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I. Introduction to compensators: Compensators are also commonly referred to as expansion joints or telescopic joints. It consists of a bellows (an elastic element) that forms the main part of its structure, along with accessories such as end tubes, supports, flanges, and conduits. It belongs to a type of compensation element. It utilizes the effective expansion and contraction of its main working element, the bellows, to absorb dimensional changes in pipelines, conduits, containers, etc., caused by thermal expansion and contraction, or to compensate for axial, lateral, and angular displacements of such pipelines, conduits, and containers. It can also be used for noise reduction and vibration damping. It is widely used in modern industry. II. Function of the compensator: The compensator is also known as a expansion joint, bellows compensator, or wave compensator. Compensators are divided into several types, including bellows compensators, sleeve compensators, rotary compensators, and square natural compensators. Among them, bellows compensators are the most commonly used; they serve to ensure the safe operation of pipelines and have the following functions: 1. Compensating for axial, lateral, and angular thermal deformations of pipelines. 2. The expansion amount of the wave compensator facilitates the installation and removal of valves and pipelines. 3. Absorb equipment vibrations and reduce the impact of such vibrations on the pipelines. 4. Absorb the deformation of pipelines caused by earthquakes and land subsidence. III. Requirements for the design of piping systems and pipe racks regarding axial, lateral, and angular compensators (1) Axial compensators: 1. For the pipe sections where axial compensators are installed, main fixed pipe racks must be provided at the blind ends of the pipes, at bends, at locations where the pipe diameter changes, at sections equipped with stop valves or pressure reducing valves, and at the entrances where side pipelines connect to the main pipeline. The main fixed pipe rack must take into account the static pressure thrust of the bellows as well as the elastic force resulting from deformation. The thrust calculation formula is as follows: Fp = 100 * P * A, where Fp represents the axial force exerted by the compensator (in N), A is the effective area corresponding to the average diameter of the corrugations (in cm2), and P is the maximum pressure in that pipe section (in MPa). The formula for calculating the axial elastic force is as follows: Fx = f * Kx * X. Where FX is the axial elastic force of the compensator (N), and KX is the axial stiffness of the compensator (N/mm) ; The f-factor: when there is \"pre-deformation\" (including the case where the pre-deformation amount △X=0), f=1/2; otherwise, f=1. In addition to the aforementioned areas, intermediate fixed pipe supports can be installed on the pipeline. The intermediate fixed pipe rack does not need to take into account the effect of pressure thrust. 2. Only one axial type compensator can be installed between the two fixed pipe supports of a pipe segment. 3. The layout of the fixed pipe racks and guide pipe racks is recommended to be configured as shown in the figure below. One end of the compensator should be close to the fixed pipe rack; if it is too long, guide racks must be installed in accordance with the requirements for the first guide rack. The maximum spacing between other guide racks can be calculated as follows: LGmax – maximum guide spacing (m) ; E-pipe material elastic modulus (N/cm2) ; i-tp pipe cross-sectional moment of inertia (cm4) ; KX – Axial stiffness of the compensator (N/mm), X0 – Displacement amount for compensating adjustment (mm). When the compensator is compressed, the symbol is “+”; when it is stretched, the symbol is “-”. When the pipe wall thickness is designed according to the standard thickness, LGmax can be selected in accordance with relevant standards. (II) Transverse and angular compensators 1. Transverse compensators installed near pipe elbows have one guide support at each end; one of these should be a flat guide support. The upper and lower moving clearances are calculated using the following formula: ε – Moving clearance (mm) ; L-Compensator effective length (mm) ; △Thermal expansion of Y-pipe section (mm) ; △X – Thermal expansion of the vertical pipe section, excluding the L length (mm) ; 2. Angular compensators should be used in groups of two or three to absorb the lateral displacement of the pipeline; between two fixed pipe supports for Z-shaped and L-shaped pipe sections, only one lateral compensator or one group of angular compensators may be installed. At this point, the axis of the planar hinge pin must be perpendicular to the plane formed by the bent pipe section (universal hinge compensators are not subject to this restriction). For a pipe segment equipped with a set of hinge compensators, the clearance ε of its planar guide frame can also be calculated using the above formula. However, the L length should be the distance between the hinge axes of the two compensators, and △X is the thermal expansion amount of the entire vertical pipe section. 3. The guide supports on both sides of the compensator should be close to it, and the type of these supports should enable the compensator to move in a directed manner. III. Installation requirements for directly-buried compensators in heating pipelines (1) Purpose: Directly-buried corrugated compensators are primarily used for axial compensation of directly-buried pipelines. They possess bending resistance, so the effect of pipeline settlement need not be considered. These products feature a large compensation capacity and a long service life. (II) Instructions for use: The directly buried corrugated compensator is mainly suitable for axial compensation; it also possesses excellent bending resistance, so the effect of pipe settlement is not a concern. It achieves free expansion and contraction compensation under the protection of a directly buried corrugated compensation housing and guide sleeve; its other properties are the same as those of ordinary corrugated compensators. (III) Selection and Installation: 3.1 Calculation of the maximum installation length of pipes. Pipes buried directly with compensation mechanisms should be fixed at two high points: one at the end of the straight pipe section, and the other at the branch point of the pipe. In a long, unbranched straight pipeline, fixed points may not be necessary between the two compensators; the natural \"stagnation points\" formed within the pipeline can serve as fixed points. The stagnation point is the fixed point in the pipeline between the two compensators; when the pipe diameters are the same and the burial depths are identical, the distance from the stagnation point to each of the two compensators is equal. The distance from the expansion compensator (including the natural compensator at corners) to the fixed point shall not exceed the maximum installation length Lmax of the pipeline. The maximum installation length of the pipeline is defined as the distance from the fixed point to the free end (the compensator), and the friction force generated at this length shall not exceed the elastic force corresponding to the allowable stress of the pipeline. Lmax is calculated using the following formula: the maximum installation length Lmax for common pipes. The combined effect of the circumferential stress generated by pressures up to 16 kgf/cm2 should be considered. 3.2 Design calculations for fixed supports: For a pipeline system with 2 branch pipes and a bent in the main pipeline, the placement of the compensators must satisfy the condition that Ln < Lmax. The thrust at the fixed points G1 and G2 is zero; therefore, there is no need to install fixed supports at these locations. However, to prevent drift of these fixed points due to uneven backfilling, variations in burial depth, or irregularities in the surface roughness of the pre-made insulation pipes, it is necessary to install supports at the pipe branches located at these fixed points, G1 and G2. Taking G1 as an example, its axial thrust can be calculated using the following formula: F1 = Pb2 + L2f – 0.8(Pb3 + L2f). Here, F1 represents the horizontal thrust on the fixed support G1, in kgf ; f: Friction force per unit length of the pipe, Kgf/m; Pb2-B2: Elastic force of the expansion joint, Kg ; Elastic force of Pb3-B3 expansion joint, Kgf; Stiffness of K2-B2 expansion joint, Kgf/mm ; △Compensation amount of L2-B2 expansion joint, mm ; Distance from L2-expansion joint to G1, m ; Suppose a branch, such as the one branching off from G2, is equipped with compensator B. Thus, G2 is also subjected to a lateral thrust, represented by F2(y) in the figure. When L5 is short (and it should indeed be short in actual installations), the magnitude of the lateral force F2(y) is given by: F2(y) = Pn * A5 + Pb5, where Pn is the operating pressure of the pipeline, in Kgf/cm2, and A5 is the effective area of the B5 expansion joint, in cm2 ; Elastic force of Pb5-B5 expansion joint in kgf. Fixed support G3 is also at a stationary point; due to the friction between the pipeline and the soil, this point is subjected to two forces of equal magnitude but opposite direction. It should be noted, however, that this point is also affected by the force exerted by the blind flange at the corner. Taking into account the effect of stationary point drift, the thrust on fixed support G3 is given by F3 = 1.2Pn*A4, where F3 represents the horizontal thrust acting on fixed support G3, in Kgf ; Pn – Operating pressure of the pipeline, Kgf/cm2 ; Effective area of A4-B4 expansion joint, cm2. 3.3 Calculation for selecting compensators: Due to the effect of soil friction, the actual thermal expansion of pipes buried directly in the ground is smaller than that of pipes installed overhead or in trenches. Extension amount during overhead and trench installation: α·△t·L. Reduction in thermal expansion due to soil friction force during direct burial installation: The actual thermal expansion amount is: Where E is the elastic modulus of the steel pipe, in kgf/cm2 ; The linear expansion coefficient of α-steel pipes is taken as 0.0133 mm/m℃ ; △t-pipe temperature difference ; A, f-same formula① ; Distance between the two fixing points of L (maximum installation length) in meters. In practical applications, the thermal expansion of directly buried pipes is calculated using a simplified algorithm from the Danish company Møller. The symbols in the formula are the same as those in the above formulas. After calculating the actual thermal elongation using equations ② or ③, select the appropriate compensator from the list. 3.4 Installation: When installing directly-buried expansion joints (excluding those that are used once and then buried), two protective rings should be provided (as shown in the figure below), and the wall thickness of these rings should not be less than that of the pipeline. The purpose of using these protective rings is to prevent soil, sand, and other materials from entering within dimension A when the pipeline expands due to heat. The dimensions shown in the figure are as follows: When the directly-buried corrugated expansion joint leaves the factory, all its exposed surfaces have been coated with rust-proof paint twice. Other requirements for the directly-buried corrugated expansion joint and the pipeline it is connected to include: (1) When the insulation pipe is buried underground, it should be filled with sand having a particle size of less than 20 millimeters, after which the original soil should be placed on top; the thickness of the sand fill should be at least 200 millimeters. (2) The burial depth of the top of the insulation pipe generally should not exceed 1.2 meters, but it should also not be less than 0.7 meters; the insulation pipe can be buried directly beneath various pipes. (3) As shown in the figure, insulation is provided everywhere except at point A; since no insulation is needed at A when the pipeline expands, it does not cause significant heat loss. Also thanks to the function of the protective ring, the directly-buried compensator can be buried directly beneath the road surface. (4) For the installation of directly-buried compensators, there is no need for cold tightening, nor is it necessary to connect all the steel pipes along the line first, cut off sections of pipe equal in length to those of the expansion joints, and then weld them together. By using directly-buried expansion joints, guide supports are not required. (5) During installation, care must be taken to ensure that the direction of the guide sleeve matches the flow direction. (6) The medium inside the compensator should be treated to remove free oxygen and chloride ions, with the chloride ion content not exceeding 25 PPm. (7) The compensator allows a system hydrostatic test at a pressure not exceeding 1.5 times the nominal pressure. (8) Before conducting the system hydrostatic test after the compensator has been installed, both ends of the pipeline must be secured to prevent the internal pressure from stretching the compensator. IV. Requirements for the installation and use of compensators 1. Before installation, the model, specifications, and piping configuration of the compensator should be checked to ensure that they meet the design requirements. 2. For compensators with an inner sleeve, care should be taken to ensure that the direction of the inner sleeve is consistent with the flow direction of the medium; for hinge-type compensators, the plane of rotation of the hinge should be aligned with the plane of displacement rotation. 3. For compensators that require \"cold tightening,\" the auxiliary components used for pre-deformation should be removed only after the piping installation is completed. 4. It is strictly prohibited to use the deformation of wave compensators to adjust the installation tolerances of pipes, as this may affect the normal functioning of the compensators, reduce their service life, and increase the load on the piping system, equipment, and supporting components. 5. During installation, it is not allowed for welding slag to splash onto the surface of the wave shell, nor is it permitted for the wave shell to suffer any other mechanical damage. 6. After the piping system is installed, the yellow auxiliary positioning elements and fasteners used for installation and transportation on the wave compensators should be removed as soon as possible. The limiting devices should then be adjusted to the specified positions in accordance with the design requirements, so that the piping system has sufficient compensation capacity under various environmental conditions. 7. All movable components of the compensator must not be blocked by external elements or have their range of movement restricted; normal operation of all moving parts must be ensured. 8. During the hydrostatic test, the secondary support brackets at the ends of the pipelines equipped with compensators should be reinforced to prevent the pipelines from moving or rotating. For compensators used in gas media and their connecting pipelines, attention should be paid to whether temporary supports are needed when filling them with water. The chloride ion content in the cleaning solution used for hydrostatic testing shall not exceed 25PPM. 9. After the hydrostatic test is completed, the water accumulated in the wave tank should be drained as soon as possible, and the inner surface of the wave tank should be dried promptly. 10. The insulation material in contact with the compensator bellows should be free of chloride ions