CC BY
30
УДК 697.112, 697.133
PERMINOV R. E BIANCO V. ALEKHIN V. N. NOSKOV A. S. KHAIT A. V. POPOVA M. N.
Хаит
Анатолий
Вильич
кандидат технических наук, старший преподаватель ФГАОУ ВПО УрФУ
e-mail: hait@mail.ru
Перминов
Роман
Эдуардович
ассистент кафедры Архитектура ФГАОУ ВПО УрФУ
e-mail: shaftcom@gmail.com
Попова
Мария
Николаевна
ведущий специалист ООО «НИАС»
e-mail: mariya.nikolaevna.ne @yandex.ru
Носков
Александр
Сергеевич
доктор технических наук, профессор, заведующий кафедрой «Гидравлики» ФГАОУ ВПО УрФУ
e-mail: referetsf@yandex.ru
Алехин
Владимир
Николаевич
кандидат технических наук, доцент, заведующий кафедрой «САПРОС» ФГАОУ ВПО УрФУ
e-mail: referetsf@yandex.ru
Bianco Vincenzo
PHD University of Genoa e-mail:
vincenzo.bianco@unige.it
Numerical model of thermal protection of building envelope
Present paper proposes a numerical model of thermal protection of building envelope based on several energy balance equations. By means of this model, energy consumption for heating/cooling is analyzed in different locations and compared to results of leading software packages Energy Plus, BEPS and TRNSYS. Additionally temperature profiles inside walls, profiles of wall surface and internal air temperatures with dependence on time were obtained, including data for Yekaterinburg.
Keywords: building envelope, dynamic numerical model, thermal protection, energy demand.
ПЕРМИНОВ Р. Э., BIANCO V., АЛЕХИН В. Н., НОСКОВ А. С., ХАИТ А. В., ПОПОВА М. Н. ЧИСЛЕННАЯ МОДЕЛЬ ТЕПЛОВОЙ ЗАЩИТЫ ОГРАЖДАЮЩИХ КОНСТРУКЦИЙ ЗДАНИЙ
Статья предлагает динамическую численную модель тепловой защиты ограждающих конструкций, основанную на уравнениях теплового баланса. При помощи данной модели произведено сравнение значений потребности в энергии для отопления и кондиционирования с передовыми программными комплексами: EnergyPlus, BEPS и TRNSYS. Получено распределение температуры в толще ограждения, графики зависимости температуры поверхности ограждающих конструкций и внутреннего воздуха от времени для Екатеринбурга.
Ключевые слова: ограждающие конструкции, динамическая численная модель, тепловая защита, потребность в энергии.
1. Introduction
Building envelope has great effect on overall building performance including energy demand, comfort, and durability. According to Crawley et al. [1] there were several hundred of building thermal performance software models in 2008 and this number is constantly growing. The majority of them are aimed at buildings thermal protection assessment and consist of similar basic modules.
Firstly, there is a weather model, allowing to determine the outer surface heat flux in terms of solar radiation (direct, diffused and reflected), convective heat transfer with atmospheric air and conductive heat transfer with ground. Secondly, the building wall model including correlation equations between the heat flux and surface temperatures (internal and external). Thirdly, internal wall surface heat transfer model allowing for heat flux from thermal radiation and convective heat transfer. Finally, energy balance equations, describing interdependence between zone air temperature, surrounding wall surface temperatures and other
considered heat sources. Every submodel will affect the prediction of the internal air temperature as well as total energy consumption of building.
Existing dynamic numerical models for predicting energy demand of buildings vary according to different approaches describing building components from lumped capacitance approach [2], combined with electrical analogy [3] to frequency domain regression methods. This paper presents the results of research to develop a model [4] for building envelope intended to analyze internal air temperature variations and energy demand of buildings located in different climatic regions.
Several requirements were imposed on this model such as accuracy sufficient for early design stage, low time-consumption and approximation to real construction operating conditions. Software was written on Python 2.7 language that allowed making it more adaptable, easily adding new factors and making corrections. Obtained calculation results were verified by comparison with leading simulation software such as TRNSYS, EnergyPlus and BEPS [5].
2. Problem statement and initial data
Current article faces the problem of transient heat exchange in building envelope. Solution of this problem requires certain initial data, such as material properties, building envelope configuration, laws determining internal microclimate change and climatic data (temperatures, wind speed, solar irradiance). Development and verification of the program is based on a typical premise bounded by four wall, roof and floor.
Geometrical dimensions of considered building and physical properties of building envelope materials are given in building description section. Climatic data include external air temperatures for each location with one-hour step, average ground temperatures for each month of the year, solar irradiance and internal air properties.
Output data of the model should contain energy consumption for heating and cooling depending on time as well as temperature variation in different parts of building envelope, used for heat protection assessment.
2.1. Building description. All geometric data concerning the test building are adopted from [5, 6] for verification purposes and specified in Table 1. Test building is represented by a standard building block of two storeys in the shape of parallelepiped with squared floor of side equal to 10 m and total height of 6 m.
In the present work, heavy type of wall structure from [6] is considered. Generic conductive and capacitive properties of building envelope are reported in Table 2, while detailed properties of structural layers forming the envelope are described in Table 3.
Table 1. Geometric data of the considered building [6]
Height m 6
Base m X m 10 x 10
Number of floors - 2
Useful (heated/cooled) surface m2 200
Volume m3 600
Total dissipating surface m2 440
Surface/Volume ratio m—1 0.73
Roof surface m2 100
Type of floor On the ground
Vertical walls orientation N — S — E — W
For each orientation
Total wall surface m2 60.00
Opaque surface m2 53.75
Windows surface m2 6.25
Table 2. Generic properties of adopted building envelope
U-value (Overall heat transfer coefficient) (W m—2 K—1) K-value (thermal mass) (kJ m-2 K-1)
Heavy wall
Vertical walls 0.40 622.92
Roof 0.35 395.28
Floor 0.42 320.65
Translucent surfaces such as windows are represented by one type for all configurations. Window surface for each orientation is equal and reported in Table 1. The glass unit thermal transmittance is assumed equal to 2.465 W/ (m K) and its transmission coefficient is equal to 0.571. Window frames are neglected as well as corner effect and the effect of thermal bridges between window frames and wall structures.
2.2. Climatic data. Detailed simulations of energy performance of buildings require extensive climatic data. Hourly profiles of different climatic parameters are widely available for most weather stations. In the current model we adopted a compromise approach between time cost and detailed prediction by using monthly-average hourly values of climatic parameters, particularly:
— external temperature;
— ground temperature.
In other words, daily external and ground temperature profiles during each month remain uniform. Yearly-average global horizontal irradiance term represents solar radiation in the way that the amount of solar radiation does not change with time but preserves mean value. All climatic data utilized in the present paper are taken from IWEC project [7]. The internal temperature setting point is 18.3 °C (Tbhs) for heating period and 24.7°C (Tb cs) for cooling period with a dead band setting of 1 °C and 2 °C in their surroundings respectively. Internal air exchange rate is taken according to minimum suitable value and equal to 0.5 volumes per hour.
3. General equations of numerical model
3.1. Simplifying assumptions. Several assumptions were made during development of model regarding thermal protection in buildings:
— material of each building envelope layer is isotropic and homogeneous;
NOMENCLATURE
Roman letters
a thermal diffusivity coefficient (m2 s)
C specific heat (J kg—1 K—1)
F surface area (m2)
g glass transmission coefficient (solar factor)
in global horizontal irradiance (W m— 2)
L effective air exchange (m3 s—1)
T temperature (°C)
t time (s, h)
q heat flux (W)
V volume (m3)
Greek letters
a absorbance coefficient
P density (kg m—3)
Subscripts
b base temperature
con convection
cs cooling system
e external
f floor
i internal
is internal sources
hs heating system
s solar
v ventilation
w wall
win windows
Table 3. Physical properties of structural layers [5]
Thickness (m) Density (kg/m3) Conductivity (W m-1 K-1) Specific heat (J kg-1 K-1) Absorbance coefficient
Vertical walls
Plaster (int.) 0.015 1400 0.7 1.09 0.6
Solid bricks 0.38 1800 0.72 0.84
Semi-rigid panels 0.07 55 0.04 0.67
Plaster (ext.) 0.015 1400 0.7 1.09
Roof
Plaster (int.) 0.015 1400 0.7 1.09 0.6
Hollow slab 0.22 918 0.667 1
Screed 0.05 500 0.16 0.88
Semi-rigid panels 0.08 55 0.04 0.67
Screed 0.05 500 0.16 0.88
Concrete (ext.) 0.03 2400 1.91 0.92
Floor
Ceramic tiles (int.) 0.02 2300 1 0.8 0.6
Screed 0.05 1800 0.94 0.88
Semi-rigid panels 0.072 55 0.04 0.67
Hollow slab (ground) 0.22 918 0.667 1
— problem is considered to be one-dimensional and calculations are made along the X axis;
— initial temperature in all nodes is equal;
— air mobility is constant;
— thermal bridges are neglected;
— variable wind impact is neglected;
— humidity conditions are considered to be constant;
— building exposure is not considered therefore global solar radiation and external convection coefficient are taken as average values.
3.2. Design model. Test building internal environment is modelled as a single air volume with homogeneous temperature distribution and specific thermal capacity. Heat exchange between this air volume and the internal surface of the building envelope is accounted as heat flux in the transient energy balance equation. Main heat fluxes that are allowed for in the current model:
— qwin represents heat transfer across translucent constructions;
— qw refers to total heat transfer through opaque constructions, such as walls, roof and floor;
— qhs/cs is heat input/extraction due to heating and cooling appliances;
— qis takes into account internal heat gains from people and equipment. It depends on function of the building and total useful surface. For a current building, a value of 400 W is considered.
— qv considers heat transfer due to ventilation according to minimum suitable air exchange rate.
3.3. Solar contributions. Without considering the exposure of each wall, heat flux from the solar radiation on the opaque surface of building envelope can be calculated as follows:
qs,w '1 j,n ' Fw
where negative sign considers the direction of heat flux, the term aw refers to the absorbance coefficient of the wall/roof
external surface and Ij n is global horizontal irradiance taken according to climatic data.
Solar radiation transmitted through translucent constructions was calculated under Eq. 2.
qsg = Ij,n ■ Fwin ■ g ■ ki (2)
where Fwin is the total window surface, coefficients k1 and g consider the presence of shadowing and solar radiation transmitted through double-glazed window correspondingly. In the present model к equals 0.8.
It is assumed that part of qsg is absorbed by the floor in compliance with its absorbance af (Eq. 3), whereas the reflected part is uniformly distributed among all interior surfaces.
qsg,f = a f ■ qsg (3)
3.4. Heat transfer through building envelope. In
addition to above mentioned heat fluxes this numerical model exploits external and internal convective heat fluxes qce w and qci was shown in Eqs. 4 and 5.
qce,w acon, w ' (Te Twe) (4)
qci,w acon, i-w ' (TW T,) (5)
where Te and T — temperatures of external and internal air respectively, whereas Twe and Twi represent temperature of external and internal wall surface. Terms acon w and acon,i-W stand for convective heat transfer coefficient. Convection terms are dependent from air flow speed, which is constantly changing and hard to define for a specific moment of time. As a temporary simplification in order to keep simulation results clear, convection terms are assumed constant and equal 5.0 for external surface and 3.0 for internal surface of the building envelope. External convection term is less than recommended by standards, but research [8] has shown that the value greatly depends on building geometry and climatic conditions, which require further studies.
Figure 1. Schematics of external walls
Figure 2. Comparison of estimation of heating energy demand in different Italian cities
Figure 3. Comparison of estimation of cooling energy demand in different Italian cities
Energy balance equations, Similar equations are used for determining heat flux rate for external describing contributions considered
and internal wall surfaces qwe and qw can be written as follows:
for modelling the floor, with difference that the external heat flux is purely conductive and can be calculated directly
(6) exploiting the ground temperature adopted from climatic data depending
(7) on the building foundation depth.
Numerical model applied in this paper utilize transient one-dimensional heat conduction Eq. 8, derived from fundamental (general) heat conduction equation in partial derivatives.
dT д T ■ = a-
dt
dx 2
(8)
where a is thermal diffusivity coefficient depending on material properties. In this particular case, equation is solved by applying surface temperature and resulting heat flux.
3.5. Ventilation contributions. Supply and exhaust ventilation system operates according to parameters stated in section 2.2. Heat flux caused by ventilation can be written as follows:
qv = Cair ■ pair ' L ' {Ti Te,
(9)
where L is effective air exchange. Cair and pair are air specific heat and air density respectively, which are considered to be equal for internal and external air.
3.6. Internal temperature calculation. Resulting heat flux inside the test building can be calculated by adding all contributions listed in section 3.2, whereas heat demand can be obtained using Eq. 10.
Q = c. V .p.(T -T-(
where T, and T,
i,(
(10)
internal air temperature during current and previous integration steps respectively. Internal air temperature at each moment of time can be easily derived from the Eq. 10.
4. Numerical model
Numerical model considered in this article as opposed to approaches mentioned in the introduction characterize building wall as a set of layers with first and second type boundary conditions. Number of layers can take any reasonable value but directly affects calculation speed. Further investigation is required to determine optimum number of layers for different wall configurations.
The temperature of each layer is assigned to a node located in the center of the layer (Fig. 1). Heat transfer between layers is based on heat conduction and described by one-dimensional heat conduction equation (Eq. 8).
Equations are solved by explicit finite difference method with first order of accuracy for each moment of time according to assigned time step. According to this method, approximate difference relations replace all
Rome
27 n
9 T-1-li-1-1-1-1-1-1-1-1-
0 0,036 0,084 0,132 0,18 0,228 0,276 0,324 0,372 0,42 0,468
Wall thickness [ni]
January February -March 1 ■ April
May -June -July ---August
Sep ¡ember ---October - — November ---December
Figure 4. Monthly temperature profiles Inside wall calculated for Rome
25
0 30 60 90 120 150 180 210 240 270 300 330 360
Time [day}
Ti----Te---Twi -Twe
Figure 5. External and internal temperature profiles for Yekaterinburg during year
derivatives from balance equations and boundary conditions and by this means, they are expressed in terms of desired nodal function values. By solving this resulting system of algebraic equations with following interpolation one can obtain an approximate solution of considered problem.
5. Verification of numerical model
In order to verify the validity of simulation results they were analyzed using a benchmark residential building and compared with consolidated simulators (TRNSYS, EnergyPlus and BEPS). This comparison is made in terms of heating energy consumption, cooling energy demand and temperature profile. Calculation in TRNSYS, EnergyPlus and BEPS are taken from [5, 6] in which the same benchmark test case is adopted.
Fig. 2 reports the estimation of heating demand for three Italian cities with different climate: Milan, Rome and Palermo. Regarding the comparison, it is reasonable to say that all the simulation programs predict similar heating energy demand for all regarded climatic conditions. Specifically, the average deviation between test model and TRNSYS in calculating heating energy demand is about 11.7%. Similarly, the average deviation between test model and BEPS is about 7.7%, which is considered to be acceptable due to several simplifications made to the test model. In particular, great effect may be caused by average value of global solar radiation. Nevertheless, Fig. 2 confirms the assumption that the steady state approach is overestimating the heating energy demand [9]. These results can be explained by the fact that test model utilizes hourly temperature profile, though monthly-averaged, and reproduces the inertia effect.
Fig. 3 shows that average deviation between test model and TRNSYS for cooling energy demand is 10.6%, while deviation between the test model and BEPS is 10.8%. The discrepancy of results grows for hot climates, which, as may be supposed, is the result of simplified solar radiation model in comparison to other simulation software.
Differences in test model results may be produced by simplified and therefore non-realistic control algorithm of heating and cooling appliances. In practical situations heating and cooling systems cannot be turned on or off immediately according to the time step dt as implemented in test model.
One of the distinctive features of the test model is the ability to plot
temperature profile inside building envelope at any desired moment of time. Temperature profiles shown in Fig. 4 were obtained for Rome for each month of the year and chiefly appear to be descending curves.
The curves have almost no sharp turns in contrast to steady state temperature profiles. Short horizontal parts of the diagram refer to internal and external wall surface temperatures, which assumed equal to temperatures of the extreme nodes. Slight steepening of slopes closer to external part of the wall coincide with the position of the insulation layer where maximum temperature drop is expected. Seasonal dew point may be derived from temperature profiles in each layer of the wall for each month in order to analyze behavior of the building envelope during the year.
Simulation results for Yekaterinburg
Internal and external temperature profiles for Yekaterinburg were obtained using the same test building as illustrated in Fig.5. Internal air temperature Ti varies about 18.3 °C, slightly increasing during summer. According to simulation results, no cooling load is required during the whole year. Extreme points of external air temperature Te and external wall surface temperature Twe correlate closely as expected, while the diagram of internal wall surface temperature Twi appears to be stepless and smooth due to insulation layer, wall thermal capacity and additional heating/cooling.
It can be easily noticed that the test building used for model comparison does not suite the Yekaterinburg climatic conditions. Internal wall surface temperature lowers to 11.2 °C in winter,
which is not acceptable. Furthermore, these curves cannot be used directly for calculation of insulation thickness unless climatic data for the coldest year or correction factors are used. The difference between internal wall surface temperature and internal air temperature derived from the Fig. 5 allows estimation of expected comfort level.
Heating energy demand for Yekaterinburg is 281 kWh/m2 per year. Total transmission heat loss involves heat loss through walls, floor and roof, which are 46.9%, 34.7% and 18.4 % respectively. Considering these values, one of the most effective means of energy saving is the increase of wall insulation thickness.
According to test model, control algorithm checks the internal temperature every time step in order to switch heating and cooling appliances on or off. This algorithm is simple but not efficient enough in terms of energy saving and does not allow for characteristics of different heating and cooling appliances. Hence, improvements should be made and considering high calculation speed the test model suits to evaluation and optimization of various control algorithms.
Conclusion
A simplified dynamic model for calculation of internal air temperature and temperatures within building envelope has been developed and implemented in terms of Python 2.7 language. By means of the developed model, calculations for several European cities have been made and compared to existing data obtained from common software. Regarding the results analysis, it was found that:
♦ Obtained calculation results shows satisfactory consistency with reference models. Average discrepancy lies within acceptable range and do not exceed 10%. Test model have development potential by implementing unaccounted factors preserving relatively high calculation speed. For instance, annual calculation used in the present article takes approximately 31 second representing high numerical efficiency of the model.
♦ Developed program allows obtaining yearly air and wall surface temperature profiles, temperature profiles within building envelope with heating and cooling energy demand for any city. For example, calculations were made for Yekaterinburg. As a result, temperature profiles within building envelope allow prediction of the behavior of constructions, for instance dew point within wall of any configuration.
♦ The program is capable of calculating the amount of heat loss through different building envelope elements separately, which makes possible the evaluation of the effect from complementary insulation of any specific part of the building envelope.
♦ In the next stage of the program development, some simplifications are to be eliminated in order to increase accuracy. For instance, hourly temperature profiles will be used and daily average global horizontal irradiance will be replaced for hourly values. Thereafter the program is to be used for solving optimization problems embracing control algorithm improvement for controlled heating systems instead of continuous feeding of energy during heating period.
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