A study of the coarse droplet formation from the liquid film in steam turbines

. The steam turbines are still the essential machines for the energy transformation. For all the deployment of the non-fossil energy sources the steam turbine remains the most important energy transforming device. In the current situation when the daily operation of the turbines is not predictable due to electricity supply from the photovoltaic and the wind power plants, the turbines work in the non-design conditions, the danger of the blade’s erosion caused by the coarse droplets is assumed. The purpose of this paper is to suggest the possible formation process of the coarse droplets in the steam turbine. The current studies were focused mostly on the measurement or identification of the coarse droplets in the steam turbine but the explanation of the archived results was not sufficient. The influence of the flow field behind the blade on the liquid film atomization was studied. The first measurements of the detailed characteristic of the flow field in the wind tunnel for the qualitative analysis of the phenomena were performed with promising results.


Introduction
Although the liquid film atomization is an important technical issue in many practical applications, a general theoretical description of this complex process is still absent.In the case of steam turbine operation, the process is responsible for undesirable effects on the reliability and efficiency of the turbine.These effects include mainly additional energy losses, blade erosion and the reduction of the blade's lifetime.Water film atomization especially occurs in low pressure parts of the turbine, where coarse water droplets are formed from the water film on the blades and casings.The study of liquid atomization, movement and its potential impact of the formed droplets on the moving blades in turbines at high speed has an important role in the never-ending effort to enhance energy production efficiency and to decrease its environmental impact [1,2].
During the operation of steam turbines, two different size groups of droplets can be encountered.Fine droplets are formed by nucleation and condensation as expanding steam passes the saturation line.These fine droplets fall mostly within a diametral range of 0.1 -1 µm.Majority of these droplets follow the flow path of the steam.However, some of them are transported by turbulent diffusion on the blades and casings, where the liquid film is formed.Subsequently, the liquid film breaks off from the surface in the form of coarse droplets.These coarse droplets have expected diametral range from 1 µm to 1 mm.As the coarse droplets break off from the surface, they are accelerated by the flow of the steam.Subsequently, they hit the rotor blades reducing the efficiency and the lifetime of the turbine.* Corresponding author: ondrej.bartos@fs.cvut.czPrevious measurements [4,5] of the size distribution function of coarse droplets in the nozzle showed the bimodal function of the coarse droplets.This bi-modal distribution can be explained only partially with the theory.The previous paper [6,9] suggested the possible explanation of the second mode.The aim of this paper is to follow up on the previous findings.For this purpose, the hot wire anemometry was used.This method is used for measuring velocity fluctuation in the blade's channel.

Droplet formation
The theory of liquid film breakup is based on the works of Rayleght, Weber and Ohnesorge [6,7].According to the theory, there are several different regimes of liquid film atomization.Among the high-speed liquid breakup atomization, we can distinguish the Rayleight-type, the Membrane-type and the Fiber-type.However, previous photogrammetric measurements in the nozzle confirm, that atomization on the trailing edge is very stochastic and all of these mentioned atomization modes can be visible.
Example of such photogrammetric measurement is shown on Fig. 1.
For description of the theoretic models the nondimensional Weber number is used.The Weber number compares drag force acting on the droplet with surface tension of the droplet and is defined by: where (ρg) is vapour density, (σ) is surface tension of the water, (wr) is the relative velocity between the vapour and the droplets and (d) is the diameter of the droplet.
Fig. 1.The photo of the trailing edge.
For the above-mentioned reason, the description of the "chaotic" atomization is still not sufficient.However, one of the possible parameters which is possible to determine is the maximum droplet diameter.For this purpose, the critical Weber number is used.The critical value is not constant for any cases, but for the low-viscosity liquid suddenly exposed in the high velocity air steam was estimated Wecrit=13 [1,7].Nevertheless, there are more values for Wecrit in literature in range of 10-40 [8].

Measurement setup
The experiment was carried out in the wind tunnel with a part which simulates a channel between the bladesnozzle section.This part has a similar expansion rate as close as possible to the situation in the real turbine.The shape of the nozzle is basically the converging nozzle and behind its trailing edge is the subbed increase of the channel crossection up to 50mm.The working fluid is in this case the compressed air.The sides of the channel are equipped by the small obstacles to avoid the flow attachment to one of the walls.The wind tunnel is on the Fig. 2.

Fig. 2.
The wind tunnel with the nozzle section.

Wind tunnel
The motivation for the wind tunnel assembly arose from a previous measurement [3] of the coarse droplets in the steam turbine under operational conditions.The measurement was performed in three steam turbines in Czechia.The amount of the acquired coarse droplets was very low due to their low number density level.Due to difficulties connected with measurements in an operating steam turbine, a wind tunnel was designed and manufactured for the analysis of the coarse droplet formation from the liquid films.The aim of the design was to create, as closely as possible, the conditions in a steam turbine while utilising the advantages of working in the laboratory.
The wind tunnel is either designed as a classical CD nozzle or only the converging nozzle.The planned operational regime is mainly subsonic or transonic.The liquid film is formed directly in the nozzle section or on the aerofoil NACA0008 which is placed 50 mm behind the nozzle throat.The aerofoil simulates the blade in the turbine, and it is possible to remove or replace it.In the nozzle section or on the aerofoil is a groove which supplies liquid to the surface.The liquid is pumped to the surface through the dosing pump with a flow between 1 ml/min to 500 ml/min.The tunnel is equipped with large optical windows that provide good visual access for the measurements.It is possible to operate the tunnel with steam in a continuous mode or with compressed air in a periodic mode.

Droplets measurement
For the droplet distribution measurement, the Spraytec Malvern device was used.The device is based on light diffraction on spherical particles according to the Mie theory for the angular light distribution.Spraytec is equipped with a 300 mm lens and laser (λ=635nm).In order to measure stable spherical droplets, the laser beam was placed 20 cm behind the trailing edge of the blade.Due to the principle of measurement (scattering of light on the droplets), the conditions for evaluation were not always met, therefore the results are calculated only for the states when the conditions for evaluation were acceptable.The typical droplet volumetric fraction bimodal distribution of Spraytec measurement of the nozzle is shown on Fig. 3 and Fig. 4.

Velocity fluctuation measurement
Measurement of the velocity fluctuations in the channel was performed by hot-wire anemometry.Generally, hot wire is capable to measure fluctuations of the velocity [10], or also of a scalar quantity [11], like the temperature [12].Here, the purpose of the measurement is investigate the range of magnitudes of instantenous velocity, so the clasical procedure is used.

Measurement and results
The measurement was performed in the wind tunnel, but at the typical operational conditions the flow field is transonic.The revealed measurement was done for the lower velocity in the tunnel which corresponds with the stagnation pressure in the settling chamber at the level 110 kPa and the expansion is to atmospheric pressure.The reason for this measurement was to analyse the velocity fluctuation in the flow field with hot wire probe.The used probe is very fine (fast measurement) and the measurement in the tunnel at standard condition can break the hot wire probe.Nevertheless, the purpose of the measurement is to prove if in the flow exist the regions where the velocity is sufficiently low for the droplets formation to satisfy the Wecrit.If exists some regions in the flow where the velocity is sufficiently low for certain time (wake behind the blade) it will be possible to explain the existence of the coarse droplets bigger than their maximum size determined by the critical Webber number for the mean flow velocity.The measured velocity histogram at one position (6mm from the centreline) and the profile of the mean velocity cross the channel is on the Fig. 6 and Fig. 7 respectively.

Analysis of results
The droplet atomization process is strongly stochastic.The way to prove the theory of the bigger droplets formation than suggest the Webber theory is based on the curvilinear particle motion.As an example, for this contribution one set of the measured velocity distribution was chosen (6mm from the centreline).The relaxation time for the four different sizes of the droplets was compared with the cumulative distribution of the low velocity time existence for the time of the measurement, from the histogram on the Fig. 6.
The relaxation time given by the: Where ρp is the particle density, d is the diameter.Cc is Cunningham factor in this case equal unity, µ is the viscosity of the fluid.The relaxation time is characterizing the time required for a particle to adjust its velocity to a new condition.It is not time to reach new velocity but it at three τ the particle velocity is almost equal to the velocity of the bulk fluid [13].In the table1.The values of the relaxation time are presented.The droplets diameter for the assessment was chosen as a droplet with the diameter 2, 3 and 4 times bigger than the droplet corresponds with the critical We for the bulk flow (74 m/s).The compare the relaxation time for all four chosen droplets group in the Table 1 with the cumulative time from the hot wire measurement in the Table 2, one can see that for group 4D the relaxation time is 0.9s, this value corresponds with the velocity cca 39m/s (blue box) and it corresponds with We for this group around We=14.This means there is some probability of the existence of this group in the bulk flow.The existence defined by the 3 * τ is not satisfied (yellow boxes) for 3D and 4D, only the group 2D.The green boxes show where is Weber number smaller than 13 and red boxes shows that the droplets should be break to smaller ones.

Conclusions
The suggested method for the explanation of the bigger droplets than the classical Weber theory is very simple and it requires the enhancement in the theoretical part as well as in the experimental, but at the moment it seems very promising.
The hot-wire anemometry with probe Dantec 55P11 was used to measure the velocity fluctuations in the channel of the nozzle and the Spraytec Malvern device was used to measure droplet distribution.Because the probe Dantec 55P11 cannot be used for high velocity measurement, the measurement was performed with lower air velocity.For the purpose of the velocity fluctuation measurement under standard conditions, future measurements with new probe will be made.These measurements will also include variable distances from the trailing edge.
We gratefully acknowledge the support by National Centre for Energy TN01000007, Grant of the Czech Technical University in Prague, Grant No. SGS 21/154 and to institutional support RVO 61388998

Fig. 3 .
Fig. 3.The droplet distribution function.An example of the bi-modal distribution of the droplets behind the trailing edge for three different surface coatings.

Fig. 4 .
Fig. 4. The droplet number density distribution function.An example of the bi-modal distribution of the droplets behind the trailing edge for three different surface coatings.
A probe type Dantec 55P11 was operated by CTA anemometer Disa 55M10.The probe has a tungsten wire of 5 micron in diameter and 1.2 mm in length.It was calibrated by Dantec calibration unit in the range of 5-180 m/s.Data acquisition device NI PCIe-6346 was used for sampling of anemometer output signal (16 bit, frequency 75 kHz, 5s).

Fig. 5 .
Fig. 5.The photo of hotwire anemometry measurement placed behind the new nozzle section.

Fig. 6 .
Fig. 6.The histogram of the measured velocities behind the trailing edge of the nozzle section.

Fig. 7 .
Fig. 7.The velocity profile of the flow in the upper half of the channel behind the nozzle section.The velocity profile is not symmetrical due to the tendency to attach the nozzle wall.

Table 1 .
The relaxation time for the chosen droplets

Table 2 .
Table of the time cumulative distribution and We for chosen diameters.