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Research Papers: Design and Analysis

Optimum Heating of Pressure Vessels With Holes

[+] Author and Article Information
Piotr Dzierwa

Faculty of Mechanical Engineering,
Cracow University of Technology,
Kraków 31-155, Poland
e-mail: Piotr.dzierwa@krakow.so.gov.pl

Jan Taler

Faculty of Mechanical Engineering,
Cracow University of Technology,
Kraków 31-155, Poland
e-mail: taler@mech.pk.edu.pl

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received August 6, 2013; final manuscript received April 27, 2014; published online September 15, 2014. Assoc. Editor: Albert E. Segall.

J. Pressure Vessel Technol 137(1), 011202 (Sep 15, 2014) (8 pages) Paper No: PVT-13-1132; doi: 10.1115/1.4027584 History: Received August 06, 2013; Revised April 27, 2014

A method for determining time-optimum medium temperature changes is presented. The heating of the pressure elements will be conducted so that the circumferential stress caused by pressure and fluid temperature variations at the edge of the opening at the point of stress concentration does not exceed the allowable value. In contrast to present standards, two points at the edge of the opening are taken into consideration. Optimum fluid temperature changes are assumed in the form of simple time functions. It is possible to increase the fluid temperature stepwise at the beginning of the heating process and then the fluid temperature can be increased with a constant rate.

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References

Taler, J., Wȩglowski, B., Zima, W., Grądziel, S., and Zborowski, M., 1999, “Analysis of Thermal Stresses in a Boiler Drum During Start-Up,” ASME J. Pressure Vessel Technol., 121(1), pp. 84–93. [CrossRef]
Kim, T. S., Lee, D. K., and Ro, S. T., 2000, “Analysis of Thermal Stress Evolution in the Steam Drum During Start-Up of a Heat Recovery Steam Generator,” Appl. Therm. Eng., 20, pp. 977–992. [CrossRef]
Krüger, K., Franke, R., and Rode, M., 2004, “Optimization of Boiler Start-Up Using a Nonlinear Boiler Model and Hard Constraints,” Energy, 29, pp. 2239–2251. [CrossRef]
Dzierwa, P., 2014, “Optimum Heating of Pressure Components of Complex Shape,” Encyclopedia of Thermal Stresses, R.Hetnarski, ed., Springer, Berlin, Germany, pp. 3532–3543.
Taler, J., Dzierwa, P., and Taler, D., 2009, “Optimum Heating of Pressure Components of Large Steam Boilers,” Forsch. Ingenieurwes., 73(3), pp.183–192. [CrossRef]
Taler, J., and Dzierwa, P., 2011, “A New Method for Optimum Heating of Steam Boiler Pressure Components,” Int. J. Energy Res., 35, pp. 897–908. [CrossRef]
TRD 301, 2001, Zylinderschalen unter innerem Überdruck. Technische Regeln für Dampfkessel (TRD) (Heymanns Beuth, Köln, Berlin, Germany), pp. 143–185.
EN 12952-3, 2012, Water-Tube Boilers and Auxiliary Installation—Part 3: Design and Calculation for Pressure Parts European Committee for Standardization, Brussels, Belgium.
Dzierwa, P., 2014, “Quasi-Steady-State Approach for Solving Transient Heat Conduction Problems,” Encyclopedia of Thermal Stresses, R.Hetnarski, ed., Springer, Berlin, Germany, pp. 4083–4092.
Varley, J., 2007, “Dealing With Cycling: TRD 301 and Euro Norm Compared,” Modern Power Systems 27, Staff Report, pp. 33–38, Foots Cray, Kent, UK.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 2006, Numerical Recipes in Fortran 77. The Art of Scientific Computing, 2nd ed., Cambridge University Press, NY.

Figures

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Fig. 1

Pressure vessel—connector junction; (a) location of points P1 and P2 and (b) circumferential stress at point P1

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Fig. 2

Functions using for approximation of optimum time changes of fluid temperature; (a) function defined by Eq. (5) and (b) function defined by Eq. (6)

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Fig. 3

Mesh of finite elements used for thermo-mechanical analysis of the drum—downcomer junction

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Fig. 4

Time changes of influence function

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Fig. 5

Optimum time changes of water temperature Tf(t) in the drum approximated by function (5)pn = 0 MPa (a = 46.68 °C, b = 0.059 °C/s, c = 200.8 °C s) and pnd = 10.87 MPa (a = 49.24 °C, b = 0.062 °C/s, c = 211.7 °C s)

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Fig. 6

Optimum time changes of water temperature Tf(t) in the drum approximated by function (6)pn = 0 MPa (a = 48.56 °C, b = 0.057 °C/s) and pnd = 10.87 MPa (a = 41.22 °C, b = 0.061 °C/s)

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Fig. 7

Temperature distribution in the drum–downcomer intersection for time t = 1500 s for optimum fluid temperature changes presented in Fig. 6; (a) pn = 0 MPa; (b) pnd = 10.87 MPa

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Fig. 8

Optimum time changes of water temperature approximated by the function (5) or (6) for pn = 0 MPa

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Fig. 9

Optimum time changes of water temperature approximated by the function (5) or (6) for pnd = 10.87 MPa

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Fig. 10

Total circumferential stress due to pressure and thermal load at points P1 and P2 during optimum drum heating for pn = 0 MPa—optimum water temperature changes approximated by function (5)

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Fig. 11

Total circumferential stress due to pressure and thermal load at points P1 and P2 during optimum drum heating for pnd = 10.87 MPa—optimum water temperature changes approximated by function (5)

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Fig. 12

Total circumferential stress due to pressure and thermal load at points P1 and P2 during optimum drum heating for pn = 0 MPa—optimum water temperature changes approximated by function (6)

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Fig. 13

Total circumferential stress due to pressure and thermal load at points P1 and P2 during optimum drum heating for pnd = 10.87 MPa—optimum water temperature changes approximated by function (6)

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Fig. 14

Distribution of the von Mises equivalent stress in the drum–downcomer intersection for time t = 1500 s for optimum fluid temperature changes presented in Fig. 6; (a) −pn = 0 MPa; (b) −pnd = 10.87 MPa

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Fig. 15

Comparison of heating curves determined by the German Standard TRD 301 and European Norm EN 12952-3

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