Nowadays, in the conditions of the need to save energy resources, it is no longer possible to simply increase the thermal and electrical power for the engineering needs of buildings. The way out from this situation is to insulate buildings. For monitoring thermal insulation and heat losses one of the main informative characteristics is thermal resistance. Experimental studies of the thermophysical characteristics of enclosed structures are defined in ISO 9869 standard. However, experimental studies have a number of significant drawbacks, among which the following should be highlighted: long duration of measurements and if necessary, the experiment can be extended; the need to use a large number of sensors to obtain a representative result; restrictions on climate parameters for conducting measurements. And also, a large number of influencing factors, such as the geometric dimensions and orientation of the building, the location of the sensors, external conditions, including weather during the tests, can lead to significant measurement errors. The proposed in work approach allows to reduce the influence of the above-mentioned factors in the process of determining thermal resistance and actual heat losses by creating a CFD model of object heat exchange. Subsequent verification of results showed that maximum deviation of the calculated and experimental data did not exceed 4%.. Thermal Resistance, heat flux measurement, Computational Fluid Dynamics Model Nowadays, in the conditions of the need to save energy resources, it is no longer possible to simply increase the thermal and electrical power for the engineering needs of buildings. The way out from this situation is to insulate buildings, reduce transport heat losses and increase the efficiency of heat generating installations [1, 2].
2023 Copyright for this paper by its authors. ventilation systems operating modes validation became one of the main tools [9, 10]. At the same time, the reliability and information content of the results of computational-theoretical and experimental studies increased [11].
For monitoring of the heat losses one of the main informative characteristics is thermal resistance [11]. Experimental studies of the thermophysical characteristics of enclosed structures are defined in ISO 9869 [12] standards. However, experimental studies have a number of significant drawbacks, among which the following should be highlighted: long duration of measurements (at least 72 hours), and if necessary, the experiment can be extended; the need to use a large number of sensors to obtain a representative result; restrictions on climate parameters for conducting measurements. And also a large number of influencing factors, such as the geometric dimensions and orientation of the building, the location of the sensors [13-15], external conditions, including weather during the tests, can lead to significant measurement errors [15].
The aim of the work is to reduce the influence of the above-mentioned factors in the process of determining actual heat losses by creating a CFD model of examined object accounting not only heat but air exchange, with subsequent verification of results, which is allows to increasing the accuracy of heat loss calculations.
In accordance with the aim the following research methodology is proposed (Fig. 1).
Tests in natural conditions to determine the thermal resistance of building envelopes are performed when the heating systems are operating and, accordingly, there is a temperature difference on the examined building envelope.
At the initial stage, the analysis and determination the parameters of the room necessary for the experiment and simulation are carried out.
In the second step, the room is thermographed in accordance with ISO 6781 [16] to find a suitable location for the sensors to avoid thermal bridges, cracks or similar.
In the third step, heat flux and temperature sensors are mounted in accordance with the recommendations of ISO 9869-1 [12] and taking into account the results of thermography.
In the next step, tests are carried out in accordance with ISO 9869-1 [12]. Then, the results of the experiment for the first 24 hours are processed, and these data are input to the CFD model. After that, the experiment continues for at least another 48 hours in accordance with the recommendations of the standard and the results are processed.
The current values of the heat flux density q (W/m2) measured by the secondary measuring devices і is calculated as a multiplication of measured signals of heat flux sensors Е (mV) and their calibration і coefficient Ksensor (W/(mV·m2)) by the formula: Tii and Tei , the air near them TiiAir and TeAiir .
These values are averaged over a single full day (24 hours) or over several full days. For the averaged of the listed values, the arithmetic means of the current values of each quantity, measured at regular intervals, should be taken. Also, it is possible to apply wavelet analysis [17].
Next, for each zone calculated averaged measured values of such parameters: • the temperature difference by the formula:
Tstructuren = Tin − Ten ;
where n = 1, 2, …, N;
• the temperature head by the formula:
T Air = Ti Air − TeAir ;
n n
(
Rstructuren = Tstructuren qn , (
At the same time, the CFD model is calculated. The distribution of temperature and heat fluxes is determined, and the parameters influencing the experiment are refined.
The next step is to verify the simulation based on the measurement results using the values of the corresponding temperatures and heat fluxes. Based on the data obtained, heat losses are calculated. 2.2.
The object of the study is a room 5.41 m long, 3.04 m wide and 3.2 m high. The thickness of the outer wall is 0.55 m, the window size is 2.1×2.0 m, the window thickness is 0.2 m, the thickness of the over-radiator section of the wall is 0.45 m, its width is 0.80 m, the width of the lateral vertical parts of the outer enclosing structure is 0.70 and 0.34 m.
In accordance with the developed methodology, thermography of the room was carried out. The results are shown in Fig. 2.
Computational fluid dynamics model created in STAR-CD software. In the model (Fig. 4), the conjugate heat exchange of the air inside the room with the heating system radiator is fixed. Heat exchange by radiation is applied by using the Discrete Beams model [8 ,9].
Emissivity of all surfaces inside the room was assumed to be 0.8, the radiator surface – 0.3 because of a number of radiator sections that re-radiate heat to each other and is necessary to reduce the radiant heat flux from the radiator in the model.
The air exchange with the environment simulated through the window slots 1 mm wide, as well as through the ventilation hole in the wall. y + z z = 0 were i – the fluid velocity vector projections onto the corresponding coordinate axis. F (ТS1 − TОС ) S1 = − z2 were i – the fluid velocity vector projections onto the corresponding coordinate axis; Т – temperature, 0С; а – thermal diffusivity, м2/с.
The conjugation condition for temperature and heat fluxes was set at the separation boundaries solid
body–gas S2, S4 (see Fig.4). The equations of motion (
x x
x x x + y +
y y
y y x + y +
z z
2 x =
x2 z z
2 y = x2 x + y + 2 y2 2 y2 x + y + 2 1 p z2x − x 2z2y − 1 py z + x x
z + y y
2 z = z z x2 z + 2 y2 z + 2 1 p z2 z − z
1
− gz
were – kinematic viscosity coefficient of air, m2/s; – air velocity, m/s; р – pressure, Pa; β – volume
expansion coefficient; – air density, kg/m3; = T − T0 – excess temperature, °С; Т – fluid flow
temperature, °С; Т0 – wall temperature, °С.
(
T − T Air e were wair – air velocity flowing around the outer surface of the outer wall is equal to 5 м/с, Тe – average temperature of the outer wall outer surface, С, ТAir – environment temperature, С.
Air exchange with the environment is carried out as follows: air with ambient (environment) temperature is supplied through the window opening into the testing room. As a result of heat exchange inside the room, the air warms up and is removed from the room through a vent hole in the wall opposite the outer one. The required air exchange rate was created due to the Velocity inlet boundary conditions with a given air velocity, as well as the direction of movement (perpendicular to the plane of the window and the vent hole. Te T Air 4 − 100 100 , The conjugation conditions for temperature and heat fluxes at the interface S2, S4 (Fig.4) were set:
As a results of CFD modeling the fields of temperature, heat flows and air movement speeds in the studied room were obtained.
In fig. 5 shows the velocity vectors in the inlet (a) and outlet (b) ventilation openings of the room under study.
a) b)
The resulting heat flux field, shown in Fig. 6, is a confirmation of the significant uneven distribution of heat fluxes along the inner surface of the investigated room outer wall. Figure 7: Temperature distribution in the enclosing structures of the test room: a) temperature field in the vertical section of the outer wall right side; b) temperature field in the central vertical section of the outer wall; c) temperature field in the horizontal section of the outer wall
7 Heat flux on the inner surface of the outer wall at point 5, 47.6 48.2
W/m2
Individual components of the room heat balance – the values of heat flows through the enclosing structures of the room – are taken from the three-dimensional model and they are the heat losses of the test room. In the explored case the heat balance of the room can be described by the following formula:
QRAD = Qew. + Qow + QAir (16) were QRAD – heat flux from the radiator; Qew – heat flux through the outer wall into the environment; Qow – heat flux through the window into the environment; QAir – heat flow with air exchange to the environment, which is calculated from the equation (16).
Then the air exchange rate in the test room can be calculated using the following equation: m =
QAir C V (Ti Air − T Air ) , were – air density, kg/m3; C – air heat capacity, kJ/(kg·K); V – test room volume, m3; Т Airi – average room temperature, С; ТОС – environment temperature, С.
According to measurements, the air exchange rate was 0.75. The obtained values of thermal conductivity coefficients for the outer wall, window and air exchange rate make it possible to determine heat losses through individual enclosing structures of the room, as well as to develop solutions to reduce them.
The considered approach determined the values of heat losses through the outer wall, through the window and taking into account air exchange, which amounted to 190 W; 245W and 175W, respectively.
A proposed approach that allows to determine not only the thermal resistance, but also the heat lossеs of buildings, taking into account air exchange. A three-dimensional CFD model of the examined object heat exchange was built with accounting convective-radiant heat transfer.
Verification of a three-dimensional model was carried out to determine the parameters of heat losses in rooms from the measured values of temperature and heat flux densities based on experimental data. The error of the temperature and heat flux values obtained as a result of verification did not exceed 4% compared with the experimental data. The parameters of local heat losses were determined accounting air exchange.
Advantages of proposed approach are reduced influence of the subjective factor on the process of thermal resistance control of building envelope and ability to obtain distribution of the temperature and heat flux for each element construction. Also, possible to predict building envelope state and heat losses with accounting conductive and convective-radiant heat transfer in different environment conditions with use CFD model.
Limitation of proposed approach at the current state laying in using the steady state CFD model which means it is not full describe transition processes in building envelope. In the development of this work planned to create non-stationary СFD models in different software environments and compare results. As well, planned to variate the number calculation cells in СFD model and with extended verification for creating practical recommendations.
These researches have been performed within of the scientific program «Information technology for energy audit of buildings as a component of the energy security of the country».
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