семинары / семинар 4 / Wet_Steam_Turbines_for_Nuclear_Power_Plants_By_Alexander_S_Leyzerovich

Design 165

Transitioning to a half-speed turbine theoretically allows designers to quadruple the annular exit area by doubling the LSB length. But in practice, the maximum LSB length of low-speed turbines does not exceed one-and-a-half times that of high-speed turbines (compare Tables 3–3 and 3–4). The explanation for this lies in the fact that the increased length unavoidably lowers the aerodynamic quality of the blades and makes their design more complicated because of the large length-to-mean diameter ratio and an increased pitch of the meridional stage profile. Maintaining an optimal circumferential speed-to-steam velocity ratio, the increased mean diameter results in an increased enthalpy drop and, as a result, a greater difference in the specific steam volume values between the blade row entrance and exit. High, supersonic steam velocities and their great variations along the row height hinder the achievement of optimal aerodynamic performances. In addition, the erosion impact of wet steam becomes more serious with longer LP stage blades.Thus, the closer the LSB is to its limiting length, the smaller the gain in efficiency, and the higher the cost of this gain. Nevertheless, there still exists a substantial margin for increasing the size of low-speed steel LSBs, whereas for high-speed steel LSB, such a margin has practically run out.

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166 Wet-Steam Turbines for Nuclear Power Plants

Table 3-4. Main characteristics of some LSBs for low-speed steam turbines of various manufacturers

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This is evident in the diagram composed by ABB and shown in Figure 3–39, where the dimensions of actual LSBs developed by various turbine manufacturers are plotted against their theoretical size limits. In theory, besides the tensile stress caused by centrifugal force, the LSB length is also limited by some additional factors, including: the bending stress in the root section caused by steam forces, blade vibration frequency, and tensile stress in the LP rotor due to the centrifugal load from the LSB. However, more often than not, these factors are rather secondary.

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168 Wet-Steam Turbines for Nuclear Power Plants

Fig. 3–39. Parameters of actual LSBs provided by various manufacturers (1: combined blade stress and cascade geometry limit; 2: rotor stress limit; 3: blade frequency limit; St: steel LSBs;Ti: titanium LSBs; S: annular exhaust area per flow; rt: tip radius; rh : hub radius; h : blade height; dm: mean blade diameter)

Source :A. P.Weiss60

It is not currently possible to radically increase the length and annular exit area of high-speed LSBs other than by transition to manufacturing the blades from titanium alloys (for example,Ti-6Al-4 V).As a rule, titanium alloy blades are called merely “titanium.” The density of titanium alloys is approximately 1.8 times less than that of steel, with the same, or even greater, strength. Because of this, the length of titanium buckets can be extended appreciably. On the other hand, titanium LSBs are considerably more expensive compared to steel ones and are much harder to machine. Nevertheless, even former critics of titanium LSBs have presently turned to developing and implementing them, and every major turbine producer disposal has made turbines with titanium blades commercially available. The effectiveness of titanium LSBs has been well proven in operational practice.61 A typical modern 1,093-mm (43-in) titanium LSB (for the rotation speed of 3,000 rpm) developed by Hitachi is shown in Figure 3–40.

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Design 169

An important additional advantage of titanium is its lesser susceptibility to erosion and corrosion compared to stainless steels. Because of this, some turbine producers also proposed using titanium blades for intermediate LP stages operating in the Wilson region, even though this might turn out to be too expensive in practice.

Fig. 3–40. Hitachi’s 43-in titanium-alloy LSB

Source : M. Machida, H.Yoda, E. Saito, and K. Namura62

With an increase in the length of the LSB, not only does the tensile stress caused by centrifugal forces grow, but the danger of WDE also increases. Longer LSBs are also more intensely heated under operating conditions of low flow and high backpressure because of friction and fanning in the ambient steam.This also lowers the blades’ strength and requires special attention to be paid to the operating conditions. These phenomena are not specific to wet-steam turbines, but are rather typical for all modern condensing steam turbines with long LSBs.

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170 Wet-Steam Turbines for Nuclear Power Plants

Roots, shrouds, and snubbers

For many years, the most widespread type of attachment bases for LSBs was a prong-and-finger (or fork-shaped) root with varying number of prongs. For example, Hitachi’s 1,016-mm (40-in) and 1,092-mm (43-in) titanium LSBs were made with sevenand nineprong roots, as shown in Figure 3–40. However, in recent years, most modern LSBs have been designed with curved-entry fir-tree roots. This attachment type is employed by almost all of the world’s major steam turbine manufacturers63

For computational calculations of the blade stress state, the LSB is digitally modeled together with its attachment base and the adjacent steeples on the rotor surface with regard to possible clearances in the joint. An example of such a 3-D finite-element model for an MHI 1,143-mm (45-in) steel LSB with a fir-tree root (for the rotation speed of 3,600 rpm) is presented in Figure 3–41.Another 3-D finite-element model example with the resultant relative stress field for Toshiba’s 1,067-mm (42-in) steel LSB (for the rotation speed of 3,000 rpm) is given in Figure 3–42. The 3-D models sometimes comprise several buckets connected by a shroud, tie-bosses, or arch bands. 64

Fig. 3–41. Computational 3-D model for calculating the stress state and vibrational characteristics of MHI’s 1,143-mm titanium LSB with its root and adjacent steeple

Source : E.Watanabe, H. Ohyama,Y. Kaneko, et al.65

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Design 171

Fig. 3–42. Three-dimensional calculation mesh and relative stress field for Toshiba’s 1,067-mm LSB

Source : S. Hisa,T. Matsuura, and H. Ogata66

The curved-entry fir-tree dovetail is currently the most suitable attachment structure for the longest LSBs. The compactness of the dovetail enables a thinner wheel configuration, and it reduces the centrifugal stress in the rotor body. In addition, the fir-tree root does not have any sharp edges or pin holes. This is especially important for blades made of titanium alloys, which are relatively brittle and sensitive to notches. In determining the dovetail shape and its machining tolerance, the difference in elasticity between the materials of the blade root and disk wheel should be considered. Of special importance for the curved entry fir-tree dovetail is a uniform distribution of load on all the blade root hooks.67 The stress contours and maximum stress values related to the tensile strength for the blade and wheel dovetail of Hitachi’s 1,016-mm (40-in) LSB under conditions of the rated rotation speed of 3,600 rpm are shown in Figure 3–43a. The maximum centrifugal stresses take place at the corner of the top hook for the blade root and at the corner of the bottom hook for the wheel dovetail. Their values are sufficiently lower than the material tensile strength. The load on each hook ranges from approximately 20% to 30% of the total load under normal conditions.

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172 Wet-Steam Turbines for Nuclear Power Plants

However, these fractional loads can be affected by errors while machining the dovetail, with resultant initial clearances on the individual hook surfaces. In Figure 3–43b, the dotted line indicates the total load on all the hooks, and the solid lines refer to the load on the individual hooks. As the rotor speed increases, the lower hooks come into contact, and the load on the hooks is equalized, but the portion for the top hook remains approximately 5% higher compared with normal conditions.

Fig. 3–43. Centrifugal stress contours and maximum stress values related to the tensile strength for 1,016-mm titanium LSBs with a fir-tree dovetail (a) and load distributions on hooks with machining errors (b)

Source :T. Suzuki, M.Watanabe, and M.Aoyama68

Modern turbine blades, including LP ones, are mainly manufactured integrally shrouded—the shrouding elements are milled together with the bucket’s profiled body.The shrouding elements of the individual blades are connected by special inserts in a wedge-shaped groove like a dovetail joint or are designed with special wedge-shaped edges that engage the blades in mesh under action of centrifugal forces. This second approach is predominantly applied to modern LSBs (Fig. 3–44).To increase the rigidity of the entire blade structure, the blades are additionally coupled with a snubber—integral tiebosses at the midspan of the blade height (Fig. 3–40). Their edges also engage under action of centrifugal forces. As a result, when the turbine rotates, all of the LSBs are tied together, forming a continuous ring of blades. One of the major advantages of such a continuous

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Design 173

annular blade structure, compared with blade sectors (several units of several blades each) more conventional in the past, is that it has fewer resonance points during rotation. An example of a vibration mode analysis of an LSB wheel is presented in Figure 3–45. This type of engaging LSBs is widely used by Japanese turbine producers (Hitachi, MHI, and Toshiba), as well as some European manufacturers. According to ALSTOM, this structure, with two contact supports (tie-bosses situated at 70% of the blade height and an integral shroud at the blade tip), applied to a 1,360-mm steel LSB (for the rotation speed of 1,500 rpm), reduces the maximum additional dynamic (vibrational) stress in the blade body by a factor of two to three times as much as that for free-standing blades. This type of connection produces well-defined and easily controlled vibration modes and significantly reduces the buffeting stresses arising when the LSBs are subjected to low steam flow and high back-pressure conditions.69

Fig. 3–44. Connection of shrouding elements of the LSB with wedge-shaped edges

Source : E.V. Levchenko,V. P. Sukhinin, B.A.Arkad’ev, et al.70

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174 Wet-Steam Turbines for Nuclear Power Plants

Fig. 3–45. Example of vibration mode analysis for a last stage wheel with “continuous cover blades” of Hitachi

Source: M. Machida, H.Yoda, E. Saito, and K. Namura71

Some other leading turbine producers, including Siemens and ABB, for many years have successfully used free-standing LSBs, not connected by shrouds, mid-span damping wire ties, or tie bosses. It might be well to note that although shrouding the blades typically reduces leakage losses, this is compensated by more effective peripheral water separation for unshrouded blades. In turn, the mid-span damping devices cause the increase in the airfoil thickness in their neighborhood, increasing profile losses. In addition, all of the obstacles in the interblade channels (like tie-bosses or wire ties) disrupt the steam flow and lead to additional energy losses. Of importance is that any local wetness concentration in the stage channels contributes considerably to blade erosion. In particular, this concerns wire ties and tie-bosses between the blades and brings another point in favor of using free-standing LSBs, as well as shrouded blades without any additional ties in the preceding stages. Free-standing LSBs manufactured by ABB and Siemens can be seen in Figures 3–7, 3–8, and 3–10a. New families of free-standing LSBs developed by Siemens for newly designed and refurbished turbines, including those for nuclear power plants, are shown in Figure 3–46.72 Along with this, the use of free-standing LSBs is possible only up to a certain threshold length.

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