 to 473 K and pressures up to 400 MPa.

Heat transfer characteristics of water flowing in a vertical upward rifled tube with low mass flux

This paper presents an experimental investigation on heat transfer characteristics of water flowing upward in a 2-m long vertical rifled tube with an hydraulic diameter of 19.1mm. The experiment was conducted at pressures ranged from 11 to 32MPa, values of mass flux from 170 to 800kgm−2s−1 and heat fluxes up to 600kWm−2. The results show that at subcritical pressures, dryout occurs at high vapor qualities and is delayed by decreasing heat flux. The influence of mass flux on the onset of dryout is non-monotonic. Compared to smooth tube, rifled tube can effectively prevent the occurrence of departure from nucleate boiling (DNB). Whereas, at near-critical pressures, the enhancement disappears and DNB even occurs in sub-cooling region. But the peak wall temperature is remarkably reduced. Based on the experimental data, correlations were obtained to predict heat transfer in single-phase, two-phase and post-dryout regions. At supercritical pressures, heat transfer is enhanced within the pseudo-critical region due to drastic variations of thermo-physical properties. Both buoyancy and flow acceleration have little effect on heat transfer. Five heat transfer correlations were evaluated with the experimental data divided into forced convection and mixed convection. The Mokry et al. correlation shows the best performance in predicting heat transfer with forced convection and the Jackson correlation gives the best prediction in mixed convection region.

An experimental investigation of pure steam and steam–air mixtures condensation outside a vertical pin-fin tube

A set of condensation experiments in the steam–air and pure steam conditions has been conducted to evaluate the heat removal capacity of a vertically pin-fin tube under free convection. Condensation heat transfer coefficient and heat transfer rate have been obtained. The bulk temperature, wall temperature and temperature near tube surface are measured in detail. As a reference, a smooth tube is tested under the same condition. For pure steam case, the pin-fin tube generates restrictions on the condensation heat transfer process in low wall subcooling region. With a higher wall subcooling, the pin-fin tube shows a larger condensation heat transfer coefficient than smooth tube does. For steam–air mixtures case, the result of the temperature measurement demonstrates that there is an air rich region near the pin-fin tube. Compared with the smooth tube, the pin-fin tube generates reduction effect on the condensation heat transfer process under low air mass fraction situation. As air mass fraction increasing, the condensation heat transfer coefficient of the pin-fin tube becomes larger than that of the smooth tube.

Numerical investigation of the mechanism of two-phase flow instability in parallel narrow channels

In this paper, the mechanism of two-phase flow instability in parallel narrow channels is studied theoretically, and the characteristic of the flow instability is discussed in detail. Due to the significant confining effect of the narrow channel on the vapor–liquid interface, the two-phase flow resistance in the narrow channel is probably different from that in conventional channel. Therefore, the vapor confined number (Nconf), defined by the size of narrow channel and bubble detachment diameter, is considered in the “Chisholm B model” to investigate the two-phase flow pressure drop. The flow instability boundaries are plotted in parameter plane with phase-change-number (Npch) and subcooling-number (Nsub) under different working conditions. It is found that the predicted result agrees well with the experimental result. According to the predicted result, the oscillation behaviors near the flow instability boundary indicate that the Supercritical Hopf bifurcation appears in high sub-cooled region and the Subcritical Hopf bifurcation appears in low sub-cooled region. Also, a detailed analysis about the effects of key parameters on the characteristic of two-phase flow instability and the flow instability boundary is proposed, including the effects of inlet subcooling, heating power, void distribution parameter and drift velocity.

Structural optimization of double-tube once-through steam generator using Pontryagin's Maximum Principle

The heat transfer performance of a double-tube once-through steam generator (DOTSG) is studied in this paper. The double-tube consists of an outer straight tube and an inner helical tube. To minimize the DOTSG volume and reduce the pressure drop, an objective function is constructed with normalized tube length and pressure drop with linear weighted method. The pitch optimization proceeds from superheated region to boiling region and then to sub-cooled region in sequence, using Pontryagin's Maximum Principle. The results show that the optimal pitch keeps constant along the axial direction in the sub-cooled region and superheated region, but varies in the boiling region. In the boiling region, the tube length is 6.4% longer while the pressure drop is 36.3% smaller compared with those obtained from minimum tube length optimization; and the pressure drop is 30.7% larger while the tube length is 4.6% smaller compared with those obtained from minimum pressure drop optimization. The theoretical analysis and analytical results show the feasibility of Pontryagin's Maximum Principle used for structural optimization in this paper.