This section presents the simplest calculation programs for ventilation and air conditioning. How to find the resistance coefficient of a ventilation grill
Ph.D. S. B. Gorunovich, PTO engineer, Ust-Ilimskaya CHPP, branch of OAO Irkutskenergo, Ust-Ilimsk, Irkutsk region.
Statement of a question
It is known that many enterprises that in the recent past had reserves of heat and electrical energy, insufficient attention was paid to its losses during transportation. For example, various pumps were included in the project, as a rule, with a large power margin, pressure losses in pipelines were compensated by an increase in supply. The main steam pipelines were designed with jumpers and long lines, allowing, if necessary, to transport excess steam to neighboring turbine units. During the reconstruction and repair of transmission networks, preference was given to the versatility of the schemes, which led to additional tie-ins (fittings) and jumpers, the installation of additional tees and, as a result, to additional local losses of total pressure. At the same time, it is known that in long pipelines at significant medium velocities, local losses of total pressure (local resistances) can lead to significant losses in costs for consumers.
At present, the requirements of efficiency, energy saving, total optimization of production make us take a fresh look at many issues and aspects of the design, reconstruction and operation of pipelines and steam pipelines, therefore, taking into account local resistance in tees, forks and fittings in hydraulic calculations pipelines becomes an urgent task.
The purpose of this work is to describe the most commonly used tees and fittings at power engineering enterprises, exchange experience in the field of ways to reduce local resistance coefficients, and methods for comparative evaluation of the effectiveness of such measures.
To assess local resistance in modern hydraulic calculations, they operate with a dimensionless coefficient of hydraulic resistance, which is very convenient because in dynamically similar flows, in which the geometric similarity of sections and the equality of Reynolds numbers are observed, it has the same value, regardless of the type of liquid (gas) , as well as on the flow rate and transverse dimensions calculated plots.
The coefficient of hydraulic resistance is the ratio of the total energy (power) lost in a given section to the kinetic energy (power) in the accepted section or the ratio of the total pressure lost in the same section to dynamic pressure in the accepted section:
where p total - lost (in this area) total pressure; p is the density of the liquid (gas); w, - speed in the i-th section.
The value of the drag coefficient depends on which design speed and, therefore, to which section it is reduced.
Exhaust and supply tees
It is known that a significant part of local losses in branched pipelines are local resistances in tees. As an object representing local resistance, the tee is characterized by the branch angle a and the ratio of the cross-sectional areas of the branches (lateral and straight) F b /F q , Fh / Fq and F B / Fn. In the tee, the flow rates Q b /Q q , Q n /Q c and, accordingly, the speed ratios w B /w Q , w n /w Q can change. The tees can be installed both in the suction sections (exhaust tee) and in the discharge sections (supply tees) in case of flow separation (Fig. 1).
The resistance coefficients of exhaust tees depend on the parameters listed above, and the inlet tees of the usual form - practically only on the branch angle and the ratio of velocities w n /w Q and w n /w Q, respectively.
The drag coefficients of conventionally shaped exhaust tees (without rounding and no flare or contraction of side branch or straight run) can be calculated using the following formulas.
Resistance in the side branch (in section B):
where Q B \u003d F B w B, Q q \u003d F q w q - volumetric flow rates in section B and C, respectively.
For type F n =F c tees and for all a, the values of A are given in Table. one.
When the ratio Q b /Q q changes from 0 to 1, the drag coefficient varies from -0.9 to 1.1 (F q =F b , a=90 O). Negative values are explained by suction action in the line at small Q B .
It follows from the structure of formula (1) that the drag coefficient will rapidly increase with a decrease in the cross-sectional area of the nozzle (with an increase in F c /F b). For example, when Q b /Q c =1, F q/F b =2, a=90 O, the coefficient is 2.75.
It is obvious that a decrease in resistance can be achieved by reducing the angle of the side branch (choke). For example, when F c =F b , α=45 O, when the ratio Q b /Q c changes from 0 to 1, the coefficient changes in the range from -0.9 to 0.322, i.e. its positive values decrease by almost 3 times.
The resistance in the forward passage should be determined by the formula:
For Fn=F c type tees, K P values are given in Table. 2.
It is easy to verify that the range of change in the drag coefficient in the forward pass
de when changing the ratio of Q b /Q c from 0 to 1 is in the range from 0 to 0.6 (F c =F b , α=90 O).
Reducing the angle of the side branch (choke) also leads to a significant reduction in resistance. For example, when F c =F b , α =45 O, when the ratio Q b /Q c changes from 0 to 1, the coefficient changes in the range from 0 to -0.414, i.e. with an increase in Q B, a "suction" appears in the direct passage, further reducing the resistance. It should be noted that dependence (2) has a pronounced maximum, i.e. maximum value the drag coefficient falls on the value of Q b /Q c =0.41 and equals 0.244 (at F c =F b , α =45 O).
The resistance coefficients of supply tees of normal shape in turbulent flow can be calculated using the formulas .
Side branch resistance:
where K B - flow compression ratio.
For type Fn=F c tees, the values of A 1 are given in Table. 3, K B =0.
If we take F c \u003d F b , a \u003d 90 O, then when the ratio Q b /Q c changes from 0 to 1, we obtain coefficient values in the range from 1 to 1.2.
It should be noted that the source provides other data for the coefficient A 1 . According to the data, A 1 =1 should be taken at w B /w c<0,8 и А 1 =0,9 при w B /w c >0.8. If we use the data from , then when the ratio Q B /Q C changes from 0 to 1, we obtain coefficient values in the range from 1 to 1.8 (F c =F b). In general, we will get slightly higher values for the drag coefficients in all ranges.
The decisive influence on the growth of the drag coefficient, as in formula (1), is exerted by the cross-sectional area B (fitting) - with increasing F g /F b, the drag coefficient increases rapidly.
Resistance in the straight passage for supply tees of the type Fn=Fc within
The values of t P are indicated in Table. four.
When the ratio Q B /Qc(3) changes from 0 to 1 (Fc=F B, α=90 O), we obtain coefficient values in the range from 0 to 0.3.
The resistance of conventionally shaped tees can also be markedly reduced by rounding off the junction of the side branch with the prefabricated hose. In this case, for exhaust tees, the angle of rotation of the flow should be rounded (R 1 in Fig. 16). For inlet tees, the rounding should also be done on the separating edge (R 2 in Fig. 16); it makes the flow more stable and reduces the possibility of it breaking away from that edge.
In practice, the rounding of the edges of the conjugation of the generatrix of the side branch and the main pipeline is sufficient when R / D (3 = 0.2-0.3.
The above formulas for calculating the resistance coefficients of tees and the corresponding tabular data refer to carefully manufactured (turned) tees. Manufacturing defects in tees made during their manufacture (“failures” of a side branch and “overlapping” of its section by an incorrect wall cut in a straight section - the main pipeline) become a source of sharp increase hydraulic resistance. In practice, this happens with a poor-quality tie-in into the main pipeline of the fitting, which occurs quite often, because. "factory" tees are relatively expensive.
The gradual expansion (diffuser) of the side branch effectively reduces the resistance of both exhaust and supply tees. The combination of rounding, bevelling and expanding the side branch further reduces the resistance of the tee. The resistance coefficients of improved tees can be determined from the formulas and diagrams given in the source. Tees with side branches in the form of smooth bends also have the least resistance, and where practicable, tees with small branch angles (up to 60 °) should be used.
In turbulent flow (Re>4.10 3) the drag coefficients of the tees depend little on the Reynolds numbers. During the transition from turbulent to laminar, there is an abrupt increase in the drag coefficient of the side branch both in the exhaust and supply tees (by about 2-3 times).
In calculations, it is important to take into account in which section it is reduced to average speed. There is a link in the source about this before each formula. The sources give a general formula, which indicates the rate of reduction with the corresponding index.
Symmetrical tee when merging and splitting
The resistance coefficient of each branch of a symmetrical tee at the confluence (Fig. 2a), can be calculated by the formula:
When the ratio Q b /Q c changes from 0 to 0.5, the coefficient changes in the range from 2 to 1.25, and then with an increase in Q b / Q c from 0.5 to 1, the coefficient acquires values from 1.25 to 2 (for the case F c =F b). Obviously, dependence (5) has the form of an inverted parabola with a minimum at the point Q b /Q c =0.5.
The resistance coefficient of a symmetrical tee (Fig. 2a) located in the injection (separation) section can also be calculated using the formula:
where K 1 \u003d 0.3 - for welded tees.
When the ratio w B /w c changes from 0 to 1, the coefficient changes in the range from 1 to 1.3 (F c =F b).
Analyzing the structure of formulas (5, 6) (as well as (1) and (3)), it can be seen that a decrease in the cross section (diameter) of the side branches (sections B) adversely affects the resistance of the tee.
The flow resistance can be reduced by a factor of 2-3 when using tees-forks (Fig. 26, 2c).
The drag coefficient of a tee-fork during flow separation (Fig. 2b) can be calculated by the formulas:
When the ratio Q 2 /Q 1 changes from 0 to 1, the coefficient changes in the range from 0.32 to 0.6.
The resistance coefficient of the tee-fork at the merger (Fig. 2b) can be calculated by the formulas:
When the ratio Q 2 /Q 1 changes from 0 to 1, the coefficient changes in the range from 0.33 to -0.4.
A symmetrical tee can be made with smooth bends (Fig. 2c), then its resistance can be further reduced.
Manufacturing. Standards
Industry energy standards prescribe for pipelines of thermal power plants low pressure(at working pressure P slave.<22 кгс/см 2 и температуре среды t<425 О С) использовать тройники сварные по ОСТ34-42-762
OST34-42-765-85. For higher environmental parameters (P work b.<40 кгс/см 2) изготавливают тройники из углеродистых и кремнемарганцовистых сталей: штампованные по ОСТ108.720.01, ОСТ108.720.02-82; сварные по ОСТ108.104.01 - ОСТ108.104.03-82; с обжатием (с вытянутой горловиной) по ОСТ108.104.04, ОСТ108.104.05-82. Из хромомолибденованадиевых сталей изготавливают тройники: штампованные по ОСТ108.720.05, ОСТ108.720.06-82; сварные по ОСТ108.104.10 - ОСТ108.104.12-82; с обжатием (с вытянутой горловиной) по ОСТ108.104.13 - ОСТ108.104.15-82 для паропроводов высокого давления (с параметрами Р раб. до 255 кгс/см 2 и температурой t до 560 О С). Существуют соответствующие нормативы и для штуцеров.
The design of tees manufactured according to the existing (above) standards is far from always optimal in terms of hydraulic losses. Only the shape of stamped tees with an elongated neck contributes to a decrease in the coefficient of local resistance, where a rounding radius is provided in the side branch according to the type shown in Fig. 1b and fig. 3c, as well as with end compression, when the diameter of the main pipeline is slightly smaller than the diameter of the tee (as shown in Fig. 3b). Forked tees are apparently made to order according to "factory" standards. In RD 10-249-98 there is a paragraph devoted to the calculation of the strength of tees-forks and fittings.
When designing and reconstructing networks, it is important to take into account the direction of movement of the media and the possible ranges of flow rates in tees. If the direction of the transported medium is clearly defined, it is advisable to use inclined fittings (side branches) and forked tees. However, there remains the problem of significant hydraulic losses in the case of a universal tee, which combines the properties of supply and exhaust, in which both merging and separation of the flow are possible in operating modes associated with a significant change in flow rates. The above qualities are typical, for example, for switching nodes of feed water pipelines or main steam pipelines at thermal power plants with "jumpers".
It should be borne in mind that for steam and hot water pipelines, the design and geometric dimensions of welded pipe tees, as well as fittings (pipes, branch pipes) welded on straight sections of pipelines, must meet the requirements of industry standards, norms and specifications. In other words, for critical pipelines, it is necessary to order tees made in accordance with the specifications from certified manufacturers. In practice, in view of the relative high cost of "factory" tees, tie-in fittings are often performed by local contractors using industry or factory standards.
In general, the final decision on the tie-in method should be taken after a comparative feasibility study. If a decision is made to carry out the tie-in “on their own”, the engineering and technical personnel need to prepare a choke template, calculate the strength (if necessary), control the quality of the tie-in (avoid “failures” of the choke and “overlap” its section with an incorrect wall cut in a straight section) . It is advisable to make the internal joint between the metal of the fitting and the main pipeline with a rounding (Fig. 3c).
There are a number constructive solutions to reduce hydraulic resistance in standard tees and line switching assemblies. One of the simplest is to increase the size of the tees themselves to reduce the relative velocities of the medium in them (Fig. 3a, 3b). At the same time, tees must be completed with transitions, the angles of expansion (narrowing) of which are also advisable to choose from a number of hydraulically optimal ones. As a universal tee with reduced hydraulic losses, you can also use a forked tee with a jumper (Fig. 3d). The use of tees-forks for switching nodes of highways will also slightly complicate the design of the node, but will have a positive effect on hydraulic losses (Fig. 3e, 3f).
It is important to note that with a relatively close location of local (L=(10-20)d) resistances of various types, the phenomenon of interference of local resistances takes place. According to some researchers, with the maximum convergence of local resistances, it is possible to achieve a decrease in their sum, while at a certain distance (L = (5-7) d), the total resistance has a maximum (3-7% higher than the simple sum) . The reduction effect could be of interest to large manufacturers ready to manufacture and supply switching units with reduced local resistances, but applied laboratory research is required to achieve a good result.
Feasibility Study
When making a constructive decision, it is important to pay attention to the economic side of the problem. As mentioned above, "factory" tees of a conventional design, and even more so made to order (hydraulically optimal), will cost significantly more than a tie-in fitting. At the same time, it is important to roughly evaluate the benefits in case of reducing hydraulic losses in a new tee and its payback period.
It is known that pressure losses in station pipelines with normal media flow rates (for Re>2.10 5) can be estimated by the following formula:
where p - pressure loss, kgf / cm 2; w is the speed of the medium, m/s; L - deployed length of the pipeline, m; g - free fall acceleration, m/s 2 ; d - design diameter of the pipeline, m; k - coefficient of friction resistance; ∑ἐ m is the sum of local resistance coefficients; v - specific volume of the medium, m 3 / kg
Dependence (7) is usually called the hydraulic characteristic of the pipeline.
If we take into account the dependence: w=10Gv/9nd 2 , where G is the consumption, t/h.
Then (7) can be represented as:
If it is possible to reduce the local resistance (tee, fitting, switching unit), then, obviously, formula (9) can be represented as:
Here ∑ἐ m is the difference between the local resistance coefficients of the old and new nodes.
Let us assume that the hydraulic system "pump - pipeline" operates in nominal mode (or in a mode close to nominal). Then:
where P n - nominal pressure (according to the flow characteristic of the pump / boiler), kgf / cm 2; G h - nominal flow rate (according to the flow characteristic of the pump / boiler), t / h.
If we assume that after replacing the old resistances, the “pump-pipeline” system will remain operational (ЫРn), then from (10), using (12), we can determine the new flow rate (after reducing the resistance):
The operation of the "pump-pipeline" system, the change in its characteristics can be visualized in Fig. four.
Obviously, G 1 >G M . If we are talking about the main steam pipeline that transports steam from the boiler to the turbine, then by the difference in flow rates ЛG=G 1 -G n it is possible to determine the gain in the amount of heat (from the turbine extraction) and / or in the amount of generated electric energy according to the operating characteristics of this turbine.
Comparing the cost of a new node and the amount of heat (electricity), you can roughly estimate the profitability of its installation.
Calculation example
For example, it is necessary to evaluate the cost-effectiveness of replacing an equal tee of the main steam pipeline at the confluence of flows (Fig. 2a) with a forked tee with a jumper of the type indicated in fig. 3y. Steam consumer - heating turbine PO TMZ type T-100/120-130. Steam enters through one line of the steam pipeline (through a tee, sections B, C).
We have the following initial data:
■ design diameter of the steam pipeline d=0.287 m;
■ nominal steam flow rate G h =Q(3=Q^420 t/h;
■ nominal pressure of the boiler Р н =140 kgf/cm 2 ;
■ specific volume of steam (at P ra b=140 kgf/cm 2 , t=560 o C) n=0.026 m 3 /kg.
We calculate the resistance coefficient of a standard tee at the confluence of flows (Fig. 2a) using the formula (5) - ^ SB1 = 2.
To calculate the resistance coefficient of a tee-fork with a jumper, assume:
■ division of flows in the branches occurs in the proportion Q b /Q c «0.5;
■ the total resistance coefficient is equal to the sum of the resistances of the inlet tee (with a 45 O outlet, see Fig. 1a) and the branch tee at the confluence (Fig. 2b), i.e. interference is neglected.
We use formulas (11, 13) and get the expected increase in consumption by G=G 1 -G n = 0.789 t/h.
According to the regime diagram of the T-100/120-130 turbine, a flow rate of 420 t/h can correspond to an electrical load of 100 MW and a thermal load of 400 GJ/h. The relationship between flow and electrical load is close to directly proportional.
The gain in electrical load can be: P e \u003d 100AG / Q n \u003d 0.188 MW.
The heat load gain can be: T e \u003d 400AG / 4.19Q n \u003d 0.179 Gcal / h.
Prices for products made of chromium-molybdenum-vanadium steels (for tees-fork 377x50) can vary widely from 200 to 600 thousand rubles, therefore, the payback period can only be judged after a thorough market research at the time of the decision.
1. This article describes various types of tees and fittings, gives a brief description of the tees used in pipelines of power plants. Formulas for determining the coefficients of hydraulic resistance are given, ways and means of their reduction are shown.
2. Prospective designs of tees-forks, a switching unit for main pipelines with reduced coefficients of local resistance are proposed.
3. Formulas are given, an example, and the expediency of a technical and economic analysis is shown when choosing or replacing tees, when reconstructing switching units.
Literature
1. Idelchik I.E. Handbook of hydraulic resistance. M.: Mashinostroenie, 1992.
2. Nikitina I.K. Handbook of pipelines of thermal power plants. Moscow: Energoatomizdat, 1983.
3. Handbook of calculations of hydraulic and ventilation systems / Ed. A.S. Yuriev. S.-Pb.: ANO NPO "World and Family", 2001.
4. Rabinovich E.Z. Hydraulics. Moscow: Nedra, 1978.
5. Benenson E.I., Ioffe L.S. Cogeneration Steam Turbines / Ed. D.P. Elder. M: Energoizdat, 1986.
You can also use the approximate formula:
0.195 v 1.8
R f . (10) d 100 1 , 2
Its error does not exceed 3 - 5%, which is sufficient for engineering calculations.
The total friction pressure loss for the entire section is obtained by multiplying the specific losses R by the length of the section l, Rl, Pa. If air ducts or channels from other materials are used, it is necessary to introduce a correction for roughness βsh according to Table. 2. It depends on the absolute equivalent roughness of the duct material K e (Table 3) and the value of v f .
table 2 |
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Correction values βsh |
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v f , m/s |
βsh at K e , mm |
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Table 3 Absolute equivalent roughness of duct material
Plasterer- |
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ka on the grid |
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K e , mm |
For steel air ducts βsh = 1. More detailed values of βsh can be found in Table. 22.12. With this correction in mind, the adjusted friction pressure loss Rl βsh , Pa, is obtained by multiplying Rl by the value βsh . Then determine the dynamic pressure on the participants
under standard conditions ρw = 1.2 kg/m3.
Next, local resistances are detected on the site, local resistance coefficients (LMR) ξ are determined and the sum of LMR in this section (Σξ) is calculated. All local resistances are entered into the statement in the following form.
STATEMENT KMS VENTILATION SYSTEMS
Etc.
AT the column “local resistances” records the names of the resistances (bend, tee, cross, elbow, grate, air distributor, umbrella, etc.) available in this area. In addition, their number and characteristics are noted, according to which the CMR values are determined for these elements. For example, for a round bend, this is the angle of rotation and the ratio of the radius of rotation to the diameter of the duct r / d , for a rectangular outlet - the angle of rotation and dimensions of the sides of the duct a and b . For side openings in an air duct or duct (for example, at the installation site of an air intake grille) - the ratio of the opening area to the cross section of the air duct
f resp / f about . For tees and crosses on the passage, the ratio of the cross-sectional area of the passage and the trunk f p / f s and the flow rate in the branch and in the trunk L o / L s is taken into account, for tees and crosses on the branch - the ratio of the cross-sectional area of the branch and the trunk f p / f s and again, the value of L about /L with. It should be borne in mind that each tee or cross connects two adjacent sections, but they refer to one of these sections, in which the air flow L is less. The difference between tees and crosses on a run and on a branch has to do with how the design direction runs. This is shown in fig. 11. Here, the calculated direction is shown by a thick line, and the directions of air flows are shown by thin arrows. In addition, it is signed exactly where in each option the trunk, passage and exit are located.
branching of the tee for the correct choice of relations fp /fc , fo /fc and L o /L c . Note that in supply ventilation systems, the calculation is usually carried out against the movement of air, and in exhaust systems, along this movement. The sections to which the considered tees belong are indicated by checkmarks. The same applies to crosses. As a rule, although not always, tees and crosses on the passage appear when calculating the main direction, and on the branch they appear when aerodynamic linking of secondary sections (see below). In this case, the same tee in the main direction can be considered as a tee per passage, and in the secondary
– as a branch with a different coefficient. KMS for crosses
accepted in the same size as for the corresponding tees.
Rice. 11. Tee calculation scheme
Approximate values of ξ for common resistances are given in Table. four.
Table 4 |
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Values ξ of some local resistances |
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Name |
Name |
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resistance |
resistance |
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Elbow round 90o, |
The grate is not adjustable |
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r/d = 1 |
may RS-G (exhaust or |
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Rectangular elbow 90o |
air intake) |
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Tee in the passage (on- |
sudden expansion |
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oppression) |
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Branch tee |
sudden constriction |
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Tee in the passage (all- |
First side hole |
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stie (entrance to the air |
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Branch tee |
–0.5* … |
boron mine) |
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Plafond (anemostat) ST-KR, |
Rectangular elbow |
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90o |
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Grille adjustable RS- |
Umbrella over exhaust |
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VG (supply) |
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*) negative CMR can occur at low Lo /Lc due to air ejection (suction) from the branch by the main flow.
More detailed data for the KMS are given in Table. 22.16 - 22.43. For the most common local resistances -
tees in the passage - KMR can also be approximately calculated using the following formulas:
0.41f "25L" 0.24 |
0.25 at |
0.7 and |
f "0.5 (11) |
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- for tees during injection (supply); |
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at L" |
0.4 you can use the simplified formula |
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prox int 0. 425 0. 25 f p "; |
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0.2 1.7f" |
0.35 0.25f" |
2.4L" |
0. 2 2 |
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– for suction tees (exhaust).
Here L" |
f about |
and f" |
f p |
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f c |
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After determining the value of Σξ, the pressure loss at local resistances Z P d, Pa, and the total pressure loss are calculated
on the section Rl βsh + Z , Pa.
The results of the calculations are entered in the table in the following form.
AERODYNAMIC CALCULATION OF THE VENTILATION SYSTEM
Estimated |
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Duct dimensions |
pressure |
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on friction |
Rlβ w |
Rd , |
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βw |
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d or |
f op, |
ff , |
Vf , |
d eq |
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l , m |
a×b |
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When the calculation of all sections of the main direction is completed, the values of Rl βsh + Z for them are summarized and the total resistance is determined.
ventilation network resistance P network = Σ(Rl βw + Z ).
After calculating the main direction, one or two branches are linked. If the system serves several floors, you can select floor branches on intermediate floors for linking. If the system serves one floor, link branches from the main that are not included in the main direction (see the example in paragraph 4.3). The calculation of the linked sections is carried out in the same sequence as for the main direction, and recorded in a table in the same form. Linkage is considered completed if the amount
pressure loss Σ(Rl βsh + Z ) along the linked sections deviates from the sum Σ(Rl βsh + Z ) along parallel connected sections of the main direction by no more than 10%. Sections along the main and linked directions from the point of their branching to the end air distributors are considered to be connected in parallel. If the circuit looks like the one shown in Fig. 12 (the main direction is marked with a thick line), then direction 2 alignment requires that the value of Rl βw + Z for section 2 equals Rl βw + Z for section 1, obtained from the calculation of the main direction, with an accuracy of 10%. Linkage is achieved by selecting the diameters of round or cross-sectional dimensions of rectangular air ducts in the linked sections, and if this is not possible, by installing throttle valves or diaphragms on the branches.
The selection of a fan should be carried out according to the manufacturer's catalogs or according to the data. The fan pressure is equal to the sum of pressure losses in the ventilation network in the main direction, determined during the aerodynamic calculation of the ventilation system, and the sum of pressure losses in the elements of the ventilation unit (air damper, filter, air heater, silencer, etc.).
Rice. 12. A fragment of the scheme of the ventilation system with the choice of a branch for linking
Finally, it is possible to choose a fan only after an acoustic calculation, when the issue of installing a silencer is decided. Acoustic calculation can be performed only after preliminary selection of the fan, since the initial data for it are the sound power levels emitted by the fan into the air ducts. Acoustic calculation is carried out, guided by the instructions of chapter 12. If necessary, calculate and determine the size of the silencer , , then finally select the fan.
4.3. An example of calculating the supply ventilation system
The supply ventilation system for the dining room is considered. The application of air ducts and air distributors to the plan is given in clause 3.1 in the first version (typical diagram for halls).
System Diagram
1000х400 5 8310 m3/h
2772 m3/h2 |
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More details on the calculation methodology and the necessary initial data can be found at,. The corresponding terminology is given in .
STATEMENT OF KMS SYSTEM P1
local resistance |
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924 m3/h |
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1. Elbow round 90о r /d =1 |
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2. Tee in the passage (pressure) |
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fp / fc |
Lo/Lc |
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fp / fc |
Lo/Lc |
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1. Tee in the passage (pressure) |
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fp / fc |
Lo/Lc |
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1. Tee in the passage (pressure) |
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fp / fc |
Lo/Lc |
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1. Rectangular elbow 1000×400 90o 4 pcs |
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1. Air intake shaft with umbrella |
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(first side hole) |
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1. Air intake louvre |
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STATEMENT OF KMS OF THE P1 SYSTEM (Branch No. 1) |
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local resistance |
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1. Air distributor PRM3 at flow rate |
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924 m3/h |
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1. Elbow round 90о r /d =1 |
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2. Branch tee (injection) |
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fo / fc |
Lo/Lc |
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APPENDIX Characteristics of ventilation grilles and shades
I. Living sections, m2, supply and exhaust louvered gratings RS-VG and RS-G
Length, mm |
Height, mm |
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Speed coefficient m = 6.3, temperature coefficient n = 5.1.
II. Characteristics of ceiling lamps ST-KR and ST-KV
Name |
Dimensions, mm |
f fact, m 2 |
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Dimensional |
Interior |
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Plafond ST-KR |
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(round) |
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Plafond ST-KV |
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(square) |
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Speed coefficient m = 2.5, temperature coefficient n = 3.
REFERENCES
1. Samarin O.D. Selection of equipment for supply ventilation units (air conditioners) of the KCKP type. Guidelines for the implementation of course and diploma projects for students of the specialty 270109 "Heat and gas supply and ventilation". – M.: MGSU, 2009. – 32 p.
2. Belova E.M. Central air conditioning systems in buildings. - M.: Euroclimate, 2006. - 640 p.
3. SNiP 41-01-2003 "Heating, ventilation and air conditioning". - M.: GUP TsPP, 2004.
4. Catalog of equipment "Arktos".
5. sanitary devices. Part 3. Ventilation and air conditioning. Book 2. / Ed. N.N. Pavlov and Yu.I. Schiller. – M.: Stroyizdat, 1992. – 416 p.
6. GOST 21.602-2003. System of design documents for construction. Rules for the implementation of working documentation for heating, ventilation and air conditioning. - M.: GUP TsPP, 2004.
7. Samarin O.D. On the regime of air movement in steel air ducts.
// SOK, 2006, No. 7, p. 90-91.
8. Designer's Handbook. Internal sanitary devices. Part 3. Ventilation and air conditioning. Book 1. / Ed. N.N. Pavlov and Yu.I. Schiller. – M.: Stroyizdat, 1992. – 320 p.
9. Kamenev P.N., Tertichnik E.I. Ventilation. - M.: ASV, 2006. - 616 p.
10. Krupnov B.A. Terminology in building thermophysics, heating, ventilation and air conditioning: guidelines for students of the specialty "Heat and gas supply and ventilation".
|
Purpose |
Basic requirement | ||||
| Noiselessness | Min. head loss | ||||
| Main channels | main channels | Branches | |||
| tributary | Hood | tributary | Hood | ||
| Living spaces | 3 | 5 | 4 | 3 | 3 |
| Hotels | 5 | 7.5 | 6.5 | 6 | 5 |
| Institutions | 6 | 8 | 6.5 | 6 | 5 |
| Restaurants | 7 | 9 | 7 | 7 | 6 |
| The shops | 8 | 9 | 7 | 7 | 6 |
Based on these values, the linear parameters of the air ducts should be calculated.
Algorithm for calculating air pressure losses
The calculation must begin with drawing up a diagram of the ventilation system with the obligatory indication of the spatial location of the air ducts, the length of each section, ventilation grilles, additional equipment for air purification, technical fittings and fans. Losses are determined first for each individual line, and then summed up. For a separate technological section, the losses are determined using the formula P = L × R + Z, where P is the air pressure loss in the calculated section, R is the loss per linear meter of the section, L is the total length of the air ducts in the section, Z is the loss in the additional fittings of the system ventilation.
To calculate the pressure loss in a circular duct, the formula Ptr is used. = (L/d×X) × (Y×V)/2g. X is the tabular coefficient of air friction, depends on the material of manufacture of the duct, L is the length of the calculated section, d is the diameter of the duct, V is the required air flow rate, Y is the air density, taking into account temperature, g is the acceleration of fall (free). If the ventilation system has square air ducts, then table No. 2 should be used to convert round values to square ones.
Tab. No. 2. Equivalent diameters of round ducts for square
| 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 | |
| 250 | 210 | 245 | 275 | |||||
| 300 | 230 | 265 | 300 | 330 | ||||
| 350 | 245 | 285 | 325 | 355 | 380 | |||
| 400 | 260 | 305 | 345 | 370 | 410 | 440 | ||
| 450 | 275 | 320 | 365 | 400 | 435 | 465 | 490 | |
| 500 | 290 | 340 | 380 | 425 | 455 | 490 | 520 | 545 |
| 550 | 300 | 350 | 400 | 440 | 475 | 515 | 545 | 575 |
| 600 | 310 | 365 | 415 | 460 | 495 | 535 | 565 | 600 |
| 650 | 320 | 380 | 430 | 475 | 515 | 555 | 590 | 625 |
| 700 | 390 | 445 | 490 | 535 | 575 | 610 | 645 | |
| 750 | 400 | 455 | 505 | 550 | 590 | 630 | 665 | |
| 800 | 415 | 470 | 520 | 565 | 610 | 650 | 685 | |
| 850 | 480 | 535 | 580 | 625 | 670 | 710 | ||
| 900 | 495 | 550 | 600 | 645 | 685 | 725 | ||
| 950 | 505 | 560 | 615 | 660 | 705 | 745 | ||
| 1000 | 520 | 575 | 625 | 675 | 720 | 760 | ||
| 1200 | 620 | 680 | 730 | 780 | 830 | |||
| 1400 | 725 | 780 | 835 | 880 | ||||
| 1600 | 830 | 885 | 940 | |||||
| 1800 | 870 | 935 | 990 |
The horizontal is the height of the square duct, and the vertical is the width. The equivalent value of the circular section is at the intersection of the lines.
Air pressure losses in bends are taken from table No. 3.
Tab. No. 3. Loss of pressure on bends
To determine the pressure loss in the diffusers, the data from Table No. 4 are used.
Tab. No. 4. Pressure loss in diffusers
Table No. 5 gives a general diagram of losses in a straight section.
Tab. No. 5. Diagram of air pressure losses in straight air ducts
All individual losses in a given section of the duct are summarized and corrected with Table No. 6. Tab. No. 6. Calculation of the flow pressure drop in ventilation systems
During design and calculations, existing regulations recommend that the difference in pressure loss between individual sections should not exceed 10%. The fan should be installed in the section of the ventilation system with the highest resistance, the most distant air ducts should have the minimum resistance. If these conditions are not met, then it is necessary to change the layout of air ducts and additional equipment, taking into account the requirements of the regulations.
The aerodynamic calculation of air ducts begins with drawing an axonometric diagram M 1:100, putting down the numbers of sections, their loads b m / h, and lengths 1, m. The direction of the aerodynamic calculation is determined - from the most remote and loaded section to the fan. When in doubt, when determining the direction, all possible options are calculated.
The calculation starts from a remote area, its diameter is calculated D, m, or flat
Square section of a rectangular duct P, m:
The beginning of the system at the fan
Administrative buildings 4-5 m/s 8-12 m/s
Industrial buildings 5-6 m/s 10-16 m/s,
Increasing as you get closer to the fan.
Using Appendix 21, we accept the nearest standard values \u200b\u200bof Dst or (a x b)st
Then we calculate the actual speed:
Or———————— ———— - , m/s.
FACT 3660 * (a * 6) st
For further calculations, we determine the hydraulic radius of rectangular ducts:
£>1 =--,m. a + b
To avoid the use of tables and interpolation of the values of specific friction losses, we apply direct solution tasks:
We define the Reynolds criterion:
Re = 64 100 * Rest * Ufact (for rectangular Rest = Ob) (14.6)
And the coefficient of hydraulic friction:
0.3164*Rae 0 25 at Rae< 60 ООО (14.7)
0.1266 * 0167 for R e > 60,000. (14.8)
The pressure loss in the calculated section will be:
Where KMS is the sum of the local resistance coefficients in the duct section.
Local resistances lying on the border of two sections (tees, crosses) should be attributed to the section with a lower flow rate.
The local resistance coefficients are given in the appendices.
Initial data:
Air duct material - galvanized sheet steel, thickness and dimensions in accordance with App. 21 .
The material of the air intake shaft is brick. Adjustable gratings of the PP type with possible sections are used as air distributors:
100 x 200; 200 x 200; 400 x 200 and 600 x 200 mm, shade factor 0.8 and maximum outlet air velocity up to 3 m/s.
The resistance of the insulated intake valve with fully open blades is 10 Pa. The hydraulic resistance of the air heater installation is 132 Pa (according to a separate calculation). Filter resistance 0-4 250 Pa. The hydraulic resistance of the muffler is 36 Pa (according to acoustic calculation). Based on architectural requirements, air ducts are designed rectangular section.
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Supply L, m3/h |
Length 1, m |
Section a * b, m |
Losses in the section p, Pa |
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PP grating at the exit |
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250×250 b =1030 |
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UDC 697.9 Determination of coefficients of local resistance of tees in ventilation systems O. D. Samarin, Candidate of Technical Sciences, Associate Professor (NRU MGSU) Considered current situation with the determination of the values of the coefficients of local resistance (LCR) of the elements of ventilation networks in their aerodynamic calculation. An analysis of some modern theoretical and experimental works in the area under consideration is given, and the shortcomings of the existing reference literature regarding the convenience of using its data for engineering calculations using MS Excel spreadsheets are identified. The main results of the approximation of available tables for CMS unified tees on a branch at discharge and suction in ventilation and air conditioning systems are presented in the form of appropriate engineering formulas. An assessment of the accuracy of the obtained dependences and the permissible range of their applicability is given, as well as recommendations for their use in the practice of mass design. The presentation is illustrated with numerical and graphical examples. Keywords:coefficient of local resistance, tee, branch, discharge, suction. |
UDC 697.9 Determination of local resistance coeffi cients of tees in ventilating systems O. D. Samarin, PhD, Assistant Professor, National Research Moscow State University of Civil Engineering (NR MSUCE) The current situation is reviewed with the definition of values of coeffi cients of local resistances (CLR) of elements of the ventilation systems at their aerodynamic calculation. The analysis of some contemporary theoretical and experimental works in this field is given and defi ciencies are identifi ed in the existing reference literature for the usability of its data to perform engineering calculations using MS Excel spreadsheets. The main results of approximation of the existing tables to the CLR for the uniform tees on the branch of the injection and the suction in the ventilating and air-conditioning systems are presented in the appropriate engineering formulas. The estimation of accuracy of the obtained dependencies and valid range of their applicability are given, as well as recommendations for their use in practice mass design. The presentation is illustrated by numerical and graphical examples. keywords:coefficient of local resistance, tee, branch, injection, suction. |
When the air flow moves in the air ducts and channels of ventilation and air conditioning systems (V and KV), in addition to pressure losses due to friction, losses on local resistances play a significant role - shaped parts of air ducts, air distributors and network equipment.
Such losses are proportional to the dynamic pressure R q = ρ v² / 2, where ρ is the air density, approximately equal to 1.2 kg / m³ at a temperature of about +20 ° C; v— its speed [m/s], determined, as a rule, in the section of the channel behind the resistance.
The coefficients of proportionality ξ, called local resistance coefficients (LRC), for various elements systems B and HF are usually determined from tables available, in particular, in and in a number of other sources. The greatest difficulty in this case is most often the search for KMS for tees or branch nodes. The fact is that in this case it is necessary to take into account the type of tee (for passage or branch) and the mode of air movement (forcing or suction), as well as the ratio of air flow in the branch to the flow in the trunk L´ o \u003d L o /L c and cross-sectional area of the passage to the cross-sectional area of the trunk F´ p \u003d F p / F s.
For tees during suction, it is also necessary to take into account the ratio of the cross-sectional area of \u200b\u200bthe branch to the cross-sectional area of the trunk F´ o \u003d F o / F s. In the manual, the relevant data are given in Table. 22.36-22.40. However, when making calculations using electronic Excel tables, which is currently quite common due to the widespread use of various standard software and the convenience of reporting the results of calculations, it is desirable to have analytical formulas for CMR, at least in the most common ranges of changes in the characteristics of tees.
Moreover, it would be useful in educational process to reduce technical work students and transferring the main load to the development of constructive solutions for systems.
Similar formulas are available in such a fairly fundamental source as, but there they are presented in a very generalized form, without taking into account the design features of specific elements of existing ventilation systems, and also use a significant number of additional parameters and require, in some cases, referring to certain tables. On the other hand, appearing in recent times programs for automated aerodynamic calculation of systems B and KV use some algorithms to determine the CMR, but, as a rule, they are unknown to the user and therefore may raise doubts about their validity and correctness.
Also, some works are currently appearing, the authors of which continue research to refine the calculation of the CMR or expand the range of parameters of the corresponding element of the system, for which the results obtained will be valid. These publications appear both in our country and abroad, although in general their number is not too large, and are based mainly on numerical modeling of turbulent flows using a computer or on direct experimental studies. However, the data obtained by the authors, as a rule, is difficult to use in the practice of mass design, since they are not yet presented in engineering form.
In this regard, it seems appropriate to analyze the data contained in the tables and obtain, on their basis, approximation dependences that would have the simplest and most convenient form for engineering practice, and at the same time adequately reflect the nature of the existing dependences for CMR tees. For their most common varieties - tees in the passage (unified branch nodes), this problem was solved by the author in the work. At the same time, it is more difficult to find analytical relationships for tees on a branch, since the dependencies themselves look more complicated here. General form approximation formulas, as always in such cases, is obtained based on the location of the calculated points on the correlation field, and the corresponding coefficients are selected by the method least squares in order to minimize the deviation of the constructed graph using Excel. Then for some of the most commonly used ranges F p / F s, F o / F s and L o / L s expressions can be obtained:
at L´ o= 0.20-0.75 and F´ o\u003d 0.40-0.65 - for tees during injection (supply);
at L´ o = 0,2-0,7, F´ o= 0.3-0.5 and F´ n\u003d 0.6-0.8 - for tees with suction (exhaust).
The accuracy of dependences (1) and (2) is shown in Figs. 1 and 2, which shows the results of processing table. 22.36 and 22.37 for KMS unified tees (branch nodes) on a branch of circular cross section during suction. In the case of a rectangular section, the results will differ insignificantly.
It can be noted that the discrepancy here is greater than for tees per pass, and averages 10-15%, sometimes even up to 20%, but for engineering calculations this may be acceptable, especially given the obvious initial error contained in the tables, and simultaneous simplification of calculations when using Excel. At the same time, the relations obtained do not require any other initial data, except for those already available in the aerodynamic calculation table. Indeed, it must explicitly indicate both the air flow rates and the cross-sections in the current and in the neighboring section, which are included in the listed formulas. First of all, this simplifies calculations when using Excel spreadsheets. At the same time Fig. 1 and 2 make it possible to verify that the found analytical dependencies quite adequately reflect the nature of the influence of all the main factors on the CMR of tees and the physical nature of the processes occurring in them during the movement of the air flow.
At the same time, the formulas given in this paper are very simple, clear and easily accessible for engineering calculations, especially in Excel, as well as in the educational process. Their use makes it possible to abandon the interpolation of tables while maintaining the accuracy required for engineering calculations, and directly calculate the coefficients of local resistance of tees on a branch in a very wide range of ratios of cross sections and air flow rates in the trunk and branches.
This is quite enough for the design of ventilation and air conditioning systems in most residential and public buildings.
- Designer's Handbook. Internal sanitary devices. Part 3. Ventilation and air conditioning. Book. 2 / Ed. N.N. Pavlov and Yu.I. Schiller. - M.: Stroyizdat, 1992. 416 p.
- Idelchik I.E. Handbook of hydraulic resistance / Ed. M.O. Steinberg. - Ed. 3rd. - M.: Mashinostroenie, 1992. 672 p.
- Posokhin V.N., Ziganshin A.M., Batalova A.V. To determine the coefficients of local resistances of disturbing elements of pipeline systems // Izvestiya vuzov: Stroitel'stvo, 2012. No. 9. pp. 108–112.
- Posokhin V.N., Ziganshin A.M., Varsegova E.V. To the calculation of pressure losses in local resistances: Soobshch. 1 // News of universities: Construction, 2016. No. 4. pp. 66–73.
- Averkova O.A. Experimental study of separated flows at the entrance to the suction holes // Vestnik BSTU im. V.G. Shukhov, 2012. No. 1. pp. 158–160.
- Kamel A.H., Shaqlaih A.S. Frictional pressure losses of fluids flowing in circular conduits: A review. SPE Drilling and Completion. 2015. Vol. 30. No. 2.Pp. 129–140.
- Gabrielaitiene I. Numerical simulation of a district heating system with emphases on transient temperature behavior. Proc. of the 8th International Conference “Environmental Engineering”. Vilnius. VGTU Publishers. 2011 Vol. 2.Pp. 747–754.
- Horikiri K., Yao Y., Yao J. Modeling conjugate flow and heat transfer in a ventilated room for indoor thermal comfort assessment. Building and Environment. 2014. No. 77.Pp. 135–147.
- Samarin O.D. Calculation of local resistances in ventilation systems of buildings // Journal of S.O.K., 2012. No. 2. pp. 68–70.
