Dimensioning of the mixing groups

Dimensioning of the mixing groups is demonstrated with an example. The technique adopted is also valid for high temperature distribution groups where the total flows that transit inside the groups must be employed due to the fact that with these distribution groups there is no mixing process.

3.7.5.1 Example

The task is to dimension mixing modules for supplying three low temperature zones for which we know the following characteristics.

Boiler

- Supply temperature T_Mc = 70°C Zone 1

- Flow mu,1 = 1854 kg/h (utility side) - Heat output Q₁ = 15.3 kW

- Supply temperature T_Mu,1 = 40.6°C - Return temperature T_Ru,1 = 33.5°C - Pressure loss ∆P_u,1 = 32 kPa Zona 2

- Flow mu,2 = 1511 kg/h (utility side) - Heat output Q₂ = 12.3 kW - Supply temperature T_Mu,1 = 40.6°C - Return temperature T_Ru,2 = 33.6°C - Pressure loss ∆P_u,2 = 29 kPa Zone 3

- Flow mu,3 = 1104 kg/h (utility side) - Heat output Q₃ = 12.2 kW - Supply temperature T_Mu,3 = 40.6°C - Return temperature T_Ru,3 = 31.1°C - Pressure loss ∆P_u,3 = 39 kPa Figure 3.7.45 System layout.

Zone 2

Zone 1 Zone 3

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Calculation of the diversion flows

The diversion flows are on the boiler side; the mixers divert part of the flow coming form the boiler to mix it with the return water from the heating circuits. In order to dimensions the heating plants we need to know the flows on the boiler side that can be calculated by using the formulas indicated in paragraph 3.7.1.2, from which we obtain:

m_c = m_u · (T_Mu - T_Ru) (TMc - TRu)

And therefore, for the three mixers, the flows on the boiler side (diversion flows) are:

(40.6 - 33.5) (70 - 33.5) mc,1 = mu,1 · (T_Mu,1 - TRu,1) = 1854 ·

(TMc - T^Ru,1) = 360 kg/h

(40.6 - 33.6) (70 - 33.6) mc,2 = mu,2 · (T_Mu,2 - TRu,2) = 1511 ·

(TMc - T^Ru,2) = 290 kg/h

(40.6 - 31.1) (70 - 31.1) mc,3 = mu,3 · (T_Mu,3 - TRu,3) = 1104 ·

(TMc - T^Ru,3) = 269 kg/h

Total flow on boiler side

The total flow on the boiler side is given by the sum of the diverted flows from each mixer:

mc = mc,1 + mc,2 + mc,3 = 360 + 290 + 269 = 919 kg/h

Return temperature to the boiler

This is given by the energy balance on the distribution manifold (return side) between the inlet and the outlet:

m_c · T_Rc = m_c,1 · T_Ru,1 - m_c,2 · T_Ru,2 + m_c,3 · T_Ru,3 from which we obtain:

T_Rc =

m_c

mc,1 · TRu,1 - mc,2 · TRu,2 - mc,3 · TRu,3 =32.8°C

Choice of the size of the mixing module 1

In order to choose the correct size we must compare the total pressure loss generated by the entire system separator+manifold+mixer+user with the head supplied by the pump in relation to the required flow. The pressure losses in the separator could be overlooked in that they are compensated for by the boiler pump, but to have a greater safety margin we prefer to take them into consideration. It is necessary to determine the pressure losses generated by each single element that makes up the system and we start by considering the mixer with the smallest size: DN 25.

Hydraulic separator. The pressure loss is evaluated when the total flow is flowing through the separator m_c . From the diagrams in paragraph 3.7.4, in correspondence with the flow rate of 919 kg/h, the pressure loss is identified ∆p_separator = 0.3 kPa.

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Figure 3.7.46 Identification of the pressure loss in the separator.

Pressure loss ∆P [kPa]

0 © 2008 Valsir S.p.A.

Manifold. We proceed in the same way, using the diagrams in paragraph 3.7.3. In correspondence with flow m_c = 919 kg/h the pressure loss is identified ∆p_manifold = 0.6 kPa considering the curve of the 3-way manifold.

Figure 3.7.47 Identification of the pressure loss in the manifold.

Pressure loss ∆P [kPa]

Flow Q [l/h]

© 2008 Valsir S.p.A.

Mixer. From the diagrams of paragraph 3.7.1 the pressure loss in the mixer is identified and the head given by the pump at maximum speed.

In this case, the flow to be considered is the flow on the utility side in that the curves are based on the flow of water of the heating circuit.

In correspondence with the flow m_u,1 = 1854 kg/h, the pressure loss is identified ∆p_mixer = 12 kPa and a pump head of H = 38 kPa.

Figure 3.7.48 Identification of the pressure loss and the pump head of the mixer.

0 10 20 30 40

0 400 800 1200 1600 1854 2000

12 38

Pressure loss ∆P [kPa]

Flow Q [l/h]

∆P P2 P1

Residual head of module Pressure loss of module Head of pump

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The total pressure loss is equal to:

∆p_total = ∆p_separatore +∆p_collettor +∆p_mixer +∆p_utility= 0.3 + 0.6 + 12 + 32 = 44.9 kPa

In comparing it with the pump head it can be seen that the mixer DN 25 is not enough to guarantee the required flow:

(H = 38 kPa) < (∆p_total= 44.9 kPa)

We therefore consider a larger mixer of DN 32 and we proceed in the same way.

Hydraulic separator. ∆p_separator = 0.1 kPa.

Manifold. ∆p_manifold = 0.3 kPa.

Mixer. ∆p_mixer = 3.3 kPa e H = 22 kPa.

The total pressure loss is equal to:

∆p_total = ∆p_separator +∆p_manifold +∆p_mixer +∆p_utility= 0.1 + 0.3 + 3.3 + 32 = 35.7 kPa

and when we compare it to the pump head we can verify that the mixer size DN 32 is sufficient for feeding the first part of the system:

(H = 38 kPa) > (∆p_total= 35.7 kPa).

Choice of the size of the mixing module 2

We use the same procedure to analyse the size DN 25 considering the pressure losses of the manifodl and the separator pertinent to DN 32. In fact the size of the manifold and the separator must correspond to the biggest mixer. By carrying out the same procedure for the second mixer we obtain a DN 25.

Hydraulic separator. ∆p_separator = 0.1 kPa.

Manifold. ∆p_manifold = 0.3 kPa.

Mixer. ∆p_mixer = 8.7 kPa e H = 42 kPa.

∆p_total = ∆p_separator + ∆p_manifold + ∆p_mixer + ∆p_utility = 0.1 + 0.3 + 8.7 + 29 = 38.1 kPa

(H = 42 kPa) > (∆p_total= 38.1 kPa).

Selection of the size of the mixing module 3

For the third mixer we obtain the size DN 25. The pressure losses in the separator and in the manifold must correspond to those of size DN 32 in that these components must be of the biggest size amongst the mixing modules.

Hydraulic separator. ∆p = 0.1 kPa.

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Manifold and hydraulic separator

The size of the manifold and the hydraulic separator, as mentioned previously, must correspond to the biggest size among all of the mixing modules. Therefore, we must use a DN 32 both for the manifold and for the hydraulic separator.

Figure 3.7.49 System layout.

Zone 1 DN 32

Zone 2 DN 25

Zone 3 DN 25

DN 32 DN 32

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