A Comparison of Modeling Techniques for Polydispersed Droplet Spectra in Steam Turbines

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Fiona R. Hughes ◽  
Jörg Starzmann ◽  
Alexander J. White ◽  
John B. Young
Keyword(s):  
Droplet Growth ◽  
Steam Turbines ◽  
Secondary Nucleation ◽  
Two Phase ◽  
Lagrangian Framework ◽  
Pressure Time ◽  
Modeling Techniques ◽  
Initial Spectrum ◽  
The Moment ◽  
Speed Accuracy

Within steam turbine flows, condensation phenomena give rise to complex droplet spectra that can span more than two orders of magnitude in size. To predict the behavior of the two-phase flow and the resulting losses, the interactions between the vapor phase and droplets of all sizes must be accurately calculated. The estimation of thermodynamic losses and droplet deposition rates, in particular, depends on the size range and shape of the droplet spectrum. These calculations become computationally burdensome when a large number of droplet groups are present, and it is therefore advantageous to capture the complete droplet spectrum in a compressed form. This paper compares several methods for reducing the complexity of the droplet spectrum: a single representative droplet size (equivalent monodispersion), the moment method (including various growth rate approximations), the quadrature method of moments (QMOM), and spectrum pruning. In spectrum pruning, droplet groups are individually nucleated, but their number is subsequently reduced by combining groups together in a manner that preserves droplet number, wetness fraction, and the shape of the initial spectrum. The various techniques are compared within a Lagrangian framework by tracking the two-phase behavior along predefined pressure–time trajectories. Primary and secondary nucleation, droplet evaporation, and a representative turbomachinery case are modeled. The calculations are compared in terms of speed, accuracy, and robustness. It is shown that both the moment methods and spectrum pruning provide an appreciable improvement in accuracy over the use of an “equivalent” monodispersion without compromising calculation speed. Although all the examined methods are adequate for primary nucleation and droplet growth calculations, spectrum pruning and the QMOM are most accurate over the range of conditions considered.

A Comparison of Modelling Techniques for Polydispersed Droplet Spectra in Steam Turbines

2015 ◽  
Author(s):  
Fiona R. Hughes ◽  
Jörg Starzmann ◽  
Alexander J. White ◽  
John B. Young
Keyword(s):  
Method Of Moments ◽  
Vapour Phase ◽  
Phase Behaviour ◽  
Droplet Growth ◽  
Quadrature Method ◽  
Steam Turbines ◽  
Two Phase ◽  
Quadrature Method Of Moments ◽  
The Moment ◽  
Speed Accuracy

Within steam turbine flows, condensation phenomena give rise to complex droplet spectra that can span more than two orders of magnitude in size. To predict the behaviour of the two-phase flow and the resulting losses, the interactions between the vapour phase and droplets of all sizes must be accurately calculated. The estimation of thermodynamic losses and droplet deposition rates, in particular, depend on the size range and shape of the droplet spectrum. These calculations become computationally burdensome when a large number of droplet groups are present, and it is therefore advantageous to capture the complete droplet spectrum in a compressed form. This paper compares several methods for reducing the complexity of the droplet spectrum: a single representative droplet size (equivalent monodispersion), the moment method (including various growth rate approximations), the quadrature method of moments, and spectrum pruning. In spectrum pruning, droplet groups are individually nucleated, but their number is subsequently reduced by combining groups together in a manner that preserves droplet number, wetness fraction, and the shape of the initial spectrum. The various techniques are compared within a Lagrangian framework by tracking the two-phase behaviour along predefined pressure-time trajectories. Primary and secondary nucleation, droplet evaporation, and a representative turbomachinery case are modelled. The calculations are compared in terms of speed, accuracy, and robustness. It is shown that both the moment methods and spectrum pruning provide an appreciable improvement in accuracy over the use of an ‘equivalent’ monodispersion without compromising calculation speed. Although all the examined methods are adequate for primary nucleation and droplet growth calculations, spectrum pruning and the quadrature method of moments are most accurate over the range of conditions considered.

Two-Phase Flow Modeling and Measurements in Low-Pressure Turbines: Part 2 — Turbine Wetness Measurement and Comparison to CFD-Predictions

2014 ◽  
Author(s):  
M. Schatz ◽  
T. Eberle ◽  
M. Grübel ◽  
J. Starzmann ◽  
D. M. Vogt ◽  
...  
Keyword(s):  
Experimental Data ◽  
Steam Turbine ◽  
Physical Models ◽  
Droplet Growth ◽  
Steam Turbines ◽  
Wet Steam ◽  
Validity And Reliability ◽  
Two Phase ◽  
Validation Data ◽  
Subsequent Formation

The correct computation of steam subcooling, subsequent formation of nuclei and finally droplet growth is the basic prerequisite for a quantitative assessment of the wetness losses incurred in steam turbines due to thermal and inertial relaxation. The same basically applies for the prediction of droplet deposition and the resulting threat of erosion. Despite the fact that there are many CFD-packages that can deal with real-gas effects in steam flows, the accurate and reliable prediction of subcooling, condensation and wet steam flow in steam turbines using CFD is still a demanding task. One reason for this is the lack of validation data for turbines that can be used to assess the physical models applied. Experimental data from nozzle and cascade tests can be found in the open literature; however, this data is only partly useful for validation purposes for a number of reasons. With regard to steam turbine test data, there are some publications, yet always without any information about the turbine stage geometries. This publication is part of a two-part paper; whereas part 1 focuses on the numerical validation of wet steam models by means of condensing nozzle and cascade flows, the focus in this part lies on the comparison of CFD results of the turbine flow to experimental data at various load conditions. In order to assess the validity and reliability of the experimental data, the method of measurement is presented in detail and discussed. The comparison of experimental and numerical results is used for a discussion about the challenges in both modeling and measuring steam turbine flows, presenting the current experience and knowledge at ITSM.

On the Effects of Unsteadiness on the Condensation Process in Low-Pressure Steam Turbines

2009 ◽  
Author(s):  
Keramat Fakhari
Keyword(s):  
Large Scale ◽  
Flow Direction ◽  
Low Pressure ◽  
Droplet Growth ◽  
Condensation Process ◽  
Steam Turbines ◽  
Two Phase ◽  
Condensation Zone ◽  
Scale Temperature ◽  
Pressure Steam

The condensation process in a turbomachine is in reality an essentially random and unsteady phenomenon. On a time-averaged basis, the condensation zone is spread over a much greater distance in the flow direction than a simple steady-flow calculation would indicate. The droplet growth rate also shows different characteristics which are observed in experiments measured in real low-pressure steam turbines. These differences are mainly introduced by the large-scale temperature fluctuations which are caused by the segmentation of blade wakes by successive blade rows. Furthermore, the additional losses by condensation have to be reconsidered for an unsteady simulation. This paper describes a time-accurate Eulerian/Lagrangian two-phase model which is implemented within the DLR in-house code TRACE [1]. The phases are coupled through appropriately generated source terms for heat, mass and momentum. For the subcooled thermodynamic properties of steam the local formulation of IAPWS-IF97 [2, 3] is used. The implementation has been validated in a previous publication of the author [4] using one and two-dimensional experiments of Laval nozzles and a cascade blade from literature. The focus of this work is on the unsteady Phenomena which are investigated in a stage of an industrial low-pressure steam turbine.

On the Performance of a Cascade of Turbine Rotor Tip Section Blading in Wet Steam. Part 5: Theoretical Treatment

2006 ◽  
Vol 220 (4) ◽  
pp. 457-472 ◽  
Author(s):  
F Bakhtar ◽  
R J K Henson ◽  
H Mashmoushy
Keyword(s):  
Dominant Role ◽  
Electrical Power ◽  
Turbine Rotor ◽  
Experimental Results ◽  
Theoretical Treatment ◽  
Steam Turbines ◽  
Wet Steam ◽  
Economic Returns ◽  
Secondary Nucleation ◽  
Two Phase

During the course of expansion of steam in turbines, the fluid first supercools and then nucleates to become a two-phase mixture. The formation and behaviour of the liquid create problems that lower the performance of turbine wet stages and the mechanisms underlying these are insufficiently understood. Steam turbines play a dominant role in the generation of the main electrical power supply, and the economic returns on improved performance are substantial. This article is the last of a set and describes the theoretical part of an investigation into the performance of a turbine rotor tip section profile in wet steam. The experimental results are described in the earlier parts of the paper. To describe the behaviour of the flow theoretically, the conservation equations describing the main flow field are combined with equations describing droplet behaviour and the set is treated by the time-marching method. Comparisons are carried out with the experimental results presented in the earlier parts of the paper and the agreement obtained is good. When the droplets present in the steam are 0.15 μm in radius at inlet to the cascade, there is considerable secondary nucleation. With droplets of 0.05 μm radius, secondary nucleation is suppressed, but at high pressure ratios, the thermodynamic loss though reduced is not eliminated.

Two Phase Flow CFD Modeling to Enhance Steam Turbines LP Stages Performance Predictability: Comparison With Data and Correlations

2020 ◽  
Author(s):  
Nicola Maceli ◽  
Lorenzo Arcangeli ◽  
Andrea Arnone
Keyword(s):  
Power Generation ◽  
Power Plants ◽  
Raw Materials ◽  
Sustainable Use ◽  
Waste To Energy ◽  
Cfd Modeling ◽  
Reliable Estimate ◽  
Primary Role ◽  
Steam Turbines ◽  
Two Phase

Abstract The whole energy market, from production plants to end-users, is marked by a strong impulse towards a sustainable use of raw materials and resources, and a reduction of its carbon foot-print. Increasing the split of energy produced with renewables, improving the efficiency of the power plants and reducing the waste of energy appear to be mandatory steps to reach the goal of sustainability. The steam turbines are present in the power generation market with different roles: they are used in fossil, combined cycles, geothermal and concentrated solar plants, but also in waste-to-energy and heat recovery applications. Therefore, they still play a primary role in the energy production market. There are many chances for efficiency improvement in steam turbines, and from a rational point of view, it is important to consider that the LP section contributes to the overall power delivered by the turbine typically by around 40% in industrial power generation. Therefore, the industry is more than ever interested in developing methodologies capable of providing a reliable estimate of the LP stages efficiency, while reducing development costs and time. This paper presents the results obtained using a CFD commercial code with a set of user defined subroutines to model the effects of non-equilibrium steam evolution, droplets nucleation and growth. The numerical results have been compared to well-known test cases available in literature, to show the effects of different modeling hypotheses. The paper then focuses on a test case relevant to a cascade configuration, to show the code capability in terms of bladerow efficiency prediction. Finally, a comprehensive view of the obtained results is done through comparison with existing correlations.

scholarly journals Characteristics of Accelerations and Pressure Gradient during Run-Down of Solitary Wave over Very Steep Beach: A Case Study

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 523 ◽  
Author(s):  
Chang Lin ◽  
Wei-Ying Wong ◽  
Rajkumar V. Raikar ◽  
Hwung-Hweng Hwung ◽  
Ching-Piao Tsai
Keyword(s):  
Free Surface ◽  
Pressure Gradient ◽  
Flow Separation ◽  
Adverse Pressure Gradient ◽  
Time Interval ◽  
Primary Vortex ◽  
Two Phase ◽  
Run Up ◽  
The Moment ◽  
External Stream

An experimental investigation is performed to elucidate the variations of accelerations and pressure gradients in the external stream of retreating flow during the run-down phase of a non-breaking solitary wave, propagating over a 1:3 sloping beach. Two solitary waves that have the incident wave heights (H0) of 2.9 and 5.8 cm, with respective still water depths (h0) of 8.0 and 16.0 cm (Cases A and B), were generated in a wave flume, resulting in the incident wave-height to water-depth ratios (H0/h0) being identically equal to 0.363. The latter case was only used to highlight the non-dimensional features of the wave celerity, the time history of horizontal velocity and the breaker type, which all exhibit similarity to those of the former. Two flow visualization techniques such as particle trajectory method and fluorescent dye strip and a high-speed particle image velocimetry (HSPIV) were utilized to provide the flow images and velocity fields. Based on the ensemble-averaged velocity fields and profiles, the partially depth-averaged (i.e., excluding the part in the boundary layer) values of accelerations and pressure gradient at a specified measuring section are then smoothed by a symmetric five-point smoothing scheme. Eventually, the smoothed values of the accelerations and pressure gradient are used to highlight the dynamic features of the external stream of retreating flow. It is found that, at the section of the incipient flow separation, the non-dimensional local acceleration (with respect to the gravity acceleration) in the offshore direction keeps increasing from the moment at which the run-up motion ends to the counterpart at which the incipient flow separation occurs. Afterwards, growth of the primary vortex develops with its core translating offshore. The corresponding non-dimensional local acceleration at the (moving) core section increases to a maximum of around 1.0 at the instant for occurrence of the hydraulic jump with abrupt rise of the free surface; and then decreases to zero at time for transformation of the curling jet into the projecting jet. The results exhibit that the external stream of retreating flow is accelerated temporally in the offshore direction for the interval between the time for the end of run-up motion and that for the formation of projecting jet. However, for later time interval up to generation of the two-phase flow field, the non-dimensional local acceleration in the offshore direction varies from zero to a negative maximum of −2.117 at the moment for the projecting jet heading downward before the impingement. It then decreases in magnitude continuously. The trend reveals that the external stream is decelerated temporally in the offshore direction for this later time interval. Further, at the section of the incipient flow separation, the non-dimensional pressure gradient (also with reference to the gravity acceleration) in the offshore direction increases from 0.225 for the time at which the run-up motion ends to 0.721 for the instant at which the incipient flow separation takes place. The trend highlights the external stream being under increasing adverse pressure gradient and more decelerated spatially with the increasing time, thus resulting in occurrence of the incipient flow separation. Afterwards, the value of the non-dimensional pressure gradient keeps increasing and eventually reaches a positive maximum of 2.011 and then decreases consecutively until the two-phase flow field is generated. In addition, due to the influence of acceleration of the external stream in the offshore direction, the non-dimensional vorticity of primary vortex core increases with increasing time up to the moment for occurrence of the projecting jet. Nevertheless, the non-dimensional vorticity of primary vortex core keeps decreasing with increasing time T for the later time interval due to the influence of deceleration of the external stream in the offshore direction. Finally, considerably large magnitudes of the non-dimensional accelerations and pressure gradient greater than 1.5 taking place at two non-dimensional times are worthy of noting. The negative maximum value of the non-dimensional convective acceleration equal to −2.005 appears at the instant for the occurrence of hydraulic jump. In addition, the negative maximum values of the non-dimensional local acceleration, total acceleration and pressure gradient unexpectedly as high as −2.117, −1.694 and 2.011, respectively, appear simultaneously at time for the projecting jet heading towards the retreating free surface. Under such a situation, the external stream of retreating flow is highly decelerated in the offshore direction under the fairly large adverse pressure gradient, thus forcing the retreating flow to move upwards rapidly. Meanwhile, the non-dimensional local acceleration in the vertical direction is surprisingly found to be 3.37. The result strongly reconfirms the evident rise of the free surface in the vicinity of the core section and reveals very rapid change from negative, via nearly zero, to positive vertical velocity.

scholarly journals Pressure Signal Analysis for the Characterization of High-Viscosity Two-Phase Flows in Horizontal Pipes

2020 ◽  
Vol 8 (12) ◽  
pp. 1000
Author(s):  
Lizeth Torres ◽  
José Noguera ◽  
José Enrique Guzmán-Vázquez ◽  
Jonathan Hernández ◽  
Marco Sanjuan ◽  
...  
Keyword(s):  
Mass Flow ◽  
Two Phase Flow ◽  
High Viscosity ◽  
Flow Rate Ratio ◽  
Phase Flow ◽  
Two Phase ◽  
Local Flow ◽  
Horizontal Pipes ◽  
Pressure Time ◽  
Mass Flow Rates

We study a high-viscosity two-phase flow through an analysis of the corresponding pressure signals. In particular, we investigate the flow of a glycerin–air mixture moving through a horizontal pipeline with a U-section installed midway along the pipe. Different combinations of liquid and air mass flow rates are experimentally tested. Then, we examine the moments of the statistical distributions obtained from the resulting pressure time series, in order to highlight the significant dynamical traits of the flow. Finally, we propose a novel correlation with two dimensionless parameters: the Euler number and a mass-flow-rate ratio to predict the pressure gradient in high-viscosity two-phase flow. Distinctive variations of the pressure gradients are observed in each section of the pipeline, which suggest that the local flow dynamics must not be disregarded in favor of global considerations.

Representing Polydispersed Droplet Behavior in Nucleating Steam Flow

2007 ◽  
Vol 129 (11) ◽  
pp. 1404-1414 ◽  
Author(s):  
A. G. Gerber ◽  
A. Mousavi
Keyword(s):  
Method Of Moments ◽  
Current Practice ◽  
Complex Geometry ◽  
Steam Flow ◽  
Steam Turbines ◽  
Two Phase ◽  
Cfd Models ◽  
Pressure Steam ◽  
Droplet Behavior ◽  
Computational Fluid Dynamics Cfd

The quadrature method of moments (QMOM) is applied to the particle size distribution (PSD) present in nucleating steam flow, with a particular emphasis on conditions relevant to low-pressure steam turbines. These machines exhibit heterogeneous and homogeneous phase transition in the presence of strong flow discontinuities due to shocks and complex geometry. They offer a particularly difficult two-phase modeling situation. The present work shows that QMOM is a robust and efficient method and, in comparison to current practice of using a monodispersed PSD in computational fluid dynamics (CFD) models, offers promise for dealing with the complex two-phase conditions present in real machines.

Influence of Turbulence Modelling to Condensing Steam Flow in the 3D Low-Pressure Steam Turbine Stage

2016 ◽  
Author(s):  
Yogini Patel ◽  
Giteshkumar Patel ◽  
Teemu Turunen-Saaresti
Keyword(s):  
Steam Turbine ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Rapid Change ◽  
Low Pressure ◽  
Turbulence Modelling ◽  
Steam Flow ◽  
Droplet Growth ◽  
Steam Turbines ◽  
Turbine Stage

With the tremendous role played by steam turbines in power generation cycle, it is essential to understand the flow field of condensing steam flow in a steam turbine to design an energy efficient turbine because condensation at low pressure (LP) turbine introduces extra losses, and erosion in turbine blades. The turbulence has a leading role in condensing phenomena which involve a rapid change of mass, momentum and heat transfer. The paper presents the influence of turbulence modelling on non-equilibrium condensing steam flows in a LP steam turbine stage adopting CFD code. The simulations were conducted using the Eulerian-Eulerian approach, based on Reynolds-averaged Navier-Stokes equations coupled with a two equation turbulence model, which is included with nucleation and droplet growth model for the liquid phase. The SST k-ω model was modified, and the modifications were implemented in the CFD code. First, the performance of the modified model is validated with nozzles and turbine cascade cases. The effect of turbulence modelling on the wet-steam properties and the loss mechanism for the 3D stator-rotor stage is discussed. The presented results show that an accurate computational prediction of condensing steam flow requires the turbulence to be modelled accurately.

An Upwind Eulerian-Eulerian Model for Non-Equilibrium Condensation in Steam Turbines

2013 ◽  
Author(s):  
Xiaofeng Zhu ◽  
Xin Yuan ◽  
Zhirong Lin ◽  
Naoki Shibukawa ◽  
Tomohiko Tsukuda ◽  
...  
Keyword(s):  
Current Model ◽  
Finite Volume Scheme ◽  
Steam Turbines ◽  
Turbine Cascade ◽  
Wet Steam ◽  
Turbine Stage ◽  
Eulerian Model ◽  
Two Phase ◽  
Eigen Value ◽  
Non Equilibrium

The present paper proposes an Eulerian-Eulerian two-phase model for non-equilibrium condensing flow in steam turbines. This model is especially suitable for upwind finite volume scheme. An approximate Roe type flux using real water/vapor property is constructed to calculate the upwind wet-steam flux. This flux fully couples the wetness fraction with other conservative variables in the Jacobian Matrix whose eigen-vector and eigen-value are analitically derived. A novel treatment of real wet-steam property is developed by constructing a 3-DOFs TTSE table according to IAPWS97 formulas. The table is actually a cubic and uses the mixture’s density, the mixture’s internal energy and wetness as independent variables. Besides homogeneous condensation, heterogeneous condensing is also integrated into the model, which facilitates simulating the effect of salt impurities. The above methods are validated through two nozzle and one turbine cascade calculations and finally applied to a model LP steam turbine stage. Results show that the current model is very robust and is able to correctly capture the non-equilibrium condensation phenomena.

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