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54 Wet-Steam Turbines for Nuclear Power Plants

Fig. 2–8. Various forms of water existing in a wet-steam turbine stage

Source : M. J. Moore20

Wet-steam flow in turbine blade rows

When the final point of steam expansion in a turbine row lies in the wet region (that is, below the saturation curve delineated by x = 1), it is significant whether the process begins at a point lying above this curve or below it. In the first case, the superheated steam usually does not have time to condense; the expansion process occurs without creating a liquid phase and discharging the latent heat of evaporation. As a result, the final steam temperature, t2 turns out to be less than the

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The Thermal Process in Wet-steam Turbines 55

saturation temperature, tsat, at the pressure after the turbine row, p2.This temperature difference, ∆t tsat –t2 , is known as the degree of subcooling, or supersaturation. It is related to the velocity of steam expansion:

the greater the degree of subcooling. It also depends on the initial steam pressure, decreasing when it increases. Subcooling values of 15–25°C were already obtained in the 1930s by Aurel Stodola, 21 but modern supersonic nozzles have made it possible to increase this value to 30–45°C.The specific volume of subcooled steam is less than that in the case of equilibrium expansion, resulting in a decrease of the available energy. The relative value of this decrease is called the subcooling loss.

The subcooled steam is not in a stable state. It occurs only in the course of a dynamic process and disappears as soon as thermodynamic equilibrium is established. Subcooled steam, being in a metastable state, passes into a thermodynamically stable state as the liquid phase arises. The condensation process commences spontaneously (that is, without any external forces acting on the steam) as a quantum change around the water microdroplets, which appear randomly in the flow and act as condensation centers, provided their diameters exceed a certain critical value.This critical diameter decreases with an increase of subcooling. Presently, researchers accept indisputably that just spontaneous nucleation after a limited degree of supersaturation is the main process responsible for creation of the liquid phase in the turbine steam flow. With the increase in enthalpy difference in the wet-steam region, the degree of steam subcooling increases, and the microdroplets’ critical diameter decreases. This promotes creation of the condensation centers and initiates condensation shocks, which are similar to compression shocks in aerodynamics.As the critical diameter of the condensation centers decreases, the average diameter of drops

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56 Wet-Steam Turbines for Nuclear Power Plants

provoking spontaneous condensation also decreases. Some generalized dependencies relating to the change of the maximum achievable subcooling degree, ∆t = tsat –t2, and the critical droplet radius, rcr, with the steam expansion velocity, p, and initial saturated steam pressure, p0s,(as applied to the LP stage channels) are shown in Figure 2–9.

Fig. 2–9. Changes of maximum achievable subcooling temperature and critical droplet radius with initial saturated steam pressure, p0s, and steam expansion velocity (1: p0s = 0.1 MPa; 2: p0s = 0.05 MPa; 3: p0s = 0.03 MPa; 4: p0s = 0.02 MPa) Source: B. M.Troyanovskii, G.A. Filippov, and A. E. Bulkin22

Subcooled (supersaturated) dry steam is described by the same thermodynamic state equations as superheated steam. This means that the Mollier diagram for this medium is obtained by extrapolating the curvilinear isobars and isotherms that apply for the superheated range. Because of the considerable delay related to subcooling, steam begins to condense not at x = 1, but at the steam dryness value corresponding to the diagram steam conditions xw< 1.The family of curves for constant values of xw are known as Wilson lines. Because the value of xw depends on the pressure decline rate, p (which, in turn, depends on the blade row’s size and profiles, stream conditions, and steam pressure), it is more reasonable to talk about a certain Wilson region enclosed by the lines corresponding to the actual characteristic values p; that is, xw(p). In the range of p values between 10 and

10,000 sec–1 , the Wilson region occupies the range of steam dryness values xw = 0.977-0.963 (Fig. 2–10a).

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The Thermal Process in Wet-steam Turbines 57

Fig. 2–10. Steam expansion process with subcooling shown on h-s axes (a:Wilson lines xw = const depending on p, isobars in the wet-steam region for subcooled steam)

In calculating values in the zone between the saturation curve where x = 1 and the Wilson line, xw it is acceptable to take thermodynamic steam properties like those for superheated steam. It is also possible to draw conventional isobars for subcooled steam within this zone in order to obtain the values of the actual available energy, H 0 , taking into account the subcooling loss calculated as:

where H0 is the available energy of the process, and H0 is the enthalpy difference corresponding to the isentropic expansion process, but reduced because of the smaller steam temperature and specific volume (Fig. 2–10b).According to theoretical estimates, if the initial pressure, p0 is not too great, this value can be calculated as:

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58 Wet-Steam Turbines for Nuclear Power Plants

where p0 and v0 are the initial pressure and specific volume of steam, respectively, ε = p/p0 is the steam pressure ratio, and k is the isentropic index, which can be taken equal to that for superheated steam under the initial pressure p0. If p0 > psat, the pressure ratio is assumed to be related to psat, and all of the steam parameters in Equation 2.3a are taken for the saturation curve. This equation can be approximated with good accuracy by the following empirical expression:

For ε = 0.5, ζsc= 0.4.A further reduction of ε < 0.5 corresponds to conditions of spontaneous condensation (Fig. 2–11).

Fig. 2–11. Energy loss with subcooling of wet steam depending on pressure ratio (1: calculated data for subcooling; 2: zone in which spontaneous condensation begins)

Source:A.V. Shcheglyaev23

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The Thermal Process in Wet-steam Turbines 59

Computation techniques have been developed by different research institutions and turbine manufacturers for simulating the expansion processes for saturated steam with non-equilibrium spontaneous condensation.24 Their results show good agreement with experimental data, indicating that these techniques can be used for designing turbine blade profiles that operate near the Wilson region with minimal subcooling losses.

If the expansion process begins at the point with initial steam wetness (as it does for most stages of wet-steam turbines), condensation is also influenced by the steam conditions at the row inlet. The most influential factor in this process is the size of water drops. For a two-phase steam-water mixture as the working fluid, the thermal processes in rows and cascades are somewhat ambiguous and intricate, because of variations in the liquid concentration and drop sizes, their uneven dispersion at the row inlet, and the differences in stream direction and velocity between the water drops and the steam stream. The drop traces within the row channels are materially different, depending on the drop diameter, d (Fig. 2–12). The smallest drops (with d < 1–5 mkm, or 0.04–0.2 mil) closely follow the main stream and pass through the channel without colliding against the profile surfaces and settling on them. The larger drops deviate from the stream lines to a degree depending on the drop’s size—the larger the drop, the greater the deviation. And, finally, the largest drops (d > 50–100 mkm, or 2–4 mil) can move through the row channel almost independently of the steam stream line and come onto the concave profile face; some of them break up against the profile edges.These drops slip along the concave profile surface generating water films, separate from the surface, collide against the opposite surface, and are reflected back again. A general pattern of their flow is shown in Figure 2–13.The drops in streams 1 and 2 of this sketch have the largest size and the smallest velocity.

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60 Wet-Steam Turbines for Nuclear Power Plants

Fig. 2–12. Drop paths of water in a nozzle channel depending on the drop size (a: inlet drop d < 1 mkm; b: inlet drop d 10 mkm; c-I: inlet drop d = 2 mkm; c-II: inlet drop d = 20 mkm, c-III: inlet drop d = 200 mkm)

Source :A.V. Shcheglyaev25

Fig. 2–13. General pattern of water motion within a nozzle channel (1: water drops along the edges; 2 and 3: water drops separating from the convex blade surface; 4: droplets reflected off the concave blade surface)

Source :A.V. Shcheglyaev26

Variations in the energy losses in an annular nozzle row placed behind the preceding turbine stage, based on the initial steam wetness and drop size, are shown in Figure 2–14a. A characteristic feature is an increase in energy losses if the expansion process commences near the saturation curve.This is explained by the substantial instability of the liquid condensation process.With transference of the saturation curve and the appearance of fine-droplet liquid in the preceding stage, the energy losses in the row sharply decrease because of less subcooling and more balanced condensation. The energy losses

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The Thermal Process in Wet-steam Turbines 61

begin to increase again with further increases in the initial wetness (y0 > 0.03).This is mainly related to mechanical interaction between the phases. Larger water drops at the stage inlet cause greater energy losses, which increase with greater steam wetness values.

Fig. 2–14. Experimental characteristics of energy losses (a) and flow amount factor (b) for slightly superheated and wet steam (I: critical drop d 40 mkm; II: critical drop d 0.4 mkm; 1: water drop r = 500 mkm; 2: water drop r = 200 mkm; 3: water drop r = 100 mkm; 4: water drop r = 10 mkm)

Source : B. M.Troyanovskii, G.A. Filippov, and A. E. Bulkin27

The flow amount factor values for wet steam also differ from those for superheated steam. This factor, µ , is the ratio between the actual steam flow amount through the row and the flow amount for the steam expansion process if it were isentropic. For the nozzle rows with superheated steam, the flow amount factor value, µ1 , can be accepted equal to approximately 0.97, and for the rotating blade rows, it varies between 0.89 and 0.97, depending on the relative blade length, l/b, and the flow turn angle, ∆β . The longer the blades and the smaller the flow turn angle, the less the aerodynamic resistance of the channels and the closer the flow amount factor value to 1.0. Experiments show that for wet steam this factor is greater than that for superheated steam (Fig. 2–14b).This effect also increases with an increase in the water drop diameter.

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62 Wet-Steam Turbines for Nuclear Power Plants

As a first approximation for the nozzle rows, the flow amount factor ratio for wet and superheated steam can be presented by the following equation:28

where x1 is the steam dryness downstream of the row at equilibrium expansion. For rotating blades of impulse-type stages, the flow amount factor depends on the enthalpy drop. If the steam pressure values upstream and downstream of the blade row are equal (that is, the channel has a constant section area and the stage is purely of an impulse type), the flow amount factors for wet and superheated steam are approximately equal. In a general way, this dependence is shown in Figure 2–15, and can be approximated by the following equation:

where Y = 1 – (sinβ2/sinβ1). It is important that for wet steam the flow amount factor > 1.0. The explanation for this lies in the fact that the actual specific volume of wet steam is less than that assumed for thermodynamic equilibrium, and this effect outweighs the influence of the decreased velocity and a certain obstruction of flow by water streams.

Fig. 2–15. Influence of wetness in the exit section of a turbine blade row on the flow amount factor, where Y = 1 – sinβ2 / sinβ1

Source :A.V. Shcheglyaev29

Another important characteristic of a two-phase flow that influences the blade row performance is a slide factor, which is determined

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The Thermal Process in Wet-steam Turbines 63

as the ratio between the average velocities of the water drops and the steam: ν = c'/c". This factor has an important influence on the efficiency and erosion reliability of the turbine stages, as well as influencing the possibility of water separation within the turbine steam path. An analysis of water distribution and its dispersion downstream of the turbine rows shows that a substantial portion of the liquid phase in the flowing steam-water mixture is in the form of large drops, and their mechanical interaction with the steam and the profile surfaces is essential. This influence is largely determined by the steam wetness, y, and the specific volume ratio for the steam and water phases, which in turn depends on the steam pressure. This specific volume ratio decreases with an increase in steam density.These relationships are confirmed by experimental data (Fig. 2–16).

Fig. 2–16. Influence of initial steam pressure, p0 , and wetness, y0, on the slide factor for a supersonic nozzle

Source : B. M.Troyanovskii30

The influence of wetness on wet-steam turbine efficiency

The amount of steam wetness significantly affects all turbine row characteristics: the amount of energy losses, flow amount factors, flow exit angles, and so on. The presence of moisture in the steam flow also changes all of the characteristics of wet-steam turbine stages, as compared with stages working on gas or superheated steam.

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