Condensation Heat Transfer Model Research Articles

Precise determination of inundation effect coefficient of film condensation on an array of horizontal new three-dimensional finned tube

To accurately evaluate the condensation heat transfer performance of new 3D finned tubes in shell-and-tube condenser, the inundation effect of the film condensation of R-134a on an array of 6 horizontal new 3D (three-dimensional) finned tubes is experimentally investigated with a new experiment method of homologous method. And the precise inundation effect coefficient of film condensation is determined. A novel test facility, whose test section contains two arrays of 8 horizontal tubes to realize the homologous method, is developed and constructed. The outer diameter of the tube and effective tube length in the test section are 19.05 and 500 mm, respectively. The condensation heat transfer coefficient of new 3D finned tube and inundation effect coefficient of new 3D finned tube bundle are determined under different conditions. The results show that the inundation effect coefficient of new 3D finned tube bundle decreases from 1.00 to 0.78 as Re increases from 75 to 1860. And the effect of heat flux on the inundation effect is more sensitive than the condensing temperature. Furthermore, for new 3D finned tube, the condensation heat transfer and inundation effect models are established, and the deviations of results between experiment and models are almost within ±6.0%. In comparison with literatures, the average inundation effect coefficient of new 3D finned tube bundle is 10.0-25.0% higher than that of 3D finned tube bundle in literatures, within 3.0% lower than that of two-dimensional finned tube bundle, and 15.2% higher than that of plain tube bundle. And the average condensation heat transfer coefficient of new 3D finned tube bundle in this article is 5.0-25.0% higher than that of 3D finned tube bundle in literatures, 10.0-30.0% higher than that of 2D finned tube bundle, and more than 10 times that of plain tube bundle. The precise inundation effect coefficients can be used as benchmark data to build precise and universal inundation effect model of 3D finned tube, and the models established in this study will help guide the thermal design of the new 3D finned tube applied in shell-and-tube condenser.

An improved heat transfer model for steam-air mixture condensation with the curvature effect on vertical tubes

The condensation heat transfer on the external surface of a vertical slender tube in the steam-air mixture environment was investigated. The condensation heat transfer was analyzed using various open experimental datasets. A new model for the steam condensation with noncondensable gases applicable to the tubular configuration was developed. The proposed model is based on the analogy between heat and mass transfer; in particular, the correlation incorporates the effects of tube curvature under turbulent free convection conditions together with the wavy film effect. In addition, the film-vapor interfacial temperature was used to calculate the heat transfer coefficient and various physical properties, through an iterative technique instead of the wall temperature, which is commonly used in experimental correlations for convenience. Thereafter, the effects of three correction factors were individually investigated. The wavy film effect considerably changed the condensation heat transfer, about 20% on average. The curvature effect was also found to make a meaningful effect according to the convection conditions. And, the adoption of interfacial temperature was found to make a maximum 7% adjustment, but it would make a more significant effect in high heat transfer conditions. Overall, the proposed model predicted the experimental datasets reasonably well, i.e., within ±30% accuracy.

A heat transfer model to predict superheated and saturated condensation of HFC/HFO refrigerant mixtures

This work proposes a new heat transfer model for superheated and saturated condensation for low global warming potential refrigerant (GWP) mixtures with hydrofluorocarbons (HFC) and hydrofluoroolefins (HFOs) constituents, and validates it with experimental data. The superheated condensation region exists upstream of the saturated region, and has been traditionally modeled as single-phase flow. However, prior research on pure fluids has shown that the heat transfer coefficients in this region are significantly higher than those associated with single-phase flow. Accurately modeling superheated condensation allows for the design of a more compact heat exchanger. In the model, the mixture effects associated with zeotropic condensation were accounted for using the equilibrium Silver, Bell and Ghaly method. The model was validated with condensation data for five low GWP refrigerant mixtures (R448A, R450A, R452A, R454B, and R454C). A total of 962 data points were compared and the resulting mean absolute percent errors (MAPEs) were equal to 8% and 12% for superheated and complete condensation, respectively. Furthermore, past investigations of pure fluids have noted an enhancement in heat transfer in the subcooled condensation region, which exists downstream of the saturated region. However, in the current study, the enhancement due to latent effects was not observed in the subcooled region and the heat transfer was well predicted (MAPE = 18%) by a single-phase correlation.

Analytical Modeling for Vapor Condensation in the Presence of Noncondensable Gas and Experimental Validation

Abstract The sensible and latent heat transfer are two essential considerations in investigating vapor condensation in the presence of noncondensable gases. In this paper, a new model for filmwise condensation heat transfer was developed using similarity-based solution. The expression of gas–liquid interfacial temperature, film thickness, and heat transfer coefficient were derived and calculated, respectively. The analytical results showed that the temperature difference between gas–liquid interfacial and cooling surface is decreased as there is an increase in cooling surface temperature. In addition, the forced-convective condensation heat transfer and film thickness on the vertical surface were experimentally carried out. The proportion of latent heat is 62–67% and relatively larger than sensible heat in the range of wall temperature (17–32.5 °C). The experimental film thickness is less than analytical film thickness by 2–10%. It is because that the liquid film may evaporate back to water vapor in the neighboring wall area due to high temperature of flue gas. Further, a new nondimensional correlation of condensation heat transfer of flue gas is fitted with Nu = 0.62Re0.5Ja0.67 and applicable range is Re = 1000–2500, Ja = 1.7–4.4. The fitting shows a good agreement between experimental and correlated values except some points in the low Nu number. The model proposed is applicable to predict the temperature and velocity distribution for condensation heat and mass transfer of multicomponent gases.

Study on Mathematical Model for Condensation Heat Transfer in Two-phase Closed Thermosyphon

The two-phase closed thermosyphon is a special heat pipe utilizing gravity instead of capillary force to return the liquid to evaporator. Some assumptions for Nusselt model are not true in the condenser section, resulting in the complexity of condensation. In this paper, a numerical model based on Nusselt’s model is developed considering vapour-liquid interfacial shear stress. The distributions of local parameters such as shear stress, liquid film thickness are analysed. The variation of average heat transfer coefficient with temperature difference is displayed. And the average heat transfer coefficients predicted by numerical model are compared with values calculated from other references. The results show that both the shear stress and liquid film thickness increase as condensation proceeds. But the growth rate decreases along the axial direction. The average heat transfer coefficients predicted by this model is lower than that calculated by Nusselt’s correlation especially at higher heat load, indicating that shear stress really reduces the heat transfer performance.

Lattice Boltzmann Modeling of Condensation Heat Transfer on Downward-Facing Surfaces with Different Wettabilities.

The model of vapor condensation heat transfer on downward-facing surfaces with different wettabilities is built by a two-dimensional (2D) lattice Boltzmann method. Dynamic evolution of condensate microdroplets on different wettability surfaces is simulated and the influence on heat transfer performance is analyzed. Moreover, the mechanism of a heterogeneous wettability surface enhancing condensation heat transfer is explored by investigating the condensate behaviors in the process of condensation. The numerical results indicate that as the contact angle of the homogeneous wettability surface increases, the initial nucleation time of the condensate is prolonged, while the departure time of the condensate is reduced significantly. The temperature adjacent to the gas-liquid interface, especially in the three-phase contact line region, is much higher than elsewhere due to the release of latent heat during condensation. Coalescence and detachment behaviors of condensate droplets cause the average heat flux to fluctuate locally with time. For the hybrid wettability surface, if the proportion of hydrophobic regions is small, the condensation heat transfer performance will be deteriorated. However, increasing the hydrophobic-hydrophilic ratio has a positive effect on enhancing heat transfer. It is found that a critical hydrophobic-hydrophilic ratio exists to optimize the heat transfer performance. For the gradient wettability surface, directional migration induced by capillary force facilitates the removal of condensate droplets, thereby enhancing the condensation heat transfer. Furthermore, a larger wetting gradient benefits to further improve the heat transfer performance. The results are valuable for optimally designing the heat transfer enhancement of vapor condensation on functionalized surfaces with heterogeneous wettability.

Improvement of the RELAP5-3D Condensation Heat Transfer Model in the Presence of Noncondensable Gases

Abstract Condensation of steam on the primary side of steam generator in a pressurized water reactor is one of the means of removing decay heat during accident scenarios such as a small break loss of coolant accident. With the presence of noncondensable gases, the rate of removal of decay heat reduces, affecting the ability of the nuclear plant to remove heat in accident scenarios. Therefore, correct prediction of heat removal capability is very significant to predict the plant behavior. In this study, an analytical model is compared with a numerical solution with the use of experiments performed at University of California, Berkeley and at MIT. A modified correlation is proposed and compared to experimental observation for various noncondensable gases.

Experimental investigation on condensation heat transfer for bundle tube heat exchanger of the PCCS (Passive Containment Cooling System)

To provide a passive cooling system for the reactor containment, Passive Containment Cooling System (PCCS) was adopted in the design of i-POWER nuclear power plant. This study focused on validation tests for condensation heat transfer of the PCCS heat exchanger using the CLASSIC facility. The tests include investigation of the condensation heat transfer in prototypic single tube and bundle tubes. From the single tube experiments, condensation heat transfer model was proposed to reflect the PCCS heat exchanger tube geometry. Experimental results in the bundle tube show consistent trend compared to the proposed heat transfer model from the single tube test. The local condensation heat transfer coefficient of inside tubes was smaller than the average value due to a shadow effect by a larger mass fraction of non-condensable gas, so that design of the PCCS should take into account degradation of the condensation heat removal in the bundle geometry.

Modifications of the turbulent diffusion layer model for the condensation heat transfer under the presence of noncondensable gases

The condensation heat transfer model of the MARS-KS1.5 code tends to under-predict the condensation in the presence of noncondensable gases. In our previous study, we adopted the diffusion layer model and modified it in order to consider the effect on turbulence on diffusive mass transfer in the diffusion layer. In this work, further modifications were made by introducing the boundary layer theory for natural convection flow.The new condensation model has been validated against 442 experimental data collected from eight different facilities. It is shown that the results of the new model for natural convection flow are more accurate result than those of the previous model. It is confirmed that the new model works well for the condensation in forced convection flow. The relative root mean square error of the new model is reduced to 0.193 from 0.242 of the previous model and 0.401 of the original one.

Simulation of Drop-Size Distribution During Dropwise and Jumping Drop Condensation on a Vertical Surface: Implications for Heat Transfer Modeling.

Accurate models for condensation heat transfer are necessary to improve condenser design. Drop-size distribution is an important aspect of heat transfer modeling that is difficult to measure for small drop sizes. The present work uses a numerical simulation of condensation which incorporates the possibility of coalescence and coalescence-induced jumping over a range of drop sizes. Results of the simulation are compared with previous theoretical models and the impact of the assumptions used in those models is explored. In particular, previous drop-size distribution models may predict heat transfer rates less accurately for high contact angles and for coalescence-induced jumping since coalescence occurs over a range of drop sizes and does not always result in departure. The influence of various input parameters (nucleation site distribution approach, nucleation site density, contact angle, maximum drop size, heat transfer modeling to individual drops, and minimum jumping size) on the drop-size distribution and overall heat transfer rate is explored. Assignment of the nucleation site spatial distribution and heat transfer model affect both the drop-size distribution and predicted overall heat transfer rate. Results from the simulation suggest that, when the contact angle is large (as on superhydrophobic surfaces) and no coalescence-induced jumping occurs, the heat transfer may not be as sensitive to the maximum drop-size as previously supposed. Furthermore, this work suggests that when coalescence-induced jumping occurs, reducing the maximum drop size may not always increase heat transfer since drops similar in size to those removed by coalescence-induced jumping can contribute significantly to the overall heat transfer rate.

Steam condensation in horizontal and inclined tubes under stratified flow conditions

In this study, an experiment on condensation heat transfer was conducted to develop a condensation model considering the structure of separated flow patterns. Multidimensional local condensation heat transfer parameters were measured in pure saturated steam at pressures of 1–5 bar and mass fluxes of 10–50 kg/m2 s in an inclinable tube with an inner diameter of 40 mm and a length of 3 m. A heat partition angle, which separated the upper and lower heat transfer areas for film condensation and convective heat transfer in stratified flow, was obtained based on the inflection point of the circumferential distribution function of local heat flux. A new condensation heat transfer model consisting of the heat partition angle and heat transfer coefficient correlations was developed based on the local heat transfer data. The experimental data for model development were obtained using circular tubes with inner diameters of 30–45 mm and inclination angles of 0–10° under pure saturated steam conditions at pressures of 1–67 bar and mass fluxes of 10–329 kg/m2 s. The model predicted the average heat transfer coefficient with an average deviation of 6.2% against the present experimental data.

A new simplified model for condensation heat transfer of zeotropic mixtures inside horizontal tubes

Simple and accurate prediction models are highly demanded for industrial design of heat exchangers using refrigerant mixtures. This paper presents some data taken during condensation of R32/R1234ze(E) and proposes a new method to predict condensation heat transfer coefficient of zeotropic mixtures inside horizontal tubes. The method is developed based on the heat transfer model by Cavallini et al. (2006) for pure fluids by including additional heat transfer resistances during zeotropic mixtures condensation. The heat transfer resistances are modified from the Bell and Ghaly (1973) method by considering the effect of interfacial roughness and non-equilibrium phenomena, following the approach by Del Col et al. (2005). This new model is easy to implement and requires low computational effort. The predicted results by the model show a satisfactory agreement with experimental data covering various mixtures and a wide range of working conditions.

The Improved Condensation Heat Transfer Models on Homogeneous and Heterogeneous Surfaces

The Improved Condensation Heat Transfer Models on Homogeneous and Heterogeneous Surfaces

Improvement of the condensation heat transfer model of the MARS-KS1.3 code using a modified diffusion layer model

The thermal-hydraulic system code, MARS-KS1.3, tends to underestimate the condensation heat transfer under the presence of non-condensable gases. To improve its condensation heat transfer model, we adopted the Herranz's diffusion layer model and further developed it, mainly focusing on thermal-hydraulic conditions in a nuclear containment during a hypothetical accident. Two key modifications include (i) the correlations to calculate heat and mass transfer on a vertical external surface for various flow conditions are adopted and (ii) a turbulent diffusion coefficient is applied to consider the effect of turbulence on mass diffusion.The modified diffusion layer model was implemented into MARS-KS1.3 and it has been validated using 157 condensation experiments from six different facilities. By using the turbulent diffusion coefficient in the modified diffusion layer model, the effect of turbulence on mass diffusion and then condensation was captured very well. For most cases, the results of the modified model are in a better agreement with the experimental data, resulting in a root-mean-square error of 21.3%. It is also shown that the modified diffusion layer model can predict local condensation heat transfer change along the condensation surface well.

Modeling of film condensation flow in oval microchannels

A theoretical film condensation heat transfer model was developed for refrigerant flowing through oval-shaped microchannels in annular flow regime with laminar liquid film flowing along the channel walls. The model considered the effects of surface tension, disjoining pressure, interfacial shear stress and interfacial thermal resistance. Study was conducted for mass fluxes in a range of 300–1500 kg/(m2 s) with two refrigerants, R134a and R1234ze(E). The local heat transfer coefficient and circumferential mean heat transfer coefficient along the flow direction were obtained. The liquid film thickness profiles at different locations are presented. Due to the effect of surface tension, the liquid film accumulates towards the semi-circular corner. The circumferential mean heat transfer coefficient is very high after entering the channel inlet, decreases along the flow direction and reaches a constant value. R134a has a slightly higher circumferential mean heat transfer coefficient than that of R1234ze(E) due to its higher liquid conductivity.

Mathematical Model for Dropwise Condensation on a Surface With Wettability Gradient

We present a mathematical model for dropwise condensation (DWC) heat transfer on a surface with wettability gradient. We adapt well-established population balance model for DWC on inclined surfaces to model DWC on a surface with wettability gradient. In particular, our model takes into account the effect of wettability gradient and energy released during drop coalescence to determine the drop departure size. We validate our model with published experimental data of DWC heat flux and drop size distribution. Based on various experimental studies on drop motion, we also propose a mechanism that explains how the energy released during drop coalescence on a surface with wettability gradient and in a condensation environment aids drop motion. The mechanism correctly explains the shift of center of mass of two coalescing drops on a surface with wettability gradient toward the drop on high wetting region. Using the model, we analyze the effect of wettability gradient on the DWC heat flux. Our model predictions show that the optimal choice of wettability gradient is governed by differential variations in population density and heat transfer through a drop with change in wettability of the surface. We also demonstrate that contact angle at which there is maximum heat transfer through a drop varies with thickness of coating layer leading to change in optimal wettability gradient.

High-pressure Condensing Refrigerant Flows Through Microchannels, Part II: Heat Transfer Models

ABSTRACTCondensation of high-pressure refrigerants in small-diameter channels over a wide range of reduced pressures approaching the critical point is investigated in this two-part study. Part I presented pressure drop measurements and a two-phase pressure drop model. In this paper, Part II of the study, a condensation heat transfer model is presented. Heat transfer coefficients were measured during condensation of R404A in circular channels (inner diameter = 0.86, 1.55, 3.05 mm) over the entire quality range. The saturation temperature was varied from 30 to 60°C, and mass flux from 200 to 800 kg m-2 s-1, to evaluate their effects on condensation heat transfer coefficient. The heat transfer model is developed using a microchannel flow regime map and the void fraction model previously developed by the authors. The resulting model predicts 93.6% of the data within ±25%. The model exhibited good agreement with data from condensing ammonia and carbon dioxide, predicting 84.8% and 97% of their data within ±25%, respectively.

Modeling and optimization of condensation heat transfer at biphilic interface

Biphilic surfaces with heterogeneous wettability and hierarchical topography can significantly enhance the condensation heat transfer performance due to the mutual benefits of the hydrophilic patterns and global superhydrophobicity, which facilitate fast nucleation and frequent droplet departure. To investigate the underlying physics of the condensation process on a biphilic surface and further explore the optimal design to achieve preferable heat transfer performance, we develop a comprehensive model that can capture the recurrent transition of filmwise-to-dropwise condensation on biphilic topographies by considering the dynamics of droplet morphology for individual droplet growth and droplet departure, and the associated droplet size distribution. The numerical results indicate that the varying droplet contact angle and the stepwise increase of the droplet contact base area substantially influence the droplet growth and the coalescence-induced droplet departure during the condensation process, and therefore contribute directly to the overall heat transfer enhancement. The model is validated by comparing the results with the heat flux measured in a custom-designed environment chamber. The developed model not only reveals the physics of condensation on biphilic surfaces but also provides important guidelines for the design and optimization of biphilic topographies for high heat flux applications.

Challenges in predicting steam-side pressure drop and heat transfer in air-cooled power plant condensers

Conventional power plant condensers operate at unsustainably high cooling water consumption rates (2–28 m3 MW h−1). Dry air-cooled condensers (ACCs) can enable reduced water consumption in power plants. However, ACCs are rarely employed because of the substantial decreases in condenser performance and power plant efficiencies compared to wet-cooled systems. ACC studies typically focus on air-side transport, assuming that the effects of steam-side pressure drop and thermal resistance are small. The objective of the present investigation is to scrutinize this assumption – quantifying the influence of steam-side effects on ACC operation. A detailed model of a representative ACC is formulated. Model results demonstrate that condensation heat transfer and pressure drop are poorly characterized at ACC operating conditions. Predicted power plant efficiency varies by 0.7% with different condensation heat transfer models. Additionally, predicted plant efficiencies vary depending on which pressure drop correlation is employed. The differences are exacerbated at low steam saturation pressures (∼4 kPa), where the cycle efficiencies range from 36.0% and 37.7% between different pressure drop correlations. Results from this study indicate that both steam side and air-side effects must be considered to improve ACC performance. Some methods for enhancing in-tube condensation are mentioned, and future ACC research needs are discussed.

Improvement of the MELCOR condensation heat transfer model for the thermal-hydraulic analysis of a PWR containment

During a hypothetical loss-of-coolant accident or a severe accident in a light water nuclear reactor (LWR), condensation heat transfer directly affects the pressure behavior and hydrogen distribution in the containment. This work aims at the improvement of the condensation heat transfer model in the MELCOR code, which is a fully-integrated computer code that models the progression of severe accidents in a LWR. It is known that MELCOR generally under-predicts the condensation heat transfer. For the improvement of MELCOR, we have assessed the MELCOR condensation model first. Other two models developed by Liao and Dehbi were also assessed for a comparative study. The assessment range is limited to the thermal-hydraulic conditions inside the containment building during a hypothetical design basis accident or a severe accident. We selected six condensation experiments of COPAIN, CONAN, Park, Anderson, Dehbi, and Kang and, then, assessed the three models against these data. The results of calculations showed that the MELCOR condensation model generally under-predicts the condensation heat transfer by about 45% and, however, it is the most precise and consistent in comparison with the other two models. Based on these results, the MELCOR model was selected as a base for model improvement. Then, four modifications were suggested: The effect of condensing surface curvature on condensation was considered into the MELCOR model first. The effective diffusion coefficient is applied for steam-air-helium tests. A multiplier to enhance condensation was obtained from the best fit of the calculated-to-measured plot. At last, to reflect the effect of superheated steam, a degradation factor deduced from the COPAIN experiment was adopted. The results of the modified MELCOR model showed very good agreements with most of the experimental data within ±30% error.