Calculation of thermal expansions of pipelines. Design of heat networks of an industrial enterprise

Compensators of thermal networks. This article will focus on the selection and calculation of thermal expansion joints.

What are compensators for? Let's start with the fact that when heated, any material expands, which means that the pipelines of heating networks lengthen with an increase in the temperature of the coolant passing through them. For trouble-free operation of the heating network, compensators are used that compensate for the elongation of pipelines during their compression and tension, in order to avoid pinching of pipelines and their subsequent depressurization.

It should be noted that for the possibility of expansion and contraction of pipelines, not only compensators are designed, but also a system of supports, which, in turn, can be both "sliding" and "dead". how rule in Russia quality control of the heat load - that is, when the temperature changes environment, the temperature at the outlet of the heat supply source changes. Due quality regulation heat supply - the number of expansion-compression cycles of pipelines increases. The resource of pipelines is reduced, the risk of pinching is increasing. Quantitative load regulation is as follows - the temperature at the outlet of the heat supply source is constant. If it is necessary to change the heat load, the coolant flow rate changes. In this case, the metal of the heating network pipelines works in lighter conditions, the minimum number of expansion-compression cycles, thereby increasing the resource of the heating network pipelines. Therefore, before choosing expansion joints, their characteristics and quantity must be determined with the amount of expansion of the pipeline.

Formula 1:

δL=L1*a*(T2-T1)where

δL - pipeline elongation,

mL1 - length of the straight section of the pipeline (distance between fixed supports),

ma - coefficient of linear expansion (for iron it is equal to 0.000012), m/deg.

T1 - Maximum temperature pipeline (the maximum temperature of the coolant is taken),

T2 - minimum temperature pipeline (you can take the minimum ambient temperature), ° С

For example, consider the solution of an elementary problem of determining the magnitude of the elongation of the pipeline.

Task 1. Determine how much the length of a straight section of a pipeline 150 meters long will increase, provided that the coolant temperature is 150 ° C, and the ambient temperature is heating period-40 °С.

δL=L1*a*(T2-T1)=150*0.000012*(150-(-40))=150*0.000012*190=150*0.00228=0.342 meters

Answer: the length of the pipeline will increase by 0.342 meters.

After determining the amount of elongation, it should be clearly understood when a compensator is needed and when it is not needed. For an unambiguous answer to this question, you need to have a clear pipeline diagram, with its linear dimensions and supports attached to it. It should be clearly understood that a change in the direction of the pipeline is able to compensate for extensions, in other words, rotation with overall dimensions not less than the dimensions of the compensator, with correct arrangement of supports, is able to compensate for the same elongation as the compensator.

And so, after we determine the amount of elongation of the pipeline, we can proceed to the selection of compensators, you need to know that each compensator has a main characteristic - this is the amount of compensation. In fact, the choice of the number of compensators comes down to the choice of the type and design features compensators. To select the type of compensator, it is necessary to determine the diameter of the heat network pipe based on bandwidth pipe the required power of the heat consumer.

Table 1. The ratio of U-shaped compensators made from bends.

Table 2. Selection of the number of U-shaped compensators based on their compensating capacity.

Task 2 Determining the number and size of compensators.

For a pipeline with a diameter of DN 100 with a length of a straight section of 150 meters, provided that the carrier temperature is 150 ° C, and the ambient temperature during the heating period is -40 ° C, determine the number of compensators. bL = 0.342 m (see Task 1). According to the Table 1 and Table 2, we determine the dimensions of n-shaped expansion joints (with dimensions of 2x2 m it can compensate for 0.134 meters of pipeline extension), we need to compensate for 0.342 meters, therefore Ncomp \u003d bL / ∂x \u003d 0.342 / 0.134 \u003d 2.55, rounded up to the nearest whole number in the direction of increase and that - 3 compensators with dimensions of 2x4 meters are required.

Currently, lens compensators are becoming more widespread, they are much more compact than U-shaped, however, a number of restrictions do not always allow their use. The resource of the U-shaped compensator is much higher than that of the lens one, due to poor quality coolant. Bottom part lens compensator is usually "clogged" with sludge, which contributes to the development of parking corrosion of the compensator metal.

Ph.D. S. B. Gorunovich, leader. design group of Ust-Ilimskaya CHPP

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

Of the advantages, one can first of all single out simplicity and reliability. In addition, this type of compensators is the most well studied and described in educational and methodological and reference literature. Despite this, often young engineers who do not have specialized programs, the calculation of compensators causes difficulties. 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.

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

The typical calculation of compensators (Fig. 1, a)), proposed by most authors ÷, involves a procedure based on the use of the Castiliano 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 section of the compensator (pipe),

;

where: s- outlet wall thickness,

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, Jxy- 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 repulse force P x:

The displacement can be interpreted as the compensating ability of the compensator:

; (4)

where: a t- coefficient of linear thermal expansion, (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 heat carrier temperature);

L account- the length of the compensated section.

Analyzing formula (3), we can conclude that the greatest difficulty is the determination of the moment of inertia Jxs, 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, graphic method definitions Jxs, while taking into account the coefficient of rigidity (Karman) k:

The first integral is determined with respect to the axis y, second relative to the axis y s(Fig. 1). The axis of the compensator is drawn on millimeter paper to scale. All curved shaft compensator L split into many sections ∆s i. Distance from the center of the segment to the axis y i measured with a ruler.

The stiffness coefficient (Karmana) is designed to reflect the experimentally proven effect of local flattening cross section bends during bending, which increases their compensating ability. AT normative document the Karman coefficient is determined by empirical formulas different from those given in , .

Stiffness factor k used to determine the 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:

; (6)

where: - characteristic of the bend.

Here: R- bend radius.

; (7)

where: α - retraction angle (in degrees).

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

where: - bend characteristic for welded and stamped bends.

Here: - equivalent radius of the welded bend.

For branches from three and four sectors α=15 deg, for a rectangular two-sector branch it is proposed to take α = 11 deg.

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

Regulatory document RD 10-400-01 provides for the following procedure for determining the coefficient of flexibility K r *:

where K r- coefficient of flexibility without taking into account the constraint of deformation of the ends of the bent section of the pipeline;

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

Value K p is determined by the formula:

, (10)

where .

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

, (11)

It can be proved that the coefficient of flexibility K r * will be greater than one, therefore, when determining the reduced length of the tap according to (7), it is necessary to take its reciprocal value.

For comparison, let's determine the flexibility of some standard taps according to OST 34-42-699-85, at overpressure R=2.2 MPa and module E t\u003d 2x10 5 MPa. The results are summarized in the table below (Table No. 1).

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

The moment of inertia of the U-shaped compensator (Fig. 1 b)) relative to the new axis y s J xs determine in the following way :

where: L pr- reduced length of the axis of the compensator,

; (13)

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

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

; (15)

where H- offset of the compensator, according to Fig. 1 b):

H=(m + 2)R.

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

; (16)

where: m 1- correction factor (factor of safety), taking into account the increase in stresses on the bent sections.

In heat networks, stuffing box, U-shaped and bellows (wavy) expansion joints are widely used. The compensators must have sufficient compensating capacity to absorb the thermal expansion of the pipeline section between the fixed supports, while the maximum stresses in the radial compensators should not exceed the allowable ones (usually 110 MPa).

Thermal elongation of the design section of the pipeline
, mm, determined by the formula

(81)

where
- average coefficient of linear expansion of steel,

(for typical calculations, you can take
),

- estimated temperature difference, determined by the formula

(82)

where - design temperature of the coolant, o C;

- estimated outdoor air temperature for heating design, o C;

L - distance between fixed supports, m (see Appendix No. 17).

The compensating capacity of stuffing box expansion joints is reduced by a margin of 50 mm.

Reaction of the stuffing box compensator- friction force in stuffing box packing is determined by the formula

where - operating pressure of the coolant, MPa;

- length of the packing layer along the axis of the gland compensator, mm;

- outer diameter of the branch pipe of the stuffing box compensator, m;

- coefficient of friction of the packing against the metal, is taken equal to 0.15.

When selecting compensators, their compensating capacity and technical parameters can be determined according to the application.

Axial reaction of bellows expansion jointsis made up of two terms:

(84)

where - axial reaction caused by wave deformation, determined by the formula

(85)

here l - temperature elongation of the pipeline section, m;

 - wave stiffness, N/m, taken according to the compensator passport;

n is the number of waves (lenses).

- axial reaction from internal pressure, determined by the formula

(86)

here - coefficient depending on the geometric dimensions and wall thickness of the wave, equal to an average of 0.5 - 0.6;

D and d are the outer and inner diameters of the waves, respectively, m;

- excess pressure of the coolant, Pa.

When calculating self-compensation the main task is to determine the maximum stressat the base of the short arm of the turn angle of the track, which is determined for the turn angles of 90 ° along formula

(87)

for angles greater than 90 o, i.e. 90+, according to the formula

(88)

where l - elongation of the short arm, m;

l is the length of the short arm, m;

E - the modulus of longitudinal elasticity, equal to the average for steel 2 10 5 MPa;

d - outer diameter of the pipe, m;

- the ratio of the length of the long arm to the length of the short arm.

When calculating angles for self-compensation, the value of the maximum stress  should not exceed [] = 80 MPa.

When arranging fixed supports at the angles of rotation used for self-compensation, it must be taken into account that the sum of the lengths of the angle arms between the supports should not exceed 60% of the maximum distance for straight sections. It should also be taken into account that the maximum angle of rotation used for self-compensation should not exceed 130°.

To date, the use of U-type expansion joints or any other 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 expansion joints 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 the pipe is not damaged when substances are transported through it. Such networks, which provide transportation of the working environment, are almost constantly exposed to such negative influences, as thermal expansion and pressure, vibration, and 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 this purpose.

What are U-shaped elements

It should be noted right away that the U-shaped type of parts is the simplest option that helps to solve the compensation problem. This category of devices has the widest range of applications in terms of temperature and pressure indicators. For the manufacture of U-shaped compensators either one long pipe is used, which is bent in the right places, or several bent, sharply bent or welded bends are welded. It is worth noting here that some of the pipelines must be periodically disassembled for cleaning. For such cases, expansion joints 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 can be attributed high flow pipes to create an element, large dimensions, the need to install additional supports, as well as the presence of welded joints.

Compensator requirements and cost

If we consider the installation of U-type expansion joints from the point of view of material resources, then their installation in systems with a large diameter will be the most disadvantageous. The consumption of pipes and material resources for the creation of a compensator will be too high. Here you can compare this equipment with Action and the parameters of these elements are approximately the same, but the cost of installation for the U-shaped is about twice as much. The main reason for this cost Money in that you need a lot of materials 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 mount 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 this installation, the device will be able to compensate for the stress on the pipeline from soil movements from any point.

Installation Calculations

The calculation of the U-shaped compensator is to find out which minimum dimensions 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 follow certain recommendations.

• The maximum stress that is recommended to take for the back of the compensator is in the range from 80 to 110 MPa.
• There is also such an indicator as the departure of the compensator to the outer diameter. This parameter is recommended to be taken within H/Dn=(10 - 40). With such values, it must be taken into account that 10Dn will correspond to a pipeline with an indicator of 350DN, and 40Dn - a pipeline with parameters of 15DN.
• Also, when calculating the U-shaped compensator, it is necessary to take into account the width of the device to its reach. Optimal values L/H=(1 - 1.5) are considered. However, the introduction of other numerical parameters is also allowed 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 choose a different type of device.

Restrictions on calculations

If the calculations are not experienced specialist, it is better to familiarize yourself with some limitations that must not be exceeded when calculating or entering data into the program. For a U-shaped pipe compensator, the following restrictions apply:

• The working medium can be either water or steam.
• The pipeline itself must be made only of steel pipe.
• The maximum temperature indicator for the working environment is 200 degrees Celsius.
• The maximum pressure observed in the network must not exceed 1.6 MPa (16 bar).
• The compensator can only be installed 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).

Installing devices

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 highly recommended to split sections from fixed support to a U-shaped compensator of the same length, throughout the network. It is also important to note here that the displacement of the fixture installation site from the center of the pipeline to one of its edges will increase the elastic deformation force, as well as the stress by about 20-40% of those values ​​that can be obtained if the structure is mounted in the middle.

Thirdly, in order to further increase the compensating ability, U-shaped expansion joints are stretched. At the time of installation, the structure will experience a bending load, and when heated, it will assume an unstressed state. When the temperature reaches the maximum value, then the device will come back to the voltage. Based on this, a stretching method was proposed. The preliminary work is to stretch the expansion joint by an amount that will be equal to half the thermal expansion of the pipeline.

Design pros and cons

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

Compensators or compensation devices are used when installing pipelines with high pressure or high temperature carrier substance. During the operation of the pipeline, a number of factors arise that must be taken into account in order to avoid destruction load-bearing structures. These factors include temperature deformations pipes, vibrations that occur during the operation of the pipeline, as well as subsidence of the foundations of concrete supports.

Compensators are designed to ensure the mobility of parts of the system relative to each other. If there is no such mobility, then the load on connecting elements, pipeline sections, welded seams. These loads exceed allowable norms and lead to the destruction of the system.

There are several types of compensators, which have different principle devices. The idea of ​​developing a U-shaped compensator appeared as a result of the phenomenon of self-compensation of pipelines with turns and bends. During the operation of the heating main, pipes due to these turns are able to show resistance to torsion and tension deformations.

However, one cannot count on self-compensation, since the absolute value of the displacement depends on the number of rotary elements. To ensure the possibility of compensating for deformations, a U-shaped elbow is equipped on a straight section of the highway, which plays the role of a compensator.

The principle of operation of the U-shaped compensator

According to its design, the U-shaped compensator is considered the simplest, since it consists of a minimum set of elements. It was this minimalism that made it possible to provide a wide range specifications(temperature, pressure). The compensator is made in one of two ways.

1. A single pipe bends in the right places with a certain bending radius, forming a U-shaped structure.
2. The compensator consists of 7 elements, including three straight bends and 4 rotary corners, which are welded into a single structure.

Due to the fact that this compensator has to be serviced frequently, because precipitation in the form of dirt or other dense structures often accumulates in the U-shaped elbow, its connecting pipes are equipped with flanges or threaded couplings. This allows you to mount and dismantle the device without the use of special tools.

U-shaped compensators are provided for both steel pipes, and for polyethylene pipes. The design is not without flaws. So, for example, the installation of a U-shaped compensator in the heating system requires spending additional material in the form of pipes, corners, sgons. For heating networks, everything is complicated by the installation of additional supports.

Installation requirements and installation cost of U-shaped devices

Despite the relative simplicity of the device, the installation of a U-shaped compensator is not always lower in cost, compared, for example, with the cost of a bellows compensator. Now we are talking about pipelines of large diameter. In this case, the cost of additional elements and their mounting exceed the cost of the bellows device, and if we take into account the need to build supports, then the difference in price will be very noticeable.

If the compensator is made by bending a straight pipe, it must be taken into account that the radius of this bend must be equal to eight radii of the pipe itself. If there are seams, the structure is made so that these seams fall on straight sections. When forming steeply curved bends, of course, one has to deviate from these rules.

Pros and cons of the U-shaped design

It is advisable to apply given type expansion joints when installing pipelines of small diameters. It should be noted here that the size range of bellows expansion joints is somewhat wider. The U-bend copes well with vibrations, but its manufacture requires a large amount of material, which significantly increases the cost of the device.

Comparison of the characteristics of bellows and U-shaped expansion joints allows us to identify the main advantages and disadvantages of each type of device. For example, a U-shaped compensator needs to be periodically serviced and cleaned from deposits. Bellows expansion joints do not suffer from such shortcomings.

Another point that I would like to note concerns the compensating ability of the two types of devices. If we consider only absolute values, then in this regard clear advantage not visible from either side. However, to increase the maximum displacement in the U-shaped compensator, you will have to increase the size of the knee. For a bellows compensator, it is enough to use a two-section corrugation, which practically does not affect the dimensions in any way.

I would like to add to the treasury of positive properties such a quality as the lack of control during operation. But in a densely populated area, there is not always free space for arranging a pipeline with a U-shaped compensator. The elbow can only be mounted on horizontal sections, while the bellows expansion joint is installed on any straight section.

Finally, another advantage of the bellows expansion joint is that it does not increase the resistance to the flow of liquid and gas. The U-bend greatly reduces the flow rate. When using this type of device in a home heating system, you will have to install circulation pump, since due to natural convection, the liquid may not circulate, encountering an obstacle on the way.

Calculations for compensators

The absence of GOST standards for U-shaped devices sometimes significantly complicates the task of project planning, so a preliminary calculation of the U-shaped compensator is necessary. First of all, it is necessary to build on the needs of the project. The dimensions of the pipeline, its diameter, maximum pressure and the magnitude of the expected displacement are taken into account.

This means that it is almost impossible to purchase a ready-made compensator. For each specific case, it must be made individually. This is another disadvantage compared to bellows devices.

When calculating the parameters, the following restrictions and conditions should be taken into account:

• steel is used as the material for the pipeline;
• compensators are designed for both water and gaseous media;
• the maximum carrier pressure does not exceed 1.6 atmospheres;
• the compensator must have the correct shape in the form of the letter "P";
• mounted only on horizontal sections;
• no effect of wind.

It should be understood that the given parameters are considered ideal. In real conditions, it is possible to observe only a couple of points. When it comes to the temperature of the environment, it is necessary to take its value to the maximum, and take the ambient temperature to the minimum.

Mounting the compensator

During the construction of the highway, certain rules should be used, which also apply to the arrangement of U-shaped expansion joints. It is installed so that the flight is directed to the right side. The parties determine when looking at the pipeline from the source to the receiver. If there is no space required for the compensator on the right, then the flight is made to the left, however, the return line will have to be led from right side, and this leads to changes in the project.

Before the direct commissioning of the heating main, a mandatory preliminary stretching of the compensator is required. Filled pipes experience excessive pressure, so if this procedure is not done, the metal will soon begin to collapse.

The tension is made with special jacks, and after starting they are removed, and the knee takes its previous position. The amount of tension is indicated by the passport data provided for each device. When installing supports, it is necessary to calculate their location, they must be located so that deformations lead only to axial displacement of the pipe on the support.