CURRENT STATE AND PROSPECTS FOR SOLVING THE PROBLEM OF MOISTURE LOSSES IN STEAM TURBINES

S. V. Polozhii

(Presented by the scientific seminar of the Department of TPP)

The operation of steam turbines in the wet-steam region is characterized by low efficiency. The urgency of solving the problem of increasing efficiency in the wet-steam region is continually growing, in connection with the enormous scale of construction of high-capacity condensing turbines with highly developed LPCs and the significant production of electrical energy in the country using wet steam. Over the last ten to twelve years, numerous studies have been carried out in our country at LPI, BITM, MEI, NZL, KhTZ, and others; a large number of works have been published on the problem of moisture losses in steam turbines, and recommendations have been given for calculating moisture losses in the LPCs of steam turbines. However, the results of these studies do not reflect the actual moisture losses in full-scale steam turbines. The formulation and methodology of experimental investigations of moisture losses are not based on a correct understanding of adiabatic condensation and of the thermodynamic and physical features of the operation of an experimental stage during the transition from superheated to wet steam, and therefore are not capable of satisfactorily solving this important problem. The use of such recommendations for determining moisture losses in turbine construction leads to the design and operation of modern steam turbines in the wet-steam region under nonoptimal conditions, with deliberately reduced economy. As a result, not only is this problem not solved, but significant damage is also caused in the form of excessive fuel consumption at condensing thermal power stations.

The kinetics of adiabatic condensation in the flow path of a turbine—the number of phase-formation centers, the intensity of the process, the growth of liquid droplets and their breakup, the dispersity and structure of the flow, and the metastability of the process—is determined, as in adiabatic steam formation, by the magnitude, nature, and interval of the pressure drop. Therefore, the problem of creating highly economical turbines operating in the wet-steam region cannot be solved without studying the kinetics of adiabatic condensation and the factors affecting it under conditions of interaction between the flow and the structural elements of the turbine flow path. Contemporary researchers of moisture losses in steam turbines do not yet stand on such positions [1, 2]. Experimental and theoretical investigations of moisture losses are therefore being carried out by contemporary researchers on artificially obtained wa-

air or water–steam mixtures, the results of which are transferred to the operation of stages in the wet-steam region, to the process of adiabatic condensation. A mechanical mixture, which is obtained in air turbines by injecting water into the air flow ahead of the stage, cannot be identified with the process of formation of the liquid phase during the expansion of wet steam in steam turbines, during adiabatic condensation—the continuous change of phases, the formation, growth, and breakup of liquid droplets, etc. This mechanical water–air mixture, in terms of the dispersion of the flow, the trajectories and velocities of motion of the liquid droplets, etc., does not reflect similar flow characteristics in full-scale stages during adiabatic condensation. Experimental investigations of moisture losses on a water–steam mixture have found still wider application. Such a mixture is obtained by cooling superheated or saturated steam by injecting cold water through nozzles. Evaporation of part of the liquid at constant pressure brings the steam to the required temperature. The water content in the steam (moisture) is determined as the difference between the amount introduced and the water discharged to the drains. Such a water–steam mixture also differs sharply from a flow with adiabatic condensation in full-scale stages. The sizes of the liquid droplets, their distribution over the flow cross section, the velocities of motion and interaction with the steam flow in experimental turbines do not model and do not reflect the natural process of adiabatic condensation. The installation of screens ahead of the turbine in the path of motion of the water–steam mixture also cannot bring these heterogeneous processes in experimental turbines and full-scale stages closer together. Therefore the results of studies of moisture losses in experimental steam turbines cannot be extended to full-scale stages with adiabatic condensation of steam [3].

Another still more significant shortcoming of modern investigations of moisture losses is the erroneousness of the very methodology of experimental investigations in test turbines. According to the modern methodology, the moisture loss in experimental turbines is determined by comparing the efficiency when it operates on superheated and wet steam, or from the result of the change in torques when changing over from superheated to wet steam. This difference in efficiency or torques when changing over from superheated to wet steam is entirely attributed to the loss from droplet moisture (the expenditure of energy for breaking up the film and accelerating the liquid droplets, the loss of energy from the impact of droplets on the working blades, and from steam supercooling). When a stage is changed over from superheated to wet steam, a change occurs in the physical and thermodynamic properties of the wet steam: the theoretical work capacity of the wet steam decreases; its density increases; the outflow velocity decreases; the velocity ratio changes, etc., in comparison with the corresponding indices of superheated steam; the design characteristics of the stage, the inlet and outlet angles, the curvature of the blades, etc., become off-design. As a result of the action of only these factors, the operation of a stage on wet steam will always have a lower efficiency and a lower torque value relative to the operation of the stage on superheated steam. The possibility of conducting tests in experimental turbines under identical conditions for superheated and wet steam (maintaining equality of the theoretical heat drops, initial and final pressures, steam density, etc.) is practically excluded because of the incompatibility of these indicators. This circumstance makes it impossible, in experimental investigations, to avoid a decrease in efficiency when changing over from superheated to wet steam for this reason. To account for this difference in stage efficiency when changing over from superheated to wet steam, it is necessary to develop a special methodology for de-

the determination of stage losses from changes in the physical and thermodynamic properties of the steam. With such an experimental arrangement it is possible to determine in experiments the true value of the stage loss due to droplet moisture and the individual components of this loss. However, such experimental data likewise cannot be recommended for the design of steam turbines, owing to the discrepancy between the structure and dispersion of the flow in experimental turbines with a water-air or water-steam mixture and the flow of wet steam in full-scale stages under adiabatic condensation.

Another important question that must be solved in investigating losses due to moisture is the allowance for, or modeling of, the design characteristics of experimental and full-scale stages. For this reason, the results of modern experimental and theoretical investigations of moisture losses also cannot be transferred to full-scale stages without taking into account the entire diversity of designs and operating conditions of full-scale wet-steam turbines.

From this brief analysis of modern investigations of moisture losses in steam turbines, the unsatisfactory state of the solution of this problem and the unsuitability of present experimental and theoretical data on moisture losses for industry become evident.

As an example of this, one may cite the investigations of MEI on moisture losses in steam turbines [4]. In [4] an analysis is presented and recommendations are given for determining moisture losses on the basis of many years of experimental investigations using the moment characteristics of stages. This method of experimental investigation of moisture losses, in the opinion of MEI, made it possible to obtain the qualitative influence of energy losses due to moisture on the economy of steam turbines. By measuring the magnitude of the torque, especially with a braked rotor

\[ \left(\frac{U}{C_0}=0\right), \]

enclosed in a floating sleeve, during operation on superheated steam near the saturation line \((M_{\mathrm{p}})\) and on wet steam \((M_{\mathrm{w}})\), in [4] the moisture loss is obtained as the ratio

\[ \frac{\Delta M}{M_{\mathrm{p}}} = \frac{M_{\mathrm{p}}-M_{\mathrm{w}}}{M_{\mathrm{p}}} \]

or

\[ M_{\mathrm{w}}=M_{\mathrm{p}}-\sum_{i=1}^{n}\Delta M_i . \]

The relative internal efficiency of the stage is determined by this method from the expression

\[ \eta_{0i}^{\mathrm{w}} = \eta_{0i}^{\mathrm{p}} - \eta_{0i}^{\mathrm{p}} \left[ \left(\frac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{p}} + \left(\frac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{r}} + \left(\frac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{ud}} \right], \]

where \(\Delta M/M_{\mathrm{p}}\) is the energy loss for subcooling \(\xi_{\mathrm{p}}\),

\[ (\Delta M/M_{\mathrm{p}})_{\mathrm{r}} \]

is the energy loss for breakup of the film and acceleration of droplets in the axial clearance \(\xi_{\mathrm{r}}\),

\[ (\Delta M/M_{\mathrm{p}})_{\mathrm{ud}} \]

is the energy loss from the off-design angle of moisture entry onto the moving blades and separation into the peripheral zone \(\xi_{\mathrm{ud}}\).

The structure of these formulas and the methodology of the experimental investigations are based on comparing the operation of a stage on superheated and wet steam—by the total reduction in torques and stage efficiency on wet steam, considering this only as the result of the presence

moisture in steam and its interaction with steam and with the structural elements of the stage ($\xi_{\mathrm{p}}$, $\xi_{\mathrm{r}}$, $\xi_{\mathrm{ud}}$). With such a formulation, studies do not assume and completely fail to take into account the main causes of the reduction in the torques and efficiency of a stage in the transition from superheated to wet steam, owing to changes in the thermodynamic and physical properties of wet steam, as discussed above.

Using the same experimental data [4], it is possible to show the erroneousness of the modern methodology for studying moisture losses and of the conclusions regarding the nature and magnitude of moisture losses in [4] (Table 1).

Table 1

Reduction in heat drop, working capacity, and stage torques
in the transition from superheated to wet steam at $\dfrac{U}{C_0}=0$, $E=P_1/P_0=0.85$

The relative decrease in the working capacity of wet steam at zero loss due to droplet moisture (col. 2 of Table 1) has the same pattern as the reduction in torques in [4], which in [4] are determined only on account of droplet moisture $\xi_{\mathrm{p}}$, $\xi_{\mathrm{r}}$, $\xi_{\mathrm{ud}}$ (Table 1, col. 3).

The absolute divergence of the working capacity and torques in the transition from superheated to wet steam, at an unchanged pressure ratio in the stage, depends on the magnitude of steam superheat ($H_0^{\mathrm{p}}$), relative to which the working capacity of wet steam is compared. The separation of the torque curves in the MEI experiments (Fig. 1) for a rotating rotor increases with increasing moisture content and velocity ratio $\dfrac{U}{C_0}$. This is also explained to a considerable extent by the change in the working capacity and physical properties of wet steam, and not only by the impact entry of liquid droplets onto the rotor blades, as presented in [4]. At constant steam moisture $y_0$ and $P_1/P_0$, with an increase in $\dfrac{U}{C_0}$ the loss due to stage friction [1] increases and, correspondingly, the stage torque decreases. At low moisture content, the decrease in torque becomes imperceptible with respect to $\dfrac{U}{C_0}$ (points C and D in Fig. 1) because of the low disk rotational speeds—the small difference in disk-friction losses. The decrease in torque during the transition of a stage from more superheated to less superheated or sat-

...value steam (Fig. 1, points B and C) is entirely explained by the change in the working capacity and physical properties of the steam when the stage operates on steam of lower potential without moisture formation. The decrease in torque in [4] when the stage passes from superheated to wet steam depends on the magnitude of the pressure drop across the nozzle cascade \(\varepsilon=P_1/P_0\)

Fig. 1

also depends on the working capacity of the superheated steam, and not only on the expenditure of energy for accelerating and breaking up droplets in the axial clearance, as is presented in [4]. For example, for a steam moisture content \(y_0=9\%\), at \(P_1/P_0=0.9\%\) \((P_1=0.5\ \text{ata},\ P_0=0.55\ \text{ata})\), the relative decrease in the working capacity of wet steam is about 30%! By the corresponding amount the torque of the stage is reduced when it operates on wet steam.

Fig. 2

As the pressure ratio on the stage is increased to \(\varepsilon=0.4\) \((P_0=1.25\ \text{ata},\ P_1=0.5\ \text{ata})\), at the same steam moisture content ...

for 9%, the reduction in the working capacity of wet steam is only 16%. The position of the MEI experimental curves (Fig. 2) follows this dependence, obtained without taking into account the loss due to fragmentation and acceleration of liquid droplets in the axial clearance. For example, for a steam moisture content of 9% at \(\varepsilon = 0.9\), the reduction in torque \(\Delta M/M_{\mathrm{p}}\) is 13%, whereas for \(\varepsilon = 0.4\) and the same moisture content it is only 3.5% (Fig. 2). This reduction in torques in [4] is attributed entirely only to the droplet moisture content \(\varepsilon_{\mathrm{p}}\). The same applies to the balance of losses and to the reduction in the relative internal efficiency of the stage during the transition from superheated to wet steam, presented in [4] (Fig. 3), which likewise do not reflect the actual losses from droplet moisture \((\xi_{\mathrm{p}}, \xi_{\mathrm{r}}, \xi_{\mathrm{ud}})\). The lower values of \(\eta_{0i}^{\mathrm{w}}\) for wet steam (curve 2, Fig. 3) are explained primarily by the lower working capacity of wet steam at an unchanged pressure ratio in the stage for superheated and wet steam.

Thus, for example, at \(\varepsilon = 0.5\) \((P_{0}=1\ \mathrm{ata},\ P_{1}=0.5\ \mathrm{ata})\), the theoretical working capacity of superheated steam, \(H_{0}^{\mathrm{p}}\), is \(28\ \mathrm{kcal/kg}\) \((t_{0}=145^\circ\mathrm{C},\ t_{1}=80^\circ\mathrm{C},\ X=1.0)\), while that of wet steam is \(24\ \mathrm{kcal/kg}\) \((y_{0}=7\%,\ y_{1}=10\%)\). If the heat losses in the stage during operation on superheated and wet steam are assumed equal to \(5\ \mathrm{kcal/kg}\), the relative internal efficiency of the stage for superheated steam will in this case be 82%, and for wet steam, 79%. Taking into account the higher losses in the wet-steam stage [1], the difference in \(\eta_{0i}\) for wet and superheated steam (curves 2 and 1 in Fig. 3) will be more significant. An increase in moisture content acts in the same direction. Along with this, in [4] there are obvious inconsistencies in the loss balance shown in Fig. 3 with the definition of these losses in the text of [4]. The loss due to acceleration and fragmentation of liquid in the axial clearance does not depend on \(U/C_{0}\), and its maximum value was determined with a braked rotor at \(U/C_{0}=0\), whereas in Fig. 3 this same loss depends on \(U/C_{0}\). The loss due to steam supercooling in the nozzles in one case also depends on \(U/C_{0}\) when it is determined with a braked rotor, while in the other case—in Fig. 3—this loss depends on \(U/C_{0}\), and at \(U/C_{0}=0\) it also proves to be equal to zero.

Fig. 3

Comparison of the stage efficiency when operating on superheated and wet steam requires accounting for all losses both from droplet moisture and from changes in the stage operating conditions in the wet-steam region:

\[ \eta_{oi}^{\mathrm{wp}} = \eta_{oi}^{\mathrm{sh}} - \eta_{oi}^{\mathrm{sh}} \left\{ \left[ \left(\frac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{p}} + \left(\frac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{r}} + \left(\frac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{ul}} \right] + \left[ \left(\frac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{rs}} + \left(\frac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{tr}} + \left(\frac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{nr}} \right] \right\}, \]

where \(\eta_{oi}^{\mathrm{sh}} = K\left(\dfrac{M \cdot n}{G \cdot H_0}\right)\), \(\left(\dfrac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{rs}}\) is the change in torque due to the reduced working capacity of wet steam, \(\left(\dfrac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{tr}}\) is the reduction in torque due to an increase in the loss from disk friction in steam, and \(\left(\dfrac{\Delta M}{M_{\mathrm{p}}}\right)_{\mathrm{nr}}\) is due to off-design operating conditions of the stage on wet steam.

REFERENCES

1. S. V. Polozhii. On the question of the effect of steam moisture on the efficiency of a turbine stage. Proceedings of Higher Educational Institutions of the USSR, Power Engineering, No. 7, 1962.

2. S. V. Polozhii. Once again on the question of the effect of steam moisture on the efficiency of a turbine stage. Proceedings of Higher Educational Institutions of the USSR, Power Engineering, No. 3, 1963.

3. S. V. Polozhii. On the question of the kinetics of the process of steam condensation in a turbine stage. Proceedings of TPI, Vol. 137, 1965.

4. M. E. Deich, G. A. Fillipov, V. V. Pryakhin, O. A. Povarov. Energy losses arising during the flow of wet steam in a turbine stage. Thermal Power Engineering, No. 12, 1966.