Integrated Optimization Method of External Wall Insulation for Granaries in Different Climate Regions in China

Abstract

The use of thermal insulation material in building envelopes is closely related to economic benefits, energy-savings, and carbon reduction of buildings. The construction forms of different components in building envelopes have an important influence on the optimization design of thermal insulation in building envelopes. In this study, an integrated optimization approach is proposed to search for the best solution of thermal insulation in external walls and the optimal combination scheme of different construction forms of envelope components in granaries. The integrated optimization approach consists of an orthogonal experimental design (OEDM) method-based determination module of an optimal combination scheme of different construction forms of components, an assessment model-based quantitative analysis module, and an integrated assessment indicator-based selection module of the best solution of external wall insulation. Firstly, the OEDM method is used to determine the optimal combination scheme of different construction forms of the foundation wall of an external wall, thermal insulation material, external window, roof, and floors in buildings. Secondly, integrated economic, energy, and carbon analysis models are developed to analyze comprehensive performance of external wall insulation. Finally, an integrated assessment indicator consisting of an energy balanced index, a carbon balanced index, and weight coefficients is presented to determine the best solution of external wall insulation. The applications of this optimization approach in different ecological grain storage zones in China demonstrated that the outdoor air temperature characteristics could affect the comprehensive performance of external wall insulation in granaries, significantly. The best solution of external wall insulation in granaries in Turpan city, Daqing city, Kaifeng city, Changsha city, Anshun city, and Danzhou city was expanded polystyrene insulation (EPS) with a layer thickness of 0.078 m, 0.048 m, 0.083 m, 0.089 m, 0.062 m, and 0.131 m, respectively. The greatest difference in the lowest entire construction cost and the lowest carbon emission of external wall insulation among different typical climate regions in China was 12.987 USD/m² and 6.3 kgCO2e/m², respectively.

1. Introduction

Both food security and building carbon emission reduction are national policies of China [1,2]. Low-temperature grain storage demonstrates significant advantages in ensuring grain quality, reducing grain storage losses, and minimizing pollution through physical temperature control methods. Low-temperature grain storage is an important development direction of green grain storage technology. However, the temperature difference between indoor air temperature and outdoor air temperature is large, so the energy consumption of low-temperature grain storage is high. The thermal performance of a building envelope has a significant impact on the energy consumption of grain storage. Different design schemes of building sectors and applications of thermal insulation material have important influence on the thermal performance of the building envelope [3,4,5]. Therefore, studies on energy-saving techniques and carbon reduction design methods of buildings are very meaningful.

The building energy conservation techniques and carbon reduction methods have been a hot research field in recent years. Li et al. [6] presented a multi-system coupled interactive optimization design framework for building layout towards low-carbon emission. Torabi et al. [7] proposed a design-compatible approach for decreasing carbon emissions in buildings based on design exploration methods and parametric calculations of whole-life carbon emissions. Cheng et al. [8] presented an intelligent and interpretable method for multi-objective low-carbon self-compacting concrete design. Kathiravel and Feng [9] presented a structural and embodied carbon performance optimization method for low-carbon buildings based on building an information modeling method. Lu and Deng [10] presented an open building information model-based approach for assessing the marginal abatement cost of these low-carbon measures. Shi et al. [11] presented a two-phase framework integrating parametric modeling for solving carbon-energy-daylight trade-offs problems by using multi-objective genetic algorithms. Li et al. [12] presented a cavity-enclosed structure design method for building facades to improve the carbon sequestration performance of alkali-activated materials. Jimenez et al. [13] proposed a cost-efficient and low-carbon facade prototype for buildings. Wu et al. [14] used a data-driven method and multi-objective optimization approach to search for the best design scheme of recycled aggregate concrete proportion. Existing research showed that the low-carbon optimization design schemes for buildings in the early design stage have better energy-saving and emission reduction effects than retrofitting existing buildings [15,16,17].

The low-carbon design of building envelopes is not a novel issue in the sustainable development of buildings [18,19]. However, some problems of low-carbon design for building envelopes remain unsolved. Firstly, a building envelope is composed of various building components. The effect of different combination schemes of different construction forms of components in building envelopes on building energy conservation and carbon reduction remains unclear [20,21]. Such as, external wall type, thermal insulation material type, external window type, roof type, and floor type. Secondly, there are significant differences in outdoor air temperature and conditions among different climate regions in China. The optimization design scheme of building envelopes should be dynamically adjusted according to the different outdoor air temperature and conditions in different climate regions [22,23]. However, the impacts of outdoor air temperature and conditions in different climate regions on the optimization design of building envelopes were not comprehensively considered in existing studies. Finally, optimization design of thermal insulation in building envelopes concerns the economic, energy conservation, and carbon reduction issues. Some researchers have begun to solve the multi-objective optimization problem of building insulation by using various methods in recent years [24,25]. However, studies on the integrated optimization design methods of building insulation are still insufficient [26,27,28], considering economic, energy conservation, and carbon reduction issues simultaneously. There is still a lack of integrated evaluation indicators that can be used to search for the best insulation design scheme of building envelopes [29,30,31].

Granary building is a type of industrial building. Thermal insulation material as a popular energy-saving method has gradually been used in building envelopes of granaries [32], such as roof insulation [32], active insulation systems with pipe-embedded envelopes [33], phase change material-based building envelopes [34], and building envelope insulation [35,36,37]. One challenge of the previous studies lies in that the optimization design method of envelope insulation in granary buildings is a multi-objective optimization problem. There are significant differences in the construction forms of envelope components in granaries [38,39]. The influence of different construction forms of envelope components in granaries on the optimization design of thermal insulation of envelopes in granary buildings should be considered. Previous studies have largely concentrated on the economic benefits, energy conservation, and carbon-saving of thermal insulation in building envelopes separately [40,41,42], overlooking the optimal combination scheme of different construction forms of components and the multi-objective optimization problem of building insulation. Addressing this research gap, an integrated optimization approach is proposed in this study to search for the best solution of thermal insulation in external walls and the optimal combination scheme of different construction forms of envelope components in granaries. The best solution of external wall insulation in granaries in different climate regions in China has been investigated by using the proposed integrated optimization approach. The innovations and main contributions of this study are as follows: (1) the optimal combination scheme of different construction forms of components in building envelopes is determined by using the orthogonal experimental design method (OEDM); (2) integrated economic, energy, and carbon emission analysis models are developed to analyze comprehensive performance of external wall insulation; and (3) the best solution of external wall insulation for granaries in different climate regions in China are determined by comparing the values of a new integrated evaluation indicator.

2. Methodology

2.1. Overview of the Integrated Optimization Approach for External Wall Insulation

An integrated optimization approach is proposed in this paper to search for the best solution of external wall insulation and the optimal combination scheme of different construction forms of components in building envelopes. Figure 1 shows the flowchart of selecting the best solution of external wall insulation. The integrated optimization approach consists of an OEDM-based determination module of different construction forms of components in building envelopes, an assessment model-based quantitative analysis module, and an integrated assessment indicator-based selection module of the best solution for external wall insulation. Firstly, an OEDM method is utilized to determine the optimal combination scheme of different construction forms of foundation wall of external wall, thermal insulation material, external window, roof, and floor in buildings. The OEDM method only requires a small number of representative experiments to cover the main combinations of different influence factors, which can significantly reduce the number of experiments. Secondly, integrated economic, energy, and carbon analysis models are developed to analyze comprehensive performance of external wall insulation. Embodied energy and embodied carbon of insulation material are considered in the energy and carbon analysis models of external wall insulation in buildings. Finally, an integrated assessment indicator consisting of an energy balanced index, a carbon balanced index, and weight coefficients is proposed to determine the optimal design scheme of external wall insulation. The best solution of external wall insulation is obtained when the value of the integrated assessment indicator is the lowest.

In the presented integrated optimization approach, optimal combination scheme of different construction forms of building components, economic benefit, carbon emission, and energy consumption of external wall insulation is determined by using the general orthogonal experimental design method, LCA-based economic analysis model, carbon emission factor method, and energy consumption simulation software, respectively. The assigned energy and carbon weight coefficients of the integrated assessment indicator can be determined according to actual engineering needs. Therefore, the presented integrated optimization approach can be applied to building external walls in different climate regions and different thermal insulation materials.

2.2. Determination of Optimal Combination Scheme of Different Construction Forms of Components

Orthogonal experimental design is an efficient multi-factor optimization method based on the mathematical statistical method. An OEDM method uses a standardized orthogonal table to organize multi-factor experiments and conducts statistical analysis on their experimental results. The OEDM method only requires a small number of representative experiments to cover the main combinations of different influence factors, which can significantly reduce the number of experiments. The orthogonal experimental design table is represented by $L_n\left(m^k\right)$. $n$ represents the number of experiments. $k$ represents the number of variables (factors). $m$ represents the number of values (levels) for each factor. The selected factors are randomly filled in the columns of the orthogonal experimental design table. Subsequently, the calculation scheme can be optimized and arranged through an orthogonal table at the given level of each factor. Finally, in order to select the optimal experimental combination, a range analysis is conducted on the experimental results to evaluate the strengths and weaknesses of various factors and levels. The range calculation formula is as follows:

$$R_i=\max \left(k_{i1},\hspace{1em}{k}_{i2},\dots k_{ij}\right)-\min \left(k_{i1},k_{i2},\dots k_{ij}\right)$$

(1)

where c indicates the range value of the $i\mathrm{th}$ factor. $k_{ij}$ indicates the mean of the $i\mathrm{th}$ factor and the $j\mathrm{th}$ level. The larger the value of each factor, the higher the importance of the corresponding factor to the experimental results.

The OEDM method is utilized in this study to determine the optimal combination scheme of different construction forms of foundation wall of external wall, thermal insulation material, external window, roof, and floor in granaries. The OEDM-based determination module of different construction forms of components in building envelopes consists of the following five steps.

Step 1: Representative and influential factors for OEDM are selected as the experimental factors and levels of the orthogonal experimental design table.

Step 2: A proper orthogonal experimental design table is determined based on the number of factors and the number of levels. The frequency of occurrence of levels in each factor is the same. The frequency of occurrence of ordered logarithms of levels in any two columns is the same.

Step 3: According to the orthogonal experimental design table, factors and levels are combined for obtaining experimental plans. Energy consumption simulations are conducted to obtain the simulation results according to experimental plans.

Step 4: Simulation results of orthogonal design experiments are analyzed, and the primary and secondary effects of each factor on the indicators are quantified by using range analysis.

Step 5: The optimal combination of factors and levels are obtained based on the above analysis results.

2.3. Integrated Economical, Energy, and Carbon Analysis Models of External Wall Insulation

2.3.1. Energy Analysis Model of External Wall Insulation in Granary

The embodied energy of thermal insulation material ($E_{\mathrm{em}}$) has an impact on energy conservation effect of external wall insulation in granary. Energy consumption of external wall insulation ($E_{\mathrm{tot}}$) consists of embodied energy and energy consumption due to the external wall cooling load ($E_{\mathrm{coo}}$) in relation to 1 m² of the wall area.

$$E_{\mathrm{tot}}=E_{\mathrm{coo}}+E_{\mathrm{em}}$$

(2)

$$E_{\mathrm{coo}}={\displaystyle \frac{Q_{\mathrm{coo}}\cdot \Delta h_{\mathrm{coo}}}{COP}}$$

(3)

$$E_{\mathrm{sav}}={\displaystyle \frac{Q_{\mathrm{coo}\cdot \Delta h_{\mathrm{coo}}}}{COP}}({\displaystyle \frac{1}{R_{\mathrm{wall}}}}-{\displaystyle \frac{1}{R_{\mathrm{wall}}+\frac{x_{\mathrm{ins}}}{{\lambda }_{\mathrm{ins}}}}})-E_{\mathrm{em}}\cdot x_{\mathrm{ins}}\cdot {\rho }_{\mathrm{ins}}$$

(4)

where $E_{\mathrm{sav}}$ represents energy conservation due to external wall insulation, kwh/m²; $Q_{\mathrm{coo}}$ represents external wall cooling load, W; $\Delta h_{\mathrm{coo}}$ indicates total operating time of the air-conditioning system throughout a whole year, h; $COP$ indicates the coefficient of performance of air-conditioning system; $R_{\mathrm{wall}}$ indicates external wall thermal resistance, (m²·K)/W; $x_{\mathrm{ins}}$ indicates thickness of external wall insulation, m; ${\rho }_{\mathrm{ins}}$ indicates density of external wall insulation, kg/m³; ${\lambda }_{\mathrm{ins}}$ indicates coefficient of thermal conductivity of insulation material, W/(m·K).

2.3.2. Economic Analysis Model of External Wall Insulation in Granary

Economic benefit and total construction cost are two key indicators for evaluating the economic performance of the roof and external wall insulation [43]. The total construction cost in the whole life-cycle ($P_{\mathrm{total}}$) consists of initial investment in external wall insulation ($P_{\mathrm{ins}}$) and economic cost caused by external wall cooling load ($P_{\mathrm{coo}}$) in relation to 1 m² of the wall area [44].

$$P_{\mathrm{total}}=K_1\cdot P_{\mathrm{coo}}+K_2\cdot P_{\mathrm{ins}}$$

(5)

$$K_1=\left\{\begin{array}{cc}{\displaystyle \frac{1}{f-i}}\left[1-{({\displaystyle \frac{1+i}{1+f}})}^{N_{\mathrm{e}}}\right]& f\ne i\\ {\displaystyle \frac{N_{\mathrm{e}}}{1+i}}& f=i\end{array}\right.$$

(6)

$$K_2=D+(1+D)\cdot {\displaystyle \frac{PWF(N_{\min },0,f)}{PWF(N_l,0,m)}}+M_{\mathrm{s}}\cdot PWF(N_{\mathrm{e}},i,f)-{\displaystyle \frac{R_{\mathrm{v}}}{{(1+f)}^{N_{\mathrm{e}}}}}$$

(7)

where $K_1$ represents the ratio of reduced economic cost of energy consumption in whole lifecycle to that of the first year; $K_2$ represents the ratio of additional economic cost of external wall insulation to the starting capital; $PWF$ represents discount coefficient; $P_{\mathrm{coo}}$ indicates economic cost caused by external wall cooling load, USD/m²; $f$ indicates the prevailing rate used in financial markets, %; $D$ represents deposit percentage, %; $i$ represents rate of price increase, %; $M_{\mathrm{s}}$ refers to the ratio of economic cost of maintenance to starting capital; $R_{\mathrm{v}}$ indicates the ratio of second-hand price of insulation to starting capital; $N_{\min }$ refers to the short-term economic analysis, year; $N_{\mathrm{e}}$ refers to life-cycle period, year; $m$ refers to loan interest rate, %.

Equation (8) is utilized to calculate economic benefit for external wall insulation ($C_{\mathrm{sav}}$).

$$C_{\mathrm{sav}}=K_1\cdot O_{\mathrm{e}n}\cdot ({\displaystyle \frac{Q_{\mathrm{coo}}\cdot \Delta h_{\mathrm{coo}}}{COP}})({\displaystyle \frac{1}{R_{\mathrm{wall}}}}-{\displaystyle \frac{1}{R_{\mathrm{wall}}+\frac{x_{\mathrm{ins}}}{{\lambda }_{\mathrm{ins}}}}})-K_2\cdot x_{\mathrm{ins}}\cdot O_{\mathrm{v}}$$

(8)

where $O_{\mathrm{en}}$ represents electricity price; $O_{\mathrm{v}}$ represents insulation material price, USD/m³.

Equation (9) is utilized to calculate optimum thickness of external wall insulation ($x_{\mathrm{opt}}$).

$$x_{\mathrm{opt}}={\displaystyle \frac{\sqrt{\frac{R_{\mathrm{wall}}^2\cdot {\lambda }_{\mathrm{ins}}\cdot K_1\cdot O_{en}\cdot \Delta T\cdot \Delta h_{\mathrm{coo}}}{K_2\cdot O_{\mathrm{v}}\cdot COP\cdot {10}^3}}-R_{\mathrm{wall}}^2\cdot k_{\mathrm{ins}}}{R_{\mathrm{wall}}}}$$

(9)

where $\Delta T$ represents indoor–outdoor temperature difference, K.

2.3.3. Carbon Analysis Model of External Wall Insulation in Granary

Carbon emission of external wall insulation ($C{E}_{\mathrm{total}}$) includes embodied carbon for insulation material ($C{E}_{\mathrm{emb}}$) and carbon emission caused by external wall cooling load ($C{E}_{\mathrm{coo}}$) in relation to 1 m² of the wall area.

$$C{E}_{\mathrm{total}}=C{E}_{\mathrm{coo}}+C{E}_{\mathrm{emb}}$$

(10)

$$C{E}_{\mathrm{coo}}={\displaystyle \frac{Q_{\mathrm{coo}}\cdot \Delta h_{\mathrm{coo}}\cdot CEF}{COP\cdot (R_{\mathrm{wall}}+\frac{x_{\mathrm{ins}}}{{\lambda }_{\mathrm{ins}}})}}$$

(11)

$$C{E}_{\mathrm{emb}}=x_{\mathrm{ins}}\cdot {\rho }_{\mathrm{ins}}\cdot CE{F}_{em}$$

(12)

where $C{E}_{\mathrm{coo}}$ represents carbon emission due to the operation of air-conditioning system, kgCO2e/m²; $C{E}_{\mathrm{emb}}$ represents embodied carbon emission of external wall insulation, kgCO2e/m²; $C{E}_{\mathrm{em}}$ represents carbon emission factor, kgCO2e/m²; $CEF$ represents carbon emission per kWh; $CE{F}_{em}$ represents carbon emission factor of insulation material.

2.4. Integrated Assessment Indicator of External Wall Insulation in Granary

The performance assessment of external wall insulation concerns economic benefit, energy conservation, and carbon-saving of the granary building. A balanced index has been successfully applied to evaluate the carbon reduction effect of various carbon reduction measures in buildings. However, a balanced index was not used to evaluate the effectiveness of various building energy-saving measures in exiting studies. Therefore, a new integrated evaluation indicator ($Bi$) consisting of an energy balanced index ($B{i}_{\mathrm{ec}}$), a carbon balanced index ($B{i}_{\mathrm{ce}}$) [45], and weight coefficients is presented to evaluate the comprehensive performance of external wall insulation. The lower the integrated evaluation indicator is, the better the comprehensive performance of external wall insulation is. The integrated evaluation indicator can be calculated by using the following equations. The weighting coefficients in Equation (13) can be dynamically adjusted based on the design requirements of specific building conditions. The sum of the weighting coefficients in Equation (13) should be 1.

$$Bi=0.5B{i}_{\mathrm{ce}}+0.5B{i}_{\mathrm{ec}}$$

(13)

$$B{i}_{\mathrm{ce}}={\displaystyle \frac{P_{\mathrm{in}}\cdot C{E}_{\mathrm{wa}}}{P_{\mathrm{wa}}\cdot C{E}_{\mathrm{re}}}}$$

(14)

$$B{i}_{\mathrm{ec}}={\displaystyle \frac{P_{\mathrm{in}}\cdot E_{\mathrm{wa}}}{P_{\mathrm{wa}}\cdot E_{\mathrm{re}}}}$$

(15)

where $P_{\mathrm{wa}}$ indicates economic cost of an external wall, USD/m². $C{E}_{\mathrm{wa}}$ indicates carbon emission of external wall, kgCO2e/m². $P_{\mathrm{in}}$ indicates additional investment capital due to insulation, USD/m². $C{E}_{\mathrm{re}}$ indicates carbon reduction due to insulation, kgCO2e/m². $E_{\mathrm{re}}$ indicates reduced energy consumption due to insulation, kW. $E_{\mathrm{wa}}$ indicates energy consumption of external wall, kW.

3. Case Study Building and Typical Climate Regions of Granary in China

3.1. Case Study of Granary Building

A multi-story granary building is used as a specific case to study the impact of external wall insulation on energy consumption and carbon emissions of buildings. The structure of the multi-story granary building is very similar to the other ordinary buildings. The multi-story granary building has the advantages of high space utilization, local temperature control, and low-temperature storage. The multi-story granary building was located in Changsha region in China, as shown in Figure 2. The multi-story granary was a four story building. The height of the building was 68 m. The total building area of this building was 31,677.37 m². The total external wall area was 18,278.4 m². The total external window area was 155.52 m². The building roof area was 3997.11 m². The building floor area was 3576.37 m². The design temperature of indoor air in the multi-story granary was 15 °C. Coefficient of performance of air-conditioning system was 2.3 in this study [46]. Because low temperatures were very helpful for ensuring grain quality, reducing grain storage losses, and minimizing chemical fumigation contamination pollution, the energy consumption due to heat loads of the concerned building was not considered in this study.

3.2. Potential Construction Form of Building Envelope Structure

In order to cope with different outdoor climate characteristics and functional requirements of the building, the multi-story granary building may have multiple potential forms of building envelope structures. Building envelopes of the multi-story granary mainly consists of a foundation wall of an external wall, thermal insulation material, an external window, roof, and floors. The roof is the part of the building envelope that receives the strongest solar radiation. The thermal performance of the roof directly affects the energy consumption level of buildings and is a key building component for reducing carbon emissions. In this study, the building roof is composed of a 10 mm floor decorative tile layer, a 25 mm cement mortar layer, a 50 mm thermal insulation board layer, a 150 mm reinforced concrete layer, and a 20 mm cement mortar layer. Potential options for roof insulation material include a 50 mm rock wool (RW) board layer (A₁), a 50 mm polyurethane (PU) board layer (A₂), a 50 mm extruded polystyrene (XPS) board layer (A₃), and a 50 mm expandable polystyrene (EPS) board layer (A₄). The external wall occupies a large proportion of the building envelope area and plays a decisive role in the energy consumption of the building during operation. The thermal performance of an external wall is mainly determined by the foundation wall type and the insulation material type. The foundation wall type and insulation material type should be considered in analyzing the impact of the external wall on energy-saving and carbon-saving of buildings. In this study, potential options for external wall insulation material include a 30 mm EPS board layer (B₁), a 30 mm XPS board layer (B₂), a 30 mm PU board layer (B₃), and a 30 mm RW board layer (B₄). Potential options for the foundation wall of the external wall include a 240 mm fly ash wall layer (C₁), a 240 mm aerated concrete wall layer (C₂), a 240 mm concrete wall layer (C₃), and a 240 mm brick wall layer (C₄). External windows are important transparent building components with natural lighting and ventilation functions. The thermal performance of external windows directly affects the energy consumption level of buildings and is a key building component for reducing carbon emissions. In this study, potential options for external windows include a 6 mm single-layer glass (D₁), broken bridge aluminum alloy window with 6 mm double-layer glass and a 9 mm air layer (D₂), broken bridge aluminum alloy window with 6 mm double-layer glass and a 12 mm air layer (D₃), and broken bridge aluminum alloy window with a 6 mm low-eglass, a 6 mm ordinary glass, and a 12 mm air layer (D₄). As an important component of building envelopes, the design and material selection of building floor have a significant impact on building energy consumption. In this study, potential options for building floor include a 120 mm reinforced concrete slab layer (E₁), a 130 mm reinforced concrete slab layer (E₂), a 140 mm reinforced concrete slab layer (E₃), and a 150 mm reinforced concrete slab layer (E₄).

3.3. Typical Climate Regions of Granary in China

The outdoor climate characteristics are one of the most important impact factors of the optimization design of external wall insulation in granaries. Typical climate regions of granary in China can be divided into seven climate zones for grain storage in China, according to the outdoor climate characteristics and geographical features [47]. These seven typical climate zones for grain storage in China are Qinghai-Tibet Plateau climate region for grain storage, Mengxin climate region for grain storage, northeast climate region for grain storage, North China climate region for grain storage, Huazhong climate region for grain storage, southwest climate region for grain storage, and South China climate region for grain storage. Seven typical cities of these seven different climate regions were chosen to investigate the influence of different climate region on the optimization design of external wall insulation in granaries. In this study, Xining city represented Qinghai-Tibet Plateau climate region for grain storage; Turpan city represented Mengxin climate region for grain storage; Daqing city represented northeast climate region for grain storage; Kaifeng city represented North China climate region for grain storage; Changsha city represented Huazhong climate region for grain storage; Anshun city represented southwest climate region for grain storage; Danzhou city represented South China climate region for grain storage south. The design temperature of indoor air was 15 °C. Because low temperatures can ensure grain quality, reduce losses, and minimize chemical fumigation contamination pollution, the energy consumption due to heat loads of the concerned building was not considered in this study. The monthly outdoor air temperature of Xining city was lower than 15 °C, so there were no cooling loadings for granaries in Xining city. External walls of granaries in Xining city were not involved of the optimization design of external wall insulation. Four commonly used types of thermal insulation materials, EPS, XPS, PU, and RW, were considered in this study. Energy consumptions of the external wall in the concerned multi-story granary building described in Section 3.1 were determined by using the professional building energy consumption simulation software DeST under different conditions.

4. Results and Discussions

4.1. Optimal Combination Scheme of Different Construction Forms of Building Components

In this study, five factors and four levels were considered in orthogonal experiments to investigate the impact of different construction forms of building components on energy consumption of the concerned granary building. Compared to comprehensive experiments, orthogonal experiment method can reduce the number of experiments, improve experimental efficiency, and find the optimal combination scheme of different sectors of building envelopes. Five factors and four levels were selected for investigating energy consumption without affecting the total building area and building envelope area. These five factors were external wall insulation, roof insulation, foundation wall type of external wall, external window type, and floor type. Orthogonal experiments were conducted to investigate the impact of the optimal combination of these five factors on energy consumption of the concerned building at different levels, as shown in Section 3.2. The level values of factors are shown in

Table 1. Value of factor level.

Level	Roof Insulation	Wall Insulation	Foundation Wall	External Window	Floor Type
1	A1	B1	C1	D1	E1
2	A2	B2	C2	D2	E2
3	A3	B3	C3	D3	E3
4	A4	B4	C4	D4	E4

. When the orthogonal experiment design method is used to determine optimal combination scheme of different construction forms of components in building envelopes, important influencing factors should be determined by conducting systematic analysis. If the systematic analysis of influencing factors is not conducted, some potential critical factors may be overlooked.

The orthogonal experimental design table was generated based on the influence factors and their levels. The interactions between different factors were not considered in this study. The professional building simulation software DeST was used to simulate the energy consumption of the concerned multi-story granary under the conditions of different orthogonal combination schemes. Due to insufficient knowledge of model structure and parameters, the simulation results of DeST software may have an error of about 10% [48]. The simulation errors have certain adverse effects on the results of insulation optimization design in external walls. To evaluate the impacts of various factors and their levels, the experimental simulation results were investigated by using the range analysis method. The range values of five factors at different levels were obtained to evaluate the impact of experimental factors on the results, as shown in

Table 2. Orthogonal experimental table and range analysis of energy consumption.

Num.	Roof Insulation (A)	Wall Insulation (B)	Foundation Wall (C)	External Window (D)	Floor (E)	Cooling Load per Unit Area (W/m2)
1	1	1	1	1	1	186.43
2	1	2	2	2	2	162.01
3	1	3	3	3	3	160.19
4	1	4	4	4	4	154.28
5	2	1	2	3	4	159.65
6	2	2	1	4	3	155.46
7	2	3	4	1	2	179.02
8	2	4	3	2	1	165.00
9	3	1	3	4	2	158.64
10	3	2	4	3	1	164.20
11	3	3	1	2	4	163.19
12	3	4	2	1	3	180.28
13	4	1	4	2	3	167.04
14	4	2	3	1	4	186.11
15	4	3	2	4	1	151.78
16	4	4	1	3	2	162.28
k1	165.72	167.94	166.84	182.96	166.85	-
k2	164.78	166.95	163.43	164.31	165.48	-
k3	166.58	163.55	167.49	161.58	165.74	-
k4	166.80	165.46	166.13	155.04	165.81	-
R	2.02	4.39	4.06	27.92	1.36	-

.

The energy consumptions in relation to 1 m² of the wall area were obtained by simulating and calculating the 16 combination schemes in the orthogonal experimental design table. The ranking of the range value of each factor was as follows: external windows > external wall insulation > foundation wall > roof insulation > floor type. The selection of external window for the concerned multi-story granary had the greatest impact on building energy consumption. The optimal combination scheme of different components of granary envelope was A₂B₃C₂D₄E₂. Therefore, this optimal combination scheme of foundation wall of external wall, thermal insulation material, external window, roof, and floor would be adopted in the concerned multi-story granary building. Because the total external wall area (18,278.4 m²) was much bigger than the total external window area (155.52 m²), the presented optimization approach was used to search for the best solution of external wall insulation in the concerned granary building. The structure of external wall described in Figure 3 would be utilized to investigate the comprehensive performance of external wall insulation in different ecological grain storage zones in China. The physical property parameters of exterior wall elements are shown in

Table 3. Physical property parameters of exterior wall elements.

Layers	Material Name	Thermal Conductivity (W/m·K)	Density (kg/m3)	Specific Heat Capacity (J/kg·K)	Thickness (mm)
1	Cement mortar	0.93	1800	1050	15
2	EPS insulation	0.039	25	1380	Optimum thickness
3	Cement mortar	0.93	1800	1050	15
4	Waterproof layer	0.23	900	1620	5
5	Reinforced concrete	1.74	2500	920	240
6	Cement mortar	0.93	1800	1050	20

.

4.2. Economic Performance Assessment of Different Insulation Materials in Changsha City

The presented integrated optimization method was utilized to analyze the economic performance of EPS, XPS, PU, and RW insulation in building an external wall in Changsha city, respectively. The design of insulation in external wall could reduce the energy consumption cost due to external wall cooling loads and increase the economic investment in external walls. The price of electricity was 0.113 USD/kWh [46]. The price of EPS insulation material was 64.3 USD/m³ [49]. The price of XPS insulation material was 74.6 USD/m³ [50]. The price of PU insulation material was 201.2 USD/m³. The price of RW insulation material was 93.1 USD/m³ [51]. The optimum insulation layer thicknesses was determined when the sum the energy consumption cost due to external wall cooling loads and the additional investment of insulation material was the smallest. The entire construction cost of the concerned four types of insulation materials in external wall of the concerned granary building in Changsha city is shown in Figure 4. As the thickness of the insulation layer increases, the entire construction costs of four kinds of insulation materials first fall and then rise. The minimum value of entire construction cost for EPS insulation material was 18.09 USD/m². The minimum value of entire construction cost for XPS insulation material was 18.22 USD/m². The minimum value of entire construction cost for PU insulation material was 23.36 USD/m². The minimum value of entire construction cost for RW insulation material was 22.22 USD/m². EPS insulation material demonstrated the best economic performance among the four kinds of insulation material. The differences among the lowest entire construction costs for four kinds of insulation material were significant. Therefore, the type of thermal insulation material should be considered in determining the best solution of external wall insulation in granaries from an economic perspective.

4.3. Carbon Assessment of Different Insulation Materials in Changsha City

The presented integrated optimization design was utilized to analyze the carbon reduction effects of EPS, XPS, PU, and RW insulation in building external wall in Changsha city, respectively. The design of insulation in external wall can reduce the electricity consumption due to external wall cooling loads and carbon emissions caused by the reduced electricity consumption. The carbon emission coefficient for EPS, XPS, PU, and RW insulation material was 81.6 kgCO2e/m³ [52], 100.05 kgCO2e/m³ [52], 109.04 kgCO2e/m³ [53], and 157.5 kgCO2e/m³ [54], respectively.

Table 4. Electricity carbon emission factors in different regions of China.

Name of Power Grid	Carbon Emission Factor (kgCO2e/KWh)
Northeast China power grid	0.7769 [55]
Northwest China power grid	0.6671 [55]
North China power grid	0.8843 [56]
Central China power grid	0.5257 [56]
East China power grid	0.7035 [57]
Southern China power grid	0.5271 [57]

shows electricity carbon emission factors in different regional power grid of China. Figure 5 shows embodied carbon of four kinds of insulation materials. The differences among embodied carbon emissions for four kinds of thermal insulation were significant. It implied that the embodied carbon emissions of thermal insulation materials had certain influence on the carbon reduction effect of thermal insulation in building external walls.

Carbon emissions of four kinds of thermal insulation in external wall of the concerned granary building in Changsha city are shown in Figure 6. As the thickness of the insulation layer increases, the carbon emissions of four kinds of insulation materials first fall and then rise. The minimum value of carbon emission for EPS thermal insulation was 10.06 kgCO2e/m². The minimum value of carbon emission for XPS thermal insulation was 10.68 kgCO2e/m². The minimum value of carbon emission for PU thermal insulation was 10.37 kgCO2e/m². The minimum value of carbon emission for RW thermal insulation was 14.22 kgCO2e/m². EPS insulation material demonstrated the best carbon-saving performance among the four kinds of insulation material. The differences among the lowest carbon emissions for four kinds of thermal insulation were significant. Therefore, the type of thermal insulation material should be considered in determining the best solution of external wall insulation in granaries from a carbon emission perspective.

4.4. Impacts of Different Climate Region on the Design of External Wall Insulation

The presented integrated optimization design was utilized to investigate economic performance and carbon emission for EPS insulation material in buildings in different typical climate regions in China, respectively. Outdoor climate characteristics had an important influence on the cooling loads of building external walls, and the varied cooling loads of external walls would influence the comprehensive performance of thermal insulation material in building external walls. Entire construction costs of EPS insulation material in external wall of the concerned granary building in six different climate regions are shown in Figure 7. The lowest entire construction cost of EPS insulation material of external wall in Turpan, Daqing, Kaifeng, Changsha, Anshun, and Danzhou cities was 16.571 USD/m², 12.379 USD/m², 17.019 USD/m², 18.089 USD/m², 14.921 USD/m², and 25.366 USD/m², respectively. The ranking of entire construction cost of EPS insulation material of external wall in six different regions was Daqing city < Anshun city < Turpan city < Kaifeng city < Changsha city < Danzhou city.

Carbon emissions of EPS insulation in external wall of the concerned granary building in six different climate regions are shown in Figure 8. Carbon emissions of EPS insulation material of external wall in Turpan, Daqing, Kaifeng, Changsha, Anshun, and Danzhou cities was 10.789 kgCO2e/m², 8.662 kgCO2e/m², 9.722 kgCO2e/m², 10.367 kgCO2e/m², 8.471 kgCO2e/m², and 14.771 kgCO2e/m²,respectively. The ranking of carbon emissions of EPS insulation material of external wall in six different regions was Anshun city < Daqing city < Kaifeng city < Changsha city < Turpan city < Danzhou city.

The greatest difference in the lowest entire construction cost among four kinds of thermal insulation materials (5.274 USD/m²) was lower than that among six different climate regions (12.987 USD/m²). The greatest difference in the lowest carbon emission of external wall insulation among four kinds of thermal insulation materials (4.161 kgCO2e/m²) was lower than that among six different climate regions (6.3 kgCO2e/m²). It indicated that different outdoor climate regions had important influence on the economic performance and carbon-saving effect of thermal insulation in external walls. Therefore, different climate regions should be considered in determining the best solution of external wall insulation in granaries from both economic and carbon emission perspectives.

4.5. Calculated Integrated Assessment Indicators for Different Climate Regions

Equations (13)~(15) were used to calculate the integrated assessment indicators of EPS insulation for building external walls in six typical climate regions in China. The calculated integrated assessment indicators of EPS insulation for building external walls in six typical climate regions are shown in Figure 9. The ranking of integrated assessment indicators for building external insulation in six different climate regions in China was Danzhou city > Changsha city > Kaifeng city > Turpan city > Anshun city > Daqing city. The comprehensive performance of external wall insulation in Danzhou city outperformed their counterparts. The largest difference among these values of integrated assessment indicators for different climate regions was 0.697, which indicated that the comprehensive performance of external wall insulation in different climate regions in China varied significantly from each other. Outdoor air temperature characteristics of different climate regions could significantly affect the comprehensive performance of thermal insulation in building external walls. The weight coefficient was set as 0.5 in this study, which was suitable for the projects that focus on energy savings and carbon savings equally. The weighting coefficients need to be determined based on the actual requirements of building engineering. The calculated integrated assessment indicators can respond to economic, energy, and carbon-saving performance of thermal insulation in building external walls, simultaneously. The calculated integrated assessment indicator overcame the shortcomings of previous assessment indexes where economic benefits, energy conservation, and carbon emission reduction were considered, respectively. The integrated assessment indicator was conducive to resolving the contradiction of different design schemes based on single factor of economic benefit, energy conservation, or carbon emission reduction.

Figure 10 demonstrates optimum thicknesses of EPS insulation layer of building external walls in six typical climate regions in China. These optimum thicknesses of EPS insulation layer of external walls were determined under influences of multiple factors (Economic issue, energy-saving issue, and carbon reduction issue). The optimum thickness of EPS insulation layer in the building external wall in Turpan city, Daqing city, Kaifeng city, Changsha city, Anshun city, and Danzhou city was 0.078 m, 0.048 m, 0.083 m, 0.089 m, 0.062 m, and 0.131 m, respectively. These optimum thicknesses of EPS insulation layers in external walls varied significantly from each other for different typical climate regions in China. Outdoor air temperature characteristics of different climate regions had important influence on the optimum thicknesses of EPS insulation layers of external walls in granaries.

Compared with the existing studies, the findings of this study were similar to those of existing investigations. Akan and Akan [58] found that the uses of EPS, PU, and RW insulation materials in building external walls in Turkey could save 10.1~61.1% building energy consumption and reduce 46~69% building carbon emissions. Annibaldi et al. [45] found the use of RW insulation in external wall in buildings in Italy could reduce 10.17 USD/m² economic cost and 10.07 Kg/m² carbon emission in the whole life cycle. The current design of thermal insulation layers for exterior walls in granary buildings lacks national design standards in China. The research findings of this paper can provide valuable references for determining the insulation material type and the optimum thicknesses of thermal insulation layers of external walls in granary buildings in different climate regions.

5. Conclusions

An integrated optimization approach has been proposed in this paper to search for the best solution of thermal insulation in the external wall and the optimal combination scheme of different construction forms of components in building envelopes. The new integrated optimization approach could respond to the economic benefit, energy conservation, and carbon-saving of thermal insulation in building external walls, simultaneously. The best solution of external wall insulation in granary buildings in different climate regions in China has been investigated by using the presented integrated optimization approach.

(1)

An integrated optimization approach was proposed for external wall insulation in buildings based on orthogonal experimental design method, comprehensive analysis models, and integrated assessment indicator. The optimization approach is very helpful to searching for the best solution of external wall insulation in real buildings.

(2)

Orthogonal experimental design method was utilized to determine the optimal combination scheme of different construction forms of components in building envelopes.

(3)

Integrated economic, energy, and carbon analysis models were developed to assess the comprehensive performance of external wall insulation.

(4)

An integrated assessment indicator consisting of an energy balanced index, a carbon balanced index, and weight coefficients was presented to determine the best solution of external wall insulation.

(5)

Outdoor climate characteristics in different climate regions in China could affect the comprehensive performance of external wall insulation in buildings, significantly. The optimum thickness of EPS insulation layer of external wall in the concerned granary in Turpan city, Daqing city, Kaifeng city, Changsha city, Anshun city, and Danzhou city was EPS insulation with a layer thickness of 0.078 m, 0.048 m, 0.083 m, 0.089 m, 0.062 m, and 0.131 m, respectively.

The findings in this study are particularly relevant to the low-carbon design and energy-saving of buildings, where multi-objective optimization is both desirable and necessary. In this study, only the optimal combination scheme of different construction forms of building components and the optimum thickness of the insulation layer in the external wall was investigated for granary buildings in different climate regions in China. Future research should focus on more multi-objective optimization methods of building insulation and carbon-saving designs for the entire building. The thermal bridges, junction losses, or long-term degradation of insulation performance may significantly affect the real-world applicability of the presented integrated optimization approach. The impacts of the above influencing factors on the optimization design of building insulation should be investigated in the future.