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The content is sourced from the ANSYS Analysis and Designers official account. 1. What is a flexible thin tube sheet? A flexible thin tube sheet is used in heat exchangers to connect the tube box shell and the shell-side shell, primarily to reduce secondary temperature stress caused by large temperature differences. In practical engineering applications, there are mainly four types of connection structures between the flexible thin tube sheet and the tube box shell as well as the shell-side shell, as shown in the figures below. As can be seen from these figures, a special feature of the flexible thin tube sheet is its folded edges with smooth transitions; the function of these folded edges is to alleviate the high bending stresses that occur at the joints where the tube sheet connects to the tube box shell and the shell-side shell, as well as the pulling forces at the joints where the tube sheet connects to the heat exchange tubes. However, the radius of these folded edges has a dual effect on the bending stresses and pulling forces at these joints: [1] If the radius R of the folded edge is too large, the ability to compensate for temperature difference stresses increases, but the diameter of the shell also increases, meaning that the diameter of the tube sheet increases as well. This in turn leads to an increase in the primary bending stress at the center of the tube sheet, and consequently, the required thickness of the tube sheet increases accordingly ； 【2】If the radius of curvature at the fold corner R is too small, although a smaller diameter of the tube sheet implies a lower required thickness, the secondary bending stress at the junction between the transition section and the shell **increases**, resulting in an insufficient ability to compensate for thermal stress differences ； 【3】Change in pulling force: If the calculated thickness of the tube sheet is large, the structural discontinuity force generated at the junction between the tube sheet and the heat exchange tubes increases. However, the shear area at this junction also increases, so the magnitude of the pulling force may either increase or decrease ； 【4】Fold radius specified in the standards: According to standard SH/T3158, the radius of the tube sheet corner R should not be less than 2 times the thickness of the tube sheet, and it should be at least 38 mm ； The GB/T 151 standard specifies the range of allowable values for the corner radius R based on the type of tube sheet structure, with this value being no less than 38 mm ； GB/T150 specifies that the radius of curvature R for circular flat covers must be greater than or equal to 3 times the thickness of the cover ； Due to differences in structural forms, the stress conditions of the structure vary significantly. Moreover, the radius of the bend directly determines the magnitude of the primary bending stress at the center of the tube sheet, as well as the secondary bending stress at the junction between the tube sheet and the shell. Therefore, designers can carry out simulation analyses in accordance with standard requirements and by using finite element calculation results, so as to design the structure appropriately and keep both the primary bending stress at the center of the tube sheet and the secondary bending stress at the connection points within reasonable values, thereby determining the optimal thickness for the tube sheet. 2. Why choose a flexible thin tube sheet structure? Flexible thin tube sheet heat exchangers are widely used to cool the high-temperature materials coming from reactors, thereby achieving heat recovery and comprehensive utilization. The tube sheet is one of the important pressure-bearing components of a heat exchanger, and it is also a component that is prone to damage during use. 【Traditional tube sheet】: (1) Due to the excessive thickness of the tube sheet, heat transfer occurs slowly in the thickness direction, resulting in high temperatures of the heat exchange tubes and the tube sheet. This reduces their pressure-bearing capacity, making them a weak point in the heat exchanger that is prone to cracking ； (2) If the tube sheet is too thick, it results in an excessive axial gap between the tube sheet and the heat exchange tubes; this allows salts to concentrate in that gap and cause scaling, leading to chloride corrosion ； (3) Under high-temperature conditions, it is difficult for thick tube sheet heat exchangers to ensure the long-term operation of the equipment. 【Flexible thin tube sheet】: (1) It can effectively reduce the temperature difference between the gas side and the water side, thereby preventing equipment failure caused by tube sheet cracking ； (2) It possesses high flexibility, which reduces the stress at the corners of the tube sheet; it also greatly alleviates the temperature difference stresses existing between the tube sheet, the heat exchange tubes, and the shell ； (3) The ability to compensate for thermal expansion has been enhanced, eliminating the need to use expansion joints or floating head structures ； It also has advantages such as material savings, easy processing, an increased heat exchange length of the heat exchange tubes, and improved heat exchange efficiency. However, due to the thin thickness of the flexible thin tube sheet, it is necessary to control the deformation caused by welding and expansion joining during the manufacturing of tube sheets for large-diameter heat exchangers. 3. What is the calculation method for flexible thin tube sheets? 【1. West German AD Code】To fully utilize the reinforcing effect of the heat exchange tubes on the tube sheet, the AD code considers only the strength of the unsupported areas and the junctions between unsupported areas and supported areas. The theoretical basis of this method is the assumption that the tubes provide fixed support for the tube sheet, which is a flat plate supported by those tubes. The calculation formula used is an empirical formula for determining the thickness of the flat plate. The AD code’s calculation formulas do not take into account thermal stress, nor do they specify allowable wall temperature differences or methods for calculation. When calculating the tube sheet thickness according to AD standards, it depends only on the maximum diameter d2 of the tube-free area, and not on the diameter of the heat exchanger; as a result, **the tube sheet thickness is reduced. 【2.Calculation method per EN 12953】 【3.Calculation method per SH/T 3158-2009】 The flexible thin tube sheet structure has extensive experience in use abroad, and due to its obvious advantages, China has also adopted this structure in the standard SH/T 3158 \"Petroleum and Chemical Industry Shell-and-Tube Waste Heat Boilers\". The minimum required thickness of the inner and outer tube sheets within and outside the tube bundle area is calculated using the following formula: [4. Calculation method per GB/T150-2011] GB/T150-2011 includes new provisions for calculating the thickness of plates subjected to tensile supports, distinguishing between regular and irregular support arrangements. These provisions relate primarily to the spacing L between supports as well as the typical structure and parameters K of such supports. The formula for calculating the thickness of plates under tensile stress is as follows: When using this formula to determine the thickness of thin tube sheets, the value of L can be determined based on a regular support arrangement in the tube routing area, while the values of L and K can be determined based on an irregular support arrangement in areas where there are no tubes. This standard fails to provide schematic diagrams showing the positions corresponding to different types of support points, but as a standard requirement, this needs to be clarified. This method also does not specify the pressure and temperature range for which the bracing structure is suitable; under high-temperature conditions, thermal stress plays a significant role in determining the mode of failure of the bracing structure. 【5.GB/T151-2014 Calculation Method】 The calculation method for flexible thin tube sheets is provided in Expendable Appendix M of the GB/T 151-2014 standard. The formula for calculating the thickness of the tube sheet is as follows: This standard is essentially consistent with the calculation method specified in SH/T 3158. Its applicable range is as follows: the design pressure on the tube side shall not exceed 1.0 MPa, the design pressure on the shell side shall not exceed 5.0 MPa, and the pressure on the shell side must be higher than that on the tube side ； The shell diameter shall not exceed 2500 mm ； The length of the heat exchange tubes shall not exceed 7000 mm ； SH/T 3518 has a broader range of applications, applicable to situations where the design pressure is not greater than 6.4 MPa. By comparing the standard calculation formulas, it can be seen that the GB/T150 standard incorporates the features of both ASME and JIS standards, and adds content regarding bracing structures with irregular arrangements, which are not specified in ASME. SH/T3158, the AD specifications, and GB/T 151 are very similar; the main difference lies in the fact that in SH/T3158 and GB/T151, the coefficient k used depends on the type of support, and the allowable stress is also multiplied by a corresponding correction factor, whereas the AD specifications use a fixed value of 0.4 for this coefficient.