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The Laval nozzle is an important component of the supersonic cyclone to achieve the change of gas–liquid two-phase, and the condensation characteristics of the Laval nozzle have an important influence on the separation performance of the supersonic cyclone. In this work, the effect of inlet water vapor mass fraction on the condensation characteristics in the Laval nozzle was investigated using numerical simulation and experimental methods by establishing a three-dimensional numerical model of air-water vapor supersonic condensation flow. The flow field structures in the Laval nozzle under different inlet water vapor mass fractions were investigated, including Mach number, pressure, and temperature and the effects of the inlet water vapor mass fraction on the liquefaction characteristics in the Laval nozzle were investigated. In addition, the droplet distribution in the Laval nozzle were also tested by a particle image velocimetry (PIV) experimental system. The comparison of simulation and experimental results indicates that the numerical model established in this work can effectively describe the real flow situation in the Laval nozzle. The results show that the inlet water vapor mass fraction has a little effect on the flow field structure in the Laval nozzle, and has the significant impact on the water vapor condensation characteristics. With increasing the inlet steam mass fraction from 5 % to 12.5 %, the nucleation rate, droplet number, and separation efficiency in the Laval nozzle increase to 4.05 × 1021 kg−1 s−1, 3.67 × 1014 kg−1, and 79.4 %, respectively, and when further increasing the inlet steam mass fraction to 15 %, these parameters decrease. [ABSTRACT FROM AUTHOR]

The back pressure at the outlet of supersonic cyclone separator usually causes aerodynamic shock wave in Laval nozzle, and the interaction of supersonic flow, shock wave and phase transition is very complicated. In order to explore the supersonic flow properties of wet gas under the action of shock wave, study was performed on the methane-water vapor mixtures. Then, a mathematical model for the supersonic condensation and flow of wet natural gas was established. Meanwhile, the effect of the outlet back pressure and inlet pressure on the supersonic condensation property of wet natural gas was analyzed to evaluate the performance of the supersonic cyclone separator under the action of shock waves. The simulation results show that the shock waves can cause the rapid increase in pressure and temperature of water vapor in a short time, leading to the condensed droplets re-evaporate and the liquid mass fraction at outlet reduces sharply. Besides, as the inlet pressure increases, the location of nucleation approaches the throat of Laval nozzle gradually, and the limit nucleation rate and the droplet number decrease accordingly. However, the liquid mass fraction increases due to the increasing of growth rate and sizes of droplets. Moreover, the nozzle loses its function of liquefaction when the back pressure is higher than 25 kPa (i.e., the pressure ratio is higher than 0.58), and then the nozzle cannot operate normally. Therefore, it is necessary to control the reasonable pressure ratio to ensure the dehydration efficiency of the supersonic separator with back pressure.

• Non-equilibrium condensation models of ammonia-hydrogen mixture were established. • Accurate nucleation model for ammonia gas was selected based on experimental data. • Condensation characteristics of ammonia under different inlet conditions were studied. • Feasibility of supersonic separator for ammonia-hydrogen separation was confirmed. Ammonia has gained significant attention as a prospective hydrogen energy carrier. However, the effective separation of ammonia and hydrogen becomes a crucial aspect after the decomposition of ammonia into hydrogen. In this study, a novel method for ammonia separation is introduced, which leverages the phase transition behavior in supersonic flow. Consequently, this study presents the development of a mathematical model to elucidate the non-equilibrium condensation phenomenon of ammonia, and the accuracy of this model is validated. The simulation results reveal that, in comparison to classical nucleation theory (CNT) and internally consistent classical theory (ICCT), the Lothe-Pound (L-P) nucleation model more accurately characterizes the nucleation process of ammonia at low temperatures. Furthermore, numerical simulations demonstrated that increasing the inlet pressure from 1.2 bar to 1.8 bar led to a 2.66% enhancement in ammonia condensation efficiency. In contrast, raising the inlet temperature from 271 K to 283 K resulted in a decrease in condensation efficiency and a reduction in the radius of the exit droplets, potentially affecting subsequent separation efficiency. When the inlet ammonia molar fraction was elevated from 11% to 14%, the ammonia condensation efficiency increased from 13.7% to 14.5%, with only a minor decrease in outlet droplet radius (from 3.42 × 10−7 m to 3.39 × 10−7 m). These findings indicate that increasing pressure, decreasing temperature, and raising ammonia concentration can all stimulate ammonia condensation. These results have potential implications for the design and optimization of separators. [ABSTRACT FROM AUTHOR]

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Abstract The condensation of water steam in Rankine cycle's turbines occurs usually at the subcritical region far away from the critical point, while that of the supercritical carbon dioxide in Brayton cycle' compressors occurs generally at the supercritical region and near the critical point. However, it's not known about that flow characteristics of those common, condensable working fluids in the range of subcritical and supercritical regions. In this paper, the equilibrium condensation and expansion characteristics of water steam and CO 2 in a Laval nozzle under the same dimensionless nozzle inlet conditions were investigated numerically. Firstly, the results show that the wetness fraction distribution of each working fluid is different under different nozzle inlet conditions, while the variation trend of wetness fraction are totally similar for both working fluids. This phenomenon implies that the main factor that influences the variation trend of wetness fraction is the nozzle inlet conditions rather than the type of working fluids. Secondly, the nozzle outlet Mach number of CO 2 is lower than that of water steam. And with the increasing of inlet total pressure, the total pressure loss decreases, and that of CO 2 is lower than that of water steam under the same nozzle inlet conditions. Highlights • Condensation characteristics of H 2 O and CO 2 in all ranges are compared. • Affecting factor of condensation is nozzle inlet conditions rather than fluids. • Condensation at supercritical region should be paid much more attention. • Total pressure loss decreases with the increasing of nozzle inlet total pressure. • Total pressure loss of CO 2 is lower than that of H 2 O under same inlet conditions. [ABSTRACT FROM AUTHOR]

Graphical abstract The numerical simulations of CH 4 -CO 2 mixture gas in the nozzle were carried out applying User Define Function, which convergent section is designed by different curves respectively. Due to the intense performance of spontaneous condensation and the stable variation of temperature and pressure, Translation of Witoszynski curve is recommended to design the convergent section in supersonic separator. Highlights • Two-dimensional models of Laval nozzle were set up with different convergent section. • The numerical simulations of CH 4 -CO 2 mixture gas in the nozzle were carried out. • Condensation and flow parameters were obtained using User Define Function. • Translation of Witoszynski curve is recommended to design the convergent section. Abstract The Laval nozzle is an important part of the supersonic separator, which structure determines the separation efficiency of supersonic separator. In order to study the flow and condensation process in Laval nozzle with different convergent section, convergent section is designed by Bicubic parametric curve, Quintic polynomial curve, Witoszynski curve and Translation of Witoszynski curve, respectively. The numerical model for the supersonic condensing flow process of CH 4 -CO 2 mixture gas is established and the User Define Function is invoked for numerical simulation. The effects of different linetypes of convergent section on the flow and condensation parameters in nozzle were investigated. The results confirm the Laval nozzle designed by Translation of Witoszynski curve has strengths such as the most stable pressure change, the best refrigeration effect, the most intense spontaneous condensation, and the nucleation rate is 1.610×1022m−3s−1, the number of droplets is as high as 2.023×1015m−3 at the nozzle outlet far better than the other nozzles. Therefore, Translation of Witoszynski curve is recommended to design the convergent section of Laval nozzle in supersonic separator. [ABSTRACT FROM AUTHOR]

The sudden expansion of steam in the last stages of turbines causes a nucleation process to take place and liquid droplets to appear. Parts of these droplets, which grow collide with the blades and seriously damage them. This mechanical destruction also coincides with a thermodynamic shock which suddenly increases the pressure and reduces the performance of the steam turbine. In the present study, an attempt is made to control the size of droplets and liquid mass fraction by injecting hot steam to reduce the level of the damage. This process is similar to extracting steam from upper stages and injecting it into downstream stages. In order to prove the concept of this method, a one-dimensional in-house, two-phase flow code with steam injection is developed. The conservation equations are formulated for the vapor/liquid mixture and the liquid phase is modeled by two additional transport equations. Size and number of droplets together with liquid mass fraction are calculated in different convergent-divergent nozzles and the results are compared with experimental values. Then, the steam with higher pressure and temperature is injected into various locations in the nozzle. The results show that injecting hot steam in the divergent point of the nozzle downstream of the throat and following the Wilson point reduces the size of droplets but increases their number, which can ultimately, degrade the erosion of the blades. It is also concluded that in such a situation, the injection mass flow rate of nearly 5% of main stream flow with a temperature of about 30% higher than the main stream temperature is efficient in controlling wet steam parameters. [ABSTRACT FROM AUTHOR]

The formation of liquid droplets in the low pressure steam turbines has devastating impacts on the turbine adiabatic efficiency and also causes the mechanical damage of blades due to the occurrence of severe erosion phenomenon. Previous investigations have shown that the injection of steam can decrease liquid mass fraction as well as the size of the averaged radius of droplets. To exploit the maximum potentials of this method, the optimization of injection variables is necessary. In the present study, the numerical solution of wet steam flow by the injection of hot steam within convergent-divergent nozzles together with a multi-objective genetic algorithm method are used to evaluate the appropriate injection parameters. It is concluded that to reduce liquid droplet size by 66% and liquid mass fraction by 13%, an injection steam flow rate of 4% of the main stream flow rate with a temperature 1.8 times of inlet steam temperature is required. Such a reduction of liquid droplet size has an enormous effect on lowering the erosion damages of blades. Furthermore, the injection drives the liquid droplets away from the solid boundaries, which is also expected to reduce the possible mechanical damages to the blades and the casings of turbine. [ABSTRACT FROM AUTHOR]

Based on Euler-Euler two-fluid model, the gas and liquid flow control equations were established. Combined with the theory of condensation nucleation and droplet growth, the condensation properties of CO2 in a Laval nozzle were simulated. The results showed that both the mathematical models and numerical calculation methods used could reflect the process of gas condensation in the Laval nozzle accurately. The condensation wave of CO2 was not obvious due to its small latent heat of condensation. As the gas flow into the nozzle, the Mach number increased while pressure and temperature decreased, the undercooling increased up to 30 K, and then declined quickly to about 5 K after the occurrence of condensation. The process of nucleation showed a sharp both in time and space. Wilson point is about 2. 21 mm from the throat, the nucleation rate increased sharply from 0 to 2. 04 X 1021 m-3 • s-1 , while the number of droplets reached the order of 1015 instantly. After the formation of condensation core, gas molecules under certain degree of undercooling accumulated and liquefied on the droplets surface, causing droplet radius as well as humidity to increase rapidly. After the process of nucleation, the existing coagulation cores kept growing with the mathematical models and numerical calculation methods used could reflect the process of gas condensation in the Laval nozzle accurately. The condensation wave of CO2 was not obvious due to its small latent heat of condensation. As the gas flow into the nozzle* the Mach number increased while pressure and temperature decreased, the undercooling increased up to 30 K, and then declined quickly to about 5 K after the occurrence of condensation. The process of nucleation showed a sharp both in time and space. Wilson point is about 2. 21 mm from the throat, the nucleation rate increased sharply from 0 to 2. 04 X 1021 m-3 • s-1 , while the number of droplets reached the order of 1015 instantly. After the formation of condensation core, gas molecules under certain degree of undercooling accumulated and liquefied on the droplets surface, causing droplet radius as well as humidity to increase rapidly. After the process of nucleation, the existing coagulation cores kept growing with the droplet radius increasing to 1. 46 X 10-7 m and the humidity up to 0. 093 5 at the exit of the Laval nozzle. [ABSTRACT FROM AUTHOR]

Proper estimation of droplet growth rate plays a crucial role on appropriate prediction of supersonic separators performance for separation of fine droplets from a gas stream. Up to now, all available researches employ empirical or semi-empirical correlations to define the relationship between droplet growth rate (dr/dt) and other operating variables such as temperatures (T and TL), Pressure (P) and condensation rate (mL). These empirical or semi-empirical equations are developed for pure component systems and should not be extended to binary or multi-components systems. A novel theoretical approach is presented in this article which provides a fundamental equation to find the droplet growth rate by resorting to mass transfer equations. The new model uses a combination of mass transfer equations and mass and energy balances to estimate the droplet growth rate, droplet temperature and condensation rate simultaneously. Although the simulation results indicate that the proposed method provides impressive results when validated with several real experimental data, however, the main advantage of the present approach is that it can be easily extended to binary or multi-components systems. To the best of our knowledge, the proposed approach has not been addressed previously.

Experimental investigations of non-equilibrium spontaneous condensation in transonic steam flow were carried out in nozzles and linear blade cascade. For the tests the geometry of the half arc nozzles were used. The linear cascade consists of the stator blades of the last stage low pressure steam turbine. The applied experimental test section is a part of small scale steam power station located at the Silesian University of Technology. The steam parameters at the test section inlet correspond to the real conditions in low pressure part of steam turbine. The static pressure measurements as well as the Schlieren pictures were used to assess the flow field in nozzles and linear stator blades cascade. The capabilities of used measurement techniques were estimated for gaining insight into condensation process in steam flow. The experimental results were compared with numerical calculations carried out by means of an in-house CFD code. [ABSTRACT FROM AUTHOR]

This study focuses on numerical modeling of condensation of water vapor in a Laval nozzle, using the liquid drop nucleation theory. Influence of nozzle geometry, pressure, and temperature on the average drop size is reported. A computer program written in MATLAB was used used to calculate the nucleation and condensation of water vapor in the nozzle. The simulation results are validated with the available experimental data in the literature for steam condensation. The model reveals that the average drop size is reduced by increasing the divergent angle of the nozzle. The results also confirm that increasing the inlet pressure has a direct effect on the average drop size while temperature rise has an inverse effect on the drop size. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents the computational results of the wet steam flow through the Laval nozzles for low and high inlet pressures. The results of the numerical modelling are compared with experimental data. The comparisons constitute validation tests of the condensation model implemented into an in-house CFD code solving the RANS equations for the real gas equation of state. The steam condensing flow is modelled by means of the single-fluid model, which means that the conservation equations are formulated for the vapour/liquid mixture. The water vapour properties are described by means of the local equation of state. An effective method of determination of water vapour properties are presented in the cases of expansion in the nozzle at high pressures. The presented results are compared with published experimental values. The validation of the in-house CFD code proves its usefulness for modelling the steam condensing flow for both low and high inlet pressures. [Copyright &y& Elsevier]

Abstract: We have measured rate constants for the homogeneous nucleation and condensation of n-butanol in a supersonic nozzle. Because our setup works at stagnation pressures of up to 10 bars we could extend the temperature range for which nucleation data is available by approximately 50 K to values between 263 K and 277 K. We observe peak nucleation rates of the order of 5×1024 m−3 s−1, a typical value expected in supersonic nozzles. We find that our data can be very well described by Hale''s scaling formalism but that this formalism slightly underpredicts the scaled nucleation rate at our temperatures. This is in contrast to a trend observed earlier by others. We suspect this to be due to our high temperatures (T / T C ≈0.5) as Hale''s scaling formalism that is applicable only at T / T C <0.5. A value for the sticking probability ζ =1.29×10−3 is found in our analysis. This rather low value is obtained because of the neglection of the Kelvin effect necessary for a fast numerical implementation of the specific method chosen to analyze our data. The same concept will be applied to study the kinetics of the homogeneous nucleation and condensation of zinc in future. [Copyright &y& Elsevier]

When water vapor in moist air reaches supersaturation in a transonic flow system, non-equilibrium condensation forms a large number of droplets which may adversely affect the operation of some thermal-hydraulic equipment. For a better understanding of this non-equilibrium condensing phenomenon, a numerical model is applied to analyze moist air condensation in a transonic flow system by using the theory of nucleation and droplet growth. The Benson model is adopted to correct the liquid-plane surface tension equation for realistic results. The results show that the distributions of pressure, temperature and Mach number in moist air are significantly different from those in dry air. The dry air model exaggerates the Mach number by 19% and reduces both the pressure and the temperature by 34% at the nozzle exit as compared with the moist air model. At a Laval nozzle, for example, the nucleation rate, droplet number and condensation rate increase significantly with increasing relative humidity. The results also reveal the fact that the number of condensate droplets increases rapidly when moist air reaches 60% relative humidity. These findings provide a fundamental approach to account for the effect of condensate droplet formation on moist gas in a transonic flow system. [ABSTRACT FROM AUTHOR]

Supersonic swirl separation technology has been widely used in natural gas processing and has achieved good results. However, there are few studies on the application of supersonic separation technology to the removal of CO 2 from natural gas, and the condensation rule of CO 2 under supersonic swirling flow condition is still unclear. In order to study the supersonic swirling condensation characteristics of CO 2 in Laval nozzle, the Euler mathematical model of the condensation flow of CO 2 –CH 4 two-component mixed gas was established, and the feasibility of CO 2 removal by supersonic separation technology was verified by numerical simulation. The results show that, in the process of axial flow and swirling flow, the variation trend of CO 2 condensation parameters is basically the same along the axial direction of the nozzle, but the distribution of parameters is significantly different along the radial direction. The increase of swirl intensity will increase the nozzle's liquefaction efficiency and reduce the working flow of the nozzle. The inlet temperature and inlet pressure had a significant influence on the liquefaction efficiency of the nozzle, while the inlet CO 2 content had little influence on the liquefaction efficiency. • The condensation characteristics of CO 2 in Laval nozzle under supersonic swirling flow were simulated. • The effect of cyclone on CO 2 condensation parameters was studied. • The distribution of CO 2 condensation parameters was compared in the process of swirl and axial flow. • The increase of swirl intensity will advance the condensation of CO 2 and increase the liquefaction efficiency. • The inlet temperature and pressure of supersonic nozzle affect the liquefaction efficiency. [ABSTRACT FROM AUTHOR]