# Exergy Analyses and Modelling of a Novel Extra-Low Temperature Dedicated Outdoor Air System

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## Abstract

**:**

## 1. Introduction

## 2. System Description

## 3. Methodology

_{X}, the multi-stage DX coil leaving air temperature at State X) and the number of cooling stages (N), which correspondingly affect the thermodynamic states of moist air entering and leaving individual cooling stages and the associated part load conditions.

#### 3.1. Case Study Building

_{X}

_{,}was set as 4 °C to 10 °C (1 °C interval) and the number of cooling stage (N) was set as 2 to 4. Single cooling stage has been excluded to avoid operating at unfavourably high temperature differential [15] and to benefit from multi-stage characteristics.

#### 3.2. Coil Performance Model Development

#### 3.2.1. Performance Curve Formulation

_{rated}is the rated total cooling capacity, kW; EIR

_{rated}is the rated power input ratio, which is the inverse of the rated energy efficiency ratio; EIR is the operating power input ratio, which is the inverse of the operating energy efficiency ratio; WB

_{ei}is the entering air wet bulb temperature at the DX coil (evaporator), °C; DB

_{ci}is the entering air dry bulb temperature at the condenser, °C; ${a}_{i}$ and ${b}_{i}$ are empirical coefficients.

#### 3.2.2. Data Collection

#### Extra-Low Temperature Side

^{2}store room at 10 °C DB. The store room is for dangerous goods. It requires to be maintained at around 10 °C DB year round. To reduce the explosion risk, no air recirculation is allowed, which resembles a DOAS configuration. The air-side operating conditions (outdoor air temperature, and the entering and leaving air dry bulb and wet bulb temperatures) and the power consumption of the two DX air-conditioners and the condenser fans in the pilot installation were monitored by a remote monitoring system. Given the two DX units were with different operating conditions and thus efficiencies, a sufficiently wide range of data were collected to develop the extra-low temperature part of CAP-FT and EIR-FT curves. Specifications of the DX air-conditioners and the configuration of the pilot installation are shown in Table 3 and Figure 4, respectively.

#### Extra-High Temperature Side

#### 3.2.3. Regression Models

_{ei}but varies very little with the condenser entering air DB temperature DB

_{ci}. The EIR-FT curve shows that the CAP increases primarily with WB

_{ei}but the power input W decreases with both WB

_{ei}and DB

_{ci}. In other words, a lower WB

_{ei}results in a higher EIR and thus lower COP.

#### 3.3. Energy Analysis

#### 3.4. Exergy Analysis

_{X}and N, which includes the calculation of moist air exergy and exergy efficiency of different system configurations.

#### 3.4.1. Moist Air Exergy

_{da}is the specific heat of dry air, kJ/kg·K; C

_{wv}is the specific heat of water vapour, kJ/kg·K; w is the humidity ratio of moist air, kg/kg dry air; ${w}_{0s}$ is the humidity ratio of dead state, kg/kg dry air; T is the temperature of moist air, K; T

_{0}is the reference environmental temperature, K; R

_{da}is the ideal gas constant of dry air, kJ/kg·K; P is the pressure of moist air, kPa; P

_{0}is the reference environmental barometric pressure (atmospheric pressure), kPa.

_{th}), mechanical exergy (ex

_{me}) and chemical exergy (ex

_{ch}). Thermal exergy is the maximum useful work when moist air is transformed from the initial temperature state to the dead temperature state. Mechanical exergy is equal to the mechanical work itself. Chemical exergy represents the maximum useful work associated with the transition of moisture content of moist air from the initial state to the dead state. They are represented by Equations (6) to (8), which are derived from Equation (5):

_{0s}in Equations (5) and (8) cannot be output directly from EnergyPlus, it has to be calculated by the ideal gas law from the reference environmental barometric pressure (P

_{0}) and the saturation pressure of water vapour (P

_{ws}), as described in Equation (9):

_{c}is the critical temperature, 647.096 K; P

_{c}is the critical pressure, 22,064 kPa.

#### 3.4.2. Exergy Flow

_{Fan}is the power input of supply fan, MWh; Ex,tot,loss is the total exergy loss of multi-stage DX system, MWh.

#### 3.4.3. Exergy Efficiency

## 4. Results and Discussion

_{X}and N explained in Section 3 and assuming only one parameter was varied, 21 cases (seven t

_{X}, and three N) were generated for hour-by-hour EnergyPlus simulations and exergy analysis. The design conditions of the 21 cases, based on common practice to allow equal sharing of load amongst cooling stages [46], are summarized in Table 5. The cooling capacity at each cooling stage was automatically adjusted according to t

_{X}, N and OA mass flow rate.

_{X}are presented in Figure 9, illustrating that in general, energy use (En) decreases with t

_{X}and increases with N, while exergy efficiency (${\eta}_{Ex}$) peaks with t

_{X}at 7 °C and decreases with N. N equals 2 and thus always results in a lower energy use and higher exergy efficiency.

_{X}is concerned, considering exergy efficiency (${\eta}_{Ex}$) is a more meaningful indicator of efficiency that accounts for quantity and quality aspects of energy flows when compared to energy [47], the optimum t

_{X}for a 2-stage XT-DOAS is 7 °C for having the highest exergy efficiency (=10.37%).

_{X}affects also the achievement of the desirable air conditions, the achievable indoor conditions for different t

_{X}were also investigated. Given the indoor temperature can be controlled, the investigations are focused on the resultant indoor relative humidity (RH). Its achievement is one specific characteristic of XT-DOAS [14]. The Root-Mean-Square Error (RMSE) value was used to quantify the deviation between the hourly resultant space RH and the desired value (35%) for different t

_{X}. RMSE can be calculated by Equation (14). A smaller RMSE

_{RH}means better humidity control:

_{RH}is the RMSE of the space RH; RH

_{spx}is the resultant space RH; RH

_{design}is the desired space RH, 35%; n is the annual operating hour.

_{RH}for different t

_{X}. It can be seen that the smallest RMSE

_{RH}occurs when t

_{X}is 7 °C (=3.38), which is accordant with the exergy analysis results.

_{X}on the energy use, exergy efficiency and achievable space RH and thus the concluded optimum N and t

_{X}, further energy and exergy analysis, as well space humidity condition evaluations were conducted.

#### 4.1. Energy Analysis

_{sys}for different N and t

_{X}which are basically determined by $\sum _{j=1}^{N}{W}_{j}$ and ${W}_{Fan}$.

_{X}but the rate of increase, as compared to the rate of drop in $\sum _{j=1}^{N}{W}_{j}$ with t

_{X}, is far less significant. Thus COP

_{sys}also increases with t

_{X}. However, as for the influence of N on $\sum _{j=1}^{N}{W}_{j}$ and thus COP

_{sys}, an analysis on the influential factors is needed. For a DX coil with defined performance curves (Section 3.2), the parameters affecting its COP, by reference to EnergyPlus, are summarized in Equations (15) through (22):

_{rated}is the rated air mass flow rate, kg/s; ${c}_{i}$ are empirical coefficients.

_{rated}and EIR

_{rated}of each cooling stage are constant terms; EIR-FT is a function of WB

_{ei}and DB

_{ci}; EIR-FF is a function of air flow fraction which is the ratio of m entering the DX coil to a constant term m

_{rated}; CAP is a function of m and $\Delta t$. DB

_{ci}is affected by the outdoor air condition which is the same for all system configuration and therefore is not necessary to consider. m is determined by t

_{X}so it is not an independent variable. Thus, COP can be described as a function of $\Delta t$ and WB

_{ei}as shown in Equation (23):

_{1}, d

_{2}, d

_{3}, and d

_{4}are constants.

_{ei}has a positive effect on COP while $\Delta t$ has a negative effect. The resultant model (Equation (25)) provides a convenient way to quantify the influences of WB

_{ei}and $\Delta t$ on the COP of a DX coil. This can be done by taking partial derivative of COP with respect to WB

_{ei}and $\Delta t$ as follows:

_{ei}, $\Delta t$ and COP, the sensitivities of WB

_{ei}and $\Delta t$ were estimated to be 2.035 and 0.179 to show that WB

_{ei}introduces much higher influence on a DX coil’s COP. The result is consistent with the visual representation in Section 3.2.3, Figure 5 and Figure 6.

_{ei}, the difference was high ranging from 7.23% to 12.67%.

_{sys}) is related to individual cooling stage’s COP and thus is also related to WB

_{ei}and $\Delta t$. Therefore, a higher COP

_{sys}can be regarded as a function of the average $\Delta t$ ($\overline{\Delta t}$) and WB

_{ei}(${\overline{WB}}_{ei}$) of all cooling stages as expressed in Equation (28). A lower $\overline{\Delta t}$ and a higher ${\overline{WB}}_{ei}$ result in a higher COP

_{sys}:

_{X}, illustrating that $\overline{\Delta t}$ decreases with t

_{X}and N, and ${\overline{WB}}_{ei}$ increases with t

_{X}and N. With the higher influence of ${\overline{WB}}_{ei}$ than $\overline{\Delta t}$ on COP

_{sys}, the results explain the preference for a smaller N (2-stage over 4-stage) and a higher t

_{X}for better COP

_{sys}and thus smaller $\sum _{j=1}^{N}{W}_{j}$.

#### 4.2. Exergy Analysis

_{X}but different N, $Ex,ep,i{n}_{1}$, $Ex,ep,ou{t}_{N}$ and ${W}_{Fan}$ are identical because they have the same entering and leaving air states (State O and State X). While for $\sum _{j=1}^{N}Ex,cd,i{n}_{j}$, as it is determined by the refrigerant pressures at the condenser, it decreases with N. However, its influence on ${\eta}_{Ex}$ (−2.39% to −5.90%), as compared to $\sum _{j=1}^{N}{W}_{j}$ (4.61% to 15.10%), is far less significant. Given $\sum _{j=1}^{N}{W}_{j}$ increases with N as confirmed earlier (Section 4.1), this can explain the percentage change in ${\eta}_{Ex}$ relative to N at 2 are always negative (−2.47% to −9.58%), and the highest occurs when N is 2.

_{X}, $Ex,ep,i{n}_{1}$ and ${W}_{Fan}$ increase with t

_{X}due to the corresponding increase in m of OA. On the contrary, $Ex,ep,ou{t}_{N}$ decreases with t

_{X}due to the higher DB and higher treated OA humidity ratio of (State X). $\sum _{j=1}^{N}Ex,cd,i{n}_{j}$ and $\sum _{j=1}^{N}{W}_{j}$ also decrease with t

_{X}as explained earlier (Section 4.1). With the counter-effect of two positive and three negative variables on ${\eta}_{Ex}$, the percentage change in ${\eta}_{Ex}$ relative to t

_{X}at 7 °C are always negative (−0.20 % to −10.52%), and the highest occurs when t

_{X}is 7 °C.

_{X}is 7 °C.

_{X}.

#### 4.3. Space Relative Humidity Control

_{X}at 7 °C, the space sensible heat ratios (SHR) and the designed equipment SHR were reviewed. Given the space relative humidity is achieved by matching the equipment sensible heat ratio (SHR

_{sys}) and the space SHR (SHR

_{spx}) [49], to explain the better humidity control for t

_{X}at 7 °C, the divergence between SHR

_{sys}and SHR

_{spx}were reviewed. The hourly SHR

_{spx}are outputs of EnergyPlus. Two indices have been employed to review the divergence between SHR

_{sys}and SHR

_{spx}for different t

_{X}, they are the index of agreement (IA) and RMSE. IA is a dimensionless indicator that enables consistency comparison between models [50]. A higher IA (from 0 to 1) means a more consistent tendency of change [51].

_{sys}and SHR

_{spx}. IA

_{SHR}and RMSE

_{SHR}are expressed in Equations (29) and (30).

_{X}are summarized in Table 9, illustrating that the highest IA

_{SHR}(=0.6705) and the smallest RMSE

_{SHR}(=0.0532) occurs when t

_{X}is at 7 °C.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${a}_{i}$ | i-th empirical coefficient |

${b}_{i}$ | i-th empirical coefficient |

CAP | total cooling capacity (kW) |

C_{da} | dry air specific heat (kJ/kg·K) |

${c}_{i}$ | i-th empirical coefficient |

COP | coefficient of performance |

C_{wv} | water vapour specific heat (kJ/kg·K) |

DB | dry bulb |

DX | direct expansion |

${d}_{i}$ | i-th empirical coefficient |

EIR | energy input ratio |

e | residual |

En | energy use (MWh) |

ex | exergy of moist air (kJ/kg dry air) |

Ex,cd,in | exergy of moist air entering in the condenser (MWh) |

Ex,cd,out | exergy of moist air out of the condenser (MWh) |

Ex,desired | exergy desired for a system (MWh) |

Ex,ep,in | exergy of moist air entering in the evaporator (MWh) |

Ex,ep,out | exergy of moist air out of the evaporator (MWh) |

Ex,loss | exergy loss of DX unit (MWh) |

Ex,needed | exergy needed for the desired effect of the system (MWh) |

Ex,tot,loss | total exergy loss of multi-stage DX system (MWh) |

FF | function of air flow fraction |

FT | function of temperature |

IA | index of agreement |

m | air mass flow rate (kg/s) |

N | cooling stage number of multi-stage DX system |

OA | outdoor air |

P | pressure (kPa) |

PLF | part load fraction |

PLR | part load ratio |

RA | return air |

R_{da} | the ideal gas constant of dry air (kJ/kg·K) |

RH | relative humidity |

RMSE | root-mean-square error |

RTF | run time fraction |

SHR | sensible heat ratio |

T | temperature (K) |

t | temperature (°C) |

$\Delta t$ | temperature difference between air in and out of DX coil (°C) |

WB | wet bulb |

W | compressor power (MWh) |

$w$ | moist air humidity ratio (kg/kg dry air) |

XT | extra-low temperature |

ZRE | standard residual |

Greek symbols | |

$\epsilon $ | exergy loss ratio |

${\eta}_{Ex}$ | exergy efficiency |

Subscripts | |

0 | reference environmental state |

0s | dead state |

c | critical state |

ch | chemical |

ci | condenser inlet |

design | design condition |

ei | evaporator (DX coil) inlet |

Fan | fan |

j | j-th stage DX coil |

me | mechanical |

rated | rated condition |

spx | conditioned spaces |

sys | multi-stage DX system |

th | thermal |

ws | saturated state of water vapour |

X | state of outdoor air treated by the last cooling stage |

y | annual value |

## Appendix A

_{ei}and DB

_{ci}in Equations (1) and (2); $\overline{y}$ is the mean of actual values; ${\widehat{y}}_{i}$ is the i-th fitted value which can be calculated from the different WB

_{ei}, DB

_{ci}and regressed coefficients; n is total number of data pairs; p is the number of independent variables.

_{i}has been introduced to standardize the ordinary least squares residual e

_{i}as shown in Equations (A3) to (A4), and the result of the scatter plots with a random distribution confirmed the validity of linear assumption [52].

_{i}and no obvious deviation is noted.

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**Figure 7.**Exergy flow of a typical DX unit. (Ex,ep,in—exergy of moist air entering in the evaporator; Ex,ep,out—exergy of moist air out of the evaporator; Ex,cd,in—exergy of moist air entering in the condenser; Ex,cd,out—exergy of moist air out of the condenser; W—Input power for DX unit; Ex,loss—exergy loss of DX unit.).

**Figure 8.**Exergy flow of a multi-stage DX system. ($Ex,ep,i{n}_{1}$—exergy of moist air entering in the evaporator of first cooling stage; $Ex,ep,ou{t}_{N}$ —exergy of moist air out of the evaporator of last cooling stage; $\sum _{j=1}^{N}Ex,cd,i{n}_{j}$ —the sum of moist air exergy entering in the all condensers; $\sum _{j=1}^{N}Ex,cd,ou{t}_{j}$ — the sum of moist air exergy out of all condensers; $\sum _{j=1}^{N}{W}_{j}$ —the sum of input power to whole system; ${W}_{Fan}$ —the power input of supply fan; Ex,tot,loss —the total exergy loss of multi-stage DX system).

Parameters | Value | |
---|---|---|

Indoor dry bulb temperature (°C) | 24.5 | |

Indoor relative humidity (%) | 35 | |

Coil sensible load (kW) | 63.82 | |

Coil latent load (kW) | 25.59 | |

State conditions (T °C [DB]/RH%) | O | 33/68 |

X | 4/100 | |

S | 18/48 | |

R | 24.5/35 | |

OA mass flow rate (kg/s) | 3.1 |

Description | Parameter | Value | ||
---|---|---|---|---|

Physical details | No. of storeys | 1 | ||

Area per floor (m^{2}) | 1296 | |||

Air-conditioned area per floor (m^{2}) | 1071 | |||

Floor to floor height (m) | 3.2 | |||

Envelope details | Wall | Resistance (m^{2}·°C/W)(thickness (m)/conductivity (W/m·°C)) | Granite panel | 0.009 (0.025/2.9) |

Cavity | 0.157 | |||

Concrete | 0.046 (0.1/2.16) | |||

Plaster | 0.053 (0.02/0.38) | |||

Heat transfer coefficient (W/m^{2}·°C) | 3.8 | |||

Single glazing window | Shading coefficient (SC) | 0.9 | ||

Window to wall ratio (WWR) | 0.5 | |||

Heat transfer coefficient (W/m^{2}·°C) | 5.5 | |||

Roof | Heat transfer coefficient (W/m^{2}·°C) | 0.8 |

Component | Parameter | Specification |
---|---|---|

DX Air Handler | Supply air volume flow rate (m^{3}/s) | 0.21 |

Outdoor air volume flow rate (m^{3}/s) | 0.21 | |

Power consumption (kW) | 2.20 | |

Condensing Unit | Cooling capacity (kW) | 22.70 |

Compressor capacity control | Variable speed | |

Power consumption (kW) | 9.63 |

Range of WB_{ei} | 6–32 °C |

Range of DB_{ci} | 6–35 °C |

Range of normalized performance coefficient | CAP-FT (0.4–27) |

EIR-FT (0.5–3.876) | |

Total number of data sets | 104 |

N | Leaving Air Temperature (°C) | OA Mass Flow Rate $\mathit{m}$ (kg/s) | |||
---|---|---|---|---|---|

Stage 1 | Stage 2 | Stage 3 | Stage 4 | ||

2 | 18.5 | 4 | - | - | 3.10 |

19 | 5 | - | - | 3.25 | |

19.5 | 6 | - | - | 3.43 | |

20 | 7 | - | - | 3.62 | |

20.5 | 8 | - | - | 3.84 | |

21 | 9 | - | - | 4.09 | |

21.5 | 10 | - | - | 4.37 | |

3 | 23 | 13 | 4 | - | 3.10 |

23 | 14 | 5 | - | 3.25 | |

24 | 15 | 6 | - | 3.43 | |

24.5 | 16 | 7 | - | 3.62 | |

24.5 | 16.5 | 8 | - | 3.84 | |

25 | 17 | 9 | - | 4.09 | |

25.5 | 18 | 10 | - | 4.37 | |

4 | 25 | 18 | 11 | 4 | 3.10 |

26 | 19 | 12 | 5 | 3.25 | |

26 | 19 | 12 | 6 | 3.43 | |

26.5 | 20 | 13.5 | 7 | 3.62 | |

26 | 20 | 14 | 8 | 3.84 | |

27 | 21 | 15 | 9 | 4.09 | |

27 | 21 | 15 | 10 | 4.37 |

Design t_{X} (°C) | Resultant Indoor Air RH (%) | |
---|---|---|

Mean | RMSE_{RH} | |

4 | 30.67 | 5.52 |

5 | 32.24 | 4.56 |

6 | 33.91 | 3.64 |

7 | 35.70 | 3.38 |

8 | 37.57 | 4.10 |

9 | 39.53 | 5.52 |

10 | 41.62 | 7.35 |

t_{X} (°C) | Cases with N | Exergy Flow (MWh) | ${\mathit{\eta}}_{\mathit{E}\mathit{x}}$ (%) | ||||||
---|---|---|---|---|---|---|---|---|---|

$\mathit{E}\mathit{x},\mathit{e}\mathit{p},\mathit{i}{\mathit{n}}_{\mathbf{1}}$ | $\sum _{\mathit{j}=\mathbf{1}}^{\mathit{N}}\mathit{E}\mathit{x},\mathit{c}\mathit{d},\mathit{i}{\mathit{n}}_{\mathit{j}}$ | $\sum _{\mathit{j}=\mathbf{1}}^{\mathit{N}}{\mathit{W}}_{\mathit{j}}$ | ${\mathit{W}}_{\mathit{F}\mathit{a}\mathit{n}}$ | $\mathit{E}\mathit{x}\mathit{,}\mathit{e}\mathit{p},\mathit{o}\mathit{u}{\mathit{t}}_{\mathit{N}}$ | $\sum _{\mathit{j}=\mathit{1}}^{\mathit{N}}\mathit{E}\mathit{x},\mathit{c}\mathit{d},\mathit{o}\mathit{u}{\mathit{t}}_{\mathit{j}}$ | Ex,tot,loss | |||

4 | 2 | 1.04 | 24.00 | 140.03 | 22.66 | 18.05 | 27.09 | 142.59 | 9.61 |

3 | 23.05 (−3.94%) | 152.41 (8.84%) | 26.65 | 154.47 | 9.06 (−5.74%) | ||||

4 | 22.75 (−5.19%) | 161.17 (15.10%) | 25.97 | 163.61 | 8.69 (−9.58%) | ||||

Average | 1.04 | 23.27 | 151.20 | 22.66 | 18.05 | 26.57 | 153.55 | 9.12 | |

5 | 2 | 1.09 | 23.60 | 129.52 | 22.79 | 17.67 | 26.52 | 132.82 | 9.98 |

3 | 23.04 (−2.39%) | 143.64 (10.90%) | 26.24 | 146.65 | 9.27 (−7.11%) | ||||

4 | 22.31 (−5.48%) | 144.57 (11.62%) | 25.28 | 147.82 | 9.26 (−7.21%) | ||||

Average | 1.09 | 22.98 | 139.24 | 22.79 | 17.67 | 26.01 | 142.43 | 9.50 | |

6 | 2 | 1.15 | 23.39 | 120.75 | 23.07 | 17.29 | 26.26 | 124.80 | 10.27 |

3 | 22.75 (−2.74%) | 132.78 (9.96%) | 25.90 | 136.55 | 9.62 (−6.34%) | ||||

4 | 22.01 (−5.90%) | 136.91 (13.39%) | 25.20 | 140.64 | 9.44 (−8.07%) | ||||

Average | 1.15 | 22.71 | 130.15 | 23.07 | 17.29 | 25.79 | 134.00 | 9.78 | |

7 | 2 | 1.21 | 23.14 | 115.15 | 23.39 | 16.90 | 26.03 | 119.96 | 10.37 |

3 | 22.40 (−3.18%) | 123.87 (7.57%) | 25.57 | 128.40 | 9.89 (−4.67%) | ||||

4 | 21.97 (−5.03%) | 127.41 (10.64%) | 24.93 | 132.15 | 9.71 (−6.37%) | ||||

Average | 1.21 | 22.50 | 122.14 | 23.39 | 16.90 | 25.51 | 126.84 | 9.99 | |

8 | 2 | 1.28 | 22.94 | 112.87 | 23.74 | 16.50 | 25.89 | 118.44 | 10.26 |

3 | 22.29 (−2.83%) | 119.81 (6.14%) | 25.45 | 125.17 | 9.87 (−3.76%) | ||||

4 | 21.79 (−5.01%) | 123.42 (9.35%) | 24.84 | 128.89 | 9.69 (−5.52%) | ||||

Average | 1.28 | 22.34 | 118.70 | 23.74 | 16.50 | 25.39 | 124.17 | 9.94 | |

9 | 2 | 1.36 | 22.64 | 111.14 | 24.14 | 16.09 | 25.66 | 117.53 | 10.10 |

3 | 21.93 (−3.14%) | 118.04 (6.21%) | 25.19 | 124.19 | 9.72 (−3.74%) | ||||

4 | 21.35 (−5.70%) | 119.44 (7.47%) | 24.44 | 125.76 | 9.67 (−4.22%) | ||||

Average | 1.36 | 21.97 | 116.21 | 24.14 | 16.09 | 25.10 | 122.49 | 9.83 | |

10 | 2 | 1.45 | 22.38 | 109.40 | 24.59 | 15.69 | 25.50 | 116.64 | 9.94 |

3 | 21.34 (−4.64%) | 114.44 (4.61%) | 24.74 | 121.39 | 9.70 (−2.47%) | ||||

4 | 21.08 (−5.80%) | 117.57 (7.47%) | 24.42 | 124.59 | 9.53 (−4.17%) | ||||

Average | 1.45 | 21.60 | 113.80 | 24.59 | 15.69 | 24.88 | 120.87 | 9.72 |

N | t_{X} (°C) | Exergy Flow (MWh) | ${\mathit{\eta}}_{\mathit{E}\mathit{x}}$ (%) | ||||||
---|---|---|---|---|---|---|---|---|---|

$\mathit{E}\mathit{x},\mathit{e}\mathit{p},\mathit{i}{\mathit{n}}_{\mathbf{1}}$ | $\sum _{\mathit{j}=\mathbf{1}}^{\mathit{N}}\mathit{E}\mathit{x},\mathit{c}\mathit{d},\mathit{i}{\mathit{n}}_{\mathit{j}}$ | $\sum _{\mathit{j}=\mathbf{1}}^{\mathit{N}}{\mathit{W}}_{\mathit{j}}$ | ${\mathit{W}}_{\mathit{F}\mathit{a}\mathit{n}}$ | $\mathit{E}\mathit{x}\mathit{,}\mathit{e}\mathit{p},\mathit{o}\mathit{u}{\mathit{t}}_{\mathit{N}}$ | $\sum _{\mathit{j}=\mathit{1}}^{\mathit{N}}\mathit{E}\mathit{x},\mathit{c}\mathit{d},\mathit{o}\mathit{u}{\mathit{t}}_{\mathit{j}}$ | Ex,tot,loss | |||

2 | 4 | 1.04 (−14.33%) | 24.00 (3.72%) | 140.03 (21.60%) | 22.66 (−3.09%) | 18.05 (6.79%) | 27.09 | 142.59 | 9.61 (−7.34%) |

5 | 1.09 (−10.07%) | 23.60 (2.01%) | 129.52 (12.48%) | 22.79 (−2.53%) | 17.67 (4.54%) | 26.52 | 132.82 | 9.98 (−3.80%) | |

6 | 1.15 (−5.27%) | 23.39 (1.08%) | 120.75 (4.86%) | 23.07 (−1.36%) | 17.29 (2.32%) | 26.26 | 124.80 | 10.27 (−1.00%) | |

7 | 1.21 | 23.14 | 115.15 | 23.39 | 16.90 | 26.03 | 119.96 | 10.37 | |

8 | 1.28 (5.92%) | 22.94 (−0.86%) | 112.87 (−1.98%) | 23.74 (1.50%) | 16.50 (−2.39%) | 25.89 | 118.44 | 10.26 (−1.14%) | |

9 | 1.36 (12.58%) | 22.64 (−2.15%) | 111.14 (−3.48%) | 24.14 (3.22%) | 16.09 (−4.80%) | 25.66 | 117.53 | 10.10 (−2.65%) | |

10 | 1.45 (20.18%) | 22.38 (−3.26%) | 109.40 (−5.00%) | 24.59 (5.15%) | 15.69 (−7.13%) | 25.50 | 116.64 | 9.94 (−4.15%) | |

Average | 1.23 | 23.16 | 119.84 | 23.48 | 16.88 | 26.13 | 124.68 | 10.08 | |

3 | 4 | 1.04 (−14.33%) | 23.05 (2.90%) | 152.41 (23.04%) | 22.66 (−3.09%) | 18.05 (6.79%) | 26.65 | 154.47 | 9.06 (−8.38%) |

5 | 1.09 (−10.07%) | 23.04 (2.84%) | 143.64 (15.95%) | 22.79 (−2.53%) | 17.67 (4.54%) | 26.24 | 146.65 | 9.27 (−6.26%) | |

6 | 1.15 (−5.27%) | 22.75 (1.55%) | 132.78 (7.19%) | 23.07 (−1.36%) | 17.29 (2.32%) | 25.90 | 136.55 | 9.62 (−2.73%) | |

7 | 1.21 | 22.40 | 123.87 | 23.39 | 16.90 | 25.57 | 128.40 | 9.89 | |

8 | 1.28 (5.92%) | 22.29 (−0.49%) | 119.81 (−3.28%) | 23.74 (1.50%) | 16.50 (−2.39%) | 25.45 | 125.17 | 9.87 (−0.20%) | |

9 | 1.36 (12.58%) | 21.93 (−2.11%) | 118.04 (−4.71%) | 24.14 (3.22%) | 16.09 (−4.80%) | 25.19 | 124.19 | 9.72 (−1.69%) | |

10 | 1.45 (20.18%) | 21.34 (−4.72%) | 114.44 (−7.62%) | 24.59 (5.15%) | 15.69 (−7.13%) | 24.74 | 121.39 | 9.70 (−1.94%) | |

Average | 1.23 | 22.40 | 129.28 | 23.48 | 16.88 | 25.68 | 133.83 | 9.59 | |

4 | 4 | 1.04 (−14.33%) | 22.75 (3.54%) | 161.17 (26.50%) | 22.66 (−3.09%) | 18.05 (6.79%) | 25.97 | 163.61 | 8.69 (−10.52%) |

5 | 1.09 (−10.07%) | 22.31 (1.53%) | 144.57 (13.47%) | 22.79 (−2.53%) | 17.67 (4.54%) | 25.28 | 147.82 | 9.26 (−4.66%) | |

6 | 1.15 (−5.27%) | 22.01 (0.15%) | 136.91 (7.46%) | 23.07 (−1.36%) | 17.29 (2.32%) | 25.20 | 140.64 | 9.44 (−2.80%) | |

7 | 1.21 | 21.97 (0.00%) | 127.41 | 23.39 | 16.90 | 24.93 | 132.15 | 9.71 | |

8 | 1.28 (5.92%) | 21.79 (−0.84%) | 123.42 (−3.13%) | 23.74 (1.50%) | 16.50 (−2.39%) | 24.84 | 128.89 | 9.69 (−0.24%) | |

9 | 1.36 (12.58%) | 21.35 (−2.84%) | 119.44 (−6.25%) | 24.14 (3.22%) | 16.09 (−4.80%) | 24.44 | 125.76 | 9.67 (−0.40%) | |

10 | 1.45 (20.18%) | 21.08 (−4.05%) | 117.57 (−7.72%) | 24.59 (5.15%) | 15.69 (−7.13%) | 24.42 | 124.59 | 9.53 (−1.90%) | |

Average | 1.23 | 21.90 | 132.93 | 23.48 | 16.88 | 25.01 | 137.64 | 9.43 |

^{#}% change based on t

_{X}= 7 °C.

t_{X} (°C) | IA_{SHR} | RMSE_{SHR} |
---|---|---|

4 | 0.6602 | 0.0545 |

5 | 0.6659 | 0.0538 |

6 | 0.6682 | 0.0535 |

7 | 0.6705 | 0.0532 |

8 | 0.6697 | 0.0534 |

9 | 0.6641 | 0.0541 |

10 | 0.6619 | 0.0543 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bao, Y.; Lee, W.L.; Jia, J. Exergy Analyses and Modelling of a Novel Extra-Low Temperature Dedicated Outdoor Air System. *Energies* **2018**, *11*, 1165.
https://doi.org/10.3390/en11051165

**AMA Style**

Bao Y, Lee WL, Jia J. Exergy Analyses and Modelling of a Novel Extra-Low Temperature Dedicated Outdoor Air System. *Energies*. 2018; 11(5):1165.
https://doi.org/10.3390/en11051165

**Chicago/Turabian Style**

Bao, Yani, Wai Ling Lee, and Jie Jia. 2018. "Exergy Analyses and Modelling of a Novel Extra-Low Temperature Dedicated Outdoor Air System" *Energies* 11, no. 5: 1165.
https://doi.org/10.3390/en11051165