On the Critical Weber Number for Coarse Water Formation in Steam Turbines

1979 ◽  
Vol 21 (5) ◽  
pp. 353-356 ◽  
Author(s):  
C. S. Ow ◽  
R. I. Crane
Keyword(s):  
Weber Number ◽  
Maximum Size ◽  
Distribution Functions ◽  
Steam Turbines ◽  
Wet Steam ◽  
Nonlinear Parameters ◽  
Upper Limit ◽  
Water Formation ◽  
Critical Weber Number ◽  
Cumulative Mass

The widely quoted experiments of Moore et al. indicate that the largest stable drops resulting from atomization behind a blade, in typical low-pressure wet-steam flows, can be described by a constant critical Weber number, Wec, of about 21, obtained graphically by fitting upper-limit distribution functions (ULDF) to measured spectra. A non-subjective re-analysis of these data has been made, using Marquardt's algorithm for the least-squares estimation of nonlinear parameters to improve the fitting. It is shown that optimization of the ULDF fit increases Wec considerably in the case of supersonic blade-exit flow. However, replacement of the computed maximum size by that corresponding to a given cumulative mass is necessary to avoid distortion of the result by the small fraction of total mass contained in the largest drops. A cumulative mass of 99.9 per cent consistently gives Wec values near 21, confirming Moore's result, but indicating the need for further work on the Mach-number dependence of Wec.

Numerical Investigation on Head-On Collisions of Binary Micro-Droplets by an Improved Multiphase Lattice Boltzmann Flux Solver

2016 ◽  
Author(s):  
Y. Wang ◽  
C. Shu
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann ◽  
Weber Number ◽  
Density Ratio ◽  
Distribution Functions ◽  
Time Step ◽  
Large Density ◽  
Wide Range ◽  
Large Density Ratio ◽  
Critical Weber Number

Head-on collisions of binary micro-droplets are of great interest in both academic research and engineering applications. Numerical simulation of this problem is challenging due to complex interfacial changes and large density ratio between different fluids. In this work, the recently proposed lattice Boltzmann flux solver (LBFS) is applied to study this problem. The LBFS is a finite volume method for the direct update of macroscopic flow variables at cell centers. The fluxes of the LBFS are reconstructed at each cell interface through lattice moments of density distribution functions (DDFs). As compared with conventional multiphase lattice Boltzmann method, the LBFS can be easily applied to study complex multiphase flows with large density ratio. In addition, external forces can be implemented more conveniently and the tie-up between the time step and mesh spacing is also removed. Moreover, it can deal with complex boundary conditions directly as those do in the conventional Navier-Stokes solvers. At first, the reliability of the LBFS is validated by simulating a micro-droplet impacting on a dry surface at density ratio 832 (air to water). The obtained result agrees well with experimental measurement. After that, numerical simulations of head-on collisions of two micro droplets are carried out to examine different collisional behaviors in a wide range of Reynolds numbers and Weber numbers of 100 ≤ Re ≤ 2000 and 10 ≤ We ≤ 500. A phase diagram parameterized by these two control parameters is obtained to classify the outcomes of these collisions. It is shown that, at low Reynolds number (Re=100), two droplets will be coalescent into a bigger one for all considered Weber numbers. With the increase of the Reynolds number, separation of the collision into multiple droplets appears and the critical Weber number for separation is decreased. When the Reynolds number is sufficiently high, the critical Weber number for separation is between 20 and 25.

Penetration Dynamics of Solid Particles into Liquids High-Speed Experimental Results and Modelling

2005 ◽  
Vol 473-474 ◽  
pp. 429-434 ◽  
Author(s):  
Olga Verezub ◽  
György Kaptay ◽  
Tomiharu Matsushita ◽  
Kusuhiro Mukai
Keyword(s):  
Contact Angle ◽  
Particle Size ◽  
Aqueous Solutions ◽  
Particle Velocity ◽  
Weber Number ◽  
High Speed ◽  
Solid Particles ◽  
Bulk Liquid ◽  
Distilled Water ◽  
Critical Weber Number

Penetration of model solid particles (polymer, teflon, nylon, alumina) into transparent model liquids (distilled water and aqueous solutions of KI) were recorded by a high speed (500 frames per second) camera, while the particles were dropped from different heights vertically on the still surface of the liquids. In all cases a cavity has been found to form behind the solid particle, penetrating into the liquid. For each particle/liquid combination the critical dropping height has been measured, above which the particle was able to penetrate into the bulk liquid. Based on this, the critical impact particle velocity, and also the critical Weber number of penetration have been established. The critical Weber number of penetration was modelled as a function of the contact angle, particle size and the ratio of the density of solid particles to the density of the liquid.

scholarly journals Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

2021 ◽  
Vol 9 (11) ◽  
pp. 1253
Author(s):  
Yuriy N. Savchenko ◽  
Georgiy Y. Savchenko ◽  
Yuriy A. Semenov
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Solution Process ◽  
Cavity Flow ◽  
Surface Tension Effect ◽  
Force Coefficient ◽  
Hodograph Method ◽  
Wide Range ◽  
Critical Weber Number ◽  
Cavity Boundary

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

A novel method for measuring the coarse water droplets in wet steam flow in steam turbines

2001 ◽  
Vol 10 (2) ◽  
pp. 123-126 ◽  
Author(s):  
Xiaoshu Cai ◽  
Lili Wang ◽  
Yongzhi Pan ◽  
Xin Ouyan ◽  
Jianqi Shen
Keyword(s):  
Steam Flow ◽  
Steam Turbines ◽  
Wet Steam ◽  
Water Droplets ◽  
Novel Method ◽  
Wet Steam Flow

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.

Fog Droplet Deposition and Coarse Water Formation in Low-Pressure Steam Turbines: A Combined Experimental and Theoretical Analysis

1988 ◽  
Vol 110 (2) ◽  
pp. 163-172 ◽  
Author(s):  
J. B. Young ◽  
K. K. Yau ◽  
P. T. Walters
Keyword(s):  
Size Spectrum ◽  
Steam Turbines ◽  
Droplet Deposition ◽  
Deposition Rates ◽  
Water Formation ◽  
Pressure Steam ◽  
Order Of Magnitude ◽  
Droplet Sizes ◽  
Inversion Procedure ◽  
Last Stage

The paper describes a theoretical and experimental study of fog droplet deposition and coarse water formation in the LP cylinders of two 500 MW steam turbines. Measurements of coarse water flow rates entering and leaving the final stage of each turbine were performed using a new design of water absorbent probe. From these measurements it was possible to deduce the rate of deposition of fog droplets onto the last stage blading of each machine. Aerodynamic and optical traverses provided experimental data on the fog droplet mean diameter and wetness faction, and the application of an inversion procedure generated an approximation to the droplet size spectrum itself. Using these data and theoretical methods for predicting inertial and diffusional deposition rates, a second estimate was obtained for the stage deposition rates. The two different approaches show excellent agreement, in contrast with previously published work, which was unable to reconcile (to within one order of magnitude) deposition theory with measured fog droplet sizes and coarse water quantities.

Transition from dripping to jetting

1999 ◽  
Vol 383 ◽  
pp. 307-326 ◽  
Author(s):  
CHRISTOPHE CLANET ◽  
JUAN C. LASHERAS
Keyword(s):  
Weber Number ◽  
Free Edge ◽  
Newtonian Liquid ◽  
Inviscid Limit ◽  
Inertia Effects ◽  
Wide Range ◽  
Critical Weber Number ◽  
Experimental Values ◽  
Outside Diameter ◽  
Good Agreement

We consider the critical Weber number (Wec≡ ρV20D/σ) at which the transition from dripping to jetting occurs when a Newtonian liquid of density ρ and surface tension σ is injected with a velocity V0 through a tube of diameter D downward into stagnant air, under gravity g. We extend Taylor's (1959) model for the recession speed of a free edge, and obtain in the inviscid limit an exact solution which includes gravity and inertia effects. This solution provides a criterion for the transition which is shown to occur at a critical Weber numberformula herewhere Bo and Boo are the Bond numbers (Bo≡[ρgD2/(2σ)]1/2), respectively based on the inside and outside diameter of the tube, and K is a constant equal to 0.37 for the case of water injected in air. This critical Weber number is shown to be in good agreement with existing experimental values as well as with new measurements performed over a wide range of Bond numbers.

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