Struct Multidisc Optim (2010) 40:529–535 DOI 10.1007/s00158-009-0370-8
INDUSTRIAL APPLICATION
Optimization of heating and cooling operations of steam gate valve Piotr Duda · Renata Dwornicka
Received: 30 October 2008 / Revised: 16 January 2009 / Accepted: 12 February 2009 / Published online: 14 March 2009 © Springer-Verlag 2009
Abstract Optimization will be done on the basis of a calculation of an initial medium temperature step and, following that, the maximum heating or cooling rate of temperature changes. Calculated results are of great practical significance because it will be possible to use them in power plants. Temperature step change can be easily implemented by suddenly opening hot water or steam supply into the interior of a pressure element, which has a lower initial temperature. The power units can be utilized in a way that will improve their longevity. The proposed method is simple and has many advantages. A quasi-steady state is not assumed and element geometry can be complicated. The optimization is based on the highest stress in the whole construction. Keywords Steam boilers · Heat transfer · Thermal stresses · Monitoring of steam boilers · Optimization
1 Introduction High thermal stresses are created during the operation of power block devices such as boiler drums, outlet headers, steam valves, turbines and heat exchangers.
P. Duda · R. Dwornicka (B) Department of Mechanical Engineering, Cracow University of Technology, Al. Jana Pawła II 37, 31-864 Kraków, Poland e-mail:
[email protected] P. Duda e-mail:
[email protected]
Due to a cyclic character of such stresses, a phenomenon of low-cyclic fatigue occurs, which may lead to the formation of fractures. Manufacturers of power block devices frequently advise the users to keep within the prescribed limits for maximum heating and cooling rates of elements. Attempts are made to develop algorithms for operating power blocks (Taler and Duda 2006; Taler et al. 2002; Duda et al. 2003). Thanks to these mathematical systems, one is able to extend the life of operating devices and shorten the duration of all transient operations. The optimum medium temperature changes can be developed using the German boiler code TRD 301 (TRD 301 1986), which is based on quasi-steady one dimensional temperature distribution inside the component. However, during transient processes a quasisteady state often does not occur and total stresses in the element, heated using the optimum medium temperature calculated by TRD 301, can exceed allowable stresses. Paper (Krueger et al. 2004) presents optimization of boiler start-up using a nonlinear boiler model. However, thermal stresses were calculated only in simple cylindrical construction element and quasisteady state was also assumed. A method to calculate thermal stresses in transient state from readily available power plant measurement was presented in (Lausterer 1997). The results demonstrate that start-up times can be reduced through optimization. However, the presented method can be applied only to simple cylindrical elements. Paper (Taler and Dzierwa 2007) presents the method for determining optimum medium temperature, which ensures that the sum of thermal stresses and stresses caused by pressure at selected points do not exceed the allowable stresses. The presented optimum medium temperature consists of initial medium
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temperature step and later increases at the optimum rate of temperature change (Taler and Dzierwa 2007). In elements of complicated geometry, it is often difficult
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to select points for stress monitoring. The aim of this paper is to present the numerical method, which could be used to find the optimum medium temperature so
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that the maximum total stress in the whole construction element would not exceed the allowable stresses. The steam gate valve (SGV) is used in the fresh and pre-heated steam pipelines in the power unit of 360 MW. It is one of the most heavily loaded elements in the power block. The SGV is installed in the steam pipeline of BP1150 boiler with a steam capacity of 1,150 t/h. It is exposed to high stresses caused by temperature and pressure given off by a flowing medium. The SGV was designed for the pressure, Pin = 18 MPa, and steam temperature, Tw = 540◦ C. The geometry of the SGV is presented in Fig. 1. It is necessary to construct pressure elements, which operate under high work parameters, out of materials that exhibit good mechanical properties. Materials should retain their properties within the wide temperature range in which they operate, especially at the yield strength Re . The actual SGV was made out of an alloy steel and designed to work at elevated temperatures designated as 14 MoV63 (13 HMF). This steel has a ferritic structure and a high yield strength, Re = 206 MPa for the temperature t = 500◦ C. Thermal and mechanical properties are presented in Figs. 2 and 3 (Richter 1983).
2 Optimization with respect to thermal stresses During heating operation, the highest equivalent thermal stress occurs on the inner surface of a thick-walled pressure element. The sign of the circumference or longitudinal thermal stress on the inner surface is negative. The optimum medium temperature Tf (t) is assumed as
linear function of temperature in time. It consists of initial medium temperature step Ts and later increases at the optimum temperature change rate vT until nominal temperature is reached. The optimization method consists of two steps: – –
calculation of temperature change rate vT by golden search method, calculation of initial fluid temperature step Ts by Levenberg–Marquardt method.
The first parameter vT is determined from the first optimization functional: (1) σeqv vT , tqss = σa where σeqv is the maximum equivalent thermal stress in the whole construction element tqss is the time when quasi-steady state occurs and σa is the allowable value of equivalent stress. When fluid temperature changes, from the initial temperature of Tf,0 at a constant temperature change rate, the heating process is transient at the beginning but later moves on to a quasi-steady state. Equivalent thermal stresses rise during the heating process till the maximum value at the quasi-steady state is achieved when t = tqss . Circumference or longitudinal thermal stresses lower during the heating process until the minimum values at the quasi-steady state are achieved. The optimum temperature change rate vT is found at the quasi-steady state using the golden search method (Press et al. 1997). Next, consider that the fluid temperature changes suddenly at the beginning of the heating process by an initial fluid temperature step, Ts , and later rises with
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the determined optimum rate of temperature change, vT calculated before. The object is to choose Ts such that the computed equivalent stress in the whole construction element in time agrees with the allowable value of stress:
where p in MPa is the saturation pressure and T in ◦ C is the saturation temperature. The constants are a = −25.72743, b = 205.38723, c = 0.2150989.
σeqv Ts , tj − σa ∼ = 0,
3 TRD code j = 1, . . . , m,
(2) TRD 301 regulation assumes a quasi-steady one dimensional temperature distribution through the wall of the construction element. For the presented steam gate valve, the following working parameters: P = 18 MPa, T = 540◦ C were considered. Allowable stress for heating operation is σa min = −187.997 MPa. Based on allowable stress, the allowable rates of temperature changes, vT1 for P1 and vT2 for P2 , are calculated. vT1 = 3.173 K min, vT2 = 5.427 K min − for heating,
where m is the number of time points during the heating process. The sum m
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can be minimized by means of different methods. Parameter Ts , for which the sum (3) is minimum, is determined using the Levenberg–Marquardt method (Seber and Wild 1989). Temperature and stress distribution in time, in the whole construction element, is computed at each iteration step. After few iterations, convergent solution is obtained. The maximum total equivalent stress in time can be calculated adding the influence of inner pressure. When the fluid in the pressure element is the pressurized water or superheated steam, the fluid pressure is independent of temperature. In the case of water or steamwater mixture at saturation temperature, pressure is the function of saturation temperature P=
T −a b
Once P1 = 0 MPa, the medium temperature can be calculated from the following equation: dTf vT2 − vT1 = vT1 + Pn Tf dt P2
The calculated rate of temperature changes, medium temperature and medium pressure are presented in Fig. 4. ANSYS software based on the finite element method was used for the calculation of time-space temperature and stress distribution. Assuming the symmetry, one fourth of the SGV is divided into eight-node finite brick elements presented in Fig. 5. Temperature distribution in time and space is calculated during the heating operation from the cold
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state (T0 = 20 C) using the allowable medium temperature obtained from TRD 301, while assuming that the heat transfer coefficient on the inner surfaces equals 2,000 W/m2 K. Next, stress analyses are carried out. In order to do so, the calculated temperature distribution in space and time is transferred to the stress model. Additionally, the stress model is constrained to ensure symmetry conditions and to allow for the possibility of free lengthening in the direction of the horizontal and vertical pipe. The basic assumption here is that the surfaces connecting the SGV with the pipeline must be planes. Figure 6 presents the maximum equivalent thermal stress and minimum thermal stress component σy
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Fig. 7 Maximum equivalent total stress and minimum total stress component σ y versus time
versus time. Thermal stress σy exceeds the allowable value σa min after 2,600 s (σy < σa min ). Total stresses in time are presented in Fig. 7. They are lower than thermal stresses, because steam pressure causes tension stresses with an opposite sign to thermal stresses. However, the allowable stresses are also exceeded. In order to limit the stresses to the allowable value, the proposed optimization method will be used.
4 Computational example As presented in the previous chapter, high thermal stresses occur in the thick walled pressure component— SGV. If the rate of temperature changes is too high, permanent deformations can take place in stress concentration locations, which lead to crack damages and rapid decrease of component life. When the rate of temperature change is too low, the power boiler startup and shut-down operations are extended in time. This increases start-up losses and extends the standstill period of the power unit. Ergo, optimizing the fluid temperature changes during power boiler start-up is necessary. The optimum fluid temperature, Tf (t), is calculated assuming that the maximum equivalent von Mises thermal stress equals the maximum allowable stress σa = 199 MPa. Initially, SGV has a uniform temperature distribution, T0 = 20◦ C. Consider that the fluid temperature changes from the initial temperature at constant rate. The heating process is transient and causes the rise of
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thermal stresses in the SGV. Figure 8 presents three equivalent stress histories in MPa for the chosen rate of temperature change, vT . Presented stresses are the maximum stresses in the whole SGV volume. It can be seen that for all three values of vT , the thermal stresses approach three asymptotes when the quasi-steady state is achieved.
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The optimum rate of temperature change, vT = 2.8 K/min, is found for the asymptote σa = 199 MPa using the golden search method (Press et al. 1997). Next, consider that the fluid temperature changes suddenly at the beginning of the heating process by an initial fluid temperature step, Ts , and later rises at the optimum rate of temperature change, vT = 2.8 K/min. For large initial steps, high thermal stresses occur at the beginning of the heating process. Figure 9 presents three maximum equivalent thermal stress histories for the chosen three initial steps. When the
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Fig. 11 Calculated maximum thermal and total equivalent stresses for heating with optimum medium temperature history
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initial step equals 86◦ C, thermal stress moves quickly to the maximum allowable stress. The optimum value of the initial step is calculated by the Levenberg– Marquardt method (Seber and Wild 1989). The determined optimum fluid temperature history is presented in Fig. 10. Both methods the golden search method and the Levenberg–Marquardt method are used from IMSL Library and ANSYS software is called from FORTRAN program. Based on the determined optimum medium temperature history thermal and total stresses are calculated and presented in Fig. 11. This plot shows thermal stresses do not exceed allowable value of 199 MPa. Total stresses at the beginning of heating process reach the allowable value but later are smaller so the heating process can be carried on faster. 5 Conclusions 1. A simple method for determining the optimum fluid temperature history in elements of simple and complicated geometry is presented. 2. The optimization is based on the highest stress in the whole construction. 3. A method calculates thermal stresses in transient state without the assumption of quasi-steady state. 4. Optimizing fluid temperature limits the thermal and total stresses during power boiler start-up and shut-down operations.
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5. The calculated results have a very high practical significance, because use of results in power plants yields better efficiencies and increased SGV life.
References Duda P, Taler J, Roos E (2003) Inverse method for temperature and stress monitoring in complex-shape-bodies. Nucl Eng Des 3960:1–17 Krueger K, Franke R, Rode M (2004) Optimization of boiler start-up using a nonlinear boiler model and hard constraints. Energy 29:2239–2251 Lausterer GK (1997) On-line thermal stress monitoring using mathematical models. Control Eng Practice 5(1):85–90 Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1997) Numerical recipes - the art of scientific computing. Cambridge University Press, Cambridge Richter F (1983) Physikalische Eigenschaften von Stählen und ihre Temperatur-abhängigkeit. Mannesmann Forschungberichte 930: Düsseldorf Seber GAF, Wild CJ (1989) Nonlinear regression. Wiley, New York Taler J, Duda P (2006) Solving direct and inverse heat conduction problems. Springer-Verlag, Berlin Taler J, Dzierwa P (2007) A new method for determining allowable medium temperature during heating and cooling of thick walled boiler components. In: Proceedings of the Congres on Thermal Stresses, Taiwan Taler J, Weglowski ˛ B, Gradziel ˛ S, Duda P, Zima W (2002) Monitoring of thermal stresses in pressure components of large steam boilers. VGB KraftwerksTechnik 1:73–78 TRD 301 (1986) Technische Regeln für Dampfkessel. Carl Heymans Verlag, Köln und Beuth-Verlag, Berlin, pp 98– 138
