ENERGY PERFORMANCE ASSESSMENT OF ENVELOPES FROM ORGANIC MATERIALS

The global trend of organic materials application for the construction low rise residential accommodation in the context of the sustainable development concept results in growing interest towards the usage of both known natural materials and their combinations as well as the search of new technological decisions. The trend of eco-buildings is starting to play an important role. The concept of eco-buildings means construction of low-energy buildings [1] that cause less harm to the environment due to minimised value of primary energy consumption and low rate of heat losses, cost of materials, etc. As Brojan, L. et al [2] states, one of the criteria, which can be applied for the assessment of environment damage, is an index of primary energy consumption, or primary energy input (PEI) index, MJ/m². In fact, this is the volume of necessary energy resources for the production and maintenance of a 1 m² surface of enclosing structures [2].

It is obvious that eco-buildings should be primarily constructed of organic materials, which meet all abovementioned requirements. The worldwide spreading of this trend in general, and in Ukraine, in particular, is becoming of special significance.

The purpose of the current research is to provide an objective comparison of different types of envelopes from natural materials of organic origin in terms of their thermophysical and physical-mechanical parameters.

To achieve this goal, a variety of the following tasks should be solved: –

a list of envelopes’ types for low storey residential buildings, based on the conducted data review should be created;

For numerical simulation and further analysis, as well as for the convenient calculation of the research purpose five blank wall cross sections types of walls from natural materials of an organic origin (Fig. 2) are used: a hempcrete wall (type “A”), an adobe wall of (type “B”), a strawbale panel wall (type “C”), an earthbag wall (type “D”) and a cordwood wall (type “E”) with the corresponding thermophysical and physical-mechanical characteristics of the structural layers (Table 1-5). In addition, for an objective assessment, the thickness of the whole walls is taken to be equal to 500 mm. To define a specific pressure on the foundation, the mass of 1 m² of the wall is divided by a wall width of 0.5 m. All dimensions presented in Fig. 2 are in mm.

The concept of the thermal inertia [23, 25, 26] is used to quantify the heat loss through the walls of the building, which shows how efficient the construction is in terms of the time period during which the stabilization of the temperature of the external and internal surfaces of the wall takes place. Korshunov O. states [26] that it is impossible to use the dependence of the duration of the quasi-stationary heat-process (time of thermal inertia) in the simple kind for a homogeneous wall for envelopes, which, in fact, are always multilayered:

where c – specific heat capacity of the wall material, J/kgK;

σ – the density of the material of the layers of the enclosing structures of walls, kg/m³;

R = δ λ the thermal resistance of the wall, m²K/W;

δ – the thickness of the layer of the enclosing structure of the wall, m;

λ – thermal conductivity of the envelope material, W/mK.

Therefore, for numerical simulation of the thermal inertia time of various variants of envelopes, an analytical dependence for multilayered walls is used [26]:

where τ u ' – the time of thermal inertia of a homogeneous wall of thickness δ with parameters of the first layer, which is determined by the dependence [26]:

L_n – layering factor of the envelope which is calculated by the formula [26];

where δ_tot – general thickness of multilayered envelope, m;

δ₁ – the thickness of the first layer of a multilayered envelope, m;

Δ δ i = ∑ j = i + 1 n δ j . – the thickness of the multilayered envelope starting from the second layer i = 2, m.

To compare the thermal inertia of walls from different structural elements, the unbiased parameter of thermal inertia D [23] was determined

Where S i = 2 π λ i c i ρ i T – the coefficient of heat absorption W/m²K, of i-th layer of the envelope, [23];

T – a period of thermal oscillations, sec.

To determine the thermal inertia D, the daily period of thermal oscillations is assumed, i.e.

T = 24 ⋅ 3600 = 86400 sec.

Figure 3.

Table 6 gives calculations of the thermophysical (the total R-value, m²K/W of multilayered construction, a non-dimensional value of the thermal inertia D, the thermal inertia of the base layer τ _u, duration of the quasi-stationary heat process τ 1 ' hours, non-dimensional layering coefficient of multilayered envelope L_n) and the physical-mechanical parameters (the specific pressure p_i on the foundation at the location of 1 m² of the designed wall type kg/m).

It could be useful to make a comparison of the normalized values of the total R-value of the multilayered construction and the total thermal inertia τ _u of the multilayered construction, which is presented in Fig. 3. From Fig. 3 it could be seen that a hempcrete wall is the best one from the considered types of the walls in terms of R-value of the multilayered construction and the total thermal inertia of the multilayered construction τ _u with almost the highest values (1.000 and 0.978 for the total τ _u and the total R-value respectively). Alongside with a hemcrete wall, a strawbale panel wall has the highest thermal resistance value, but it has almost five times smaller value of the total thermal inertia time (1.000 and 0.181 respectively). Walls “B”, “D” have almost the same values of both parameters. The wall type “E” has also a big difference between the compared parameters (0.717 for the total R-value and 0.295 for the total τ _u).

Figure 4.

Nevertheless, for the more objective, multi-criteria evaluation of the parameters of each of the investigated variants of the envelopes installation, the method of the Analytical Hierarchy Process, AHP [28] is used, as well as the methods proposed by the authors for determining the integral criterion of energy efficiency potential. Due to the fact, that during the assesment of the energy efficiency potential of the specific envelope of organic materials the influence of thermophysical parameters (R-value, coefficient of heat absorption S, thermal inertia D, thermal conductivity λ, specific heat capacity of material c) and physical-mechanical parameters (density ρ, mass m, thickness of layer δ) which were analysed have different dimensions, it is necessary to use a non-dimentional integral criterion for energy efficiency potential assesment of the multilayered envelopes.

It should be noted, that both methods for multi-criteria evaluation (based on AHP and proposed by authors) of the considered envelopes use one-scale non-dimentional units, which allow comparing their energy-efficient potential more objectively.

The integral criterion for energy efficiency potential assesment of the multilayered envelope of buildings is the normalized ratio of the total indicator of the energy efficiency potential of the specific envelope to the sum of values of the total indicators of the energy efficiency potential of the whole envelopes.

The use of such method of comparison as AHP allows us to apply a multicriteria assessment to choose a proper type of walls enclosing in terms of their multi-dimensional thermophysical and physical-mechanical characteristics.

According to AHP [28] a three-level hierarchy (model), has been built to determine the integral criterion for energy efficiency potential. This model represents the influence of the thermophysical and physical-mechanical characteristics of natural materials of organic origin on the target function (integral criterion of wall energy efficient potential’s assessment) that can be described as the quantitative integral presentation of the indicator that takes into account the influence of different parameters by its nature (Fig. 4). Numbers presented on Fig. 4 show an influence of factor’s weights (Level II, in the bottom part of each criteria rectangle) and numerical assessment of each altenative (Level I, in the bottom part of each wall type rectangle).

The methodology of creating a hierarchical model for determining the integral criterion of energy efficiency potential assessment for envelopes from organic materials is listed below.

By pairwise comparing [28] the priority of each of the yriteria (fte thermal inertia ofthe first iayer τ _u layering factor of the envelope L_n, the total thermal inertia time of multilayered wall τ _u, the total R-value of multilayered wall, the dimensionless index of wall thermal inertia D and pressure p on the foundation) has been weighted for each of the alternative wall types. The weight of each criteria (local priorities, Level II in Fig. 4) shows how much the influence factor contributes to the goal (Level III, target function in Fig. 4). The global priorities (Level I) show how much each wall type weighs in terms of the energy efficiency potential.

Each of the abovementioned local priorities is a matrix [27, 28], which is filled in the following way,

where r ₁, r ₂, r ₃, r_n , are the corresponding values of the priorities of the evaluated parameters of the matrix, which characterize the values of the investigated yarameters (thermal resistance R, heat absorption coefficient S, unbiased parameter of heat inertia D, thermal conductivity λ, specific heat capacity of the wall material c, density ρ, mass g, layer thickness δ). Knowing the line elements of the matrix (6), elements of all other lines are calculated. The arbitrary element a_jj = r_i /r_j , with known elements a_kj = r_k /r_j , k, and i = 1 , n ¯ of a rertain n-th line, is calculated as a_jj = a_kj / a_kj , and, j , k , = 1 , n ¯ .

The advantage vector of each i-th parameter is m_i calculated as the average geometric value of the elements of each matrix line divided by the sum of all the average geometric values for the estimated parameters using the formula [28]

Then, the advantage vector for the first line of the matrix which is obtained by the formula (6) is calculated, taking into account the average geometric elements of each of the lines using the formula

where x ₁, x ₂, ... x_n is the advantage vector of of the first, second, n-th line of the matrix, respectively.

By analogy, the components of the eigen vector and the advantage vector for other m_n lines are determined.

As the set of the relative weights of the alternatives, we use the components of our eigen vector that corresponds to the maximal characteristic number η _max [28]. Moreover, in order to evaluate the coherence of the mattix, the condition η _max ≥ n must be fulfilled.

As an indicator of the degree of the consistency in the elements of matrix A, the consistency index (CI) is used [28]

where n is the rank of the matrix.

To assess the adequacy of the consistency degree, the consistency ratio (CR) is used which is equal to

where MRCI is an average random consistency index, the average value which is randomly calculated for a large number of pair comparisons matrices that were generated on the fundamental scale [28].

The resulting vector of the advantages of a certain matrix in pairwise comparisons is considered as acceptable, if the CR does not exceed the coherence threshold in the range of 0.10 ... 0.20.

Tables 7, 8 give the meanings and fillings of all the components of the matrix – its eigen vector η _max, the consistency index CI of the pair of comparisons, as well as the consistency ratio CR for the “Criteria” matrix.

In this matrix (Table 7), in each cell, expert assessments of the benefits of one of the factor of influence over the other has been evaluated by the most common 9-point Saati scale [28]. At the same time, the filling of the matrix (Table 7) is carried out according to the rule: the number of more than one unit is put in a cell if the evaluated parameter on the left has an advantage over the parameter above it on the desired criterion. Numbers less than one are placed in the corresponding cells if the evaluated parameter on the left has a lower advantage over the estimated criterion over the parameter above it. After that, each local vector of the advantages (weight) of each of the influencing factors (level II) is multiplied by the global vector of alternatives advantage. All the weights of the vectors of advantages for the remaining matrices and factors of influence have been found on the given algorithm.

To determine the integral criterion of wall energy efficienct potential of the envelope (Level III), the product of each of the identified alternative vectors is summed by the weight of each criterion (Table 7). This allows to quantify the energy efficient potential of each type of the envelope.

The method proposed by the authors for determining the integral criterion of the energy efficiency potential of the envelope is as follows: 1.

Normalized indicators with different units of measurement are determined by the formula (11) n n o r m , j = n j n max , j ,

where n_j – the value of the j-th comparison parameter (lines of the first column of table 6) obtained by the formulas (2) ... (5).

n_max,j – the maximum value of the j-th comparison parameter for each j-th line of table 6 for different types of envelopes;

2.

In order to take into account the negative quantitative influence of the pressure parameter on the foundation (the higher the pressure on the foundation, the lower the estimation of the parameter), the inverse of the normal value of the parameter of dependence on Ohe formulas is calculated: (12) c i = 1 n n o r m , i = n max , f n f , i , (13) d i = c i c max , j = n max , f n f , i ⋅ c max , j ,

where n_max,f – the maximum ealue of the parameter “Pressure on the foundation p” o f the five considered walls;^r

n_f,i – pressure on the foundation for the i-th version of the wall arrangement;

c_max,f – the maximum value of the parameter “Pressure on the foundation p”, honvert ed to the normalized value, from the range of five different types of envelopes;

Figure 5.

The cordwood wall has the very similar values of the integral criterion of energy efficiency potential assessment of envelopes by different calculated methods (0.216 and 0.227 by AHP and authorship respectively), the largest difference, approximately twice as much, is observed in the earthbags wall, with 0.053 by AHP and 0.097, according to the authors’ method. It could be said that the divergence of the criteria’s values of the energy efficiency potential calculated by the AHP in comparison with the author’s technique is related to the subjective evaluation of the advantages of one comparison criterion over another.

From Fig. 5 it can be concluded that the hempcrete envelope is the most effective wall type (coefficient of 0.445 for AHP and 0.335 for authors), the strawbale panels wall and cordwood one can also be acceptable from the standpoint of the energy efficiency potential criterion. They have respectively 0.216 for AHP and 0.227 by the authors for the cordwood wall, and 0.194 and 0.218 for the wall made of strawbale panels.

Obviously, the obtained values of the integral criterion of energy efficiency potential which were determined by different methods can not be considered fully completed, because they do not reflect additional, necessary to the authors’ opinion, data for analysis – climate factor, the lifetime of the wall construction (or of the building) without overhaul and the cost of the wall type installation. Due to the lack of this additional data, the optimal choice of the wall type is still an ambiguous challenge.

However, if we compare the envelope types not only in the context of thermophysical and physical-mechanical characteristics but also in the context of an economic factor (the cost of materials and work during the installation), an environmental factor (primary energy consumption for materials production, transportation and installation), a climate factor, a durability factor (lifetime period of construction), the assessment of the energy efficiency potential will be more objective and complete. Thus, it is necessary to recognize the additional criteria for a more objective comparison and choice for the best option of wall types.