*Article* **Energy-Optimal Structures of HVAC System for Cleanrooms as a Function of Key Constant Parameters and External Climate**

**Mieczysław Porowski \* and Monika Jakubiak**

Institute of Environmental Engineering and Building Installations, Poznan University of Technology, Pl. M. Sklodowskiej-Curie 5, 60-965 Poznan, Poland; monika.ja.mackowiak@doctorate.put.poznan.pl **\*** Correspondence: mieczyslaw.porowski@put.poznan.pl

**Abstract:** This article presents approximating relations defining energy-optimal structures of the HVAC (Heating, Ventilation, Air Conditioning) system for cleanrooms as a function of key constant parameters and energy-optimal control algorithms for various options of heat recovery and external climates. The annual unit primary energy demand of the HVAC system for thermodynamic air treatment was adopted as the objective function. Research was performed for wide representative variability ranges of key constant parameters: cleanliness class—Cs (ISO5÷ISO8), unit cooling loads—. qj (100 <sup>÷</sup> 500) W/m2 and percentage of outdoor air—α<sup>o</sup> (5 ÷ 100)%. HVAC systems are described with vectors x with coordinates defined by constant parameters and decision variables, and the results are presented in the form of approximating functions illustrating zones of energy-optimal structures of the HVAC system x∗ = f (Cs, . qj , αo). In the optimization procedure, the type of heat recovery as an element of optimal structures of the HVAC system and algorithms of energy-optimal control were defined based on an objective function and simulation models. It was proven that using heat recovery is profitable only for HVAC systems without recirculation and with internal recirculation (savings of 5 ÷ 66%, depending on the type of heat recovery and the climate), while it is not profitable (or generates losses) for HVAC systems with external recirculation or external and internal recirculation at the same time.

**Keywords:** cleanrooms; ventilation; air conditioning; energy consumption; optimization

#### **1. Introduction**

HVAC systems for cleanrooms generate very high energy consumption for thermodynamic treatment and forcing through air. The literature provides a lot of data confirming this thesis. According to Kircher et al. [1], the energy consumption of HVAC systems for cleanrooms in the USA is 30 ÷ 50% times higher than for commercial buildings. According to Tschudi et al. [2], as well as Zhuang et al. [3], this range is wider and equals 10 ÷ 100%. Shan and Wang [4], as well as Tsao et al. [5,6], report that the percentage of energy consumption by HVAC systems in factories with advanced technologies equals 30 ÷ 65%, while, according to Hu et al. [7] and Zhao et al. [8], the percentage for cleanrooms with semiconductor manufacturing equals 40 ÷ 50% of the total energy consumption. Highenergy inputs for air conditioning for cleanrooms inspire research aimed to reduce the energy consumption. Such studies address two issues: the optimization of the structure of the HVAC system or the optimization of control algorithms according to the energy criterion. The support tool here is software for determining energy consumption by the HVAC system of cleanrooms; significant results of work in this area were obtained by Hu et al. [9–11]. In Reference [9], the authors presented a validated FES (Fab Energy Simulation) simulation tool to determine energy consumption in an application for a semiconductor manufacturing fab. The mathematical model for the HVAC system was based on the energy balance equations for the individual components. In relation to the commercial comparable program "CleanCalc II", the FES program allowed for the definition of a few additional parameters by the user while showing excellent consistency of the results (2.33%). The

**Citation:** Porowski, M.; Jakubiak, M. Energy-Optimal Structures of HVAC System for Cleanrooms as a Function of Key Constant Parameters and External Climate. *Energies* **2022**, *15*, 313. https://doi.org/10.3390/ en15010313

Academic Editors: Roberto Alonso González Lezcano and Fabrizio Ascione

Received: 24 November 2021 Accepted: 27 December 2021 Published: 3 January 2022

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**Copyright:** © 2022 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 (https:// creativecommons.org/licenses/by/ 4.0/).

study [10] developed a new ECF (energy conversion factor) calculator in an application for high-tech factories, including HVAC systems. In turn, in article [11], the authors presented the integration of both tools: the FES program and the ECF calculator in order to optimize energy consumption by HVAC systems in technologically advanced factories (high-tech fabs).

Research on optimizing structures of the HVAC system for cleanrooms was performed by Lin et al. [12], who modified a classic MAU (Make-up Air Unit) + FFU (Filter Fan Unit) + DCC (Dry Cooling Coil) in the recirculation channel, replacing the DCC with FDCU (Fan Dry Cooling Unit) modules in the ceiling of a cleanroom. As a result of elimination of under pressure above the suspended ceiling and air infiltration, as well as the reduction of forcing through losses, they achieved a reduction in energy consumption of the HVAC system with FDCU by 4.3% compared to the system with the DCC. Hu and Tsao [13] investigated five cases of structures of HVAC system of semiconductor manufacturing rooms. The HVAC structures were different combinations of elements: RCU (Recirculation Air Unit), MAU, FCU (Fan Coil Unit), FFU and DCC. The authors compared the annual electricity consumption in each of these systems, calculating the "Energy Consumption Evaluation" coefficient with values of 1.08, 1.12, 1.19 and 3.80 in relation to the optimal system—MAU + DCC + FFU.

Shan and Wang [4] presented simulation results for three typical options of the structure of the HVAC system for cleanrooms in the pharmaceutical industry: "Interactive option", "Partially decoupled option" and "Fully decoupled option". They proved, for the chosen application, that using the "Partially decoupled option" made it possible to reduce the consumption of electricity and gas for cooling and heating by 69.8% and 87.8%, respectively.

Tsao et al. [14] presented simulation results for eight different combinations of a structure of the HVAC system of a semiconductor manufacturing room. These combinations included: the location of a fan in MAU (push-through vs. draft-through), one or two temperature levels of cooling water from chillers and using condensation heat recovery in chillers for reheating in MAU. They proved the possibility of reducing electricity consumption by 38.65% compared to the standard option.

Additionally, Kim et al. [15] simulated the operation of a HVAC system for cleanrooms for four options: Variable Air Volume (VAV), AIR WASHer System (AIRWASH), Dedicated Outdoor Air System (DOAS) and Integrated with Indirect and Direct Evaporative Coolers (IDECOAS). The simulation tool used was the EES (f-chart Software 2009) program. The scope of the simulation included two types of systems (type 1—percentage of outdoor air α = 100% and type 2—α = 100%) and six types of climates. The simulation results proved that DOAS and IDECOAS applications make it possible to reduce the annual demand for cold and heat by 67.5% and 59.5%, respectively, compared to a VAV system. Yin et al. [16,17] energetically optimized a classic HVAC system: MAU + FFU + DCC, in which, as part of the modification, only part of the recirculation air was cooled in the DCC, and reheating in MAU was replaced by a mixing operation in a space above the suspended ceiling. Eventually, the demand for cold in the DCC was decreased by 40 ÷ 52% compared to the classic system [17]. Similarly, Ma et al. [18] optimized the heat exchanger system in the MAU unit by resigning from reheating and achieving energy savings for pumping in the MAU unit in the range of 10.7–17.2%. The mentioned authors also optimized the structure of the filtration system by filtering the return and outdoor air separately. They proved that, by replacing the HEPA filters on the return with fine filters, the energy consumption could be reduced from 25.8% to 45% due to the lower air flow resistance [19].

Additionally, Yin et al. [20] optimized an existing classic HVAC system (MAU + FFU + DCC) in a semiconductor manufacturing factory. Based on the results of the measurements and numerical simulations for a HVAC system upgrade option, they proved that, by implementing high-temperature chillers, heat recovery from DCC to MAU and resigning from reheating, the energy consumption can be reduced by 20.2% compared to the existing HVAC system.

Chen et al. [21] analyzed the possibilities and energy effects of the application of adiabatic humidification for HVAC systems of selected cleanrooms. They indicated the system "spray nozzles using high-pressure water atomization" as the most advantageous in the case of adiabatic humidification. Xu et al. [22] presented the results of research on the efficiency of FFU fans. The evaluation criteria were the TPE (total pressure efficiency) and EPI (energy performance index) values. They proved that greater energy efficiency is usually associated with larger fans. Energy consumption for the various HVAC system structures of operating theaters was one of the criteria for multicriteria evaluating these systems presented by Fan et al. [23]. By solving the MCDM (multicriteria decision-making) problem, the authors proved a relationship between energy consumption, ventilation effectiveness and user satisfaction. Research in this area, especially with regards to recirculation and heat recovery, was also carried out by Ozyogurtcu et al. [24], who analyzed the energy consumption of four different HVAC systems in hospital operating rooms. They proved that the optimal energy is the HVAC system with a recuperator and regulated air recirculation.

The research on the optimization of the structure of the cooling system for HVAC systems of cleanrooms was conducted by Jia et al. [25]. The authors investigated two free cooling systems integrated with the central cooling system: tap water and cooling tower. They proved that the COP coefficients of a tap water free cooling system were about 7.4 and 2.2 times higher than that of mechanical cooling and tower cooling systems. In turn, the results of research on the optimization of an integrated cooling and heat generation system for HVAC systems in an electronics factory were presented by Zheng and Li [26]. The authors developed the GMEL (Grade Match Between Energy and Load) method that allows for the optimal use of cold and waste heat for the mutual compensation of loads. For the case study, they achieved energy savings of 26.7/52.4% in the summer and winter, respectively.

Research on the optimization of the control of HVAC systems of cleanrooms with the structure MAU + DCC was led by Wang et al. [27], demonstrating savings of 7.09% compared to the classic PDI controller. In turn, Zhuang et al. [28] developed and implemented an energy-optimized control strategy for multizone HVAC systems in a pharmaceutical plant on a simulation platform, achieving 20% energy savings compared to the standard control strategy.

A series of papers dedicated to research concerning the energy-optimal control of a HVAC system for cleanrooms, mainly in the pharmaceutical industry, was published by Zhuang, Wang and Shan [3,29–31].

In paper [29], the authors presented a probabilistic method of optimal control of HVAC systems based on the ADV strategy ("Adaptive Full-Range Decoupled Ventilation Strategy"). They proved that the implementation of this strategy makes it possible to reduce the annual average energy cost compared to the DV (Dedicated Outdoor Air Ventilation), PD (Partially Decoupled Control) and IC (Interactive Control) strategies by 18.2%, 13.6% and 6.5%, respectively.

In another study [31], the authors showed savings of 6.8 ÷ 40.8% as a result of the implementation of the ADV over IC strategy.

Using a simulation platform, Zhuang et al. [30] also tested and implemented the ADV strategy for a HVAC system for cleanrooms of a pharmaceutical factory in Hong Kong. In this case, they proved that the implementation of this strategy makes it possible to reduce the annual energy consumption by 21.64%, 15.63% and 7.77%, respectively, compared to the PD, IC and DV strategies.

In paper [3], the authors addressed solving the problem of energy-optimal control of a multizone HVAC system of a classic structure (MAU + AHU) and different loads in individual zones (rooms). They proposed the Coordinated Demand—Controlled Ventilation (CDCV) strategy, the implementation of which made it possible to reduce the demand for reheating by 89.6% and to reduce the total energy demand by 63.3%.

In turn, Chang et al. [32] investigated six strategies for controlling a cleanroom HVAC system, indicating the energy-optimal variant. They proved that the setting of the required room temperature is of key importance here; increasing this temperature by 1 ◦C resulted in a reduction of energy consumption by 1%. Loomans et al. [33,34] and Molnaar [35], on the other hand, simulated and experimentally tested three ventilation strategies in pharmaceutical cleanrooms: Fine-tuning, DCF (Demand Controlled Filtration) and Optimizing airflow pattern. They proved that, using the DCF strategy, it is possible to reduce the energy consumption of fans by up to 70% and 93.6% in the case studies under consideration.

Shao et al. [36] investigated experimentally the effect of airflow reduction as a factor of reducing energy consumption on the relative concentration of particles in a cleanroom. The obtained results and correlations allowed for optimal energetic determination of the air stream as a function of the cleanliness class of the room.

To summarize the current state of research concerning the optimization of HVAC system for cleanrooms, the following can be stated:


Therefore, there is a methodological gap at the stage of determining the set of acceptable structures of HVAC systems of cleanrooms fulfilling the functional function described by: cleanliness class, temperature, relative humidity, air velocity, degree of turbulence, overpressure, concentration of pollutants and share of outside air.

At the same time, there is a need to undertake research on support tools in order to determine, from a set of acceptable variants, the optimal structure and algorithms of HVAC system control.

Therefore, for the needs of the application, methods and tools are sought that allow, at the starting point, to define a set of acceptable structures of HVAC systems on the basis of output data—the standard parameters defining the utility function, decision variables and limiting conditions. Next, relationships are sought on the basis of which optimal structures and algorithms for controlling HVAC systems can be determined. In applications, it is important that the arguments in these relations are constant parameters constituting the output data in the optimization procedure.

The aim of the presented paper is to calculate approximating functions describing optimal structures of the HVAC system for cleanrooms depending on key constant parameters (arguments): cleanliness class (Cs), percentage of outdoor air (αo) and unit cooling load (qj) and determination of the energy-optimal control algorithms for heat recovery options and the outdoor climate. The annual unit primary energy demand of the HVAC system for thermodynamic air treatment was adopted as the objective function.

The proposed method is an original approach, both from the scientific and the application points of view.

#### **2. Research Problem, General Algorithm**

Every HVAC system can be described by a vector with coordinates defined by constant parameters and decision variables. With regards to cleanrooms, the constant parameters are primarily temperature, relative humidity, cleanliness class, percentage of outdoor air, unit cooling load and pressure gradients.

For determined combinations of constant parameters values of a HVAC system, a single optimization problem can be defined concerning calculating the optimal HVAC system for which the annual energy demands (final, primary) reach the minimum values.

The constant parameters of a HVAC system for cleanrooms are within realistic value ranges. In general, one can define a set of combinations of constant parameter values in which each constant parameter takes values representing the entire range of variability.

The research problem comes down to calculating the set of optimal structures of a HVAC system assigned to combinations of values of constant parameters representing realistic ranges of variability of these parameters in cleanrooms.

On this basis, it is possible to calculate approximating relations defining structures of HVAC systems as a function of combinations of constant parameter values.

The general algorithm of the optimization procedure partly based on the methodology presented earlier by the authors of References [37,38] is presented in Figure 1. The algorithm includes:

	- combinations of decision variables values xj for normalizing constant parameters (matrices **W**i, **W**, **G**i, **G**<sup>j</sup> and **W**g) and
	- the HVAC system (matrices **X**<sup>J</sup> , **G** and **X**);

Constant parameters are by definition invariant in the optimization procedure, but in general, they can be functions of both time and space. The decision variables change during the optimization procedure and are the arguments of the x describing the HVAC system, the constraint conditions and the objective function. The fragment of the procedure in Figure 1, leading to the determination of the set of acceptable HVAC system structures, the **X** matrix, is based on the methodology described in detail in Reference [37]. After determining the **X** matrix, in the next step of the optimization procedure, the real required ranges for the variability of key fixed parameters in cleanroom applications, are determined: cleanliness class (Csk), share of outside air (αok) and unit cooling load (qjk). Then, on this basis, a representative set of combinations of the values of the key parameters of the HVAC system constants is determined, and for each of these combinations, the optimal structure of the HVAC system x∗ ngk is determined based on an algorithm from the set of permissible structures (**X** matrices). In the next step, on the basis of the obtained results, the general algorithm assumes the development of approximating relations defining energy-optimal structures of HVAC systems as a function of key constant parameters x∗ ngk = f(Csk, αok, qjk). In the final stage of the optimization procedure, the objective function is determined—the minimum annual demand for primary energy for thermodynamic treatment, the optimal type of heat recovery for various outdoor climate options and the energy-optimal control algorithms.

The algorithm structure of the general optimization procedure includes three basic steps:


**Figure 1.** Optimization procedure—general algorithm.

### **3. Acceptable Structures of HVAC System**

The starting point in determining the permissible structures of the HVAC system is the determination of a set of parameters standardized by this system. A wide range of normalized constant parameters in a cleanroom was used:


The procedure leading to the determination of acceptable structures of the HVAC system based on the methodology previously developed by the authors of Reference [37] is presented in Appendix A. This procedure uses system analysis and matrix calculus. The forms of the determined matrices are listed in Appendix A; these matrices are described in the following order:


Acceptable variants xng of the structure of the HVAC system for cleanrooms are presented synthetically in a form of a general model in Figure 2. .

Vo, . Vc, . V, . Ve, . V1, . V2, ΔV—volume stream of outdoor air, processing air, supply air, exhaust air, external recirculation air, internal recirculation air and balance sheet difference. . . . .

α<sup>o</sup> = Vo . <sup>V</sup> , <sup>α</sup><sup>c</sup> <sup>=</sup> Vc . <sup>V</sup> , <sup>α</sup><sup>1</sup> <sup>=</sup> V1 . <sup>V</sup> , <sup>α</sup><sup>2</sup> <sup>=</sup> V2 . <sup>V</sup> —percentage of outdoor air, processing air, external recirculation air and internal recirculation air;

E1, E2, E3—filtration efficiency of the 1◦, 2◦ and 3◦ stages;

HR—heat recovery.

Acceptable variants xng of the HVAC system include:

x1—CAV air system without recirculation:


x2—CAV air system with external recirculation:


x3—CAV air system with internal recirculation (room):


x4—CAV system with external and internal recirculation (room):


In variants x3 and x4, alternatives to internal recirculation RU (RDCU) are: FFU (FFU + DCC) or FFU + FDCU.

**Figure 2.** General model of the acceptable variants of structures of the HVAC system for cleanrooms: x1—without recirculation (α<sup>1</sup> = 0, α<sup>2</sup> = 0, α<sup>o</sup> = 1); x2—with external recirculation (α<sup>1</sup> = 0, α<sup>2</sup> = 0); x3—with internal recirculation (α<sup>1</sup> = 0, α<sup>2</sup> = 1); x4—with external and internal recirculation (α<sup>1</sup> = 0, α<sup>2</sup> = 0). Variants of internal recirculation (α<sup>2</sup> = 0): (**a**) RU or RDCU, (**b**) FFU or FFU + DCC, (**c**) FFU + FDCU.

#### **4. Optimal Structures of HVAC System**

*4.1. Optimal Structure Selection Algorithm*

The calculation algorithm of the optimal structure of the HVAC system is shown in Figure 3. The starting point includes constant parameters of the HVAC system and set of acceptable variants xng ∈ X. Selection of the optimal structure of the HVAC system is a permissibility function of recirculation (hygienic function) and values of three air streams:

**Figure 3.** *Cont*.

**Figure 3.** Calculation algorithm of the optimal structure of the HVAC system.


In case recirculation is not allowed, the only system acceptable is x1; if allowed, all systems are possible: x1, x2, x3 and x4.

Unit stream of outdoor air . Vjo, depending on the conditions, is within the range corresponding to the percentage of outdoor air α<sup>o</sup> = 5 ÷ 100%.

Unit air stream as a function of the cleanliness class . Vjs is calculated based on the average air speed from the range (wmin, wmax) required for a specific room cleanliness class according to ASHRAE [39]. Unit air stream for discharging cooling loads using AHU is calculated—taking into consideration the designations in Figure 4—using relation:

$$
\dot{\mathbf{V}}\_{\rm jc} = \frac{\dot{\mathbf{q}}\_{\rm jc}}{\rho c\_{\rm P} \Delta t\_{\rm SC}},
\tag{1}
$$

whereby: .

$$
\dot{\mathbf{q}}\_{\rm jc} = \mathbf{q}\_{\rm j} - \mathbf{q}\_{\rm jDC} \tag{2}
$$

with:

qj—unit cooling loads;

qjc—unit cooling load discharged using AHU;

qjDC—unit cooling load discharged by dry coolers in the recirculation circuit (DCC, RDCU and RCU).

**Figure 4.** Isotherms characteristic for calculating the . Vjc (AHU) air stream.

In a specific case, when . qjDC = 0

$$
\dot{\mathbf{q}}\_{\dot{\mathbf{p}}} = \dot{\mathbf{q}}\_{\dot{\mathbf{p}}} \tag{3}
$$

In the first step, requirement . Vjc = min (corresponding to the minimum energy consumption) implies relation:

$$
\Delta \mathbf{t}\_{\text{SC}} = \Delta \mathbf{t}\_{\text{SC,max}} - \delta \mathbf{t}\_{\text{SC}} = (\mathbf{t}\_{\text{R}} - \mathbf{t}\_{\text{DP}}) - \delta \mathbf{t}\_{\text{SC}} \tag{4}
$$

which means that

$$\mathbf{t}\_{\mathbf{SC}} = \mathbf{t}\_{\mathbf{SCmin}} = \mathbf{t}\_{\mathbf{DP}} + \delta \mathbf{t}\_{\mathbf{SC}} \tag{5}$$

where:

δtSC—realistic tolerance range with temperature tSC in relation to temperature tDP, δtSC = (0 ÷ 1) ◦C

tDP—dew point temperature.

In the physical interpretation, this requirement means that the minimum air flow to dissipate cooling loads . Vjc is determined assuming the maximum possible temperature difference ΔtSC between the air in the room and the supply air. In turn, the minimum supply air temperature tSCmin is theoretically equal to the dew point temperature tDP; in practice, it should be slightly higher (here, the real tolerance range δtSC was adopted). .

Then, on the basis of the values of air flows . Vjs, Vjc and . Vjo, which are comparative terms, the algorithm determines the optimal structure of the HVAC system x1, x2, x3 or x4, and the resulting temperature difference ΔtR and the supply temperature tS are calculated according to the relations:

• system x1 (α<sup>1</sup> = 0, α<sup>2</sup> = 0, α<sup>c</sup> = 1):

$$
\Delta \mathbf{t}\_{\mathbb{R}} = \Delta \mathbf{t}\_{\mathbb{S}\mathbb{C}} \tag{6}
$$

$$\mathbf{t}\_{\mathbf{S}} = \mathbf{t}\_{\mathbf{S}\mathbf{C}} \tag{7}$$

• system x2 (α<sup>1</sup> = 0, α<sup>2</sup> = 0, α<sup>c</sup> = 1):

$$
\Delta \mathbf{t}\_{\mathbb{R}} = \Delta \mathbf{t}\_{\mathbb{S}\mathbb{C}} \tag{8}
$$

tS = tSC (9)

• system x3 (α<sup>1</sup> = 0, α<sup>2</sup> = 0, α<sup>c</sup> = 0):

$$
\Delta \mathbf{t}\_{\mathbb{R}} = \boldsymbol{\alpha}\_{\mathbb{C}} \cdot \Delta \mathbf{t}\_{\mathbb{S}\mathbb{C}} = (1 - \boldsymbol{\alpha}\_{\mathbb{Z}}) \cdot \Delta \mathbf{t}\_{\mathbb{S}\mathbb{C}} \tag{10}
$$

$$\mathbf{t\_{S}} = \boldsymbol{\alpha}\_{\text{c}} \cdot \mathbf{t\_{SC}} + (1 - \boldsymbol{\alpha}\_{\text{c}}) \, \mathbf{t\_{R}} \tag{11}$$

$$\mathbf{t}\_{\rm SC} = \frac{1}{\alpha\_{\rm c}} \cdot \mathbf{t}\_{\rm S} + (1 - \frac{1}{\alpha\_{\rm c}}) \cdot \mathbf{t}\_{\rm R} \tag{12}$$

• system x4 (α<sup>1</sup> = 0, α<sup>2</sup> = 0, α<sup>c</sup> = 0):

$$
\Delta \mathbf{t}\_{\rm R} = \boldsymbol{\alpha}\_{\rm C} \cdot \Delta \mathbf{t}\_{\rm SC} = \begin{pmatrix} 1 \ - \ \boldsymbol{\alpha}\_{2} \end{pmatrix} \Delta \mathbf{t}\_{\rm SC} \tag{13}
$$

$$\mathbf{t\_{S}} = \boldsymbol{\alpha}\_{\text{c}} \cdot \mathbf{t\_{SC}} + (1 - \boldsymbol{\alpha}\_{\text{c}}) \, \mathbf{t\_{R}} \tag{14}$$

$$\mathbf{t}\_{\rm SC} = \frac{1}{\alpha\_{\rm c}} \cdot \mathbf{t}\_{\rm S} + (1 - \frac{1}{\alpha\_{\rm c}}) \cdot \mathbf{t}\_{\rm R} \tag{15}$$

whereby:

$$
\alpha\_{\mathbb{C}} = 1 \, - \, \alpha\_{\mathbb{Z}} = \alpha\_{\mathbb{O}} + \alpha\_{1} \tag{16}
$$

In the next step, a significant limitation is the relationship resulting from the air distribution system required in the room:

$$
\Delta \mathbf{t}\_{\mathbb{R}} \le \Delta \mathbf{t}\_{\mathbb{S}\mathbb{C}} \tag{17}
$$

indirectly related to relation:

$$\mathfrak{tsC} \le \mathfrak{ts} \tag{18}$$

and a comparative section:

$$
\Delta \mathbf{t}\_{\rm R} \le \Delta \mathbf{t}\_{\rm Rmax} \tag{19}
$$

It should be noted that the maximum value of the temperature difference

$$
\Delta \mathbf{t}\_{\text{Rmax}} = \mathbf{t}\_{\text{R}} - \mathbf{t}\_{\text{Smin}} \tag{20}
$$

is the result of comfort limitations (air supply system) and, indirectly, of the room cleanliness class.

At this stage, it may turn out that the determined temperature difference ΔtSC, which corresponds to the air stream . Vjc = min, is greater than the permissible temperature difference ΔtRmax for comfort or technological reasons. In such a case, the algorithm assumes a decrease in the value of the temperature difference ΔtSC according to the relation:

$$
\Delta \mathbf{t}\_{\text{SC}} \equiv \Delta \mathbf{t}\_{\text{SC}} - \delta \mathbf{t} \tag{21}
$$

with:

δt = (0.5 ÷ 1.0) ◦C—iterative temperature jump, and the procedure is repeated.

Based on the algorithm (Figure 3), the optimal variants of the HVAC system structure of cleanrooms were determined as a function of the relationship between the streams . Vjs, . Vjc and . Vjo; these variants are summarized in Table 1.

**Table 1.** Optimal variants of the HVAC structure x∗ <sup>n</sup><sup>g</sup> of clean air as a function of the relation of streams . Vjs, . Vjc and . Vjo.


#### *4.2. Optimal Structure Selection Algorithm*

By analyzing realistic required ranges of variability of the key constant parameters in applications for cleanrooms, the following conclusions can be made:


Therefore, further analyses include variants of combinations of key constant parameters of a HVAC system, in which each constant parameter takes values representing the mentioned variability ranges.

#### *4.3. Approximating Functions*

Optimal structures of the HVAC system for cleanrooms are calculated based on the algorithm in Figure 3 for representative variants of combinations of key constant parameters: cleanliness class Cs, unit cooling load qj (qj = qjc) and percentage of outdoor air α<sup>o</sup> are shown in Table 2. The analyses were performed with the temperature of tR = +22 ◦C and relative humidity ϕ<sup>R</sup> = (50 ± 5)%.


**Table 2.** Optimal structures of the HVAC system for cleanrooms x∗ ng .

1/ w = 0.25 m/s (300 1/h, H = 3 m), 2/ w = 0.06 m/s (72 1/h, H = 3 m), 3/ w = 0.025 m/s (30 1/h, H = 3 m) [39], 4/ <sup>α</sup>os = Vjo/Vjs, 5/ <sup>α</sup><sup>o</sup> = Vjo/Vj, 6/ qj = qjc and 7/ <sup>Δ</sup>tSCmax = 11 ◦C.

The unit air stream . Vjs as a function of the cleanliness class Cs was determined by assuming the average air velocities from the compartments assigned to the ASHRAE cleanliness classes [39].

For cleanliness classes with optimal structures of the HVAC system x3 or x4 based on the results in Table 2, limit percentages of the outdoor air αog were calculated (equal to the percentages of air of an AHU for discharging cooling loads). Value αog is calculated using:

$$\alpha\_{\rm og} = \frac{\dot{\mathbf{V}}\_{\rm jc}}{\dot{\mathbf{V}}\_{\rm js}} \tag{22}$$

These values represent the selection criterion of the optimal structure of the HVAC system according to relation:

$$
\alpha\_{\mathcal{O}} \ge \alpha\_{\mathcal{O}} \text{optimal structure} \; \overleftarrow{\mathbf{x}}\_{\mathcal{O}} \tag{23}
$$

$$
\alpha\_{\text{o}} < \alpha\_{\text{og}} \text{optimal structure} \; \overline{\text{x}}\_{4} \tag{24}
$$

For cleanliness classes that include the optimal HVAC structures x2, x3 and x4 (here, ISO Class 8)—based on the results in Table 2—an additional limit unit cooling load . qjg was calculated using relation: .

$$
\dot{\mathbf{q}}\_{\rm jg} = \dot{\mathbf{V}}\_{\rm js} \rho \mathbf{c}\_{\rm p} \Delta t \mathbf{S} \mathbf{C}\_{\rm max} \tag{25}
$$

In the physical interpretation, parameter . qjg is the maximum cooling load that can be discharged by the air flow . Vjc <sup>=</sup> . Vjs resulting from the room cleanliness class.

Values . qjg represent the selection criteria of the optimal structure of the HVAC system according to relation: .

$$\dot{\mathbf{q}}\_{\dot{\mathbf{q}}} \ge \dot{\mathbf{q}}\_{\dot{\mathbf{q}}} \text{optimal structure } \overline{\mathbf{x}}\_2 \tag{26}$$

$$
\dot{\mathbf{q}}\_{\mathbf{j}} < \dot{\mathbf{q}}\_{\mathbf{j}\text{\textquotedblleft optimal structure }} \overline{\mathbf{x}}\_{\mathbf{3}} \text{ or } \overline{\mathbf{x}}\_{\mathbf{4}} \tag{27}
$$

The parameter calculation results <sup>α</sup>og and . qjg are shown in Table 3.

**Table 3.** Limit percentages of the outdoor air <sup>α</sup>og and limit unit cooling load . qj for optimal structures of the HVAC system.


\*/ in applications . qj <sup>&</sup>lt; . qjg, \*\*/ is not calculated, because the optimal structure of the HVAC system is x2 . Vj <sup>=</sup> . Vjk .

Based on the calculation results presented in Tables 2 and 3, the authors calculated the approximating functions in the form of diagrams illustrating zones of optimal structures of the HVAC system for cleanrooms.

These functions, in coordinate system x∗ <sup>n</sup><sup>g</sup> = f(CS, αo, qj) for cleanliness classes ISO Class 5, ISO Class 7 and ISO Class 8, are shown in Figure 5.

**Figure 5.** The function x∗ <sup>n</sup><sup>g</sup> = f(CS, αo, qj) of the zone of optimal structures of the HVAC system for cleanrooms ISO Class 5 (M3.5—cl. 100), ISO Class 7 (M5.5—cl. 10,000) and ISO Class 8 (M6.5—cl. 100,000).

Directional coefficients of limit lines equations between zones of the optimal structures x3 and x4 in Figure 5 were calculated based on the data in Table 3 and relation:

$$\mathbf{a} = \frac{\Delta \dot{\mathbf{q}}\_{\mathrm{j}}}{\Delta \alpha\_{\mathrm{og}}} \tag{28}$$

Δ . qj —difference in values of the unit cooling loads in Table 3;

Δαog—difference of the limit value of the percentage of outdoor air in Table 3 assigned to a defined difference <sup>Δ</sup> . qj .

Based on calculation results (Tables 2 and 3) illustrated by the approximating functions x∗ <sup>n</sup><sup>g</sup> = f(CS, αo, qj) in Figure 5, the following conclusions can be made:

	- a = 33.3—for ISO Class 5 (M3.5—cl.100);
	- a = 8.0—for ISO Class 7 (M5.5—cl.10,000);
	- a = 3.33—for ISO Class 8 (M6.5—cl.100,000),

ness classes. The limit line in system . qj = f(αo) between the zone of optimal structures x2 and x3 or x2 and x4 is ordinate . qjg (horizontal line). For cleanliness classes ISO Class 8 (M6.5—cl. 100,000) the limit unit cooling load equals . qjg = 332 W/m2. For unit cooling loads . qj <sup>≥</sup> . qjg, the optimal structure of the HVAC system is a system with external recirculation x2, while, for . qj <sup>&</sup>lt; . qjg, optimal structures are systems with internal recirculation x3 or systems with internal and external recirculation x4. The limit of division of optimal zones x3 and x4 is line . qj = aαo.

6. Approximating functions in the form of a graph x∗ <sup>n</sup><sup>g</sup> = f(CS, αo, qj) with zones of optimal structures of the HVAC system for cleanrooms in Figure 5 are of great application significance at the stage of selecting and designing energy-efficient HVAC systems of such rooms. Based on cleanliness class Cs of unit cooling loads . qj and the percentage of outdoor air αo, they make it possible to unambiguously calculate an energy-optimal structure of a HVAC system for a cleanroom. For "middle" cleanliness classes between ISO5 and ISO7, zones of optimal HVAC structures can be calculated using interpolation.

#### **5. Heat Recovery, Energy-Optimal Control**

#### *5.1. Objective Function, Simulation Models*

For each HVAC system with energy-optimal structure x∗ ng , where heat recovery occurs as a cumulative variable, it is possible to calculate an objective function defining the quantitative optimization criterion.

Based on this criterion, the energy-optimal type of the heat recovery and energyoptimal control algorithms are determined.

The objective function defines the annual primary energy demand of the HVAC system, which is possible to calculate using relation [37]:

$$\mathbf{E\_{P}} = \frac{\mathbf{w\_{H}}}{\eta\_{\rm H,t}} \cdot \mathbf{Q\_{H,n}} + \frac{\mathbf{w\_{el}}}{\eta\_{\rm el,t}} \cdot \mathbf{Q\_{el,n}} + \frac{\mathbf{w\_{C}}}{\eta\_{\rm C,t}} \cdot \mathbf{Q\_{C,n}} + \frac{\mathbf{w\_{B}}}{\eta\_{\rm B,t}} \cdot \mathbf{Q\_{B,n}} + \mathbf{w\_{el}} \mathbf{E\_{el,pom}} \tag{29}$$

or

$$\mathbf{E\_{p}} = \mathbf{w\_{H}}\mathbf{Q\_{K,H}} + \mathbf{w\_{el}}\mathbf{Q\_{K,H\_{el}}} + \mathbf{w\_{C}}\mathbf{Q\_{K,C}} + \mathbf{w\_{B}}\mathbf{Q\_{K,B}} + \mathbf{w\_{el}}\mathbf{E\_{el,pm}}\tag{30}$$

whereby:

$$\mathbf{Q}\_{\rm K,H} = \frac{1}{\eta\_{\rm H,t}} \mathbf{Q}\_{\rm H,n} \tag{31}$$

$$\mathbf{Q\_{K,H\_{el}}} = \frac{1}{\eta\_{\mathrm{H\_{el},t}}} \mathbf{Q\_{H\_{el},n}} \tag{32}$$

$$\mathbf{Q}\_{\mathbf{K}, \mathbf{C}} = \frac{1}{\eta\_{\mathbf{C}, \mathbf{t}}} \mathbf{Q}\_{\mathbf{C}, \mathbf{n}} \tag{33}$$

$$\mathbf{Q}\_{\mathbf{K},\mathbf{B}} = \frac{1}{\mathbf{r}\_{\mathbf{B},\mathbf{t}}} \mathbf{Q}\_{\mathbf{B},\mathbf{n}} \tag{34}$$

with:

QH,n (QHel,n)—annual heat demand (net) of water heaters (electric heaters), kWh/ym2; QC,n—annual cold demand (net) of cooler, kWh/ym2;

QB,n—annual heat demand (net) of steam humidifiers, kWh/ym2;

QK,H (QK,Hel)—annual final energy demand of water heaters (electric heaters)—final heat kWh/ym2;

QK,C—annual final energy demand of coolers—final cold, kWh/ym2;

QK,B—annual final energy demand of steam humidifiers—final heat of humidifiers, kWh/ym2; Eel,pom—annual demand for final electrical energy for the drive of auxiliary devices, kWh/ym2;

ηH,t—seasonal average total efficiency of a heating system with water air heaters, ηH,t = ηH,g ηH,s ηH,d ηH,e, with ηH,t = 0.81 (ηH,g = 0.90—generation, ηH,s = 1.0—accumulation, ηH,d = 0.94—distribution and ηH,e = 0.95—regulation and control);

ηHel,t—seasonal average total efficiency of a heating system with electric heaters, with ηHel,t = 0.95;

ηC,t—seasonal average total efficiency of a system with air coolers; ηC,t = ESEER ηC,s ηC,d ηC,e, with ηC,t = 3.0 (ESEER = 3.5—European Seasonal Energy Efficiency Ratio, ηC,s = 0.95—accumulation, ηC,d = 0.94—distribution and ηC,e = 0.97—regulation and control); ηB,t—seasonal average total efficiency of a heating system for supplying steam humidifiers, ηB,t = ηB,g ηB,d ηB,e (ηB,g—generation, ηB,d—distribution and ηH,e—regulation and control), with ηB,t = 0.95;

wi—input coefficient of nonrenewable primary energy for generation and providing the final energy carrier (or energy) (wH—concerns heat, wC—concerns cold, wB—concerns steam, wel—concerns electrical energy) with wH = 1.1—gas/oil boiler, wC = 3.0—chiller with electrical drive and wB = 3.0—electric steam generator).

The energy demand (net) of heaters, coolers and steam humidifiers is calculated using algorithms of energy-optimal thermodynamic air treatment according to the following criterion:

$$\mathbf{f\_c = \sum\_{i=1}^{n} \dot{\mathbf{m\_i}} \Big| \Delta \mathbf{h\_i} \Big| = \min} \tag{35}$$

where:

. mi—mass stream in i-operation;

Δhi—change of the specific enthalpy in i-operation.

Tools for calculating the objective function are simulation models of the operations of HVAC systems throughout the year. Algorithms of these models were presented in papers [37,38], while, for the presented application, the general algorithm of the simulation model is shown in Figure 6.

The starting point of the general algorithm are the output data on the basis of which the family of characteristic boundary isotherms is determined. Then, for each acceptable variant of the HVAC structure, algorithms for optimal air treatment are determined and the annual demand for net energy, auxiliary energy and primary energy corresponding to these algorithms. In conclusion, the optimal variant is determined.

#### *5.2. Objective Function, Simulation Models*

The objective functions were defined for representative variants of the HVAC system for cleanrooms with energy-optimal structures x∗ 1, x<sup>∗</sup> 2, x<sup>∗</sup> <sup>3</sup> and x<sup>∗</sup> <sup>4</sup> (Figure 2), respectively; the variants are shown in Table 4.

As decision variables, the optimization algorithm includes: p—the type of heat recovery and q—external climate.

**Figure 6.** General algorithm of the simulation model for x∗ ng of the HVAC system.




1/ According to Table 2; 2/ p = 1—rotary energy regenerator (RRt), <sup>φ</sup><sup>t</sup> = const. (stepless regulation), p = 2—rotary enthalpy regenerator (RRx), φ<sup>t</sup> = const., φ<sup>x</sup> = const. (stepless regulation), p = 3—cross-flow or countercurrent exchanger with bypass (R+ bypass), φ<sup>t</sup> = φtmax or φ<sup>t</sup> = 0, p = 4—crossflow or countercurrent exchanger with bypass and electric preheater (Hel+ R + bypass) and p = 5—no heat recovery and 3/ q = 1, 2, 3—continental climate, subarctic and subtropical [41].

In calculations based on the simulation models [37], the following assumptions and output data were considered:


As a result, component Eel,pom in Equations (29) and (30) is defined as:

$$\mathbf{E}\_{\rm el,pom} = \Delta \mathbf{E}\_{\rm R} = \frac{\dot{\mathbf{v}}\_{\rm o} \Delta \mathbf{p}\_{\rm HR}}{\eta\_{\rm W}} \cdot \mathbf{r} \cdot 10^{-3} \text{ } \rm kWh/y/m^2 \tag{36}$$

with:

ΔER—final energy demand for forcing through by heat recovery exchangers.

Considering energy inputs for forcing through air by heat recovery exchangers is necessary for evaluating the energy profitability of applying such exchangers.

Omission of the energy demand for fans as a component of the objective function (29) can be justified as follows:


### *5.3. Algorithms of Energy-Optimal Control*

For representative variants of the HVAC system shown in Table 4, the structures of which are shown in Figure 2, algorithms of energy-optimal control were defined in accordance with criterion (35). The algorithms are shown in Figures 7–10.

**Figure 7.** ISO8 variant (**a**) x∗ <sup>11</sup> − x<sup>∗</sup> <sup>12</sup>, (**b**) x<sup>∗</sup> <sup>13</sup> − x<sup>∗</sup> <sup>14</sup>, (**c**) x<sup>∗</sup> <sup>15</sup> (without recirculation).

**Figure 8.** ISO8 variants (**a**) x∗ <sup>21</sup> − x<sup>∗</sup> <sup>22</sup>, (**b**) x<sup>∗</sup> <sup>23</sup> − x<sup>∗</sup> <sup>24</sup> and (**c**) x<sup>∗</sup> <sup>25</sup> (external recirculation).

**Figure 9.** ISO5 variants (**a**) x∗ <sup>31</sup> − x<sup>∗</sup> <sup>32</sup>, (**b**) x<sup>∗</sup> <sup>33</sup> − x<sup>∗</sup> <sup>34</sup> and (**c**) x<sup>∗</sup> <sup>35</sup> (internal recirculation).

For the identification of zones of optimal thermodynamic treatment of air in Figures 7–10 h–x, the following designations are used:

(MR)—maximum heat recovery, (VR)—regulated heat recovery, H1—heating (preheater), H2—heating (secondary heater), Hel—heating (electric heater), C —sensible cooling (without drying), C—cooling with drying, B—steam humidification and R—recirculation.

At the same time, the following designations of the characteristic points are used (Figure 2):

R—air condition in the room, S—condition of air supplied to the room, SC—air condition downstream AHU and D—air condition at the cooler surface.

**Figure 10.** ISO7 variants (**a**) x∗ <sup>41</sup> − x<sup>∗</sup> <sup>42</sup>, (**b**) x<sup>∗</sup> <sup>43</sup> − x<sup>∗</sup> <sup>44</sup> and (**c**) x<sup>∗</sup> <sup>45</sup> (external and internal recirculation).

Equations of the limit isotherms and limit lines between the zones of optimal thermodynamic treatment of air in Figures 7–10 h–x take the following form:

• isotherm tS

$$\mathbf{t}\_{\rm S} = \mathbf{t}\_{\rm R} - \frac{\mathbf{q}\_{\rm j}}{\dot{\mathbf{V}}\_{\rm j} \rho c\_{\rm P}} \tag{37}$$

• isotherm tSC

$$\mathbf{t}\_{\rm SC} = \mathbf{t}\_{\rm R} - \frac{\mathbf{q}\_{\rm j}}{\dot{\mathbf{V}}\_{\rm jc} \rho \mathbf{c}\_{\rm p}} \tag{38}$$

• isotherm tG

$$\mathbf{t}\_{\rm G} = \mathbf{t}\_{\rm R} - \frac{1}{\alpha\_{\rm O}} (\mathbf{t}\_{\rm R} - \mathbf{t}\_{\rm S}) \tag{39}$$

• isotherm tG

$$\mathbf{t}\_{\mathbf{G}'} = \mathbf{t}\_{\mathbf{R}} - \frac{\mathbf{t}\_{\mathbf{R}} - \mathbf{t}\_{\mathbf{S}}}{\alpha\_{\mathbf{o}} (1 - \phi\_{\mathbf{t}\_{\max}})} \tag{40}$$

• isotherm tG

$$\mathbf{t}\_{\mathbf{C}^{\prime\prime}} = \frac{\mathbf{t}\_{\mathbf{G}} \left( \frac{\mathbf{w}\_{\mathbf{H}}}{\eta\_{\mathbf{H},\mathbf{t}}} + \frac{\mathbf{w}\_{\mathbf{C}}}{\eta\_{\mathbf{C},\mathbf{t}}} \right) - \frac{\mathbf{w}\_{\mathbf{C}}}{\eta\_{\mathbf{C},\mathbf{t}}} \phi\_{\mathbf{t}} \mathbf{t}\_{\mathbf{R}}}{\frac{\mathbf{w}\_{\mathbf{H}}}{\eta\_{\mathbf{H},\mathbf{t}}} + \frac{\mathbf{w}\_{\mathbf{C}}}{\eta\_{\mathbf{C},\mathbf{t}}} (1 - \phi\_{\mathbf{t}})} \tag{41}$$

• limit line (MR)C/(MR)CH2—x11

$$\mathbf{t}\_{\mathbf{x}\mathbf{g}} = \frac{1}{1 - \phi\_{\mathbf{t}}} \left( \frac{\mathbf{x} - \mathbf{x\_{D}}}{\mathbf{x\_{S\_{2}}} - \mathbf{x\_{D}}} \mathbf{t\_{S}} - \frac{\mathbf{x} - \mathbf{x\_{S\_{2}}}}{\mathbf{x\_{S\_{2}}} - \mathbf{x\_{D}}} \mathbf{t\_{D}} \right) - \frac{\phi\_{\mathbf{t}}}{1 - \phi\_{\mathbf{t}}} \mathbf{t\_{R}} \tag{42}$$

• limit line (MR)C/(MR)CH2—x12

$$\mathbf{t}\_{\rm xg} = \frac{(\mathbf{t}\_{\rm S} - \mathbf{t}\_{\rm D}) \left[ \mathbf{x} - \boldsymbol{\Phi}\_{\rm x} \left( \mathbf{x} - \mathbf{x}\_{\rm R\_2} \right) - \mathbf{x}\_{\rm D} \right] - \left( \boldsymbol{\Phi}\_{\rm t} \mathbf{t}\_{\rm R} - \mathbf{t}\_{\rm D} \right) \left( \mathbf{x}\_{\rm S\_2} - \mathbf{x}\_{\rm D} \right)}{\left( 1 - \boldsymbol{\Phi}\_{\rm t} \right) \left( \mathbf{x}\_{\rm S\_2} - \mathbf{x}\_{\rm D} \right)} \tag{43}$$

• limit line C/CH2

$$\mathbf{t}\_{\mathbf{x}\mathbf{g}} = \mathbf{t}\_{\mathbf{D}} + (\mathbf{t}\_{\mathbf{S}} - \mathbf{t}\_{\mathbf{D}}) \frac{\mathbf{x} - \mathbf{x}\_{\mathbf{D}}}{\mathbf{x}\_{\mathbf{S}\_2} - \mathbf{x}\_{\mathbf{D}}} \tag{44}$$

• limit line (MR)C/(MR)CH2R—x31

$$\mathbf{t}\_{\rm Zg} = \frac{1}{1 - \phi\_{\rm t}} \left( \frac{\mathbf{x} - \mathbf{x\_D}}{\mathbf{x\_{R\_3}} - \mathbf{x\_D}} \mathbf{t\_R} - \frac{\mathbf{x} - \mathbf{x\_{R3}}}{\mathbf{x\_{R\_3}} - \mathbf{x\_D}} \mathbf{t\_D} \right) - \frac{\phi\_{\rm t}}{1 - \phi\_{\rm t}} \mathbf{t\_R} \tag{45}$$

$$\mathbf{x}\_{\text{R}\_{\text{B}}} = \mathbf{x}\_{\text{D}} + (\mathbf{x}\_{\text{S}\_{2}} - \mathbf{x}\_{\text{D}}) \frac{\mathbf{t}\_{\text{R}} - \mathbf{t}\_{\text{D}}}{\mathbf{t}\_{\text{SC}} - \mathbf{t}\_{\text{D}}} \tag{46}$$

• limit line (MR)C/(MR)CH2R—x32

$$\mathbf{t}\_{\rm xg} = \frac{(\mathbf{t}\_{\rm SC} - \mathbf{t}\_{\rm D}) \left[ \mathbf{x} - \boldsymbol{\phi}\_{\rm x} (\mathbf{x} - \mathbf{x}\_{\rm R2}) - \mathbf{x}\_{\rm D} \right] - (\boldsymbol{\phi}\_{\rm t} \mathbf{t}\_{\rm R} - \mathbf{t}\_{\rm D}) (\mathbf{x}\_{\rm R\_2} - \mathbf{x}\_{\rm D})}{(1 - \boldsymbol{\phi}\_{\rm t}) (\mathbf{x}\_{\rm R\_2} - \mathbf{x}\_{\rm D})} \tag{47}$$

• limit line CR/CH2R

$$\mathbf{t}\_{\mathbf{x}\mathbf{g}} = \mathbf{t}\_{\mathbf{D}} + \frac{\mathbf{t}\_{\mathbf{SC}} - \mathbf{t}\_{\mathbf{D}}}{\mathbf{x}\_{\mathbf{S}\_2} - \mathbf{x}\_{\mathbf{D}}} (\mathbf{x} - \mathbf{x}\_{\mathbf{D}}) \tag{48}$$
