2.3. Hydraulic calculation of the heating system

The calculation consists in selecting the diameters of the pipelines of the heating system so that, with the calculated coolant flow rates, the pressure loss in all circulation rings is no more than the calculated circulation pressure DPp . As the design scheme of the system, an axonometric scheme of pipelines is used.

The calculation is recommended to perform in the following order.

1. Select the calculated circulation rings, the main of which is the ring having the greatest length. In real projects, the calculation of all rings is carried out; in an educational project, it is sufficient to perform the calculation of two rings — the longest and shortest lengths. In the design scheme all parts of the calculated rings of the system are numbered. The boundaries of the plots are the points of confluence or separation of flows and the point of the expected change in diameters. In monotube heating systems, the riser with all appliances is considered as one site. It should be borne in mind that in a single-pipe heating system, the total number of rings is equal to the number of risers, in a two-pipe system - the number of heating devices. In a two-pipe system, several circulating rings pass through the outermost riser (according to the number of heating devices). The calculation is performed for the most unfavorable ring passing through the heater of the lower floor.

The diagram gives thermal loads of heating devices. In the course project, you can ignore the heat loss in pipelines passing through unheated rooms (attics, basements, etc.), since they are significantly reduced due to the mandatory thermal insulation of pipes. Also, the heat fluxes entering the heated premises from the pipes located in them (risers, liners) are not taken into account. Heat loads of heating devices are assumed to be equal to the heat losses of the rooms in which they are located.

For all the calculated sections of the circulation rings, their thermal loads lead — the sum of the thermal loads of the heating devices to which the coolant is supplied to or from which Q1, W is given,    and lengths l , m. The calculation is conveniently carried out in the form of a table (see examples 2 and 3).

2. The calculated heat fluxes for the system sections are determined by the formula

QLitch = ΣQ1 β1 β2 + Q2 + Q3 , (2.1)

where ΣQ1 is the sum of the thermal loads of the heating devices to which the coolant is supplied to or from which this heat transfer is carried out; Q2 and Q3 are the losses of heat from the cooling of water in the highways and the flow of heat into the room from the pipes located in them; β1 and β2 are the coefficients of the instrument operation conditions (adj. 6).

As mentioned above, in this project it is possible to accept Q2 = 0 and Q3 = 0 , formula (2.1) then takes the form

Qout = ΣQ1 β1 β2. (2.2)

3. The calculated circulation pressure for each calculated ring DPP , Pa is determined .

In systems with natural circulation

; (2.3)

ΔRe = ΔRe, pr + ΔRe, tr, (2.4)

where Dе - natural circulation pressure in the ring; DРе, pr is the pressure resulting from the cooling of water in the devices; DRe. mp - the same due to the cooling of water in the pipes, DPe. tr is taken into account only for systems with upper wiring and is determined from reference data [4, adj. four]. In the course project
DRe. tr is taken 150 Pa.

The pressure arising from the cooling of water in the devices is determined for systems with natural and pump circulation using the same formulas. An example of design schemes for its determination in various systems is given in Fig. 2.7, 2.8.

For two-pipe water heating systems (Fig. 2.7)

ΔRe, pr = g h (ρ0 - ρg) , (2.5)

where h is the distance from the center of the boiler or water heater to the center of the heating device in the calculation ring, m (the distance h to the center of the device on the first floor is shown, through which the most unfavorable circulating ring passes); ρ0 and ρg are the densities of hot and chilled water in the heating system, kg / m3.

For one-pipe water heating systems at the upper wiring (Fig. 2.8)

ΔRe, pr = g hpr (ρ0 - ρg) + g h1 (ρ1 - ρg) +

+ g h2 (ρ2 - ρg) + ..., (2.6)

where hpr - vertical distance from the center of the heat generator to the center of the heating device of the first floor, m; h1 , h2, etc., is the vertical distance from the center of heating devices of one floor to the center of devices of the next floor, m; rg , r1 , r2 , .... ro is the density of water entering the system, the mixture of water in the corresponding section and cooled water, kg / m3.

For one-pipe water heating systems with lower wiring (Fig. 2.9) and placement of heating devices on the descending and ascending parts of the riser in the formula (2.6) for the sections corresponding to h1 , h2, etc., instead of rg substitute the density of water in the corresponding sections of the ascending riser

ΔRe, pr = g hpr (ρ0 - ρg) + g h1 (ρ4 - ρ1) + g h2 (ρ3 –ρ2) +…. (2.7)

The density of water is determined depending on its temperature according to reference data [4, adj. 3] or adj. 5. The water temperature in the sections of the riser of a single pipe water heating system is determined by the formula

ti = tg - , (2.8)

where tg is the temperature of hot water supplied to the heating system, ° С; S Qi is the total thermal load of the instruments on the riser located above (earlier) the considered section along the flow of water, W; DTt - differential temperature of the coolant on the riser, equal to the difference (tg - tо), ° С;
Qst - thermal load of the riser, watts.

Fig. 2.9. The design scheme of a single-pipe water heating system with bottom distribution and pump circulation. Designations see in fig. 2.7

In systems with pump circulation, the calculated circulation pressure for each calculated ring DPP, Pa is determined by the formula

ΔPp = ΔPnas + E ΔPe, (2.9)

where Dpnas - circulation pressure created by the pump or hydraulic elevator, Pa; E - the proportion of natural pressure, which is advisable to take into account in the calculations; Dе is the natural pressure caused by cooling of water in the system and determined by the formula (2.4).

Usually take Dpnas = 10¸12 kPa, E = 0.4¸0.5 for two-pipe or E = 1 for one-pipe heating systems.

In case of heat supply from the CHP or CHP and the use of a hydraulic elevator (see Fig. 2.2), the circulation pressure is also determined by the formula (2.9), but Dpnas is calculated as

ΔPnas = , (2.10)

where Dpc is the differential pressure in the flow and return lines of the heat and power plant, Pa, (on assignment); U is the mixing ratio, which is the ratio of the mass of the mixed chilled water Gp to the mass of water supplied from the heat network to the Gc system, and is determined by the formula

, (2.11)

where T is the temperature of superheated water in the supply line of the CHP, ° C (on assignment); tg is the temperature of water entering the heating system, ° С (usually 95 ° С is assumed, in one-pipe systems it is allowed up to
105 ° C, in closed systems, taken on assignment); t0 is the water temperature at the outlet of the heating system, ° С, usually assumed to be 70 ° С (60–65 ° С is recommended when connected to the heating network through a water heater).

4. Determine the water flow in the areas of calculated circulation rings Guc , kg / h

, (2.12)

where Quch is the calculated heat fluxes in the areas defined by the formula (2.2), W; c is the heat capacity of water, equal to 4.2 kJ / (kg × ° С).

5. Assign preliminary diameters of pipelines of sections of a large circulation ring. It is recommended to take such diameters for which, at the estimated costs Guch, the specific pressure loss for friction R approximately corresponds to the average value of the specific pressure loss in the calculated circulation ring Rav

Rav = 0.65 , (2.13)

where 0.65 - the approximate share of pressure loss along the length of the total losses; DPr - the calculated circulation pressure for the ring to be calculated according to claim 3, Pa; S l - total length of sections of the ring, m.

The calculation is carried out using tables or nomograms for the hydraulic calculation of piping systems of water heating systems (Appendix 10).
From this, the diameters of the sections, the velocities and the calculated specific pressure losses R are determined from the previously determined values ​​of G and Rcr.

For example, the estimated flow rate Guch = 1000 kg / h, Rsr = 1.9 Pa / m, according to the nomogram, the diameter of the section d = 70 mm is chosen, for which for a given calculated flow rate the specific pressure loss in the section R = 2.1 Pa / m close to the value of Rav , the speed of water movement while
V = 0.091 m / s.

Similarly, determine the parameters for all sections of the ring. The calculation task is to select pipe diameters such that the total pressure loss of all sections in the S-ring (Rl + Z) will be less than the calculated circulation pressure DPp with a margin of up to 10–15%, i.e. the condition

Σ (Rl + Z) <ΔPp, (2.14)

where l is the length of sections, m; Rl is the pressure loss along the length of the sections; Z - pressure loss in local resistances in areas, Pa; Rl + Z - total pressure loss in areas;

Z = , (2.15)

where Sx is the sum of coefficients of local resistances at the site, taken by adj. 7, 8; r is the density of water taken in this calculation for all areas equal to 980 kg / m3; V - water velocity at the site, m / s.

The complex rV2 / 2 = Pv is called dynamic pressure, it is determined by adj. 10. Formula (2.15) is reduced to the form

Z = Σξ Pv. (2.16)

If, on the first attempt, it is not possible to fulfill the requirements of inequality (2.14), one should change the diameters of the pipelines in one or several sections, which will lead to an increase or decrease in S (Rl + Z) and make it possible to achieve this condition.

6. In order for the total coolant flow rate to be distributed to all risers in accordance with their design load, it is necessary to ensure equality of pressure losses when skipping the estimated coolant flow rates in all rings. In the course project such a calculation is performed for two rings - the largest and the smallest.

When comparing pressure losses, common areas are excluded from the summation and the condition is

Σ (Rl + Z) of the non-common parts of a large ring Σ (Rl + Z) of the non-common parts of a small ring , (2.17)

The discrepancy can be up to 15%. The pressure loss in the non-common areas of the small ring is determined in the same way as for the sections of the large ring.

A small ring usually has only one section, a non-large ring, a riser. By selecting the diameter of this riser or changing the diameters of the non-common sections of the large ring, condition (2.17) should be satisfied. This linking process is facilitated if, initially, in the hydraulic calculation of a large ring, such diameters of sections are assigned for which the pressure loss in the riser was at least 70% of the total pressure loss in the ring.

If it is impossible to achieve the condition (2.17) by changing the diameters, it is allowed to equalize the pressure losses in the circulation rings by installing an additional hydraulic resistance on the small ring - a diaphragm whose diameter, mm, is determined by the formula

d = 11.3 , (2.18)

where g is the flow rate of the coolant passing through the diaphragm, kg / h; DP is the pressure loss, Pa, which should be created by the diaphragm — the unresolved difference in pressure loss in the large and small rings from formula (2.17).

Example 2. Designing and calculating a water-heating system with lower wiring and forced circulation due to pressure drop in the CHP network.

Initial data: a residential building with heat losses as in Example 1. The CHP plant is set as a heat source, heat carrier is water with temperatures of 130–70 ° С, supply pressure is 0.6 MPa, in the return flow 0.5 MPa, i.e. .Dpc = 0.10 MPa.

Decision. The building has a single pipe water heating system with lower wiring with heat carrier parameters tg = 105 ° С, tо = 70 ° С. A thermal unit with a hydraulic elevator is located in the basement of the building, the supply and circulation lines are laid in the basement along the longitudinal external walls with a slope of 0.003 in the direction of entry.

The risers are laid openly, including in the corners of the building. Heating devices are attached to the ascending and descending branches of the risers. In the nodes connecting the heaters to the risers are provided offset shifting sections and taps of double adjustment of the type КРДШ.

Cast iron sectional radiators MS-140-108 were used as heating devices. On branching pipelines cork valves are provided as stop valves. For emptying the risers, tees with plugs are provided in their lower part; Mayevsky's taps are installed on the upper floor to remove air from the system.

The staircase is equipped with an independent riser with one heating device attached according to the flow-through scheme. In accordance with the specified heat source to reduce the temperature of the coolant provides for the installation of hydraulic elevator. The tracing of pipelines in the basement and their axonometric diagram are shown in fig. 2.10 and 2.11. To determine the circulation pressure, the mixing ratio U in the elevator is determined by the formula (2.11):

.

By the formula (2.10) is determined for all rings of the calculated system

MPa Pa.

The calculation is performed for the ring passing through the riser 1, as this is the largest ring. Since the riser heats the corner rooms, the heat losses of these rooms are distributed between the two radiators, and most of the heat load is assigned to the radiators attached to the ascending part of the riser with a higher temperature. To determine the natural circulation pressure in this ring, the pipeline temperatures at characteristic intermediate sections are calculated using formula (2.8). It is assumed that the cooling of water occurs only in heating devices, and the temperature drop in the riser is 35 ° C (Fig. 2.11).

Fig. 2.10. Basement plan (for example 2)

Water temperatures are determined at successive sections of the riser st. 1 (fig. 2.11)

t1 = 105 - 1500 × 35/7300 = 97.8 ° C.

t2 = 105 - 2650 × 35/7300 = 92.3 ° C.

t3 = 105 - 5250 × 35/7300 = 79.8 ° С.

t4 = 105 - 6100 × 35/7300 = 75.7 ° C.

Fig. 2.11. Calculated axonometric scheme (for example 2)

By appl. 5 the corresponding density of water is determined: rg = 954.68 kg / m3; ro = 977.81 kg / m3; r1 = 960.0 kg / m3; r2 = 963.8 kg / m3; r3 = 972.0 kg / m3; r4 = 974.5 kg / m3.

The position of the center of the heat node is assigned 0.5 m above the basement floor, i.e. the distance from the center of the heat node to the center of the 1st floor device is 2.5 m. The pressure from the water cooling in the devices is determined by the formula (2.7)

DRe. pr = 9.81 ∙ 2.5 (977.8 - 954.68) + 9.81 · 2.8 (974.5 - 960.0) +

+ 9.81 ∙ 2.8 (972.0 - 963.8) = 1190.5 Pa.

Due to the fact that the heating scheme with the lower wiring is calculated, the pressure from the cooling of water in the pipes is not taken into account.

By the formula (2.9) is determined by the circulating pressure in the calculated ring

Dрр = 13700 + 1 ∙ 1190 = 14890 Pa.

The calculated axonometric scheme of the large circulation ring was made, the calculated sections were established (Fig. 2.11). The calculated riser (ascending and descending branches) is considered as one section. Further calculations are performed in tabular form (Table 2.1).

For illustration, the sequence of calculations for section 1–2 is given:

By appl. 6 assigned the coefficients of the operating conditions of the devices b1 = 1.04, b2 = 1.02.

Is determined Quch by the formula (2.1)

Quc = 53800 ∙ 1.02 ∙ 1.04 = 57071 W.

G is determined by the formula (2.12)

Guch = 3,6 = 1405.7 kg / h.

For the appointment of diameters, the average value of specific pressure loss is determined by the formula (2.13)

Pa / m

According to certain values ​​of Rav and G, according to the nomogram (approx. 10), the diameter of the section d = 25 mm is selected, the parameters are determined: R = 285 Pa / m;
V = 0.7 m / s and Pv = 240 Pa.

Determined by the pressure loss along the length of this section

R L = 285 ∙ 5.0 = 1425 Pa.

The sum of the local resistance coefficients is determined according to the table. 2.2, å x = 3,5.

The pressure losses in local resistances at the site are determined by the formula (2.16)

Pa.

The total pressure loss at the site is determined.

R ∙ L + Z = 1425 + 840 = 2265 Pa.

All data are summarized in table. 2.1.

Table 2.1

Hydraulic calculation of the heating system

Table 2.2

Описание местных сопротивлений в системе отопления

Расчет системы в данном примере проводится для двух циркуляционных колец. Большое кольцо проходит через стояк 1 (участки 1 – 2 – 3 – 4 – 5 – 6 – 7 – 8 – 9 – 10 –11– 12), малое – через стояк 2 (участки 1 – 2 – 3 –
4 – 9 – 10 –11– 12).

As a result, the pressure loss in the large ring is 14544.5 Pa, which does not exceed the calculated circulation pressure Dрр = 14890 Pa, the pressure margin is . Thus, the efficiency of the design ring of the heating system with the assigned diameters under the specified conditions is ensured.

Check the condition of equation (2.17):

S (Rl + Z) of the non-common sections of a large ring = 6183 Pa;

S (Rl + Z) of the non-common sites of the small ring = 720 Pa.

The discrepancy is