To compensate for thermal expansion, U-shaped compensators are most widely used in heating networks and power plants. Despite its numerous disadvantages, among which are: relatively large dimensions (the need to install compensatory niches in heating networks with channel laying), significant hydraulic losses (compared to stuffing box and bellows); U-shaped compensators have a number of advantages.

The advantages include, first of all, simplicity and reliability. In addition, this type of compensators is the most well studied and described in educational, methodological and reference literature. Despite this, young engineers who do not have specialized programs often find it difficult to calculate compensators. This is due primarily to a rather complex theory, to the presence large quantity correction factors and, unfortunately, with the presence of typos and inaccuracies in some sources.

Below is a detailed analysis of the procedure for calculating a U-shaped compensator using two main sources, the purpose of which was to identify possible typos and inaccuracies, as well as compare the results.

The typical calculation of compensators (Fig. 1, a)), proposed by most authors, involves a procedure based on the use of Castiliano’s theorem:

Where: U- potential energy of deformation of the compensator, E- modulus of elasticity of the pipe material, J- axial moment of inertia of the compensator (pipe) section,

Where: s- wall thickness of the outlet,

D n- outer diameter of the outlet;

M- bending moment in the compensator section. Here (from the equilibrium condition, Fig. 1 a)):

M = P y x - P x y+M 0 ; (2)

L- full length of the compensator, J x- axial moment of inertia of the compensator, J xy- centrifugal moment of inertia of the compensator, S x- static moment of the compensator.

To simplify the solution, the coordinate axes are transferred to the elastic center of gravity (new axes Xs, Ys), Then:

S x = 0, J xy = 0.

From (1) we obtain the elastic resistance force Px:

Displacement can be interpreted as the compensating ability of the compensator:

Where: b t- linear thermal expansion coefficient, (1.2x10 -5 1/deg for carbon steels);

t n- initial temperature (average temperature of the coldest five-day period over the past 20 years);

t To- final temperature ( Maximum temperature coolant);

L uch- length of the compensated section.

Analyzing formula (3), we can come to the conclusion that the greatest difficulty is in determining the moment of inertia J xs, especially since it is first necessary to determine the center of gravity of the compensator (with y s). The author reasonably suggests using an approximate, graphical method for determining J xs, while taking into account the stiffness coefficient (Karman) k:

The first integral is determined relative to the axis y, second relative to the axis y s(Fig. 1). The axis of the compensator is drawn to scale on graph paper. The entire curved axis of the compensator L is divided into many segments Ds i. Distance from the center of the segment to the axis y i measured with a ruler.

The stiffness coefficient (Karman) is intended to reflect the experimentally proven effect of local flattening cross section bending bends, which increases their compensating ability. IN regulatory document The Karman coefficient is determined using empirical formulas different from those given in , . Hardness coefficient k used to determine reduced length L prD arc element, which is always greater than its actual length l G. In the source, the Karman coefficient for bent bends:

where: l - bending characteristic.

Here: R- radius of retraction.

Where: b- retraction angle (in degrees).

For welded and short-bent stamped bends, the source suggests using other dependencies to determine k:

Where: h- bending characteristics for welded and stamped bends.

Here: R e - equivalent radius of the welded bend.

For bends of three and four sectors b = 15 degrees, for a rectangular two-sector bend it is proposed to take b = 11 degrees.

It should be noted that in , coefficient k ? 1.

Regulatory document RD 10-400-01 provides the following procedure for determining the flexibility coefficient TO R * :

Where TO R- flexibility coefficient without taking into account the constrained deformation of the ends of the curved section of the pipeline; o is a coefficient that takes into account the tightness of the deformation at the ends of the curved section.

In this case, if, then the flexibility coefficient is taken equal to 1.0.

Magnitude TO p determined by the formula:

Here P is excess internal pressure, MPa; Et is the elastic modulus of the material at operating temperature, MPa.

It can be proven that according to the flexibility coefficient TO R * will be greater than one, therefore, when determining the reduced length of the bend according to (7), it is necessary to take its inverse value.

For comparison, we will determine the flexibility of some standard bends according to OST 34-42-699-85, at excess pressure R=2.2 MPa and modulus E t=2x 10 5 MPa. We summarize the results in the table below (Table No. 1).

Analyzing the results obtained, we can conclude that the procedure for determining the flexibility coefficient according to RD 10-400-01 gives a more “strict” result (less bend flexibility), while additionally taking into account the excess pressure in the pipeline and the elastic modulus of the material.

Moment of inertia of the U-shaped compensator (Fig. 1 b)) relative to the new axis y s J xs defined as follows:

Where: L etc- reduced length of the compensator axis,

y s- coordinate of the center of gravity of the compensator:

Maximum bending moment M Max(valid at the top of the compensator):

Where N- compensator overhang, according to Fig. 1 b):

Н=(m + 2)R.

The maximum stress in the section of the pipe wall is determined by the formula:

where: m1 - correction factor (safety factor), taking into account the increase in stress in bent sections.

For bent elbows, (17)

For welded bends. (18)

W- moment of resistance of the branch section:

Allowable stress (160 MPa for expansion joints made of steels 10G 2S, St 3sp; 120 MPa for steels 10, 20, St 2sp).

I would like to immediately note that the safety factor (correction) is quite high and increases with increasing pipeline diameter. For example, for a 90° bend - 159x6 OST 34-42-699-85 m 1 ? 2.6; for 90° bend - 630x12 OST 34-42-699-85 m 1 = 4,125.

Fig.2.

In the guidance document, the calculation of a section with a U-shaped compensator, see Fig. 2, is carried out according to an iterative procedure:

Here the distances from the compensator axis to fixed supports L 1 and L 2 backrest IN and the departure is determined N. In the process of iterations, both equations should be achieved so that they become equal; the largest of a pair of values is taken = l 2. Then the desired compensator overhang is determined N:

The equations represent the geometric components, see Fig. 2:

Components of elastic resistance forces, 1/m2:

Moments of inertia about the central axes x, y.

Strength parameter A, m:

[у ск] - permissible compensation voltage,

The permissible compensation stress [y sk ] for pipelines located in a horizontal plane is determined by the formula:

for pipelines located in a vertical plane according to the formula:

where: - nominal permissible stress at operating temperature (for steel 10G 2S - 165 MPa at 100°? t? 200°, for steel 20 - 140 MPa at 100°? t? 200°).

D- inner diameter,

I would like to note that the authors were unable to avoid typos and inaccuracies. If we use the slenderness factor TO R * (9) in the formulas for determining the reduced length l etc(25), coordinates of the central axes and moments of inertia (26), (27), (29), (30), then an underestimated (incorrect) result will be obtained, since the flexibility coefficient TO R * according to (9) is greater than one and must be multiplied by the length of the bent bends. The reduced length of bent elbows is always greater than their actual length (according to (7)), only then will they gain additional flexibility and compensation ability.

Therefore, in order to adjust the procedure for determining geometric characteristics according to (25) and (30), it is necessary to use the inverse value TO R *:

TO R *=1/ K R *.

In the design diagram of Fig. 2, the supports of the compensator are fixed ("crosses" are usually used to denote fixed supports (GOST 21.205-93)). This may prompt the “calculator” to count distances L 1 , L 2 from fixed supports, that is, take into account the length of the entire compensation section. In practice, the lateral movements of sliding (moving) supports of an adjacent pipeline section are often limited; distances should be measured from these movable but limited lateral movement supports L 1 , L 2 . If you do not limit the transverse movements of the pipeline along the entire length from fixed to fixed support, there is a danger of the sections of the pipeline closest to the compensator falling off the supports. To illustrate this fact, Fig. 3 shows the results of calculations for temperature compensation of a section of the main pipeline DN 800 made of steel 17G 2S with a length of 200 m, a temperature difference from - 46 C° to 180 C° in the MSC Nastran program. The maximum lateral movement of the central point of the compensator is 1.645 m. Possible water hammers also pose an additional danger of derailment from the pipeline supports. Therefore, the decision on lengths L 1 , L 2 should be taken with caution.

Fig.3.

The origin of the first equation in (20) is not entirely clear. Moreover, it is not dimensionally correct. After all, in brackets under the modulus sign the quantities are added R X And P y (l 4 +…) .

The correctness of the second equation in (20) can be proven as follows:

in order to, it is necessary that:

This is really true if you put

For a special case L 1 =L 2 , R y =0 , using (3), (4), (15), (19), one can arrive at (36). It is important to take into account that in the notation system in y = y s .

For practical calculations, I would use the second equation in (20) in a more familiar and convenient form:

where A 1 = A [y sk].

In the special case when L 1 =L 2 , R y =0 (symmetrical compensator):

The obvious advantages of the technique in comparison with is its greater versatility. The compensator Fig. 2 can be asymmetrical; normativeness makes it possible to carry out calculations of compensators not only for heating networks, but also for critical pipelines high pressure, which are in the register of RosTechNadzor.

Let's carry out comparative analysis results of calculation of U-shaped compensators using methods, . Let's set the following initial data:

a) for all expansion joints: material - Steel 20; P=2.0 MPa; E t=2x 10 5 MPa; t?200°; loading - pre-stretching; bent bends according to OST 34-42-699-85; compensators are located horizontally, made of pipes with fur. processing;
b) design diagram with geometric symbols according to Fig. 4;

Fig.4.

c) we summarize the standard sizes of compensators in table No. 2 along with the calculation results.

Bends and pipes of the compensator, D n H s, mm	Standard size, see Fig. 4	Pre-stretch, m	Maximum stress, MPa	Allowable stress, MPa
			according to	according to	according to	according to

Today, the use of U-shaped or any other expansion joints is carried out if the substance passing through the pipeline is characterized by a temperature of 200 degrees Celsius or higher, as well as high pressure.

General description of compensators

Metal compensators are devices that are designed to compensate or balance the influence of various factors on the operation of pipeline systems. In other words, the main purpose of this product is to ensure that there is no damage to the pipe when transporting substances through it. Such networks providing transportation working environment, are almost constantly exposed to such negative influences as thermal expansion and pressure, vibration, as well as subsidence of the foundation.

It is in order to eliminate these defects that it is necessary to install flexible elements, which have come to be called compensators. The U-shaped type is just one of many types that are used for these purposes.

What are U-shaped elements

It’s worth noting right away that the U-shaped type of parts is the simplest option that helps solve the compensation problem. This category of devices has the widest range of applications in terms of temperature and pressure indicators. To make U-shaped expansion joints, either one long pipe is used, which is bent into in the right places, or resort to welding several bent, steeply curved or welded bends. It is worth noting here that some of the pipelines must be periodically disassembled for cleaning. For such cases, compensators of this type are manufactured with connecting ends on flanges.

Since the U-type compensator is the simplest design, it has a number of certain disadvantages. These include the large consumption of pipes to create the element, large dimensions, the need for installation of additional supports, as well as the presence of welded joints.

Compensator requirements and cost

If we consider the installation of U-shaped compensators from the point of view of material resources, then their installation in systems with a large diameter will be most unprofitable. The consumption of pipes and materials to create a compensator will be too high. Here you can compare this equipment with the Action and parameters of these elements are approximately the same, but the cost of installation for the U-shaped one is approximately twice as much. The main reason for this expenditure of money is that a lot of materials are needed for construction, as well as the installation of additional supports.

In order for the U-shaped compensator to be able to completely neutralize the pressure on the pipeline, no matter where it comes from, it is necessary to install such devices at one point with a difference of 15-30 degrees. These parameters are suitable only if the temperature of the working substance inside the network does not exceed 180 degrees Celsius and does not fall below 0. Only in this case and with such installation will the device be able to compensate for the stress on the pipeline from ground movements from any point.

Installation calculations

The calculation of a U-shaped compensator is to find out which minimum sizes the device is enough to compensate for the pressure on the pipeline. In order to carry out the calculation, certain programs are used, but this operation can be performed even through online applications. The main thing here is to adhere to certain recommendations.

The maximum stress that is recommended for the back of the compensator is in the range from 80 to 110 MPa.
There is also such an indicator as the extension of the compensator to the outer diameter. This parameter is recommended to be taken within the range H/Dn=(10 - 40). With such values, it must be taken into account that 10Dn will correspond to a pipeline with parameters of 350DN, and 40Dn will correspond to a pipeline with parameters of 15DN.
Also, when calculating a U-shaped compensator, it is necessary to take into account the width of the device relative to its reach. Optimal values are considered L/H=(1 - 1.5). However, it is also possible to introduce other numerical parameters here.
If during the calculation it turns out that for a given pipeline it is necessary to create an expansion joint of this type that is too large, then it is recommended to select a different type of device.

Calculation restrictions

If the calculations are not carried out by an experienced specialist, then it is better to become familiar with some restrictions that cannot be exceeded when making calculations or entering data into the program. For a U-shaped compensator made of pipes, the following restrictions apply:

The working substance can be either water or steam.
The pipeline itself must be made only of steel pipe.
The maximum temperature for the working environment is 200 degrees Celsius.
The maximum pressure observed in the network should not exceed 1.6 MPa (16 bar).
Installation of the compensator can only be carried out on horizontal type pipeline.
The dimensions of the U-shaped compensator should be symmetrical, and its shoulders should be the same.
The pipeline network should not experience additional loads (wind or any other).

Device installation

Firstly, it is not recommended to place fixed supports further than 10DN from the compensator itself. This is due to the fact that the transmission of the pinching moment of the support will greatly reduce the flexibility of the structure.

Secondly, it is strongly recommended to divide sections from the fixed support to the U-shaped compensator of the same length throughout the entire network. It is also important to note here that shifting the installation location of the device from the center of the pipeline to one of its edges will increase the force of elastic deformation, as well as stress, by approximately 20-40% of the values that can be obtained if the structure is mounted in the middle.

Thirdly, in order to further increase the compensating ability, stretching of U-shaped compensators is used. At the time of installation, the structure will experience a bending load, and when heated it will take on a relaxed state. When the temperature reaches its maximum value, the device will come back into voltage. Based on this, a stretching method was proposed. The preliminary work is to stretch the compensator by an amount that will be equal to half the thermal elongation of the pipeline.

Pros and cons of the design

If we talk in general about this design, then we can say with confidence that it has such positive qualities as ease of production, high compensation ability, no need for maintenance, and the forces transmitted to the supports are insignificant. However, among the obvious disadvantages, the following stand out: high consumption of material and a large amount of space occupied by the structure, high hydraulic resistance.

Initial data:

pipe diameter with bent radius bends R = 1 m, coolant temperature  = 110°C, and ground temperature t gr.= 4°C;

1. Linear extension of the compensated section of the heat pipeline.

∆L=a*l(t 1 -t VC ), mm

∆L=1.2·0.01(110-(-25)) ·48=81.64

Taking into account the pre-stretching of the compensator

∆X=ε*∆ L

∆X=0.5 ·81.64=40.82

The calculation was made for section 11 with a pipe diameter of 0.07

3. Technological part

3.1 Description of the designed heat supply system

The course project has developed an open one. centralized. water dependent vehicle system consisting of three elements:

Heat source

Heat consumers

Heating networks

Open heat supply systems are systems in which hot water is drawn for consumer needs directly from the heating network. In this case, water withdrawal can be partial or complete. The remaining hot water in the system is used for heating and ventilation. The water consumption in the heating network is compensated by the additional amount of water supplied to the heating network. The main advantage of an open heating system is its economic benefits. Thermal energy production is carried out as follows: diagram of a hot water boiler house.

To prevent metal corrosion, the water temperature at the boiler inlet when operating on gas fuel must be at least 60 °C to avoid condensation of water vapor contained in the flue gases. Since the return water temperature is almost always below this value, in boiler rooms with steel boilers some hot water supplied to the return line by a recirculation pump. To the collector network pump Make-up water comes from the tank (a pump that compensates for the water consumption of consumers). The source water supplied by the pump passes through a heater, chemical water treatment filters and, after softening, through a second heater, where it is heated to 75-80 °C. Next, the water enters the column of the vacuum deaerator. The vacuum in the deaerator is maintained by suctioning the steam-air mixture from the deaerator column using a water-jet ejector. The working fluid of the ejector is water supplied by a pump from the tank of the ejector unit. The steam-water mixture removed from the deaerator head passes through a heat exchanger - a vapor cooler. In this heat exchanger, water vapor condenses, and the condensate flows back into the deaerator column. The deaerated water flows by gravity to the make-up pump, which supplies it to the suction manifold of the network pumps or to the make-up water tank.

Heating of chemically purified and source water in heat exchangers is carried out by water coming from the boilers. In many cases, the pump installed on this pipeline (shown by the dashed line) is also used as a recirculation pump. If the heating boiler room is equipped with steam boilers, then hot water for the heating system is obtained in surface steam-water heaters. Steam-water water heaters are most often free-standing, but in some cases heaters are used that are included in the circulation circuit of the boiler, as well as built over boilers or built into boilers. The project adopted a scheme for the joint connection of heating and hot water systems, according to the principle of linked regulation (see Sheet 2). Thermal energy is routed using two pipe water, dead-end heating networks (see Sheet 1, 2). The length of heating networks from the boiler house to the most remote consumer is 262 m. The diameter of the pipelines is selected in accordance with hydraulic calculations (see paragraph 2.4) and ranges from 50 to 380 mm. A U-shaped compensator is installed along the vehicle route in sections 9 and 11. To distribute heat and account for it along the route, pipeline units are provided where valves are installed. IN Soviet period approximately 50% of all heat supply systems were open type. This system has several disadvantages. First of all, the low sanitary and hygienic quality of water. Heating appliances and pipeline networks impart color and odor to the water; various impurities and bacteria appear. Various methods are used to purify water in an open system, but their use reduces the economic effect.

3.2 Operation of the heat supply system.

A set of works to maintain the heat supply system in good condition and use it for its intended purpose. In large cities and industrial areas, special enterprises are being created to operate heating networks from the district boiler house, boiler houses and heating networks from them. The organizational structure of operation of heat supply enterprises depends on their capacity, the nature of consumers and heat sources. Structural units such as network districts, engineering services and production and technical departments are directly related to operation. The main production and technical unit is the network district, which carries out all the operation of networks and their structures, conducts thermal supervision of consumers, distributes and accounts for heat. Network districts have a staff of network and heating station inspectors, repair personnel and adjusters. The operational activities of the districts in relation to relationships with consumers are carried out by on-duty personnel working around the clock. Network districts are assisted the following engineering services: repair of heating networks, emergency repair service of the heat supply system, electrical equipment, connections, control room, thermal inspection, production laboratory, instrumentation and automation, automated control system department. The dispatch service and the automated control system department are created for dispatch control of heat supply and the operation of an automated dispatch control system for centralized heat supply and an automated control system for technological processes of centralized heat supply. To service heat and power associations, repair and production bases are created that provide: medium and major repairs of equipment, restoration repairs of building structures of heating networks; emergency restoration work with the help of mobile teams; adjustment and testing of equipment of boiler houses, pumping stations, heating points; production of spare parts and products; storage of instruments, materials, equipment. When operating heat supply systems, systematically conducted hydraulic and temperature tests are of great importance. The purpose of hydraulic tests is to identify sections of heating pipelines that have undergone external or internal corrosion. Every year in summer period All heat pipes are tested for tightness and strength using stationary testing stations and mobile pump-presses. The purpose of temperature tests is to check the strength of heating network equipment under conditions of temperature deformation and to determine the actual compensating ability of network expansion joints. During testing, the water temperature in the supply pipelines is maintained equal to the design temperature, in the return pipelines - no higher than 90°C.

Before putting into operation new heating networks and heat consumption systems, their acceptance tests must be carried out and they must be accepted by the customer from the installation organization according to an act in accordance with the current rules, after which they must be presented for inspection and approval for operation to the state energy authority supervision and heat supply organization. Design and as-built documentation must be submitted at the same time.

The admission of heat consumption systems of buildings under construction and heating networks into temporary operation for finishing work is permitted subject to the completion of work according to the approved start-up scheme and the conclusion of a heat supply contract.

Admission of heat consumption systems and heating networks for both permanent and temporary operation is possible only if there are trained personnel who have passed the knowledge test in the established manner, and by order of the enterprise (organization) a person has been appointed responsible for the heating sector who has passed the knowledge test in the established order.

List of information sources.

SNiP 2.01.01-82 Construction climatology and geophysics. 1982

SNiP 41-02-2003 Heat networks. 2003.

SNiP 2.04.01-85*. Internal water supply and sewerage of buildings. 1985

SNiP 41-03-2003 Thermal insulation pipeline equipment.2003

SNiP 23-01-99 Construction climatology.1999

GOST 21.605-82. Thermal networks (thermomechanical part) working drawings. 1986

E.Ya.Sokolov., Heating and heating network; M., Energoizdat, 2009., -472

B.N. Golubkov., Heating equipment and heat supply of industrial enterprises - M., Energy, 2008

Manyuk V.I., Kaplinsky Ya.I., Khizh E.B. Etc. Setup and operation of water heating networks: Handbook. Ed.4 Id.: Lan., 2009, -432.

Borovkov V.M. Repair heating equipment and heating networks (1st ed.) textbook., Publisher: Lan., 2011, -208 (SPO stamp)

Thermotechnical reference book. Under the general editorship of V.N. Grenev and P.D. Lebedev. M., "Energy", 1975.

Shchekin R.V. reference book on heat supply and ventilation, vol. I, K., “Budivelnik”, 1976

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Calculation of U-shaped compensators

Ph.D. S.B. Gorunovich,

hands design group of Ust-Ilimsk CHPP

The advantages include, first of all, simplicity and reliability. In addition, this type of compensators is the most well studied and described in educational, methodological and reference literature. Despite this, young engineers who do not have specialized programs often find it difficult to calculate compensators. This is primarily due to a rather complex theory, the presence of a large number of correction factors and, unfortunately, the presence of typos and inaccuracies in some sources.

The typical calculation of compensators (Fig. 1, a)), proposed by most authors, involves a procedure based on the use of Castiliano’s theorem:

Where: U- potential energy of deformation of the compensator, E- modulus of elasticity of the pipe material, J- axial moment of inertia of the compensator (pipe) section,

Where: s- wall thickness of the outlet,

D n- outer diameter of the outlet;

M- bending moment in the compensator section. Here (from the equilibrium condition, Fig. 1 a)):

M = P yx - P xy+M 0 ; (2)

L- full length of the compensator, J x- axial moment of inertia of the compensator, J xy- centrifugal moment of inertia of the compensator, S x- static moment of the compensator.

To simplify the solution, the coordinate axes are transferred to the elastic center of gravity (new axes Xs, Ys), Then:

S x= 0, J xy = 0.

From (1) we obtain the elastic resistance force P x:

Displacement can be interpreted as the compensating ability of the compensator:

Where: b t- linear thermal expansion coefficient, (1.2x10 -5 1/deg for carbon steels);

t n- initial temperature (average temperature of the coldest five-day period over the past 20 years);

t To- final temperature (maximum coolant temperature);

L uch- length of the compensated section.

The stiffness coefficient (Karman) is intended to reflect the experimentally proven effect of local flattening of the cross-section of bends during bending, which increases their compensating ability. In the regulatory document, the Karman coefficient is determined using empirical formulas different from those given in,. Hardness coefficient k used to determine reduced length L prD arc element, which is always greater than its actual length l G. In the source, the Karman coefficient for bent bends:

where: l - bending characteristic.

Here: R- radius of retraction.

Where: b- retraction angle (in degrees).

For welded and short-bent stamped bends, the source suggests using other dependencies to determine k:

Where: h- bending characteristics for welded and stamped bends.

Here: R e - equivalent radius of the welded bend.

For bends of three and four sectors b = 15 degrees, for a rectangular two-sector bend it is proposed to take b = 11 degrees.

It should be noted that in , coefficient k ? 1.

Regulatory document RD 10-400-01 provides the following procedure for determining the flexibility coefficient TO R* :

In this case, if, then the flexibility coefficient is taken equal to 1.0.

Magnitude TO p determined by the formula:

Here P- excess internal pressure, MPa; E t- modulus of elasticity of the material at operating temperature, MPa.

It can be proven that according to the flexibility coefficient TO R* will be greater than one, therefore, when determining the reduced length of the bend according to (7), it is necessary to take its inverse value.

Moment of inertia of the U-shaped compensator (Fig. 1 b)) relative to the new axis y sJ xs defined as follows:

Where: L etc- reduced length of the compensator axis,

y s- coordinate of the center of gravity of the compensator:

Maximum bending moment M Max(valid at the top of the compensator):

Where N- compensator overhang, according to Fig. 1 b):

Н=(m + 2)R.

The maximum stress in the section of the pipe wall is determined by the formula:

Where: m 1 - correction factor (safety factor), taking into account the increase in stress in bent sections.

For bent elbows, (17)

For welded bends. (18)

W- moment of resistance of the branch section:

Allowable stress (160 MPa for expansion joints made of steels 10G 2S, St 3sp; 120 MPa for steels 10, 20, St 2sp).

Fig.2. Design diagram of the compensator according to RD 10-400-01.

In the guidance document, the calculation of a section with a U-shaped compensator, see Fig. 2, is carried out according to an iterative procedure:

Here the distances from the axis of the compensator to the fixed supports are set L 1 and L 2 backrest IN and the departure is determined N. In the process of iterations, both equations should be achieved so that they become equal; the largest of a pair of values is taken = l 2. Then the desired compensator overhang is determined N:

The equations represent the geometric components, see Fig. 2:

Components of elastic resistance forces, 1/m2:

Moments of inertia about the central axes x, y.

Strength parameter A, m:

[у ск] - permissible compensation voltage,

The permissible compensation stress [y sk ] for pipelines located in a horizontal plane is determined by the formula:

for pipelines located in a vertical plane according to the formula:

where: - nominal permissible stress at operating temperature (for steel 10G 2S - 165 MPa at 100°? t? 200°, for steel 20 - 140 MPa at 100°? t? 200°).

D- inner diameter,

I would like to note that the authors were unable to avoid typos and inaccuracies. If we use the slenderness factor TO R* (9) in the formulas for determining the reduced length l etc(25), coordinates of the central axes and moments of inertia (26), (27), (29), (30), then an underestimated (incorrect) result will be obtained, since the flexibility coefficient TO R* according to (9) is greater than one and must be multiplied by the length of the bent bends. The reduced length of bent elbows is always greater than their actual length (according to (7)), only then will they gain additional flexibility and compensation ability.

Therefore, in order to adjust the procedure for determining geometric characteristics according to (25) and (30), it is necessary to use the inverse value TO R*:

TO R*=1/ K R*.

Fig.3. Results of calculation of compensation stresses on a section of a DN 800 pipeline with a U-shaped compensator using the MSC/Nastran software package (MPa).

The correctness of the second equation in (20) can be proven as follows:

in order to, it is necessary that:

This is really true if you put

For a special case L 1 =L 2 , R y=0 , using (3), (4), (15), (19), one can arrive at (36). It is important to take into account that in the notation system in y = y s.

For practical calculations, I would use the second equation in (20) in a more familiar and convenient form:

where A 1 = A [y sk].

In the special case when L 1 =L 2 , R y=0 (symmetrical compensator):

The obvious advantages of the technique in comparison with is its greater versatility. The compensator Fig. 2 can be asymmetrical; normativity allows us to carry out calculations of compensators not only for heating networks, but also for critical high-pressure pipelines that are in the register of RosTechNadzor.

Let us conduct a comparative analysis of the results of calculating U-shaped compensators using methods, . Let's set the following initial data:

a) for all expansion joints: material - Steel 20; P=2.0 MPa; E t=2x 10 5 MPa; t?200°; loading - pre-stretching; bent bends according to OST 34-42-699-85; compensators are located horizontally, made of pipes with fur. processing;

b) design diagram with geometric symbols according to Fig. 4;

Fig.4. Calculation scheme for comparative analysis.

c) we summarize the standard sizes of compensators in table No. 2 along with the calculation results.

Bends and pipes of the compensator, D n H s, mm	Standard size, see Fig. 4	Pre-stretch, m	Maximum stress, MPa	Allowable stress, MPa
					according to	according to	according to	according to

conclusions

compensator thermal pipeline voltage

Analyzing the results of calculations using two different methods: reference and normative, we can come to the conclusion that despite the fact that both methods are based on the same theory, the difference in the results is very significant. The selected standard sizes of compensators “pass with a margin” if they are calculated according to and do not pass according to the permissible stresses if they are calculated according to. The most significant impact on the result is made by the correction factor m 1 , which increases the voltage calculated by the formula by 2 or more times. For example, for the compensator in the last line of table No. 2 (from pipe 530Ch12) the coefficient m 1 ? 4,2.

The result is also influenced by the value of the permissible stress, which for steel 20 is significantly lower.

In general, despite its greater simplicity, which is due to the presence of a smaller number of coefficients and formulas, the methodology turns out to be much more rigorous, especially for large-diameter pipelines.

For practical purposes, when calculating U-shaped expansion joints for heating systems, I would recommend “mixed” tactics. The flexibility coefficient (Karman) and permissible stress should be determined according to the standard, i.e.: k=1/TO R* and further according to formulas (9)h(11); [u sk] - according to formulas (34), (35) taking into account RD 10-249-88. The “body” of the method should be used according to, but without taking into account the correction factor m 1 , i.e.:

Where M Max determine by (15) h (12).

The possible asymmetry of the compensator, which is taken into account, can be neglected, since in practice, when laying heating networks, movable supports are installed quite often, the asymmetry is random and does not have a significant impact on the result.

Distance b you can count not from the nearest adjacent sliding supports, but make a decision to limit lateral movements already on the second or third sliding support, if counted from the axis of the compensator.

Using this “tactic”, the calculator “kills two birds with one stone”: a) strictly follows the regulatory documentation, since the “body” of the technique is a special case. The proof is given above; b) simplifies the calculation.

To this we can add an important saving factor: after all, to select a compensator from a 530Ch12 pipe, see table. No. 2, according to the reference book, the calculator will need to increase its dimensions by at least 2 times, but according to the current standard, this compensator can also be reduced by one and a half times.

Literature

1. Elizarov D.P. Thermal power plants of power plants. - M.: Energoizdat, 1982.

2. Water heating networks: Reference Guide for design / I.V. Belyaykina, V.P. Vitaliev, N.K. Gromov et al., ed. N.K. Gromova, E.P. Shubina. - M.: Energoatomizdat, 1988.

3. Sokolov E.Ya. District heating and heating networks. - M.: Energoizdat, 1982.

4. Standards for calculating the strength of pipelines of heating networks (RD 10-400-01).

5. Standards for calculating the strength of stationary boilers and steam and hot water pipelines (RD 10-249-98).

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The following restrictions were adopted in the calculation:

The pipeline is filled with water or steam
The pipeline is made of steel pipe
The maximum temperature of the working environment does not exceed 200 °C
The maximum pressure in the pipeline does not exceed 1.6 MPa (16 bar)
The compensator is installed on a horizontal pipeline
The compensator is symmetrical, and its arms are the same length
Fixed supports are considered absolutely rigid
The pipeline does not experience wind pressure or other loads
The resistance of frictional forces of movable supports during thermal elongation is not taken into account
Smooth bends

It is not recommended to place fixed supports at a distance of less than 10DN from the U-shaped compensator, since transferring the pinching moment of the support to it reduces flexibility.

It is recommended that the pipeline sections from the fixed supports to the U-shaped compensator be of the same length. If the compensator is not located in the middle of the site, but is shifted towards one of the fixed supports, then the forces of elastic deformation and stress increase by approximately 20-40%, in relation to the values obtained for the compensator located in the middle.

To increase the compensating ability, preliminary stretching of the compensator is used. During installation, the compensator experiences a bending load, when heated it assumes a non-stressed state, and at maximum temperature it comes into tension. Pre-stretching the compensator by an amount equal to half the thermal elongation of the pipeline allows you to double its compensating capacity.

Application area

U-shaped compensators are used to compensate temperature extensions pipes on long straight sections, if there is no possibility of self-compensation of the pipeline due to turns of the heating network. The absence of compensators on rigidly fixed pipelines with a variable temperature of the working environment will lead to an increase in stress that can deform and destroy the pipeline.

Flexible expansion joints are used

For above-ground installation for all pipe diameters, regardless of coolant parameters.
When laid in tunnels and general manifolds on pipelines from DN25 to DN200 at a coolant pressure of up to 16 bar.
For ductless installation for pipes with diameters from DN25 to DN100.
If the maximum operating temperature exceeds 50°C

Advantages

High compensation capacity
Maintenance free
Easy to manufacture
Low forces transmitted to fixed supports

Flaws

High pipe flow
Large footprint
High hydraulic resistance

Construction and finishing. Equipment. Wallpaper. Coloring. Facade

Calculation of thermal expansion of pipelines. U-shaped compensator: description, characteristics and dimensions

General description of compensators

What are U-shaped elements

Compensator requirements and cost

Installation calculations

Calculation restrictions

Device installation

Pros and cons of the design

Send your good work in the knowledge base is simple. Use the form below

Calculation of U-shaped compensators

Ph.D. S.B. Gorunovich,

hands design group of Ust-Ilimsk CHPP

Similar documents

The following restrictions were adopted in the calculation:

Application area

Flexible expansion joints are used

General description of compensators

What are U-shaped elements

Compensator requirements and cost

Installation calculations

Calculation restrictions

Device installation

Pros and cons of the design

Send your good work in the knowledge base is simple. Use the form below

Calculation of U-shaped compensators

Ph.D. S.B. Gorunovich,

hands design group of Ust-Ilimsk CHPP

Similar documents

The following restrictions were adopted in the calculation:

Application area

Flexible expansion joints are used

Related materials: