Operation 317
Fig. 4–46. Comparison of measured and calculated metal temperatures in the HP flange (a) and IP flange (b) of the HP–IP cylinder casing of a K-500-60/1500 turbine at start-up (measured temperatures in the HP section: 1: steam in the intercasing space; 2: flange metal near the heated surface; 3: flange metal on the external insulated surface; calculated metal temperatures: 4: flange metal on the external insulated surface, 5: stud bolt at flange mid-height; 6: measured metal temperature differences across the HP flange width; 7: calculated metal temperature difference across the HP flange width; 8: measured metal temperatures in the IP steam admission chamber)
Source :V.A.Akerman, N. S. Gabrijchuk,V. B. Kirillov,A. S. Leyzerovich, et al. 134
Choosing the number and location of metal temperature measurements should be based on the implied mechanism for shaping the stress state and the assumed schema of stress calculations. For bulky and potentially critical high-temperature stator elements, the set of metal temperature measurements should provide all of the means to estimate the thermal-stress state of these elements. In addition to radial temperature differences, axial and circular temperature unevenness can also play a significant role. However, because the corresponding thermal fluxes are of secondary importance, they can be estimated by using temperature measurements on the external surface of the considered element, with emphasis placed on the temperature distribution across the element thickness. It is especially desirable to measure the metal temperature as close as possible to the heated surface where the metal temperature gradient is the greatest.
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318 Wet-Steam Turbines for Nuclear Power Plants
Experimental acquisition of the data about the boundary heat conditions in the whole range of their variations may be the most important part of the start-up tests.This primarily concerns the temperature of steam sweeping the potentially critical elements. Depending on the turbine design features, they may be the steam-chests of the HP stop and control valves, casings of the high-temperature cylinders in the inlet and first-stage chamber zones, and/or rotors in the steam admission and first-stage zones. For wet-steam turbines, the boundary conditions are somewhat easier to determine, because for most of the critical elements, the heating steam temperature can be considered equal to the saturation temperature at the corresponding pressure, and the heat transfer coefficients for wet-steam are so high (in the order of 104 W/m2 × °C or greater) that an error in setting this value cannot significantly affect the calculation results. During start-up tests and regular load changes, it is necessary to establish static dependencies of the heating steam pressures on the steam flow amount through the turbine (that is, the turbine load), which makes it possible to plot the static dependence for the heating steam temperatures equal to the saturation temperatures. Such a static dependence for the heating steam temperature in the first HP steam extraction chamber of the K-500-60/1500 turbine is shown in Figure 4–47a.
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Operation 319
(a)
(b)
Fig. 4–47. Static dependencies on turbine load for heating steam temperature in the first steam extraction chamber (a) and heat transfer conditions in the IP steam admission chamber (b) of the HP–IP cylinder of a K-500-50/1500 turbine based on start-up tests at the Novovoronezh nuclear power plant (1: approximate generalization of calculated procession of experimental data;
2: approximate generalization of preliminary calculated data)
Source :V.A.Akerman, N. S. Gabrijchuk,V. B. Kirillov,A. S. Leyzerovich, et al. 135
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320 Wet-Steam Turbines for Nuclear Power Plants
For wet-steam turbines, deep steam throttling in the HP control valves at low steam flow rates can result in the appearance of superheated steam in the first stages of the HP steam path.This effect was fixed in the start-up tests of the K-220-44 turbine, with the main steam pressure of 4.3 MPa (44 atm; 625 psi) (Fig. 4–48). In this case, the steam flow rate through the turbine is estimated from the total load of the main and house (auxiliary power) generators. If the metal temperature is lower than the steam saturation temperature, and the heat flux from the heated surface into the metal thickness is more than that from steam to the heated surface, even with superheated steam, the turbine is heated with steam condensation on the heated surfaces, as it is with wet steam. Otherwise, the heat transfer process is determined by thermal convection, as it is in superheated-steam turbines.
Fig. 4–48. Static dependencies on the total turbine load for heating steam temperatures in the HP cylinder chambers of a K-220-44 turbine based on startup tests at the Kola nuclear power plant (1: in the steam admission chamber downstream from the first two control valves (with nozzle-group steam control); 2: at the control stage; 3: in the front seal first chamber (connected to the fourth steam extraction); 4: in the fourth steam extraction chamber)
Source :A. S. Leyzerovich,V. B. Kirillov, S. P. Kruzhkova, et al.136
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Operation 321
Similar heat transfer conditions take place in the IP section, if it exists, and in the first stages of the LP cylinders if the IP section is absent. For power steam turbines, the heat transfer convection processes can be regarded as stationary or quasi-stationary, because any real nonstationary effects manifest themselves only during very short time periods incommensurable with the heating duration.
The temperature fields of elements of wet-steam turbines that are heated by superheated steam are shown in Figure 4–8 (the IP portion of the integrated HP–IP rotor and the outer casing cross-section for the IP steam admission chamber) and Figure 4–10a (the first stages’ disk of the LP rotor). For the casing elements, the heat transfer conditions in the casing chambers can be determined in the same manner as for superheated-steam turbines. The methodology for determining these data was described in detail in the author’s previous publications.137 Experimental data of the heat transfer conditions for the integrated HP–IP cylinder’s IP steam admission chamber of the K-500-60/1500 turbine are presented in Figure 4–47b in the form of a static dependence on the turbine load. The generalization of these data combined with experimental data for similar chambers with tangential steam admission for superheated-steam turbines allows description of this dependence in the dimensionless criterial form (Fig. 4–49):
Nu = 0.021 × Re0.8 × Pr0.43
where the Nusselt and Reynolds numbers (Nu and Re, respectively) are calculated based on a conventional circular steam velocity in the chamber and the equivalent diameter of the chamber cross-section. According to experiments conducted by Turboatom, the heat transfer conditions in the HP steam admission chamber of the K-220-44 turbine, when it is swept by superheated steam, are on the order of 180–200 W/(m2 ×°C), which agrees well with estimates based on criterial equations. 138
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322 Wet-Steam Turbines for Nuclear Power Plants
Fig. 4–49. Generalization of static dependence for heat transfer conditions from steam to casing in the IP steam admission chambers of various turbines on the basis of their start-up tests (1: LMZ’s K-200-130 turbine; 2: LMZ’s K-300- 240 turbine; 3:Turboatom’s K-500-60/1500 turbine)
As to the rotors (IP or LP) heated by superheated steam, the heat transfer conditions for their typical surfaces can be calculated with the use of well-known experimental data already presented in the form of dimensionless criterial equations. Some of these equations were presented in the author’s previous book,139 and more detailed, comprehensive data on this point can be found in numerous papers, special monographs on heat transfer conditions in turbomachinery, and technical guidelines on calculation temperature fields in steam turbine rotors and casings.
While calculating the temperature fields of the rotors, their heating steam temperatures are often taken to be equal to the steam temperatures at the inlet (or outlet) of the adjacent blade rows (Figs. 4–8b, 4–10, and 4–12b).Yet, in many cases, the heating steam temperatures near the heated surfaces of the rotor body can significantly differ from the steam temperatures in the steam path’s main stream. For large steam turbines with relatively great stage heights and especially three-dimensional steam path designs, the steam temperature significantly varies along the stage height. This pattern becomes more intricate with regard to
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Operation 323
steam leaking out or, on the contrary, sucking into the main stream through the root seals. Depending on the stage features, there could appear different patterns of steam movement through the diaphragm gland seals and pressure balance holes.140 Because of this, it is always desirable to have data on heating steam temperature conditions near the rotor surfaces measured experimentally.
This task was included in the scope of start–up tests for the Turboatom K-220-44 turbine, with standard welded LP rotors, at the Kola nuclear power plant (see Fig. 3–4). Welded rotors are widely used for large wet-steam turbines (see chapter 3), and in the absence of an IP section, the thermal-stress state of such rotors can severely limit the rate of raising the steam reheat temperature (after the MSR) at start-ups.
The system of experimental temperature measurements that were installed in the LP cylinder of one of the Kola turbines is shown in Figure 4–50. Diagrams of the measured steam temperatures during shutdown and start-up of the turbine can be seen in Figure 4–51, and results of generalizing and processing them in the form of static dependencies on the turbine load for steam temperature decreases relating to the inlet steam temperature are given in Figure 4–52.141 The temperatures of steam sweeping the rotor body surfaces, particularly in the diaphragm seals, are considerably higher than the steam temperatures in the main stream at the inlet of the corresponding stages at the mid-height of the nozzles.This is explained by the fact that the gland seals are mainly fed by steam from the previous stage’s root section, which has a higher temperature due to the end energy losses.The steam temperature drops in the stages along the main steam stream remain practically independent of the steam flow rate. Unlike this, the steam temperature differences between the main steam stream and the diaphragm seal inlet are invariable only at significantly high flow rates through the turbine, and these differences fall almost to zero with approaching no-load conditions. At the same time, for stages working with saturated or wet steam (in this case, these are the fourth and fifth stages), the measured steam temperatures in the diaphragm seals and the main steam stream do not practically differ, and correspond to the saturation temperature for the steam pressure at the stage inlet. The temperature of steam sweeping the rotor in the steam admission zone is lower than the stagnation temperature at the LP cylinder inlet, apparently due to steam leaking through the axial clearances between the fixed blades and disks of the first stages of both flows of the cylinder.
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324 Wet-Steam Turbines for Nuclear Power Plants
Fig. 4–50. Experimental temperature measurements in the LP cylinder of a K-220-44 turbine for investigating the boundary and initial conditions of heating for the rotor (I: steam temperature measurements [1–15]; II: rotor metal surface temperature measurements at stopped turbine [16–18]); installation (a) and head (b) of a temperature probe for measuring the rotor surface temperature
Source B. N. Lyudomirskii, A. S. Leyzerovich, and Y. N. Kolomtsev142
Fig. 4–51. Variation in measured steam temperatures in the LP cylinder of a K-220-44 turbine during shutdown (a) and subsequent start-up (b) (numbering of temperature curves is given in accordance with designations in Fig. 4–50;V: vacuum in condenser)
Source B. N. Lyudomirskii, A. S. Leyzerovich, and Y. N. Kolomtsev143
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Operation 325
Fig. 4–52. Static dependencies of steam temperature decreases in the LP cylinder of a K-220-44 turbine (numbering of temperature curves is given in accordance with designations in Fig. 4–50; I: measurement under stationary operating conditions; II: measurements at start-ups and shutdowns)
Source B. N. Lyudomirskii, A. S. Leyzerovich, and Y. N. Kolomtsev144
Processing the obtained experimental data for transients also showed that if the steam temperatures in the main steam stream, tc( ), follow the variation in the steam temperature at the cylinder inlet with virtually no lag, for the steam temperatures in the diaphragm seals, ts( ), this time lag is significant, and the dynamics of these temperatures as
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326 Wet-Steam Turbines for Nuclear Power Plants
related to the main stream steam temperatures can be described with sufficient accuracy by the following transfer function:
W |
(s) = |
L(ts ) |
(1+ Ts)-1 |
(4.1) |
||
|
|
|||||
L(tc |
∆ts ) |
|||||
|
||||||
|
|
|
|
|||
where L and s are the Laplace operator and Laplace transfer parameter, respectively; ∆ts is the static difference of the steam temperatures, tc(τ) and ts(τ); and T is the time constant. In the case of a piecewise linear approximation of the main stream steam temperature variation, tc(τ), the change in temperature for steam sweeping the rotor surface, ts(τ), will be :
ts(τ) = tc(τ) – ∆ts – [wT + (δts – wT) × exp(–τ1/T)], |
(4.2) |
where w = const is the rate of a linear piecewise approximation of the steam temperature change, tc(τ), within the considered time period; τ1 is the amount of time counted from the beginning of varying tc(τ) at the rate w, and δts = tc – ts – ∆ts at τ1 = 0. Numerical solution of this equation with reference to T for the steam temperatures at the stage inlet, tc(τ), and near the rotor surface, ts(τ), taken from the measured results give an average value T ≈ 10 min.The scatter of the calculated values depends considerably on the assigned accuracy of the solution, and with an allowable error of ±2 °C, it amounted to ±5 min. Under these conditions, it is hardly possible to establish more detailed connections between variations of T and load, relative rotor expansion, and other factors. It is of interest that these static and dynamic dependencies are quite close to experimental results obtained for the IP rotor of a supercritical-pressure 800-MW turbine.145
The obtained generalized dependencies were used for calculating the heating steam temperatures for the main rotor surfaces at start-ups with arbitrary changes in the steam temperature at the LP cylinder inlet (after the MSR). Comparison of these calculations with the measured data for an actual start–up is shown in Figure 4–53. The steam temperature determination error did not exceed 10°C in dynamics and 1–2°C for stationary conditions, which is quite satisfactory for practical purposes.
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