2. Dimensioning criteria for the channel network

The network of channels has a tree structure with the root representing the AHU and the leaves the terminal units of each zone.

The different supply air conditions determine the different thermal zones. The calculation proceeds by considering the sensible thermal load Φið Þτ (of the ith environment), variable over time, and evaluating the constant flow rate Gi able to compensate these loads in each room. The calculation is also based on the usual constraint related to the temperature difference between air supply and room and takes into account the flow rate required for ventilation. The mixing box serving the zone, where the ith room is included, will supply the computed airflow rate required by the zone; into the mixing box will enter hot and cold airflow rates coming from the terminal trunks of the dual duct system.

For the first trunk departing from AHU, one can write the conservation of mass and energy as

$$\mathbf{G} = \sum\_{i} \mathbf{G}\_{i} = \mathbf{G}\_{\mathbf{f}}(\boldsymbol{\tau}) + \mathbf{G}\_{\boldsymbol{h}}(\boldsymbol{\tau}) \tag{1}$$

$$\sum\_{i} \Phi\_{i}(\tau) + c\_{p} G\_{h}(\tau) [t\_{h}(\tau) - t\_{r}(\tau)] + c\_{p} G\_{c}(\tau) [t\_{c}(\tau) - t\_{r}(\tau)] = 0 \tag{2}$$

where G is the total mass flow rate carried by the trunk; Gcð Þτ and Ghð Þτ are the flow rates carried by the cold and hot trunks at the temperatures tcð Þτ and thð Þτ , respectively; trð Þτ is the room temperature; cp is the specific heat at constant pressure of moist air; and Φið Þτ is the thermal load, varying over time, in each environment. The subscripts "c" and "h" refer to the cold and hot channels, respectively. These relationships, in conditions of maximum sensible load in summer Φs,sum and in winter Φs,win (subscripts "sum" and "win" refer to these conditions, respectively) become

$$\mathbf{G} = \mathbf{G}\_{\mathbf{c},sum} + \mathbf{G}\_{\mathbf{h},sum} \tag{3}$$

$$\Phi\_{\rm s,sum} + c\_p G\_{\rm h,sum} (t\_{\rm h,sum} - t\_{\rm r,sum}) = c\_p G\_{\rm c,sum} (t\_{\rm r,sum} - t\_{\rm c,sum}) \tag{4}$$

$$\mathbf{G} = \mathbf{G}\_{\mathbf{c}, w \dot{m}} + \mathbf{G}\_{\mathbf{h}, w \dot{m}} \tag{5}$$

rates required by individual environments and served by the trunk, as it has been previ-

vmax, m=s

35

http://dx.doi.org/10.5772/intechopen.80093

b. Similarly, the airflow rates of hot and cold channels in the first trunk departing from the AHU are evaluated, once that the temperatures tc,sum, tc,win, th,sum, and th,win have been set.

<sup>7</sup> <sup>10</sup><sup>4</sup> <sup>30</sup>

<sup>5</sup> <sup>10</sup><sup>3</sup> <sup>15</sup>

4.5 <sup>10</sup><sup>4</sup> <sup>25</sup>

2.5 <sup>10</sup><sup>4</sup> 22.5

Air Conditioning Systems with Dual Ducts: Innovative Approaches for the Design of the Transport Network…

1.7 <sup>10</sup><sup>4</sup> <sup>20</sup>

<sup>10</sup><sup>4</sup> 17.5

<sup>2</sup> <sup>10</sup><sup>3</sup> 12.5

c. By considering the summer case, the ratio is calculated between the total flow rate in the

d. Once this ratio, representing the request of cold, is known, the corresponding values for the kth trunk of the same ratio Gc, <sup>k</sup>=Gk are chosen, for example, according to the values of column B of Table 2 [21]. In Table 2, one can set the range of values in column A, related to the first trunk departing from the AHU, and then obtain, from column B and C, the values of the ratio to assign to the trunks, for cold and hot duct, respectively, at each level of the network. This procedure avoids to solve the equations for each trunk, which require the

e. From the total flow rate Gk of the trunk, one can obtain the airflow rate of the cold channel

f. For each trunk, one can calculate the airflow of the hot duct Gh, <sup>k</sup> as a percentage of the

flow rate of the relative cold duct, with reference to the column C of Table 2.

cold channel, Gc,sum, and the total airflow rate of the plant G.

A BC

Gc,sum=G Gc,k=Gk Gh,k=Gc,<sup>k</sup> 1.00.90 1 0.7 0.890.85 0.95 0.7 0.840.80 0.9 0.75 0.790.75 0.85 0.75 ≤0.74 0.8 0.8

Table 2. Conventional ratios for the sizing of hot and cold ducts, in the absence of perimeter heating.

thermal loads be known for each level of the network.

Gc, <sup>k</sup> of the trunk from the ratio of column B.

ously described.

Airflow rate through the trunks

Table 1. Maximum air speed in the ducts.

Qhk, Qck, m<sup>3</sup>=h

105

<sup>7</sup> <sup>10</sup><sup>4</sup>

4.5 <sup>10</sup><sup>4</sup>

2.5 <sup>10</sup><sup>4</sup>

1.7 <sup>10</sup><sup>4</sup>

<sup>5</sup> <sup>10</sup><sup>3</sup>

10<sup>4</sup>

$$\Phi\_{\rm s,win} + c\_p G\_{\rm c,win}(t\_{\rm r,win} - t\_{\rm c,win}) = c\_p G\_{\rm h,win}(t\_{\rm h,win} - t\_{\rm r,win}) \tag{6}$$

We can write similar equations for any trunk.

For the channels of the first trunk, departing from AHU, the airflow rates Gc,sum, Gc,win, Gh,sum, and Gh,win can be calculated from the equations above, once the temperature values tc,sum, tc,win, th,sum, and th,win are properly set; similar equations allow one to calculate the airflow rates for the other trunks, for cold and hot air, and winter and summer conditions, at all levels of the network.

With regard to the control of the relative humidity in the environment, it should be recalled that by normal practice, it is performed centrally, while the temperature control is assigned to the mixing boxes. Usually the air treated by the AHU exits with a moisture content corresponding to the thermodynamic state characterized by the temperature of the environment (tr,sum or tr,win) and 45% of relative humidity.

Once the layout of the network is given, the sizing of the channels can be derived if the air speeds in the various trunks k are properly set; a usual criterion to choose the air speeds, starting from the range of values of the airflow rates Qhk, Qck carried by the trunks, is reported as example in Table 1 [20, 21].

In practical cases, as it is well known, a conventional sizing criterion is used. The criterion is based on the assumption that for each trunk, and therefore for each level of the network, it is possible to establish a priori the distribution between heat demand and cold demand, satisfied by hot duct and cold duct, respectively, once this distribution is known for the main trunk departing from the AHU (and therefore for the system as a whole). The method proceeds as follows:

a. The total airflow rates at each level of the network, that related to system (departing from the AHU) and those related to the various trunks, are determined from the supply airflow Air Conditioning Systems with Dual Ducts: Innovative Approaches for the Design of the Transport Network… http://dx.doi.org/10.5772/intechopen.80093 35


Table 1. Maximum air speed in the ducts.

For the first trunk departing from AHU, one can write the conservation of mass and energy as

where G is the total mass flow rate carried by the trunk; Gcð Þτ and Ghð Þτ are the flow rates carried by the cold and hot trunks at the temperatures tcð Þτ and thð Þτ , respectively; trð Þτ is the room temperature; cp is the specific heat at constant pressure of moist air; and Φið Þτ is the thermal load, varying over time, in each environment. The subscripts "c" and "h" refer to the cold and hot channels, respectively. These relationships, in conditions of maximum sensible load in summer Φs,sum and in winter Φs,win (subscripts "sum" and "win" refer to these

For the channels of the first trunk, departing from AHU, the airflow rates Gc,sum, Gc,win, Gh,sum, and Gh,win can be calculated from the equations above, once the temperature values tc,sum, tc,win, th,sum, and th,win are properly set; similar equations allow one to calculate the airflow rates for the other trunks, for cold and hot air, and winter and summer conditions, at all levels of the network. With regard to the control of the relative humidity in the environment, it should be recalled that by normal practice, it is performed centrally, while the temperature control is assigned to the mixing boxes. Usually the air treated by the AHU exits with a moisture content corresponding to the thermodynamic state characterized by the temperature of the environ-

Once the layout of the network is given, the sizing of the channels can be derived if the air speeds in the various trunks k are properly set; a usual criterion to choose the air speeds, starting from the range of values of the airflow rates Qhk, Qck carried by the trunks, is reported

In practical cases, as it is well known, a conventional sizing criterion is used. The criterion is based on the assumption that for each trunk, and therefore for each level of the network, it is possible to establish a priori the distribution between heat demand and cold demand, satisfied by hot duct and cold duct, respectively, once this distribution is known for the main trunk departing from the

a. The total airflow rates at each level of the network, that related to system (departing from the AHU) and those related to the various trunks, are determined from the supply airflow

AHU (and therefore for the system as a whole). The method proceeds as follows:

Gi ¼ Gcð Þþ τ Ghð Þτ (1)

G ¼ Gc,sum þ Gh,sum (3)

G ¼ Gc,win þ Gh,win (5)

Φið Þþ τ cpGhð Þτ ½ �þ thð Þ� τ trð Þτ cpGcð Þτ ½ �¼ tcð Þ� τ trð Þτ 0 (2)

Φs,sum þ cpGh,sumðth,sum � tr,sumÞ ¼ cpGc,sumð Þ tr,sum � tc,sum (4)

Φs,win þ cpGc,winðtr, win � tc,winÞ ¼ cpGh,winð Þ th,win � tr,win (6)

<sup>G</sup> <sup>¼</sup> <sup>X</sup> i

X i

34 HVAC System

conditions, respectively) become

We can write similar equations for any trunk.

ment (tr,sum or tr,win) and 45% of relative humidity.

as example in Table 1 [20, 21].


Table 2. Conventional ratios for the sizing of hot and cold ducts, in the absence of perimeter heating.

rates required by individual environments and served by the trunk, as it has been previously described.


In order to evaluate the order of magnitude of the airflow rate, let us consider the mass balance:

$$\mathcal{G}\_{\mathfrak{n}} = \left[ \sum \mathcal{G}\_{\mathfrak{i}} \right]\_{\mathfrak{n}} = \mathcal{G}\_{\mathfrak{c},\mathfrak{n}}(\mathfrak{r}) + \mathcal{G}\_{\mathfrak{h},\mathfrak{n}}(\mathfrak{r}) \tag{7}$$

either one of the hot and cold networks always carries the most part of the flow rate of the

Air Conditioning Systems with Dual Ducts: Innovative Approaches for the Design of the Transport Network…

In the first case (method 1), the cold channel carries air at a temperature equal to or slightly lower (1 or 2�C) than the minimum supply air temperature, among those required by the different zones (which varies in time). The hot duct delivers air at a constant temperature th, higher than the absolute maximum value of the zone supply temperature [19]. The value of the minimum supply air temperature tin,min<sup>j</sup> can be over time either lower or higher than the room temperature tr (this occurs generally in summer time and in winter time, respectively); as a consequence, the value tc of the cold network temperature can be either lower or higher than tr. As alternative (method 2), the hot channel transports air at a temperature value slightly higher (1 ÷ 2�C) than the maximum inlet temperature (variable with time) required by the zones, while the cold duct delivers air at a constant temperature, lower than the absolute minimum

The new approach implies reduced overall dimensions (reduced space requirements) and lower installation costs of the networks and therefore represents an improvement with regard

tcð Þ¼ τ tin,minð Þ� τ δ, δ ¼ 1 � 2

Φs,sum þ cpGh,sumðth,sum � tr,sumÞ ¼ cpGc,sum tr,sum � t

∗

∗

<sup>¼</sup> ½ � thð Þ� <sup>τ</sup> tinð Þ<sup>τ</sup> tinð Þ� τ t

∗

�

<sup>n</sup> <sup>¼</sup> Gc,nð Þþ <sup>τ</sup> Gh,nð Þ<sup>τ</sup> (15)

∗

Φs,sum ¼ cpGn,sum½ � tr,sum � tinð Þτ (17)

c,win � � <sup>¼</sup> cpGh,winð Þ th,win � tr,win (18)

Φs,win ¼ cpGn,win½ � tinð Þ� τ tr,win (19)

<sup>c</sup> ð Þ<sup>τ</sup> � � <sup>¼</sup> Gh,nð Þ<sup>τ</sup> ½ � th � tinð Þ<sup>τ</sup> (20)

<sup>c</sup> ð Þ<sup>τ</sup> � � (21)

c,sum � � (16)

C (14)

http://dx.doi.org/10.5772/intechopen.80093

37

to the two critical aspects of the dual duct systems currently designed.

Gn <sup>¼</sup> <sup>X</sup>Gi h i

Φs,win þ cpGc,win tr,win � t

Gc,nð Þτ tinð Þ� τ t

Gc,n Gh,n

By substitution we obtain for both summer and winter:

trunks k.

value of the zone supply temperature.

For the generic zone n, once that the values of

are fixed and the mass balance is written as

the energy balance becomes

for summer conditions and

for the winter ones.

with reference to the generic zone n of the plant, and the energy balance

$$\left[\sum\_{i} \Phi\_{i}(\tau)\right]\_{n,\text{sum}} + c\_{p} \mathbf{G}\_{\text{l,sum},n}(\tau)[t\_{\text{l,sum}}(\tau) - t\_{r,\text{sum}}] = c\_{p} \mathbf{G}\_{\text{c,sum},n}(\tau)[t\_{r,\text{sum}} - t\_{\text{c,sum}}(\tau)] \tag{8}$$

in summer and

$$\left[\sum\_{i} \Phi\_{i}(\tau)\right]\_{n,\text{win}} + c\_{p} \mathbf{G}\_{c,\text{win},n}(\tau)[t\_{\tau,\text{win}} - t\_{c,\text{win}}(\tau)] = c\_{p} \mathbf{G}\_{\text{h},\text{win},n}(\tau)[t\_{\text{h},\text{win}}(\tau) - t\_{\tau,\text{win}}] \tag{9}$$

in winter. On the other hand, we also have in summer:

$$\left[\sum\_{i} \Phi\_{i}(\mathsf{r})\right]\_{n,\text{sum}} = c\_{p}\mathsf{G}\_{n}[t\_{r,\text{sum}} - t\_{in,\text{sum}}(\mathsf{r})] = [\mathsf{G}\_{c,n}(\mathsf{r}) + \mathsf{G}\_{h,n}(\mathsf{r})][t\_{r,\text{sum}} - t\_{in,\text{sum}}(\mathsf{r})] \tag{10}$$

and in winter:

$$\left[\sum\_{i} \Phi\_{i}(\tau)\right]\_{n,\text{win}} = c\_{p} G\_{\text{n}}[t\_{\text{in},\text{win}}(\tau) - t\_{\text{r},\text{win}}] = [G\_{\text{c},\text{n}}(\tau) + G\_{\text{h},\text{n}}(\tau)][t\_{\text{in},\text{win}}(\tau) - t\_{\text{r},\text{win}}] \tag{11}$$

where the subscript "in" refers to the variable for inlet conditions (supply air conditions). By substitution, one obtains for both summer and winter:

$$G\_{h,n}(\tau)[t\_h(\tau) - t\_{\dot{m}}(\tau)] = G\_{c,n}(\tau)[t\_{\dot{m}}(\tau) - t\_c(\tau)]\tag{12}$$

$$\frac{G\_{c,n}}{G\_{h,n}} = \frac{[t\_h(\tau) - t\_{in}(\tau)]}{[t\_{in}(\tau) - t\_c(\tau)]} = \frac{\Delta t\_{h,in}}{\Delta t\_{c,in}} \tag{13}$$

Generally, temperatures of the cold and hot channel are kept almost constant, while the zone supply temperature varies over time, tending to tc in summer and to th in winter. It implies that the computed airflow rates, for the hot and the cold duct, are significant fractions of the total airflow rate in the trunks. The air supplied to each zone, in summer, comes largely from the cold duct and in winter flows largely in the hot one. Then, both the cold and the hot ducts should each be able to carry more than 80–90% of the flow rate of the zone.

The trunk, which consists of the pair of hot and cold ducts, is coherently dimensioned to carry 1.7–1.8 times the supply airflow rate of the zone, once that one sets the values of the airspeed, and this occurs at all the levels of the network, with consequently considerable overall dimensions and high costs.

#### 3. The new method for network dimensioning

As alternative method for network dimensioning, an innovative approach is presented here, based on the choice of not constant values for the temperatures of hot and cold duct, where either one of the hot and cold networks always carries the most part of the flow rate of the trunks k.

In the first case (method 1), the cold channel carries air at a temperature equal to or slightly lower (1 or 2�C) than the minimum supply air temperature, among those required by the different zones (which varies in time). The hot duct delivers air at a constant temperature th, higher than the absolute maximum value of the zone supply temperature [19]. The value of the minimum supply air temperature tin,min<sup>j</sup> can be over time either lower or higher than the room temperature tr (this occurs generally in summer time and in winter time, respectively); as a consequence, the value tc of the cold network temperature can be either lower or higher than tr. As alternative (method 2), the hot channel transports air at a temperature value slightly higher (1 ÷ 2�C) than the maximum inlet temperature (variable with time) required by the zones, while the cold duct delivers air at a constant temperature, lower than the absolute minimum value of the zone supply temperature.

The new approach implies reduced overall dimensions (reduced space requirements) and lower installation costs of the networks and therefore represents an improvement with regard to the two critical aspects of the dual duct systems currently designed.

For the generic zone n, once that the values of

$$t\_c(\tau) = t\_{in, min}(\tau) - \delta, \qquad \qquad \delta = 1 - 2^{\stackrel{\circ}{C}} \mathbb{C} \tag{14}$$

are fixed and the mass balance is written as

$$\mathbf{G}\_{\mathfrak{n}} = \left[\sum \mathbf{G}\_{i}\right]\_{\mathfrak{n}} = \mathbf{G}\_{\mathfrak{c},\mathfrak{n}}(\mathfrak{r}) + \mathbf{G}\_{\mathfrak{h},\mathfrak{n}}(\mathfrak{r}) \tag{15}$$

the energy balance becomes

In order to evaluate the order of magnitude of the airflow rate, let us consider the mass balance:

n,sum <sup>þ</sup> cpGh,sum,nð Þ<sup>τ</sup> <sup>½</sup>th,sumð Þ� <sup>τ</sup> tr,sum� ¼ cpGc,sum,nð Þ<sup>τ</sup> ½ � tr,sum � tc,sumð Þ<sup>τ</sup> (8)

n,sum <sup>¼</sup> cpGn½tr,sum � tin,sumð Þ<sup>τ</sup> � ¼ ½ � Gc,nð Þþ <sup>τ</sup> Gh,nð Þ<sup>τ</sup> ½ � tr,sum � tin,sumð Þ<sup>τ</sup> (10)

n,win <sup>¼</sup> cpGn½tin,winð Þ� <sup>τ</sup> tr,win� ¼ ½ � Gc,nð Þþ <sup>τ</sup> Gh,nð Þ<sup>τ</sup> ½ � tin,winð Þ� <sup>τ</sup> tr,win (11)

Gh,nð Þτ ½thð Þ� τ tinð Þτ � ¼ Gc,nð Þτ ½ � tinð Þ� τ tcð Þτ (12)

Δtc,in

(13)

where the subscript "in" refers to the variable for inlet conditions (supply air conditions). By

<sup>¼</sup> ½ � thð Þ� <sup>τ</sup> tinð Þ<sup>τ</sup>

Generally, temperatures of the cold and hot channel are kept almost constant, while the zone supply temperature varies over time, tending to tc in summer and to th in winter. It implies that the computed airflow rates, for the hot and the cold duct, are significant fractions of the total airflow rate in the trunks. The air supplied to each zone, in summer, comes largely from the cold duct and in winter flows largely in the hot one. Then, both the cold and the hot ducts

The trunk, which consists of the pair of hot and cold ducts, is coherently dimensioned to carry 1.7–1.8 times the supply airflow rate of the zone, once that one sets the values of the airspeed, and this occurs at all the levels of the network, with consequently considerable overall dimen-

As alternative method for network dimensioning, an innovative approach is presented here, based on the choice of not constant values for the temperatures of hot and cold duct, where

½ � tinð Þ� <sup>τ</sup> tcð Þ<sup>τ</sup> <sup>¼</sup> <sup>Δ</sup>th,in

þ cpGc,win,nð Þτ ½tr,win � tc,winð Þτ � ¼ cpGh,win,nð Þτ ½ � th,winð Þ� τ tr,win (9)

<sup>n</sup> <sup>¼</sup> Gc,nð Þþ <sup>τ</sup> Gh,nð Þ<sup>τ</sup> (7)

Gn <sup>¼</sup> <sup>X</sup>Gi h i

with reference to the generic zone n of the plant, and the energy balance

X i Φið Þτ h i

X i Φið Þτ h i

X i Φið Þτ h i

X i Φið Þτ h i

sions and high costs.

and in winter:

n,win

in winter. On the other hand, we also have in summer:

substitution, one obtains for both summer and winter:

Gc,n Gh,n

should each be able to carry more than 80–90% of the flow rate of the zone.

3. The new method for network dimensioning

in summer and

36 HVAC System

$$\left(\Phi\_{\rm s,sum} + c\_p G\_{\rm h,sum} (t\_{\rm h,sum} - t\_{\rm r,sum}) \right) = c\_p G\_{\rm c,sum} \left(t\_{\rm r,sum} - t\_{\rm c,sum}^\*\right) \tag{16}$$

$$\Phi\_{\rm s,sum} = \mathfrak{c}\_p \mathbf{G}\_{n,sum} [t\_{r,sum} - t\_{in}(\tau)] \tag{17}$$

for summer conditions and

$$\left(\Phi\_{s,\min} + c\_p G\_{c,\min} \left(t\_{r,\min} - t\_{c,\min}^\*\right) = c\_p G\_{h,\min} (t\_{h,\min} - t\_{r,\min})\right) \tag{18}$$

$$\Phi\_{s,win} = \mathcal{c}\_p \mathcal{G}\_{n,win}[t\_{in}(\tau) - t\_{r,win}] \tag{19}$$

for the winter ones.

By substitution we obtain for both summer and winter:

$$\mathcal{G}\_{c,n}(\tau) \left[ t\_{in}(\tau) - t\_c^\*(\tau) \right] = \mathcal{G}\_{h,n}(\tau) [t\_h - t\_{in}(\tau)] \tag{20}$$

$$\frac{\mathbf{G}\_{c,n}}{\mathbf{G}\_{h,n}} = \frac{[t\_h(\tau) - t\_{in}(\tau)]}{[t\_{in}(\tau) - t\_c^\*(\tau)]} \tag{21}$$

Eq. (21) says that, both in winter and summer, the cold airflow rates Gc,n flowing through the cold trunks and supplying the mixing boxes represent higher fractions of the total flow rates of the zones if the differences, between the constant hot duct temperature and the supply temperatures, are high and if the differences between those and the minimum supply air temperature are small.

For each zone, sensible thermal loads can be calculated as a function of time, and the same can be done for the supply air temperature values in the environments of the zone:

$$t\_{in}(\tau) = t\_r - \frac{\Phi\_{s,n}(\tau)}{c\_p G\_n} \tag{22}$$

The room temperature in summer is equal to 26�C for both the buildings; the room tempera-

Air Conditioning Systems with Dual Ducts: Innovative Approaches for the Design of the Transport Network…

http://dx.doi.org/10.5772/intechopen.80093

39

For a day type for each month of the year and a daily period of 12 h (from 6:00 AM to 6:00 PM), the thermal loads of the different zones have been obtained as a function of time. Therefore, it has been possible to define the thermal zones and to evaluate the airflow rates required for each environment, to cope with the maximum sensible load in summer, the maximum sensible load in winter, and the ventilation needs. The AHU processes a total flow rate of air that obviously is the sum of the greatest of the three previous values, extended to all the zones.

In order to limit a priori the network extension, two AHUs have been used for building A, one serving 12 zones and 20 trunks as one serving 11 zones and 18 trunks. For building B, three

Data for each network, namely, the lengths, airflow rates and maximum speeds in the trunks,

k lk½ � <sup>m</sup> vmax½ � <sup>m</sup>=<sup>s</sup> Qk <sup>m</sup><sup>3</sup> ½ � <sup>=</sup><sup>h</sup> lk½ � <sup>m</sup> vmax½ � <sup>m</sup>=<sup>s</sup> Qk <sup>m</sup><sup>3</sup> ½ � <sup>=</sup><sup>h</sup> 2.00 22.50 35980.30 2.00 22.50 32022.85 3.00 15.00 7582.58 3.00 15.00 7877.03 1.00 12.50 2641.67 1.00 12.50 2708.71 2.00 12.50 1993.48 2.00 12.50 2708.71 3.00 12.50 2947.43 3.00 12.50 2459.61 7.00 22.50 28397.72 7.00 20.50 24145.83 4.50 20.00 19172.40 4.50 17.50 15317.31 1.00 15.00 8705.97 1.00 20.00 9131.37 1.00 12.50 2697.94 1.00 12.50 2247.55 3.00 12.50 2033.26 3.00 12.50 2708.71 2.00 12.50 3974.76 2.00 12.50 4175.11 4.00 15.00 10466.43 4.00 15.00 6185.94 10.00 12.50 3919.05 10.00 12.50 3203.69 1.00 15.00 28397.72 1.00 15.00 24145.83 1.00 12.50 2861.81 1.00 12.50 2950.86 3.00 12.50 3517.49 3.00 12.50 2944.17 1.00 12.50 2846.02 1.00 12.50 2933.49 2.00 15.00 10466.43 2.00 12.50 6185.94

ture in winter is equal to 22 and 20�C, respectively, for building A and building B.

AHUs have been used, each one serving 6 zones and 11 trunks.

are given in Tables 3 and 4 for building A and building B, respectively.

Network AA Network AB

19 2.00 12.50 3562.29 20 2.00 12.50 2985.09

Table 3. Data of the networks AA and AB of building A.

The minimum value of the supply air temperature tin,minð Þτ reduced by δ, hour by hour, represents the temperature of the cold channel t ∗ <sup>c</sup> ð Þτ . For each trunk k of the network, for each time interval j, one can write the energy and mass balances, in winter and in summer, as

$$\mathbf{G}\_k = \mathbf{G}\_{\mathbf{c},k\dot{\jmath}} + \mathbf{G}\_{h,k\dot{\jmath}} \tag{23}$$

$$\left[\Phi\_{s,sum,kj} + c\_p G\_{\text{h,sum,k}} \right] \left[t\_{\text{h,sum}} - t\_{r,sum} \right] = c\_p G\_{\text{c,sum,k}j} \left[t\_{\text{r,sum}} - t\_{cj}^\* \right] \tag{24}$$

$$\left[\Phi\_{s,\,\mathrm{win},k\rangle} + c\_p \mathbf{G}\_{\mathrm{c,\,win,k}}\right] \mathbf{t}\_{\mathrm{r,\,win}} - \mathbf{t}\_{\mathrm{c\,j}}^\* \left[ = c\_p \mathbf{G}\_{\mathrm{h,\,win,k}} [\mathbf{t}\_{\mathrm{h,\,win}} - \mathbf{t}\_{\mathrm{r,\,win}}] \right.\tag{25}$$

Once that the air velocity values in all different trunks are fixed, referring to Table 1, for example, and from the maximum values of the cold and hot airflow rates in the trunks, the diameters of the hot and cold ducts of each trunk can be evaluated. Once the lengths of the various trunks of the network are known, one can calculate the surfaces of the ducts and so the weight of the network.

With a similar approach, we can write

$$t\_h(\tau) = t\_{\text{in,max}}(\tau) + \delta, \qquad \qquad \delta = 1 - 2^{\stackrel{\circ}{C}} \mathbb{C} \tag{14'}$$

and fix the temperature tcð Þτ , for example, equal to the dew point value. With the same consideration of the previous case, we obtain Eq. (20<sup>0</sup> ) and Eq. (21<sup>0</sup> ) as

$$\mathcal{G}\_{\mathbf{c},n}(\tau)[t\_{in}(\tau)-t\_{\mathbf{c}}] = \mathcal{G}\_{\mathbf{h},n}(\tau)\left[t\_{\mathbf{h}}^{\*}(\tau)-t\_{in}(\tau)\right] \tag{20'}$$

$$\frac{\mathbf{G}\_{\mathbf{c},n}}{\mathbf{G}\_{\mathbf{h},n}} = \frac{\left[t\_h^\*(\boldsymbol{\pi}) - t\_{\rm in}(\boldsymbol{\pi})\right]}{\left[t\_{\rm in}(\boldsymbol{\pi}) - t\_{\rm c}\right]} \tag{21'}$$

#### 4. Application example of the proposed method

The proposed method is applied here to calculate the dual duct networks of two reference buildings. The first (building A) is a day center for dialysis located in the city of Lecce (Southern Italy); the second is a private hospital located in the city of Rome (Central Italy).

The room temperature in summer is equal to 26�C for both the buildings; the room temperature in winter is equal to 22 and 20�C, respectively, for building A and building B.

Eq. (21) says that, both in winter and summer, the cold airflow rates Gc,n flowing through the cold trunks and supplying the mixing boxes represent higher fractions of the total flow rates of the zones if the differences, between the constant hot duct temperature and the supply temperatures, are high and if the differences between those and the minimum supply air temper-

For each zone, sensible thermal loads can be calculated as a function of time, and the same can

tinð Þ¼ <sup>τ</sup> tr � <sup>Φ</sup>s,nð Þ<sup>τ</sup>

The minimum value of the supply air temperature tin,minð Þτ reduced by δ, hour by hour,

time interval j, one can write the energy and mass balances, in winter and in summer, as

Φs,sum, kj þ cpGh,sum, kj½th,sum � tr,sum� ¼ cpGc,sum, kj tr,sum � t

∗ cj h i

Once that the air velocity values in all different trunks are fixed, referring to Table 1, for example, and from the maximum values of the cold and hot airflow rates in the trunks, the diameters of the hot and cold ducts of each trunk can be evaluated. Once the lengths of the various trunks of the network are known, one can calculate the surfaces of the ducts and so

thð Þ¼ τ tin,maxð Þþ τ δ, δ ¼ 1 � 2

<sup>h</sup>ð Þ� <sup>τ</sup> tinð Þ<sup>τ</sup> � �

The proposed method is applied here to calculate the dual duct networks of two reference buildings. The first (building A) is a day center for dialysis located in the city of Lecce (Southern Italy); the second is a private hospital located in the city of Rome (Central Italy).

and fix the temperature tcð Þτ , for example, equal to the dew point value. With the same

Gc,nð Þτ tinð Þ� τ tc ½ �¼ Gh,nð Þτ t

∗

cpGn

<sup>c</sup> ð Þτ . For each trunk k of the network, for each

∗ cj h i

¼ cpGh,win, kj½ � th,win � tr,win (25)

Gk ¼ Gc, kj þ Gh, kj (23)

�

) as

tinð Þ� <sup>τ</sup> tc ½ � <sup>21</sup><sup>0</sup> ð Þ

) and Eq. (21<sup>0</sup>

∗

C ð14<sup>0</sup>

<sup>h</sup>ð Þ� <sup>τ</sup> tinð Þ<sup>τ</sup> � � <sup>ð</sup>20<sup>0</sup>

(22)

(24)

Þ

Þ

be done for the supply air temperature values in the environments of the zone:

represents the temperature of the cold channel t

the weight of the network.

With a similar approach, we can write

consideration of the previous case, we obtain Eq. (20<sup>0</sup>

Gc,n Gh,n

4. Application example of the proposed method

¼ t ∗

Φs,win, kj þ cpGc,win, kj tr,win � t

ature are small.

38 HVAC System

For a day type for each month of the year and a daily period of 12 h (from 6:00 AM to 6:00 PM), the thermal loads of the different zones have been obtained as a function of time. Therefore, it has been possible to define the thermal zones and to evaluate the airflow rates required for each environment, to cope with the maximum sensible load in summer, the maximum sensible load in winter, and the ventilation needs. The AHU processes a total flow rate of air that obviously is the sum of the greatest of the three previous values, extended to all the zones.

In order to limit a priori the network extension, two AHUs have been used for building A, one serving 12 zones and 20 trunks as one serving 11 zones and 18 trunks. For building B, three AHUs have been used, each one serving 6 zones and 11 trunks.

Data for each network, namely, the lengths, airflow rates and maximum speeds in the trunks, are given in Tables 3 and 4 for building A and building B, respectively.


Table 3. Data of the networks AA and AB of building A.


Table 4. Data of the networks BA, BB, and BC of building B.

The diameters of the hot and cold channels are representative of the size of the whole network; the peripheral surface of the ducts stands as indicative parameter for the weight of the network and therefore of its cost. As an index of the overall dimension of the single trunk k, the covering factor Fk was also introduced, according to [16, 19]:

$$F\_k = \frac{G\_{k,\max}}{G\_k} \tag{26}$$

5. Analysis of results

7�C in winter).

The results of the dimensioning of the networks with the first approach (method 1) refer to the networks AA, AB and BA, BB, and BC in the case of air temperature tc in the cold duct taken equal to the minimum required (minus 1�C) and of the air temperature th in the hot duct taken as equal to 40�C. Results obtained with the second approach (method 2) refer to the same networks, in the case of air temperature th in the hot duct taken equal to the maximum required (plus 1�C) and of air temperature tc in the cold duct taken as equal to the dew point value (for building A, 13�C in summer and 10�C in winter, for building B, 13�C in summer and

Air Conditioning Systems with Dual Ducts: Innovative Approaches for the Design of the Transport Network…

http://dx.doi.org/10.5772/intechopen.80093

41

In order to make a comparison between the results obtained with the traditional sizing method, the savings are briefly presented in Tables 5 and 6, respectively, for building A and building B, as they are obtained for the five networks, in terms of the peripheral surface of the

In Table 7 we report the savings of side surface and the network factor by considering the

For the building A, the maximum value obtained for Fnet is 1.33, and it occurs for the network AA when the hot duct temperature th varies (method 2); it decreases to 1.15, for the networks AB when we use the method 1. For the building B, the maximum is obtained for the network BC when method 2 is used; the minimum occurs for the network BA with method 2 again. The achieved values of Fnet with the proposed methods are always smaller than those obtained by

Method 1 Method 2 Traditional method

Saved surface (%)-Fnet Fnet

Saved surface (%)-Fnet Fnet

� C.

C:

Method 1 Method 2 Traditional method

<sup>C</sup>, tc, win <sup>¼</sup> <sup>10</sup>�

C, tc, win ¼ 7

Network AA 31–1.26 14–1.33 1.76 Network AB 22–1.15 13–1.21 1.60

Table 5. Savings' percentage of the total side surface and network factors for building A.

Network BA 18–1.41 14–1.283 1.65 Network BB 25–1.34 18–1.36 1.70 Network BC 19–1.43 15–1.47 1.80

Table 6. Savings' percentage of the total side surface and network factors for building B.

C. For method 2: tc, sum <sup>¼</sup> <sup>13</sup>�

C. For method 2: tc, sum <sup>¼</sup> <sup>13</sup>�

channels and of the evaluated values of the network factor Fnet.

whole building A and the whole building B.

using the traditional design criteria.

For method 1: th <sup>¼</sup> <sup>40</sup>�

For method 1: th <sup>¼</sup> <sup>40</sup>�

It is defined as the ratio between the airflow rate Gk that flows through the kth trunk and Gk, max

$$\mathbf{G}\_{k,\max} = \frac{\pi}{4} \mathbf{v}\_k \left[ \mathbf{D}\_{hk}^2 + \mathbf{D}\_{ck}^2 \right] \tag{27}$$

which represents the flow rate that the trunk, already dimensioned, could carry if the air flowed at the maximum set speed.

The Fk factor takes values between 1 and 2; it approaches 1 when only one of the two ducts actually carries the entire flow rate of the trunk, while the other duct carries only a small correction. The factor tends instead to 2 when the both hot and cold ducts can both carry the entire flow rate of the trunk. With regard to the whole network, the Fnet factor can be defined as the weighted average of Fk, where the weights are the products between the lengths and the flow rates of the trunks:

$$F\_{net} = \frac{\sum\_{k} F\_{k} G\_{k} l\_{k}}{\sum\_{k} G\_{k} l\_{k}} \tag{28}$$
