Design of heating networks for an industrial enterprise in Tambov

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 and methodological reference books. Despite this, often young engineers who do not have specialized programs, the calculation of compensators causes difficulties. 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 graphic method definitions 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 overpressure 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 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 iteration, 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 encourage 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 calculation results for temperature compensation plot main pipeline DN 800 made of steel 17G 2S, length 200 m, 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 scheme with geometric designations 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

Compensators for heating networks. This article will discuss the selection and calculation of compensators for heating networks.

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

It is worth noting that to allow expansion and contraction of pipelines, not only compensators are designed, but also a system of supports, which, in turn, can be either “sliding” or “dead”. How usually in Russia regulation of the thermal load is qualitative - that is, with temperature changes environment, the temperature at the outlet of the heat supply source changes. Due to quality regulation heat supply - the number of expansion-compression cycles of pipelines increases. The service life of pipelines is reduced, and the risk of pinching increases. 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 changes. In this case, the metal of the heating network pipelines operates under easier conditions, there are a minimum number of expansion-compression cycles, thereby increasing the service life of the heating network pipelines. Therefore, before choosing compensators, their characteristics and quantity, you need to determine the amount of expansion of the pipeline.

Formula 1:

δL=L1*a*(T2-T1)where

δL is the amount of pipeline extension,

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

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

T1 - maximum pipeline temperature (the maximum coolant temperature is assumed),

T2 - minimum temperature pipeline (minimum ambient temperature can be accepted), °C

As an example, let’s consider solving an elementary problem of determining the amount of pipeline extension.

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 season-40 °C.

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, you should clearly understand when an expansion joint is needed and when it is not needed. To answer this question unambiguously, you need to have a clear pipeline diagram, with its linear dimensions and supports applied to it. It should be clearly understood that changing the direction of the pipeline can compensate for elongations, in other words, turning 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 have determined the amount of pipeline elongation, 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 type and design features compensators. To select the type of compensator, it is necessary to determine the diameter of the heating network pipe based on bandwidth pipe the required power of the heat consumer.

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

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

Task 2 Determining the number and size of compensators.

For a pipeline with a diameter of DN 100 with a straight section length 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 Problem 1). From the Table. 1 and Table 2 we determine the dimensions of n-shaped compensators (with dimensions of 2x2 m it can compensate for 0.134 meters of pipeline extension), we need to compensate 0.342 meters, therefore Ncomp = bL/∂x = 0.342/0.134 = 2.55, round to the nearest integer In the direction of increasing this, 3 compensators measuring 2x4 meters are required.

Currently, lens compensators are becoming more widespread; they are much more compact than U-shaped ones, however, a number of restrictions do not always allow their use. The service life of a U-shaped compensator is significantly higher than that of a lens compensator, due to bad quality coolant. Bottom part The lens compensator usually becomes “clogged” with sludge, which contributes to the development of parking corrosion of the compensator metal.

In heating networks, gland, U-shaped and bellows (wavy) expansion joints are widely used. Compensators must have sufficient compensating capacity to accommodate the thermal elongation of the pipeline section between fixed supports, while the maximum stresses in radial expansion joints should not exceed the permissible ones (usually 110 MPa).

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

(81)

Where
- average linear expansion coefficient of steel,

(for standard calculations you can take
),

- calculated temperature difference, determined by the formula

(82)

Where - design coolant temperature, o C;

- calculated outside 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 the stuffing box determined by the formula

Where - working pressure of the coolant, MPa;

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

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

- coefficient of friction of the packing on the metal is assumed to be 0.15.

When selecting compensators, their compensating capacity and technical parameters can be determined by application.

Axial reaction of bellows expansion jointsconsists of two terms:

(84)

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

(85)

here l is the temperature expansion 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 thickness of the wave wall, equal on average to 0.5 - 0.6;

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

- excess coolant pressure, Pa.

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

(87)

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

(88)

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

l is the length of the short arm, m;

E - modulus of longitudinal elasticity, equal on average for steel to 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 one.

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

When placing fixed supports at corners of turns used for self-compensation, it is necessary to take into account that the sum of the lengths of the arms of the angle between the supports should not be more than 60% of the maximum distance for straight sections. It should also be taken into account that the maximum rotation angle used for self-compensation should not exceed 130 o.

Calculation of a U-shaped compensator is to define minimum sizes compensator sufficient to compensate for temperature deformations of the pipeline. By filling out the form above, you can calculate the compensating capacity of a U-shaped compensator of given dimensions.

The algorithm of this online program is based on the method for calculating a U-shaped compensator given in the Designer’s Handbook “Design of Heat Networks” edited by A. A. Nikolaev.

1. The maximum stress in the back of the compensator is recommended to be in the range from 80 to 110 MPa.


2. The optimal ratio of the expansion joint overhang to the outer diameter of the pipe is recommended to be taken in the range H/Dн = (10 - 40), while a compensator overhang of 10DN corresponds to a DN350 pipeline, and an overhang of 40DN corresponds to a DN15 pipeline.


3. The optimal ratio of the width of the compensator to its reach is recommended to be taken in the range L/H = (1 - 1.5), although other values ​​can be accepted.


4. If a compensator is needed to compensate for the calculated thermal expansions, it is too large sizes, it can be replaced with two smaller compensators.


5. When calculating the thermal elongation of a pipeline, the temperature of the coolant should be taken as maximum, and the temperature of the environment surrounding the pipeline as minimum.

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

1. 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.


2. 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.


3. 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. Preliminary stretching of the compensator by an amount equal to half thermal elongation pipeline, allows you to double its compensating capacity.

Application area

U-shaped compensators are used to compensate for thermal expansion of 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

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

Advantages

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

Flaws

• High consumption pipes
• Large footprint
• High hydraulic resistance

This Guidance Document (RD) applies to steel pipelines of water heating networks with operating pressure up to 2.5 MPa and operating temperature up to 200 °C and steam pipelines with operating pressure up to 6.3 MPa and operating temperature up to 350 °C, laid on supports (above ground and in closed channels), as well as channelless in the ground. The RD provides for determining the wall thickness of bends, tees and tie-ins from the condition of ensuring them bearing capacity from the action of internal pressure, as well as assessment of the static and cyclic strength of the pipeline.

Snip -85

When calculating supports, one should take into account the depth of soil freezing or thawing, soil deformation (heaving and subsidence), as well as possible changes in soil properties (within the limits of load absorption) depending on the time of year, temperature regime, drainage or watering of areas adjacent to the route, and other conditions. 8.43. Loads on supports arising from the influence of wind and from changes in the length of pipelines under the influence of internal pressure and changes in the temperature of the pipe walls must be determined depending on the adopted system for laying and compensating for longitudinal deformations of pipelines, taking into account the resistance to pipeline movements on the supports.

Calculation of U-shaped compensators

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.

Calculation of the U-shaped compensator

diameter of the pipe with bent bends of radius R = 1 m.

reach l = 5 m; coolant temperature t = 150°C, and temperature inside the chamber t inc. = 19.6°C; permissible compensation stress in the pipeline s add = 110 MPa. Heating systems and district heating are an important link in the energy sector and engineering equipment of cities and industrial areas.

Pipes are the best choice

Pipeline design made of polypropylene for cold and hot water supply systems is carried out in accordance with regulations building codes and rules (SNiP) 2.04.01 85 “Internal water supply and sewerage of buildings”, taking into account the specifics polypropylene pipes.

The choice of pipe type is made taking into account the operating conditions of the pipeline: pressure, temperature, required service life and aggressiveness of the transported liquid. When transporting aggressive liquids, pipeline operating condition coefficients should be applied according to Table.

2 from CH 550 82.

Hydraulic calculation of pipelines made of PP R 80 consists of determining pressure loss(or pressure) to overcome hydraulic resistance that occurs in the pipe, in connecting parts, in places of sharp turns and changes in the diameter of the pipeline.

Hydraulic pressure loss in the pipe determined by nomograms.

Page 7); Improving the thermal and hydraulic conditions of the heating system

Bending longitudinal compensation stress at the rigid attachment point of the smaller arm b(a) = 45.53 MPa Bending longitudinal compensation stress at the rigid attachment point of the larger arm b(b) = 11.77 MPa Bending longitudinal compensation stress at the bending point b(c) = 20.53 MPa.

The results of the program Px=1287.88 H were taken as calculated when determining the standard horizontal load on fixed support should be taken into account: unbalanced internal pressure forces when using stuffing box expansion joints in areas with shut-off valves, transitions, rotation angles, stubs; you should also take into account the frictional forces in the moving supports and on the ground for channelless laying, as well as the reaction of compensators and self-compensation.

Online calculation of the L-shaped compensator

Performing calculations using START programs ensures reliability and safety during the operation of pipeline systems for various purposes, facilitates coordination of the project with regulatory authorities (Rostekhnadzor, Glavsgosexpertiza), reduces costs and time for commissioning.

START was developed by NTP Truboprovod LLC - expert organization Rostechnadzor. There is a certificate of conformity from the Federal Agency for Technical Regulation and Metrology.