Fast and Accurate Analysis of Steam Condensing Flows Using Ideal Gas Equation

2020 ◽  
Vol 13 (3) ◽  
Author(s):  
Changhyun Kim ◽  
JaeHyeon Park ◽  
Jehyun Baek
Keyword(s):  
Phase Transition ◽  
Ideal Gas ◽  
Droplet Growth ◽  
Wet Steam ◽  
Accurate Analysis ◽  
Machine Performance ◽  
Condensing Flows ◽  
Droplet Sizes ◽  
Condensation Model ◽  
Non Equilibrium

Abstract When the steam is used in fluid machinery, the phase-transition can occur and it affects not only the flow fields but also the machine performance. Therefore, to achieve accurate prediction on steam condensing flow using computational fluid dynamics, the phase-transition phenomena should be considered and the proper model which can reflect the non-equilibrium characterisic is required. In the previous study of us, a non-equilibrium condensation model was implemented in T-flow, and several cases on nozzles and cascades were under the consideration. The model showed quite good predictions on the pressure variations including condensation shock. However, the pressure discrepancies in downstream regions were found in all nozzle cases, and the use of ideal gas law as equation of state seemed to be responsible for them. Therefore, IAPWS-95 or IF97 are usually adopted for wet-steam codes, but it entails highly increased computational costs. In this study, the wet-steam model is modified to ensure the accuracy of pressure in nozzle’s downstream region while maintaining the usage of ideal gas equation, which has a benefit to solve the problem quickly. The numerical results of the nozzles are compared with those of the previous wet-steam model, and the results of equilibrium condensation model are also appended. As a result, the accurate predictions are feasible by using the modified non-equilibrium condensation model. In addition, the corrections on liquid surface tension and droplet growth rate are carried out for underestimated droplet sizes and enthalpy, entropy changes throughout the nozzles are investigated.

The Influence of Non-Equilibrium Wet Steam Effects on the Aeroelastic Properties of a Turbine Blade Row

2016 ◽  
Author(s):  
Christopher Fuhrer ◽  
Marius Grübel ◽  
Damian M. Vogt ◽  
Paul Petrie-Repar
Keyword(s):  
Steam Turbine ◽  
Turbine Blade ◽  
Ideal Gas ◽  
Test Case ◽  
Steam Turbines ◽  
Wet Steam ◽  
Flow Conditions ◽  
Flutter Analysis ◽  
Last Stage ◽  
Non Equilibrium

Turbine blade flutter is a concern for the manufacturers of steam turbines. Typically, the length of last stage blades of large steam turbines is over one meter. These long blades are susceptible to flutter because of their low structural frequency and supersonic tip speeds with oblique shocks and their reflections. Although steam condensation has usually occurred by the last stage, ideal gas is mostly assumed when performing flutter analysis for steam turbines. The results of a flutter analysis of a 2D steam turbine test case which examine the influence of non-equilibrium wet steam are presented. The geometry and flow conditions of the test case are supposed to be similar to the flow near the tip in a steam turbine as this is where most of the unsteady aerodynamic work contributing to flutter is done. The unsteady flow simulations required for the flutter analysis are performed by ANSYS CFX. Three fluid models are examined: ideal gas, equilibrium wet steam (EQS) and non-equilibrium wet steam (NES), of which NES reflects the reality most. Previous studies have shown that a good agreement between ideal gas and EQS simulations can be achieved if the prescribed ratio of specific heats is equal to the equilibrium polytropic index of the wet steam flow through the turbine. In this paper the results of a flutter analysis are presented for the 2D test case at flow conditions with wet steam at the inlet. The investigated plunge mode normal to chord is similar to a bending mode around the turbine axis for a freestanding blade in 3D. The influence of the overall wetness fraction and the size of the water droplets at the inlet are examined. The results show an increase of aerodynamic damping for all investigated interblade phase angles with a reduction of droplet size. The influence of the wetness fraction is in comparison of less importance.

Numerical Solution of Wet Steam Flow through Blade Cascade

2016 ◽  
Vol 821 ◽  
pp. 31-38
Author(s):  
Vladimír Hric ◽  
Jan Halama
Keyword(s):  
Equations Of State ◽  
Suction Side ◽  
Steam Flow ◽  
Droplet Growth ◽  
Wet Steam ◽  
Two Phase ◽  
Blade Cascade ◽  
Flow Through ◽  
Wet Steam Flow ◽  
Non Equilibrium

The paper concerns with the numerical modeling of wet steam flow through a blade cascade in transonic regime with non-equilibrium condensation in 2D. Real thermodynamics of vapor phase is implemented in the way which mostly avoid iterations in order to calculate thermodynamic properties. This equation of state is represented by the function for non-dimensional entropy with independent variables scaled density and scaled internal energy. Other equations of state are used for comparison, namely special gas equation which comes from IAPWS-95 formulation and simple pseudo perfect gas relation. We applied simple homogeneous non-equilibrium approach to model two-phase flow. Laminar compressible Navier-Stokes system of equations is used for the mixture properties. Liquid phase is described by the standard method of moments of droplet number distribution function. We consider obtained numerical results to be in good agreement with the measured data. We note the fact that robust and accurate closure of supplementary liquid system (nucleation rate and droplet growth model) is still not available and most often ad-hoc corrections are proposed by the authors. Results show differences among used equations of state as well. This is apparent mainly in the vicinity of condensation shock region on the suction side.

Towards Scale Resolving Computations of Condensing Wet Steam Flows

2019 ◽  
Author(s):  
Pascal Post ◽  
Marwick Sembritzky ◽  
Francesca di Mare
Keyword(s):  
Steam Turbine ◽  
Two Phase Flow ◽  
Ideal Gas ◽  
Phase Flow ◽  
Wet Steam ◽  
Two Phase ◽  
Upwind Schemes ◽  
Computational Speed ◽  
Euler Model ◽  
Non Equilibrium

Abstract In this paper we present a turbomachinery density-based CFD solver optimized for CPUs as well as GPUs, which accounts for complex thermodynamics including non-equilibrium condensation and two-phase flow, making extensive use of tabulation techniques. The two-phase flow is treated by means of the mono-dispersed Source-Term Euler-Euler model. The non-equilibrium wet-steam model is validated in classical nozzle test cases and its application in turbomachinery configuration is demonstrated in a well-documented steam turbine cascade in the context of classic RANS modeling. Finally, the LES-solver performance and scalability, together with its accuracy, are assessed and discussed on the basis of the well-known and theoretically relevant experiment by Comte-Bellot and Corrsin. For both, standard RANS computations, where an upwind schemes has been adopted, as well as for the LES computations, where a central scheme in skew-symmetric form has been employed, the solver shows remarkable computational speed and accuracy for non-ideal gas applications, rendering it suitable for more complex LES computations in steam turbine flows.

scholarly journals Coupled Model of Heat and Mass Balance for Droplet Growth in Wet Steam Non-Equilibrium Homogeneous Condensation Flow

Energies ◽  
2017 ◽  
Vol 10 (12) ◽  
pp. 2033 ◽  
Author(s):  
Xu Han ◽  
Zhonghe Han ◽  
Wei Zeng ◽  
Jiangbo Qian ◽  
Zhi Wang
Keyword(s):  
Mass Balance ◽  
Coupled Model ◽  
Droplet Growth ◽  
Wet Steam ◽  
Homogeneous Condensation ◽  
Condensation Flow ◽  
Non Equilibrium

Numerical Analysis on Non-Equilibrium Steam Condensing Flow in Rotating Machinery

2016 ◽  
Author(s):  
Changhyun Kim ◽  
JaeHyeon Park ◽  
DongIl Kim ◽  
Jehyun Baek
Keyword(s):  
Phase Transition ◽  
Equilibrium Phase ◽  
Flow Fields ◽  
Droplet Generation ◽  
Steam Turbines ◽  
Wet Steam ◽  
Design And Optimization ◽  
Wet Steam Flow ◽  
Steam Parameters ◽  
Non Equilibrium

Flow of steam, different from other gas flows, involves droplet generation in flow expansion process. This phase transition affects not only the flow fields, but also machine performance including efficiency. In addition, it is totally harmful for machine structures as blades and casing. Therefore, prevention or preparation of droplet generation in steam flows is dreadfully important in stable machine operation. Nowadays, Computational Fluid Dynamics (CFD) is widely used in machine design and optimization process. Thus, simulation with CFD should consider this droplet generation phenomena to predict internal flows precisely. Many studies that analyze steam condensing flow in nozzles, cascades and steam turbines were carried out. Though, the flows of wet-steam which include non-equilibrium phase-transition phenomena are still difficult to predict, especially in the 3D rotating cases as steam turbines. Therefore, more studies are required to get comparable results with experiment. In this study, non-equilibrium wet-steam model was implemented on T-Flow to simulate realistic non-equilibrium steam condensing flow. In the cases of White cascade, characteristics of wet-steam flow were studied and pressure distributions were compared with experimental results for model validation. To use implemented wet-steam model for calculating flows in rotation, especially in steam turbines, a study of steam condensing flow in single stage steam turbine was conducted. Interaction between the stator and rotor using frozen rotor or mixing plane method in steady calculations were compared in order to find the effects of used interface on flow fields and steam condensation. As a result, condensing flows were predicted well even in the rotating cases by using non-equilibrium wet-steam model. The wet-steam parameters (nucleation, droplet size, wetness) are differed throughout the spans due to 3D effects and influenced by selection of interface as expected. In addition, droplet generation enhances entropy rise throughout the domain. The case using mixing plane seems to be overestimate the size of high wetness zone and it is recommended to use frozen rotor in multi-phase calculations. However, to apply this model in general cases, comparison with experimental data from real steam turbines should be conducted in further studies.

Numerical Simulations of Unsteady Wet Steam Flows With Non-Equilibrium Condensation in the Nozzle and the Steam Turbine

2006 ◽  
Author(s):  
Shigeki Senoo ◽  
Alexander J. White
Keyword(s):  
Heat Release ◽  
Steam Turbine ◽  
Laval Nozzle ◽  
Expansion Rate ◽  
Droplet Growth ◽  
Layer Model ◽  
Pressure Distributions ◽  
Condensing Flows ◽  
Two Layer Model ◽  
Non Equilibrium

Numerical techniques for non-equilibrium condensing flows are presented. Conservation equations for homogeneous gas-liquid two-phase compressible flows are solved by using a finite volume method based on an approximate Riemann solver. The phase change consists of the homogeneous nucleation and growth of existing droplets. Nucleation is computed with the classical Volmer-Frenkel model, corrected for the influence of the droplet temperature being higher than the steam temperature due to latent heat release. For droplet growth, two types of heat transfer model between droplets and the surrounding steam are used: a free molecular flow model and a semi-empirical two-layer model which is deemed to be valid over a wide range of Knudsen number. The computed pressure distribution and Sauter mean droplet diameters in a convergent-divergent (Laval) nozzle are compared with experimental data. Both droplet growth models capture qualitatively the pressure increases due to sudden heat release by the non-equilibrium condensation. However the agreement between computed and experimental pressure distributions is better for the two-layer model. The droplet diameter calculated by this model also agrees well with the experimental value, whereas that predicted by the free molecular model is too small. Condensing flows in a steam turbine cascade are calculated at different Mach numbers and inlet superheat conditions and are compared with experiments. Static pressure traverses downstream from the blade and pressure distributions on the blade surface agree well with experimental results in all cases. Once again, droplet diameters computed with the two-layer model give best agreement with the experiments. Droplet sizes are found to vary across the blade pitch due to the significant variation in expansion rate. Flow patterns including oblique shock waves and condensation-induced pressure increases are also presented and are similar to those shown in the experimental Schlieren photographs. Finally, calculations are presented for periodically unsteady condensing flows in a low expansion rate, convergent-divergent (Laval) nozzle. Depending on the inlet stagnation subcooling, two types of self-excited oscillations appear: a symmetric mode at lower inlet subcooling and an asymmetric mode at higher subcooling. Plots of oscillation frequency versus inlet sub-cooling exhibit a hysteresis loop, in accord with observations made by other researchers for moist air flow.

Research on wet steam spontaneous condensing flows considering phase transition and slip

2013 ◽  
Vol 22 (4) ◽  
pp. 320-326 ◽  
Author(s):  
Ke Cui ◽  
Huan-long Chen ◽  
Yan-ping Song ◽  
Hiroharu Oyama
Keyword(s):  
Phase Transition ◽  
Wet Steam ◽  
Condensing Flows

scholarly journals Shock interactions in inviscid air and $$\hbox {CO}_2$$–$$\hbox {N}_2$$ flows in thermochemical non-equilibrium

Shock Waves ◽  
2021 ◽  
Author(s):  
C. Garbacz ◽  
W. T. Maier ◽  
J. B. Scoggins ◽  
T. D. Economon ◽  
T. Magin ◽  
...  
Keyword(s):  
Chemical Species ◽  
High Energy ◽  
Ideal Gas ◽  
Shock Interaction ◽  
Interaction Patterns ◽  
Shock Interactions ◽  
Wave Interference ◽  
Type V ◽  
The Impact ◽  
Non Equilibrium

AbstractThe present study aims at providing insights into shock wave interference patterns in gas flows when a mixture different than air is considered. High-energy non-equilibrium flows of air and $$\hbox {CO}_2$$ CO 2 –$$\hbox {N}_2$$ N 2 over a double-wedge geometry are studied numerically. The impact of freestream temperature on the non-equilibrium shock interaction patterns is investigated by simulating two different sets of freestream conditions. To this purpose, the SU2 solver has been extended to account for the conservation of chemical species as well as multiple energies and coupled to the Mutation++ library (Multicomponent Thermodynamic And Transport properties for IONized gases in C++) that provides all the necessary thermochemical properties of the mixture and chemical species. An analysis of the shock interference patterns is presented with respect to the existing taxonomy of interactions. A comparison between calorically perfect ideal gas and non-equilibrium simulations confirms that non-equilibrium effects greatly influence the shock interaction patterns. When thermochemical relaxation is considered, a type VI interaction is obtained for the $$\hbox {CO}_2$$ CO 2 -dominated flow, for both freestream temperatures of 300 K and 1000 K; for air, a type V six-shock interaction and a type VI interaction are obtained, respectively. We conclude that the increase in freestream temperature has a large impact on the shock interaction pattern of the air flow, whereas for the $$\hbox {CO}_2$$ CO 2 –$$\hbox {N}_2$$ N 2 flow the pattern does not change.

scholarly journals A Study of Moist Air Condensation Characteristics in a Transonic Flow System

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 4052
Author(s):  
Jie Wang ◽  
Hongfang Gu
Keyword(s):  
Mach Number ◽  
Relative Humidity ◽  
Transonic Flow ◽  
Flow System ◽  
Plane Surface ◽  
Droplet Growth ◽  
Moist Air ◽  
Dry Air ◽  
Hydraulic Equipment ◽  
Non Equilibrium

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.

Sign in / Sign up

Export Citation Format

Share Document