Parametric optimisation of stress relief groove shape in flat ends of boilers

Abstract

Flat ends of boilers with stress relief grooves have been used for many years. The existing standards set the value for the endplate thickness and admissible range of values for radius of the groove and the minimum thickness of the endplate under the relief groove. However, the codes do not specify the optimal parameters values for the endplate with stress relief groove. In this paper, the authors study the optimal choice of parameters for circular groove, and then propose its shape modification to elliptical, which considerably decreases stress concentration appearing in the zone of the groove. In the next step, the elliptical shape is replaced by the groove modelled by two spline functions, which results in further reduction of stress concentration. Finally, the groove with shape including several spline functions is proposed as an optimal one. In the performed study, the finite element modelling and the simple search method in optimisation procedures are used.

Optimization of Flat Ends in Pressure Vessels

“…The set of inequalities presented in Equation 4results in a triangular area in the (r d , e h1 ) coordinates, which limits the values for the lowest thickness in the groove and the radius of the groove. The latest experiments have shown that the inclination angle of the groove γ ( Figure 1a) has no real influence on the stress concentration when its value exceeds 60 • [9], so all the numerical calculations presented in the paper assume an angle value γ = 90 • . In such a case, the problem of the search for optimal parameters is reduced to the determination of only two design variables when using the EN 12952:3 code, i.e., the minimum thickness of the endplate measured at the bottom of the groove, e h1 , and the radius of the groove, r ik (see Figure 1a).…”

“…Figure 4 illustrates the admissible areas for the (e h1 , r d ) pairs obtained for the two thicknesses of the reinforced cylindrical shell part (thickness e s ). The optimization process and optimized parameters using the EN 12953:3 code were presented in papers [9,13]. The performed numerical calculations for the elastic-plastic material exemplified the presence of the point, where the minimum of the equivalent plastic strains appeared.…”

“…Even in this case, due to the lack of continuity of the curvature along the contour in the area where the inner edge of the cylindrical wall transforms to the curved one, a certain stress concentration is still observed [5][6][7][8]. Effectively modeling the junction between the pressure boiler wall and the flat head of the boiler has been a challenge for researchers for many years [1][2][3][4]7,9]. Usually, the minimization of the stress peak is achieved by the introduction of respective functions approximating the curved shape of the shell, which provides continuity of the curvature on the inner skin of the vessel.…”

“…This results in a variation of admissible groove parameters calculated according to the respective code applied in boiler calculations. In previous studies [9,[12][13][14], it was observed that the geometries of relieve grooves, acceptable from the point of view of the Standard EN 12952:3, may significantly differ in strength, durability, or other engineering parameters. Experimental tests were performed for the cylindrical pressure vessel with flat ends made from 16Mo3 steel with an external diameter 406.4 mm [12].…”

Influence of Crack Presence on Operating Conditions of Pressure Vessels With Flat Endplates

“…2b). The problem of minimization of the notch effect in the groove attracts researchers from many years and several successful proposals how to choose the optimal groove have been described [4][5][6][7][8][9][10].…”