Non-equilibrium Condensation Research Articles

Nanoparticles-induced heterogeneous condensation and geometry optimizations to enhance liquefaction efficiency and mitigate exergy loss in a novel hydrogen liquefaction two-phase expander

Hydrogen liquefaction methods primarily rely on various refrigeration cycles and nanoparticles are integrated into process to enhance the liquid hydrogen production yield by modifying material properties. Besides, the nanoparticles can induce the heterogeneous condensation in a novel hydrogen liquefaction transonic two-phase expander(TTPE). The TTPE is modeled as a De Laval nozzle for simplification and numerical technology is applied to improve the efficiency and minimize the exergy loss of hydrogen liquefaction by focusing on non-equilibrium condensation. For the first time, a mathematical model is established for a heterogeneous non-equilibrium condensing flow with hydrogen liquefaction incorporating the effect of nanoparticle. By introducing nanoparticles with boundary conditions set at a concentration of 10181/kg and a 10 nm radius, the efficiency of hydrogen liquefaction can be maximally enhanced by 4.29 %. Additional, by optimizing the geometrical structure of the de Laval nozzle, efficiency is improved by 2.93 % and 9.30 %, respectively, with further potential enhancements. Detailed analyses for TTPE are conducted of hydrogen liquefaction flow losses, thermal efficiency and total exergy loss under different flow conditions. Precise control of nanoparticle concentration and size, along with the regulation of intake compression and expansion state are necessary to enhance the feasibility of the liquefaction process. Finally, we discuss future research directions aimed at comprehensively enhancing the liquid hydrogen yield and reducing total energy consumption losses through effective and achievable strategies.

A novel condensation heat transfer correction based on non-equilibrium film theory and degradation mechanism for zeotropic mixture

Energy conversion based on thermodynamic cycle using zeotropic mixtures is an effective strategy for advancing global low-carbon development in the context of carbon neutrality. However, the deficiencies of existing heat transfer mixtures models and the complex condensation mechanisms of zeotropic refrigerants pose significant challenges to the size design and optimization of heat exchangers, which can directly impact the economic efficiency and operational safety of thermodynamic cycle systems. Thus, there is an urgent need for a simplified and universal correction method that incorporates mixing effects to improve prediction accuracy of conventional models. In the present study, a non-equilibrium condensation heat transfer model based on film theory was developed and validated to analyze the influence of various parameters on heat transfer degradation and heat transfer coefficients of zeotropic mixtures inside horizontal circular tubes. Through multi-factor sensitivity analysis and dimensionless method, a degradation factor characterizing the gradient contributions to heat transfer degradation was proposed. Based on the proposed factor, a simplified non-equilibrium model considering mixing effect without complex computations was developed. Using the new developed non-equilibrium model, prediction of a database containing 1813 experimental points was conducted. A deviation of 15.7 % between the predicted values and the experimental values was achieved, demonstrating remarkable predictive accuracy and significant generalizability compared to existing mixture models. Extending this corrective method to various pure substance models resulted in a significant improvement in accuracy.

Non-Condensation Turbulence Models with Different Near-Wall Treatments and Solvers Comparative Research for Three-Dimensional Steam Ejectors

Steam ejectors are important energy-saving equipment for solar thermal energy storage; however, a numerical simulation research method has not been agreed upon. This study contributes to a comprehensive selection of turbulence models, near-wall treatments, geometrical modeling (2-D and 3-D), solvers, and models (condensation and ideal-gas) in the RANS equations approach for steam ejectors through validation with experiments globally and locally. The turbulence models studied are k-ε Standard, k-ε RNG, k-ε Realizable, k-ω Standard, k-ω SST, Transition SST, and linear Reynolds Stress. The near-wall treatments assessed are Standard Wall Functions, Non-equilibrium Wall Functions, and Enhanced Wall Treatment. The solvers compared are pressure-based and density-based solvers. The root causes of their distinctions in terms of simulation results, applicable conditions, convergence, and computational cost are explained and compared. The complex phenomena involving shock waves, choking, and vapor condensation captured by different models are discussed. The internal connections of their performance and flow phenomena are analyzed from the mechanism perspective. The originality of this study is that both condensation and 3-D asymmetric effects on the simulation results are considered. The results indicate that the k-ω SST non-equilibrium condensation model coupling the low-Re boundary conditions has the most accurate prediction results, best convergence, and fit for the widest range of working conditions. A 3-D asymmetric condensation model with a density-based solver is recommended for simulating steam ejectors accurately.

Numerical investigation of spindle position effects on steam ejector performance with a nonequilibrium condensation model

AbstractThis research studied the performance of a spindle‐controlled steam ejector using models such as ideal gas and wet steam under various operating conditions based on computational fluid dynamics (CFD). A wet steam model incorporating nonequilibrium condensation was employed to simulate the complex flow phenomena within the ejector. The structure of the flow, entrainment ratio (Er), and shock wave characteristics of the steam ejector were examined in two different models. Results indicate that the spindle position has a substantial impact on steam ejector performance. For the ideal gas and wet steam models, the optimal spindle position (SP‐5) at a .1 MPa motive pressure achieves the highest entrainment ratios (Er) of 1.01 and 1.042, respectively. However, an ejector with a fixed geometry achieves Er values of only .517 and .549 for the ideal gas and wet steam models, under identical working conditions. This represents a substantial improvement of 89.8% over the fixed‐geometry ejector. The wet steam model consistently predicts 2%–4% higher Er values compared with the ideal gas model across all spindle positions. The study also reveals that increasing the motive pressure from .1 to .3 MPa reduces Er by up to 45.8% at the optimal spindle position, with the shock train length extending to 35% of the mixing chamber at .3 MPa. These findings offer insights for improving the design and optimization of variable‐geometry steam ejectors, potentially increasing efficiency in industrial applications.

Analysis of non-equilibrium condensation characteristics of supercritical carbon dioxide during transcritical flow in the Laval nozzle

During near critical operation, the non-equilibrium phase transition risk of supercritical carbon dioxide compressors usually poses significant challenges to the stability of the whole system. Analyzing the condensation characteristics in the Laval nozzle is considered an effective and feasible method for understanding condensation behavoir of supercritical carbon dioxide in rotating machinery due to the similarity and measurability of flow. In this paper, the Euler-Euler Source numerical model coupled with high-accuracy carbon dioxide real gas property table is established for transonic compressible flow in the Laval nozzle. The non-equilibrium effects of expansion and condensation during transonic flow in the nozzle are discussed and the relationships between inlet parameters, droplet distribution and nucleation rates are also analyzed. The numerical result shows that the non-equilibrium characteristic during the expansion process causes the delay of condensation in the nozzle, resulting in an overestimation of the prediction of carbon dioxide condensation region based on the homogeneous equilibrium model. Shock wave of transonic flow further amplifies the deviation of results and leads to over 12 % overestimation of liquid mass fraction. Increasing the inlet pressure and decreasing the inlet temperature can cause the forward movement of the condensation onset and the reduce of the nucleation region. For supercritical carbon dioxide in the transonic flow, the value of critical pressure ratio can be taken as 0.54∼0.55. These results provide valuable suggestions in the analysis of non-equilibrium condensing flow and designing inlet conditions for experiments.

Optimization of hydrogen recirculation ejector for proton-exchange membrane fuel cells (PEMFC) systems considering non-equilibrium condensation

In proton exchange membrane fuel cell (PEMFC) systems, unconsumed hydrogen recirculation is enabled by utilizing an ejector, and the PEMFC system's efficiency is thereby enhanced. Apart from the structural parameters, an ejector's performance is also significantly affected by the non-equilibrium condensation phenomenon. Therefore, the ejector structural parameters' impact upon non-equilibrium condensation intensity and ejector efficiency is investigated under design conditions. Structural optimization of the ejector is performed within its operating range to uphold optimal efficiency in the presence of fluctuations in secondary flow pressure. The result shows that non-equilibrium condensation negatively affects the ejector's efficiency, but its impact diminishes with larger mixing chamber diameters and nozzle divergence angles. The optimized ejector performs best with a 2.40 mm diameter mixing chamber and an 11.0o nozzle divergence angle. On average, the optimized ejector's performance improves by 16.8%, reaching a maximum improvement of 22.8% within the effective operating range.

Numerical Investigation of Two-Phase Shock Waves in CO2 Flows Using a Modified Hertz–Knudsen Model

Abstract Understanding the complex behavior of two-phase shocks in CO2 flows is essential for a variety of applications, including carbon capture and storage () and transcritical refrigeration cycles. This study presents a comprehensive numerical investigation of two-phase shock waves using the multispecies user-defined real gas model in Ansys Fluent. The simulations are performed for de-Laval nozzles, exploring the two-phase shock features for three-dimensional (3D), two-dimensional (2D), and two-dimensional axisymmetric geometries. The nonequilibrium condensation, subsequent evaporation, and denucleation occurring across the shock are modeled through a set of user-defined scalar transport equations implemented within Ansys Fluent. The two-phase computational fluid dynamics (CFD) simulations are carried out in proximity to the critical point where real gas effects are relevant. The CO2 real gas properties are computed using an in-house Python code and integrated into the solver via user-defined functions as external look-up tables. This study provides valuable insights into the physical processes underlying two-phase shocks in CO2 flows and their sensitivity to geometric variations and thermodynamic conditions. The findings contribute to the development and modification of predictive models and optimized designs for systems involving two-phase CO2 flows. The results highlight the influence of geometry configurations and thermodynamic conditions on shock location and intensity, providing comparisons for shock waves occurring in two-phase flows and supercritical single-phase flows.

Effect of the water erosion on the non-equilibrium condensation in steam turbine cascade

In the final stage of steam turbines, droplets formed by non-equilibrium condensation continuously impact and erode the blades, leading to changes in surface roughness and leading edge erosion. This study investigates the effects of roughness changes and leading edge erosion, induced by water erosion, on non-equilibrium condensation in steam turbine cascades using numerical simulation methods. In a Moses-Stein nozzle, the mechanism of roughness influencing non-equilibrium condensation is analyzed. Subsequently, entropy generation theory is applied to assess the loss distribution caused by roughness variations in a Dykas cascade. Furthermore, flow field analysis and entropy generation theory are utilized to examine the loss distribution pattern resulting from leading edge erosion. Results show that increased roughness delays non-equilibrium condensation, reducing average outlet humidity (from 0.05351 to 0.04361 as roughness rises from 0 to 500 µm). The effect of roughness on thermodynamic entropy generation exhibits a non-linear relationship, balancing steam flow losses with mitigated phase-change-related losses at a roughness of 896 µm. Significant blade erosion (>3 mm) alters leading edge geometry, causing local flow separation and a substantial increase in airfoil losses.

Shock waves characteristics and losses estimation of non-equilibrium condensation flow in nozzle and steam turbine cascade

The investigation of transonic non-equilibrium condensation is paramount due to its profound influence on the shock patterns and the distribution of losses. This study numerically investigates the shock wave morphology, evolution, and quantitative loss calculation under the influence of non-equilibrium condensation within the Moses-Stein nozzle and Dykas cascade. The results indicate that the vapor near the nozzle wall undergoes phase transition first and forms “X-shaped” condensation shock, which impervious to back pressure variations. Conversely, the “λ-shaped” aerodynamic shock moves towards the throat with increasing back pressure, triggering boundary layer separation. The entropy generation of “λ-shocks” accounts for over 98% and represents the primary source of shock losses. Strong pressure side shock induces shock wave-boundary layer interactions with the blade suction wall, resulting in reflected shocks. However, the latent heat released by non-equilibrium condensation mitigates this effect, increasing the total pressure loss coefficient by 0.188. The decrease in Mach number under high back pressure causes a notable increase in the trailing edge shock angle, with the wave foot shifting upstream. Notably, the proportion of shock losses attributed to the suction side of trailing edge exceeds 80%, significantly surpassing other regions, which progressively increases with rising back pressure. Therefore, it is crucial for cascade optimization. The findings can provide references for the optimization design of low-pressure steam turbine blade profiles. The results can serve as a guide for optimizing the blade profiles of low-pressure steam turbine.

Influence of boundary effect on supersonic flows and non-equilibrium condensation in a Laval nozzle for natural gas dehydration

The natural gas extraction process is often accompanied by large amounts of water vapor, so natural gas dehydration is the first step in achieving natural gas utilization. Current work focuses on a clean technology that captures water vapor in natural gas through expansion refrigeration. Using water vapor as a medium, a mathematical model for predicting spontaneous condensation caused by non-equilibrium state is established and validated. The influence of boundary effect including surface roughness and wall temperature on supersonic flows and non-equilibrium condensation are studied. The surface roughness affects the energy and momentum exchange between the fluid in the main stream area and near the wall, and thus affects the Wilson point, boundary layer, and non-equilibrium condensation. When the roughness rises by 0.1 mm, the boundary layer thickness increases by 56.7%, and the radial nucleation range decreases by 11.4% from y=±5.27 mm to y=±4.67 mm. The influence of wall temperature on the central area in the nozzle is not significant, but it affects the presence of liquid phase. The radial scope of liquid-phase drops by 3.58% when the wall temperature increases by 100 K.

Numerical investigation of non-equilibrium condensation of carbon dioxide from a gas mixture of carbon dioxide and argon in a supersonic nozzle under cryogenic conditions

This study involved a numerical investigation of the homogeneous nucleation of CO2 from a CO2–Ar gas mixture in a supersonic nozzle with a throat size of 2.11 mm, a total pressure of 61.15 kPa, and a total temperature of 293.15 K. The flow conditions covered the cryogenic temperature range (∼75 K). Therefore, the surface tension of the clusters was calculated using the Tolman–Tanaka correction, and nucleation growth was evaluated considering both free molecular and continuum regimes. Numerical simulations were conducted for a wide range of CO2 mole fractions (3%–39%). In particular, the effect of the CO2 mole fraction on the condensation-shock position—approximately the Wilson point—was investigated. For 3%, 12%, 24%, and 39%, the condensation shock occurred at 0.048, 0.043, 0.046, and 0.054 m from the throat, respectively. When the mole fraction was low (≤10%), the condensation-shock position moved downstream as the mole fraction decreased. This trend was attributed to a lower nucleation rate. In contrast, when the mole fraction was high (≥10%), the condensation-shock position moved downstream as the mole fraction increased. This was because the CO2 equilibrium pressure rose more rapidly than the CO2 vapor pressure as the mole fraction increases.

Prediction of the non-equilibrium condensation characteristic of CO2 based on a Laval nozzle to improve carbon capture efficiency

The supersonic separator is considered as a more efficient and environmentally friendly technology within the field of decarbonization. The flow state of the vapor and the operating environmental conditions are significant factors which affects the separation efficiency. The effect of the inlet pressure (subcritical, near-critical, supercritical), temperature (supercritical), and the outlet back pressure on the CO2 non-equilibrium condensation flow characteristics is numerically calculated. The results show that when the pressure is higher or the temperature is lower, the non-equilibrium condensation process is promoted and the formation of droplets is more stable. The nucleation interval increases with the pressure increases. The peak nucleation rate increases with the temperature decreases. The condensation shock wave is weakened and the condensable area is reduced with the back pressure increases, resulting in the liquid mass fraction significantly decreases. The critical condensation back pressure reflects the ability of the vapor to resist back pressure shocks during the condensation process. The effect of inlet pressure, temperature, and expansion angle on the critical condensation back pressure is analysed. The condensation shock wave is enhanced by increasing the pressure, expansion angle, and decreasing the temperature, the vapor has a stronger ability to resist the influence of back pressure.

Model optimization and mechanism analysis of two-stage ejector considering nonequilibrium condensation

Two-stage ejectors are widely used in multi-effect distillation and refrigeration systems owing to their vacuum and pressurization capabilities. However, most studies on two-stage ejectors are based on the dry-gas hypothesis, which neglects the universal physical phenomenon of condensation. A wet-steam model of two-stage ejectors is established and compared to the dry-gas model in this paper. Simulation results indicate that the proposed wet-steam model more accurately describes the performance and complex flow field characteristics of the two-stage ejector. Moreover, the nonequilibrium condensation mechanism of the fluid within the two-stage ejector under variable conditions is revealed. The results show that as the two-stage main nozzle pressure increases from 300 kPa to 550 kPa, the liquid mass fraction increases, and the droplet nucleation rate of the two stages decreases by 14.17 % and 13.14 %. When the first-stage actuating pressure is increased, the first-stage fluid restricts the expansion state of the second-stage main jet core and weakens the vapor condensation in the region of the shock chain. Furthermore, the experimental results demonstrate that compared with the dry-gas model, the prediction error of entrainment ratio and the secondary flow obtained by the proposed model are reduced by 26.67 % and 43.04 %, respectively.

A comprehensive investigation and optimization of superheat degree on performance of supersonic nozzle by considering non-equilibrium condensation and entropy generation analysis

A comprehensive investigation and optimization of superheat degree on performance of supersonic nozzle by considering non-equilibrium condensation and entropy generation analysis

Effects of motive flow temperature on holding steam ejector Performance under Condenser temperature change by considering Entropy generation and Non-equilibrium condensation

The condenser plays a crucial role as one of the key components in a power plant, directly influencing its overall efficiency. Any alteration in the power plant’s efficiency has a substantial impact on both energy consumption and the environment. The holding steam ejector (HSE) is essential for condenser operation by creating a vacuum and effectively removing air. The primary objective of this study is to evaluation the motive flow temperature (MFT) by considering various parameters such as steam price, production entropy, air suction, and entrainment ratio (ER). The investigation focuses on different temperatures within the power plant condenser. The study examines the changes in MFT within the range of 350 ˚C to 400 ˚C, as well as the variation in condenser temperature (CDT) spanning from 47 ˚C to 67 ˚C. The results demonstrate that varying the MFT impacts the functional parameters of the HSE. As the MFT increases, there is an increasing trend in the ER. Simultaneously, there is a decreasing trend observed in the cost of steam production, production entropy, and air suction. When the MFT increased from 350 ˚C to 400 ˚C, the suction air mass flow rate for temperatures of 47 ˚C, 57 ˚C and 67 ˚C decreases by 2.22%, 2.09% and 1.99%, respectively. These results highlight the influence of temperature on various parameters, showcasing how adjustments in the MFT and CDTs can affect the flow characteristics and associated factors in the system.

Controlling nonequilibrium Bose-Einstein condensation with engineered environments

Controlling nonequilibrium Bose-Einstein condensation with engineered environments

Modeling polydispersed droplets in non-equilibrium condensing CO2 flows through turbine cascades using moment-based methods for efficient energy utilization

The efficiency of a power cycle is significantly influenced by the condensation process and the size distribution of the droplets, as these factors directly affect heat transfer rates and overall energy conversion efficiency. Accurate numerical modeling of thermodynamic non-equilibrium condensation is crucial for predicting droplet nucleation and growth in carbon dioxide flows. This study applies moment-based polydispersed droplet models, such as the quadrature method of moments, to account for the droplet size spectrum. Additionally, discrete methods based on a predefined shape of the polydispersed droplet size spectrum are utilized and evaluated to reduce numerical complexity. Our results demonstrate that polydispersed models provide higher accuracy compared to monodispersed models when simulating steam and supercritical carbon dioxide flows in converging–diverging nozzles. In turbine cascades, the choice of model significantly influences the predicted mean droplet size and efficiency. Isentropic efficiency evaluations reveal higher values for carbon dioxide compared to steam, with efficiencies of 94.6–95.8% versus 91.8–92.9% for wet cases and 96.5–97.2% versus 95.8–96.5% for dry cases. Notably, spontaneous droplet nucleation slightly affects the efficiency of the blade cascade in carbon dioxide flows, whereas steam flows experience efficiency reductions between 3.58% and 4.01%. This work advances the understanding of droplet condensation processes in turbine cascades, highlighting the superior performance of polydispersed models and providing quantitative insights into their impact on efficiency.

Supersonic separation benefiting the decarbonization of natural gas and flue gas

Supersonic separation utilizes the cryogenics created by gas expansion to purify the mixture. This method is a novel carbon capture scheme. In this work, the models of N2-CO2 (flue gas) and CH4-CO2 (natural gas) are established to calculate the condensation flow. The condensation behavior of CO2 in natural gas and flue gas is clarified respectively, and the difference between the two is compared for the first time. Under the same conditions, CO2 in flue gas reaches the limit non-equilibrium state first, forming non-equilibrium condensation with limit nucleation rate of 7.78 × 1020 m−3s−1 and maximum droplet growth rate of 8.19 × 10−3 m s−1. However, the maximum droplet growth rate in natural gas is only 2.22 × 10−3 m s−1, which implies that the interphase mass transfer rate in flue gas is larger during the CO2 condensation. In addition, the condensation behavior of CO2 in natural gas is more sensitive to the changes of inlet parameters. This work provides an invaluable contribution to the development of supersonic carbon capture.

Carbon dioxide separation from natural gas using a supersonic nozzle

Carbon Dioxide (CO2) is often released in the process of natural gases and is one of greenhouse gases that are being treated as the most troublesome environmental issues. One of the promising ways to economically remove CO2 in natural gas processes is to use the technology of supersonic separation that makes use of non-equilibrium condensation in supersonic swirling flows in convergent-divergent nozzle using wet outlet. In the present study, the mixture of Methane (CH4) and CO2 was considered as natural gas. Two-dimensional convergent–divergent nozzle was employed to produce supersonic swirling flow with non-equilibrium condensation. The Peng–Robinson real gas model was used for the mixture gas. A nucleation equation and a droplet growth equation were incorporated into the governing equations of the compressible Navier–Stokes with the k-ω turbulence closure. The predicted results were verified and validated with existing experimental data. The convergent–divergent nozzle was varied to investigate its effect on the non-equilibrium condensation of CO2 in the mixture flow. The Technique for Order of Preference by Similarity to Ideal Solution method was applied to achieve the optimum case with amounts of wetness (the mass fraction of liquid CO2 to the summation of the mass fraction of liquid and vapor CO2 at the outlet of the nozzle) and kinetic energy. Three locations of wet outlets for the optimum case were analyzed. The results show that an increase in the divergent angle of the nozzle, swirling intensity, and inlet supply pressure results in more nucleation of CO2. However, the enhancement of mole fractions of CO2 decreases the nucleation rate and wetness. The exit wetness from wet outlets was increased with increasing distance from the throat.

All-optical temporal logic gates in localized exciton polaritons

Exciton polaritons—quasi-particle excitations consisting of strongly coupled photons and excitons—present fascinating possibilities for photonic circuits, owing to their strong nonlinearity, ultrafast reaction times and their ability to form macroscopic quantum states at room temperature via non-equilibrium condensation. Past implementations of transistors and logic gates with exciton polaritons have been mostly realized using the spatial propagation of polariton fluids, which place high demands on the fabrication of the microcavities and typically require complex manipulations. In this work we have implemented the full set of logical gate functionalities (that is, temporal AND, OR and NOT gates) in localized exciton polaritons at room temperature, on the basis of precisely controlling the interplay between polariton condensate and exciton reservoir dynamics, using a two-pulse excitation scheme. The dynamics intrinsically covers the cascadability required by the logical operations, enabling efficient information processing without the need for spatial flow. The temporal polariton logic gates demonstrate advantages in ultrafast switching, universality and simplified compatibility with other dimensional controls, showing great potential for building polariton logic networks in strongly coupled light–matter systems.