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1
DOI:10.22337/2587-9618-2024-20-1-154-161
TAKING INTO ACCOUNT MOISTURE IN INCREASING THE ACCURACY OF CALCULATING HEAT LOSSES OF A
BUILDING
Kirill P. Zubarev
National Research Moscow State University of Civil Engineering, Moscow, RUSSIA Research Institute ofBuilding Physics ofRussian Academy of Architecture and Construction Sciences, Moscow, RUSSIA
RUDN University, Moscow, RUSSIA
Abstract: A discrete-continuous approach was applied to the moisture transfer equation, which made it possible to obtain an analytical solution for the moisture potential. The new method was applied to study the unsteady-state moisture regime of the facade heat-insulating composite system with expanded polystyrene insulation and aerated concrete base. It was found that the mass moisture content of building materials achieved in the walls during the period of operation is lower than the mass moisture content used in construction regulations, which makes it possible to increase the accuracy of calculating the transmission heat losses of the building. Calculations of heat losses of a two-storey building in the climatic conditions of Moscow (Russia) showed a decrease in the heating system load by 5 %, and the reduction in heat losses for specific premises of the building ranged from 3.6to7 %.
Keywords: building envelope, effect of moisture on thermal conductivity, heat and moisture transfer, mathematical model, discrete-continuous approach
УЧЕТ ВЛАЖНОСТИ В ПОВЫШЕНИИ ТОЧНОСТИ РАСЧЕТА
ТЕПЛОВЫХ ПОТЕРЬ ЗДАНИЯ
К.П. Зубарев
Национальный исследовательский Московский государственный строительный университет, г. Москва, РОССИЯ Научно-исследовательский институт строительной физики Российской академии архитектуры и строительных
наук, г. Москва, РОССИЯ Российский университет дружбы народов, г. Москва, РОССИЯ
Аннотация: К уравнению влагопереноса применен дискретно-континуальный подход, позволивший получить аналитическое решение для потенциала влажности. Новый метод был применен для исследования нестационарного влажностного режима системы фасадной теплоизоляционной композиционной с утеплителем из пенополистирола и основанием из газобетона. Было получено, что массовая влажность строительных материалов, достигаемая в стенах за период эксплуатации ниже массовой влажности, используемой в нормативных документах по строительству, что дает возможность повысить точность расчета трансмиссионных тепловых потерь здания. Расчеты тепловых потерь двухэтажного здания в климатических условиях г. Москвы (Россия) показали снижение нагрузки на систему отопления на 5 %, а для конкретных помещений здания снижения тепловых потерь составило от 3.6 до 7 %.
Ключевые слова: ограждающая конструкция здания, влияние влаги на теплопроводность, тепло- и влагоперенос, математическая модель, дискретно-континуальный подход
1. INTRODUCTION
1.1. The role of moisture in construction
The moisture regime of building envelopes is a highly sophisticated scientific problem in construction. Research on distribution of moisture
over the thickness of fences has a huge applied relevance [1]. From a medical point of view, wet building material is a breeding ground for bacteria, which can cause various human diseases, such as asthma and allergy. A change in moisture content of a building material directly affects its
thermal conductivity and the heat-shielding shell of the building. Errors in assessing moisture state of building fences can lead to condensation and mold on the internal surfaces of building envelopes, as well as waterlogging of the wall material, which is directly related to the durability ofthe building [2,3].
1.2. Influence of moisture on heat losses of a building
It is a common knowledge that moisture content rise of a building material causes an increase in its thermal conductivity, which negatively affects thermal protection ofbuildings [4-7]. The dependence of thermal conductivity on moisture is described by the formula [4-7]:
Xw = Â0 + w -AA„
(1)
a = k ■ f-a t ■ n ■ (1+
where i is a heat transfer coefficient, W/(m2-°C); F is a heat transfer surface area, m2; At is a temperature difference on different sides of the building envelope °C; « is a coefficient that depends on the position of the building envelope in relation to the outer air, °C; ft are
additional heat losses that are dependent on the orientation of the building envelope over the cardinal points.
The heat transfer coefficient in equation (3) is the reciprocal of the reduced resistance to heat transfer [4-7]:
k =
1
R
(4)
where is a coefficient of thermal
conductivity of the material at moisturew, W/(m-°C); w is mass moisture content of the
material, kg/kg; A0 is a thermal conductivity coefficient of dry material, W/(m-°C); A2W is
change in the thermal conductivity of the material when its mass moisture changes by 1 %, W/(m-°C •%).
There is a variety of methods for calculating the heat loss of a building.
In the general case, heat losses of the building premises are a sum of transmission and infiltration heat losses:
Q=Qtr+a
■inf ■
(2)
where Ract is reduced heat transfer resistance,
m2-0C/(W).
The reduced resistance to heat transfer of the enclosing structure of the building wall is calculated with the formula [4-7]:
Ract =
1
+ 1 /,. -V, nk -Xk
(5)
R
where R
is conditional heat transfer
where Q is total heat loss of the building premise, W; Qtr are transmission heat losses of
the building premise, W; Qinj is infiltration
heat loss of the building premise, W. Transmission heat losses through a certain enclosing structure are estimated using the following expression [4-7]:
resistance, (m2-0C)/W; lj - ^ . are specific heat
losses through a linear thermal inhomogeneity
of the j-th type, W/(m2-0C); nk ■ %k are specific
heat losses through point thermal inhomogeneity of the k-th type, W/(m2-0C). Conditional resistance of heat transfer for the outer wall of the building is determined by the formula [4-7].:
n __
con
1
(6)
k
a
ext
where ain is a coefficient of heat transfer between outer air and the outer surface of the wall, (m2-°C)/W; aext is a coefficient of heat transfer between the indoor air of the room and the inner surface of the wall, (m2-°C)/W; ^ is
the thickness of i-th material of the wall, m; ^
is a coefficient of thermal conductivity of the ith material ofthe wall, W/(m-°C). So, an increment of the calculation accuracy of mass moisture content w in the building wall will make the thermal conductivity coefficients of building materials by equation (1) more precise, which according to equations (2)-(6) will refine the heat loss of the building.
material moisture , % by weight (1 kg/kg =100 % by weight).
Moisture transfer differential equation based on the moisture potential F can be formulated as:
= (-m + E,(0)^^^. (8)
or ^ dw f0 ox
The equation (7) can be solved in the following form using discrete-continuous approach [911]:
F = p \{Et. A J2 • e*' A)-1 -(E, ■ Af )•.
■L + (Et ■ A)~l (eE'-A-T - £) • B + eE> ^ ■ F0. (9)
2. THEPROBLEM
Assessment of the impact of the building material operational humidity determined using the proposed method on the heat losses of the building.
3. MATERIALS AND METHODS
The mathematical model for the joint moisture transfer of vaporous and liquid moisture was proposed by V.G. Gagarin and V.V. Kozlov. V.G. Gagarin derived a necessary and sufficient condition for the potentiality of a vector field during the water vapor and liquid transfer, which thereafter allowed V.G. Gagarin and V.V. Kozlov to develop a formula for the moisture potential F [8]:
F (w, t) = E, (t) • p(w) + - ]p{£)d C (7) № 0
where F is moisture potential, Pa; Et is saturated water vapor pressure, Pa; y is relative air humidity, %; ¡j, is vapor permeability coefficient, kg/(m-s-Pa)\ ¡i is moisture conductivity coefficient, kg/(m - s - kg/kg), which depends on moisture, t is temperature,"C; w is
4. RESULTS AND DISCUSSION
4.1. Application of a discrete-continuous approach to assess the unsteady-state moisture regime of afacade heat-insulating composite system with externalplaster layers The developed method for assessing the unsteady-state moisture regime was applied to study the facade heat-insulating composite system with external plaster layers with a 300 mm thick aerated concrete base and 120 mm thick expanded polystyrene insulation built in Moscow.
The change in the mass humidity of the building envelope along the wall thickness is presented (Figure 1).
Figure 1. Change in the mass moisture content of the building envelope across the 'wall thickness
The change in the humidity of the insulation layer during the year was obtained according to the proposed method for assessing the unsteady-state moisture regime (Figure 2).
Time t, day
Figure 2. Change in the moisture of the insulation layer during theyear according to theproposed methodfor assessing the unsteady-state moisture regime
As a result of the research, it was discovered that maximum moisture for the facade heat-insulating composite system with aerated concrete base and expanded polystyrene insulation will be observed at the beginning of January (Figure 2), which corresponds to the maximum temperature difference on different sides of the fence. This result is explained by the low inertia of the insulation layer. Consequently, it was discovered that for facade heat-insulating composite systems, the period of maximum moisture differs from the period of maximum moisture for enclosing structures that do not contain insulation.
4.2. Comparison of the operational moisture of the building -wall obtained using the discrete-continuous approach -with standard -values To evaluate the effect of the proposed method, the operating humidity was compared according to the proposed method for assessing the unsteady-state moisture regime with the values given in the official regulatory document Set of Rules 50.13330.2012 "Thermal protection of buildings" (Russian regulatory document). The construction of the wall illustrated in Figure 1 was taken for the study.
Comparison of the operational moisture of a building wall with a base made of aerated concrete (aerated concrete layer thickness 0.3 m) and expanded polystyrene insulation (insulation layer thickness 0.12 m) obtained using the proposed calculation method based on a discrete-continuous approach with standard values (Table 1) was carried out. As we can see from Table 1, the actual values of the operating moisture content of building materials obtained by the proposed formula are significantly lower than the moisture content of building materials taken according to the standards. According to the formula (1), a decrease in the mass moisture content of building material leads to a decrease in its thermal conductivity. Thus, it gives a possibility to save energy when determining the exact amount of mass moisture in the building envelope materials by taking into account the refined thermal conductivity coefficient.
Table 1. Comparison of the operational humidity of a building -wall -with aerated concrete base and expandedpolystyrene insulation obtained using theproposed calculation method based on a discrete-
continuous approach -with standard values
Material Regulatory values for operating humidity, % by weight The result of calculating the unsteady-state moisture regime according to the proposed formula (9),%by weight
Aerated concrete 12.0 3.4
Expanded polystyrene 10.0 1.8
4.3. Increasing energy savings by improving the calculation accuracy of heat losses of a building
To assess the reduction of heat losses in the building envelope, two calculations of heat losses were made for a two-storey cottage building in Moscow (Russia). The first calculation was carried out at standard values of humidity, whereas the second one was carried
out in agreement with the calculated values that were obtained during the modeling of the non-stationary state of the enclosing structure of the buildingwall (Table 1).
The temperature of the coldest five-day period was set as the outside temperature according to the climatological data of the construction area.
Comparison of the composition of the transmission heat losses of the wall of a cottage house building according to the standard values and according to the proposed method for defining the unsteady-state moisture regime with the aid a discrete-continuous approach is presented (Figure 3).
Figure 3. Comparison of the transmission heat losses composition of the wall of the cottage house
building: A - distribution of heat losses in the wall obtained in the calculation at the moisture content of materials taken according to the standard values; B - distribution of heat losses in the wall that were obtained when making calculations at the -values of the moisture content of materials determinatedfrom the results of the assessment of the unsteady-state moisture regime (1- heat losses of the -wall along the surface of the -wall through dry material; 2 - heat losses of the -wall through heat engineering inhomogeneities; 3 - heat losses of the -wall due to moisture; 4 - energy saving achieved by taking into account the unsteady-state moisture regime)
As may be inferred from Figure 3, taking into account the unsteady-state moisture regime led to energy savings of 1600 W due to a decrease in transmission heat losses. Transmission heat losses through building walls are not the only source of building heat losses. In order to estimate the overall reduction of heat losses in the total costs of the building for heating and ventilation, it is also essential to determine the transmission heat losses through the floor, ceiling, windows and doors of the building as well as heat losses for heating the infiltrated air.
The comparison of the results of the calculations of heat losses at the moisture content of the building wall materials taken according to standard values as well as at the moisture content of the building wall materials gained from the results of the assessment of the unsteady-state moisture regime using the proposed method is presented (Table 2).
Table 2. Comparison of the results of heat loss calculations at the moisture content of the building -wall materials taken according to standard -values as -well as at the moisture content of the building -wall materials gained from the results of the assessment of the unsteady-state moisture regime using the given
method ispresented
Heat loss according to the standard humidity values, W Heat loss
Building envelopes according to the calculated humidity values, W
Walls 10980 9380
Windows 8470 8470
Roof coating 3030 3030
Doors 1070 1070
Floor 1405 1405
Infiltration 6075 6075
Total heat losses 31030 29430
Thus, for the building under consideration, energy saving when calculating heat losses by taking into account the unsteady-state moisture regime of the building wall using the method for calculating the unsteady-state moisture regime suggested in this article is 1600 W (5%). To illustrate the reduction of heat losses in each separate room, a plan of the second floor of a two-storey cottage house is presented with heat losses calculated at the temperature of the coldest period of five days (figure 4). As can be noticed from Figure 4, the reduction of heat losses of the building is large for each room and can be presented as a table 3.
Figure 4. Plan of the secondfloor ofatwo-storey cottage house with heat losses calculated at the temperature of the coldestperiod of five
days (1- room number; 2 -purpose of the room; 3 - table withparameters of the room; 4 - indoor air temperature in the room during cold season (winter); 5 - heat loss of the room
determined at the normative humidity of the building materials of the 'wall; 6 - heat losses of the room at the moisture content of the building materials of the 'wall determined by the calculation of the unsteady-state moisture regime; 7 - the outer 'wall of the building; 8 - the window of the building; 9 - stairs)
Table 3. Reduction of heat losses due to the assessment of the unsteady-state moisture regime by the suggested method
No. Room Heat loss according tothe Heat loss according tothe Percentage of heat loss reduction, %
name standard calculated
humidity values, W humidity values, W
1 Bedroom 1260 1180 6.3
2 Study 550 530 3.6
3 Bedroom 1450 1370 5.5
4 Living-room 1610 1530 5.0
5 Bedroom 2150 2000 7.0
6 Bathroom 550 530 3.6
7 Sitting-room 2070 1930 6.8
As is obvious from Table 3, the actual heat losses obtained during the modelling are from 3.6 to 7.0 % less than those calculated for different rooms from, which is significant when projecting buildings.
5. CONCLUSIONS
The assessment of the unsteady-state moisture regime made allows us to make a conclusion that moisture content in the thickness of the building envelope materials is lower than is accepted according to regulatory documents. The energy saving of the building was assessed by applying the proposed methodology by calculating heat losses of the building. Comparative calculations for the studied two-storey building showed a total reduction of the building's heat demand for heating and ventilation in the amount of 5 %. At once, the reduction of heat loss can reach from 3.6 to 7 % depending on the room.
REFERENCES
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7. Vieira G.B., Petrichenko M.R., Musorina T.A., Zaborova D.D. Behavior of a hollowed-wood ventilated façade during temperature changes // Magazine of Civil Engineering, 2018, Vol. 79, No. 3, pp. 103111.
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9. Zubarev K.P. Derivation of the equation of unsteady-state moisture behaviour in the enclosing structures of buildings using a discrete-continuous approach // International Journal for Computational Civil and Structural Engineering, 2021, Vol. 17, No. 4, - pp. 83-90.
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11. Zolotov A.B., Mozgaleva M.L., Akimov P.A., Sidorov V.N. Ob odnom diskretno-kontinualnom podkhode k resheniyu odnomernoy zadachi teploprovodnosti [About one discrete-continual method of solution of one-dimensional heat conductivity problem], // Academia. Architecture and Construction (Academia. Arkhitektura i stroitelstvo), Iss. 3, 2010, pp. 287-291.
СПИСОК ЛИТЕРАТУРЫ
1. Zaborova D., Musorina T. Environmental and energy-efficiency considerations for selecting building envelopes // Sustainability. 2022, Vol. 14, No. 10. P. 5914.
2. Kotlyarova E. Improving the methodology for assessing the level of environmental safety of urban areas as the basis of their life cycle // E3S Web ofConferences, 2023, Vol. 389, No. 09062.
3. Kotlyarova E. Basic Scientific Principles of Improving the Methodology for the Assessment of the Level of Environmental Safety of Urbanized Territories // AIP Conference Proceedings, 2023, Vol. 2560, No. 020010.
4. Gamayunova O., Gumerova E., Miloradova N. Smart glass as the method of improving the energy efficiency of high-rise buildings // E3S Web of Conferences, 2018, Vol. 33, No. 02046.
5. Gamayunova O., Radaev A., Petrichenko M., Shushunova N. Energy audit and energy efficiency of modular military towns // E3S Web of Conferences, 2019, Vol. 110, No. 01088.
6. Zaborova D., Vieira G., Musorina T., Butyrin A. Experimental study of thermal stability of building materials // Advances in Intelligent Systems and Computing. Cham, 2018, Vol. 692 pp. 482-489.
7. Vieira G.B., Petrichenko M.R., Musorina T.A., Zaborova D.D. Behavior of a hollowed-wood ventilated façade during temperature changes // Magazine of Civil Engineering, 2018, Vol. 79, No. 3, pp. 103111.
8. Gagarin V.G., Kozlov V.V., Zubarev
K.P. Determination of maximum moisture zone on enclosing structures. // Cold Climate HVAC 2018: Sustainable Buildings in Cold Climates, 2019, pp. 925932.
9. Zubarev K.P. Derivation of the equation of unsteady-state moisture behaviour in the
enclosing structures of buildings using a discrete-continuous approach // International Journal for Computational Civil and Structural Engineering, 2021, Vol. 17, No. 4, - pp. 83-90.
10. Sidorov V.N. Matskevich S.M. Discrete-analytical solution of the unsteady-state heat conduction transfer problem based on the finite element method. // IDT 2016 -Proceedings of the International Conference on Information and Digital Technologies 2016. 2016, - pp. 241-244.
11. Золотое A.B., Мозгалева М.Л., Акимов П.А., Сидоров В.Н. Об одном дискретно-континуальном подходе к решению одномерной задачи теплопроводности. // Academia. Архитектура и строительство, Iss. 3, 2010, pp. 287-291.
Zwèarev Kirill Pavlovich, Ph.D. (Candidate of Engineering Sciences), Associate Professor, Associate Professor at the Department of General and Applied Physics of the Moscow State University of Civil Engineering, 129337, Moscow, Yaroslavskoe shosse, 26; Lecturer at the Department of Heat and Gas Supply and Ventilation of the Moscow State University of Civil Engineering, 129337, Moscow, Yaroslavskoe shosse, 26; Senior Researcher at the Laboratory of Building Thermal Physics of the Research Institute of Building Physics of Russian Academy of Architecture and Construction Sciences, 127238, Moscow, Lokomotivny proezd, 21; Associate Professor at the Department of Civil Engineering, Academy of Engineering, the Peoples' Friendship University of Russia (RUDN University) 117198, Moscow, st. Miklukho-Maclaya, 6; Leading Researcher at the Scientific Center of Engineering and Construction Technologies, Academy of Engineering, the Peoples' Friendship University of Russia (RUDN University) 117198, Moscow, st. Miklukho-Maclaya, 6; e-mail.: zubarevkirill93@mail.ru
Зубарев Кирилл Павлович, кандидат технических наук, доцент, доцент кафедры общей и прикладной физики Национального исследовательского Московского государственного строительного университета 129337, г. Москва, Ярославское шоссе, 26; преподаватель кафедры теплогазоснабжения и вентиляции Национального исследовательского Московского государственного строительного университета 129337, г. Москва, Ярославское шоссе, 26; старший научный сотрудник лаборатории строительной теплофизики Научно-
исследовательского института строительной физики Российской академии архитектуры и строительных наук 127238, г. Москва, Локомотивный проезд, 21; доцент департамента строительства инженерной академии Российского университета дружбы народов 117198, г. Москва, ул. Миклухо-Маклая, 6; ведущий научный сотрудник научного центра техники и технологий строительства Российского университета дружбы народов 117198, г. Москва, ул. Миклухо-Маклая, 6; e-mail.: zubarevkirill93@mail.ru
