Numerical simulation of a new hollow stationary dehumidity blade in last stage of steam turbine

Abstract

As a result of adopting saturation steam and long blade, problems of water erosion of last stage blade for steam turbine become more prominent. In order to improve the operation reliability and efficiency of steam turbine, it is necessary to investigate the nonequilibrium condensing wet steam two phase flow and the dehumidity method. A wet steam model with user defined function based on FLUENT software was investigated to simulate the steam condensing flow in the cascades. The simulation consequences show that the pressure variations in simulation depict a good agreement with the experiment data. On the basis of the discrete phase model simulation results and experiment data, the efficiency of existing dehumidity blade with suction slot was calculated. A new stationary dehumidity blade was designed to elevate the dehumidity efficiency: the efficiency in the suction surface was increased by 21.5%, and that in the pressure surface was increased by 12.2%.

Keywords

steam turbine / hollow stationary blade / dehumidity / numerical simulation

Introduction

Steam turbine plays a dominant role in power generation around the world. The increase of wetness in steam turbine exit would cause severe erosion to the turbine blades at the low-pressure stages and a reduction of aerodynamic efficiency and safety in the operation. As the steam pressure in the low pressure cylinder decreased, it condensed into primary droplets (with diameters from 0.01 to 2 μm), which would deposit on the blade surface and grow into the water film. The continuously dynamic impact secondary droplets (with diameters from 20 to 200 μm), which are formed in the process of water film rupture at the trailing edge of stationary blade on movable vanes is the main reason for water erosion [1-3]. So, in order to decrease the amount of secondary droplets, it is necessary to investigate the wet steam flow, the movement of droplets of different size, and the volume of sediment.

The most effective existing measure to prevent or mitigate the water erosion is slotting suction ports in suitable locations of the hollow stationary blades’ pressure surface or suction surface, by making use of static pressure between the inner and outer slots to remove the water film or stream on the surface [4-6]. In order to improve the efficiency of this method, many researches were conducted to study the effect of geometric parameters (as position, width, pressure, the angle between suction slot and the blade’s surface, etc) on the dehumidity efficiency [7-11]. Actually, according to the calculation results obtained in this paper based on the experimental results in Ref. [11] and the outlet parameters of low pressure cylinder of steam turbine, the existing dehumidity technology of hollow stationary blades with suction slots is inefficient.

In this research, a new hollow stationary blade was proposed to elevate dehumidity efficiency by combining the blowing slot technology with the suction slot. The results indicate that the new hollow blade could decrease the amount of secondary droplet caused by primary droplet at the trailing edge of the blade, and improve the dehumidifying efficiency of suction slot from the view of water film reduction on the blade surface.

Model of simulation

Physical model and boundary conditions of numerical simulation

A two-dimensional model was built for the FLUENT simulation. Considering that the water erosion generally occurs in the upper part of the blade, the cross section in 0.73 relative height of the static blade was chosen as calculating sample [7]. The inlet and outlet parameters in cascades come from a certain 600 MW steam turbine with supercritical (SC) parameters. The geometric parameters of physical model are listed in Table 1.

The new hollow stationary blade is displayed in Fig. 1. Two blowing slot are introduced into the ordinary dewetting blade. A high-parameter steam would blow from these two blowing slot to change the steam condensing process characteristic near the blade surface (Researches on the dewetting blade with suction slot had been conducted completely [7-10], so the simulation of this blade was not included in this research).

Using the latest preprocessing software-ICEM, the mesh grid of the simulation model was generated to the next step calculation. The quality of mesh grid exceeded 0.9 and the boundary layer of blade was refined into smaller scale particularly in order to enhance the simulation accuracy. The mesh grid of simulation model is illustrated in Fig. 2.

The boundary conditions are presented in Table 2. In this paper, multiphase wet steam module in FLUENT was used to the computation and user defined function codes were compiled. The realizable k-ϵ turbulence model was selected from turbulence equations, the SIMPLE algorithm was set for the pressure and velocity coupling, and second order upwind scheme was used for discrete equations.

Wet steam two phase model with user defined function

Wet steam is a mixture of two phases, in which vaporous phase takes a dominant part, and water droplets formed by condensation of liquid phase takes a lesser part. The Eulerian-Eulerian approach was adopted for modeling the wet steam flow [12,13]. The flow mixture was modeled using the compressible Navier-Stokes equations, in addition to two transport equations for the liquid-phase mass-fraction, and the number of liquid-droplets per unit volume. The phase change model, which involves the formation of liquid-droplets in a homogeneous nonequilibrium condensation process, was based on the classical nonisothermal nucleation theory.

The control equation for condensed phase is expressed as

(1){\displaystyle \frac{\partial \rho \beta }{\partial t}}+\nabla (\rho v\beta )=\mathrm{\Gamma },

where β is liquid mass fraction, and Г is the mass condensation rate (kg/m).

The control equation for unit volume density of droplet is expressed as

(2){\displaystyle \frac{\partial \rho \eta }{\partial t}}+\nabla (\rho v\eta )=\rho I,

where η is the unit volume density of droplet, and I is condensation nucleation rate (kg/s).

And the relationship between wet steam density (ρ) and water vapor density ( ρ_v ) is

(3)\rho ={\displaystyle \frac{{\rho }_v}{\mathrm{1}-\beta }}.

In the numerical simulation of wet steam flow, the general assumptions are as followed:

1)　The speed slippage between droplets and steam is ignored;

2)　Forces between droplets are zero;

3)　The quantity of condensation phase is small (β<0.2); and

4)　The volume of liquid phase is not considered.

In order to simulate the two phase flow characteristic with wet steam model, the codes of user defined function were written. This function was programmed based on the IAPWS-IF 97 for the thermodynamic properties of water and steam, which can calculate most of the liquid phase characteristic, such as liquid density, droplet nucleation rate, droplet growth rate and critical radius.

Discrete phase model (DPM)

In wet steam, the number of secondary water droplets is small while the mass of single droplet is heavy. In order to simulate the droplets movement, this second phase was simulated with a discrete second phase in a Lagrangian frame of reference. The interact forces between particles and the influence of droplets’ volume were ignored because the share of wet steam volume of secondary droplets is very small. The random orbital track model was employed in DPM. In addition, the following assumptions were adopted:

1)　The droplets are ball;

2)　The deformation, growth and rupture of droplets are ignored;

3)　When droplets encounter the wall, deposition happens, but not rebounds.

On the other hand, throughout most of the similar researches about droplets deposition, the stationary blade inlet angle of droplets was ignored in the simulations or experiments. Actually, the factor of inlet angle plays an important role in the deposit process. Thus, the relation between mass fraction, inlet angle and droplet diameter was investigated previously to obtain more accurate simulation results of deposit position and amount [10], as listed in Table 3.

The relation between the diameter d and mass fraction Y_d was calculated from the Rosin-Rammler formula (4),

(4)Y_{\mathrm{d}}={\mathrm{e}}^{-{\left(d/\overline{d}\right)}^n},

where \overline{d} is the mean diameter, n is the spread parameter.

The mean diameter of droplets was 23. 21 μm, of which approximately 95% of the water droplets diameters were less than 100 μm, and the droplets with diameters of 40-100 μm would flow into the diaphragm because of their large inertia. Therefore, the diameter range of secondary water droplets in the simulation was 2-40 μm.

The relation between diameter and inlet angle was calculated by the fitting Eq. (5), obtained previously [10] based on the experimental data from the study of Valha [14],

(5)y=-\mathrm{0.9044}d+\mathrm{88.9931},

where, y is the inlet angle of droplet, and the d is the droplet diameter.

Simulation of two phase flow in cascades of last stage

Simulation results of vapor phase

The simulation results of vapor phase in the ordinary stationary blade and that in the new blade were presented in this sub section. A comparison and analysis of stagnation pressure reveals that the structural change would have little effect on the steam dynamic characteristic.

Experimental verification

An existing experimental result was introduced to verify the reliability of numerical simulation data. Although the blade profiles of the experiment and simulation were similar to each other, some differences existed in operation parameters and dimension [5]. To eliminate the interference of these differences, a non-dimensional parameter-s was investigated to convert simulation and experimental data [15]. The definition of non-dimensional parameter is

(6)s={\displaystyle \frac{p-p_{\mathrm{o}\mathrm{u}\mathrm{t}}}{p_{\mathrm{i}\mathrm{n}}-p_{\mathrm{o}\mathrm{u}\mathrm{t}}}},

in which, p-p_out is the differential pressure between the measuring point and the outlet, and p_in-p_out is the differential pressure between the inlet and outlet.

A good agreement with measured and simulated results is depicted in Fig. 3, which illustrates the reliability of the simulations in Section 3, including both the ordinary and the new blade.

Comparison and analysis of vapor phase

From Fig. 4, it can be concluded that the combination of suction slot and blowing slot in the hollow blade would not cause an intensive turbulence in the flow passage. The turbulence only occurred near the slot and diminished in a very short time. As demonstrated in Fig. 5, there is little difference between the ordinary and the new blade, which means that the new blade makes no difference in the power capability of steam flow.

Simulation results of liquid phase

The simulation results of liquid phase in the ordinary stationary blade and the new blade were presented in this sub section. Similarly, a comparison and analysis of liquid density, droplet nucleation rate, droplet growth rate and critical radius were made to illustrate the improvement of the new stationary blade in respect of reducing the amount of water film.

Comparison and analysis of vapor phase

The overall liquid density did not change a lot in the flow passage which can be observed in Fig. 6. However, an obvious decline of liquid density, droplet growth rate and critical radius can be noticed in Figs. 7(b), (d) and (f). It can be concluded that the blowing slot on the suction surface have a great effect on the liquid phase, and the mass of water deposition on the suction surface would be reduced markedly by the blowing activity, the evaporation of higher pressure and temperature steam flow from the blowing slot. The higher parameter steam would evaporate part of the tiny water droplets near the blade surface and blow the others back to the steam mainstream. Although the effect on the pressure surface is not so continuous and these liquid-phase characteristic would gradually restore its former level before 0.7 relative width of blade, the dewetting efficiency can also be increased by this new technology.

Generally speaking, from the analysis of simulation results of the vapor and liquid phase, it could be summarized that the new hollow stationary dehumidity blade would obviously decrease the droplet amounts (liquid density) in the region near the blade surface without having negative impact on the work capacity in the last stage of the steam turbine. In other words, the new design would decrease the water film gathered on the blade surface which is the main reason for the water erosion.

Simulation of droplet movement and deposition

Ordinary stationary blades

The simulation results of droplet movement and deposition in the ordinary blade were converted into a fitting equation and curve, which depicts a good agreement with the experimental data of Valha [14], shown in previous works [10]. This accordance verified the reliability of DPM in simulating droplet deposition. From the results of the integration of the deposition rate equation, it can be concluded that the amount of water deposition on the blade accounts for 63.58% of the overall amount of inlet-droplet, in which, the percentage of the amount of deposition on the pressure surface is 54.66% and that on the suction surface is 8.89%, in which 3.57% of the water droplets are deposited behind the 0.2 relative length on the blade surface.

New stationary blades

To the new blade, the amount of water deposition on the blade accounts for 48.73% of the overall amount of inlet-droplet which decreases by 23.36%, using the same approach to analyze the simulation results of the new blade. The percentage of the amount of deposition on the pressure surface is 43.06% and that on the suction surface is 5.66%. The simulation results and fitting curves are exhibited in Table 4 and Fig. 8, respectively.

Results and discussion

To calculate the dehumidty efficiency of hollow stationary blade with suction slots and the new model, conversion calculation method was introduced by combining DPM simulation results and operation outlet parameters of steam turbine.

Dehumidity efficiency of hollow stationary blade with suction slot

The droplet (diameter≤40 μm) average mass flow rate at 73% cross section was calculated based on the blade dimension and wet-steam parameters of 600 MW steam turbine. Considering the mass fraction of droplet within range of d = 40 μm, the mass flow rate equals 101.43 g/(m·s).

From the simulation results of water deposition rate in Section 4, it is known that the water deposition mass flow rate on pressure surface V₁=55.46 g/(m·s). And the water deposition mass flow rate on suction surface V₂= 9.02 g/(m·s), in which, a portion of V₂ is unable to be suctioned to the slot because these droplets deposited behind the location of the suction slot, and this portion of mass flow rate V₃=3.63 g/(m·s).

According the experiment data [11], the suction capability on the pressure surface V_p=12 g/(m·s), and on the suction surface V_s=7 g/(m·s). So, the dehumidity efficiency of hollow stationary blade with suction slot is,

{\eta }_p={\displaystyle \frac{\mathrm{12}}{\mathrm{55.46}}}\times \mathrm{100}\%=\mathrm{21.64}\%,

{\eta }_{\mathrm{s}}=\left(\mathrm{1}-{\displaystyle \frac{\mathrm{3.63}}{\mathrm{9.02}}}\right)\times \mathrm{100}\%=\mathrm{59.76}\%,

in which, η_p is the dehumidity efficiency of suction slot on pressure surface, η_s is the dehumidity efficiency of suction slot on suction surface.

Dehumidity efficiency of new hollow stationary blade

Using the same approach, the dehumidity efficiency of the new hollow stationary blade can be calculated. The water deposition mass flow rate on pressure surface V_{\mathrm{1}}^{\prime }=\mathrm{49.44}\mathrm{g}/(\mathrm{m}·\mathrm{s}). The water deposition mass flow rate on suction surface V_{\mathrm{2}}^{\prime }=\mathrm{5.733}\mathrm{g}/(\mathrm{m}·\mathrm{s}), in which the un-suctionable portion of mass flow rate V_{\mathrm{3}}^{\prime }=\mathrm{1.53}\mathrm{g}/(\mathrm{m}·\mathrm{s})..

So the dehumidity efficiency of the new hollow stationary blade is

{\eta }_p^{\prime }={\displaystyle \frac{\mathrm{12}}{\mathrm{49.44}}}\times \mathrm{100}\%=\mathrm{24.27}\%,

{\eta }_{\mathrm{s}}^{\prime }=\left(\mathrm{1}-{\displaystyle \frac{\mathrm{1.57}}{\mathrm{5.733}}}\right)\times \mathrm{100}\%=\mathrm{72.61}\%.

Discussion

Comparing the isograms of stagnation pressure in the flow passage of the new blade with that of the ordinary blade, little difference is found in the general distribution. It can be concluded that if the steam pressure from the blowing slot is suitable, the power capability of steam flow would not be changed. The new blade has a great application prospect because it does not sacrifice the generating efficiency of the steam turbine to evaluate the dewetting ability.

From the simulation results of liquid phase and calculation, it is found that the liquid density, droplet growth rate and critical radius have been declined on the suction surface and pressure surface. This consequence is caused by the introduction of the blowing slot which can prevent the droplet deposition and growing process. In addition, the high-parameter steam blowing from the slot would also evaporate some tiny droplets to decrease the amount of deposition, which could be seen from the variation of liquid density in simulation results.

In general, the combination technology could effectually improve the dehumidity efficiency in the last stage of steam turbine, in which the technology of blowing slot and suction slot was studied systematically, the safety and economical efficiency were proved in the actual operation in power plants. On the other hand, if there is no construction restriction this new model could be used on the steam turbines in the thermal power stations with ultra supercritical or supercritical parameters or in nuclear power plants.

Conclusions

In this paper, the two-phase flow of wet steam and the droplet deposition at the last stage of static blade of a steam turbine in SC power plants were simulated. The good agreement between the simulation results and the experimental data proved the reliability of these simulation and calculation methods in this paper.

A conversion calculation method was introduced to calculated the dehumidity efficiency of the ordinary hollow stationary blade with suction slot. The results show that the dehumidity efficiency of the ordinary dewetting technology cannot remove all the water film deposited on the blade surface. The dehumidity efficiency on the pressure surface and suction surface are 21.64% and 59.76%, respectively.

In order to improve the dehumidity efficiency, a combination technology with blowing slot was introduced into the existing hollow stationary blade with suction slot. The simulation results indicate that, through the blowing activity of the steam flow from the blowing slot, the new blade could not only decrease the amount of secondary droplet caused by the primary droplet at the trailing edge of the blade, but also improve the dehumidifying efficiency of suction slot from the view of water film reduction on the blade surface. The new blade suggested in this paper can increase the dehumidity efficiency on the pressure surface and suction surface to 24.27% and 72.61%, respectively.

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