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.

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.

Nucleation and Droplet Growth Rate of Homogeneously Condensing Flows within an industrial Steam turbine

2007 ◽  
Author(s):  
Keramat Fakhari ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Growth Rate ◽  
Steam Turbine ◽  
Droplet Growth ◽  
Condensing Flows

Self-preserving development within turbulent boundary layers in strong adverse pressure gradients

1965 ◽  
Vol 23 (4) ◽  
pp. 767-778 ◽  
Author(s):  
A. A. Townsend
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Outer Part ◽  
Pressure Rise ◽  
Adverse Pressure Gradient ◽  
Pressure Gradients ◽  
Layer Model ◽  
Pressure Distributions ◽  
Two Layer Model ◽  
Local Parameters

The development of a turbulent boundary layer in a strong adverse pressure gradient can be described by the two-layer model proposed by Stratford (1959), in which the outer part of the flow is assumed to be unmodified by the pressure-rise and the inner part described by two local parameters, the surface stress and the pressure gradient. The description suggests that the modification of the original flow is in some sense self-preserving, and it is shown here that self-preserving development of the modification is consistent with the Reynolds equations of turbulent flow in particular pressure distributions. For these distributions, the predictions of the two-layer model are confirmed without any need to make the sharp and arbitrary distinction between the two parts of the boundary layer.

Coherent structures of nonlinear barotropic-baroclinic interaction in unequal depth two-layer model

2021 ◽  
Vol 408 ◽  
pp. 126347
Author(s):  
Jiaqi Zhang ◽  
Ruigang Zhang ◽  
Liangui Yang ◽  
Quansheng Liu ◽  
Liguo Chen
Keyword(s):  
Coherent Structures ◽  
Layer Model ◽  
Two Layer Model

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.

scholarly journals A linear cascade tunnel for flow investigations of steam turbine rotor tip blades in subsonic nucleating flows

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Vital Kumar Yadav Pillala ◽  
B. V. S. S. S. Prasad ◽  
N. Sitaram ◽  
M. Mahendran ◽  
Debasish Biswas ◽  
...  
Keyword(s):  
Steam Turbine ◽  
Turbine Rotor ◽  
Turbine Cascade ◽  
Flow Measurements ◽  
Linear Cascade ◽  
Dry Air ◽  
Steam Turbine Rotor ◽  
Pressure Distributions ◽  
Working Medium ◽  
Exit Mach Number

AbstractThe paper presents details of a unique experimental facility along with necessary accessories and instrumentation for testing steam turbine cascade blades in wet and nucleating steam. A steam turbine rotor tip cascade is chosen for flow investigations. Cascade inlet flow measurements show uniform conditions with dry air and steam and dry air mixture of different ratios. Exit flow surveys indicate that excellent flow periodicity is obtained. Blade surface static pressure and exit total pressure distributions are also presented with dry air and with steam and dry air mixture of different ratios as the working medium at an exit Mach number of 0.52.

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