# From Entropy Generation to Exergy Efficiency at Varying Reference Environment Temperature: Case Study of an Air Handling Unit

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions [1]. Continuous energy transformations take place in heating, ventilation, and air conditioning (HVAC) systems and devices thereof. Tighter thermal insulation requirements for buildings have significantly reduced heat transfer losses through the building envelope. However, in order to ensure adequate air quality in buildings, ventilation systems are becoming more and more important, leading to an increased need to improve and more thoroughly analyze such systems.

## 2. Air Handling Unit as a Thermodynamic System

_{R}required for ventilation, when the reference temperature is T

_{e}. In this case the AHU should provide fresh air required to ventilate the room with a specific heat flow:

_{R}is supplied to and exhausted from the ventilated room. The outdoor air at temperature T

_{R}reaches the HRE, where it warms up from T

_{e}to T

_{c}. Then, in the HP condenser this air is warmed up to temperature T

_{K}and then slightly warms up in the supply fan (FN) and, having reached temperature T

_{Ri}, is supplied to the room. The air exhausted from the room at temperature T

_{Ro}, having warmed up to T

_{h}, in the HRE gives its heat to the supplied air and its temperature drops to T

_{w}. Next, in the HP evaporator the air continues to give away its heat by cooling to T

_{E}and is exhausted.

_{w}(see Figure 1).

_{ln m}is the logarithmic mean temperature difference, ${\dot{M}}_{c}$, ${\dot{M}}_{h}$ are the mass flow rates of cold and hot fluids, respectively, c

_{p,c}, c

_{p,h}are the specific heat capacities of cold and hot fluids, respectively, T

_{c}, T

_{h}are the temperatures of cold and hot fluids in the inlet and outlet, respectively.

- Heat recovery exchanger:$${\dot{M}}_{V}({h}_{h}-{h}_{w})={\dot{M}}_{V}\left({h}_{c}-{h}_{e}\right)$$
- Evaporator:$${\dot{M}}_{f}({h}_{1}-{h}_{5})={\dot{M}}_{V}\left({h}_{E}-{h}_{w}\right)$$

_{f}

_{5}–T

_{f}

_{1}in the evaporator and T

_{f}

_{3}–T

_{f}

_{4}in the condenser.

_{f}

_{2}to T

_{f}

_{3}. T

_{e}, along with the reference temperature, is always below the temperatures of the working fluids in the condenser. The problem of the varying reference temperature discussed below is not relevant to it. Meanwhile T

_{e}in the evaporator in the majority of engineering solutions for the AHU is between the temperatures of the Freon and air. As a result, in this case, the interpretation of directions of exergy flows should be given appropriate attention.

_{c}

_{1}= T

_{e}, then the indices in the equations change accordingly, corresponding with Figure 1:

_{ex}. AHU performance does not go beyond the FTL and, by essence, corresponds with the definition of the COP of a heat pump that considers the equivalence of electricity and exergy and is widely used in engineering practice:

## 3. The Specifics of Exergy Analysis in HVAC Processes

#### 3.1. Produced Entropy Calculation Approaches for Heat Exchangers

_{ex}, along with $\Delta {\dot{S}}_{irr}$ or ${\dot{L}}_{c}^{h}$ at least the exergy flow that is supplied to the system should be known.

#### 3.2. Exergy Efficiency of Stationary Heat Transfer Process at Varying RT

_{h}= 20 °C and T

_{c}= –20 °C. The selected temperatures are close to the natural environment. The process is shown in Figure 6 from the point of view of the Zero Law of Thermodynamics (ZLT), the FLT, the SLT, and exergy.

_{c}≠ T

_{e}or T

_{h}≠ T

_{e}. In addition to this, in the cases of the ZTL, the FTL, and the STL T

_{e}is not a parameter that affects the process indicators. In terms of the FTL there is a stable heat flow ${\dot{Q}}_{c}^{h}=const$, while in terms of the STL, the produced entropy is $\Delta {S}_{c}^{h}{}_{irr}=const.$ The RT, i.e., outdoor air temperature T

_{e}, here on the x-axis shown as a variable and is prominent in the exergy analysis of the process. The exergy balance equation of the process discussed herein is ${\dot{E}}_{h}^{}{}_{}={\dot{E}}_{c}^{}{}_{}+{\dot{L}}_{c}^{h}$. The dependence of these three members on T

_{e}, is shown in the portion of the figure that is dedicated to exergy. Based on Equation (11), the destroyed exergy is linearly linked to $\Delta {S}_{c}^{h}{}_{irr}$ and in all cases, ${\dot{L}}_{c}^{h}\ge 0$. Within the temperature range ${T}_{h}\ge {T}_{e}\ge {T}_{c}$ exergy flows formed by both temperatures are given to the system ${\dot{E}}_{h}^{+}$ and ${\dot{E}}_{c}^{+}$, which are denoted with a superscript index “+”. There is no resulting exergy flow that leaves the system here. We have a case of ${\dot{E}}_{h}^{+}+{\dot{E}}_{c}^{+}{{}_{}}_{}={\dot{L}}_{c}^{h}$.

_{h}and T

_{c}, the direction of exergy flows depends on the position of T

_{e}with respect to these temperatures. In other words, both exergy flows that characterize the heat transfer process are always directed at RT and follow it as it changes.

_{e}= 0 K to T

_{e}>> T

_{h}, is shown in Figure 7. Exergy flow data, shown in Figure 6, is denoted by a dashed line. When T

_{e}equals any of these temperatures (T

_{e}= T

_{h}or T

_{e}= T

_{c}), then the corresponding exergy equals 0. Destroyed exergy is proportional to T

_{e}and always above 0.

_{h}= 20 °C and T

_{c}= −20 °C) in the thermodynamic system shown in Figure 6, within the reference temperature range 30 °C ≥ T

_{e}≥ −30 °C, is shown in Figure 8a.

_{ex}= 1 and minimum η

_{ex}= 0 values; in addition to this, it is generally not symmetrical with respect to 0 °C (the average value of T

_{h}= 20 °C and T

_{c}= −20 °C). The maximum value always corresponds with T

_{e}= 0 K. The minimum value η

_{ex}= 0 is always within the range between T

_{e}= T

_{h}and T

_{e}= T

_{c}, which, in this case, is (T

_{h}= 20 °C, T

_{c}= −20 °C).

_{e}. In addition to this, the exergy efficiency of a system and a process taking place therein is $0\le {\eta}_{ex}\le 1$. Therefore, the thermal exergy flow moves from the thermal source to the environment. The solution of an element developed hereby can be reliably used in the thermodynamic (exergy) analysis of the energy transformation chain of HVAC systems.

#### 3.3. Features of Exergy Analysis of Heat Exchangers in the AHU

_{e}, an algorithm is required to solve the separate cases shown here (e.g., (b), (c), and (d)).

_{e}is calculated using equation:

_{i}is the enthalpy of state i of the working fluid, c

_{p}is the specific heat capacity.

_{e}that corresponds with the reference temperature T

_{e}is determined as follows:

- HRE:$${\dot{M}}_{V}({k}_{h}-{k}_{w})={\dot{M}}_{V}\left({k}_{c}-{k}_{e}\right)+{\dot{L}}_{HRE}$$
- Evaporator:$${\dot{M}}_{f}({k}_{1}-{k}_{5})={\dot{M}}_{V}\left({k}_{E}-{k}_{w}\right)+{\dot{L}}_{EV}$$
- Condenser:$${\dot{M}}_{f}({k}_{2}-{k}_{4})={\dot{M}}_{V}\left({k}_{K}-{k}_{c}\right)+{\dot{L}}_{CN}$$

## 4. Case Study—Results and Discussion

^{3}/h and power input for fans (supply and exhaust) is 2 × 77 W. The efficiency of the HRE is 70%, the isentropic efficiency of the HP compressor is 0.8, and the power consumption efficiency of the fan is 0.82. The environment (as well as reference) temperature range is T

_{e}= −30, …, +10 °C while the room air temperature is 22 °C. Freon is 410a, isotherm in the evaporator is ${T}_{EVizot}={T}_{f5}={T}_{f1}$= −30 °C, isotherm in the condenser is ${T}_{CNizot}={T}_{f3}={T}_{f4}$= 30 °C (Figure 3.).

_{e}= −20 °C does not have a numeric significance in terms of the discussed issues of exergy analysis from the methodical point of view. The warming up of air in fans has been assessed in the calculations but is not reflected in the chart directly due to relatively low numeric value.

_{e}= −30 °C and 10 °C. Not only the positions of temperatures of the working fluid with respect to each other change, but also the heat flow transferred within them, which is shown on the x-axis at different scales.

_{e}= −30 °C, −20 °C and 10 °C) are shown in Figure 12.

_{e}. In addition to this, the reference state parameters for the thermodynamic state parameters (enthalpy and entropy) of these different working fluids are autonomous. In this stage, air coenthalpies have been chosen for graphical representation while the Freon coenthalpies have been reduced at a ratio of ${\dot{M}}_{f}/{\dot{M}}_{V}$.

_{e}= −30 °C, …, +10 °C. These results have been obtained by using Equations (9) and (10).

_{AHU}(Equation (7)) or exergy efficiency η

_{ex}(Equation (8)). The dependence of these indicators on outdoor air temperature (RT) is depicted in Figure 16. It also illustrates the aforementioned statement that the effectiveness of the HRE (Equations (5) and (6)) has an important role regarding AHU performance indicators. For this purpose, two cases are presented: When ε

_{T}equals 70% and 80%.

_{T}allows to achieve better AHU performance indicators, especially at lower reference temperature values. It can be noted that the exergy efficiency of the HRE remains nearly stable (in both cases of ε

_{T}) due to the fact that it is supplied with the air at reference temperature. The exergy efficiency of the entire device responds more to the reference temperature by dropping several times in the analyzed range (from –30 °C to +10 °C). It occurs mostly due to destroyed exergy in the evaporator and fan being almost independent of the reference temperature (see Figure 15). Additional calculations show that without the HRE, the performance coefficient of AHU would practically correspond with the HP and in this numeric case would be almost 3.

_{e}, which, in terms of exergy analysis, is reference temperature. In a specific location the variation of temperature is typical of that location only. The assessment and choice of solutions in terms of engineering and economy depends on a longer period, seasonal processes and indicators of device performance that can be only revealed by employing dynamic process modelling. One of its main components is exergy analysis. The peculiarities of processes in AHUs are listed and demonstrated therein. The reflection of these specifics in dynamic modelling algorithms enhances the application of exergy analysis in the assessment and choice of HVAC systems.

## 5. Conclusions

- Two exergy flows that characterize the transferred heat flow formed by two temperatures are always directed at the reference temperature and correspond with its change. Such interpretation of the direction of exergy as the reference temperature changes corresponds with the fundamental axioms of thermodynamic (exergy) analysis:
- (a)
- Exergy losses ${\dot{L}}_{}\ge 0$ when $\Delta {\dot{S}}_{irr}^{}=const$ are always proportional to T
_{e}; - (b)
- the exergy efficiency of a system and the process taking place therein is $0\le {\eta}_{ex}\le 1$.

- Even though there are two ways to determine the entropy produced during the heat transfer process (on the basis of entropy balance and Carnot factor), in order to determine the exergy efficiency of this process, at least one of the two exergy flows has to be known.
- As the temperature change in heat exchangers is nearly rectilinear, i.e., when temperature changes are not significant, both the Carnot factor and methods based on coenthalpies can be used for exergy analysis. The decision depends on the information available.

- Process parameters in the AHU and its HP components, as well as performance indicators thereof, change within the range of change of RT. There is a trend that as the RT increases, most of the indicators drop. However, to each component there a specific nature of variation of the produced entropy, destroyed exergy and exergy efficiency.
- With regards to RT, heat pump evaporator and fans are distinguished by a constantly non-decreasing destroyed exergy indicator. Here exergy analysis shows the potential of improving general thermodynamic efficiency indicators of AHUs.
- Even without being an indicator for AHU performance comparison, entropy generation shows the distribution of process irreversibility in components as well as the specifics of changes in processes. It also allows to verify the intermediate results of exergy analysis.
- Within the selected, rather wide range of RT, the change in the AHU coefficient of performance remains quite high and drops 30% to 40% when RTs are higher. Absolute values are highly dependent on the effectiveness of the heat recovery exchanger.
- Exergy efficiency of AHU in this range of RT of −30 °C, …, +10 °C drops from 45–55% to 12–15% even though the exergy efficiency of the HRE basically does not change. The main reason for this is the aforementioned stable (essentially independent of the RT) value of the destroyed exergy for evaporator and fans.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Abbreviations | |

AHU | Air Handling Unit |

CM | Compressor |

CN | Condenser |

COP | Coefficient of Performance |

EV | Evaporator |

FLT | First Law of Thermodynamics |

FN | Fan |

HP | Heat Pump |

HRE | Heat Recovery Exchanger |

HVAC | Heating, Ventilation and Air Conditioning |

RT | Reference Temperature |

SLT | Second Law of Thermodynamics |

TV | Throttle Valve |

ZLT | Zero Law of Thermodynamics |

Variables | |

A | surface area (m^{2}) |

c_{p} | specific heat capacity (kJ/kg·K) |

e | specific exergy (kJ/kg) |

$\dot{E}$ | exergy flow rate (kW) |

h | enthalpy (kJ/kg) |

$\dot{K}$ | coenthalpy rate (kW) |

k | specific coenthalpy (kJ/kg) |

l | specific destroyed exergy (kJ/kg) |

$\dot{L}$ | destroyed exergy (kW) |

$\dot{M}$ | mass flow rate (kg/s) |

$\dot{Q}$ | heat transfer flow rate (kW) |

R_{i} | inlet to room (K) |

R_{o} | outlet from room (K) |

$\dot{s}$ | specific entropy (kJ/kg·K) |

$\dot{S}$ | entropy (kW/K) |

T | temperature (K) |

U | overall heat transfer coefficient (W/m·K) |

Δ | difference (–) |

${\epsilon}_{T}$ | effectiveness of heat recovery exchanger (–) |

${\eta}_{C}$ | Carnot factor (–) |

η_{ex} | exergy efficiency (–) |

Subscripts | |

a | air |

AHU | air handling unit |

c | cooler fluid |

e | state of reference environment |

CNizot | isotherm in the condenser |

EVizot | isotherm in the evaporator |

f | Freon / refrigerant |

h | hotter fluid |

i | state of fluid |

irr | produced / irreversible |

ln m | logarithmic mean |

R | room |

V | ventilation |

w | warm exhausted air after HRE |

1 | in |

2 | out |

Superscripts | |

h | hotter fluid |

q | heat transfer |

+ | to the system |

– | out of the system |

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**Figure 2.**Schemes of energy calculations for components of the AHU: (

**a**) Heat exchanger, (

**b**) evaporator, (

**c**) condenser. ${\dot{M}}_{f}$—the mass flow rate of Freon (kg/s); ${\dot{M}}_{V}$—the mass flow rate of the air used for ventilation (kg/s).

**Figure 3.**Temperature variation in the condenser (CN) and the evaporator (EV) of the heat pump. Specific numeric values correspond with the numeric case study analyzed below.

**Figure 4.**State parameters for determining produced entropy in a counter-current heat exchanger. (

**a**) entropies of working fluids; (

**b**) temperatures of working fluids.

**Figure 5.**Graphical representation of destroyed exergy ${\dot{L}}_{c}^{h}=f({\eta}_{Ci},{\dot{Q}}_{c}^{h})$ in the heat transfer process in the heat exchanger.

**Figure 6.**Heat transfer process from the positions of the ZLT, FLT, SLT and exergy when reference temperatures are close to the temperatures of heat sources.

**Figure 8.**Exergy efficiency of the heat transfer process between temperatures T

_{h}= 20 °C, T

_{c}= −20 °C at a varying RT: (

**a**) 30 °C ≥ T

_{e}≥ −30 °C; (

**b**) from T

_{e}= 0 K to higher values.

**Figure 9.**Possible positions of temperatures of working fluids and outdoor air with respect to each other in heat exchangers of the AHU.

**Figure 10.**The variation of air and Freon temperature in the heat exchangers of the AHU when T

_{e}= −20 °C.

**Figure 11.**Temperatures in the heat exchangers and heat flows therein at outdoor air temperatures of (

**a**) −30 °C; (

**b**) +10 °C.

**Figure 12.**Carnot factors in heat exchangers and heat flows therein at outdoor air temperatures of (

**a**) −30 °C, (

**b**) −20 °C and (

**c**) +10 °C.

**Figure 13.**Coenthalpies and heat flows in heat exchangers at outdoor air temperatures of (

**a**) −30 °C; (

**b**) −20 °C, and (

**c**) +10 °C.

**Figure 14.**Entropy produced in AHU components $\Delta {\dot{S}}_{irr}$ at different reference temperatures (

**a**). Chart (

**b**) shows an extract from the lower part of chart (

**a**), using Equations (9) and (10).

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**MDPI and ACS Style**

Streckienė, G.; Martinaitis, V.; Bielskus, J.
From Entropy Generation to Exergy Efficiency at Varying Reference Environment Temperature: Case Study of an Air Handling Unit. *Entropy* **2019**, *21*, 361.
https://doi.org/10.3390/e21040361

**AMA Style**

Streckienė G, Martinaitis V, Bielskus J.
From Entropy Generation to Exergy Efficiency at Varying Reference Environment Temperature: Case Study of an Air Handling Unit. *Entropy*. 2019; 21(4):361.
https://doi.org/10.3390/e21040361

**Chicago/Turabian Style**

Streckienė, Giedrė, Vytautas Martinaitis, and Juozas Bielskus.
2019. "From Entropy Generation to Exergy Efficiency at Varying Reference Environment Temperature: Case Study of an Air Handling Unit" *Entropy* 21, no. 4: 361.
https://doi.org/10.3390/e21040361