Droplet Growth Model Research Articles

Evaluation of a New Droplet Growth Model for Small Droplets in Condensing Steam Flows

As the condensation phenomenon occurs in the low-pressure stages of steam turbines, an accurate modelling of the condensing flows is very crucial and has a significant impact on the development of highly efficient steam turbines. In order to accurately simulate condensing steam flows, it is essential to choose the right condensation model. Further research to enhance condensation models is of special importance because the outcomes of numerical studies of condensation models in recent years have not been entirely compatible with the experiments and there are still uncertainties in this area. Therefore, the main aim of this paper is to evaluate a proposed droplet growth model for modelling condensation phenomenon in condensing steam flows. The new model is derived to profit from the advantages of models based on the continuum approach for large droplets and those based on the kinetic theorem for small droplets, which results in the model being robust for a wide range of Knudsen numbers. The model is implemented into a commercial CFD tool, ANSYS Fluent 2022 R1, using UDFs. The results of the CFD simulations are validated against experimental data for linear cascades within the rotor and stator blade geometries of low-pressure steam turbine stages. The findings clearly demonstrate the superiority of the new model in capturing droplet growth, particularly for very small droplets immediately following nucleation. In contrast, widely used alternative droplet growth models tend to either underpredict or overpredict the droplet growth rate. This research significantly contributes to the ongoing efforts to enhance condensation modeling, providing a more accurate tool for optimizing the design and operation of low-pressure steam turbines, ultimately leading to a higher energy efficiency and a reduced environmental impact.

An investigation comparing various numerical approaches for simulating the behaviour of condensing flows in steam nozzles and turbine cascades

The process of condensation takes place within the low-pressure stages of the steam turbine when undergoing rapid expansion. The dry supercooled steam turns into very tiny liquid droplets, and the resulting wet steam mixture causes additional losses and maintenance problems. Accurate simulation of steam condensing flows helps to obtain accurate information about the thermodynamics of such flows and use this information in the design of highly efficient steam turbine stages. In this study, by using the available numerical models in commercial CFD codes, seven cases are considered for simulating steam condensing flows. The important difference between these cases is the use of different condensation models and different equations of state to calculate the thermodynamic properties of wet steam. The objective of this research is to identify an appropriate model that can be used to simulate the flow of steam condensation effectively. In recent studies, it is still necessary for further improvement of the modelling methods because the numerical results did not fully match the experimental findings, underscoring the persisting uncertainties within this domain. The current study explores various condensation models and equations of state for calculating the thermodynamic properties of wet steam. This diversity of approaches is novel and allows for the comparison of different models to determine the most suitable one for effective flow simulation. The geometries of the IWSEP nozzle (International Wet Steam Experimental Project) and linear cascade of the last-stage rotor blades were considered. To identify the most appropriate model for the simulation of steam condensing flows, the numerical results are validated against in-house experiments. The results indicate that combining the Young droplet growth model with the Vukalovich and Young equations in cases 1 and 2 is not a suitable method for modelling steam condensing flows. However, cases 3 & 4, which are the combination of Gyarmathy and Fuchs-Sutugin droplet growth models with NIST real gas models, are the most appropriate ones. The findings of this research confirm the high sensitivity of the modelling of such flows, and emphasize that the necessary care should be taken in choosing the appropriate numerical model.

A novel carbon dioxide capture technology (CCT) based on non-equilibrium condensation characteristics: Numerical modelling, nozzle design and structure optimization

The carbon capture technology (CCT) is widely studied to decrease carbon emissions and improve the global climate. Supersonic separation is becoming a new strategy for decarbonization. In order to simulate the non-equilibrium condensing flow of CO2 in the supersonic nozzle more accurately, the mathematical model is modified and verified, and non-equilibrium condensation of carbon dioxide in different states and different inlet superheat levels are analysed numerically. In order to improve the separation efficiency of the supersonic decarbonization technology and reduce the energy loss, the nozzle structure is appropriately designed and optimized. Firstly, the model is verified by gas properties, different droplet growth models and surface tension models. The result shows that the real gas model can predict the non-equilibrium condensing flow in the nozzle more accurately than the ideal gas model. Among the four droplet growth models, the most suitable one was selected in order to predict the non-equilibrium condensation properties of CO2. The droplet surface tension is corrected by introducing temperature and the droplet radius, and the droplet condensation process is enhanced. Secondly, the condensing flow through the nozzle is predicted in different states (subcritical, near-critical and supercritical). The result shows that the prediction based on the modified model is basically consistent with experimental data. Analysing the predicted Wilson line, it is found that the non-equilibrium effect of the flow is quite different at different inlet conditions. The condensation locations gradually approach the nozzle throat, the condensation interval narrows with an increase in pressure, and the peak of the nucleation rate increases gradually. Furthermore, the effect of inlet superheat on the non-equilibrium condensing flow is investigated. As the temperature rises, the flow loss decreases and the thermal efficiency increases from 61.15% to 67.62%. Finally, four nozzles with different convergence shapes are calculated. One of them demonstrates stronger stability, lower losses and the highest thermal efficiency which is about 67.64%. Additionally, when the expansion angle is 7°, the average of the liquid mass fraction is the highest, about 21.7%.

Cyclic Appearance and Disappearance of Aerosol Nucleation in the Boundary Layer of Drops of Volatile Liquid

The cyclic appearance and disappearance of nucleation was observed in the boundary layer of drops of 1,3-propanediol, 1,2-propanediol, and glycerol, close to the boiling point and exposed to a cooler airflow. Although continuous nucleation has previously been widely observed, the cyclic nature of the phenomenon observed here is unusual. It was observed in experiments with free-falling drops and fixed drops in an upflow of air. To investigate this unexpected phenomenon further, the phenomenon was reproduced in two finite volume models. The first model used 1D potential flow solutions to approximate the airflow around the spherical windward face of the droplet. The second model used CFD to model the airflow. Both models used classical nucleation theory, the Stefan–Fuchs model of droplet growth by condensation, mass transfer by evaporation, diffusion, convection, and heat transfer by diffusion and convection. Despite several simplifications, the most important being the assumption that the drop has a uniform temperature, both models predict the frequency of nucleation to be better than the order of magnitude. These models also predict the experimentally observed power law dependence of nucleation frequency on air speed. It is proposed that the cyclic nature of the phenomenon is caused by the following process: the depletion of condensable vapour around the freshly nucleated aerosol due to condensation onto the aerosol results in reduced supersaturation, which stops further nucleation, and then the replenishment of this vapour by diffusion and convection from the parent drop, with nucleation of aerosol recommencing when the supersaturation has recovered sufficiently—then, the repetition of these steps in a cycle. It is proposed that the process depends mostly on the maximum saturation ratio in the boundary layer, which itself is determined by four key dimensionless numbers: the Lewis number, the Peclet number, the Reynolds number, and the ratio of the vapour pressure of the condensable compound at drop surface temperature to the vapour pressure of the same species at ambient temperature. A practical application of the phenomenon may be as a means of validation of thermo-fluid models, which include nucleation.

Numerical and experimental investigation on condensation inside a turbine designed for an 100 kW polymer electrolyte membrane fuel cell system

This work presents mathematical modelling of moist air condensation process in a fuel cell turbine. A condensation model based on the classical nucleation theory and the Hertz–Knudsen droplet growth model is established. The numerical approach is validated through experimental results of the MS nozzle and a fuel cell turbine, and the simulation fits the experimental data well. Influences of inlet temperature and pressure on condensation process in the turbine is examined. Results show that increase of inlet temperature apparently weakens condensation and inlet heating can be realized by arranging a gas-to-gas heat exchanger in the air supply subsystem without consuming additional energy. Moreover, at the same mass flow rate increase of inlet pressure reduces the expansion ratio, thereby curbing the condensation. Compared with the matching scheme of a bypass valve, turbocharger matching with a back-pressure valve allows higher inlet pressure to be achieved and can effectively suppress the condensation.

Sensitivity analysis of nucleation and droplet growth models in the prediction of natural gas non-equilibrium condensation in Laval nozzle

Supersonic separation is a promising technology for purifying natural gas by removing impurities like H2O and heavy hydrocarbons. The condensation process of natural gas has obvious non-equilibrium characteristics, the accurate prediction of which is challenging and essential for efficient separators design. Euler-Euler two-fluid model was developed to investigate non-equilibrium condensation of four two-component gas mixtures: H2O, CO2, H2S and n-C9H20 in CH4. Various nucleation and droplet growth models were employed to analyze the sensitivity in predicted results. The obtained results show significant differences in condensation characteristics among four gas mixtures due to varying isentropic expansion coefficients. The choice of nucleation models had a pronounced impact on H2O and n-C9H20, especially using the internally consistent classical theory(ICCT). However, noticeable differences emerged for CO2 and H2S only when using ICCT compared to classical nucleation theory (CNT). Furthermore, results for H2O and n-C9H20 exhibits high sensitivity to calibration factors in the Gy and Yg droplet growth models. Conversely, due to the essentially continuous flow of initial droplet sizes for CO2 and H2S, the Nusselt number and results show minimal response to such calibrations. These results can provide a reference for determination or development of nucleation and droplet growth model for natural gas non-equilibrium condensation.

Iridescent Water Droplets Beyond Mie Scattering

AbstractLooking at a cup of hot tea, an observer can see color patterns and granular textures both on the water surface and in the steam. Motivated by this example, we model the appearance of iridescent water droplets. Mie scattering describes the scattering of light waves by individual spherical particles and is the building block for both effects, but we show that other mechanisms must also be considered in order to faithfully reproduce the appearance. Iridescence on the water surface is caused by droplets levitating above the surface, and interference between light scattered by drops and reflected by the water surface, known as Quetelet scattering, is essential to producing the color. We propose a model, new to computer graphics, for rendering this phenomenon, which we validate against photographs. For iridescent steam, we show that variation in droplet size is essential to the characteristic color patterns. We build a droplet growth model and apply it as a post‐processing step to an existing computer graphics fluid simulation to compute collections of particles for rendering. We significantly accelerate the rendering of sparse particles with motion blur by intersecting rays with particle trajectories, blending contributions along viewing rays. Our model reproduces the distinctive color patterns correlated with the steam flow. For both effects, we instantiate individual droplets and render them explicitly, since the granularity of droplets is readily observed in reality, and demonstrate that Mie scattering alone cannot reproduce the visual appearance.

Numerical analysis method for intra-stage non-equilibrium two-phase condensing flow in wet steam turbine and its application

To improve the numerical calculation performance of the intra-stage wet steam non-equilibrium condensing flow in a wet steam turbine, this paper proposed a numerically modified wet steam non-equilibrium condensation (NEC) model by considering the interphase heat and mass transfer in the Euler/Euler coordinate system. The model was developed based on nucleation kinetics, and the expressions of the critical droplet formation free energy and the nucleation rate were given. First, combining the experimental data, the non-isothermal effect nucleation model was modified by the surface tension coefficient method. Then, the low-pressure modified droplet growth model, which is suitable for describing any range of Knudsen numbers, was employed to calculate the droplet surface heat and mass transfer process, and the steam/liquid two-phase control equations and the turbulence model were presented. Meanwhile, the parameter transfer and coupling problem between the vapor and liquid phases was solved. Subsequently, the modified model and the original model were adopted to solve the wet steam condensing flow at the 1D Moses-Stein nozzle numerically, and the results showed that the modified model could calculate the distribution characteristics of pressure and droplet radius more accurately and fit the experimental results better. Afterward, the characteristicsof the non-equilibrium condensing flow of wet steam in the steam turbine cascade were investigated. Finally, combined with the experimental result on the pressure distribution in the steam turbine plane static cascade, the validity of the proposed numerically modified model was further verified, which provided a theoretical basis for the high-accuracy numerical analysis of the condensing flow in the nuclear power wet steam turbine cascade.

Modeling condensing flows of humid air in transonic nozzles

The ability to accurately model condensing flows is crucial for understanding such flows in many applications. Condensing flows of pure steam have been studied extensively in the past, and several droplet growth models have been derived. The rationale for the choice of growth models for condensation in humid air is less established. Furthermore, only a few validation cases for condensation in such flows exist. This paper aims to identify existing limitations of common droplet growth laws. The Hertz—Knudsen model is compared to heat-transfer-based models by Gyarmathy and Young, using an Euler—Lagrange approach in Ansys Fluent. For this, an adaption for Young’s growth law is introduced, allowing its application in condensation of different gas mixtures. The numerical model has been validated and applied to flows in nozzles and turbines in previous publications. The accuracy of the droplet growth models is investigated in transonic nozzle test cases. A case with pure steam and a case with humid air at two different humidity values are considered. Finally, the influence of humidity, Knudsen number, and droplet radius on the growth rate of each model is shown analytically. Flows at lower humidity values with longer condensation zones are shown to benefit from the higher sensitivity of the Hertz—Knudsen model to the mass fraction of water vapor in the flow. Heat-transfer-based models tend to overestimate condensation in such flows. However, the ability to empirically adapt the growth model by Young and its applicability in different Knudsen numbers results in good agreement with validation data over a wide range of cases.

Modified heat transfer correction function for modeling multiphase condensing flows in transonic regime

Water droplet formation and growth in the nucleation process are crucial aspects of steam condensation in moist air flow, and they are accompanied by intensive heat exchange between phases. This study proposes a mathematical model for predicting heat transfer coefficients in the condensation process, which is applicable for single-phase and multiphase flows. The proposed model based on the correction function forms a continuous model for the low Knudsen number regime, and in the region of large Knudsen numbers, it employs a simplified droplet growth model based on Hertz and Knudsen's approach derived from the kinetic theorem. The proposed model was compared with existing models based on the continuous approach, that is, models derived by Gyarmathy, Fuchs-Sutigin, and Young, as well as models based on the kinetic theorem. Furthermore, the proposed model was implemented into a numerical CFD tool, and numerical studies were conducted for two representative cases of single-species and multispecies flows, that is, steam and humid-air expansion in a converging-diverging nozzle. For steam studies, the proposed model showed a similar convergence with the experiment as Young's model however, its agreement with the experimental results for multispecies condensation flow was better. The proposed model is promising for the study of condensation when there is rapid droplet growth, which occurs in multispecies flows, even if further study is needed to find a correlation between the condensation coefficient and fluid properties.

A single-parameter hygroscopicity model for functionalized insoluble aerosol surfaces

Abstract. The impact of molecular level surface chemistry for aerosol water-uptake and droplet growth is not well understood. In this work, spherical, nonporous, monodisperse polystyrene latex (PSL) particles treated with different surface functional groups are exploited to isolate the effects of aerosol surface chemistry for droplet activation. PSL is effectively water insoluble and changes in the particle surface may be considered a critical factor in the initial water uptake of water-insoluble material. The droplet growth of two surface modified types of PSL (PSL-NH2 and PSL-COOH) along with plain PSL was measured in a supersaturated environment with a Cloud Condensation Nuclei Counter (CCNC). Three droplet growth models – traditional Köhler (TK), Flory–Huggins Köhler (FHK) and the Frenkel–Halsey–Hill adsorption theory (FHH-AT) were compared with experimental data. The experimentally determined single hygroscopicity parameter, κ, was found within the range from 0.002 to 0.04. The traditional Köhler prediction assumes Raoult's law solute dissolution and underestimates the water-uptake ability of the PSL particles. FHK can be applied to polymeric aerosol; however, FHK assumes that the polymer is soluble and hydrophilic. Thus, the FHK model generates a negative result for hydrophobic PSL and predicts non-activation behavior that disagrees with the experimental observation. The FHH-AT model assumes that a particle is water insoluble and can be fit with two empirical parameters (AFHH and BFHH). The FHH-AT prediction agrees with the experimental data and can differentiate the water uptake behavior of the particles owing to surface modification of PSL surface. PSL-NH2 exhibits slightly higher hygroscopicity than the PSL-COOH, whereas plain PSL is the least hygroscopic among the three. This result is consistent with the polarity of surface functional groups and their affinity to water molecules. Thus, changes in AFHH and BFHH can be quantified when surface modification is isolated for the study of water-uptake. The fitted AFHH for PSL-NH2, PSL-COOH, and plain PSL is 0.23, 0.21, and 0.18 when BFHH is unity. To simplify the use of FHH-AT for use in cloud activation models, we also present and test a new single parameter framework for insoluble compounds, κFHH. κFHH is within 5 % agreement of the experimental data and can be applied to describe a single-parameter hygroscopicity for water-insoluble aerosol with surface modified properties.

Mechanisms of trace water vapor desublimation over airfoil in transonic cryogenic wind tunnels

Cryogenic wind tunnels can provide a larger operating Reynolds number compared to conventional ones. However, the internationally known “moisture contamination problem” resulting from the residual trace water vapor desublimation in the cryogenic wind tunnel may affect the accuracy of the aerodynamic data. Due to extreme difficulties in experiments, the detailed trace water desublimation characteristics remain unrevealed. An Euler–Euler two-phase flow model based on classical nucleation theory and a droplet growth model were established to predict the trace water vapor spontaneous desublimation in the nitrogen flow over airfoil in a transonic cryogenic wind tunnel. The proposed model was validated by experimental data obtained from the literature and showed good agreements. The verified model was applied to 0.152-m National Advisory Committee for Aeronautics 0012 airfoil in a Langley 0.3-m transonic cryogenic wind tunnel under a series of operating conditions. The simulated results reveal that the water vapor desublimation process in a transonic cryogenic wind tunnel can be divided into two patterns by a critical region. In pattern I, over the upper critical total temperature, the water vapor desublimates quickly during the rapid expansion of gas flow over the airfoil surface. In pattern II, below the lower critical total temperature, the water vapor is sufficiently supercooled and desublimates completely into small ice particles in the free-stream flow. For pattern I, the desublimation characteristics were analyzed in detail, and the influences of the desublimation process on the aerodynamic data were quantitatively evaluated, which can provide theoretical guidance for the practical operation of transonic cryogenic wind tunnels.

Effects of crystal formation on the initial frost thickness and density on cold surfaces

In refrigeration and air-source heat pump systems, water vapor in moist air circulating across the heat exchanger fins condenses into liquid nuclei when the surface temperature is below the dew point. The supercooled liquid droplets grow and coalesce until a liquid-to-solid phase transition occurs, preceding the growth of crystals on the ice beads and the subsequent development of a frost layer within and on top of the crystals. This paper describes a comprehensive, three-stage model for frost nucleation, in which a novel crystal growth model stage was integrated with droplet growth and frost layer growth models. The overall model was experimentally validated for both hydrophobic and hydrophilic surface types and various environmental conditions focused on surface temperatures between 0 and −10 °C, relative humidities between 70 and 90%, and air temperatures between 0 and 20 °C. Model results indicated that the surface contact angle affected the ice beads' shape and size. The air's water vapor content affected the frost layer's thickness and density. If the humidity increased, the mass transfer potential increased, prompting the crystal growth–frost growth transition to occur quickly and at high density values. The cold surface temperature also affected the stage transitions. At −9 °C surface temperature, crystal growth lasted approximately 2 min while it increased to 21 min at −5 °C. Frost thickness was initially higher at −9 °C due to a shorter droplet growth stage, but the thickness increase slowed during frost layer growth, resulting in a temporarily higher thickness at −5 °C.

Modeling of self-excited oscillation of non-equilibrium condensation in transonic moist air flow

Atmospheric air is a popular working fluid in gas power plants and turbomachinery which always contains water vapor. The vapor condensation occurs in transonic flow when the temperature drops below dew point during the accelerating expansion and affects the performance of equipment and safety. The unsteady condensation model based on nucleation and droplet growth model, and the Shear Stress Transport (SST) viscous turbulence model for moist air condensing in transonic flows was proposed. The prediction accuracy of steady and unsteady condensing flows was validated by experimental data and theory. The unsteady frequency and fluctuation intensity of pressures for symmetric and asymmetric condensing oscillation modes were discussed. A new formula (f0 = 1.992Φ01.539ws0.3853) of dimensional frequency related with inlet relative humidity and saturated vapor mass fraction was obtained. Then, periodic mass flux, pressure loss and droplet mass generation rate distributions at different carrier gas pressure were analyzed. The pressure loss coefficient represents the energy loss. As the carrier gas pressure increases, the mass flow rate increases, but the energy of condensation-induced shock decreases. Combined with the analysis of the distribution of liquid mass fraction, it is also found that Mach number and pressure fluctuation are induced by condensation wave due to heat release. Finally, the velocity phase diagrams and heat addition of per unit volume at different oscillation modes were assessed. It reveals the maximum heat addition amounts of per unit volume for three symmetric modes are 1.28 × 103, 1.48 × 103 and 1.54 × 103 MW m−3 along the increase of humidity.

Two semi-analytical approaches for solving condensation shocks in supersonic nozzle flows

The paper describes two methods for solving condensation shocks in steady-state quasi-one- dimensional flows. A single-fluid-model has been implemented by solving the algebraic form of compressible flow conservation equations, in conjunction with nucleation and droplet growth laws from gas-kinetic theory. The second method assumes the condensation shock problem as a flow discontinuity, the downstream state of the shock being defined as a weak-detonation, and determined from intersections on the Rayleigh and Hugoniot curves. Both approximations have been implemented with complex multi-parameter equations-of-state based on the Helmholtz free energy, taking into account the non-ideal gas flow behavior of steam and carbon dioxide. In order to reproduce operating conditions of engineering applications, where non-equilibrium condensation occurs such as steam turbines, injectors, supercritical carbon dioxide compressors and supersonic gas flow separators. Both gas-kinetic and flow discontinuity approaches have been tested for several nozzle geometries and results have been compared with low- and high-pressure experimental data of steam and carbon dioxide. The results show that both models are able to model properly the pressure recovery that occurs in supersonic condensing flows. It has been found a low deviation 4% from experimental data of steam, and deviations within 8 % were found for the carbon dioxide case. The average droplet radius size distribution obtained from the droplet growth model is in the same order of magnitude of that of reported by experimental data available in open literature. Finally both methods were implemented in a converging-diverging nozzle of a carbon dioxide ejector in order to explore the effects of the stagnation temperature and to determine conditions free of condensation.

Distribution of condensation droplets in the last stage of steam turbine under small flow rate condition

The parameter variation, condensation and distribution of wet steam are very complicated when the steam turbine works under small flow rate condition. In this paper, the two-phase fluid model, the homogeneous nucleation model and the droplet growth model are combined to study the parameter variation in the last stage flow field, the condensation and distribution rule of wet steam and the interaction among them under small flow rate condition. The results show that the condensation location of wet steam, the number and size of droplets are influenced greatly by the location of vortex and the parameters of flow field. The droplet is mainly distributed on the side of pressure surface and the downstream of trailing edge of rotor blade. And the distribution of droplet corresponds to the distribution of the vortex. At 5%THA condition, the flow angle fluctuates violently, and the velocity triangle presents a distribution of “X“ shape. Besides, the vortex at corresponding locations is obvious, which corresponds to the distribution of droplets. The larger the droplet number, the larger the droplet size is.

Numerical approaches for moist air condensing flows modelling in the transonic regime

The paper presents mathematical modelling of water vapour condensation process in the moist air transonic internal flows. The condensation model based on the classical theory of nucleation and molecular-kinetic droplet growth model is implemented into a commercial software ANSYS Fluent. Two approaches are shown in the paper, one in which the air with water droplets is treated as a fluid mixture and second where the water droplets and humid air are computed as separate phases. Both models are validated against in-house and literature experimental studies of internal flow in nozzles. The impact of air humidity and contamination on the condensation process in internal flows for different conditions is examined. The latent heat release in the condensation process influences the flow structure, thus the analysis of condensation wave and shock wave position change with the change of relative air humidity is presented. Moreover, the importance of inertia force and the resulting velocity difference between phases is highlighted. The paper shows that the impact of the condensation in transonic flow is non-negligible and should be taken under consideration in high-velocity flow simulations.

Droplet Growth Model for Dropwise Condensation on Concave Hydrophobic Surfaces.

In this paper, mathematical models for predicting the droplet growth and droplet distribution of dropwise condensation on hydrophobic concave surface are developed and a theoretical analysis of the results of the model simulation is made. Under the assumptions of the Cassie–Baxter wetting mode and the consideration of noncondensable gases, the droplet growth model is not only established by heat transfer through a single droplet but also considered the thermal conductive resistance of the surface promoting layer. In addition, a droplet distribution model has been built based on the population balance theory. According to the calculation, the main thermal resistance in the droplet growth process is the conductive resistance inside the droplet. With the increase of contact angle, the above-mentioned thermal resistance increases; thus, the higher the hydrophobicity is, the slower the droplet growth and the less the droplet density are. Besides, the lower the temperature of the condensing surface is, the faster the droplets grow and the less the droplet density is. The models provide a mathematical tool for predicting the droplet radius at the initial stage of dewing on the concave surface and contribute to the design of functional surfaces in the field of water harvesting.

Numerical investigation of wet inflow in steam turbine cascades using NURBS-based mesh generation method

In this paper, the impact of existence of wetness in the inflow of stationary cascades of steam turbine blades has been numerically investigated. A new mesh generation method based on non-uniform rational B-splines (NURBS) has been adopted to reduce the numerical error of the wet inflow simulation. Moreover, two common meshing scenarios namely blade-to-blade (BB) and periodic-to-periodic boundary (PP) are studied and different angle of the grid at the trailing edge have been considered. The classical nucleation theory corrected by Courtney–Kantrowitz model and the Young's droplet growth model are employed to simulate the condensation phenomenon. By validating against experimental data, the results showed that implementing the proposed NURBS-based meshing technique decreased the prediction errors of static pressure distribution and droplet average radius by 35.64% and 78.44%, respectively, in comparison to typical grid generation methods. In addition, it was observed that existence of wetness at inlet significantly decreased the supercooling degree and postponed the nucleation process. Thus, the nucleation rate could be ameliorated in the case when we have a specific amount of wetness fraction in the inflow.

Optimization of the primary nozzle based on a modified condensation model in a steam ejector

The beauty and complexity of steam ejectors have fascinated scientists for decade. A modified condensation model is presented to evaluate the steam ejector performance and to optimize the steam ejector geometry. Four models consisting of different nucleation models and droplet growth models are employed to predict the non-equilibrium condensation phenomenon in a nozzle and in a steam ejector. The results show that the modified condensation model is more appropriate than the other three models. The internal flow structures as well as p-h diagram are applied in the steam ejector performance analysis. The results show that the steam ejector entrainment ratio predicted by the modified condensation model is smaller than the value predicted by the dry gas model. Given that the nucleation process mainly occurs in the steam ejector primary nozzle, only the primary nozzle is optimized using the Multi-Objective Genetic Algorithm method based on the modified condensation model. The optimal results indicate that the entrainment ratio of the optimized steam ejector increases by about 27.5% against the original value. The findings are of fundamental and practical relevance. It hopes that experimenters will be motivated to check our predictions.