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:Loveliness: Abstract: Bellows heat exchangers are efficient shell-and-tube heat exchangers, and it is necessary to conduct studies on their strength and safety in order to expand their scope of application. It introduces the methods and main contents of the strength design for bellows heat exchangers, summarizes the problems that occur during their operation, and through analysis of design calculation examples, explains the issues that should be taken into account in the design and selection of bellows heat exchangers. This information is provided as a reference for departments involved in the design, manufacturing, safety inspection, and use of bellows heat exchangers. 1. Overview In the early 1990s, China developed an efficient heat exchange component – the corrugated heat exchange tube. A corrugated heat exchange tube consists of two parts: a corrugated tube and a joint. A bellows heat exchanger made using bellows instead of smooth straight tubes can improve heat transfer efficiency by 2 to 4 times; such an efficient heat exchanger also has advantages such as resistance to scaling and low temperature difference stress. However, since the bellows are made from thin-walled (wall thickness of 05–10 mm) smooth tubes, their stress state becomes complex after molding. The strength and stiffness of its tube bundle differ significantly from those of smooth tubes, making the stress analysis of the tube bundle and tube sheet in such heat exchangers difficult. Due to the unresolved issues regarding the strength of the tube bundles and tube sheets, the application scope of such efficient equipment is limited, and it also poses safety risks. To enable such energy-efficient products to be applied in a wider range of industrial fields such as petroleum and chemicals, it is essential to conduct strength studies on bellows heat exchangers and establish corresponding design standards. This work was included in the projects of the **Standardization Technical Committee for Boilers and Pressure Vessels in 2002; units such as Shenyang University of Chemical Technology and Shenyang Special Equipment Inspection Institute (formerly Shenyang Boiler Inspection Institute) were responsible for drafting it. The design method for bellows heat exchangers was listed as an appendix to GB151 \"Shell and Tube Heat Exchangers,\" and it was officially issued in 2004 under the title \"Design Standard Example for Austenitic Stainless Steel Bellows Heat Exchangers\" (hereinafter referred to as the \"standard example\"). This article introduces the main contents of the standard cases, summarizes and analyzes the problems that have arisen during the more than ten years of operation of bellows heat exchangers, and illustrates the issues that should be considered in the design and selection of bellows heat exchangers through case studies. 2. Introduction to Standard Cases The bellows heat exchanger is also a type of shell-and-tube heat exchanger; its overall design, manufacturing, and inspection comply with the requirements specified in GB151. However, due to variations in the stiffness of the tube bundle, the design calculations for the pressure-bearing components associated with it differ. Based on theoretical analysis and experimental research, the standard case specifies the design and calculation methods for the tube bundle and tube sheet of bellows heat exchangers, in line with the principle of integrating safety and reliability, economic rationality, and advanced technology, as a supplement to GB151. 2-1 Scope of Application The type of heat exchanger is the same as that specified in GB151. The design pressure PN ≤ 40 MPa. Considering that the corrugated heat exchange tubes are made from thin-walled pipes and have significant residual stresses from the forming process, their operating pressure cannot be too high in order to avoid stress corrosion and fatigue failure. The standard specifications define two nominal diameters for the heat exchange tubes: the outer diameter of the wave crest/wave trough is 32/25 mm and 42/33 mm, while the outer diameter of the tube billet is 25 mm and 33 mm; these are the two commonly used specifications in current engineering applications. The baffle spacing is determined based on engineering practice experience; its maximum value is approximately 2/3 of the maximum spacing specified in clause 5953 of GB151, without taking fluid-induced vibrations into account. Considering bellows forming and more than a decade of actual use, the standard case is only applicable when the bellows material is austenitic stainless steel. 2-2 Design of corrugated heat exchange tubes After a smooth tube is formed into a corrugated tube through expansion molding, due to residual stresses and local stress concentrations, the load-bearing capacity of the corrugated tube is much lower than that of the corresponding smooth tube (i.e., the tube blank). The axial stiffness and stability of the corresponding bellows also **decrease**. Article 3 of the standard case provides the formulas for calculating the allowable internal pressure, allowable external pressure, axial stiffness, and critical pressure of bellows, which are derived from experiments and theoretical analysis. 2-2-1 Allowable internal pressure of corrugated heat exchange tubes Detailed calculations of the stresses in various parts of the corrugated tube are still under investigation. The stress distribution under internal pressure has been determined through numerous tests using stress measurement methods; blast tests were also conducted. The actual blast pressure was close to the theoretical value calculated for the corresponding pipe billet using the mean diameter formula, with the measured value being higher than the theoretical value. 2-2-2 Allowable external pressure of corrugated heat exchange tubes: In shell-and-tube heat exchangers, the tubes are subjected to pressures from both the tube side and the shell side; therefore, the stability of the tubes under external pressure must also be taken into consideration. Most bellows are of the nodal shape, that is, they consist of a straight section and a spherical wave crest portion. The stiffness of the straight sections is much lower than that of the peak sections, and tests have also shown that when the bellows is subjected to external pressure, it is the straight edges that fail first. The entire bellows can be regarded as a cylinder subjected to external pressure, with the peak portion acting as a rigid member. In this way, the calculated length of the pipe under external pressure is **significantly reduced**, and it is safe to use the maximum wavelength within a single pipe as the calculated length in standard cases. Based on engineering practice experience and experimental research, the standard case adopts the design calculation method for externally pressurized cylinders in Chapter 6 of GB150. Based on L/d1 and d1/δt, by directly using the external pressure calculation charts in Chapter 6 of GB150, the values of A and B can be determined, thereby obtaining the allowable external pressure for the bellows. 2-3 Design calculations for tube sheets: To date, most **heat exchanger standards for calculating the strength of tube sheets treat the tube sheet as an equivalent circular plate that is subjected to a uniformly distributed load, is placed on an elastic foundation, and has its strength reduced due to the tube holes. The tube sheet design in GB151 is also based on this consideration. For bellows heat exchangers, the main difference compared to conventional (smooth-tube) shell-and-tube heat exchangers lies in the stiffness of the heat exchange tubes. Based on this consideration, the standard specification specifies that parameters related to the axial stiffness of the tube are incorporated into the calculated value of the bellows stiffness; thereafter, the design calculations for the tube sheets of bellows heat exchangers are carried out directly using the calculation formulas for the corresponding tube sheet types in GB151. 3. Common failure modes of bellows heat exchangers and analysis of their causes (1) Thinning and cracking at the transition areas between the troughs or crests of the bellows heat exchange tubes. During the operation of bellows heat exchangers, thinning and cracking at the troughs of the bellows-type heat exchange tubes and in their surrounding areas, leading to internal leakage, is the main cause of failure. The cause of failure is that at the baffle in the shell side, vibration and friction as well as impacts occur between the troughs of the bellows and the holes in the baffle, resulting in thinning of the bellows wall and eventually cracking and leakage. Some manufacturers now use thicker baffle plates to bring the peaks of the bellows into contact with the tube holes, thereby minimizing the gap between the tube and the holes and preventing vibration-induced friction; others fit a sleeve over the bellows at the baffle plate location. These are all good measures to avoid and reduce this form of bellows failure. (2) Flattening of the corrugated heat exchange tube (circumferential instability). Cylindrical buckling due to bellows instability is another form of failure in bellows heat exchangers. This is mainly because the wall thickness of the bellows is relatively thin, generally below 1 mm, resulting in a very low ability to resist external pressure-induced instability. In the design of heat exchangers, the pressure-bearing capacity of the heat exchange tubes is generally not checked or calculated. As a result, when the pressure in the shell side reaches or exceeds the critical pressure of the tubes themselves, the tubes become unstable and flatten out. The standard case specifies the method for calculating the allowable external pressure of corrugated heat exchange tubes. (3) Excessive axial bending deformation of the corrugated heat exchange tube (axial instability). This form of failure is caused by the effects of tube-side pressure and temperature difference stress. The bellows material is austenitic stainless steel, which has a much higher linear expansion coefficient than carbon steel; therefore, temperature differences can still cause stress even when the temperatures in the tube side and shell side are the same. Additionally, the axial stiffness of the bellows is very low, so when the pressure on the tube side is high or the wall temperature of the tube side is higher than that of the shell side, excessive axial bending deformation of the bellows-type heat exchange tube can occur, leading to failure. The unsupported span ratio of the baffle specified in the standard case is smaller than the value specified in GB151, which is to prevent axial instability of the heat exchange tubes. (4) Corrosion fracture and overall embrittlement failure of corrugated heat exchange tubes. This form of failure is mainly caused by the corrosion of the medium. Austenitic stainless steels are most susceptible to intergranular corrosion; when bellows heat exchangers are used in media with high chloride ions and hydrogen sulfide, the bellows tubes corrode and break. In practice, it has been found that some heat exchange tubes have experienced overall embrittlement. (5) Cracking at the joint between the bellows and the thick-walled pipe. The corrugated heat exchange tube consists of a corrugated tube and joints at both ends. Due to differences in welding processes and skills, it is difficult to ensure the quality of the circumferential welds at these joints, which leads to cracking in those areas. :victory: