Numerical Sensitivity Study and Calibration of Non-Equilibrium Wet Steam Model

2013 ◽  
Author(s):  
F. J. Moraga ◽  
L. Wang ◽  
W.-M. Ren
Keyword(s):  
Droplet Diameter ◽  
Sensitivity Study ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Transfer Model ◽  
Wet Steam ◽  
Cfd Simulations ◽  
Pressure Profiles ◽  
Non Equilibrium

Comparisons between one- and two-dimensional experiments and non-equilibrium wet steam CFD simulations are conducted paying attention not only to pressure profiles and wetness but also to the more difficult to match droplet diameter. To achieve the objective of optimizing the match of data the heat transfer model between the droplet and its surrounding vapor proposed by Young and the corrections to classical nucleation theory proposed by Moore and popularized by Gerber are adopted. It is found that the proposed models produce a better agreement with droplet diameter, without affecting the overall quality of the predictions for other quantities.

The Feasibility of an Euler-Lagrange Approach for the Modelling of Wet Steam

2020 ◽  
Author(s):  
Tim Wittmann ◽  
Christoph Bode ◽  
Jens Friedrichs
Keyword(s):  
Optimal Parameter ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Droplet Growth ◽  
Wet Steam ◽  
Discrete Phase Model ◽  
Ansys Fluent ◽  
Validation Data ◽  
Numerical Validation ◽  
Lagrange Approach

Abstract This study investigates the applicability of an Euler-Lagrange approach for the calculation of nucleation and condensation of steam flows. Supersonic nozzles are used as generic validation cases, as their high expansion rates replicate the flow conditions in real turbines. Experimental and numerical validation data for these nozzles are provided by the International Wet Steam Modelling Project of Starzmann et al. (2018). In contrast to most participants of that project, an Euler-Lagrange approach is utilized for this study. Therefore, the classical nucleation theory with corrections and different droplet growth laws is incorporated into the Discrete Phase Model of ANSYS Fluent. Suggestions for an efficient implementation are presented. The Euler-Lagrange results show a good agreement with the experimental and numerical validation data. The sensitivities of the Euler-Lagrange approach to modelling parameters are analysed. Finally, an optimal parameter set for the calculation of nucleation and condensation is proposed.

Numerical Investigation of Nonisothermal Cavitating Flows on Hydrofoils by Means of an Extended Schnerr–Sauer Model Coupled With a Nucleation Model

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Maria Grazia De Giorgi ◽  
Antonio Ficarella ◽  
Donato Fontanarosa
Keyword(s):  
Mass Transfer ◽  
Heat Source ◽  
Temperature Drop ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Transfer Model ◽  
Nonuniform Field ◽  
Cavitating Flows ◽  
Two Phase ◽  
Vapor Cavity

Abstract This work aimed to investigate cavitating flows of water, liquid hydrogen, and nitrogen on hydrofoils numerically, using the open source code openfoam. The Eulerian homogeneous mixture approach has been used, consisting in a mass transfer model, which is based on the combination of a two-phase incompressible unsteady solver with a volume of fluid interface tracking method. Thermal effects have been introduced by means of the activation of energy equation and latent heat source terms plus convective heat source term. The dependency of the saturation conditions to the temperature has been defined using Antoine-like equations. An extended Schnerr–Sauer model based on the classical nucleation theory (CNT) has been implemented for the computation of the interfacial mass transfer rates. In order to investigate the nucleation effects, an extension of the CNT has been considered by coupling the population balance equation (PBE)/extended quadrature-based method of moments with the computational fluid dynamics (CFD) model, which has been defined in combination with a transport equation for the nuclei density. Results showed that nucleation determined a nonuniform field of nuclei density so as to produce a reduction of the temperature drop inside the vapor bubbles, as well as a warmed wake downstream the vapor cavity. Unsteady computations also revealed an influence of the nucleation on the dynamics of the vapor cavity and the bubble detachment.

Numerical Simulation of Non-Equilibrium Condensation in Supercritical CO2 Compressors

2019 ◽  
Author(s):  
Kevin W. Brinckman ◽  
Ashvin Hosangadi ◽  
Zisen Liu ◽  
Timothy Weathers
Keyword(s):  
Critical Point ◽  
Residence Time ◽  
Supercritical Co2 ◽  
Equilibrium Phase ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Working Fluid ◽  
Modeling Framework ◽  
Test Loop ◽  
Non Equilibrium

Abstract There is increasing interest in supercritical CO2 processes, such as Carbon Capture and Storage, and electric power production, which require compressors to pressurize CO2 above the critical point. For supercritical compressor operation close to the critical point there is a concern that the working fluid could cross into the subcritical regime which could lead to issues with compressor performance if condensation was to occur in regions where the fluid dropped below the saturation point. Presently, the question of whether there is sufficient residence time at subcritical conditions for condensation onset in supercritical CO2 compressors is an unresolved issue. A methodology is presented towards providing a validated simulation capability for predicting condensation in supercritical CO2 compressors. The modeling framework involves the solution of a discrete droplet phase coupled to the continuum gas phase to track droplet nucleation and growth. The model is implemented in the CRUNCH CFD® Computational Fluid Dynamics code that has been extensively validated for simulation at near critical conditions with a real fluid framework for accurate predictions of trans-critical CO2 processes. Results of predictions using classical nucleation theory to model homogeneous nucleation of condensation sites in supersaturated vapor regions are presented. A non-equilibrium phase-change model is applied to predict condensation on the nuclei which grow in a dispersed-phase droplet framework. Model validation is provided against experimental data for condensation of supercritical CO2 in a De Laval nozzle including the Wilson line location. The model is then applied for prediction of condensation in the compressor of the Sandia test loop at mildly supercritical inlet conditions. The results suggest that there is sufficient residence time at the conditions analyzed to form localized nucleation sites, however, droplets are expected to be short lived as the model predicts they will rapidly vaporize.

scholarly journals Non-Equilibrium Crystallization Pathways of Manganese Oxides in Aqueous Solution

2018 ◽  
Author(s):  
Wenhao Sun ◽  
Daniil A. Kitchaev ◽  
Denis Kramer ◽  
Gerbrand Ceder
Keyword(s):  
Metal Oxide ◽  
Metal Oxides ◽  
Transition Metal Oxides ◽  
Manganese Oxides ◽  
Energy Landscape ◽  
Metastable Phases ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Pourbaix Diagram ◽  
Non Equilibrium

<p>Aqueous precipitation of transition metal oxides often proceeds through non-equilibrium phases, whose appearance cannot be anticipated from traditional phase diagrams. Without a precise understanding of which metastable phases form, or their lifetimes, targeted synthesis of specific metal oxides can become a trial-and-error process. Here, we derive a new thermodynamic potential for the free-energy of a metal oxide in water, which reveals a hidden metastable energy landscape above the equilibrium Pourbaix diagram. By combining this ‘Pourbaix potential’ with classical nucleation theory, we interrogate how solution conditions can influence the multistage oxidation pathways of manganese oxides. We calculate that even within the same phase stability region of a Pourbaix diagram, subtle variations in <i>p</i>H and redox potential can redirect a crystallization pathway through different metastable phases. Our theoretical framework offers a predictive platform to navigate through the thermodynamic and kinetic energy landscape towards the rational synthesis of target metal oxide phases.</p>

The Feasibility of an Euler–Lagrange Approach for the Modeling of Wet Steam

2021 ◽  
Vol 143 (4) ◽  
Author(s):  
Tim Wittmann ◽  
Christoph Bode ◽  
Jens Friedrichs
Keyword(s):  
Optimal Parameter ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Droplet Growth ◽  
Wet Steam ◽  
Discrete Phase Model ◽  
Validation Data ◽  
Numerical Validation ◽  
Discrete Phase ◽  
Lagrange Approach

Abstract This study investigates the applicability of an Euler–Lagrange approach for the calculation of nucleation and condensation of steam flows. Supersonic nozzles are used as generic validation cases, as their high expansion rates replicate the flow conditions in real turbines. Experimental and numerical validation data for these nozzles are provided by the International Wet Steam Modeling Project of Starzmann et al. (2018, “Results of the International Wet Steam Modeling Project,” Proc. Inst. Mech. Eng. A, 232(5), pp. 550–570). In contrast to most participants of that project, an Euler–Lagrange approach is utilized for this study. Therefore, the classical nucleation theory with corrections and different droplet growth laws is incorporated into the discrete phase model of ansysfluent. Suggestions for an efficient implementation are presented. The Euler–Lagrange results show a good agreement with the experimental and numerical validation data. The sensitivities of the Euler–Lagrange approach to modeling parameters are analyzed. Finally, an optimal parameter set for the calculation of nucleation and condensation is proposed.

Modelling of condensing steam flows in Laval nozzles with ANSYS CFX

2017 ◽  
Vol 232 (5) ◽  
pp. 571-575 ◽  
Author(s):  
Marius Grübel ◽  
Jörg Starzmann ◽  
Markus Schatz ◽  
Damian M Vogt
Keyword(s):  
Measurement Data ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Test Cases ◽  
Wet Steam ◽  
Flow Solver ◽  
Spontaneous Condensation ◽  
Ansys Cfx ◽  
Fluid Properties ◽  
Laval Nozzles

The results of the International Wet Steam Modelling Project presented at the Wet Steam Conference in Prague in 2016 again gave rise to a discussion about the suitability of the flow solver ANSYS CFX for the prediction of spontaneous condensation. In this article, the main reason for the discrepancy between results obtained with CFX and measurement data is identified. It could be found that in CFX the temperature of already existing droplets is used for evaluating the fluid properties involved in the nucleation process. This is not in agreement with the isothermal classical nucleation theory, which is based on the assumption that clusters of critical radius are formed at vapour temperature. The most dominant parameter affected by this is the surface tension, the evaluation of which can be altered easily by the user. The influence of the correction is illustrated by means of standard Laval nozzle test cases, and a significant improvement of the results compared to measurement data can be observed.

scholarly journals Numerical investigation of condensing flow of low pressure steam turbine at different flow rate conditions

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 161-167 ◽  
Author(s):  
Kezhen Huang ◽  
Lin Cai ◽  
Jianshu Gao ◽  
Zhuo Liu ◽  
Xinggang Yu
Keyword(s):  
Steam Turbine ◽  
Numerical Investigation ◽  
Low Pressure ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Wet Steam ◽  
Pressure Steam ◽  
Static Performance ◽  
Wet Steam Flow ◽  
Two Stages

The numerical investigation on the wet steam flow in the last two stages of a 1000 MW fossil-fired low pressure steam turbine is presented in this paper. The non-equilibrium model via the classical nucleation theory is employed to simulate the condensing flow of the wet steam. The characteristics of the flow filed from design condition to low volume flow condition are calculated and the static performance of last stage moving blade is also obtained. The development of the backflow phenomenon is clearly captured through the analysis of the velocity triangle.

Instabilities and bifurcation of non-equilibrium two-phase flows

1997 ◽  
Vol 348 ◽  
pp. 1-28 ◽  
Author(s):  
STEPHAN ADAM ◽  
GÜNTER H. SCHNERR
Keyword(s):  
Equilibrium Phase ◽  
Practical Interest ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Droplet Growth ◽  
Sudden Increase ◽  
Pressure Amplitude ◽  
Two Phase ◽  
Supersonic Wind Tunnel ◽  
Non Equilibrium

New instabilites of unsteady transonic flows with non-equilibrium phase transition are presented including unsymmetric flow patterns with moving oblique shock systems in supersonic nozzles with perfectly symmetric shapes. The phenomena were first detected when performing experiments in our supersonic wind tunnel with atmospheric supply and could be perfectly reproduced by numerical simulations based on the Euler equations, i.e. neglecting the viscosity of the fluid. The formation of the liquid phase is modelled using the classical nucleation theory for the steady state together with the Hertz–Knudsen droplet growth law and yields qualitatively and quantitatively excellent agreement with experiments in the unsteady flow regime with high-frequency oscillations including the unstable transient change of the structure from symmetric to unsymmetric flow.For engineering applications the sudden increase or decrease of the frequency by a factor 2 or more and of the pressure amplitude at the bifurcation limits is of immediate practical interest, e.g. for flutter excitation of turbomachinery blading.

scholarly journals Non-Equilibrium Crystallization Pathways of Manganese Oxides in Aqueous Solution

2018 ◽  
Author(s):  
Wenhao Sun ◽  
Daniil A. Kitchaev ◽  
Denis Kramer ◽  
Gerbrand Ceder
Keyword(s):  
Metal Oxide ◽  
Metal Oxides ◽  
Transition Metal Oxides ◽  
Manganese Oxides ◽  
Energy Landscape ◽  
Metastable Phases ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Pourbaix Diagram ◽  
Non Equilibrium

<p>Aqueous precipitation of transition metal oxides often proceeds through non-equilibrium phases, whose appearance cannot be anticipated from traditional phase diagrams. Without a precise understanding of which metastable phases form, or their lifetimes, targeted synthesis of specific metal oxides can become a trial-and-error process. Here, we derive a new thermodynamic potential for the free-energy of a metal oxide in water, which reveals a hidden metastable energy landscape above the equilibrium Pourbaix diagram. By combining this ‘Pourbaix potential’ with classical nucleation theory, we interrogate how solution conditions can influence the multistage oxidation pathways of manganese oxides. We calculate that even within the same phase stability region of a Pourbaix diagram, subtle variations in <i>p</i>H and redox potential can redirect a crystallization pathway through different metastable phases. Our theoretical framework offers a predictive platform to navigate through the thermodynamic and kinetic energy landscape towards the rational synthesis of target metal oxide phases.</p>

Numerical Investigation of Non-Isothermal Cavitating Flows on Hydrofoils by Means of an Extended Schnerr-Sauer Model Coupled With a Nucleation Model

2018 ◽  
Author(s):  
Maria Grazia De Giorgi ◽  
Antonio Ficarella ◽  
Donato Fontanarosa
Keyword(s):  
Mass Transfer ◽  
Heat Source ◽  
Temperature Drop ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Transfer Model ◽  
Uniform Field ◽  
Cavitating Flows ◽  
Two Phase ◽  
Vapor Cavity

The present work aims to investigate cavitating flows of water, liquid hydrogen and nitrogen on hydrofoils numerically, using the open source code OpenFOAM. The Eulerian homogeneous mixture approach has been used, consisting in a mass transfer model which is based on the combination of a two-phase incompressible unsteady solver with a Volume of Fluid (VOF) interface tracking method. Thermal effects have been introduced by means of the activation of energy equation and latent heat source terms plus convective heat source term. The dependency of the saturation conditions to the temperature has been defined using Antoine-like equations. An extended Schnerr-Sauer model based on the Classical Nucleation Theory (CNT) has been implemented for the computation of the interfacial mass transfer rates. In order to investigate the nucleation effects, an extension of the Classical Nucleation Theory has been considered by coupling the Population Balance Equation/Extended Quadrature-Based Method of Moments (PBE-EQBMM) with the CFD model, which has been defined in combination with a transport equation for the nuclei density. Results showed that nucleation determined a non-uniform field of nuclei density so as to produce a reduction of the temperature drop inside the vapor bubbles, as well as a warmed wake downstream the vapor cavity. Unsteady computations also revealed an influence of the nucleation on the dynamics of the vapor cavity and the bubble detachment.

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