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Dynamic assessment of the thermal performance of hemp wool insulated external building walls according to the Moroccan climatic zoning
Journal of Energy Storage 26 (2019) 101007
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Dynamic assessment of the thermal performance of hemp wool insulated external building walls according to the Moroccan climatic zoning
T
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Maryam Dlimi , Omar Iken, Rachid Agounoun, Imad Kadiri, Khalid Sbai Moulay Ismail University of Meknes, Laboratoire d’Etude des Matériaux Avancés et Applications (LEM2A), Ecole Supérieure de Technologie de Meknès (ESTM), Km 5, route d’Agouray, N6, 50040, Meknes, Morocco
A R T I C LE I N FO
A B S T R A C T
Keywords: Thermal inertia Cooling and heating transmission loads Hemp wool Optimum insulation thickness Energy savings Life-cycle cost
This paper deals with the assessment of the dynamic thermal performance of Moroccan external walls. Firstly, based on the quadrupole method, the thermal capacity and thermal resistance of an uninsulated brick wall were calculated for different thicknesses of the brick layer. The optimum brick thickness chosen corresponds to the one that maximally enhance the thermal inertia and thermal resistance. Afterwards, the brick wall was externally insulated with hemp wool, a bio-based insulation material. For an hypothetical lifespan of 20 years, and based on the life cycle cost analysis, annual heating and cooling requirements, optimum insulation thicknesses, energy savings and payback periods were calculated for all wall orientations and considering the six climatic zones of Morocco. It was found that the optimal brick thickness was equal to 0.20 m and the optimal insulation thicknesses vary between 1 and 6 cm for the different climatic zones and the different wall orientations. Moreover, a comparison with the minimum technical specifications fixed by the Moroccan thermal regulation showed that our results allow the reduction of annual heating and cooling requirements by a minimum percentage of 56% for the city of Ifrane, and a maximum percentage of 79% for the city of Marrakech. Finally, annual greenhouse gas (GHG) emissions were also calculated and it was found that they can be decreased, with the use of optimum thicknesses of hemp wool, by a minimum of 32% for the city of Ifrane and a maximum of 75% for the city of Errachidia.
1. Introduction
1.2. State of art
1.1. Background
Thanks to its porous structure, its hygrometric, regulating and thermal insulating properties, hemp is among the most studied biobased insulation materials [4]. Hemp provides two co-products used in construction: fiber and shiv (hemp hurds). The hemp fibers replace the traditional fibers and are used in the manufacture of rolls and panels of hemp wool. These rolls and panels are used vertically for the thermal insulation of walls. Concerning the hemp shiv, its use in the building essentially values the porosity of its particles. Thanks to this porosity, hemp shives are characterized by a low density and insulating properties. These particles are mainly used to make light or extra light mortars and concretes [5]. Therefore, hemp can be used as hemp concrete inside a wood frame structure, or as hemp wool for insulation, or even as hemp-lime mortar for coating. These different uses of hemp have led researchers to carry out several studies. For instance, Costantine et al. [6] investigated experimentally the thermal behavior of hemp concrete for external building wall insulation. Results obtained for indoor temperature and relative humidity
The building envelope plays a key role in determining levels of thermal, visual, acoustic and olfactory comfort. Thus, it is considered as a major element to improve the energy efficiency of buildings and reduce greenhouse gas emissions, whether in the new or existing constructions [1]. Thermal insulation is the solution to both increase thermal comfort and reduce energy consumption related to the use of heating and air conditioning systems. In order to reduce the environmental impacts and the problems of pollution related to the building sector, most of the recent researches are focused on the investigation of new bio-based insulation materials [2]. Since they are eco-friendly, the production of the bio-based materials and their subsequent transformations have a reduced impact on the environment. Indeed, the use of these materials allows the storage of the Carbone and help reducing greenhouse gas emissions [3].
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Corresponding author. E-mail address: [email protected] (M. Dlimi).
https://doi.org/10.1016/j.est.2019.101007 Received 17 July 2019; Received in revised form 17 September 2019; Accepted 7 October 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature a As c Cel Cenr Ci Cins Cth COP Qh d Hu hi ho i IT j k kins L Lins Lopt
M N p Pb Qc qi qe t Tin Tsa Tx = L, max Tx = L, min Tx = 0, max Tx = 0, min
Outdoor surface wall solar absorptivity Annual energy savings ($ m2) Specific heat (J/kg.K) Cost of electricity ($/kWh) Cost of energy consumption ($ m2) Cost of insulation material ($ m2) Cost of insulation material ($ /m3) Internal thermal capacity (kJ/m2.K) Coefficient of performance of air-conditioning system Yearly heating transmission load (J/m2) Discount rate (%) Heating value of electricity (J/m3) Inside convective heat transfer coefficient (W/m2.K) Outside convective heat transfer coefficient (W/m2.K) Inflation rate (%) Incident solar radiation for vertical surfaces (W/m2) Complex argument Thermal conductivity (W/m.K) Thermal conductivity of insulation material (W/m.K) Total thickness of a wall (m) Insulation thickness (m) Optimum insulation thickness (m)
Layers number of composite wall Lifetime of building (years) Laplace variable Payback period (years) Yearly cooling transmission load (J/m2) Heat flux of indoor surface of the wall (W/m2) Heat flux of outdoor surface of the wall (W/m2) Time (s) Indoor air temperature (∘ C) Sol-air temperature (∘ C) Maximum indoor surface temperature (∘ C) Minimum indoor surface temperature (∘ C) Maximum outdoor surface temperature (∘ C) Minimum outdoor surface temperature (∘ C)
Greek symbols α ρ x ηs ω Δx Δt
Thermal diffusivity (m2/s) Density (kg/m3) Coordinate direction normal to wall (m) Efficiency of the heating system Angular frequency (s−1) Space step (m) Time step (s)
use of thermal insulation with optimum insulation thickness. Over a given lifetime of the building, the optimum insulation thickness corresponds to the value that provides the lowest total cost defined as the sum of insulation and energy consumption costs [13]. Nematchoua et al. [14] calculated the required insulation thickness with the corresponding energy savings for buildings in two different cities with two different climates. Two wall structures were considered: compressed stabilized earth wall and concrete block wall. The insulation material used was the extruded polystyrene. Results showed that in the city of Yaounde which is characterized by an equatorial climate, optimum insulation thickness and energy savings for the south facing wall were equal to 0.08 m and 51.69 $/m2, respectively. For the city of Garoua which is characterized by a tropical climate, optimum insulation thickness calculated for a north orientation wall was obtained as 0.11 m and energy savings as 97.82 $/m2. Besides, based on the isotropic model of Duffie and Beckman [15], Ibrahim et al. [16] determined the optimum insulation thickness according to cooling requirements in buildings located in the city of Beirut, Lebanon. The insulation material chosen was extruded polystyrene, and the optimum insulation thicknesses obtained were 4.9, 4.8, 4.1 and 4.1 cm for the west, east, north and south orientations, respectively. On the other hand, based on an analytical method, optimum insulation thickness of expanded polystyrene for building walls located in Tunis, Tunisia was calculated by Daouas [17]. The south orientation was considered as the most economical one since the value of optimum insulation thickness was found equal to 10.1 cm, with a percentage of 71.33% as energy savings and 3.29 years as payback period.
underlined the ability of hemp concrete to dampen the outdoor climatic conditions. Furthermore, Seng et al. [7] have used several experimental methods to characterize the thermo-physical properties of a precast hemp concrete block. The founded results showed that the choice of the experimental method has a significant influence on the determination of the different thermal properties of the prefabricated hemp concrete block; especially the heat capacity. On the other hand, Mazhoud et al. [8] investigated thermal and hygric properties of two different hemplime plasters made with hemp shiv of different sizes (cut into small and large sizes). Thermal properties, moisture buffer value, water vapor permeability and sorption isotherm were measured. The authors found that hemp-lime plasters possess high hygrothermal qualities, with a thermal conductivity of around 0.2 W/m.K. They also showed that the hemp-lime plaster made with the largest hemp shiv is less conductive than the other one with smallest hemp shiv. Nevertheless, from a hygric point of view, the latter is a better regulator. Besides, hygric properties of two different hemp wools based on organic and polyester binders were investigated by Collet et al. [9]. It was found that the two kinds of hemp wool show similar vapour resistance and are characterised by high water content. The thermal comfort of a room as well as the energy consumption of heating and air conditioning systems are greatly influenced by the dynamic thermal performance of a multilayer wall which is known as thermal inertia [10]. In this context, Li et al. [11] explored the effects of coupling the thermal inertia of both the thermal mass and the air conditioning system on the demand response period for a commercial building. The results showed a great accuracy of the coupled model since the effect of the thermal inertia of the air conditioning system on the demand reduction was considerable. Moreover, in order to improve the passive cooling strategy based on the building night ventilation, Chahwane et al. [12] developed an algorithm adapted for different types of commercial buildings thermal masses where the indoor air temperature is conditioned in the whole year. The effectiveness of the developed algorithm was shown in the realized energy savings (more than 30%), the decreased discomfort hours (57%) and the reduction of the electric power of the ventilation system. Thermal inertia is not the only parameter responsible of reducing the energy consumption due to heating and air-conditioning systems. Consequently, more significant energy savings can be achieved with the
1.3. Aim of the study The majority of the studies dealing with the use of bio-based materials for the thermal insulation of buildings are rather concentrated on the evaluation of the materialshygrothermal performances, and lack economic analysis. Moreover, these studies, concentrated especially in Europe, are little treated in Africa, hence the interest of our study, which is focused in Morocco, a country where hemp is cultivated for centuries but its use in the building industry is very limited. The aim of the current study is to evaluate the thermal performance of typical Moroccan buildings external walls under the climatic conditions of six 2
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different regions: Agadir, Tangier, Fez, Ifrane, Marrakech and Errachidia. Firstly, based on the quadrupole method, the thermal behavior of a double sided brick wall is assessed by the determination of the optimum thickness of the brick layer providing the maximum thermal inertia. In the second part of this study, hemp wool insulation is integrated at the external side of the brick wall. Then, considering heating and cooling requirements, optimum insulation thickness, energy savings and payback periods are determined for all wall orientations and for the six climatic zones under investigation. A computer Matlab code is developed for the solution of the transient one dimensional heat equation using the finite difference method and based on the implicit scheme. Moreover a comparative study is conducted between heating and cooling requirements values obtained using optimal insulation thicknesses and the values fixed by the Moroccan thermal regulation for each climatic zone. Finally, annual GHG emissions related to each climatic zone are calculated.
Table 1 Thermophysical properties of building materials. Material
λ (W/m.K)
ρ (kg/m3)
c (J/kg.K)
Brick [18] Hemp wool [19] Cement mortar [20]
0.68 0.04 0.72
1600 35 1865
840 1200 840
cities of each climatic zone are: Agadir, Tangier, Fez, Ifrane, Marrakech and Errachidia [24]. Considering these six climatic zones, the current study focuses on the calculation of heating and cooling requirements covering a winter period from November to March and a summer period from June to September. In calculations, the 15th day of each month is considered as a representative day for the whole month. The diurnal variations of the external environment temperature will be calculated by means of the sol-air temperature Tsa(t) which includes solar radiation effects and is expressed as follows [25]:
2. Studied configurations In Morocco, typical building constructions are generally based on bricks and cement mortar. In order to enhance the thermal performance of external building walls, investigations are conducted aiming to maximize thermal inertia and thermal resistance. The first configuration depicted in Fig. 1(a) is a composite wall structure consisting of 2 cm inner and outer cement mortar and a solid brick layer of variable thicknesses. In the second configuration (Fig. 1(b)), an insulation layer varying from 1 to 10 cm is introduced and located on the external side of the double sided brick wall. The materials used in the wall structure and their thermal properties are given in Table 1.
Tsa (t ) = Ta (t ) +
aIT (t ) ε ΔR − ho ho
(1)
where Ta(t) is the outdoor air temperature, he is the combined (convective and radiative) outdoor heat transfer coefficient, a and IT(t) are the external wall surface solar absorbtivity and the total solar radiation, respectively. ε ΔR expresses the correction factor and is assumed to be 4∘ ho C for horizontal surfaces and 0 for vertical ones [26]. The outdoor air temperature Ta(t) and the hourly values of total solar radiation IT(t) are provided using Meteonorm data [27] specific to each Moroccan city. The external wall surface solar absorbtivity is taken equal to 0.55 [28], and ho = 22 W/m2K according to ASHRAE standard [26]. Sol-air temperature and solar radiations of the 15th day of the months of January (Ifrane) and August (Errachidia) are presented in Figs. 2 and 3. Ifrane and Errachidia cities were chosen since they require the highest heating and cooling loads, respectively. As shown in Figs. 2(a) and 3(a), sol-air temperature is strongly dependent to solar radiation (Figs. 2(b) and 3(b)) whose distribution depends mainly on the season, the orientation of the wall and the period of the day. For the winter representative day (Ifrane), the highest solar radiation is reached by the south orientation with a maximum value exceeding 290 W/m2. With solar radiation values of 198 and 213 W/m2, respectively, east and west orientations are less subjected to solar radiation than the southern orientation. The north orientation is the least exposed to solar radiation, with a value barely exceeding 124 W/m2. It is also seen that the maximum peak values of solar radiations for all wall orientations are reached at different times of the day: 13:00, 11:00, 16:00 and 14:00 for south, east, west and north orientations respectively.
3. Overview on the Moroccan climate Located in the North West of Africa, between the arid regions of the Western Sahara and the moderate Mediterranean and Atlantic regions [21], Morocco is a country characterized by a large variety of climates. Firstly, a typical Mediterranean climate reigns on the Mediterranean coast and the Rif. Then, a Sub-Mediterranean climate with oceanic influences characterizes the northern Atlantic plains and becomes continental in the interior. On the other hand, the plains of Doukkala up to the Souss basin are characterized by a degradation of the climate of the North Atlantic plains, with increasing aridity towards the south, because of the Saharan influences that are beginning to be felt. Further, the middle and high Atlas are characterized by the mountain climate, while the Saharan area knows a typical desert climate [22]. Since the Moroccan territory is characterized by various climates, the country was subdivided into six climatic zones in coordination with the Direction of the National meteorology [23]. The representative
Fig. 1. (a): Uninsulated wall configuration, (b): Hemp wool insulated wall configuration. 3
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Fig. 2. (a): Daily sol-air temperature and (b): Daily solar radiation for January 15, for the city of Ifrane.
Fig. 3. (a): Daily sol-air temperature and (b): Daily solar radiation for August 15, for the city of Errachidia.
earth tilt, the sun is getting closer to the south hemisphere, thus, south orientation in north hemisphere is the most exposed to solar radiations. Unlike to summer, the sun has a position closer to the north hemisphere, allowing to the eastern orientation during morning, and the western orientation during evening, to be the most exposed to solar radiations.
4. Characterization of thermal inertia based on the quadrupole method The thermal inertia defines the ability of a material to store heat and then restore it gradually. Specific heat and density are the two material properties involved in the characterization of the thermal inertia. According to its layout in a wall, a building material with high density and specific heat leads to increasing the thermal inertia of a wall. Two types of thermal inertia are distinguished: the transmission inertia, characterized by the two notions of time lag and decrement factor, and inner inertia representing the capacity of the internal surface of a wall to absorb, store and restore heat. Being the subject of this study, the inner inertia is characterized by the internal thermal capacity Cth. This thermal capacity can be calculated through the analytical resolution of the heat equation using the thermal quadrupole method [29]. In this section, the inner thermal inertia of the two sided uninsulated brick wall with fixed thicknesses of cement mortar on its internal and external surfaces is assessed (Fig. 1(a)). The study focuses on the calculation of the thermal capacity Cth of the multilayer wall, and this, for different thicknesses of the solid brick layer.
Fig. 4. Internal thermal capacity variation with solid brick thickness.
For the summer representative day (Errachidia), the trend has changed and the east and west orientations are exposed to the highest solar radiation reaching a maximum value of 738 and 730 W/m2 respectively, followed by the south orientation with a maximum solar radiation value of 427 W/m2. The north orientation is always the least exposed to solar radiation reaching a maximum value of 157 W/m2. The maximum peak values of solar radiations are reached for the south, east, north and west orientations at 16:00, 11:00, 16:00 and 20:00, respectively. The difference in the distribution of solar radiation from a season period to another one can be explained by the fact that in winter, due to 4
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Fig. 5. (a)-Distribution of inside and outside surface temperatures and (b)-Internal and external surface heat fluxes distribution.
4.1. Quadrupoles method
Zt (ω) = B (ω)
The quadrupole method is a well known analytical tool in heat transfer modeling through a solid medium. Depending on the transient regime, Laplace or Fourier transforms are the basis of this method. Switching from Laplace to Fourier transform is possible by substituting the Laplace variable p by jω where j = −1 is the complex argument and ω is the angular frequency [30]. The period P is equal to 24 hours since the outside temperature changes diurnally. The one-dimensional heat conduction problem in a homogeneous wall of thickness L, thermal conductivity k and thermal diffusivity α, can be analytically described by linking temperatures and heat fluxes on its both sides by a transfer matrix [31]. In the case where the homogeneous wall is subjected to sinusoidal temperature variations on its boundary sides, Fourier transform is applied and the transfer matrix, including resistances of both outer and inner surfaces, is expressed as Eq. (2) [32]:
Zin (ω) =
1 1 ⎡ θout (ω) ⎤ = ⎡ 1 he ⎤·⎡ A (ω) B (ω) ⎤·⎡ 1 hi ⎤·⎡ θin (ω) ⎤ ⎥ ⎢ C (ω) D (ω) ⎥ ⎢ ⎥ ⎢ ϕ (ω) ⎥ ⎢ ϕout (ω) ⎥ ⎢ ⎣ ⎦ ⎦ ⎣0 1 ⎦ ⎣ ⎦ ⎣ 0 1 ⎦ ⎣ in θin (ω) ⎤ ⎡ = Mout (ω)·M (ω)·Min (ω)· ⎢ ϕin (ω) ⎥ ⎣ ⎦
Cth (ω) = −
Ai (ω) Bi (ω) ⎤ whereMi (ω) = ⎡ , i = 1, 2, …N . ⎢ Ci (ω) Di (ω) ⎥ ⎣ ⎦
(4)
(5)
Ri Li ⎤ Bi (ω) = sinh ⎡2π (1 + j ) ⎢ 2π (1 + j )(Li /Λi) Λi (ω) ⎥ ⎦ ⎣
(6)
2π (1 + j )(Li /Λi) Li ⎤ sinh ⎡2π (1 + j ) ⎢ Ri Λ i (ω) ⎥ ⎣ ⎦
After the determination of the optimum thickness of the brick layer allowing the maximization of the thermal inertia of our studied uninsulated wall, external thermal insulation is added in order to increase its thermal resistance (Fig. 1(b)). The insulation material chosen in our study is the hemp wool, a bio-based insulation material with thermophysical properties close to those of the expanded polystyrene, the most classical insulation material [19].
(7)
A composite wall structure consisting of 4 parallel layers with different materials and thicknesses (Fig. 1(b)) is considered. Taking into account constant thermophysical properties (Table 1) and no heat generation, the heat transfer through each layer of the external insulated wall is governed by the transient 1D heat equation expressed as Eq. (12):
where (Ri = Li /ki) represents the thermal resistance of the layer i, and 2αi Λi (ω) = 2π defines the thermal wavelength of the material layer i ω at an angular frequency ω. The wall can be represented by three impedances acting as heat accumulators and expressed as Eqs. (8)–(10):
B (ω) D (ω) − 1
(11)
5.1. Numerical model
Li ⎤ Ai (ω) = Di (ω) = cosh ⎡2π (1 + j ) ⎢ Λ (ω) ⎥ i ⎣ ⎦
Zout (ω) =
1 ωI [Zin (ω)]
5. Financial analysis for the calculation of optimal insulation thickness
For each layer transmission matrix, the quadrupole terms are expressed as Eqs. (5)–(7):
Ci (ω) =
(10)
The variation of the internal thermal capacity versus the variation of the solid brick thickness is depicted in Fig. 4. One can note that the internal thermal capacity value increases with the increase of the solid brick thickness until reaching a maximum value and then decreases. The maximum value of the internal thermal capacity is reached when the solid brick insulation is equal to 20 cm. Thus, the thermal inertia of the double sided brick wall is maximized, and it only remains the introduction of an insulating layer to enhance its thermal resistance.
For a multilayer wall, M (ω) corresponds to the total matrix of the entire wall and is obtained as follows in Eq. (3): (3)
B (ω) A (ω) − 1
As mentioned above and as recommended by the international standard ISO 13786 [33], inner thermal inertia is characterized by the thermal capacitance Cth related to the internal surface of the wall. Its expression depends on the imaginary part of the inside impedance Zin(ω) and is written as follows in Eq. (11):
(2)
M (ω) = MN (ω)·… ·M2 (ω)·M1 (ω)
(9)
kj ∂2Tj / ∂x 2 = ρj cj
∂Tj ∂t
, j = (1, 2…,M )
(12)
where kj, ρj and cj are the thermal conductivity, the density and the specific heat of the layer, respectively. Tj is the temperature, x and t are spatial and temporal coordinates. Eq. (12) is solved with the specification of an initial and two boundary conditions. As initial condition, an arbitrary uniform temperature field is assumed. The outdoor and indoor boundary conditions are given respectively as follows in
(8) 5
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0.33 6.57 5.98 0.327 6.00 0.350 1.33 2.92 6.74 0.133 1.12 16.66 10.55 0.100
∂T = ho (Tsa (t ) − Tx = 0) − k1 ⎛ ⎞ ⎝ ∂x ⎠ x = 0
(13)
∂T = hi (Tx = L − Tin ) − kM ⎛ ⎞ ⎝ ∂x ⎠ x = L
(14)
where hi = 9 W/m2 and ho = 22 W/m2 are the combined inner and outer heat transfer coefficients, respectively. The outside surface of the wall is subjected to the sol-air temperature Tsa(t) and its inside surface is exposed to the indoor air temperature maintained constant at the fixed design temperatures Tin = 20 ∘ C in winter, and Tin = 26∘C in summer, according to the Moroccan Standard NM ISO 7730 RTCM [35]. To obtain the temperature distribution through the investigated wall, the implicit finite difference method [36] is applied to solve the transient 1D heat conduction equation. The finite difference equations are solved using matrix functions in Matlab [37]. The accuracy and reliability of the developed Matlab code is validated with the numerical results of Jin et al [20]. Based on the determination of the heat flux time lag and heat flux decrement factor, the authors investigated the effect of the thermal properties on the thermal performances of a wall. For this aim, the transient 1D heat equation was solved for a brick wall with the fallowing thermal properties k = 0.62 W/mK, c = 840 J/kgK, ρ = 1800 kg/m3, and with the fallowing 2πt π − ), boundary conditions: Tin = 26 ∘ C, Tsa = 30 + 5 × sin( 24 2 hi = 8.7 W/m2 and ho = 18.6 W/m2. The implicit finite difference method was used to discretize the transient 1D heat equation, with a space grid size of 0.5 mm and a time step of 20 s. The variations of the outside (Tx = 0 ) and inside (Tx = L ) surface temperatures as well as the internal and external surface heat fluxes qi and qe using the two numerical codes are depicted in Fig. 5. It can be seen that the distribution of temperatures and heat fluxes obtained with our numerical code are in good agreement with those obtained in the study of Jin et al. [20] with a maximum difference of 1%. Moreover, the transient 1D heat equation was solved in other studies in order to determine time lag and decrement factor for different materials and under different climatic conditions. In these studies, other numerical codes and software were used. The values of time lag and decrement factor calculated by the methods used in these studies as well as by the numerical code used in this paper are presented in Table 2. Finally, it can be seen from Fig. 5 and Table 2 that the results of the present study are in good agreement with those of these different studies, which demonstrates that the home-made Matlab code is effective and accurate.
6.65 0.137
Difference in
Asan [39] (Crank–Nicolson)
Eqs. (13) and (14) [34]:
Present study
5.2. Heating and cooling transmission loads calculation Annual heating and cooling transmission loads are calculated from November to March and June to September, respectively. The day 15 of each month is considered as a representative day for the whole month. Firstly, the hourly variation of the inside surface heat flux is expressed as follows in Eq. (15):
10.67 0.012
qi = hi (Tx = L − Ti )
(15)
Afterwards, daily total loads are obtained by the integration over a 24h period of the hourly inside surface heat flux. Finally, annual heating and cooling transmission loads are then calculated from the addition of daily total loads over the winter and summer periods considered. Fig. 6 represents the variations of annual heating and cooling transmission loads compared to the increase of the insulation thickness. One can note that when the insulation thickness is increased from 1
Time lag Decrement factor
Ozel [38] (Implicit scheme)
Table 2 Time lag and decrement factor calculated by our numerical method and those used in other studies.
Present study
Difference in %
Belhadj [40] (Energy Plus Software)
Present study
Difference in %
M. Dlimi, et al.
6
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Fig. 6. Variation of annual heating and cooling loads with insulation thickness.
the north and south facing external walls have been neglected as thermal insulation increases cooling transmission loads rather than decreasing them. In addition, heating transmission loads are relatively less important in the climatic zones of Errachidia, Fez and Marrakech. While cooling transmission loads are highest in the zone of Errachidia, followed by the
to 6 cm, heating and cooling requirements are significantly reduced, whereas when the insulation thickness exceeds 7 cm, this decrease becomes less significant. By comparing the heating and cooling loads of each climatic zone, we note that the zone of Ifrane is the one that represents the maximum of heating requirements and the minimum of cooling ones. In addition, 7
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Table 3 Parameters used in calculations.
Q Cel Qh + Cenr = PWF ⎛⎜ c Cel ⎞⎟ 6 × COP 3.6 10 H u ηs ⎠ ⎝
Parameter
Value
Electricity cost (Cel), [44] Heating value (Hu), [45] Efficiency of the heating system (ηs), [45] Coefficient of performance of the cooling system (COP), [46] Insulation cost (Cins), [47] Discount rate (d), [48] Inflation rate (i), [48] Lifetime period (N), [43]
0.1346 $/kWh 3.6 × 106 J/m3 0.99 2.5 100 $/m3 2.25% 1.8% 20 years
(16)
PWF is the present worth factor which is defined as Eqs. (17) and (18):
PWF =
(1 + r ) N − 1 i−d d−i , if {i > d r = } or {i < d r = } r (1 + r ) N 1+d 1+i (17)
PWF =
N , if i = d 1+i
(18)
Qc, Qh, Cel and COP represent the annual cooling and heating transmission loads per unit area, the cost of electricity and the cooling system performance, respectively. The total cost is the sum of the cost of energy consumption and the cost of insulation material. The total cost per unit area of wall is given by Eq. (19):
zone of Marrakech and then by the zone of Fez. As for the climatic zones of Agadir and Tangier, these represent moderate heating and cooling requirements. In order to be able to determine which thickness of insulation will maximally improve the thermal and economical performances of the multilayer wall, an optimum economic insulation thickness must be calculated.
Q Cel Qh Ct = Cenr + Ci = PWF ⎛⎜ c + Cel ⎞⎟ + Cins Lins 6 COP 3.6 × 10 H u ηs ⎠ ⎝
(19)
Cins is the cost of the insulation material by unit volume and Lins is the insulation thickness. Resulting energy savings are calculated from the difference between the total cost of the wall without insulation and the total cost of the wall with optimum insulation thickness [42]. Annual energy savings As are obtained by dividing the result of the difference between the energy costs of the wall without insulation and the wall with optimum insulation thickness divided by the present worth factor PWF. The payback period Pb is defined as the insulation cost divided by annual energy savings, it can be directly calculated as follows in Eq. (20) if interest and inflation rates are not taken into account:
5.3. Life cycle cost analysis The optimum economic insulation thickness represents the value providing the lowest total life-cycle cost. This one represents the sum of the cost of the energy consumption and the insulation cost. Since the optimal thickness value of insulation is not influenced by other loads, it is calculated by only considering external walls heat transmission [41]. Using heating and cooling transmission loads as input data, and based on the present worth method, the inflation rate i and the discount rate d, an economic model is set for the determination of the optimal insulation thickness. The cost of energy consumption during a building lifetime of N years is given by the Eq. (16) [17]:
Pb =
Ci. Lins (opt ) As
Fig. 7. Variation of costs with insulation thickness for all wall orientations and for the city of Marrakech. 8
(20)
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Fig. 8. Variation of total Costs with insulation thickness for all wall orientations.
thickness. It corresponds to the lowest value shown by the total cost curve. Fig. 8 shows the variation of the total costs for the six climatic zones studied and for all wall orientations. It is seen that the south, east and west orientations give equal insulation thicknesses except for the cities of Marrakech and Tangier where the insulation thickness of the south facing external walls decreases. The lowest insulation thickness is given by the north facing external walls for all the investigated climatic zones. The values of optimum insulation thickness, percentages of energy savings, minimum total costs and payback periods for all orientations and all the climatic zones investigated are depicted in Table 4. The insulation thicknesses vary between a minimum value of 1 cm and a maximum value of 6 cm. The eastern and western orientations provide high values of the minimum total cost and energy savings, and a low value of the payback period. On the other hand, the north orientation is the most economical one according to the minimum total
When the inflation and the interest rates are considered, the payback period Pb is given as the Eq. (21) [43]:
Ci. Lins (opt ) ⎤ ln ⎡1 − r ⎥ ⎢ As ⎦ Pb = ⎣ 1 ln ⎡ 1 + r ⎤ ⎣ ⎦
(21)
All the parameters needed for the above economic calculations are summarized in Table 3. For the climatic zone of Marrakech, and considering the four orientations, Fig. 7 presents the variation of the energy consumption cost, the insulation cost and the total cost in respect to insulation thickness. It is clearly shown that the energy cost decreases, while the insulation cost knows a linear increase with the increase of the insulation thickness. The total cost, which represents the sum of energy and insulation costs, allow the determination of the optimum insulation 9
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and the north orientations. For all orientations, a reduction percentage of 73% is obtained with the use of optimal insulation thickness.
Table 4 Results summary. Climatic zone
Z1: Agadir
Z2: Tangier
Z3: Fez
Z4: Ifrane
Z5: Marrakech
Z6: Errachidia
Wall orientation
Optimum insulation thickness (m)
Minimum total cost ($/m2)
Energy savings (%)
Payback period (years)
South East North West
0.03 0.03 0.02 0.03
7.70 7.62 6.54 8.09
30.45 35.32 24.22 32.94
11.92 10.60 12.51 10.89
South East North West
0.02 0.03 0.01 0.03
6.44 7.72 2.57 8.11
23.36 29.67 78.64 33.84
19.17 12.13 7.24 10.62
South East North West
0.04 0.04 0.03 0.04
8.96 10.38 8.51 10.60
35.46 42.56 34.55 43.91
8.51 6.50 10.13 6.17
East West
0.01 0.01
3.57 3.83
2.95 8.92
68.53 55.23
South East North West
0.04 0.06 0.04 0.06
9.68 12.97 9.33 13.85
39.72 50.29 38.12 53.53
7.32 3.97 7.79 3.45
South East North West
0.06 0.06 0.04 0.06
13.29 14.86 9.55 14.63
51.58 55.28 45.69 55.35
3.76 4.08 5.60 3.14
5.4. Comparison with Moroccan thermal regulation Our results were compared to the minimum technical specifications fixed by the Moroccan thermal regulation for the thermal performance of buildings. Fig. 12 presents a comparison between the annual heating and cooling requirements provided by the optimum insulation thicknesses and the ones specified by the Moroccan thermal regulation for the six climatic zones studied. We notice that for all the climatic zones investigated, the annual heating and cooling requirements calculated in this study are much lower than those fixed by the Moroccan thermal regulation. For instance, heating and cooling requirements related to the city of Marrakech know the maximum percentage of reduction reaching almost 79%. On the other hand, the lowest percentage of heating and cooling requirements reduction concerns the city of Ifrane with a value of 56%. For the remaining four climatic zones, heating and cooling transmission loads are reduced respectively by, 72.30, 58.57, 61.54 and 72.48% for the cities of Agadir, Tangier, Fez and Errachidia. 5.5. Comparison with other studies Table 5 summarizes the results obtained in other studies related to the determination of optimum insulation thickness considering the effect of wall orientation. One can note that when only heating loads are considered, the south orientation is the most economical one. However, when only cooling loads are taken into account, the north orientation is the most economical one. Whereas, when both heating and cooling loads are investigated, the most economical orientation differs according to the climate of each studied city. Indeed, it corresponds to either the south orientation, the north orientation, or both south and north orientations at the same time. The same trend is obtained for the results of our study where the most economical orientation corresponds to the north orientation for the cities of Agadir, Tangier, Fez and Errachidia, while it corresponds to both south and north orientation for the city of Marrakech. The results of the present study are in harmony with those obtained by Nematchoua et al., Ozel and Al-Sanea and Zedan [14,49,51]. Our results were also compared with those obtained by Torres et al. [52]. In their study, the authors compared the performance of 7 biobased insulation materials (including hemp) to that of polyurethane, one of the best conventional insulation materials. Taking into account three different climates (cold semiarid, hot semiarid and tropical rainforest) as well as two different positions of the insulating material (inside the air cavity or on the interior surface of the wall), the authors investigated the performance of the seven insulation materials. A multi
cost, but provides very high value of the payback period. In order to evaluate the impact of the integration of thermal insulation, Figs. 9 and 10 illustrate the variation during a 24h period, of inside and outside surface temperatures for an uninsulated wall and an insulated wall with optimum hemp wool thickness. A typical day of winter (January 15, for Ifrane) and another one of summer (August 15, for Errachidia) are selected. It is seen that when the wall is insulated, the amplitude of the indoor and outdoor surface temperatures variation has been damped, thus allowing a decrease in the inside surface temperature of the wall by an average of 1.5 ∘C for the representative day of winter and 2 ∘C for the representative day of summer. Besides, as depicted in Fig. 11, the effect of the wall orientation on daily heating and cooling requirements was also investigated. It is seen that for the winter representative day, the south orientation knows the maximum load followed by the east, west and then the north orientation. However, when the wall is insulated with optimum insulation thickness, these loads are decreased by 32% for all wall orientations. Concerning the summer representative day, the highest load occurs for the eastern orientation, followed by the western one and then the south
Fig. 9. Inside surface temperatures for uninsulated walls (WI) and walls insulated with optimum insulation thickness (OPT) for all orientations: (a)-January 15, (Ifrane), (b)-August 15, (Errachidia). 10
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Fig. 10. Outside surface temperatures for uninsulated walls (WI) and walls insulated with optimum insulation thickness (OPT) for all orientations: (a)-January 15, (Ifrane), (b)-August 15, (Errachidia).
Fig. 11. Inside surface heat flux for uninsulated walls (WI) and walls insulated with optimum insulation thickness (OPT) for all orientations: (a)-January 15, (Ifrane), (b)-August 15, (Errachidia).
impacts as well as the risk of condensation of the insulation materials; whereas the life cycle cost analysis (LCCA) used in our study considers only heating and cooling requirements as input parameters. Finally, the results obtained in the study of Torres et al. [52] place hemp at the top of the bio-based insulation materials, and therefore show the relevance of its use in the construction field, whether in renovation or new construction. Consequently, this qualitative performance of hemp makes it particularly attractive for evaluating its thermal behaviour in new climates, as in the case of our study focused on Morocco. 6. Calculation of greenhouse gas emissions (GHG) The expression used for the determination of the GHG emissions varies depending on the fuel source type. In this study, electricity was used for both heating and cooling requirements. Therefore, annual GHG emissions per unit area of building external walls can be derived through Eq. (22) [53]:
Fig. 12. Annual heating and cooling requirements for the six climatic zones investigated.
mGHG =
objective optimisation was used to assess the condensation risk, as well as the cost and the environmental impacts simultaneously. The optimal solutions obtained at each optimisation loop of the process corresponded to the bio-based materials, and particularly hemp, since it offers the best compromise solution which minimize simultaneously economic and environmental impacts. However, one can note that the optimal thicknesses of hemp obtained in the study of Torres et al. (for instance, 22 cm for a cold semi-arid climate) are much greater than those obtained in our case. This could be explained first of all by the difference between the climates considered in the two studies, and then also by the difference between the optimization method used by Torres et al., considering both of the economic and environmental
aGHG E COP
(22)
where E (kWh/m2.year) is the electricity consumption due to heating and cooling requirements and COP is the coefficient of performance of the system. aGHG = 0.743 kg CO2eq/kWh [54] represents the coefficient of GHG emissions. This means that the entire upstream process, from the extraction of raw materials, transport, to the final use of energy by the user, will emit 0.743 g of greenhouse gases. Annual GHG emissions were calculated for both uninsulated and insulated external walls for the six climatic zones studied. As shown in Fig. 13, annual GHG emissions are reduced, for the climatic zones Z1, Z2, Z3, Z4, Z5 and Z6, by respectively, 4.04, 5.65, 9.52, 4.00, 8.46 and 15.90, (kg/m2 · year) 11
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Table 5 Summary of the results of other studies concerned by the determination of optimum insulation thickness for all wall orientations. Reference study thickness (cm)
Ozel [50] (heating) Ibrahim et al. [16] (heating) Ibrahim et al. [16] (cooling) Ozel (cooling) [38] Al-Sanea and Zedan [51] (heating+cooling) Daouas [17] (heating+cooling) Ozel [49] (heating+cooling) Ozel [49] (heating+cooling) Nematchoua et al. [14] (heating+cooling)
Location
Insulation materials
Optimum insulation
South
North
East
West
Kars, Turkey
Extruded polystyrene
9.2
10.2
9.8
9.8
Zahle, lebanon
Expanded polystyrene
3.4
4.7
3.9
4
Beirut, lebanon
Expanded polystyrene
4.1
1.9
4.8
4.9
Antalya, Turkey
Extruded polystyrene
3.6
3.1
4
4
Riyadh, KSA
Molded polystyrene
8.75
8.75
9.2
9.25
Tunis, Tunisia
Expanded polystyrene
10.1
10.1
11.7
11.6
Elazğ, Turkey
Extruded polystyrene
5.5
5.5
6
6
Elazğ, Turkey
Polyurethane
7
7.5
7.5
7.5
Yaoundé, Cameroon
Expanded polystyrene
8
7
8
8
optimal thicknesses vary from 1 to 6 cm depending on the diversity of the climatic conditions of the six zones studied. The minimum and maximum energy savings were found in the cities of Ifrane (3%) and Errachidia (52%), respectively. Moreover, annual GHG emissions were also calculated. Obtained results show that the integration of hemp wool with optimum thicknesses leads to siginficant mitigations in the annual GHG emissions for all the climatic zones studied. Finally, the comparison of our results with the specifications required by the Moroccan thermal regulation, show that the use of optimal thicknesses can reduce heating and cooling requirements to values lower than those set by the Moroccan thermal regulation, with percentages of 72.30, 58.57, 61.54, 56, 79 and 72.48% for the climatic zones of Agadir, Tangier, Fez, Ifrane, Marrakech and Errachidia, respectively. The numerical models used in this study consider diverse simplifications which may affect the results. In future works, the study will be revolved at the level of a whole building and taking into account the expected consequences of climate change in order to anticipate how must be future walls.
Fig. 13. Annual GHG emissions for uninsulated and insulated external walls with optimum hemp wool thicknesses for all the climatic zones studied.
Declaration of Competing Interest
when external walls are insulated with optimum hemp wool thicknesses. This means that the GHG emissions related to that external walls are mitigated by 55.12, 49.95, 63.43, 32.14, 68.84 and 74.94 (%).
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
7. Conclusion Supplementary material This study deals with the numerical analysis of the thermal performance of buildings external walls located in six different regions in the Moroccan country. In the first part of this work, an uninsulated brick wall is considered, and the quadrupoles method was used in order to determine the optimal thickness of the brick layer which maximizes the thermal inertia of the multilayer wall. For this reason, the internal thermal capacity and the thermal resistance of the uninsulated wall were calculated for thicknesses of the brick layer ranging from 10 to 30 cm. The findings show that the optimal thickness of the brick layer is equal to 20 cm. Afterwards, our multilayer wall was insulated from its outer side with hemp wool, and a second study was conducted in order to determine the optimum economic insulation thickness for the different orientations of the multilayer wall. Based on a numerical code developed in Matlab and using the life cycle cost analysis (LCCA), the optimal thickness of hemp wool, the heating and cooling requirements, the energy savings as well as the payback period have been calculated for a hypothetical building lifespan equal to 20 years and for the six climatic zones of the Moroccan country. The results found show that
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Dynamic assessment of the thermal performance of hemp wool insulated external building walls according to the Moroccan climatic zoning
T
⁎
Maryam Dlimi , Omar Iken, Rachid Agounoun, Imad Kadiri, Khalid Sbai Moulay Ismail University of Meknes, Laboratoire d’Etude des Matériaux Avancés et Applications (LEM2A), Ecole Supérieure de Technologie de Meknès (ESTM), Km 5, route d’Agouray, N6, 50040, Meknes, Morocco
A R T I C LE I N FO
A B S T R A C T
Keywords: Thermal inertia Cooling and heating transmission loads Hemp wool Optimum insulation thickness Energy savings Life-cycle cost
This paper deals with the assessment of the dynamic thermal performance of Moroccan external walls. Firstly, based on the quadrupole method, the thermal capacity and thermal resistance of an uninsulated brick wall were calculated for different thicknesses of the brick layer. The optimum brick thickness chosen corresponds to the one that maximally enhance the thermal inertia and thermal resistance. Afterwards, the brick wall was externally insulated with hemp wool, a bio-based insulation material. For an hypothetical lifespan of 20 years, and based on the life cycle cost analysis, annual heating and cooling requirements, optimum insulation thicknesses, energy savings and payback periods were calculated for all wall orientations and considering the six climatic zones of Morocco. It was found that the optimal brick thickness was equal to 0.20 m and the optimal insulation thicknesses vary between 1 and 6 cm for the different climatic zones and the different wall orientations. Moreover, a comparison with the minimum technical specifications fixed by the Moroccan thermal regulation showed that our results allow the reduction of annual heating and cooling requirements by a minimum percentage of 56% for the city of Ifrane, and a maximum percentage of 79% for the city of Marrakech. Finally, annual greenhouse gas (GHG) emissions were also calculated and it was found that they can be decreased, with the use of optimum thicknesses of hemp wool, by a minimum of 32% for the city of Ifrane and a maximum of 75% for the city of Errachidia.
1. Introduction
1.2. State of art
1.1. Background
Thanks to its porous structure, its hygrometric, regulating and thermal insulating properties, hemp is among the most studied biobased insulation materials [4]. Hemp provides two co-products used in construction: fiber and shiv (hemp hurds). The hemp fibers replace the traditional fibers and are used in the manufacture of rolls and panels of hemp wool. These rolls and panels are used vertically for the thermal insulation of walls. Concerning the hemp shiv, its use in the building essentially values the porosity of its particles. Thanks to this porosity, hemp shives are characterized by a low density and insulating properties. These particles are mainly used to make light or extra light mortars and concretes [5]. Therefore, hemp can be used as hemp concrete inside a wood frame structure, or as hemp wool for insulation, or even as hemp-lime mortar for coating. These different uses of hemp have led researchers to carry out several studies. For instance, Costantine et al. [6] investigated experimentally the thermal behavior of hemp concrete for external building wall insulation. Results obtained for indoor temperature and relative humidity
The building envelope plays a key role in determining levels of thermal, visual, acoustic and olfactory comfort. Thus, it is considered as a major element to improve the energy efficiency of buildings and reduce greenhouse gas emissions, whether in the new or existing constructions [1]. Thermal insulation is the solution to both increase thermal comfort and reduce energy consumption related to the use of heating and air conditioning systems. In order to reduce the environmental impacts and the problems of pollution related to the building sector, most of the recent researches are focused on the investigation of new bio-based insulation materials [2]. Since they are eco-friendly, the production of the bio-based materials and their subsequent transformations have a reduced impact on the environment. Indeed, the use of these materials allows the storage of the Carbone and help reducing greenhouse gas emissions [3].
⁎
Corresponding author. E-mail address: [email protected] (M. Dlimi).
https://doi.org/10.1016/j.est.2019.101007 Received 17 July 2019; Received in revised form 17 September 2019; Accepted 7 October 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Energy Storage 26 (2019) 101007
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Nomenclature a As c Cel Cenr Ci Cins Cth COP Qh d Hu hi ho i IT j k kins L Lins Lopt
M N p Pb Qc qi qe t Tin Tsa Tx = L, max Tx = L, min Tx = 0, max Tx = 0, min
Outdoor surface wall solar absorptivity Annual energy savings ($ m2) Specific heat (J/kg.K) Cost of electricity ($/kWh) Cost of energy consumption ($ m2) Cost of insulation material ($ m2) Cost of insulation material ($ /m3) Internal thermal capacity (kJ/m2.K) Coefficient of performance of air-conditioning system Yearly heating transmission load (J/m2) Discount rate (%) Heating value of electricity (J/m3) Inside convective heat transfer coefficient (W/m2.K) Outside convective heat transfer coefficient (W/m2.K) Inflation rate (%) Incident solar radiation for vertical surfaces (W/m2) Complex argument Thermal conductivity (W/m.K) Thermal conductivity of insulation material (W/m.K) Total thickness of a wall (m) Insulation thickness (m) Optimum insulation thickness (m)
Layers number of composite wall Lifetime of building (years) Laplace variable Payback period (years) Yearly cooling transmission load (J/m2) Heat flux of indoor surface of the wall (W/m2) Heat flux of outdoor surface of the wall (W/m2) Time (s) Indoor air temperature (∘ C) Sol-air temperature (∘ C) Maximum indoor surface temperature (∘ C) Minimum indoor surface temperature (∘ C) Maximum outdoor surface temperature (∘ C) Minimum outdoor surface temperature (∘ C)
Greek symbols α ρ x ηs ω Δx Δt
Thermal diffusivity (m2/s) Density (kg/m3) Coordinate direction normal to wall (m) Efficiency of the heating system Angular frequency (s−1) Space step (m) Time step (s)
use of thermal insulation with optimum insulation thickness. Over a given lifetime of the building, the optimum insulation thickness corresponds to the value that provides the lowest total cost defined as the sum of insulation and energy consumption costs [13]. Nematchoua et al. [14] calculated the required insulation thickness with the corresponding energy savings for buildings in two different cities with two different climates. Two wall structures were considered: compressed stabilized earth wall and concrete block wall. The insulation material used was the extruded polystyrene. Results showed that in the city of Yaounde which is characterized by an equatorial climate, optimum insulation thickness and energy savings for the south facing wall were equal to 0.08 m and 51.69 $/m2, respectively. For the city of Garoua which is characterized by a tropical climate, optimum insulation thickness calculated for a north orientation wall was obtained as 0.11 m and energy savings as 97.82 $/m2. Besides, based on the isotropic model of Duffie and Beckman [15], Ibrahim et al. [16] determined the optimum insulation thickness according to cooling requirements in buildings located in the city of Beirut, Lebanon. The insulation material chosen was extruded polystyrene, and the optimum insulation thicknesses obtained were 4.9, 4.8, 4.1 and 4.1 cm for the west, east, north and south orientations, respectively. On the other hand, based on an analytical method, optimum insulation thickness of expanded polystyrene for building walls located in Tunis, Tunisia was calculated by Daouas [17]. The south orientation was considered as the most economical one since the value of optimum insulation thickness was found equal to 10.1 cm, with a percentage of 71.33% as energy savings and 3.29 years as payback period.
underlined the ability of hemp concrete to dampen the outdoor climatic conditions. Furthermore, Seng et al. [7] have used several experimental methods to characterize the thermo-physical properties of a precast hemp concrete block. The founded results showed that the choice of the experimental method has a significant influence on the determination of the different thermal properties of the prefabricated hemp concrete block; especially the heat capacity. On the other hand, Mazhoud et al. [8] investigated thermal and hygric properties of two different hemplime plasters made with hemp shiv of different sizes (cut into small and large sizes). Thermal properties, moisture buffer value, water vapor permeability and sorption isotherm were measured. The authors found that hemp-lime plasters possess high hygrothermal qualities, with a thermal conductivity of around 0.2 W/m.K. They also showed that the hemp-lime plaster made with the largest hemp shiv is less conductive than the other one with smallest hemp shiv. Nevertheless, from a hygric point of view, the latter is a better regulator. Besides, hygric properties of two different hemp wools based on organic and polyester binders were investigated by Collet et al. [9]. It was found that the two kinds of hemp wool show similar vapour resistance and are characterised by high water content. The thermal comfort of a room as well as the energy consumption of heating and air conditioning systems are greatly influenced by the dynamic thermal performance of a multilayer wall which is known as thermal inertia [10]. In this context, Li et al. [11] explored the effects of coupling the thermal inertia of both the thermal mass and the air conditioning system on the demand response period for a commercial building. The results showed a great accuracy of the coupled model since the effect of the thermal inertia of the air conditioning system on the demand reduction was considerable. Moreover, in order to improve the passive cooling strategy based on the building night ventilation, Chahwane et al. [12] developed an algorithm adapted for different types of commercial buildings thermal masses where the indoor air temperature is conditioned in the whole year. The effectiveness of the developed algorithm was shown in the realized energy savings (more than 30%), the decreased discomfort hours (57%) and the reduction of the electric power of the ventilation system. Thermal inertia is not the only parameter responsible of reducing the energy consumption due to heating and air-conditioning systems. Consequently, more significant energy savings can be achieved with the
1.3. Aim of the study The majority of the studies dealing with the use of bio-based materials for the thermal insulation of buildings are rather concentrated on the evaluation of the materialshygrothermal performances, and lack economic analysis. Moreover, these studies, concentrated especially in Europe, are little treated in Africa, hence the interest of our study, which is focused in Morocco, a country where hemp is cultivated for centuries but its use in the building industry is very limited. The aim of the current study is to evaluate the thermal performance of typical Moroccan buildings external walls under the climatic conditions of six 2
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different regions: Agadir, Tangier, Fez, Ifrane, Marrakech and Errachidia. Firstly, based on the quadrupole method, the thermal behavior of a double sided brick wall is assessed by the determination of the optimum thickness of the brick layer providing the maximum thermal inertia. In the second part of this study, hemp wool insulation is integrated at the external side of the brick wall. Then, considering heating and cooling requirements, optimum insulation thickness, energy savings and payback periods are determined for all wall orientations and for the six climatic zones under investigation. A computer Matlab code is developed for the solution of the transient one dimensional heat equation using the finite difference method and based on the implicit scheme. Moreover a comparative study is conducted between heating and cooling requirements values obtained using optimal insulation thicknesses and the values fixed by the Moroccan thermal regulation for each climatic zone. Finally, annual GHG emissions related to each climatic zone are calculated.
Table 1 Thermophysical properties of building materials. Material
λ (W/m.K)
ρ (kg/m3)
c (J/kg.K)
Brick [18] Hemp wool [19] Cement mortar [20]
0.68 0.04 0.72
1600 35 1865
840 1200 840
cities of each climatic zone are: Agadir, Tangier, Fez, Ifrane, Marrakech and Errachidia [24]. Considering these six climatic zones, the current study focuses on the calculation of heating and cooling requirements covering a winter period from November to March and a summer period from June to September. In calculations, the 15th day of each month is considered as a representative day for the whole month. The diurnal variations of the external environment temperature will be calculated by means of the sol-air temperature Tsa(t) which includes solar radiation effects and is expressed as follows [25]:
2. Studied configurations In Morocco, typical building constructions are generally based on bricks and cement mortar. In order to enhance the thermal performance of external building walls, investigations are conducted aiming to maximize thermal inertia and thermal resistance. The first configuration depicted in Fig. 1(a) is a composite wall structure consisting of 2 cm inner and outer cement mortar and a solid brick layer of variable thicknesses. In the second configuration (Fig. 1(b)), an insulation layer varying from 1 to 10 cm is introduced and located on the external side of the double sided brick wall. The materials used in the wall structure and their thermal properties are given in Table 1.
Tsa (t ) = Ta (t ) +
aIT (t ) ε ΔR − ho ho
(1)
where Ta(t) is the outdoor air temperature, he is the combined (convective and radiative) outdoor heat transfer coefficient, a and IT(t) are the external wall surface solar absorbtivity and the total solar radiation, respectively. ε ΔR expresses the correction factor and is assumed to be 4∘ ho C for horizontal surfaces and 0 for vertical ones [26]. The outdoor air temperature Ta(t) and the hourly values of total solar radiation IT(t) are provided using Meteonorm data [27] specific to each Moroccan city. The external wall surface solar absorbtivity is taken equal to 0.55 [28], and ho = 22 W/m2K according to ASHRAE standard [26]. Sol-air temperature and solar radiations of the 15th day of the months of January (Ifrane) and August (Errachidia) are presented in Figs. 2 and 3. Ifrane and Errachidia cities were chosen since they require the highest heating and cooling loads, respectively. As shown in Figs. 2(a) and 3(a), sol-air temperature is strongly dependent to solar radiation (Figs. 2(b) and 3(b)) whose distribution depends mainly on the season, the orientation of the wall and the period of the day. For the winter representative day (Ifrane), the highest solar radiation is reached by the south orientation with a maximum value exceeding 290 W/m2. With solar radiation values of 198 and 213 W/m2, respectively, east and west orientations are less subjected to solar radiation than the southern orientation. The north orientation is the least exposed to solar radiation, with a value barely exceeding 124 W/m2. It is also seen that the maximum peak values of solar radiations for all wall orientations are reached at different times of the day: 13:00, 11:00, 16:00 and 14:00 for south, east, west and north orientations respectively.
3. Overview on the Moroccan climate Located in the North West of Africa, between the arid regions of the Western Sahara and the moderate Mediterranean and Atlantic regions [21], Morocco is a country characterized by a large variety of climates. Firstly, a typical Mediterranean climate reigns on the Mediterranean coast and the Rif. Then, a Sub-Mediterranean climate with oceanic influences characterizes the northern Atlantic plains and becomes continental in the interior. On the other hand, the plains of Doukkala up to the Souss basin are characterized by a degradation of the climate of the North Atlantic plains, with increasing aridity towards the south, because of the Saharan influences that are beginning to be felt. Further, the middle and high Atlas are characterized by the mountain climate, while the Saharan area knows a typical desert climate [22]. Since the Moroccan territory is characterized by various climates, the country was subdivided into six climatic zones in coordination with the Direction of the National meteorology [23]. The representative
Fig. 1. (a): Uninsulated wall configuration, (b): Hemp wool insulated wall configuration. 3
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Fig. 2. (a): Daily sol-air temperature and (b): Daily solar radiation for January 15, for the city of Ifrane.
Fig. 3. (a): Daily sol-air temperature and (b): Daily solar radiation for August 15, for the city of Errachidia.
earth tilt, the sun is getting closer to the south hemisphere, thus, south orientation in north hemisphere is the most exposed to solar radiations. Unlike to summer, the sun has a position closer to the north hemisphere, allowing to the eastern orientation during morning, and the western orientation during evening, to be the most exposed to solar radiations.
4. Characterization of thermal inertia based on the quadrupole method The thermal inertia defines the ability of a material to store heat and then restore it gradually. Specific heat and density are the two material properties involved in the characterization of the thermal inertia. According to its layout in a wall, a building material with high density and specific heat leads to increasing the thermal inertia of a wall. Two types of thermal inertia are distinguished: the transmission inertia, characterized by the two notions of time lag and decrement factor, and inner inertia representing the capacity of the internal surface of a wall to absorb, store and restore heat. Being the subject of this study, the inner inertia is characterized by the internal thermal capacity Cth. This thermal capacity can be calculated through the analytical resolution of the heat equation using the thermal quadrupole method [29]. In this section, the inner thermal inertia of the two sided uninsulated brick wall with fixed thicknesses of cement mortar on its internal and external surfaces is assessed (Fig. 1(a)). The study focuses on the calculation of the thermal capacity Cth of the multilayer wall, and this, for different thicknesses of the solid brick layer.
Fig. 4. Internal thermal capacity variation with solid brick thickness.
For the summer representative day (Errachidia), the trend has changed and the east and west orientations are exposed to the highest solar radiation reaching a maximum value of 738 and 730 W/m2 respectively, followed by the south orientation with a maximum solar radiation value of 427 W/m2. The north orientation is always the least exposed to solar radiation reaching a maximum value of 157 W/m2. The maximum peak values of solar radiations are reached for the south, east, north and west orientations at 16:00, 11:00, 16:00 and 20:00, respectively. The difference in the distribution of solar radiation from a season period to another one can be explained by the fact that in winter, due to 4
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Fig. 5. (a)-Distribution of inside and outside surface temperatures and (b)-Internal and external surface heat fluxes distribution.
4.1. Quadrupoles method
Zt (ω) = B (ω)
The quadrupole method is a well known analytical tool in heat transfer modeling through a solid medium. Depending on the transient regime, Laplace or Fourier transforms are the basis of this method. Switching from Laplace to Fourier transform is possible by substituting the Laplace variable p by jω where j = −1 is the complex argument and ω is the angular frequency [30]. The period P is equal to 24 hours since the outside temperature changes diurnally. The one-dimensional heat conduction problem in a homogeneous wall of thickness L, thermal conductivity k and thermal diffusivity α, can be analytically described by linking temperatures and heat fluxes on its both sides by a transfer matrix [31]. In the case where the homogeneous wall is subjected to sinusoidal temperature variations on its boundary sides, Fourier transform is applied and the transfer matrix, including resistances of both outer and inner surfaces, is expressed as Eq. (2) [32]:
Zin (ω) =
1 1 ⎡ θout (ω) ⎤ = ⎡ 1 he ⎤·⎡ A (ω) B (ω) ⎤·⎡ 1 hi ⎤·⎡ θin (ω) ⎤ ⎥ ⎢ C (ω) D (ω) ⎥ ⎢ ⎥ ⎢ ϕ (ω) ⎥ ⎢ ϕout (ω) ⎥ ⎢ ⎣ ⎦ ⎦ ⎣0 1 ⎦ ⎣ ⎦ ⎣ 0 1 ⎦ ⎣ in θin (ω) ⎤ ⎡ = Mout (ω)·M (ω)·Min (ω)· ⎢ ϕin (ω) ⎥ ⎣ ⎦
Cth (ω) = −
Ai (ω) Bi (ω) ⎤ whereMi (ω) = ⎡ , i = 1, 2, …N . ⎢ Ci (ω) Di (ω) ⎥ ⎣ ⎦
(4)
(5)
Ri Li ⎤ Bi (ω) = sinh ⎡2π (1 + j ) ⎢ 2π (1 + j )(Li /Λi) Λi (ω) ⎥ ⎦ ⎣
(6)
2π (1 + j )(Li /Λi) Li ⎤ sinh ⎡2π (1 + j ) ⎢ Ri Λ i (ω) ⎥ ⎣ ⎦
After the determination of the optimum thickness of the brick layer allowing the maximization of the thermal inertia of our studied uninsulated wall, external thermal insulation is added in order to increase its thermal resistance (Fig. 1(b)). The insulation material chosen in our study is the hemp wool, a bio-based insulation material with thermophysical properties close to those of the expanded polystyrene, the most classical insulation material [19].
(7)
A composite wall structure consisting of 4 parallel layers with different materials and thicknesses (Fig. 1(b)) is considered. Taking into account constant thermophysical properties (Table 1) and no heat generation, the heat transfer through each layer of the external insulated wall is governed by the transient 1D heat equation expressed as Eq. (12):
where (Ri = Li /ki) represents the thermal resistance of the layer i, and 2αi Λi (ω) = 2π defines the thermal wavelength of the material layer i ω at an angular frequency ω. The wall can be represented by three impedances acting as heat accumulators and expressed as Eqs. (8)–(10):
B (ω) D (ω) − 1
(11)
5.1. Numerical model
Li ⎤ Ai (ω) = Di (ω) = cosh ⎡2π (1 + j ) ⎢ Λ (ω) ⎥ i ⎣ ⎦
Zout (ω) =
1 ωI [Zin (ω)]
5. Financial analysis for the calculation of optimal insulation thickness
For each layer transmission matrix, the quadrupole terms are expressed as Eqs. (5)–(7):
Ci (ω) =
(10)
The variation of the internal thermal capacity versus the variation of the solid brick thickness is depicted in Fig. 4. One can note that the internal thermal capacity value increases with the increase of the solid brick thickness until reaching a maximum value and then decreases. The maximum value of the internal thermal capacity is reached when the solid brick insulation is equal to 20 cm. Thus, the thermal inertia of the double sided brick wall is maximized, and it only remains the introduction of an insulating layer to enhance its thermal resistance.
For a multilayer wall, M (ω) corresponds to the total matrix of the entire wall and is obtained as follows in Eq. (3): (3)
B (ω) A (ω) − 1
As mentioned above and as recommended by the international standard ISO 13786 [33], inner thermal inertia is characterized by the thermal capacitance Cth related to the internal surface of the wall. Its expression depends on the imaginary part of the inside impedance Zin(ω) and is written as follows in Eq. (11):
(2)
M (ω) = MN (ω)·… ·M2 (ω)·M1 (ω)
(9)
kj ∂2Tj / ∂x 2 = ρj cj
∂Tj ∂t
, j = (1, 2…,M )
(12)
where kj, ρj and cj are the thermal conductivity, the density and the specific heat of the layer, respectively. Tj is the temperature, x and t are spatial and temporal coordinates. Eq. (12) is solved with the specification of an initial and two boundary conditions. As initial condition, an arbitrary uniform temperature field is assumed. The outdoor and indoor boundary conditions are given respectively as follows in
(8) 5
Journal of Energy Storage 26 (2019) 101007
0.33 6.57 5.98 0.327 6.00 0.350 1.33 2.92 6.74 0.133 1.12 16.66 10.55 0.100
∂T = ho (Tsa (t ) − Tx = 0) − k1 ⎛ ⎞ ⎝ ∂x ⎠ x = 0
(13)
∂T = hi (Tx = L − Tin ) − kM ⎛ ⎞ ⎝ ∂x ⎠ x = L
(14)
where hi = 9 W/m2 and ho = 22 W/m2 are the combined inner and outer heat transfer coefficients, respectively. The outside surface of the wall is subjected to the sol-air temperature Tsa(t) and its inside surface is exposed to the indoor air temperature maintained constant at the fixed design temperatures Tin = 20 ∘ C in winter, and Tin = 26∘C in summer, according to the Moroccan Standard NM ISO 7730 RTCM [35]. To obtain the temperature distribution through the investigated wall, the implicit finite difference method [36] is applied to solve the transient 1D heat conduction equation. The finite difference equations are solved using matrix functions in Matlab [37]. The accuracy and reliability of the developed Matlab code is validated with the numerical results of Jin et al [20]. Based on the determination of the heat flux time lag and heat flux decrement factor, the authors investigated the effect of the thermal properties on the thermal performances of a wall. For this aim, the transient 1D heat equation was solved for a brick wall with the fallowing thermal properties k = 0.62 W/mK, c = 840 J/kgK, ρ = 1800 kg/m3, and with the fallowing 2πt π − ), boundary conditions: Tin = 26 ∘ C, Tsa = 30 + 5 × sin( 24 2 hi = 8.7 W/m2 and ho = 18.6 W/m2. The implicit finite difference method was used to discretize the transient 1D heat equation, with a space grid size of 0.5 mm and a time step of 20 s. The variations of the outside (Tx = 0 ) and inside (Tx = L ) surface temperatures as well as the internal and external surface heat fluxes qi and qe using the two numerical codes are depicted in Fig. 5. It can be seen that the distribution of temperatures and heat fluxes obtained with our numerical code are in good agreement with those obtained in the study of Jin et al. [20] with a maximum difference of 1%. Moreover, the transient 1D heat equation was solved in other studies in order to determine time lag and decrement factor for different materials and under different climatic conditions. In these studies, other numerical codes and software were used. The values of time lag and decrement factor calculated by the methods used in these studies as well as by the numerical code used in this paper are presented in Table 2. Finally, it can be seen from Fig. 5 and Table 2 that the results of the present study are in good agreement with those of these different studies, which demonstrates that the home-made Matlab code is effective and accurate.
6.65 0.137
Difference in
Asan [39] (Crank–Nicolson)
Eqs. (13) and (14) [34]:
Present study
5.2. Heating and cooling transmission loads calculation Annual heating and cooling transmission loads are calculated from November to March and June to September, respectively. The day 15 of each month is considered as a representative day for the whole month. Firstly, the hourly variation of the inside surface heat flux is expressed as follows in Eq. (15):
10.67 0.012
qi = hi (Tx = L − Ti )
(15)
Afterwards, daily total loads are obtained by the integration over a 24h period of the hourly inside surface heat flux. Finally, annual heating and cooling transmission loads are then calculated from the addition of daily total loads over the winter and summer periods considered. Fig. 6 represents the variations of annual heating and cooling transmission loads compared to the increase of the insulation thickness. One can note that when the insulation thickness is increased from 1
Time lag Decrement factor
Ozel [38] (Implicit scheme)
Table 2 Time lag and decrement factor calculated by our numerical method and those used in other studies.
Present study
Difference in %
Belhadj [40] (Energy Plus Software)
Present study
Difference in %
M. Dlimi, et al.
6
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Fig. 6. Variation of annual heating and cooling loads with insulation thickness.
the north and south facing external walls have been neglected as thermal insulation increases cooling transmission loads rather than decreasing them. In addition, heating transmission loads are relatively less important in the climatic zones of Errachidia, Fez and Marrakech. While cooling transmission loads are highest in the zone of Errachidia, followed by the
to 6 cm, heating and cooling requirements are significantly reduced, whereas when the insulation thickness exceeds 7 cm, this decrease becomes less significant. By comparing the heating and cooling loads of each climatic zone, we note that the zone of Ifrane is the one that represents the maximum of heating requirements and the minimum of cooling ones. In addition, 7
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Table 3 Parameters used in calculations.
Q Cel Qh + Cenr = PWF ⎛⎜ c Cel ⎞⎟ 6 × COP 3.6 10 H u ηs ⎠ ⎝
Parameter
Value
Electricity cost (Cel), [44] Heating value (Hu), [45] Efficiency of the heating system (ηs), [45] Coefficient of performance of the cooling system (COP), [46] Insulation cost (Cins), [47] Discount rate (d), [48] Inflation rate (i), [48] Lifetime period (N), [43]
0.1346 $/kWh 3.6 × 106 J/m3 0.99 2.5 100 $/m3 2.25% 1.8% 20 years
(16)
PWF is the present worth factor which is defined as Eqs. (17) and (18):
PWF =
(1 + r ) N − 1 i−d d−i , if {i > d r = } or {i < d r = } r (1 + r ) N 1+d 1+i (17)
PWF =
N , if i = d 1+i
(18)
Qc, Qh, Cel and COP represent the annual cooling and heating transmission loads per unit area, the cost of electricity and the cooling system performance, respectively. The total cost is the sum of the cost of energy consumption and the cost of insulation material. The total cost per unit area of wall is given by Eq. (19):
zone of Marrakech and then by the zone of Fez. As for the climatic zones of Agadir and Tangier, these represent moderate heating and cooling requirements. In order to be able to determine which thickness of insulation will maximally improve the thermal and economical performances of the multilayer wall, an optimum economic insulation thickness must be calculated.
Q Cel Qh Ct = Cenr + Ci = PWF ⎛⎜ c + Cel ⎞⎟ + Cins Lins 6 COP 3.6 × 10 H u ηs ⎠ ⎝
(19)
Cins is the cost of the insulation material by unit volume and Lins is the insulation thickness. Resulting energy savings are calculated from the difference between the total cost of the wall without insulation and the total cost of the wall with optimum insulation thickness [42]. Annual energy savings As are obtained by dividing the result of the difference between the energy costs of the wall without insulation and the wall with optimum insulation thickness divided by the present worth factor PWF. The payback period Pb is defined as the insulation cost divided by annual energy savings, it can be directly calculated as follows in Eq. (20) if interest and inflation rates are not taken into account:
5.3. Life cycle cost analysis The optimum economic insulation thickness represents the value providing the lowest total life-cycle cost. This one represents the sum of the cost of the energy consumption and the insulation cost. Since the optimal thickness value of insulation is not influenced by other loads, it is calculated by only considering external walls heat transmission [41]. Using heating and cooling transmission loads as input data, and based on the present worth method, the inflation rate i and the discount rate d, an economic model is set for the determination of the optimal insulation thickness. The cost of energy consumption during a building lifetime of N years is given by the Eq. (16) [17]:
Pb =
Ci. Lins (opt ) As
Fig. 7. Variation of costs with insulation thickness for all wall orientations and for the city of Marrakech. 8
(20)
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Fig. 8. Variation of total Costs with insulation thickness for all wall orientations.
thickness. It corresponds to the lowest value shown by the total cost curve. Fig. 8 shows the variation of the total costs for the six climatic zones studied and for all wall orientations. It is seen that the south, east and west orientations give equal insulation thicknesses except for the cities of Marrakech and Tangier where the insulation thickness of the south facing external walls decreases. The lowest insulation thickness is given by the north facing external walls for all the investigated climatic zones. The values of optimum insulation thickness, percentages of energy savings, minimum total costs and payback periods for all orientations and all the climatic zones investigated are depicted in Table 4. The insulation thicknesses vary between a minimum value of 1 cm and a maximum value of 6 cm. The eastern and western orientations provide high values of the minimum total cost and energy savings, and a low value of the payback period. On the other hand, the north orientation is the most economical one according to the minimum total
When the inflation and the interest rates are considered, the payback period Pb is given as the Eq. (21) [43]:
Ci. Lins (opt ) ⎤ ln ⎡1 − r ⎥ ⎢ As ⎦ Pb = ⎣ 1 ln ⎡ 1 + r ⎤ ⎣ ⎦
(21)
All the parameters needed for the above economic calculations are summarized in Table 3. For the climatic zone of Marrakech, and considering the four orientations, Fig. 7 presents the variation of the energy consumption cost, the insulation cost and the total cost in respect to insulation thickness. It is clearly shown that the energy cost decreases, while the insulation cost knows a linear increase with the increase of the insulation thickness. The total cost, which represents the sum of energy and insulation costs, allow the determination of the optimum insulation 9
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and the north orientations. For all orientations, a reduction percentage of 73% is obtained with the use of optimal insulation thickness.
Table 4 Results summary. Climatic zone
Z1: Agadir
Z2: Tangier
Z3: Fez
Z4: Ifrane
Z5: Marrakech
Z6: Errachidia
Wall orientation
Optimum insulation thickness (m)
Minimum total cost ($/m2)
Energy savings (%)
Payback period (years)
South East North West
0.03 0.03 0.02 0.03
7.70 7.62 6.54 8.09
30.45 35.32 24.22 32.94
11.92 10.60 12.51 10.89
South East North West
0.02 0.03 0.01 0.03
6.44 7.72 2.57 8.11
23.36 29.67 78.64 33.84
19.17 12.13 7.24 10.62
South East North West
0.04 0.04 0.03 0.04
8.96 10.38 8.51 10.60
35.46 42.56 34.55 43.91
8.51 6.50 10.13 6.17
East West
0.01 0.01
3.57 3.83
2.95 8.92
68.53 55.23
South East North West
0.04 0.06 0.04 0.06
9.68 12.97 9.33 13.85
39.72 50.29 38.12 53.53
7.32 3.97 7.79 3.45
South East North West
0.06 0.06 0.04 0.06
13.29 14.86 9.55 14.63
51.58 55.28 45.69 55.35
3.76 4.08 5.60 3.14
5.4. Comparison with Moroccan thermal regulation Our results were compared to the minimum technical specifications fixed by the Moroccan thermal regulation for the thermal performance of buildings. Fig. 12 presents a comparison between the annual heating and cooling requirements provided by the optimum insulation thicknesses and the ones specified by the Moroccan thermal regulation for the six climatic zones studied. We notice that for all the climatic zones investigated, the annual heating and cooling requirements calculated in this study are much lower than those fixed by the Moroccan thermal regulation. For instance, heating and cooling requirements related to the city of Marrakech know the maximum percentage of reduction reaching almost 79%. On the other hand, the lowest percentage of heating and cooling requirements reduction concerns the city of Ifrane with a value of 56%. For the remaining four climatic zones, heating and cooling transmission loads are reduced respectively by, 72.30, 58.57, 61.54 and 72.48% for the cities of Agadir, Tangier, Fez and Errachidia. 5.5. Comparison with other studies Table 5 summarizes the results obtained in other studies related to the determination of optimum insulation thickness considering the effect of wall orientation. One can note that when only heating loads are considered, the south orientation is the most economical one. However, when only cooling loads are taken into account, the north orientation is the most economical one. Whereas, when both heating and cooling loads are investigated, the most economical orientation differs according to the climate of each studied city. Indeed, it corresponds to either the south orientation, the north orientation, or both south and north orientations at the same time. The same trend is obtained for the results of our study where the most economical orientation corresponds to the north orientation for the cities of Agadir, Tangier, Fez and Errachidia, while it corresponds to both south and north orientation for the city of Marrakech. The results of the present study are in harmony with those obtained by Nematchoua et al., Ozel and Al-Sanea and Zedan [14,49,51]. Our results were also compared with those obtained by Torres et al. [52]. In their study, the authors compared the performance of 7 biobased insulation materials (including hemp) to that of polyurethane, one of the best conventional insulation materials. Taking into account three different climates (cold semiarid, hot semiarid and tropical rainforest) as well as two different positions of the insulating material (inside the air cavity or on the interior surface of the wall), the authors investigated the performance of the seven insulation materials. A multi
cost, but provides very high value of the payback period. In order to evaluate the impact of the integration of thermal insulation, Figs. 9 and 10 illustrate the variation during a 24h period, of inside and outside surface temperatures for an uninsulated wall and an insulated wall with optimum hemp wool thickness. A typical day of winter (January 15, for Ifrane) and another one of summer (August 15, for Errachidia) are selected. It is seen that when the wall is insulated, the amplitude of the indoor and outdoor surface temperatures variation has been damped, thus allowing a decrease in the inside surface temperature of the wall by an average of 1.5 ∘C for the representative day of winter and 2 ∘C for the representative day of summer. Besides, as depicted in Fig. 11, the effect of the wall orientation on daily heating and cooling requirements was also investigated. It is seen that for the winter representative day, the south orientation knows the maximum load followed by the east, west and then the north orientation. However, when the wall is insulated with optimum insulation thickness, these loads are decreased by 32% for all wall orientations. Concerning the summer representative day, the highest load occurs for the eastern orientation, followed by the western one and then the south
Fig. 9. Inside surface temperatures for uninsulated walls (WI) and walls insulated with optimum insulation thickness (OPT) for all orientations: (a)-January 15, (Ifrane), (b)-August 15, (Errachidia). 10
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Fig. 10. Outside surface temperatures for uninsulated walls (WI) and walls insulated with optimum insulation thickness (OPT) for all orientations: (a)-January 15, (Ifrane), (b)-August 15, (Errachidia).
Fig. 11. Inside surface heat flux for uninsulated walls (WI) and walls insulated with optimum insulation thickness (OPT) for all orientations: (a)-January 15, (Ifrane), (b)-August 15, (Errachidia).
impacts as well as the risk of condensation of the insulation materials; whereas the life cycle cost analysis (LCCA) used in our study considers only heating and cooling requirements as input parameters. Finally, the results obtained in the study of Torres et al. [52] place hemp at the top of the bio-based insulation materials, and therefore show the relevance of its use in the construction field, whether in renovation or new construction. Consequently, this qualitative performance of hemp makes it particularly attractive for evaluating its thermal behaviour in new climates, as in the case of our study focused on Morocco. 6. Calculation of greenhouse gas emissions (GHG) The expression used for the determination of the GHG emissions varies depending on the fuel source type. In this study, electricity was used for both heating and cooling requirements. Therefore, annual GHG emissions per unit area of building external walls can be derived through Eq. (22) [53]:
Fig. 12. Annual heating and cooling requirements for the six climatic zones investigated.
mGHG =
objective optimisation was used to assess the condensation risk, as well as the cost and the environmental impacts simultaneously. The optimal solutions obtained at each optimisation loop of the process corresponded to the bio-based materials, and particularly hemp, since it offers the best compromise solution which minimize simultaneously economic and environmental impacts. However, one can note that the optimal thicknesses of hemp obtained in the study of Torres et al. (for instance, 22 cm for a cold semi-arid climate) are much greater than those obtained in our case. This could be explained first of all by the difference between the climates considered in the two studies, and then also by the difference between the optimization method used by Torres et al., considering both of the economic and environmental
aGHG E COP
(22)
where E (kWh/m2.year) is the electricity consumption due to heating and cooling requirements and COP is the coefficient of performance of the system. aGHG = 0.743 kg CO2eq/kWh [54] represents the coefficient of GHG emissions. This means that the entire upstream process, from the extraction of raw materials, transport, to the final use of energy by the user, will emit 0.743 g of greenhouse gases. Annual GHG emissions were calculated for both uninsulated and insulated external walls for the six climatic zones studied. As shown in Fig. 13, annual GHG emissions are reduced, for the climatic zones Z1, Z2, Z3, Z4, Z5 and Z6, by respectively, 4.04, 5.65, 9.52, 4.00, 8.46 and 15.90, (kg/m2 · year) 11
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Table 5 Summary of the results of other studies concerned by the determination of optimum insulation thickness for all wall orientations. Reference study thickness (cm)
Ozel [50] (heating) Ibrahim et al. [16] (heating) Ibrahim et al. [16] (cooling) Ozel (cooling) [38] Al-Sanea and Zedan [51] (heating+cooling) Daouas [17] (heating+cooling) Ozel [49] (heating+cooling) Ozel [49] (heating+cooling) Nematchoua et al. [14] (heating+cooling)
Location
Insulation materials
Optimum insulation
South
North
East
West
Kars, Turkey
Extruded polystyrene
9.2
10.2
9.8
9.8
Zahle, lebanon
Expanded polystyrene
3.4
4.7
3.9
4
Beirut, lebanon
Expanded polystyrene
4.1
1.9
4.8
4.9
Antalya, Turkey
Extruded polystyrene
3.6
3.1
4
4
Riyadh, KSA
Molded polystyrene
8.75
8.75
9.2
9.25
Tunis, Tunisia
Expanded polystyrene
10.1
10.1
11.7
11.6
Elazğ, Turkey
Extruded polystyrene
5.5
5.5
6
6
Elazğ, Turkey
Polyurethane
7
7.5
7.5
7.5
Yaoundé, Cameroon
Expanded polystyrene
8
7
8
8
optimal thicknesses vary from 1 to 6 cm depending on the diversity of the climatic conditions of the six zones studied. The minimum and maximum energy savings were found in the cities of Ifrane (3%) and Errachidia (52%), respectively. Moreover, annual GHG emissions were also calculated. Obtained results show that the integration of hemp wool with optimum thicknesses leads to siginficant mitigations in the annual GHG emissions for all the climatic zones studied. Finally, the comparison of our results with the specifications required by the Moroccan thermal regulation, show that the use of optimal thicknesses can reduce heating and cooling requirements to values lower than those set by the Moroccan thermal regulation, with percentages of 72.30, 58.57, 61.54, 56, 79 and 72.48% for the climatic zones of Agadir, Tangier, Fez, Ifrane, Marrakech and Errachidia, respectively. The numerical models used in this study consider diverse simplifications which may affect the results. In future works, the study will be revolved at the level of a whole building and taking into account the expected consequences of climate change in order to anticipate how must be future walls.
Fig. 13. Annual GHG emissions for uninsulated and insulated external walls with optimum hemp wool thicknesses for all the climatic zones studied.
Declaration of Competing Interest
when external walls are insulated with optimum hemp wool thicknesses. This means that the GHG emissions related to that external walls are mitigated by 55.12, 49.95, 63.43, 32.14, 68.84 and 74.94 (%).
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
7. Conclusion Supplementary material This study deals with the numerical analysis of the thermal performance of buildings external walls located in six different regions in the Moroccan country. In the first part of this work, an uninsulated brick wall is considered, and the quadrupoles method was used in order to determine the optimal thickness of the brick layer which maximizes the thermal inertia of the multilayer wall. For this reason, the internal thermal capacity and the thermal resistance of the uninsulated wall were calculated for thicknesses of the brick layer ranging from 10 to 30 cm. The findings show that the optimal thickness of the brick layer is equal to 20 cm. Afterwards, our multilayer wall was insulated from its outer side with hemp wool, and a second study was conducted in order to determine the optimum economic insulation thickness for the different orientations of the multilayer wall. Based on a numerical code developed in Matlab and using the life cycle cost analysis (LCCA), the optimal thickness of hemp wool, the heating and cooling requirements, the energy savings as well as the payback period have been calculated for a hypothetical building lifespan equal to 20 years and for the six climatic zones of the Moroccan country. The results found show that
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