EFFECT OF HVAC SYSTEM SIZE ON THE OPTIMUM INSULATION THICKNESS OF THE BUILDINGS IN DIFFERENT CLIMATE ZONES

Thermal insulation is one of the most effective methods of reducing energy consumption in buildings. Therefore, the parameters influencing the optimum insulation thickness are widely investigated. In this study, the optimum insulation thickness is obtained using the life cycle analysis method and the genetic algorithm by considering the size of the heating and cooling systems as an optimization variable, which has not been addressed in the earlier researches. Furthermore, the effect of the climate conditions on the optimum insulation thickness is comprehensively studied using five different climate zones, including Hot-Dry, Cold-Dry, Moderate-Humid, Hotsemi Humid, and Hot-Humid. It is found that the optimum thickness of expanded polystyrene insulation increases between 5%-19% considering the size variation of the heating systems including the central heating system and wallhung gas boilers. By size variation of the cooling systems including the evaporative cooler and split air conditioner, this increase is between 8-19%. This is because the cost reduction due to the reduction of the required size of the heating and cooling systems can be expended for insulating the building with larger thickness which results in lower energy consumption. Based on the obtained results, the energy cost saving increases between 3.5%-14.5% and also, the payback period decreases about 1 to 3 months, depending on the considered heating and cooling systems and climate zone. The results confirm that the optimum insulation thickness can be determined with significant inaccuracy, ignoring the size variation of the heating and cooling systems as a result of thermal insulation.


INTRODUCTION
Energy consumption is rapidly increasing due to increasing population, urbanization, migration to large cities and improvement in standard of living [1]. Using the energy saving methods, improving the existing technologies [2][3][4] or returning to renewables [5,6] are an excellent approaches to reduce the energy consumption, which is distributed among four main sectors: industrial, building (residential/commercial), transportation and agriculture [7]. Having 40% of all Europe's energy consumption, the building sector is the largest energy consumer following the industrial sector and 63% of this share is assigned to residential buildings [8]. In many countries, the energy required for space heating and cooling in buildings has the highest share of all and particularly in Iran, 42% of the country's energy is consumed in buildings [9].
Because of the limited energy-sources and environmental pollution coming from using the fuels, the energy saving has become unavoidable [10]. The thermal insulation of building is one of the most effective methods to preserve energy and reduce energy consumption of the buildings [11]. For that reason, there are many studies about determining the optimum thickness of the insulation and the parameters affecting it. An important factor influences the optimum insulation thickness for the buildings is the weather conditions. Liu et al. [12] investigated the optimum insulation thickness for an exterior wall in hot-humid climate areas of China. The results show that the optimum thickness for extruded polystyrene (XPS) is between 5.3 to 6.9 cm and for EPS is between 8.1 and 10.5 cm. Using thermoeconomic analysis method, Dombayci et al. [13] found that the optimal thickness of EPS for Turkish cities of Ankara, Izmir, Trabzon, and Kars is 4.6 cm, 7.7 cm, 6 cm and 10.7 cm, respectively. Also, the highest and lowest energy savings were obtained in Kars with 56.6% and in Izmir with 27%. Nematchoua et al. [14] compared the optimum insulation thickness of wall in equatorial and tropical climates. They reported that the optimum insulation thickness for south orientation in equatorial region was 0.03 lower than that for In this study, the optimum insulation thickness is analyzed and compared considering the heating, ventilating and air conditioning (HVAC) system size as an optimization variable, which are neglected in the previous studies, in different climate zones including Cold-Dry, Moderate-Humid, Hot-Dry, Hot-semi Humid, and Hot-Humid. A wide variety of HVAC systems are used in residential buildings, which makes it difficult to choose the HVAC system for investigation. To make the results of this research more applicable, more widely used systems have been selected, including four different centralized and decentralized heating and cooling systems, which are the central heating system, wall-hung gas boiler, evaporative cooler and split air conditioner. After estimation of building heating and cooling load using Design Builder software, the optimum insulation thickness is determined using the genetic algorithm. The effect of size variation of the HVAC system on the energy cost savings and the payback period are also considered.

PROTOTYPE BUILDING
The prototype building is chosen from the Mehr Mass-Housing Construction project which is a typical residential building in Iran with 4-story and 16 apartment units. Every apartment's area is 95m^2 and the overall foundation is 1397m^2. The ground floor contains the parking, storerooms and the janitor room and every apartment contains two bedrooms, a bathroom, a washroom and a kitchen. The photo and the floor plan of the prototype building is shown in Figure 1. In this study, the building external walls ( Figure 2) are considered as a composite structure, which is generally formed with bricks in the middle, plaster layers on both sides, insulation material on the inside of the brick layer and granite on the most outside layer. The window-to-wall ratio is 32.5% for both northern and southern walls, while for eastern and western walls the ratio is 4.5%. The characteristics of the materials used in the elements of the building are listed in Table 1.

HVAC SYSTEM
HVAC systems, depending on the location of the primary equipment, can be classified into two major types of central system or decentralized or local system. Conditioning entire building as a whole unit is performed by a central system, whereas a decentralized system conditions separately a specific zone as part of a building.
In this paper, various HVAC systems are selected and compared in terms of the effect on the optimum insulation thickness. As heating systems, a central heating system and a wall-hung gas boiler, and as cooling systems, two decentralized cooling systems including evaporative cooler and split air conditioner are used to satisfy the thermal comfort of occupants in the prototype building. It should be noted that the cooling load of the prototype building is not high enough to use the central cooling system. Based on the required capacity and the system manufacturer, the efficiency of the central heating systems and the wall-hung gas boilers, used as the HVAC systems in this study, lies in the range of 75 -86%, 79-89%, respectively. The coefficient of performance (COP) of the split air conditioners varies from 2 to 2.8 and the efficiency of the evaporative coolers is 51 -53%. More information about HVAC systems used in this study can be found in Table 2.

CLIMATE ZONES
In this study, the effect of the outdoor design conditions, required for the thermal load estimation of the prototype building, on the optimum insulation thickness is also considered. Figure 3 displays five different climate zones of Iran including Hot-Dry, Hot-Humid, Hot-semi Humid, Cold-Dry, and Moderate-Humid which were classified based on the outdoor design conditions [28]. In this study, one city of each climate zone is selected: Isfahan from Hot-Dry zone, which is the largest climatic zone of Iran, Abadan from Hot-Semi Humid zone, Bandar Abbas from Hot-Humid zone, Tabriz from Cold-Dry zone and Rasht from Moderate & Humid zone. Tehran is also selected because of its importance as the capital of Iran with approximately 8.3 million populations and 3.3 million houses which have a large share in the energy consumption of Iran. Characteristics of the selected cities are presented in Table 3.

METHODOLOGY Thermal Load Estimation
In this paper, the cooling and heating loads of the prototype building are calculated using Design Builder 5.5. Design Builder software is high-quality, easy-to-use simulation software that helps you to quickly assess the environmental performance of new and existing buildings, graphically. The energy simulation engine of this software is Energy Plus 8.6 which is built by U.S Department of energy and is one of the most accurate software on the energy basis and has a very high calculation accuracy. The model of the prototype building and plan view including kitchens, bedrooms, bathrooms, halls, guestrooms and stairways in Design Builder software are depicted in Figure 4. All thermal loss or gain caused by heat transfer from/to the walls and glazing, infiltration or ventilation, internal loads, solar heat gain are considered for estimating loads. Internal loads including cooking, computer, TV, refrigerators, wash machine, etc. with time schedule have been considered. Lights are assumed LED with power of 7.5 W/m2. For all residential areas of the building such as bedrooms, halls and reception rooms, kitchens, bathrooms, and sanitary facilities, the temperatures required for the thermal comfort (22℃ in winter and 26℃ in summer) is specified. For all spaces of the apartment, the details of time schedule including the number of occupants, their kind of activities and clothing and the number hours of their residence in the considered space are also determined. In addition to the precise definition of exterior and interior walls, ceiling and floor of units and the ceiling referred to the highest floor, the material and dimensions of all doors and windows were determined. The windows by different dimensions for the living room, the bedroom and the kitchen were selected from a double-walled type. The wooden doors for each unit measured 2m×1m. Four people are considered in every apartment: three with adult metabolism and one with child metabolism. To validate the modeling, a four-story building in Tehran that manually calculated by Gholizadeh et al. [34] is simulated again in Design Builder and the calculated thermal loads are compared in Figure 5. As can be seen, the results from Design Builder are very close to manual results by an approximate error of 3.7% which proves the accuracy of the modeling method.

P1-P2 Method
Optimization methods have important role in different research fields of the thermal engineering [35][36][37]. One of the most common economic analysis methods is life cycle cost (LCC) analysis in which the time value of money considered and the detailed consideration of the complete range of costs is implemented [38,39]. In this study, the P_1-P_2 method which is one of the LCC analysis methods is used for optimizing the insulation thickness. In this method, all of the economic parameters are concentrated into the two economic indicators named P_1 and P_2. The first indicator (P_1) is the ratio of the life-cycle fuel cost to the first year fuel cost. A low value of P_1 indicates that fuel costs are high and that consequently, potential fuel savings are important. The second indicator (P_2) is the ratio of life cycle expenditures incurred as a result of the additional investment to the initial investment [20]. A high value Journal of Thermal Engineering, Research Article, Vol. 8, No. 2, pp. xx-xx, March, 2022 8 of P_2 indicates that the investment has a low first cost but higher costs over the life of the equipment. The equations for P_1 and P_2 are defined as (Nematchoua et al. 2015): is the ratio of the annual maintenance and operation cost to the original first cost, is the ratio of the resale value to the first cost.
can be taken as 1 if the maintenance and operation cost is zero [20]. If the inflation rate d is equal to the interest rate i, then becomes [40]: The cost of insulation is given by: is the cost of insulation in $/m 2 and is the cost of insulation in $/ . The life cycle cost (LCS) over the life time can be formulated with -method as: is the energy cost, which is calculated using the heating and cooling loads obtained from Design Builder model, the efficiency of the heating and cooling systems and the fuel (electricity or natural gas) cost. In Table  4, the financial parameters used in this study are listed. The data are taken from the market and the official websites of Central bank, Ministry of Energy and National Iranian Gas Company (NIGC) in 2017 (Central bank of the Islamic republic of Iran, Ministry of Energy, National Iranian Gas Company).
In this study, the HVAC system size is considered as an optimization variable; therefore, the capital investment made by reducing the system size ( ) should be deducted from the total insulation cost [41]: is the total cost of insulation. It is clear that when the thickness of the insulation increases, the quantity ( − ) also increases and ( ) decreases. As a result, first decreases, drops to a minimum, and then increases. To calculate LCS in this case, Eq. (6) should be substituted in Eq. (5) and the following equation is used instead: The optimum value of LCS can be determined by maximizing Eq. (7). It should be noted that is calculated using the cost of the HVAC systems in the market. To study the effect of system size, all simulations are performed once with a fixed HVAC system size, similar to the previous studies. Afterwards, the HVAC system size varies in each simulation, so that a new HVAC system is selected by increasing the insulation thickness, because the building thermal load reduces, and as a result, the required size of HVAC system decreases. The energy consumption of the new HVAC system is then calculated, which affects the obtained optimum insulation thickness. Payback periods for different insulation thicknesses are derived from the LCS graphs over the life time of 10 years by comparing each case with the uninsulated case [42]. Genetic Algorithm Optimization By using MATLAB's optimization toolbox and the genetic algorithm method, both optimum values of insulation thickness and LCS are obtained. Genetic algorithms search parallel from a population of points. Therefore, it has the ability to avoid being trapped in local optimal solution like traditional methods, which search from a single point. On the other hand, Genetic algorithms use probabilistic selection rules, not deterministic ones. Since the genetic algorithm was used to solve the optimization problem, a fitness function must be selected. The fitness function is the sum of capital and operating costs of the system. The optimization variable is the insulation layer thickness. To find the total cost function, annual simulations need to be done for each insulation layer thickness. For this reason, both genetic algorithm and Energy Plus software must work simultaneously. Initially, each layer thickness is simulated using Design Builder software. Then, the required outputs are imported to the genetic algorithm in MATLAB. The initial population of genetic algorithm is 9. For all cases, the algorithm converged on a solution before the 51st generation. Parameters used inside the toolbox are as follows: the maximum number of generations is taken to be 100, crossover function as two-point because it is the most accurate among all crossover functions and mutation function as constraint dependent. Figure 6 indicates the variation of best fitness and mean fitness for a life time of 10 years for wall-hung boilers in Tehran. The value of LCS can be calculated by subtracting the best fitness value in which is the minimum total cost from the total cost of the uninsulated case. It can be seen that the total cost value is considerably higher for the case in which the system size is fixed (Figurer 6 (a)) than when the system size variation is considered (Figurer 6 (b)). The flowchart of the calculation process in this study, from calculating thermal loads to getting final results, is illustrated in Figurer 7.

RESULTS AND DISCUSSION
In Figures 8-11, the effect of insulation thickness on the energy cost (Cen), insulation cost (Cins) and total cost (Cins+ Cen) using the HVAC system with a fixed size and also, insulation cost (Cins-Cpt) and total cost (Cins -Cpt + Cen) with considering the size variation of HVAC system is shown in different climate zones. It is found that both total cost (Cins+ Cen and Cins -Cpt + Cen) reduces initially with insulation thickness but after reaching the lowest value, there is an increasing trend with insulation thickness in all climate zones and by using all HVAC systems. This is because the energy cost decreases drastically even at low insulation thickness, whereas the insulation cost is practically small in the small thicknesses. As the insulation thickness and consequently, the insulation cost, increases, the energy cost decreases slightly; therefore, the total costs increases. This trend is the same in the cities of Tehran and Isfahan, both of which located in Hot-Dry zone. Looking Figure 8 (c) and 9 (c), it is observed that, in Tabriz (Cold-Dry zone), the increasing trend after reaching the lowest value is slow using both heating systems, because the heating load in this zone is high and the reduction of energy costs with insulation is so significant that the higher optimum insulation thicknesses can be used in comparison with the other cities. It should be noted that in Abadan (Hot-semi Humid) and Bandar Abbas (Hot-Humid), the increasing trend after reaching the lowest value occurs in the lower optimum insulation thickness comparing with other cities; this is because of the lower heating load in these zones, which requires in the lower optimum insulation thickness.
It is interesting to note that the higher optimum insulation thickness is obtained considering the reduction of the HVAC system size, because the cost reduction due to the system size can be expended for insulating the building with larger thickness which results in lower energy consumption. Looking Figure 8 (a), it is seen that the total cost of 1500 $ is obtained using the optimum insulation thickness of 5.6 cm; whereas, by reducing the size of the central heating, the total cost of 850 $ is obtained using the optimum insulation thickness of 6.4 cm. The optimum insulation thickness of 7.3 cm by total cost of 2300 $ (see Figure 8(c)) and 2.1 cm by total cost of 500 $ (see Figure 8 (f)) are obtained in Cold-Dry zone (Tabriz) and in Hot-Humid zone (Bandar Abbas), respectively. Because of the same climate conditions, the results for Tehran and Isfahan are approximately similar.
Comparison of Figure 9 with Figure 8 shows that the optimum insulation thickness using the wall-hung gas boiler is higher than that using the central heating system, because the initial cost of the central heating system is slightly higher than that of the wall-hung gas boiler and also because of the easier choice and purchase of decentralized systems, which have low heat capacities and cost. This difference between the initial cost of the central heating system and wall-hung gas boiler can be used for higher insulation thickness. For example, the optimum insulation thickness is 6.4 cm for central heating system and 6.5 cm for wall-hung gas boiler, considering the effect of reducing the cost of heating system by insulation for Tehran. However, due to the life time of 10 years, the thickness difference is negligible.  Figure 9. Effect of insulation thickness on life cycle costs using wall-hung gas boiler Figure 10 illustrates the effect of insulation thickness on the different costs using the split air conditioner. It is observed that the lowest optimum insulation thickness (2.3 cm) and total cost ($ 420) is obtained in Cold-Dry zone (Tabriz), while the highest optimum insulation thickness (7.1 cm) and total cost ($ 2400) belongs to the Hot-Humid zone (Bandar Abbas). In Figure 11, the variation of costs by the insulation thickness using an evaporative cooler as a cooling system is shown. It should be noted that the evaporative cooler is not applicable in the zones of Moderate-Humid, Hot-semi Humid and Hot-Humid, due to the high outdoor air humidity. It is also clear that the two cities of Tehran and Isfahan have very close optimum insulation thickness as a result of similar heating and cooling loads. Table 5 shows the required HVAC system size for supplying the building thermal load in two cases without insulation and with the optimum insulation thickness in all climate zones. As can be seen, the insulation of building significantly reduces the required HVAC system size. For example, the size (capacity) of the wall-hung gas boilers reduces from 24 kW to 16 kW in Tehran. This size reduction is from 10.5 kW to 3.5 kW using the split air conditioner for supplying the building cooling load in Abadan, which causes considerable energy savings regarding the electricity cost.
(b) Hot-Dry (Isfahan) (a) Hot-Dry (Tehran) (c) Cold-Dry (Tabriz) Figure 11. Effect of insulation thickness on life cycle costs using evaporative cooler  Figure 12 shows the effect of the insulation thickness on the energy cost savings for all heating and cooling systems and different climate zones over a life time of 10 years. As previously mentioned, in all climatic zones, because the initial cost of the centralized heating system is more than the decentralized one, as well as by increasing the insulation thickness and reducing the heating load, the decentralized heating system are more flexible in reducing capacity and initial costs than the centralized heating system; therefore, the larger optimum insulation thickness and the higher energy cost saving can be expected using the wall-hung gas boiler. For instance, in Rasht, the optimum insulation thickness considering the cost reduction effect due to the smaller size of heating system, for the central heating system is 5.5cm with an energy cost saving of 4008$ and for the wall-hung gas boiler is 6.3 cm with energy cost saving of 4298 $. The results show that the thermal insulation of building walls concerning cooling loads results in more significant energy cost saving compared that concerning heating loads in climate zones of Iran.
A summary of the results of Figures 8-12 including the optimum insulation thicknesses, energy cost savings and also, payback periods are listed in Table 6. It is interesting to note that the energy cost saving increases by about 5% and 11% by size variation of the central heating system for Hot-Dry (Isfahan) and Cold-Dry (Tabriz) climate zones, respectively. This increase is about 14.5% and 6% by size variation of the wall-hung gas boiler for Cold-Dry (Tabriz) and Hot-Dry (Isfahan& Tehran) climate zones, respectively. The energy cost saving by size variation of cooling systems is obtained about 10.7% for Hot-Dry climate zone (Isfahan) and about 10.3% for Hot-Humid climate zone (Bandar Abbas). In all climate zones, the payback period decreases about 1-3 months considering the size variation of heating and cooling systems, respectively. Results show that considering system size as an optimization variable led to a reduction of energy consumption from 2% to 14.5% depending on the HVAC system and climate zone.
Since it is generally necessary to introduce one insulation thickness for the buildings in different climate zones, and to introduce two or more insulation thicknesses due to the difference in air temperature or humidity in cold or hot seasons of the year is not practical, one optimum insulation thickness for different combinations of heating and cooling systems (considering the larger and the most effective thickness in the considered climate zone) is listed in Table 7.

CONCLUSION
In this paper, the effect of size variation of HVAC system by increasing the insulation thickness has been investigated at different climate zones. The findings can be summarized as follows:  By reducing the HVAC system size as a result of thermal insulation, the higher optimum insulation thickness and thus, the lower energy consumption is obtained.  Using central heating system, the optimum insulation thickness with and without considering the size variation of the HVAC system in climate zones of Cold-Dry, Moderate-Humid, Hot-Dry, Hot-semi Humid, and Hot-Humid increases 12.3%, 12.7%, 9.5%, 14.2% and 10%, respectively. Using wall-hung gas boiler, the increases are 13.5%, 12.5%, 6%, 9% and 9.5%, respectively.  Using evaporative cooler, the optimum insulation thickness with and without considering the size variation of the HVAC system in climate zones of Cold-Dry and Hot-Dry increases 10.5% and 9.3%, respectively. Using split air conditioner, the increases are 6.6%, 6.6%, 5%, 9.4% and 10.3%, respectively.  Considering the size reduction of HVAC system by thermal insulation, the maximum increase of the energy cost saving is obtained 14.5% using the wall-hung gas boiler as a heating system in Cold-Dry climate zone (Tabriz). The energy cost saving increases 10.3% using split air conditioner in Hot-Humid climate zone (Bandar Abbas).  In all climate zones, the payback period decreases about 5% -6% considering the size variation of heating and cooling systems.  Based on the results, ignoring the size variation of the HVAC system as a result of thermal insulation leads to a significant inaccuracy in determining optimum insulation thickness.  The proposed calculation process in this study can be used for more accurate determination of the optimum insulation thickness which affects the building energy consumption significantly.  As the future works, the optimum insulation thickness can be obtained by the proposed calculation process using other heating and cooling systems such as absorption chiller and floor heating systems. Furthermore, the effect of other building types, the building orientation and the window-to-wall ratio on the optimum insulation thickness, along with the effect of HVAC system size, can be considered.