Condensation Coefficient Research Articles

Analysis of air-steam condensation tests on a vertical tube of the passive containment cooling system under natural convection

This paper presents an analytical study of the air-steam condensation on a vertical tube of a passive containment cooling system under natural convection conditions. From JNU (Jeju National University) condensation tests, the heat transfer coefficient (HTC) of steam condensation in the presence of air was measured on an outer surface of a cylindrical tube of 40 mm in outer diameter and 1.0 m in length. Using the experimental results from the JNU tests and those obtained in MIT, TIT, and UW-Madison, the validity of empirical correlations to determine condensation HTCs on condenser tubes with different lengths was evaluated. In addition, the mechanistic models using the heat and mass transfer analogy were applied to calculate the condensate rate of air-steam mixture. Combined with a couple of empirical heat transfer expressions for heat and mass transfer analogy, three different formulations to compute the vapor mass flux were applied and their prediction results were compared to the experimental results by JNU tests and MIT tests. The experimentally determined Sherwood number was also presented for both experiments, provided one employs the Collier/Stephan modeling to calculate the mass transfer rate by air-steam condensation.

Review of Micro–Nanoscale Surface Coatings Application for Sustaining Dropwise Condensation

Condensation occurs in most of the heat transfer processes, ranging from cooling of electronics to heat rejection in power plants. Therefore, any improvement in condensation processes will be reflected in the minimization of global energy consumption, reduction in environmental burdens, and development of sustainable systems. The overall heat transfer coefficient of dropwise condensation (DWC) is higher by several times compared to filmwise condensation (FWC), which is the normal mode in industrial condensers. Thus, it is of utmost importance to obtain sustained DWC for better performance. Stability of DWC depends on surface hydrophobicity, surface free energy, condensate liquid surface tension, contact angle hysteresis, and droplet removal. The required properties for DWC may be achieved by micro–nanoscale surface modification. In this survey, micro–nanoscale coatings such as noble metals, ion implantation, rare earth oxides, lubricant-infused surfaces, polymers, nanostructured surfaces, carbon nanotubes, graphene, and porous coatings have been reviewed and discussed. The surface coating methods, applications, and enhancement potential have been compared with respect to the heat transfer ability, durability, and efficiency. Furthermore, limitations and prevailing challenges for condensation enhancement applications have been consolidated to provide future research guidelines.

Understanding aerosol–cloud interactions through modeling the development of orographic cumulus congestus during IPHEx

Abstract. A new cloud parcel model (CPM) including activation, condensation, collision–coalescence, and lateral entrainment processes is used to investigate aerosol–cloud interactions (ACIs) in cumulus development prior to rainfall onset. The CPM was applied with surface aerosol measurements to predict the vertical structure of cloud development at early stages, and the model results were evaluated against airborne observations of cloud microphysics and thermodynamic conditions collected during the Integrated Precipitation and Hydrology Experiment (IPHEx) in the inner region of the southern Appalachian Mountains (SAM). Sensitivity analysis was conducted to examine the model response to variations in key ACI physiochemical parameters and initial conditions. The CPM sensitivities mirror those found in parcel models without entrainment and collision–coalescence, except for the evolution of the droplet spectrum and liquid water content with height. Simulated cloud droplet number concentrations (CDNCs) exhibit high sensitivity to variations in the initial aerosol concentration at cloud base, but weak sensitivity to bulk aerosol hygroscopicity. The condensation coefficient ac plays a governing role in determining the evolution of CDNC, liquid water content (LWC), and cloud droplet spectra (CDS) in time and with height. Lower values of ac lead to higher CDNCs and broader CDS above cloud base, and higher maximum supersaturation near cloud base. Analysis of model simulations reveals that competitive interference among turbulent dispersion, activation, and droplet growth processes modulates spectral width and explains the emergence of bimodal CDS and CDNC heterogeneity in aircraft measurements from different cloud regions and at different heights. Parameterization of nonlinear interactions among entrainment, condensational growth, and collision–coalescence processes is therefore necessary to simulate the vertical structures of CDNCs and CDSs in convective clouds. Comparisons of model predictions with data suggest that the representation of lateral entrainment remains challenging due to the spatial heterogeneity of the convective boundary layer and the intricate 3-D circulations in mountainous regions.

Modelling and simulation of a pillow plate thermosiphon reboiler

Thermosiphon reboilers are the most widely used evaporators in the process industry. Experimental studies suggested a superior performance of pillow plate thermosiphon reboilers over conventionally used tubular designs. This contribution presents a comprehensive model to simulate fluid dynamic as well as thermal performance of pillow plate thermosiphon reboilers. Experimental heat transfer coefficients are extracted from measurements at a thermosiphon reboiler test rig. With this information, correlations for the single phase heat transfer coefficient and the heat transfer coefficient with nucleate boiling as well as convective boiling are presented. A correlation for the heat transfer coefficient for film condensation inside the pillow plate and the two-phase pressure drop between the pillow plates is presented. These correlations are implemented in a modular structured simulation program. Good agreements were shown for the heat transfer with water experiments. The fluid dynamic could be described satisfactory with larger uncertainties at small circulation rates.

Modeling of evaporation and condensation processes: a chemical kinetics approach

The processes of evaporation and condensation are considered in the framework of chemical kinetics. At the phenomenological level, the processes of evaporation and condensation were considered using formal kinetics, and at the molecular level, these processes were considered using collision theory. In the framework of formal kinetics, the rate equations for the processes of evaporation and condensation were obtained. In the framework of collision theory, the equations for the rate of evaporation and condensation and for the condensation coefficient were obtained. A comparison of the calculated and available experimental data for the case of evaporation of water into air and for the case of evaporation of metals in a vacuum was made. From these comparisons, the energy characteristics of the surface of water and some metals and the condensation coefficients for these substances were determined.

Molecular gas dynamics analysis on condensation coefficient of vapour during gas–vapour bubble collapse

This study investigates the influence of the condensation coefficient of vapour on the collapse of a bubble composed of condensable gas (vapour) and non-condensable gas (NC gas). We simulated vapour and NC gas flow inside a bubble based on the molecular gas dynamics analysis in order to replicate the phase change (viz., evaporation and condensation) precisely, by changing the initial number density ratio of the NC gas and vapour, the initial bubble radius and the value of the condensation coefficient. The results show that the motion of the bubble is unaffected by the value of the condensation coefficient when that value is larger than approximately 0.4. We also discuss NC gas drift at the bubble wall during the final stage of the bubble collapse and its influence on the condensation coefficient. We conclude that vapour molecules can behave as NC gas molecules when the bubble collapses, owing to the large concentration of NC gas molecules at the gas–liquid interface. That is, the condensation coefficient reaches almost zero when the bubble collapses violently.

Numerical Modeling of Film Condensation in Horizontal Mini- and Macrocircular Tubes

A partial differential–integral equation has been derived to connect vapor condensation and the development of condensate film thickness in both the tangential and axial directions in a horizontal circular condenser tube. A high-order explicit numerical scheme is used to solve the strongly nonlinear equation. A simple strategy is applied to avoid possible large errors from high-order numerical differentiation when the condensate becomes stratified. A set of empirical friction factor and Nusselt number correlations covering both laminar and turbulent film condensation have been incorporated to realistically predict film thickness variation and concurrently allow for the predictions of local heat transfer coefficients. The predicted heat-transfer coefficients of film condensation for refrigerant R134a and water vapor in horizontal circular mini- and macrotubes, respectively, have been compared with the results from experiments and the results from the simulations of film condensation using computational fluid dynamics (CFD), and very good agreements have been found. Some of the predicted film condensations are well into the strong stratification regime, and the results show that, in general, the condensate is close to annular near the inlet of the condenser tube and becomes gradually stratified as the condensate travels further away from the inlet for all the simulated conditions. The results also show that the condensate in the minitubes becomes stratified much earlier than that in the macrotubes.

Experimental study on the interfacial wave and local heat transfer coefficient of stable steam jet condensation in a rectangular mix chamber

An experimental study on the interfacial wave and local heat transfer coefficient of stable steam jet condensation in a rectangular mix chamber was carried out. In experiments, the interfacial wave amplitude was obtained and analyzed, and an empirical correlation predicting the dimensionless wave amplitude was established. To evaluate the local average heat transfer coefficient, a thermal equilibrium model was developed, and the local average heat transfer characteristics were obtained and discussed. The results indicate that the interfacial wave amplitude increases with water mass flux and the axial dimensionless position, decreases with the steam mass flux, and changes little with inlet water temperature. The local average heat transfer coefficients are within the range of 0.98–6.24 MW/m2 °C, and they increase with the interfacial wave amplitude. The interfacial fluctuation could promote the steam jet condensation and corresponding heat transfer coefficients.

Condensation heat transfer characteristics of low-GWP refrigerants in a smooth horizontal mini tube

In this paper, a comprehensive study on heat transfer coefficient (HTC) and pressure drop of the two-phase condensation for R1234ze(E), R290, R161 and R41 were obtained in a smooth horizontal tube with 2 mm inner diameter, for these refrigerants being considered as environmentally friendly working fluid candidates in refrigeration and air conditioning systems. HTCs of R32 and R134a were also investigated as a baseline in this study. Condensation temperatures were from 35 °C to 45 °C. The mass flux ranged from 200 kg/m2·s to 400 kg/m2·s and the heat flux from 8 to 30 kW/m2. The results show that with the increasing saturated temperature and heat flux, the condensation heat transfer coefficients decrease, the HTCs of R161 are the highest while those of R1234ze(E) are the lowest at the same working condition. The pressure drop decreases while the saturation temperature rises. The predicted values of HTCs by 7 models were compared with experimental data. The results show that although different models are suitable for different refrigerants, Koyama et al.’s model is prevailing over other models for most refrigerants. On the basis of Koyama et al.’s model, a modified ϕv correlation with Weber number was taken into consideration and the revised model shows an improved prediction accuracy.

Mass and heat transfer between evaporation and condensation surfaces: Atomistic simulation and solution of Boltzmann kinetic equation

Boundary conditions required for numerical solution of the Boltzmann kinetic equation (BKE) for mass/heat transfer between evaporation and condensation surfaces are analyzed by comparison of BKE results with molecular dynamics (MD) simulations. Lennard–Jones potential with parameters corresponding to solid argon is used to simulate evaporation from the hot side, nonequilibrium vapor flow with a Knudsen number of about 0.02, and condensation on the cold side of the condensed phase. The equilibrium density of vapor obtained in MD simulation of phase coexistence is used in BKE calculations for consistency of BKE results with MD data. The collision cross-section is also adjusted to provide a thermal flux in vapor identical to that in MD. Our MD simulations of evaporation toward a nonreflective absorbing boundary show that the velocity distribution function (VDF) of evaporated atoms has the nearly semi-Maxwellian shape because the binding energy of atoms evaporated from the interphase layer between bulk phase and vapor is much smaller than the cohesive energy in the condensed phase. Indeed, the calculated temperature and density profiles within the interphase layer indicate that the averaged kinetic energy of atoms remains near-constant with decreasing density almost until the interphase edge. Using consistent BKE and MD methods, the profiles of gas density, mass velocity, and temperatures together with VDFs in a gap of many mean free paths between the evaporation and condensation surfaces are obtained and compared. We demonstrate that the best fit of BKE results with MD simulations can be achieved with the evaporation and condensation coefficients both close to unity.

Determination of condensation heat transfer inside a horizontal smooth tube

A mathematical model has been developed with the open source toolbox OpenFOAM to simulate the heat transfer process during flow condensation inside a smooth horizontal tube. The proposed model borrows some of the ideas of a recent boiling model, already developed in OpenFOAM 4.0. Modifications have been brought to this model to take into account the specific nature of flow condensation. A new coefficient called the “condensation area fraction” is introduced and a new library is added to the solver to simulate the wall heat flux during the condensation process. In order to assess the performance of the new model, numerical simulations are conducted for mass fluxes ranging from 100 to 750 kg/m2 s, with a nominal saturation temperature of 40 °C and a hydraulic diameter between 7 and 12 mm. The numerical predictions are compared to the results of two experimental works and good agreement has been found between measurements and model’s predictions. It shows the validity of the suggested numerical solution for modeling of flow condensation inside of a horizontal smooth tube. Moreover, the effect of some parameters such as mass flux, tube hydraulic diameter, vapor quality and difference between the wall and saturation temperature on the heat transfer coefficient are investigated. Finally, a new relationship for the prediction of the total heat transfer coefficient of flow condensation is proposed.

Comparison of empirical models with an experimental database for condensation on banks of tubes

Empirical models for calculating the heat-transfer coefficients for condensation on banks of tubes were compared with the experimental data set obtained by the various previous investigators consisting more than 4000 data points for 6 different condensing fluids and 13 different tube bank configurations. All the banks considered in this study, involved the condensation of the pure vapours, the exceptions are that of the Briggs and Sabaratnam (2003) and Shah (1978, 1981), since their pure vapours consisted of incondensable air. For the forced convection flow region (F < 3.5), it was observed that some of the data were underpredicted by the recent models, recommending that the effect of the shear stress due to high vapor velocity overcomes the effect of the inundation on the heat transfer rate while vice versa is the case for the models overpredicting results. Similarly, for the free convection flow region (F > 3.5), it is suggested that the data overprediction by some of the models was due to the boundary layer separation and inundation effects, whereas the data underprediction was due to the generation of the turbulence within the condensate film due to high velocity on the condensate film. The inclusion of the inundation effect to a pure forced convection model of Shekriladze and Gomelauri (1966) as recommended by Cipollone et al. (1983) lead the model of Cavallini et al. (1985) to be the most accurate model compared to the other models for steam only. It was found that the Fujii and Oda model (1986) is the most accurate model among the empirical models been demonstrated in this paper, giving an agreement with the experimental data base to within an average absolute of the errors of about 21.5%. It accounts for the effects of the shear stress on the surface of the film condensate and the inundation within the bank.

Numerical simulation for the tip leakage vortex cavitation

The tip leakage vortex (TLV) cavitation is investigated by a commercial Reynolds averaged Navier-Stokes (RANS) solver. A referenced test on a NACA0009 hydrofoil is used to validate the numerical simulation. Considering the local rotation characteristics of the vortical flow, a rotation-curvature corrected Shear-Stress-Transport model (SST-CC model) is applied to simulate the time-averaged turbulent flow. Compared to the original SST model, the SST-CC model improves the prediction of the velocity in TLV on the measured sections in downstream, and the vorticity and pressure features along the TLV trajectory are analysed numerically. In order to increase the prediction accuracy for the TLV cavitation, the empirical condensation coefficient (Fc) in Zwart's cavitation model is calibrated based on the referenced experiment. By introducing a vortex identification parameter (f∗) related to the strain rate tensor and the vorticity tensor, a relationship between the Fc and f∗ is built, and the effects of the rotational motion of the vortex on the cavity are embodied in a modified Zwart's cavitation model. Compared to the conventional Zwart's cavitation model, the modified cavitation model significantly improves the prediction of the TLV cavitation and gets a better agreement with the referenced test on different conditions with various gap widths.

The Effect of Menisci on Kinetic Analysis of Evaporation for Molten Alkali Metal Salts (CsNO3, CsCl, LiCl, and NaCl) in Small Cylindrical Containers

Using isothermal thermogravimetric data of alkali metal salts (CsNO3, CsCl, LiCl, and NaCl), we conducted kinetic analysis on atmospheric evaporation to investigate the effect of meniscus on determining the condensation coefficient. In the process of evaporation into an atmospheric gas, molten salt decomposed at the interface between molten salt and an atmospheric gas reacts with chemical compositions of the atmospheric gas to be an equilibrium state. In this atmospheric evaporation, the interface shape of molten salts is affected by the container diameter and the contact angle at the container wall. In the analysis results, the formed concave/convex meniscus led to underestimating the condensation coefficient of molten salts. However, whether the values of the condensation coefficient of molten salts were affected by menisci, the range of the predicted values was still low from 10−3 to 10−5. This result means that the presence of the foreign gas (air and Ar) is a dominant parameter in determining the condensation coefficient of atmospheric evaporation.

The Correction and Evaluation of Cavitation Model considering the Thermodynamic Effect

Two cavitation models with thermodynamic effects were established based on the Rayleigh-Plesset equation to predict accurately the cavitation characteristics in the high-temperature fluid. The evaporation and the condensation coefficient of the cavitation model were corrected. The cavitation flow of NACA0015 airfoil was calculated using the modified cavitation model, where the influence of the thermodynamic effects of airfoil cavitation was analyzed. The result showed that the pressure coefficient distribution and the bubble volume fraction simulated have the same tendency of Zwart-Gerber-Belamri model’s result. According to the experimental data, the two models provide more accurate results. At the room temperature, the values ofdpv/dTobtained by the two improved models are approximately equal. The difference between the two models’ results increases gradually with the temperature increasing, but it is still small. The simulation results are consistent with the experimental data when the evaporation coefficient is 10 and 1. When the evaporation coefficient is 1, the bubble growth is inhibited, the volume fraction becomes lower, and the cavitation area becomes flat. As the temperature increases, the cavitation area and the bubble volume fraction at airfoil front edge become larger, showing that the temperature plays a “catalytic” role in the cavitation process.

The study of a condensation coefficient of lead atoms with thermal energies

The study of a condensation coefficient of lead atoms with thermal energies

Experimental Study of Condensation Heat Transfer in Helical Coil Heat Exchanger

Helical coils are used as one of the heat transfer enhancement techniques in many engineering applications such as in nuclear industry, chemical and petrochemical industries, HVAC systems, and many other engineering applications. In nuclear industry, helical coils are used as a method for exchanging heat in large sodium-cooled fast breeder reactor. In comparison with straight-tube heat exchangers, rate of heat transfer for helical coil heat exchanger is significantly high. This is due to secondary flow pattern in planes normal to the main flow direction of fluid in the helical coiled tube. The present work is an experimental investigation on heat transfer characteristics during steam condensing inside a small diameter vertical helical coil tube with the cooling water flowing in the shell in counter flow direction. The effect of mass flow rate and saturation temperature of steam on the heat transfer coefficient is investigated and plotted. The results confirm the significant improvement in the heat transfer coefficient for condensation of steam.

Development of a new empirical correlation for steam condensation rates in the presence of air outside vertical smooth tube

In the past several decades, experimentalists have proposed a large number of correlations to estimate steam condensation rates in the presence of noncondensable gases within free convection regime. However, these correlations are in different forms, and even express conflicting dependencies of the condensation coefficient on some parameters. This study is to aim at developing a new correlation which can faithfully reflect the complex dependencies of condensation coefficient on pressure, air mass fraction and wall subcooling. Considering that more measured data can certainly help to analyze the relationship between condensation coefficient and these parameters, total 374 sets of experimental data have been obtained. It is found that there is a negative power function relation between condensation coefficient and wall subcooling, and the exponent varies with wall subcooling and total pressure. The new correlation, covering two orders of magnitude in the condensation heat transfer coefficient, is valid for pressure ranging from 0.2 to 0.5 MPa, air mass fraction ranging from 0.1 to 0.8 and wall subcooling ranging from 10 to 70 °C. Finally, we have made comparison with experimental data obtained by other investigators which shows that the new correlation is applicative for not only steam-air condensation but also steam-nitrogen and steam-argon condensation, and it can be extended to larger scope of engineering applications.

Outer heat transfer coefficient for condensation of pure components on single horizontal low-finned tubes

The outer heat transfer coefficient is determined for the condensation of pure components (iso-propanol, n-pentane, n-heptane, iso-octane and water) on low-finned carbon steel, stainless steel and titanium tubes. The outer heat transfer coefficient on these tubes is 3 to 8 times higher than on a smooth tube with the same reference surface area. The experimental data are compared with theoretical models from literature for the condensation of refrigerants and water. These models do not predict all experimental data for the condensation of iso-propanol and hydrocarbons on low-finned tubes with the accuracy given in the respective papers. Therefore, a new approach for calculation of the outer heat transfer coefficient based on dimensionless numbers is developed. With this new equation, it can be predicted with a maximum deviation of ±20%.

Heat transfer during condensation of steam from steam-gas mixtures in the passive safety systems of nuclear power plants

A theoretical model for calculation of heat transfer during condensation of multicomponent vapor-gas mixtures on vertical surfaces, based on film theory and heat and mass transfer analogy is proposed. Calculations were performed for the conditions implemented in experimental studies of heat transfer during condensation of steam-gas mixtures in the passive safety systems of PWR-type reactors of different designs. Calculated values of heat transfer coefficients for condensation of steam-air, steam-air-helium and steam-air-hydrogen mixtures at pressures of 0.2 to 0.6 MPa and of steam-nitrogen mixture at the pressures of 0.4 to 2.6 MPa were obtained. The composition of mixtures and vapor-to-surface temperature difference were varied within wide limits. Tube length ranged from 0.65 to 9.79m. The condensation of all steam-gas mixtures took place in a laminar-wave flow mode of condensate film and turbulent free convection in the diffusion boundary layer. The heat transfer coefficients obtained by calculation using the proposed model are in good agreement with the considered experimental data for both the binary and ternary mixtures.