Non-equilibrium Condensation Process Research Articles

A study of the application of wet steam modeling for thermocompressor simulation in TVC desalination

Recently, the wet steam model, grounded in classical nucleation theory, has been utilized for computational fluid dynamics (CFD) simulations of thermocompressors and steam ejectors. However, this model, which accounts for the formation of liquid droplets in a homogeneous non-equilibrium condensation process, presents computational challenges due to its complexity. Unlike the ideal gas model, it involves solving multiple equations concurrently with the Navier-Stokes equations, rendering it computationally intensive and difficult to converge. The primary objective of this study is to evaluate the feasibility and efficacy of employing this intricate wet-steam model for modeling steam thermocompressors, specifically analyzing its impact on pressure, temperature, and Mach number contours. This paper aims to investigate the influence of modeling non-equilibrium condensation on various parameters affecting ejector performance. Utilizing numerical simulations conducted via ANSYS Fluent software, employing both 2-D axisymmetric wet steam and ideal gas models, our study reveals that non-equilibrium condensation leads to a higher entrainment ratio and critical back pressure. Additionally, our findings indicate that while the wet steam model notably affects temperature contours, its effect on pressure and velocity contours is comparatively minimal. The CFD analysis found that pathline trajectories were similar with both ideal gas and wet steam models. Droplet formation and evaporation within the thermocompressor revealed a gradual evaporation up to the midpoint of the constant area section, followed by a rise in liquid mass fraction due to droplet formation. However, after the constant area section, a shock wave led to a sudden pressure increase and decrease in liquid mass fraction of wet steam. These changes persist through the diffuser section of the ejector.Furthermore, to enhance the reliability of our results, this research integrates a robust validation methodology. We compare experimental results obtained from ejector studies in the literature with our simulations. Moreover, we introduce an experimental section in our research, specifically addressing zero suction mass flow rate conditions, thereby offering a practical validation approach.

Research on non-equilibrium condensation of supercritical carbon dioxide in sCO2 power systems

Based on the consideration of sustainable development and energy efficient transformation, people propose using renewable energy to upgrade traditional power generation systems. The supercritical carbon dioxide (sCO2) Brayton cycle has a great utilization potentiality in thermodynamic systems, such as solar thermal power generation systems. When the CO2 fluid flows into the compressors of sCO2 power systems, there is a risk of non-equilibrium condensation due to local expansion and acceleration, which seriously threatens the stability of the whole system. The convergent-divergent nozzle is usually used to study non-equilibrium condensation. In this paper, the wet steam model is used to simulate the non-equilibrium condensation of the CO2 fluid near its critical region in a convergent-divergent nozzle. The phase change model and the thermophysical equation of state are verified by experimental data. The non-equilibrium condensation process is analyzed, and the droplet nucleation process and droplet growth process are described. Non-equilibrium condensation releases the latent heat and forms a condensation shock wave. The influences of the shock wave effect on temperature, pressure, and other parameters are discussed. The initial condensation position and critical subcooled temperature under different inlet conditions are analyzed.

Feasibility investigation of non-equilibrium condensing nitrogen droplets as tracer particles in cryogenic wind tunnels

Application of high-precision non-intrusive flow field measurement techniques in transonic cryogenic wind tunnels (CWT) is confined to the lack of suitable tracer particles. The present study explored the feasibility of utilizing non-equilibrium condensing nitrogen droplets as tracer particles. A numerical model of the nitrogen non-equilibrium condensation was established. Accordingly, the non-equilibrium condensation process of nitrogen droplets and feasibility analysis of tracing were investigated. The results reveal that the occurrence of nitrogen droplets as well as the droplet concentration and mean radius can be regulated in the nucleation zone and droplet growth zone by varying gas temperature or pressure. Furthermore, the feasibility of employing nitrogen droplets as tracer particles in the working conditions of CWT is confirmed through the analysis of tracking capability, response time, concentration, and duration of droplet traceability. Formulas correlating used to calculate duration of droplet traceability have been proposed. This study proved the potential application of condensing nitrogen droplets as tracer particles in CWT.

Design and Internal Flow Characteristic Investigation of High-Temperature H2/Steam-Mixed Working Fluid Turbine

In this paper, an improved RSM-CFD method is used to optimally design a mixed turbine of non-equilibrium condensing steam (NECS) and hydrogen (H2), of which the response surface method (RSM) and computational fluid dynamics (CFD) are coupled to take into account the effects of the wet steam non-equilibrium condensation process of the multimixed working fluid. A single-stage H2/Steam (NEC)-mixed turbine was developed based on the improved RSM-CFD, and the effect mechanism of the H2 component ratio (ωH2) on the flow characteristics, internal power, and isentropic efficiency within the turbine stage were investigated. The results show that the isentropic efficiency (η) increases with the increase in the hydrogen component ratio (ωH2), since hydrogen, as a non-condensable component, can inhibit the nucleation and growth of steam, reducing the pressure pulsation on the blade surface; furthermore, it accelerates the transport and diffusion of liquid droplets, inhibits the flow separation, and reduces the flow loss in the flow channel. However, the internal power of the turbine (P) tends to decrease with increasing ωH2, since the increase in hydrogen reduces the pressure difference on the blade and lowers the torque of the fluid acting on the blade, and at the same time, the vortex and radial flow intensify, and the enthalpy drop inside the stage decreases. On this basis, the optimum operating conditions are found where the hydrogen component ratio (volume percent) ωH2 = 53%. Accordingly, the hydrogen component ratio should be maintained in the range of 38–68%, considering the work capacity and hydrogen yield of the mixed working fluid.

A two-phase density-based solver for simulating wet steam flows with non-equilibrium condensation. I. Approach and verification

This paper presents a new two-phase density-based solver based on the finite difference method for simulating high-speed wet steam flows with non-equilibrium condensation. The solver employs the Eulerian–Eulerian approach to model the wet steam flow using a fifth-order accurate weighted compact nonlinear scheme. The phase change of wet steam involves droplet growth in a non-equilibrium condensation process based on the internally consistent classical theory. To speed up computation, a tabulated equation of state approach with curvilinear grids is developed, and an improved Harten-Lax–van Leer-contact-type Riemann solver is used to compute inviscid fluxes. Furthermore, the automatic differentiation technique is applied to avoid manually deriving complicated derivatives when computing flux Jacobian matrices and thermodynamic properties. A numerical investigation is conducted on flow via various kinds of nozzles and blades, and the results demonstrate that the numerical model accurately predicts the behaviors observed in the experiments.

Numerical study on CO2 non-equilibrium condensation considering shock waves for the potential of flue gas decarbonization

This work proposes a CFD model based on spontaneous condensation theory and evaluates the potential of non-equilibrium phase transition principle for flue gas decarbonization in supersonic separators. The effects of inlet supercooling degree and convergent curve on non-equilibrium condensation behavior of CO2 and shock wave are discussed in detail. Based on the gas equation of state, the influence of thermodynamic model on flow behavior and non-equilibrium condensation process is quantified. The results show that increased inlet supercooling prolongs droplet growth process and increases liquid fraction in the separator. When the inlet supercooling increases by 10 K, the liquid fraction increases by 38.5%. Using Translation of Witoszynski curve and Witoszynski curve to design the converging part of the separator can simultaneously obtain larger droplet size and higher liquid fraction, which is conducive to the liquefaction and separation of CO2. The ideal gas model overestimates the expansion level of flue gas and underestimates the liquid produced by spontaneous condensation, with errors of 4.03% and 28.5%, respectively.

Effect of NaCl presence caused by salting out on the heterogeneous-homogeneous coupling non-equilibrium condensation flow in a steam turbine cascade

Steam turbine is one of the most important components in fossil-fired and nuclear power plants, its efficiency is of great importance for saving energy and decreasing consumption. The steam density rapidly decreases when the steam expanses, and NaCl dissolved in steam starts precipitating. However, the presence of NaCl will not only affect the non-equilibrium condensation decreasing the steam turbine efficiency, but also erode the steam turbine blade reducing the steam turbine safety and shortening maintenance cycle. The main objective of the current work is to investigate the effect of the NaCl presence on the non-equilibrium condensation process and the loss in steam turbine cascade. Firstly, a non-equilibrium condensation model including homogeneous and heterogeneous condensation process is presented and its accuracy is checked in a steam turbine cascade by comparing with available experimental data. And the results show the accuracy and robustness of the model is quite trustworthy. Secondly, the influence of NaCl concentration on the non-equilibrium condensation flow is investigated in a steam turbine cascade. The results show that the NaCl presence has a significant effect on condensation flow. With the NaCl concentration increasing, the droplets nucleation rate decreases, diminishing the tiny droplet emerging, which weakens homogeneous condensation. As a result, the condensation loss caused by the homogeneous condensation decreases, and even the condensation loss caused by the homogeneous condensation becomes zero when the NaCl particle number reaches 7.5×1014 per kilogram in steam flow. However, the condensation loss caused by the heterogeneous condensation shows a reverse tendence, which increases with the NaCl concentration. At last, the condensation loss and entropy generation caused by the non-equilibrium condensation are checked in steam turbine cascade under different NaCl concentration conditions. The results show that the condensation loss reduces by 9.2% and increases by 42% at the 7.5×10141/kg and 10171/kg NaCl concentrations, respectively. Meanwhile, when the NaCl particle number reaches 7.5×1014 per kilogram, the isentropic efficiency is highest, about 0.884, compared with other cases considering condensation effect. This study proves that the NaCl concentration has a nonnegligible effect on the condensation loss and entropy generation, which must be considered in future steam turbine study.

Experimental observation of a dissipative phase transition in a multi-mode many-body quantum system

Dissipative phase transitions are a characteristic feature of open systems. One of the paradigmatic examples for a first order dissipative phase transition is the driven nonlinear single-mode optical resonator. In this work, we study a realization with an ultracold bosonic quantum gas, which generalizes the single-mode system to many modes and stronger interactions. We measure the effective Liouvillian gap of the system and find evidence for a first order dissipative phase transition. Due to the multi-mode nature of the system, the microscopic dynamics is much richer and allows us to identify a non-equilibrium condensation process.

Non-equilibrium condensation of carbon dioxide in flue gas with the coexistence of swirl flows and supersonic flows

To achieve clean use of fossil energy and reduce carbon dioxide emissions, this work studies a potential clean technology for capturing carbon dioxide. Because the capturing process involves supersonic flows, swirl flows and heat and mass transfer, the flow structure and non-equilibrium condensation process in supersonic nozzles are not well understood. Taking the separation of carbon dioxide from flue gas as the research background, this work develops and validates a two-component steam (CO2-N2) condensation model to study the non-equilibrium condensation of carbon dioxide in flue gas with the coexistence of supersonic flows and swirl flows. The results show that the supersonic nozzle has the potential to liquefy carbon dioxide in flue gas considering swirl flows. Swirl flow move the starting point of nucleation towards the nozzle throat, greatly increases the peak nucleation rate, and weakens the mass and heat transfer process of non-equilibrium condensation. When the swirl intensity increases from 0 to 0.42, the liquid fraction in decreases from 0.101 to 0.081, with a decrease range of 19.8%. When using single-phase assumption without considering condensation, the calculation results misestimates the temperature drop characteristics and the expansion characteristics of steam, and the maximum error can reach 13.6%.

Interplay of Thermalization and Strong Disorder: Wave Turbulence Theory, Numerical Simulations, and Experiments in Multimode Optical Fibers.

We address the problem of thermalization in the presence of a time-dependent disorder in the framework of the nonlinear Schrödinger (or Gross-Pitaevskii) equation with a random potential. The thermalization to the Rayleigh-Jeans distribution is driven by the nonlinearity. On the other hand, the structural disorder is responsible for a relaxation toward the homogeneous equilibrium distribution (particle equipartition), which thus inhibits thermalization (energy equipartition). On the basis of the wave turbulence theory, we derive a kinetic equation that accounts for the presence of strong disorder. The theory unveils the interplay of disorder and nonlinearity. It unexpectedly reveals that a nonequilibrium process of condensation and thermalization can take place in the regime where disorder effects dominate over nonlinear effects. We validate the theory by numerical simulations of the nonlinear Schrödinger equation and the derived kinetic equation, which are found in quantitative agreement without using any adjustable parameter. Experiments realized in multimode optical fibers with an applied external stress evidence the process of thermalization in the presence of strong disorder.

Effect of the surface tension correction coefficient on the nonequilibrium condensation flow of wet steam

In view of the nonequilibrium characteristics of water vapor in the condensation process, various models have different degrees of deviation in the prediction of the condensation process. Water droplet surface tension appears in the exponential term of the nucleation rate in the form of a third power, which has a significant effect on the distribution of parameters such as condensation location, water droplet number and wetness. In order to improve the accuracy of numerical simulation, the correction coefficient is used to modify the plane surface tension calculation model. The nonequilibrium condensation process in the Moses-Stein nozzle is simulated. By comparison with the experimental data, the influence of the surface tension correction coefficient on the calculation accuracy of the model is analysed. The functional relationship between the superheat at the steam inlet and the optimal surface tension correction coefficient is obtained. After correction, the error between the simulation results and the experimental values of each working condition of the nozzle is reduced to less than 2%. In addition, this conclusion is verified by the nonequilibrium condensation flow in the turbine cascades. The deviations between the three simulation results and the experimental values are 1.86%, 2.10% and 1.88% respectively, and the simulation accuracy is significantly improved. The results show that with the increase in the surface tension correction coefficient, condensation will be inhibited under the same working conditions. There is an optimal value of the correction coefficient. Under different working conditions, there is a significant positive correlation between the optimal surface tension correction coefficient and the inlet superheat. It can significantly improve the simulation accuracy by using the corrected surface tension value. The results can provide a reference for the calculation of wet steam condensation flow.

Characteristics of non-equilibrium condensing flow in three-dimensional supersonic rectangular nozzles

Abstract Fluid flow inside a supersonic nozzle with a rectangular cross-section induces secondary flow due to the shape of the upper wall curvature. The secondary flow forms longitudinal vortices near the wall of the nozzle corner which destabilizes the nozzle outlet flow due to the early transition of the flow from laminar to turbulent. It is known that non-equilibrium homogeneous condensation occurs in a supersonic rectangular nozzle due to the rapid expansion of the condensable fluid with large latent heat such as water vapor. Homogeneous condensation takes place through the formation of water nuclei from its vapor when foreign nuclei are absent in the flow. The irreversibility of the non-equilibrium condensation process causes loss in flow transportation energy in the form of total pressure loss. Although numerous researches have been conducted about the effect of non-equilibrium condensation process in supersonic nozzles, however, the interactions between nozzle shape, non-equilibrium condensation, and longitudinal vortices have not been studied convincingly. Therefore, numerical simulations have been carried out for two supersonic three-dimensional rectangular nozzles in order to understand the effect of nozzle shape and non-equilibrium condensation on the longitudinal vortices at the nozzle corner. Furthermore, total pressure distribution in the nozzle was analysed to understand the effect of degree of supersaturation and expansion rate on the total pressure loss. In this research, characteristics of simulated flow fields including total pressure loss were in good agreement with the published literature.

Numerical study on carbon dioxide capture in flue gas by converging-diverging nozzle

To combat global warming, reducing the emission of CO2 greenhouse gas which mainly comes from the flue gas produced by the burning of fossil fuels remains a top priority. In order to study the possibility of converging-diverging nozzle capturing CO2 in flue gas, a mathematical model of N2-CO2 condensation flow (the main component of flue gas after desulfurization, denitration and drying) is established, in which N2 is carrier gas and CO2 is condensable gas. By adding transport equations and source terms to describe the relationship between gas and liquid phase, the complex heat and mass transfer process in supersonic compressible condensation flow can be accurately predicted. In order to investigate the influence of non-equilibrium condensation on the flow behavior, the single-phase flow is compared with the condensation flow. The results show that the single-phase flow model overestimates the gas expansion characteristics. Weak condensation shock occurs in the nonequilibrium condensation process, which leads to the decrease of the cooling performance of nozzle. In addition, the distribution characteristics of condensation parameters in non-equilibrium state are clarified. It is found that supersonic technology is a possible carbon capture method. The reliability of condensation flow model is proved by theoretical analysis and experimental validation.

A Novel Dehumidification Strategy to Reduce Liquid Fraction and Condensation Loss in Steam Turbines.

Massive droplets can be generated to form two-phase flow in steam turbines, leading to erosion issues to the blades and reduces the reliability of the components. A condensing two-phase flow model was developed to assess the flow structure and loss considering the nonequilibrium condensation phenomenon due to the high expansion behaviour in the transonic flow in linear blade cascades. A novel dehumidification strategy was proposed by introducing turbulent disturbances on the suction side. The results show that the Wilson point of the nonequilibrium condensation process was delayed by increasing the inlet superheated level at the entrance of the blade cascade. With an increase in the inlet superheated level of 25 K, the liquid fraction and condensation loss significantly reduced by 79% and 73%, respectively. The newly designed turbine blades not only remarkably kept the liquid phase region away from the blade walls but also significantly reduced 28.1% averaged liquid fraction and 47.5% condensation loss compared to the original geometry. The results provide an insight to understand the formation and evaporation of the condensed droplets inside steam turbines.

Specific features of n-decane vapors self-ignition in air at temperatures of 600–800 K

Experiments of n-decane/air self-ignition at the temperature range 600–800 K were carried out by rapid compression machine. It allowed obtaining temperature-concentration limits of transition from single-stage to two-stage ignition. High-speed video recording has let established that hot stage ignition always initiates near the piston surface or quartz window. These locations depend on gas temperature. Combustion of the test mixture occurs in the entire volume after that. Couple sequential photos of cool flame shows that it starts same near piston surface and has a complicated volumetric structure caused by the roll-up gas vortex. It is shown that partial n-decane pressure increasing during compression causes the non-equilibrium condensation process near the inner surfaces of combustion chamber. This leads to significant redistribution of n-decane concentration and determines local characteristics self-ignition of n-decane/air mixture.

Nonequilibrium dynamical transition process between excited states of holographic superconductors

We study the dynamics of the holographic s-wave superconductors described by the Einstein-Maxwell-complex scalar field theory with a negative cosmological constant. If the eigenfunction of the linearized equation of motion of the scalar field in the planar RNAdS black hole background is chosen as the initial data, the bulk system will evolve to the intermediate state that corresponds to the excited state superconductor on the boundary. The process can be regarded as the non-equilibrium condensation process of the excited state of holographic superconductor. When the linear superposition of the eigenfunctions is chosen as the initial data, the system will go through a series of the intermediate states corresponding to different overtone numbers, which can be regarded as the dynamical transition process between the excited states of holographic superconductor. Because the intermediate states are metastable, the bulk system eventually evolves to the stationary state that corresponds the ground state of the holographic superconductor. We also provide a global and physical picture of the evolution dynamics of the black hole and the corresponding superconducting phase transition from the funneled landscape view, quantifying the weights of the states and characterizing the transitions and cascades towards the ground state.

Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics

We develop the theory of weak wave turbulence in systems described by the Schr\"odinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schr\"odinger equation, and the Schr\"odinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schr\"odinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. We interpret the inverse cascade as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schr\"odinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schr\"odinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterise such "warm cascade" states.

Accurate condensing steam flow modeling in the ejector of the solar-driven refrigeration system

The ejectors are widely employed in power engineering installations, both refrigeration, and thermal ones. In the paper, a steam ejector of a solar-driven refrigeration system is investigated numerically, using different CFD models, to reveal the flow structures and evaluate its performance. A modified nucleation model adopting the Benson and Shuttleworth surface tension definition is proposed. The model composed by the modified nucleation model and Young's droplet growth equation demonstrates the superiority in predicting the non-equilibrium condensation phenomenon. An ejector experimental data is contrasted with three different numerical models, the results show that the effect of the non-equilibrium condensation (NEC) on the steam ejector performance cannot be ignored, and the modified model can accurately predict the ejector performance. An investigation of a steam ejector being a crucial part of a solar-driven refrigeration system is carried out employing different models. The internal flow structures and ejector performance are investigated, the difference of results predicted by three numerical models are compared and analyzed. The results show that the non-equilibrium condensation process reduces the entrainment ratio in critical mode, but it will enlarge the critical mode zone. Besides, the treatment of steam property has a certain impact on the calculation results.

Performance of steam ejector with nonequilibrium condensation for multi-effect distillation with thermal vapour compression (MED-TVC) seawater desalination system

The single-phase and two-phase flow models are developed and compared for the performance evaluation of a steam ejector for the multi-effect distillation with thermal vapour compression (MED-TVC) seawater desalination system. The results show that a single-phase flow model with ignoring the phase change predicts an unphysical temperature of the steam in the supersonic flow with the minimum value of approximately 122 K, which raises the query of the formation of the ice. The two-phase wet steam model corrects the distribution of the flow parameter by predicting the heat and mass transfer during the phase change. The steam achieves the first nonequilibrium condensation process inside the primary nozzle and another four alternating condensation and re-evaporation processes. The single-phase flow model under-predicts the entropy loss coefficient by approximately 15% than the two-phase wet steam model. The performance comparison is achieved against the single-phase model to present the accuracy of the two-phase model for the steam ejector simulation. This demonstrates that the nonequilibrium condensation is essential for the performance analysis of steam ejectors for MED-TVC seawater desalination system.

Non-equilibrium condensation of water vapour in supersonic flows with shock waves

The fluid flow and heat and mass transfer in a supersonic separator are not understood well due to the complicated interaction of the supersonic flow, swirling flow, phase transition and shock waves. In the present study, we develop a wet steam model to investigate the flow structure inside a supersonic separator with the co-existence of non-equilibrium condensation and shock waves. A study of the effect of the inlet subcooling and inlet saturation on the condensation behaviour is conducted to evaluate the performance of the supersonic separation with a focus on the shock wave. The numerical result shows that the degree of supersaturation of the water vapour can reach a maximum value of 4.28 within the designed supersonic separator and generate a peak nucleation rate of approximately 1021 kg m−3 s−1. The occurrence of the shock wave changes the equilibrium thermodynamic state, which leads to the re-evaporation of the condensed droplet. Higher inlet subcooling and inlet saturation not only shift downstream the position of the shock wave, but also induce an earlier condensation and higher liquid fraction. For the present nozzle, when the inlet subcooling and inlet saturation are about 34 K and 0.28 respectively, the shock wave intersects the region of the intense nucleation process, the non-equilibrium condensation process is terminated due to the increase of the pressure and temperature downstream the shock wave. Stronger swirling flow results in non-uniform distribution of the static pressure and decreases the nucleation rate of water vapour. The high swirling flow with a maximum swirl velocity of 150 m/s weakens the liquid fraction by 25% compared to the no swirling flow. This indicates that it is important to balance the swirling flow and condensation process to achieve an efficient performance of the supersonic separator.