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Accelerated start-up of the steam turbine by means of controlled cooling steam injection
Energy 173 (2019) 1242e1255
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Accelerated start-up of the steam turbine by means of controlled cooling steam injection Janusz Badur, Mateusz Bryk* sk, 80-231, Poland Institute of Fluid Flow Machinery, Polish Academy of Sciences, Fiszera 14 St., Gdan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 October 2018 Received in revised form 21 January 2019 Accepted 11 February 2019 Available online 20 February 2019
The paper presents the results of a Thermal-FSI analysis of accelerated start-up of a turbine controlled by an additional injection of cooling steam. The work contains a description of the phenomena that occur during the start-up as well as the accompanying effects. Attention is paid to structural elements that limit the speed of regulation of the steam unit. In order to estimate the possibility of accelerating the turbine start-up, four turbine starting simulations were carried out. Two simulations relate to the 3 h start-up, two consecutive ones to the 2 h start-up. Then the results of flow and strength simulation were presented. In the work, global stress of the rotor of the HP turbine part and the local rotor stress in the first rotor notch were analyzed. As a result of the simulations and analyses, the possibility of reducing the required start-up time from 3 h to 2 h was confirmed. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Thermal-FSI analysis Steam turbine start-up CFD model CSD model
1. Introduction Current trends in the design of new power units, characterized by steadily increasing work parameters as well as retrofits made on older units, force a change of approach both to the problem of designing new generating units (‘blocks’) and to the methods of repairing devices in operation. A new element that is challenging is Energy Network requirements strictly related to the variability of power in the system, which is caused by the impact of renewable energy in Europe [1]. In the situation of the aforementioned, the most important aspect is the adaptation of high power steam units to work with RES (Renewable Energy Source) installations. The wind is wayward and within a few minutes the value of its speed may change radically, which proportionally translates into the electric power generated by wind farms; this situation occurred in Poland in 2015 [1]. Coal-fired units had to reduce their load rapidly due to the sudden increase in electricity generation from renewable sources. In addition, it is postulated that certain blocks constitute the so-called ‘basis’ of the load, that is, they would produce electricity at the lowest cost, due to the higher efficiency of installations with higher powers [2,3]. This translates into unambiguous unit fuel consumption, energy price and environmental aspects related to the production of the above-mentioned energy.
* Corresponding author. E-mail address: [email protected] (M. Bryk). https://doi.org/10.1016/j.energy.2019.02.088 0360-5442/© 2019 Elsevier Ltd. All rights reserved.
In spite of the above, over time the constructed supercritical blocks will have to reduce their power to accommodate the development of wind farms. Currently, from the aspects of stable boiler operation and steam flow in the turbine, this load should not take less than 40% of rated load [4e6]. The blocks on which the deviation is made, should be adjusted (as much as possible) to the new conditions in terms of their minimum burden. In the past, but also currently, when due to an unforeseen event affecting the system, e.g. when the available power is not sufficient despite the turbine power reaching nominal capacity, it is possible to partially overload the turbine set in relation to condensation blocks. This operation is characterized by a decrease in efficiency, namely it consists of the partial shutdown of the regeneration system, which reduces the power of the turbine set by venting the flow of the working medium, so that its smaller part flows through the turbine flow channel by performing work [7,8]. The increasing power of installed RES sources and their dependence on weather conditions determines the maintenance of large steam blocks in the hot reserve [2,3]. In order to equal to this task, it is possible to take steps to make the work of the block more flexible, described in the aforementioned work [1,9], or to carry out modernization, and sometimes to change the structure. The situation of controlling the system's power currently comes down to the need for more frequent starts and shutdowns of turbine sets, including those of high power. In order to meet this requirement, it is possible to accelerate the start-up of the turbine set by considering the elastic-plastic adaptation of the structure,
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Nomenclature e P T t v
total energy, J pressure, N/m2 temperature, K time, s velocity, m/s
Notation for vector quantities ! b mass force, m/s2 Sk k source, kg/m3s Sε ε sources, kg/m4s ! Jk diffusive flux of k, kg/m2s ! Jε diffusive flux of ε, kg/m2s !c t total tensor of irreversible tension, Pa ! t tensor of mechanical viscosity, Pa ! R tensor of Reynold's viscosity, Pa ! D tensor of diffusion viscosity, Pa !c total heat flux, W/m2 q !D diffusive heat flux, W/m2 q
which is described in Refs. [1,9] or use the cooling of the intake vapor, a working medium with lower parameters [9e12]. 2. Thermodynamic aspects of energy block flexibility 2.1. Steam unit elasticity The ‘elasticity’ term determines the possibility of smooth power regulation in the optimally short time, due to constraints in the block as a result of primary regulation, secondary regulation and load changes resulting from the impact of renewable sources. Speaking here of flexibility, we mean to equalize the power outage and the frequency generated after the primary regulation as quickly as possible. This activity is related with the operation of turbines in transient processes, for which the efficiency of energy generation is lower than in steady states, therefore the aim is to minimize the time required until the turbine set achieves a new set power value. However, the rate of change is limited by the flow and strength conditions occurring during transient operation. Transient work and transient conditions have a major impact on the start-up and withdrawal of turbine sets. The thermodynamic aspects that take place during the change of block loads are presented below, which are strictly connected with the possibility of adapting the block to the conditions imposed by the power system and renewable sources. As an example, the start-up of the turbine set will be recalled from the cold state. 2.2. Phenomena during start-up The turbine start-up procedure consists of increasing the rotor speed of the turbine set to the nominal RPM, typically 3000 (in Poland), and loading the turbine to a partial or nominal load. Increasing the speed and loading is related to increasing the parameters of fresh steam (temperature and pressure) and increasing the mass flow through the turbine [13,14]. The consequence of these changes is the heating of the turbine elements, mainly in the HP and SP parts of the turbine. The thermal loads on the hulls cause cyclical changes in stress and strains. These changes cause, after a
! q !t q !ph q ! v
1243
molecular heat flux, W/m2 turbulent heat flux, W/m2 phase change heat flux, W/m2 velocity vector, m/s
Greek symbols density, kg/m3 number of Poisson
r n
Subscripts red reduced HMH Huber-Mises-Hencky 1,2,3 main directions of the stress tensor Acronyms BOT CFD CSD RES H-M-H
Thermal Limit of the Unit system Computational Fluid Dynamic Computational Solid Dynamic Renewable Energy Sources Huber-Mises-Hencky
certain number of cycles, cracks as a result of thermal fatigue of the material. On the other hand, in the case of long-term states of the determined hull work, the phenomenon of creeping of materials is characteristic. Both phenomena are described in detail in the literature [8,15e17]. At the beginning of the start-up, the places near the inlet reach the highest temperatures and the accompanying stress and strains are the greatest. The heat is transported to the element and spread in its interior at a limited speed, and for this reason surfaces in direct contact with hot steam have a higher temperature than deeper-located regions. Layers of material with a higher temperature undergo thermal expansion, but this expansion is limited by adjacent layers at a lower temperature. This differential expansion is the reason for the generation of internal thermal stress [18]. A disadvantageous phenomenon of a thermal nature is the socalled ‘cat ridge’, caused by the temperature difference between the upper and lower halves of the hull [7,8,18]. The upper half has a higher temperature than the lower one and for this reason the hull tends to bend upwards. In addition to these undesirable thermal phenomena, other undesirable dynamic processes take place during start-up, which further reduce the lifetime of the turbine. These phenomena are resonance vibrations of rotating elements [14]. 3. Critical structural elements limiting the speed of regulation During power changes, critical structural elements limiting the speed of regulation were divided into two groups, the first of them concerns thermal stress, vibrations and strains, the second one concerns the issue of creeping and low-cycle transmission [4,5,9,16]. 3.1. Steam turbine components particularly exposed to thermal stress and deformations In Fig. 1, those places subject to special attention are marked when adapting the machine for quick starts and withdrawals. These
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4. Working vanes and rotor discs of the first stages of the highpressure part; 5. Working vanes and rotor discs of the first stages of the mediumpressure part; 6. The high pressure impeller; 7. Medium-pressure impeller; 8. High-pressure inner hull; 9. Medium-pressure inner hull. Fig. 1. Critical structural elements limiting the speed of regulation [9].
As a result of creeping there is: are areas [9,18e22]: 1. The vicinity of the fresh steam inlet to the first stage WP - this area includes the inlet spiral, the guide vanes, and the corresponding rotor area together with the 1 rotor blade; 2. An analogous place in the area of the steam inlet overheated to the SP body; 3. Glands located on the hot side of the WP body; 4. Analogue stuffings in the hot part of the SP; 5. Main thrust bearing; 6. Glands on the cold side of the WP body; 7. Similar stuffings on the cold side of the SP. The phenomena taking place in the above-mentioned points are described in Chapter 2 of this work. They are associated with temperature changes during start-up and shut-down, which leads to the generation of stress and thermal deformations, the values of which have been determined for the critical points listed in Fig. 1 and should not be exceeded. However, the working conditions imposed by the Energy Network, force power plants to adapt and coexist with renewable energy sources. One of the previously mentioned possibilities is the elasticplastic adaptation of the structure as well as non-project limitations aimed at making the block's work more flexible, while simultaneously accommodating in the time regimes of regulation without excessive reduction of the life of the turbine set.
3.2. Steam turbine components exposed to creep Turning to the second group referring to low-cycle fatigue and creep, in order to calibrate the display of critical construction elements, Fig. 2 is attached. The components of the reaction steam turbine exposed to creep are shown in Fig. 2 [14]: 1. Fresh steam pipelines and high pressure valve chambers; 2. Overheated steam pipelines and medium pressure valve chambers; 3. Shrink rings;
Fig. 2. Turbine components exposed to creep [14].
1) A decrease in structural clearances as a consequence of progressive permanent deformations during the life of the turbine. As a result of the decreasing clearance, there is the possibility of seizing and leakage in the flow associated with leaks, which may lead to turbine failure. 2) (in the case of a share turbine) A reduction in the initial radial difference, i.e., the radius of the inner disk and the radius of the outer shaft. This may lead to a decrease in the effectiveness of the connection. 3) A decrease in tension value of bolt tension, due to increasing inelastic deformation. This leads to a reduction in the tightness of the connection and the need to periodically tighten the screws to maintain tightness.
4. Possibilities of accelerated start-up The chapter presents possible variants of accelerated turbine start-up. The following methods are described in the literature: - elastic-plastic material adaptation [9], - cooling of turbine components by means of cooling steam injection [11,23e26], - optimization of start-up curves [24,27e29]. The first refers to the plasticization of the material due to higher stress values, which would occur due to accelerated start-up without structural changes. Simulations carried out in this study show that the amount of permanent deformation does not differ significantly from the values assumed at the design stage. However, the acceleration of the start-up time in this case is not significant. The second assumes the injection of steam with lower parameters in order to accelerate the start-up by reducing the stresses occurring in the structure. In the literature there are many ways to supply steam with lower parameters(Temperature, Pressure) in order to reduce the temperature gradient and, consequently, the thermal loads on the turbine structure. These methods assume internal and external cooling of turbine elements in an accelerated start-up. The results of the analyses lead to conclusions about the possibility of shortening the turbine start-up thanks to the applied method, although it requires modification of the turbine construction. The third method assumes optimization of turbine inlet steam control in order to shorten the start-up time. Analyses made in this study indicate that it is possible to control the start-up in such a way that, at the same time, the start-up time does not exceed the maximum stress. After the research, the authors decided to carry out an analysis of accelerated turbine start-up by means of cooling steam injection. However, the place of injection of cooling steam is different than in the cases analyzed in the literature. This method of start-up acceleration was chosen because of the promising analyses carried out in the works.
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5. Analyzed geometry 5.1. Reference model Based on the actual geometry of the part HP of the 18K390 w power plant (Fig. 3), a two-dimensional turbine from the Bełchato turbine model was created for the purpose of numerical analysis. Due to the extensive flow and strength calculations, two models had to be prepared. The first one as reference is shown in Fig. 4.
Fig. 4. Reference model of part HP 18K390 turbine.
5.2. Modified model The second model, with the injection of cooling steam is the same, the only changes are visible near the inlet to the first stage of the turbine and this is shown in Fig. 5. The edges marked with the letters A and B are additional inlets that are used in the analysis case with additional cooling steam injection.
Fig. 5. Close-up to the area of additional steam inlets.
5.3. The simplifications used in the model Due to the complexity of the two-dimensional geometry and the difficulty of two-dimensional modeling of phenomena in the exact representation of the turbine, it was simplified. Here are the following changes in relation to real geometry: - simplifying cutting geometry for blades, both steering and rotor; - simplification of the blades themselves, the right blades replace the four-edge elements. In addition, these elements are shorter compared to the actual blades due to the blockage of the flow; - simplification of the flow channel (green color in the Fig. 6); - no seals between the inner casing and the impeller as well as between the outer casing and the impeller; The main focus of the analysis is not on the flow but on the phenomena that arise as a result of the liquid's influence on the solid. The influence of steam on the sealing ring and the part of the external and internal body was not focused. In the work, the authors focus on the idea of cooling the fresh steam in order to accelerate the start-up of the turbine. The possibilities of cooling steam with steam with different parameters are numerous [9e12], so the authors chose this one because of the possibility of eliminating the sudden change in the direction of the steam flow in the inlet spiral elbow. Cooling steam can be taken from the lower parts of the boiler. In the case of the block in question, the lowest steam temperature from the low part of the boiler is approximately 300 C [9], which corresponds to the saturation temperature of steam at a given pressure. Additionally, the cooling steam pressure will be always higher than the pressure at the inlet because of boiler losses [8,23,30,31].
Fig. 6. Flow channel of the analyzed geometry.
6. Model CFD 6.1. Equations of behaviour For the fluid flow simulation, three basic formulas of conservation are fulfilled. These three main formulations which describe CFD are presented below [32e34]: Conservation of mass equation:
vt ðrÞ þ divðr! vÞ¼0
(1)
Conservation of momentum equation:
! c ! vt ðr! v Þ þ div r! v 5! v þp I ¼ div ! t þrb Conservation of energy equation:
vt ðreÞ þ div
P ! !t eþ r v ¼ div ! q þ q
r
! !c !D þrb! þ t ! v þ q v
These are balance equations in conservative form, where: r- gas density, [kg/m3] ! ! !c ! t ¼ t þ R þ D - total tensor of irreversible stress, [Pa] ! v ¼ vi ei e mean velocity, [m/s] ! q e molecular heat flux, [W/m2] !t q - turbulent heat flux, [W/m2] !D q - diffusive heat flux, [W/m2] P - pressure, [Pa] e ¼ uþ Fig. 3. Axial section of part HP of the 18K390 turbine [14].
(2)
.
b ¼
. 1. 2 n $ v - total energy, . 9; 81 ez . [m/s2]
[J]
(3)
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6.2. Model of turbulence
or in the equivalent form provided by the formula (8):
The above three equations, i.e. (1e3), were complemented by two evolution equations for parameters, which allow to define tensile tensor components [35]: Evolution equation concerning turbulent energy k:
sred ¼ pffiffiffi
! vt ðrkÞ þ divðrk! v Þ ¼ div J k þ Sk
8. Thermal-FSI
(4)
Evolution equation concerning energy dissipation ε:
! vt ðrεÞ þ divðrε! v Þ ¼ div J ε þ Sε
(5)
A more detailed description of the used models in CFD codes can be also found in Refs. [33,35]. The pressure of the liquid walls is omitted as a pressure that causes negligible stress in walls. Because of that, the equation of momentum conservation is not important due to the mechanical reasons but only due to thermal reasons, as the equation which describes heat convection and movement of the hot fluid, which flows through flow channel. For that reason, the viscous and turbulent stress influence is negligible. More important ! is the assumption of gravity in element of mass force: rðx; tÞ b or a precise equation of water state which gives actual water density in each point and in each moment: rðx; tÞ. The heat exchange model in a steam turbine is noteworthy. This is divided into: -conduction, -convection, -radiation. Due to the considered start-up issue, the most important method of heat exchange is convection between the turbine elements and the steam that is passing them. The second in the process is conduction observed during the whole turbine operation cycle. The influence of radiation was omitted due to its greatest impact being during cooling down of the turbine [14,17]. Therefore, in the formula for total energy (3) radiation was omitted. 7. CSD model The following strength hypothesis was used to simulate the stress generated in the material: The Huber-Mises-Hencky reduced stress given by formula (6) [23,36]:
sHMH ¼
i 1 þ vh ðs1 s2 Þ2 þ ðs2 s3 Þ2 þ ðs3 s1 Þ2 6E
(6)
where:
n -number of Poisson E - Young's modulus
s1 ; s2 ; s3 - main stress The condition of safe mechanical condition assumes the function (7):
1
sred ¼ pffiffiffi 2
1
2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðs11 s22 Þ2 þ ðs33 s22 Þ2 þ ðs11 s33 Þ2
(8)
Thermal-FSI analysis consists in CFD analysis, the results of which are exported to a solid state solver (CSD). Next, the CSD solver on the basis of imported data (temperature, pressure) determines the stress and displacements in the analyzed geometry [37e39]. The principle of the analysis is shown in Fig. 7. There are two types of Thermal-FSI analysis: - One-way FSI - Two-way FSI In the one way FSI, following CFD calculations, the solution is exported to the CSD solver and the stress and displacements determined on their basis. In the case of two-way FSI analysis, both models (CFD and CSD) are coupled together during the entire simulation. After calculating one CFD time step, the results are exported to the CSD solver. Stress and displacement are then determined. Then, due to deformations of the analyzed geometry, an automatic remeshing is carried out. The next time step in the CFD solver is calculated with the new mesh. The entire process is carried out automatically until the last time step [40e42]. The work involved one-way Thermal-FSI analyzes. Temperature fields were imported, from which the stress fields in the analyzed geometry were determined. 9. Boundary and initial conditions 9.1. The applicable inlet and outlet conditions of the flow channel As the inlet boundary condition, inlet pressure was used, and outlet pressure as outlet condition. For reference geometry, this is illustrated in Fig. 8. In the case of modified geometry, inlet pressure was also used as the inlet boundary condition. Similarly, the outlet pressure condition was applied analogously to the outlet edge. This is shown in Fig. 8. The start-up was carried out from the warm state, ie when the turbine's HP part is preheated to 130 C [14]. 9.2. Inlet and outlet parameters The parameters at the inlet and outlet of the geometry were implemented in accordance with the actual start-up curves for the analyzed unit, Fig. 9 [14]. Due to the fact that the analysis is a 2D analysis, it was necessary to implement an enthalpy decrease in the turbine. Since the existing blade profiles are simplified, it was necessary to write the code for the temperature drop in the turbine, using UDF [23,43] (User Defined Function) code. Taking into account the real temperature drops in the turbine, the enthalpy drop in the flow channel
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sxx syy 2 þ szz syy 2 þ ðsxx szz Þ2 þ 6 t2xy þ t2yz þ t2xz
(7)
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Fig. 7. Principle of operation of the Thermal-FSI [33].
appropriate degrees of freedom of the analyzed rotor were limited (Fig. 10). Support A prevents the shaft from moving in the positive direction of the OX axis, which simulates the work of the bearing. Support B prevents the shaft from moving in the negative direction of the OY axis. Condition B has been implemented due to the problem of extrapolation of displacements [14]. Fig. 8. Marking of inlet and outlet edges.
10. CFD results was mapped using the abovementioned code. It should be mentioned that the turbine fan work in the initial start-up phase is also taken into account here. In addition, due to the twodimensional analysis, it was necessary to use as inlets - edges from which the vapor flow occurs in the normal direction to the edge.
The chapter presents the results of flow analysis for 3 h and 2 h start-up for both types of geometry. The temperature fields observed during the standard start-up and using the cooling steam injection control were compared.
9.3. The materials used in the analysis
10.1. Comparison of temperature fields at 180 min for the 3 h turbine start-up without cooling steam injection with the start of the turbine, in which 300 C cooling steam injection was applied
Domain materials found in the analysis are presented in Table 1. In order to analyze the possibility of accelerating the start-up of the turbine by means of a controlled injection of cooling steam, a two-dimensional, one-sided Thermal-FSI analysis was carried out. This analysis consists in importing the resulting temperature field from the CFD solution to the CSD solver in which the stress fields in the structure are determined. 9.4. Strength analysis In the case of a solid body, the stress behaviour was only analyzed in the turbine rotor. This step was applied due to the twodimensional analysis. The physical properties of the shaft material are summarized in Table 2. Additionally the chemical composition of ST10Ts steel is given by Table 3. Consideration of the entire construction in terms of strength would not make much sense due to axial and radial clearances present in the real construction (which are not present in the analysis). In addition, the strength analysis carried out is analogous to that described by Dominiczak R. in Ref. [14]. According to the assumptions taken from Ref. [14], the
In sub-section 10.1, the temperature fields were compared in the 180th minute of the 3 h start-up. Fig. 11 shows the temperature redistribution at the 180th minute of start-up without the use of cooling steam injection. We are dealing with a standard temperature distribution for turbine startup. The highest temperature field occurs from the inlet to the 6th stage of the turbine. Due to the simplification of the flow channel, there is no temperature change in the external hull of the turbine, outside the area of direct interaction of the working medium with the solids. This fact does not affect the analysis, as the authors focused on the impact on the most thermally loaded elements, i.e. the area of the inlet to the HP part of the turbine as well as the area of the first stages of the turbine. Fig. 12 shows the temperature field distribution for 180 min start-up with the use of cooling steam injection. It can be seen that the use of cooling steam injection control reduces the field of influence of high temperatures to the first turbine stages. In addition, the temperature at the turbine outlet is reduced. This is due to the mixing of the main steam stream with the additional cooling steam streams. The observed reduction in the impact of high temperatures will translate into a reduction in the value of stress arising in
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Fig. 9. Parameters change during start-up [14].
Table 1 Domain materials used in the analysis [14].
Table 3 The chemical composition of ST10Ts steel.
Domain
Material
Element
Fe
Ni
Cr
Mn
Si
C
P
S
Shaft Inner hull Outer hull Sealing rings Stator blades Rotor blades Fluid
St10ts Stg10T G20Mo5 St12T St12T St12T Water vapor
Wt %
42
32
19
2
1.13
0.08
0.04
0.03
Fig. 10. Support conditions for stress analysis of the turbine rotor. Table 2 Physical properties of ST10Ts steel. T [C]
b [1/K]
l [W/m$K]
Cp [J/kg$K]
E [GPa]
Re [MPa]
20 100 200 300 400 500 600
0.0000104 0.0000107 0.0000110 0.0000140 0.0000170 0.0000120 0.0000123
24.0 24.4 24.8 25.1 25.6 26.1 26.4
439 500 534 571 625 704 831
212 208 202 195 186 171 142
698 647 608 570 515 440 315
the construction of the turbine. The difference in the temperature field in the flow channel results directly from the mixing of high performance steam with lower temperature steam. Although this will affect the efficiency of the turbine, the power of the turbine remains unchanged due to the increased steam flow rate. Additionally, the purpose of the analysis is to determine the possibility of reducing the start-up time of the turbine and not to test its efficiency.
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Fig. 11. 180-th minute of the 3 h start-up without cooling steam injection.
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Fig. 12. 180-th minute of the 3 h start-up with 300 C cooling steam injection.
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Fig. 13. 120-th minute of the 2 h start-up without cooling steam injection.
Fig. 14. 120-th minute of the 2 h start-up with 300 C cooling steam injection.
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10.2. Comparison of temperature fields at 120 min for the 2 h turbine start-up without cooling steam injection with the start of the turbine, in which 300 C cooling steam injection was applied In the sub-section 10.2, the temperature fields were compared in the 120th minute of the 2 h start-up. Fig. 13 shows the temperature field in the final accelerated startup phase without injection of cooling steam. Compared to a 3-h start, a much higher temperature gradient is observed in both the flow channel and the turbine construction. In this case, the high temperature field reaches the 5th turbine stage. Large temperature gradients will translate into high stress values in the turbine construction. The use of cooling steam injection in accelerated start up limits the high temperature field. This is shown in Fig. 14. As in the case of 3 h start-up, in the 2 h start-up the field of the highest temperatures was limited to the first stage of the turbine. In addition, the temperature gradients occurring here assume lower values than in the case of starting without the injection of cooling steam.
Fig. 16. Axial stress in 180-th minute of the 3 h start-up without cooling steam injection.
Fig. 17. H-M-H stress in 180-th minute of the 3 h start-up with 300 C cooling steam injection.
11. CSD results
11.1. Comparison of stress fields at 180 min for the 3 h turbine startup without cooling steam injection with the start of the turbine, in which 300 C cooling steam injection was applied The area of H-M-H stress in the 180th minute of 3 h start-up without cooling is shown in Fig. 15. Redistribution of stress field took place. The largest stresses arose in the area of notches from 8 to 24 and they range from 130 MPa to about 373.7 MPa. The smallest observed stress values are at the level of 26.7 MPa. As a result of geometry heating, the thermal load is reduced, so the stress around the first degrees is less. High stress values in the right part of the shaft result from a different field of temperature distribution than in the remaining section of the shaft (thick elements heat up more slowly). Axial stresses are shown in Fig. 16. The highest compressive stress values occur in the area of the notches from 8 to 24 and the tensile ones in the rotor axis below the notches from 8 to 24. The axial stresses show the character of the stress state. The dominant character of compressive stresses in the top layers of the rotor is observed. The H-M-H stress in the last minute of the 3 h start-up with cooling is shown in Fig. 17. There is a full analogy in places where maximum stress occurs. The difference, as in previous cases, occurs
Fig. 15. H-M-H stress in 180-th minute of the 3 h start-up without cooling steam injection.
Fig. 18. Axial stress in 180-th minute of the 3 h start-up with 300 C cooling steam injection.
H-M-H stress comparison for 3h turbine start-up
stress [Mpa]
As in the case of the flow analysis results, an analogous comparison of results was performed for the strength analysis. The first two subsections 11.1 and 11.2 concerns the results of the strength analysis for the 3 h start-up and subsections 11.3 and 11.4 of the analysis for the 2 h start-up. All the results are summarized in subsection 11.5. In addition, the point of the first notch for the rotor blade was analyzed in subsection 11.6. The authors analyzed a point in the vicinity of which damage often occurs due to changes in temperature with a high gradient [19,23].
500 450 400 350 300 250 200 150 100 50 0 0
2000
4000
300 C cooling steam injection
6000 time [s]
8000
10000
12000
without cooling steam injection
Fig. 19. H-M-H stress comparison for 3 h turbine start-up.
in stress values, which amount to 330.93 MPa. In addition, the use of cooling steam injection leads to a more uniform stress field in the thickest part of the rotor. The lowest reduced stress value of H-M-H is 23.65 MPa, which is similar to that of no cooling steam injection. Axial stresses in the 180th minute of a cooling start are shown in Fig. 18. As in the case of H-M-H stress and in the case of axial stress, there is a full analogy to the case without cooling. Differences also occur in the value of stress. The highest compressive stress assume the value of 328.01 MPa and tensile the 104.09 MPa. The use of cooling steam injection leads to a higher proportion of tensile stress in the thinnest part of the shaft. This is due to the difference in temperature at this point. 11.2. Stress comparison during the 3 h turbine start up Fig. 19 presents a comparison of the stress course during the 3 h start-up with the injection of cooling steam and without cooling. In the initial phase of the start-up, the stress generated in the structure for the cooling start take values of around 100 MPa lower than in the case of a start-up without cooling. This is due to the more homogeneous temperature field around the inlet and before the first stages due to the additional inlets from which the temperature
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Compressive stress comparison for 3h turbine start-up 0 -50 0
2000
4000
6000
8000
10000
12000
stress [MPa]
-100 -150 -200 -250 -300 -350 -400 -450
time [s] without cooling steam injection
300 stC cooling steam injection
Fig. 20. Compressive stress comparison for 3 h turbine start-up.
Table 4 Comparison of the highest stress in the structure with the yield point for 3 h startup. 3 h start-up
t [s]
s [MPa]
T [C]
Re(T) [MPa]
without cooling steam injection with 300C cooling steam injection
3826 3826
437.07 379.47
357 357
538.65 538.65
Fig. 24. Axial stress in 120-th minute of the 2 h start-up with 300 C cooling steam injection.
lower values than without cooling. Additionally, Table 4 compares the stress values with the yield point for a given temperature. It can be seen that in both cases the highest stress values occur in 3826s and are below the yield point. Fig. 21. H-M-H stress in 120-th minute of the 2 h start-up without cooling steam injection.
Fig. 22. Axial stress in 120-th minute of the 2 h start-up without cooling steam injection.
̊
11.3. Comparison of stress fields at 120 min for the 2 h turbine startup without cooling steam injection with the start of the turbine, in which 300 C cooling steam injection was applied The H-M-H stress field in the 120th minute of the accelerated start up without injection of cooling steam is presented in Fig. 21. The highest stress values occur in the area of notches from 8 to 24 and in the thinnest cross-section of the rotor. Due to the higher temperature gradient, a significant increase in stress in the construction of the turbine is observed and in this case it amounts to 580.65 MPa. The minimum stress is 41.5 MPa. The axial stress field in the 120th minute of accelerated start
H-M-H stresses comparison for 2h turbine start-up 700
Fig. 23. H-M-H stress in 120-th minute of the 2 h start-up with 300 C cooling steam injection.
stress [Mpa]
is also redistributed. After 1400 s (23 min), stress increase in both cases and after reaching the maximum in 3,800 s (63 min) decrease. The character of both curves is similar. The difference is that in the case of cooling, the values of stress assume lower values during the entire start-up. Fig. 20 shows the course of the compressive stress during the start-up. Due to the dominant compressive stress, it is not surprising that their values are high. Also in this case in the entire start-up range, the compressive stress in the case of cooling takes
600 500 400 300 200 100 0 0
1000
2000
3000
without cooling steam injection
4000 time [s]
5000
6000
7000
8000
300 stC cooling steam injection
Fig. 25. H-M-H stress comparison for 2 h turbine start-up.
J. Badur, M. Bryk / Energy 173 (2019) 1242e1255
the stress values which, for cooling start-up, assume lower values (see Fig. 25).
Compressive stresses comparison for 2h turbine start-up 0 0
2000
4000
6000
8000
-100 stress [Mpa]
1253
11.4. Stress comparison during the 2 h turbine start up
-200 -300 -400 -500 -600
time [s] without cooling steam injection
300 stC cooling steam injection
Fig. 26. Compressive stress comparison for 2 h turbine start-up.
Table 5 Comparison of the highest stress in the structure with the yield point for 2 h startup. 2 h start-up
t [s]
s [MPa]
T [C]
Re(T) [MPa]
without cooling steam injection with 300 cooling steam injection
6245 7200
589.63 360.71
522 552
415.8 382.2
Fig. 25 shows the course of stress in the rotor during accelerated start-up. Stress patterns show a full analogy to the curves observed during the 3 h start-up. In this case, the use of cooling causes a reduction in the value of stress generated in the rotor by about 20 MPa at the start of the start-up, to about 200 MPa in the final phase of the start-up. Table 5 presents the highest stress comparison for 2h-start up. As in the case of 3 h start-up, so in the case of a 2 h start-up, the compressive stresses are of decisive importance. The curves of compressive stress during accelerated start-up are shown in Fig. 26 . The stress pattern for accelerated start-up shows a full analogy to the accelerated start-up (Fig. 20), with the difference that in the case of 2 h start, the generated stress values are much greater (in case without cooling). In the case of an accelerated start-up, the yield strength of the shaft structure is exceeded for the case without cooling steam injection. The material is plasticized and the yield point is exceeded by almost 174 MPa.
without injection of cooling steam is presented in Fig. 22. In the area of the notches from 8 to 24 there are compressive stresses whereas tensile stress occur in the thinnest shaft section and rotor axis directly under the notches 8e24. A high temperature gradient increases the compressive stress in the structure. The H-M-H stress field in the 120th minute of the accelerated start-up with the injection of cooling steam is presented in Fig. 23. The nature of the stress field is analogical to the previous cases. The difference occurs in the stress values which, for cooling start-up, assume lower values. The use of cooling steam injection reduces the stress generated in the consortium from 580 MPa to 38 MPa. The axial stress field in the 120th minute of the accelerated start-up with the injection of cooling steam is presented in Fig. 24. The nature of the stress field is analogous to the previous cases. In the area of the notches from 8 to 24, there are compressive stresses while stretching occurs in the thinnest section of the shaft and the rotor axis directly under the notches 8e24. The difference occurs in Fig. 28. Analyzed point in the notch.
H-M-H stresses comparison for 3h and 2h turbine start-up 700
stress [Mpa]
600 500 400 300 200 100 0 0
2000
4000
6000 8000 time [s] 3h start-up without cooling steam injection 3h start-up with cooling steam injection 2h start-up without cooling steam injection 2h start-up with cooling steam injection
10000
Fig. 27. H-M-H stress comparison for 3 h and 2 h turbine start-up.
12000
1254
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The use of cooling steam injection keeps the maximum stresses in the shaft below the yield point. Although the difference is 22 MPa, it is an extreme state, which confirms the possibility of shortening the turbine start-up time while maintaining stresses within the limits of maintaining normal turbine movement.
Table 6 Comparison of the highest stress in the notch with the yield point for 3 h start-up. 3 h start-up
t [s]
s [MPa]
T [C]
Re(T) [MPa]
without cooling steam injection with 300C cooling steam injection
2386 2386
213.82 174.99
363 363
535.35 535.35
11.5. Stress comparison during the 3 h and 2 h turbine start up
11.6. Stress arising in the first notch of the rotor As the stress fields analyzed in sections 11.1e11.5 were the global stress in the rotor, the local stress profile was analyzed in sections 11.6.1e11.6.3. 11.6.1. K.F.A. Location of the analyzed notch point The stresses generated in the first blade rotor notch were compared. This location was chosen due to the high values of stress arising during the start-up in this place as well as operational problems related to this [9,14,17e21]. Fig. 28 shows the point in the notch being analyzed. 11.6.2. K.F.B. Stress in notch during the 3 h turbine start up Based on the strength analysis for the 3 h start-up, the results shown in Fig. 29 were obtained. As it can be seen, in the initial phase of the start-up the stress is greater for the start-up with the applied cooling by about 44 MPa. However, after 1900 s (31 min), the values of the stress generated during the cooling start-up are lower than for the start-up without cooling. After 1900s (31 min), the stress generated in the notch for start-up with applied cooling assume values of about 50 MPa lower. After reaching the maximum stress value in about 2860 s (47 min), due to the heating of the appropriate material layers, the stress decreases and in the final phase of the start-up the stress remains at a similar level. Table 6 presents the highest stress comparison in the notch for 3h-start up.
H-M-H stress comparison for the notch during 2h turbine start-up 300 250 stress [Mpa]
In order to clearly visualize the effects of the injection of additional cooling steam, the graph in Fig. 27 is presented. The results of the strength analysis referring to the locations of greatest stress agree with the analysis carried out in Ref. [14]. In addition, the character of the highest stress (compressive) values is consistent with theory [14,17e21]. It can be seen that shortening the start-up time to 2 h with the applied cooling is possible to obtain. Stresses generated in the rotor during accelerated start-up take on lower values than in the case of a 3 h start-up without cooling.
200 150 100 50 0 0
1000
2000
3000
4000 5000 6000 7000 8000 time [s] without cooling steam injection with 300 C cooling steam injection
̊ Fig. 30. H-M-H stress comparison for the notch for 2 h turbine start-up. ̊ Table 7 Comparison of the highest stress in the notch with the yield point for 2 h start-up. 2 h start-up
t [s]
s [MPa]
T [C]
Re(T) [MPa]
without cooling steam injection with 300C cooling steam injection
1925 1925
256.12 209.12
382 382
524.35 524.35
11.6.3. K.F.C. Stress in notch during the 2 h turbine start up Fig. 30 shows the H-M-H stress curves in the notch for accelerated start-up. The nature of stress patterns is analogous to the curves in Fig. 29. Reducing the start-up time causes an increase in stress arising in the notch. Just as during the 3 h start-up, in the case of a 2 h start-up, a reduction in the stress value is observed compared to the start-up without cooling. In this case, after a period of about 1920 s (32 min), the stress value for both runs decreases and the difference between them is about 50 MPa. Table 7 presents the highest stress comparison in the notch for 2h-start up. 12. Conclusion The analyses carried out provided information̊ on the basis of which the following main conclusions could be formulated: ̊
H-M-H stress comparison for the notch during 3h turbine start-up 250 stress [Mpa]
200 150 100 50 0 0
2000
4000
without cooling steam injection
6000 time [s]
8000
10000
12000
with 300 C cooling steam injection
Fig. 29. H-M-H stress comparison for the notch for 3 h turbine start-up.
- it is possible to reduce the start-up time from the state of a warm steam turbine 18K370 from 3 h to 2 h, while maintaining the strength requirements. - acceleration of the start-up time by 1 h without cooling leads to an increase in stress levels in the turbine structure. - the use of cooling steam injection leads to maintaining the thermal load within the limits imposed by the BOT system. - the applied method of cooling steam injection is structurally achievable, requires simple changes to the turbine, which do not require large amounts of money. - the maximum stresses for a start-up of 3 h occur in the 3826 s of the start-up without the use of cooling steam injection and reaches a value of 437.07 MPa - the maximum axial compressions for a start of 2 h, occur in 6245 s of the start without applied cooling steam injection and reaches a value of 589.63 MPa
J. Badur, M. Bryk / Energy 173 (2019) 1242e1255
- the control of the cooling steam injection can be carried out in the same way as in the work [29]. - cooling steam injection allows the reduction of the maximum global stress in the structure by 57.65 MPa at 3 h start-up and by 228.92 MPa at 2 h start-up. - the selected method of start-up acceleration does not cause the yield strength of the shaft material to be exceeded. The Thermal-FSI analyzes carried out confirm the possibility of reducing the start-up time from the warm state 18K390 turbine from 3 h to 2 h. The use of internal cooling steam injection during start-up allowed the reduction of the level of stress occurring in the rotor of the HP turbine part during the 3 h start-up. In addition, the level of stress generated in the rotor during the accelerated start-up with the injection of cooling steam is lower than the stress values occurring during the 3 h start-up without cooling. The use of cooling reduces the area of high temperatures in the construction of the turbine. This translates into a reduction of thermal loads occurring during start-up. The injection of cooling steam itself can also be used in the turbine adjustment process, when the turbine power should be increased suddenly without generating high thermal loads. References łkowski P, Kornet S, Banas K, Zio łkowski PJ, [1] Kowalczyk T, Badur J, Zio Stajnke M, Bryk M. The problem of thermal unit elasticity under the conditions of dynamic RES development. Acta Energetica 2017;31(2). [2] Domachowski Z, Klimacki Z. Auto-control of frequency and active power of the separated eletroenergetic system, vol. 92. Gdansk: IFFMT Nr; 1990 [in Polish]. [3] Domachowski Z. Automatic control of thermal turbines. Gdansk: Publishing House of Gdansk University of Technology; 2011 [in Polish]. łkowski P. Issues to improve the safety of 18K370 steam [4] Bzymek G, Badur J, Zio turbine operation. In: E3S web of conferences, vol. 13; 2017. 04003. [5] Chmielniak T, Kosman G. Thermal loads of steam turbines. Warszawa: WNT; 1990 [in Polish]. [6] Chmielniak T, Kosman G, Rusin A. Creep of steam turbine components. Warszawa: WNT; 1990 [in Polish]. [7] Kruczek S. Boilers. Structures and calculations. Wrocław: Publishing House of the Wrocław University of Technology; 2011 [in Polish]. [8] Taler J, Dzierwa P, Taler D, Harchut P. Optimization of the boiler start-up taking into account thermal stresses. Energy 2015;92:160e70. ski D, Kornet S, Kowalczyk T, Bryk M, Zio łkowski PJ, Stajnke M, [9] Badur J, Sławin łkowski P. Overdesign limitations from the maintaining availability of large Zio steam turbine. Energetyka 2016;(11):652e4. [10] Kosman G, Rusin A, Taler J, Pawlik M. Issues of design and operation of boilers and turbines for supercritical coal blocks. Gliwice: Publishing House of the Silesian University of Technology; 2010. [11] Kosman W. Optimization of start-up conditions to reduce thermal loads in cooled components of a supercritical steam turbine. J Power Technol 2011;91: 47e53. [12] Kosman W. Analysis of thermal loads during supercritical start-up of steam turbines with external cooling. Arch Energy 2013;XLIII(1e2):147e55 [in Polish]. [13] Cywnar L. Start-up of steam boilers. Warszawa: WNT; 1978 [in Polish]. [14] Dominiczak K, Rza˛ dkowski R, Radulski W, Szczepanik R. Neural networks in the steam turbine rotor thermal limitation system. Warszawa: Scientific Publishing House of the Institute of Exploitation Technology e PIB; 2015 [in Polish]. łkowski P. Analysis of unsteady flow forces [15] Badur J, Kornet S, Sławinski D, Zio acting on the thermowell in a steam turbine control stage. J Phys Conf Ser 2016;760.
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[16] Chmielniak T, Kosman G, Rusin A. Creep of steam turbine components. Warszawa: WNT; 1990 [in Polish]. [17] Lipka J. Durability of rotary machines. Warszawa: WNT; 1967 [in Polish]. [18] Banaszkiewicz M. Steam turbines start-ups. Transact IFFM 2014;126:169e98. [19] Banaszkiewicz M. On-line monitoring and control of thermal stress in steam turbine rotors. Appl Therm Eng 2016;94:763e76. [20] Banaszkiewicz M. Control and optimization of turbine start-ups. In: Proc. 3rd international conference for 200 MW turbine users, Kra˛ g; 2005. 16-18 Feb. [21] Banaszkiewicz M. Start-ups and viability monitoring control system of steam turbines. In: Proc. 10th symposium of information and training ‘diagnostics and repairs long-exploited power equipment e extending working time of ; 2008. 1e3 Oct. energy devices e opportunities and limitations’, ustron [22] Banaszkiewicz M. Multilevel approach to lifetime assessment of steam turbines. Int J Fatigue 2015;73:39e47. [23] Bryk M. Analysis of fast starts up and shut downs of large power steam turbine. Master's thesis. Gdansk University of Technology, Promoter Prof. Dr. J. Głuch; October 2017. [24] Kosman G, Rusin A. The influence of the start-ups and cyclic loads of steam turbines conducted according to European standards on the component's life. Energy 2001;26:1083e99. [25] Rivas C. et all. Steam turbine and system for start-up. United States Patent US 8,419,349 B2, Apr, 16; 2013. [26] Inomata et all. Steam turbine, method of cooling steam turbine and heat insulating method for steam turbine. United States Patent US 8,727,705 B2, May 20; 2014. [27] Dong-mei J, Jia-qi S, Quan S, Heng-Chao G, Jian-xing R, Quan-jun Z. Optimization of start-up scheduling and life assessment for a steam turbine. Energy 2018;160:19e32. [28] Dong-Mei J, Jia-Qi S, Yue D, Jian-Xing R. The optimization of the start-up scheduling for a 320 MW steam turbine. Energy 2017;125:345e55. [29] Hengliang Z, Danmei X, Yanzhi Y, Liangying Y. Online optimal control schemes of inlet steam temperature during startup of steam turbines considering low cycle fatigue. Energy 2016;117:105e15. łkowski P, Sławin ski D, Kornet S. An approach for estimation of [30] Badur J, Zio water wall degradation within pulverized-coal boilers. Energy 2015;92: 142e52. [31] Taler J, Dzierwa P, Taler D, Harchut P. Optimization of the boiler start-up taking into account thermal stresses. Energy 2015;92:160e70. [32] Badur J, Banaszkiewicz M, et al. Numerical simulation of 3D flow through a control valve. In: Intern. Conf.SYMKOM' 99, Arturowek-Łodz; 1999. łkowski P, Kornet S, Kowalczyk T, Banas K, Bryk M, Zio łkowski PJ, [33] Badur J, Zio Stajnke M. Enhanced energy conversion as a result of fluid-solid interaction in micro and nanoscale. J Theor Appl Mech 2018;56:329e32. [34] Huber TM. The proper work of deformation as a measure of material stress. Tech J 2018;22:1904 [in Polish]. łkowski P, Kornet S, Banas K, Kowalczyk T, Bryk M, Stajnke M, [35] Badur J, Zio łkowski PJ. The effort of the steam turbine caused by a flood wave load. AIP Zio Conf Proc 2017;1822:020001. sk; 2005 [in [36] Badur J. Five lecture of contemporary fluid termomechanics. Gdan Polish]. [37] Badur J, Bryk M. Analysis of unsteady boiling during high-temperature body sk: IFFM Transactions; 2017. dipping in water. Gdan łkowski P, Sławin ski D, Zio łkowski PJ, Kornet S, Stajnke M. [38] Badur J, Bryk M, Zio On a comparison of Huber-Mises-Hencky with Burzynski-Pecherski equivalent stress for glass body during nonstationary thermal load. AIP Conf Proc 2017;1822:020002. [39] Badur J, Ziolkowski P, Zakrzewski W, Slawinski D, Kornet S, Kowalczyk T, Hernet J, Piotrowski R, Felicjancik J, Ziolkowski PJ. An advanced Thermal-FSI approach to flow heating/cooling. J Phys Conf 2014;530:1e8. [40] Banas K, Badur J. On an approach to the thermo-elastic-plastic failure based on the Burzynski-Pecherski criterion. In: Ciarletta M, et al., editors. Proc. 11th int. Cong. On thermal stress. Italy: University of Salerno; 2016. p. 19e22. 5e9 June. ski D, Zio łkowski P, Badur J. Analysis of unsteady flow forces [41] Kornet S, Sławin on the thermowell of steam temperature sensor, vol. 129. Gdansk: IFFMT; 2015. p. 25e49. łkowski P, Jo łkowski PJ, Stajnke M, Badur J. Thermal[42] Kornet S, Zio zwik P, Zio FSI modeling of flow and heat transfer in a heat exchanger based on minichanels. J Power Technol 2017;97(5):373e81. [43] Ansys® academic research, release 17.1, UDF manual. 2009.
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Accelerated start-up of the steam turbine by means of controlled cooling steam injection Janusz Badur, Mateusz Bryk* sk, 80-231, Poland Institute of Fluid Flow Machinery, Polish Academy of Sciences, Fiszera 14 St., Gdan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 October 2018 Received in revised form 21 January 2019 Accepted 11 February 2019 Available online 20 February 2019
The paper presents the results of a Thermal-FSI analysis of accelerated start-up of a turbine controlled by an additional injection of cooling steam. The work contains a description of the phenomena that occur during the start-up as well as the accompanying effects. Attention is paid to structural elements that limit the speed of regulation of the steam unit. In order to estimate the possibility of accelerating the turbine start-up, four turbine starting simulations were carried out. Two simulations relate to the 3 h start-up, two consecutive ones to the 2 h start-up. Then the results of flow and strength simulation were presented. In the work, global stress of the rotor of the HP turbine part and the local rotor stress in the first rotor notch were analyzed. As a result of the simulations and analyses, the possibility of reducing the required start-up time from 3 h to 2 h was confirmed. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Thermal-FSI analysis Steam turbine start-up CFD model CSD model
1. Introduction Current trends in the design of new power units, characterized by steadily increasing work parameters as well as retrofits made on older units, force a change of approach both to the problem of designing new generating units (‘blocks’) and to the methods of repairing devices in operation. A new element that is challenging is Energy Network requirements strictly related to the variability of power in the system, which is caused by the impact of renewable energy in Europe [1]. In the situation of the aforementioned, the most important aspect is the adaptation of high power steam units to work with RES (Renewable Energy Source) installations. The wind is wayward and within a few minutes the value of its speed may change radically, which proportionally translates into the electric power generated by wind farms; this situation occurred in Poland in 2015 [1]. Coal-fired units had to reduce their load rapidly due to the sudden increase in electricity generation from renewable sources. In addition, it is postulated that certain blocks constitute the so-called ‘basis’ of the load, that is, they would produce electricity at the lowest cost, due to the higher efficiency of installations with higher powers [2,3]. This translates into unambiguous unit fuel consumption, energy price and environmental aspects related to the production of the above-mentioned energy.
* Corresponding author. E-mail address: [email protected] (M. Bryk). https://doi.org/10.1016/j.energy.2019.02.088 0360-5442/© 2019 Elsevier Ltd. All rights reserved.
In spite of the above, over time the constructed supercritical blocks will have to reduce their power to accommodate the development of wind farms. Currently, from the aspects of stable boiler operation and steam flow in the turbine, this load should not take less than 40% of rated load [4e6]. The blocks on which the deviation is made, should be adjusted (as much as possible) to the new conditions in terms of their minimum burden. In the past, but also currently, when due to an unforeseen event affecting the system, e.g. when the available power is not sufficient despite the turbine power reaching nominal capacity, it is possible to partially overload the turbine set in relation to condensation blocks. This operation is characterized by a decrease in efficiency, namely it consists of the partial shutdown of the regeneration system, which reduces the power of the turbine set by venting the flow of the working medium, so that its smaller part flows through the turbine flow channel by performing work [7,8]. The increasing power of installed RES sources and their dependence on weather conditions determines the maintenance of large steam blocks in the hot reserve [2,3]. In order to equal to this task, it is possible to take steps to make the work of the block more flexible, described in the aforementioned work [1,9], or to carry out modernization, and sometimes to change the structure. The situation of controlling the system's power currently comes down to the need for more frequent starts and shutdowns of turbine sets, including those of high power. In order to meet this requirement, it is possible to accelerate the start-up of the turbine set by considering the elastic-plastic adaptation of the structure,
J. Badur, M. Bryk / Energy 173 (2019) 1242e1255
Nomenclature e P T t v
total energy, J pressure, N/m2 temperature, K time, s velocity, m/s
Notation for vector quantities ! b mass force, m/s2 Sk k source, kg/m3s Sε ε sources, kg/m4s ! Jk diffusive flux of k, kg/m2s ! Jε diffusive flux of ε, kg/m2s !c t total tensor of irreversible tension, Pa ! t tensor of mechanical viscosity, Pa ! R tensor of Reynold's viscosity, Pa ! D tensor of diffusion viscosity, Pa !c total heat flux, W/m2 q !D diffusive heat flux, W/m2 q
which is described in Refs. [1,9] or use the cooling of the intake vapor, a working medium with lower parameters [9e12]. 2. Thermodynamic aspects of energy block flexibility 2.1. Steam unit elasticity The ‘elasticity’ term determines the possibility of smooth power regulation in the optimally short time, due to constraints in the block as a result of primary regulation, secondary regulation and load changes resulting from the impact of renewable sources. Speaking here of flexibility, we mean to equalize the power outage and the frequency generated after the primary regulation as quickly as possible. This activity is related with the operation of turbines in transient processes, for which the efficiency of energy generation is lower than in steady states, therefore the aim is to minimize the time required until the turbine set achieves a new set power value. However, the rate of change is limited by the flow and strength conditions occurring during transient operation. Transient work and transient conditions have a major impact on the start-up and withdrawal of turbine sets. The thermodynamic aspects that take place during the change of block loads are presented below, which are strictly connected with the possibility of adapting the block to the conditions imposed by the power system and renewable sources. As an example, the start-up of the turbine set will be recalled from the cold state. 2.2. Phenomena during start-up The turbine start-up procedure consists of increasing the rotor speed of the turbine set to the nominal RPM, typically 3000 (in Poland), and loading the turbine to a partial or nominal load. Increasing the speed and loading is related to increasing the parameters of fresh steam (temperature and pressure) and increasing the mass flow through the turbine [13,14]. The consequence of these changes is the heating of the turbine elements, mainly in the HP and SP parts of the turbine. The thermal loads on the hulls cause cyclical changes in stress and strains. These changes cause, after a
! q !t q !ph q ! v
1243
molecular heat flux, W/m2 turbulent heat flux, W/m2 phase change heat flux, W/m2 velocity vector, m/s
Greek symbols density, kg/m3 number of Poisson
r n
Subscripts red reduced HMH Huber-Mises-Hencky 1,2,3 main directions of the stress tensor Acronyms BOT CFD CSD RES H-M-H
Thermal Limit of the Unit system Computational Fluid Dynamic Computational Solid Dynamic Renewable Energy Sources Huber-Mises-Hencky
certain number of cycles, cracks as a result of thermal fatigue of the material. On the other hand, in the case of long-term states of the determined hull work, the phenomenon of creeping of materials is characteristic. Both phenomena are described in detail in the literature [8,15e17]. At the beginning of the start-up, the places near the inlet reach the highest temperatures and the accompanying stress and strains are the greatest. The heat is transported to the element and spread in its interior at a limited speed, and for this reason surfaces in direct contact with hot steam have a higher temperature than deeper-located regions. Layers of material with a higher temperature undergo thermal expansion, but this expansion is limited by adjacent layers at a lower temperature. This differential expansion is the reason for the generation of internal thermal stress [18]. A disadvantageous phenomenon of a thermal nature is the socalled ‘cat ridge’, caused by the temperature difference between the upper and lower halves of the hull [7,8,18]. The upper half has a higher temperature than the lower one and for this reason the hull tends to bend upwards. In addition to these undesirable thermal phenomena, other undesirable dynamic processes take place during start-up, which further reduce the lifetime of the turbine. These phenomena are resonance vibrations of rotating elements [14]. 3. Critical structural elements limiting the speed of regulation During power changes, critical structural elements limiting the speed of regulation were divided into two groups, the first of them concerns thermal stress, vibrations and strains, the second one concerns the issue of creeping and low-cycle transmission [4,5,9,16]. 3.1. Steam turbine components particularly exposed to thermal stress and deformations In Fig. 1, those places subject to special attention are marked when adapting the machine for quick starts and withdrawals. These
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4. Working vanes and rotor discs of the first stages of the highpressure part; 5. Working vanes and rotor discs of the first stages of the mediumpressure part; 6. The high pressure impeller; 7. Medium-pressure impeller; 8. High-pressure inner hull; 9. Medium-pressure inner hull. Fig. 1. Critical structural elements limiting the speed of regulation [9].
As a result of creeping there is: are areas [9,18e22]: 1. The vicinity of the fresh steam inlet to the first stage WP - this area includes the inlet spiral, the guide vanes, and the corresponding rotor area together with the 1 rotor blade; 2. An analogous place in the area of the steam inlet overheated to the SP body; 3. Glands located on the hot side of the WP body; 4. Analogue stuffings in the hot part of the SP; 5. Main thrust bearing; 6. Glands on the cold side of the WP body; 7. Similar stuffings on the cold side of the SP. The phenomena taking place in the above-mentioned points are described in Chapter 2 of this work. They are associated with temperature changes during start-up and shut-down, which leads to the generation of stress and thermal deformations, the values of which have been determined for the critical points listed in Fig. 1 and should not be exceeded. However, the working conditions imposed by the Energy Network, force power plants to adapt and coexist with renewable energy sources. One of the previously mentioned possibilities is the elasticplastic adaptation of the structure as well as non-project limitations aimed at making the block's work more flexible, while simultaneously accommodating in the time regimes of regulation without excessive reduction of the life of the turbine set.
3.2. Steam turbine components exposed to creep Turning to the second group referring to low-cycle fatigue and creep, in order to calibrate the display of critical construction elements, Fig. 2 is attached. The components of the reaction steam turbine exposed to creep are shown in Fig. 2 [14]: 1. Fresh steam pipelines and high pressure valve chambers; 2. Overheated steam pipelines and medium pressure valve chambers; 3. Shrink rings;
Fig. 2. Turbine components exposed to creep [14].
1) A decrease in structural clearances as a consequence of progressive permanent deformations during the life of the turbine. As a result of the decreasing clearance, there is the possibility of seizing and leakage in the flow associated with leaks, which may lead to turbine failure. 2) (in the case of a share turbine) A reduction in the initial radial difference, i.e., the radius of the inner disk and the radius of the outer shaft. This may lead to a decrease in the effectiveness of the connection. 3) A decrease in tension value of bolt tension, due to increasing inelastic deformation. This leads to a reduction in the tightness of the connection and the need to periodically tighten the screws to maintain tightness.
4. Possibilities of accelerated start-up The chapter presents possible variants of accelerated turbine start-up. The following methods are described in the literature: - elastic-plastic material adaptation [9], - cooling of turbine components by means of cooling steam injection [11,23e26], - optimization of start-up curves [24,27e29]. The first refers to the plasticization of the material due to higher stress values, which would occur due to accelerated start-up without structural changes. Simulations carried out in this study show that the amount of permanent deformation does not differ significantly from the values assumed at the design stage. However, the acceleration of the start-up time in this case is not significant. The second assumes the injection of steam with lower parameters in order to accelerate the start-up by reducing the stresses occurring in the structure. In the literature there are many ways to supply steam with lower parameters(Temperature, Pressure) in order to reduce the temperature gradient and, consequently, the thermal loads on the turbine structure. These methods assume internal and external cooling of turbine elements in an accelerated start-up. The results of the analyses lead to conclusions about the possibility of shortening the turbine start-up thanks to the applied method, although it requires modification of the turbine construction. The third method assumes optimization of turbine inlet steam control in order to shorten the start-up time. Analyses made in this study indicate that it is possible to control the start-up in such a way that, at the same time, the start-up time does not exceed the maximum stress. After the research, the authors decided to carry out an analysis of accelerated turbine start-up by means of cooling steam injection. However, the place of injection of cooling steam is different than in the cases analyzed in the literature. This method of start-up acceleration was chosen because of the promising analyses carried out in the works.
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5. Analyzed geometry 5.1. Reference model Based on the actual geometry of the part HP of the 18K390 w power plant (Fig. 3), a two-dimensional turbine from the Bełchato turbine model was created for the purpose of numerical analysis. Due to the extensive flow and strength calculations, two models had to be prepared. The first one as reference is shown in Fig. 4.
Fig. 4. Reference model of part HP 18K390 turbine.
5.2. Modified model The second model, with the injection of cooling steam is the same, the only changes are visible near the inlet to the first stage of the turbine and this is shown in Fig. 5. The edges marked with the letters A and B are additional inlets that are used in the analysis case with additional cooling steam injection.
Fig. 5. Close-up to the area of additional steam inlets.
5.3. The simplifications used in the model Due to the complexity of the two-dimensional geometry and the difficulty of two-dimensional modeling of phenomena in the exact representation of the turbine, it was simplified. Here are the following changes in relation to real geometry: - simplifying cutting geometry for blades, both steering and rotor; - simplification of the blades themselves, the right blades replace the four-edge elements. In addition, these elements are shorter compared to the actual blades due to the blockage of the flow; - simplification of the flow channel (green color in the Fig. 6); - no seals between the inner casing and the impeller as well as between the outer casing and the impeller; The main focus of the analysis is not on the flow but on the phenomena that arise as a result of the liquid's influence on the solid. The influence of steam on the sealing ring and the part of the external and internal body was not focused. In the work, the authors focus on the idea of cooling the fresh steam in order to accelerate the start-up of the turbine. The possibilities of cooling steam with steam with different parameters are numerous [9e12], so the authors chose this one because of the possibility of eliminating the sudden change in the direction of the steam flow in the inlet spiral elbow. Cooling steam can be taken from the lower parts of the boiler. In the case of the block in question, the lowest steam temperature from the low part of the boiler is approximately 300 C [9], which corresponds to the saturation temperature of steam at a given pressure. Additionally, the cooling steam pressure will be always higher than the pressure at the inlet because of boiler losses [8,23,30,31].
Fig. 6. Flow channel of the analyzed geometry.
6. Model CFD 6.1. Equations of behaviour For the fluid flow simulation, three basic formulas of conservation are fulfilled. These three main formulations which describe CFD are presented below [32e34]: Conservation of mass equation:
vt ðrÞ þ divðr! vÞ¼0
(1)
Conservation of momentum equation:
! c ! vt ðr! v Þ þ div r! v 5! v þp I ¼ div ! t þrb Conservation of energy equation:
vt ðreÞ þ div
P ! !t eþ r v ¼ div ! q þ q
r
! !c !D þrb! þ t ! v þ q v
These are balance equations in conservative form, where: r- gas density, [kg/m3] ! ! !c ! t ¼ t þ R þ D - total tensor of irreversible stress, [Pa] ! v ¼ vi ei e mean velocity, [m/s] ! q e molecular heat flux, [W/m2] !t q - turbulent heat flux, [W/m2] !D q - diffusive heat flux, [W/m2] P - pressure, [Pa] e ¼ uþ Fig. 3. Axial section of part HP of the 18K390 turbine [14].
(2)
.
b ¼
. 1. 2 n $ v - total energy, . 9; 81 ez . [m/s2]
[J]
(3)
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6.2. Model of turbulence
or in the equivalent form provided by the formula (8):
The above three equations, i.e. (1e3), were complemented by two evolution equations for parameters, which allow to define tensile tensor components [35]: Evolution equation concerning turbulent energy k:
sred ¼ pffiffiffi
! vt ðrkÞ þ divðrk! v Þ ¼ div J k þ Sk
8. Thermal-FSI
(4)
Evolution equation concerning energy dissipation ε:
! vt ðrεÞ þ divðrε! v Þ ¼ div J ε þ Sε
(5)
A more detailed description of the used models in CFD codes can be also found in Refs. [33,35]. The pressure of the liquid walls is omitted as a pressure that causes negligible stress in walls. Because of that, the equation of momentum conservation is not important due to the mechanical reasons but only due to thermal reasons, as the equation which describes heat convection and movement of the hot fluid, which flows through flow channel. For that reason, the viscous and turbulent stress influence is negligible. More important ! is the assumption of gravity in element of mass force: rðx; tÞ b or a precise equation of water state which gives actual water density in each point and in each moment: rðx; tÞ. The heat exchange model in a steam turbine is noteworthy. This is divided into: -conduction, -convection, -radiation. Due to the considered start-up issue, the most important method of heat exchange is convection between the turbine elements and the steam that is passing them. The second in the process is conduction observed during the whole turbine operation cycle. The influence of radiation was omitted due to its greatest impact being during cooling down of the turbine [14,17]. Therefore, in the formula for total energy (3) radiation was omitted. 7. CSD model The following strength hypothesis was used to simulate the stress generated in the material: The Huber-Mises-Hencky reduced stress given by formula (6) [23,36]:
sHMH ¼
i 1 þ vh ðs1 s2 Þ2 þ ðs2 s3 Þ2 þ ðs3 s1 Þ2 6E
(6)
where:
n -number of Poisson E - Young's modulus
s1 ; s2 ; s3 - main stress The condition of safe mechanical condition assumes the function (7):
1
sred ¼ pffiffiffi 2
1
2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðs11 s22 Þ2 þ ðs33 s22 Þ2 þ ðs11 s33 Þ2
(8)
Thermal-FSI analysis consists in CFD analysis, the results of which are exported to a solid state solver (CSD). Next, the CSD solver on the basis of imported data (temperature, pressure) determines the stress and displacements in the analyzed geometry [37e39]. The principle of the analysis is shown in Fig. 7. There are two types of Thermal-FSI analysis: - One-way FSI - Two-way FSI In the one way FSI, following CFD calculations, the solution is exported to the CSD solver and the stress and displacements determined on their basis. In the case of two-way FSI analysis, both models (CFD and CSD) are coupled together during the entire simulation. After calculating one CFD time step, the results are exported to the CSD solver. Stress and displacement are then determined. Then, due to deformations of the analyzed geometry, an automatic remeshing is carried out. The next time step in the CFD solver is calculated with the new mesh. The entire process is carried out automatically until the last time step [40e42]. The work involved one-way Thermal-FSI analyzes. Temperature fields were imported, from which the stress fields in the analyzed geometry were determined. 9. Boundary and initial conditions 9.1. The applicable inlet and outlet conditions of the flow channel As the inlet boundary condition, inlet pressure was used, and outlet pressure as outlet condition. For reference geometry, this is illustrated in Fig. 8. In the case of modified geometry, inlet pressure was also used as the inlet boundary condition. Similarly, the outlet pressure condition was applied analogously to the outlet edge. This is shown in Fig. 8. The start-up was carried out from the warm state, ie when the turbine's HP part is preheated to 130 C [14]. 9.2. Inlet and outlet parameters The parameters at the inlet and outlet of the geometry were implemented in accordance with the actual start-up curves for the analyzed unit, Fig. 9 [14]. Due to the fact that the analysis is a 2D analysis, it was necessary to implement an enthalpy decrease in the turbine. Since the existing blade profiles are simplified, it was necessary to write the code for the temperature drop in the turbine, using UDF [23,43] (User Defined Function) code. Taking into account the real temperature drops in the turbine, the enthalpy drop in the flow channel
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sxx syy 2 þ szz syy 2 þ ðsxx szz Þ2 þ 6 t2xy þ t2yz þ t2xz
(7)
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Fig. 7. Principle of operation of the Thermal-FSI [33].
appropriate degrees of freedom of the analyzed rotor were limited (Fig. 10). Support A prevents the shaft from moving in the positive direction of the OX axis, which simulates the work of the bearing. Support B prevents the shaft from moving in the negative direction of the OY axis. Condition B has been implemented due to the problem of extrapolation of displacements [14]. Fig. 8. Marking of inlet and outlet edges.
10. CFD results was mapped using the abovementioned code. It should be mentioned that the turbine fan work in the initial start-up phase is also taken into account here. In addition, due to the twodimensional analysis, it was necessary to use as inlets - edges from which the vapor flow occurs in the normal direction to the edge.
The chapter presents the results of flow analysis for 3 h and 2 h start-up for both types of geometry. The temperature fields observed during the standard start-up and using the cooling steam injection control were compared.
9.3. The materials used in the analysis
10.1. Comparison of temperature fields at 180 min for the 3 h turbine start-up without cooling steam injection with the start of the turbine, in which 300 C cooling steam injection was applied
Domain materials found in the analysis are presented in Table 1. In order to analyze the possibility of accelerating the start-up of the turbine by means of a controlled injection of cooling steam, a two-dimensional, one-sided Thermal-FSI analysis was carried out. This analysis consists in importing the resulting temperature field from the CFD solution to the CSD solver in which the stress fields in the structure are determined. 9.4. Strength analysis In the case of a solid body, the stress behaviour was only analyzed in the turbine rotor. This step was applied due to the twodimensional analysis. The physical properties of the shaft material are summarized in Table 2. Additionally the chemical composition of ST10Ts steel is given by Table 3. Consideration of the entire construction in terms of strength would not make much sense due to axial and radial clearances present in the real construction (which are not present in the analysis). In addition, the strength analysis carried out is analogous to that described by Dominiczak R. in Ref. [14]. According to the assumptions taken from Ref. [14], the
In sub-section 10.1, the temperature fields were compared in the 180th minute of the 3 h start-up. Fig. 11 shows the temperature redistribution at the 180th minute of start-up without the use of cooling steam injection. We are dealing with a standard temperature distribution for turbine startup. The highest temperature field occurs from the inlet to the 6th stage of the turbine. Due to the simplification of the flow channel, there is no temperature change in the external hull of the turbine, outside the area of direct interaction of the working medium with the solids. This fact does not affect the analysis, as the authors focused on the impact on the most thermally loaded elements, i.e. the area of the inlet to the HP part of the turbine as well as the area of the first stages of the turbine. Fig. 12 shows the temperature field distribution for 180 min start-up with the use of cooling steam injection. It can be seen that the use of cooling steam injection control reduces the field of influence of high temperatures to the first turbine stages. In addition, the temperature at the turbine outlet is reduced. This is due to the mixing of the main steam stream with the additional cooling steam streams. The observed reduction in the impact of high temperatures will translate into a reduction in the value of stress arising in
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Fig. 9. Parameters change during start-up [14].
Table 1 Domain materials used in the analysis [14].
Table 3 The chemical composition of ST10Ts steel.
Domain
Material
Element
Fe
Ni
Cr
Mn
Si
C
P
S
Shaft Inner hull Outer hull Sealing rings Stator blades Rotor blades Fluid
St10ts Stg10T G20Mo5 St12T St12T St12T Water vapor
Wt %
42
32
19
2
1.13
0.08
0.04
0.03
Fig. 10. Support conditions for stress analysis of the turbine rotor. Table 2 Physical properties of ST10Ts steel. T [C]
b [1/K]
l [W/m$K]
Cp [J/kg$K]
E [GPa]
Re [MPa]
20 100 200 300 400 500 600
0.0000104 0.0000107 0.0000110 0.0000140 0.0000170 0.0000120 0.0000123
24.0 24.4 24.8 25.1 25.6 26.1 26.4
439 500 534 571 625 704 831
212 208 202 195 186 171 142
698 647 608 570 515 440 315
the construction of the turbine. The difference in the temperature field in the flow channel results directly from the mixing of high performance steam with lower temperature steam. Although this will affect the efficiency of the turbine, the power of the turbine remains unchanged due to the increased steam flow rate. Additionally, the purpose of the analysis is to determine the possibility of reducing the start-up time of the turbine and not to test its efficiency.
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Fig. 11. 180-th minute of the 3 h start-up without cooling steam injection.
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Fig. 12. 180-th minute of the 3 h start-up with 300 C cooling steam injection.
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Fig. 13. 120-th minute of the 2 h start-up without cooling steam injection.
Fig. 14. 120-th minute of the 2 h start-up with 300 C cooling steam injection.
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10.2. Comparison of temperature fields at 120 min for the 2 h turbine start-up without cooling steam injection with the start of the turbine, in which 300 C cooling steam injection was applied In the sub-section 10.2, the temperature fields were compared in the 120th minute of the 2 h start-up. Fig. 13 shows the temperature field in the final accelerated startup phase without injection of cooling steam. Compared to a 3-h start, a much higher temperature gradient is observed in both the flow channel and the turbine construction. In this case, the high temperature field reaches the 5th turbine stage. Large temperature gradients will translate into high stress values in the turbine construction. The use of cooling steam injection in accelerated start up limits the high temperature field. This is shown in Fig. 14. As in the case of 3 h start-up, in the 2 h start-up the field of the highest temperatures was limited to the first stage of the turbine. In addition, the temperature gradients occurring here assume lower values than in the case of starting without the injection of cooling steam.
Fig. 16. Axial stress in 180-th minute of the 3 h start-up without cooling steam injection.
Fig. 17. H-M-H stress in 180-th minute of the 3 h start-up with 300 C cooling steam injection.
11. CSD results
11.1. Comparison of stress fields at 180 min for the 3 h turbine startup without cooling steam injection with the start of the turbine, in which 300 C cooling steam injection was applied The area of H-M-H stress in the 180th minute of 3 h start-up without cooling is shown in Fig. 15. Redistribution of stress field took place. The largest stresses arose in the area of notches from 8 to 24 and they range from 130 MPa to about 373.7 MPa. The smallest observed stress values are at the level of 26.7 MPa. As a result of geometry heating, the thermal load is reduced, so the stress around the first degrees is less. High stress values in the right part of the shaft result from a different field of temperature distribution than in the remaining section of the shaft (thick elements heat up more slowly). Axial stresses are shown in Fig. 16. The highest compressive stress values occur in the area of the notches from 8 to 24 and the tensile ones in the rotor axis below the notches from 8 to 24. The axial stresses show the character of the stress state. The dominant character of compressive stresses in the top layers of the rotor is observed. The H-M-H stress in the last minute of the 3 h start-up with cooling is shown in Fig. 17. There is a full analogy in places where maximum stress occurs. The difference, as in previous cases, occurs
Fig. 15. H-M-H stress in 180-th minute of the 3 h start-up without cooling steam injection.
Fig. 18. Axial stress in 180-th minute of the 3 h start-up with 300 C cooling steam injection.
H-M-H stress comparison for 3h turbine start-up
stress [Mpa]
As in the case of the flow analysis results, an analogous comparison of results was performed for the strength analysis. The first two subsections 11.1 and 11.2 concerns the results of the strength analysis for the 3 h start-up and subsections 11.3 and 11.4 of the analysis for the 2 h start-up. All the results are summarized in subsection 11.5. In addition, the point of the first notch for the rotor blade was analyzed in subsection 11.6. The authors analyzed a point in the vicinity of which damage often occurs due to changes in temperature with a high gradient [19,23].
500 450 400 350 300 250 200 150 100 50 0 0
2000
4000
300 C cooling steam injection
6000 time [s]
8000
10000
12000
without cooling steam injection
Fig. 19. H-M-H stress comparison for 3 h turbine start-up.
in stress values, which amount to 330.93 MPa. In addition, the use of cooling steam injection leads to a more uniform stress field in the thickest part of the rotor. The lowest reduced stress value of H-M-H is 23.65 MPa, which is similar to that of no cooling steam injection. Axial stresses in the 180th minute of a cooling start are shown in Fig. 18. As in the case of H-M-H stress and in the case of axial stress, there is a full analogy to the case without cooling. Differences also occur in the value of stress. The highest compressive stress assume the value of 328.01 MPa and tensile the 104.09 MPa. The use of cooling steam injection leads to a higher proportion of tensile stress in the thinnest part of the shaft. This is due to the difference in temperature at this point. 11.2. Stress comparison during the 3 h turbine start up Fig. 19 presents a comparison of the stress course during the 3 h start-up with the injection of cooling steam and without cooling. In the initial phase of the start-up, the stress generated in the structure for the cooling start take values of around 100 MPa lower than in the case of a start-up without cooling. This is due to the more homogeneous temperature field around the inlet and before the first stages due to the additional inlets from which the temperature
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Compressive stress comparison for 3h turbine start-up 0 -50 0
2000
4000
6000
8000
10000
12000
stress [MPa]
-100 -150 -200 -250 -300 -350 -400 -450
time [s] without cooling steam injection
300 stC cooling steam injection
Fig. 20. Compressive stress comparison for 3 h turbine start-up.
Table 4 Comparison of the highest stress in the structure with the yield point for 3 h startup. 3 h start-up
t [s]
s [MPa]
T [C]
Re(T) [MPa]
without cooling steam injection with 300C cooling steam injection
3826 3826
437.07 379.47
357 357
538.65 538.65
Fig. 24. Axial stress in 120-th minute of the 2 h start-up with 300 C cooling steam injection.
lower values than without cooling. Additionally, Table 4 compares the stress values with the yield point for a given temperature. It can be seen that in both cases the highest stress values occur in 3826s and are below the yield point. Fig. 21. H-M-H stress in 120-th minute of the 2 h start-up without cooling steam injection.
Fig. 22. Axial stress in 120-th minute of the 2 h start-up without cooling steam injection.
̊
11.3. Comparison of stress fields at 120 min for the 2 h turbine startup without cooling steam injection with the start of the turbine, in which 300 C cooling steam injection was applied The H-M-H stress field in the 120th minute of the accelerated start up without injection of cooling steam is presented in Fig. 21. The highest stress values occur in the area of notches from 8 to 24 and in the thinnest cross-section of the rotor. Due to the higher temperature gradient, a significant increase in stress in the construction of the turbine is observed and in this case it amounts to 580.65 MPa. The minimum stress is 41.5 MPa. The axial stress field in the 120th minute of accelerated start
H-M-H stresses comparison for 2h turbine start-up 700
Fig. 23. H-M-H stress in 120-th minute of the 2 h start-up with 300 C cooling steam injection.
stress [Mpa]
is also redistributed. After 1400 s (23 min), stress increase in both cases and after reaching the maximum in 3,800 s (63 min) decrease. The character of both curves is similar. The difference is that in the case of cooling, the values of stress assume lower values during the entire start-up. Fig. 20 shows the course of the compressive stress during the start-up. Due to the dominant compressive stress, it is not surprising that their values are high. Also in this case in the entire start-up range, the compressive stress in the case of cooling takes
600 500 400 300 200 100 0 0
1000
2000
3000
without cooling steam injection
4000 time [s]
5000
6000
7000
8000
300 stC cooling steam injection
Fig. 25. H-M-H stress comparison for 2 h turbine start-up.
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the stress values which, for cooling start-up, assume lower values (see Fig. 25).
Compressive stresses comparison for 2h turbine start-up 0 0
2000
4000
6000
8000
-100 stress [Mpa]
1253
11.4. Stress comparison during the 2 h turbine start up
-200 -300 -400 -500 -600
time [s] without cooling steam injection
300 stC cooling steam injection
Fig. 26. Compressive stress comparison for 2 h turbine start-up.
Table 5 Comparison of the highest stress in the structure with the yield point for 2 h startup. 2 h start-up
t [s]
s [MPa]
T [C]
Re(T) [MPa]
without cooling steam injection with 300 cooling steam injection
6245 7200
589.63 360.71
522 552
415.8 382.2
Fig. 25 shows the course of stress in the rotor during accelerated start-up. Stress patterns show a full analogy to the curves observed during the 3 h start-up. In this case, the use of cooling causes a reduction in the value of stress generated in the rotor by about 20 MPa at the start of the start-up, to about 200 MPa in the final phase of the start-up. Table 5 presents the highest stress comparison for 2h-start up. As in the case of 3 h start-up, so in the case of a 2 h start-up, the compressive stresses are of decisive importance. The curves of compressive stress during accelerated start-up are shown in Fig. 26 . The stress pattern for accelerated start-up shows a full analogy to the accelerated start-up (Fig. 20), with the difference that in the case of 2 h start, the generated stress values are much greater (in case without cooling). In the case of an accelerated start-up, the yield strength of the shaft structure is exceeded for the case without cooling steam injection. The material is plasticized and the yield point is exceeded by almost 174 MPa.
without injection of cooling steam is presented in Fig. 22. In the area of the notches from 8 to 24 there are compressive stresses whereas tensile stress occur in the thinnest shaft section and rotor axis directly under the notches 8e24. A high temperature gradient increases the compressive stress in the structure. The H-M-H stress field in the 120th minute of the accelerated start-up with the injection of cooling steam is presented in Fig. 23. The nature of the stress field is analogical to the previous cases. The difference occurs in the stress values which, for cooling start-up, assume lower values. The use of cooling steam injection reduces the stress generated in the consortium from 580 MPa to 38 MPa. The axial stress field in the 120th minute of the accelerated start-up with the injection of cooling steam is presented in Fig. 24. The nature of the stress field is analogous to the previous cases. In the area of the notches from 8 to 24, there are compressive stresses while stretching occurs in the thinnest section of the shaft and the rotor axis directly under the notches 8e24. The difference occurs in Fig. 28. Analyzed point in the notch.
H-M-H stresses comparison for 3h and 2h turbine start-up 700
stress [Mpa]
600 500 400 300 200 100 0 0
2000
4000
6000 8000 time [s] 3h start-up without cooling steam injection 3h start-up with cooling steam injection 2h start-up without cooling steam injection 2h start-up with cooling steam injection
10000
Fig. 27. H-M-H stress comparison for 3 h and 2 h turbine start-up.
12000
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The use of cooling steam injection keeps the maximum stresses in the shaft below the yield point. Although the difference is 22 MPa, it is an extreme state, which confirms the possibility of shortening the turbine start-up time while maintaining stresses within the limits of maintaining normal turbine movement.
Table 6 Comparison of the highest stress in the notch with the yield point for 3 h start-up. 3 h start-up
t [s]
s [MPa]
T [C]
Re(T) [MPa]
without cooling steam injection with 300C cooling steam injection
2386 2386
213.82 174.99
363 363
535.35 535.35
11.5. Stress comparison during the 3 h and 2 h turbine start up
11.6. Stress arising in the first notch of the rotor As the stress fields analyzed in sections 11.1e11.5 were the global stress in the rotor, the local stress profile was analyzed in sections 11.6.1e11.6.3. 11.6.1. K.F.A. Location of the analyzed notch point The stresses generated in the first blade rotor notch were compared. This location was chosen due to the high values of stress arising during the start-up in this place as well as operational problems related to this [9,14,17e21]. Fig. 28 shows the point in the notch being analyzed. 11.6.2. K.F.B. Stress in notch during the 3 h turbine start up Based on the strength analysis for the 3 h start-up, the results shown in Fig. 29 were obtained. As it can be seen, in the initial phase of the start-up the stress is greater for the start-up with the applied cooling by about 44 MPa. However, after 1900 s (31 min), the values of the stress generated during the cooling start-up are lower than for the start-up without cooling. After 1900s (31 min), the stress generated in the notch for start-up with applied cooling assume values of about 50 MPa lower. After reaching the maximum stress value in about 2860 s (47 min), due to the heating of the appropriate material layers, the stress decreases and in the final phase of the start-up the stress remains at a similar level. Table 6 presents the highest stress comparison in the notch for 3h-start up.
H-M-H stress comparison for the notch during 2h turbine start-up 300 250 stress [Mpa]
In order to clearly visualize the effects of the injection of additional cooling steam, the graph in Fig. 27 is presented. The results of the strength analysis referring to the locations of greatest stress agree with the analysis carried out in Ref. [14]. In addition, the character of the highest stress (compressive) values is consistent with theory [14,17e21]. It can be seen that shortening the start-up time to 2 h with the applied cooling is possible to obtain. Stresses generated in the rotor during accelerated start-up take on lower values than in the case of a 3 h start-up without cooling.
200 150 100 50 0 0
1000
2000
3000
4000 5000 6000 7000 8000 time [s] without cooling steam injection with 300 C cooling steam injection
̊ Fig. 30. H-M-H stress comparison for the notch for 2 h turbine start-up. ̊ Table 7 Comparison of the highest stress in the notch with the yield point for 2 h start-up. 2 h start-up
t [s]
s [MPa]
T [C]
Re(T) [MPa]
without cooling steam injection with 300C cooling steam injection
1925 1925
256.12 209.12
382 382
524.35 524.35
11.6.3. K.F.C. Stress in notch during the 2 h turbine start up Fig. 30 shows the H-M-H stress curves in the notch for accelerated start-up. The nature of stress patterns is analogous to the curves in Fig. 29. Reducing the start-up time causes an increase in stress arising in the notch. Just as during the 3 h start-up, in the case of a 2 h start-up, a reduction in the stress value is observed compared to the start-up without cooling. In this case, after a period of about 1920 s (32 min), the stress value for both runs decreases and the difference between them is about 50 MPa. Table 7 presents the highest stress comparison in the notch for 2h-start up. 12. Conclusion The analyses carried out provided information̊ on the basis of which the following main conclusions could be formulated: ̊
H-M-H stress comparison for the notch during 3h turbine start-up 250 stress [Mpa]
200 150 100 50 0 0
2000
4000
without cooling steam injection
6000 time [s]
8000
10000
12000
with 300 C cooling steam injection
Fig. 29. H-M-H stress comparison for the notch for 3 h turbine start-up.
- it is possible to reduce the start-up time from the state of a warm steam turbine 18K370 from 3 h to 2 h, while maintaining the strength requirements. - acceleration of the start-up time by 1 h without cooling leads to an increase in stress levels in the turbine structure. - the use of cooling steam injection leads to maintaining the thermal load within the limits imposed by the BOT system. - the applied method of cooling steam injection is structurally achievable, requires simple changes to the turbine, which do not require large amounts of money. - the maximum stresses for a start-up of 3 h occur in the 3826 s of the start-up without the use of cooling steam injection and reaches a value of 437.07 MPa - the maximum axial compressions for a start of 2 h, occur in 6245 s of the start without applied cooling steam injection and reaches a value of 589.63 MPa
J. Badur, M. Bryk / Energy 173 (2019) 1242e1255
- the control of the cooling steam injection can be carried out in the same way as in the work [29]. - cooling steam injection allows the reduction of the maximum global stress in the structure by 57.65 MPa at 3 h start-up and by 228.92 MPa at 2 h start-up. - the selected method of start-up acceleration does not cause the yield strength of the shaft material to be exceeded. The Thermal-FSI analyzes carried out confirm the possibility of reducing the start-up time from the warm state 18K390 turbine from 3 h to 2 h. The use of internal cooling steam injection during start-up allowed the reduction of the level of stress occurring in the rotor of the HP turbine part during the 3 h start-up. In addition, the level of stress generated in the rotor during the accelerated start-up with the injection of cooling steam is lower than the stress values occurring during the 3 h start-up without cooling. The use of cooling reduces the area of high temperatures in the construction of the turbine. This translates into a reduction of thermal loads occurring during start-up. The injection of cooling steam itself can also be used in the turbine adjustment process, when the turbine power should be increased suddenly without generating high thermal loads. References łkowski P, Kornet S, Banas K, Zio łkowski PJ, [1] Kowalczyk T, Badur J, Zio Stajnke M, Bryk M. The problem of thermal unit elasticity under the conditions of dynamic RES development. Acta Energetica 2017;31(2). [2] Domachowski Z, Klimacki Z. Auto-control of frequency and active power of the separated eletroenergetic system, vol. 92. Gdansk: IFFMT Nr; 1990 [in Polish]. [3] Domachowski Z. Automatic control of thermal turbines. Gdansk: Publishing House of Gdansk University of Technology; 2011 [in Polish]. łkowski P. Issues to improve the safety of 18K370 steam [4] Bzymek G, Badur J, Zio turbine operation. In: E3S web of conferences, vol. 13; 2017. 04003. [5] Chmielniak T, Kosman G. Thermal loads of steam turbines. Warszawa: WNT; 1990 [in Polish]. [6] Chmielniak T, Kosman G, Rusin A. Creep of steam turbine components. Warszawa: WNT; 1990 [in Polish]. [7] Kruczek S. Boilers. Structures and calculations. Wrocław: Publishing House of the Wrocław University of Technology; 2011 [in Polish]. [8] Taler J, Dzierwa P, Taler D, Harchut P. Optimization of the boiler start-up taking into account thermal stresses. Energy 2015;92:160e70. ski D, Kornet S, Kowalczyk T, Bryk M, Zio łkowski PJ, Stajnke M, [9] Badur J, Sławin łkowski P. Overdesign limitations from the maintaining availability of large Zio steam turbine. Energetyka 2016;(11):652e4. [10] Kosman G, Rusin A, Taler J, Pawlik M. Issues of design and operation of boilers and turbines for supercritical coal blocks. Gliwice: Publishing House of the Silesian University of Technology; 2010. [11] Kosman W. Optimization of start-up conditions to reduce thermal loads in cooled components of a supercritical steam turbine. J Power Technol 2011;91: 47e53. [12] Kosman W. Analysis of thermal loads during supercritical start-up of steam turbines with external cooling. Arch Energy 2013;XLIII(1e2):147e55 [in Polish]. [13] Cywnar L. Start-up of steam boilers. Warszawa: WNT; 1978 [in Polish]. [14] Dominiczak K, Rza˛ dkowski R, Radulski W, Szczepanik R. Neural networks in the steam turbine rotor thermal limitation system. Warszawa: Scientific Publishing House of the Institute of Exploitation Technology e PIB; 2015 [in Polish]. łkowski P. Analysis of unsteady flow forces [15] Badur J, Kornet S, Sławinski D, Zio acting on the thermowell in a steam turbine control stage. J Phys Conf Ser 2016;760.
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