## Keywords

room, model, with, consists, mathematical, components, ANSYS, calculation, temperature, content, calculated, parameters, heat, moisture, Fluent, exchange, microclimate, four, line, error, which, experimental, transfer, results, air,, Thermophysical, Russian], 2016, experiment., Basis

## Transcript

Simulation of the processes of heat- and the

mass transfer in the rooms of public building

with the natural ventilation

Maria Prorokova1,*, Vyacheslav Bukhmirov1

1State Educational Institution of Higher Professional Education Ivanovo State Power University

named after V.I. Lenin, 1153003 Ivanovo, Russia

Abstract. In the article the mathematical model of the processes of heat

exchange and mass exchange in the room of building with the natural

ventilation is shown. The verification of mathematical model is performed

via the comparison of the results of calculation in ANSYS Fluent with the

data of experiment. Experiment was conducted in the room of educational

institution. In the experiment were measured the temperature of air, air

speed and moisture content in air. A low relative error in the calculation

with the use of a mathematical model makes its use for predicting the

parameters of microclimate after the introduction of the energy-saving

measures possible

1 The mathematical model of the processes of heat exchange

and mass exchange in the room

The prediction of the parameters of microclimate in the rooms of habitable, public and

office buildings is urgent task. Solution of this problem will make it possible to estimate

influence on the microclimate of the rooms of factors, connected with the energy-saving

measures [1].

For the solution of this problem in Ivanovo State Power University was used the method

of mathematical simulation. The thermal, humid and air regime of room was described by

such parameters as the temperature of air (Тв, 0С), air speed (w, m/s), moisture content (d,

kg/kgd.a.) and the concentration of carbon dioxide (СО2, ppm). For calculating these

parameters the system of differential equations, which contains the equation of the

conservation of energy, pulse and quantity of substance, and also the integral-differential

equation of the transfer of the radiant energy, was solved [2-4].

The standard k-ε model of turbulence was used for calculating the turbulent properties

of air in the room [5]. The realization of the mathematical model of the processes of heatmass transfer is executed in ANSYS Fluent [6]. The solution of the equations of the transfer

in ANSYS Fluent is based on the method of final volumes.

* Corresponding author: prorokova_mv@list.ru

DOI: 10.1051/, (2017) 7920100792 matecconf/201MATEC Web of Conferences 01007

Thermophysical Basis of Energy Technologies - 2016

© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative

Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).

2 The verification of the mathematical model

The verification of the mathematical model of microclimate in the room was executed by

the comparison of the results of calculation in ANSYS Fluent with the data of experiment.

In the experiment in the room were measured the temperature, air speed and moisture

content in air. Measurements are taken on height 0.1, 0.6 and 1.7 m from the floor (for the

rooms, in which the people the large part of the time sit) [7].

During the first stage calculation in ANSYS Fluent is built the geometric model of

experimental room (figure 1) and with the aid of the grid editor Meshing to the calculated

region it is superimposed Cartesian multilevel grid (method CutCell). The automatic

generation of adapted grid made it possible to obtain grid from 1488278 the elements and

1817190 the units with the quality of the elements average by the volume of calculated

region 0.98. The exterior view of calculated grid is represented in the figure 2.

**11**
**2**
**8**
**7**
**5**
**4**
**3 8**
**1**
**12**
**9**
**6**
**10**
Fig. 1. The geometric model of the experimental room: 1, 3, 4, 5, 8 – table; 2, 10 – the sensors, which

measure the parameters of air; 6 – the source of the heat (oil cooler); 7 – window; 8 – the source of

the heat (heat-fan); 9 – sensor for measuring the parameters of surrounding air; 11, 12 - the door.

In the calculation it is accepted:

– air in the room is of four component mixture of nitrogen (N2), of oxygen (O2), of

carbon dioxide (CO2) and of water vapour (H2O);

– air is subordinated by ideal gas law;

– air in the room is diathermy;

– air it enters evenly only on the perimeter of window.

For describing the boundary conditions of task the results of the experiment were used:

the mean temperature of the surfaces of room, the temperature of air, the moisture content

in air, air velocity and the composition of surrounding air, the temperature of the surface of

man, composition and the temperature of air, which inhales and breathes out men, power of

the source of heat (oil cooler).

DOI: 10.1051/, (2017) 7920100792 matecconf/201MATEC Web of Conferences 01007

Thermophysical Basis of Energy Technologies - 2016

**2**
Fig. 1. Computational grid.

With the mathematical simulation of microclimate in the experimental room the

influence of air composition on the basic parameters of microclimate was investigated.

Calculations are executed for two air compositions:

– air in the room and tributary, and breathed out by man consists of the mixture of two

gases: of nitrogen (N2) and oxygen (O2);

– air in the room is the four-component mixture, which consists of nitrogen (N2), of

oxygen (O2), of carbon dioxide (CO2) and of water vapour (H2O).

Problem is solved for steady state of heat exchange and mass exchange with the

application of the method Pseudo Transient.

The results of calculation and experiment are given in the figures 3, 4 and 5.

In the tables 1 and 2 is given an relative error in calculated temperature and moisture

content in air in ANSYS Fluent (in comparison with the experiment).

Fig. 3. The temperature of air in the room: continuous line – air consists of four components (N2, O2,

CO2 and H2O); dashed line – air consists of two components (N2 and O2); point – the experiment.

DOI: 10.1051/, (2017) 7920100792 matecconf/201MATEC Web of Conferences 01007

Thermophysical Basis of Energy Technologies - 2016

**3**
Fig. 4. The velocity of air in the room: continuous line – air consists of four components (N2, O2, CO2

and H2O); dashed line – air consists of two components (N2 and O2); point – the experiment.

Fig. 5. Moisture content of the air in the room: continuous line – air consists of four components (N2,

O2, CO2 and H2O); dashed line – air consists of two components (N2 and O2); point – the experiment.

Table 1. An error in the calculated temperature of air in ANSYS Fluent.

№ the

point

Height

above

floor

level, m

**Тв, К**
(experiment)

Air consists of two

components

Air consists of four

components

**Тв, К**
(calculation)

Relative

error, %

**Тв, К**
(calculation)

Relative

error, %

**1**
**0.1 303.1 301.94 3.85 302.18 3.06**
**0.6 303.1 303.67 1.89 303.05 0.17**
**1.7 303.2 303.95 2.48 303.37 0.56**
**2**
**0.1 303.4 302.05 4.44 302.50 2.96**
**0.6 303.5 303.80 0.98 303.35 0.49**
**1.7 303.6 304.47 2.84 303.33 0.88**
DOI: 10.1051/, (2017) 7920100792 matecconf/201MATEC Web of Conferences 01007

Thermophysical Basis of Energy Technologies - 2016

**4**
Table 2. An error in the calculated moisture content of the air in ANSYS Fluent.

№ the

point

Height

above

floor

level, m

d, kg/kgd.a.

(experiment)

Air consists of two

components

Air consists of four

components

d, kg/kgd.a.

(calculation)

Relative

error, %

d, kg/kgd.a.

(calculation)

Relative

error, %

**1**
**0.1 0.0143 0.0127 11.19 0.0130 9.09**
**0.6 0.0143 0.0127 11.19 0.0142 0.70**
**1.7 0.0142 0.0127 10.56 0.0151 6.34**
The analysis of figures 3, 4 and 5 and tables 1 and 2 shows that the calculation of water

vapour and carbon dioxide in air increases the accuracy of the mathematical simulation of

microclimate. A difference in the calculated and experimental values of the air speed and

moisture content is caused by both the error in the numerical calculation and by error in the

experimental determination of these parameters.

3 Conclusion

Is proposed and realized in ANSYS Fluent the mathematical model of the processes of heat

transfer and mass transfer in the room of building, which considers water vapour and

carbon dioxide in air. Is proven the authenticity of mathematical model with the aid of the

comparison of the results of calculation with the experimental data.

References

1. V.V. Bukhmirov, M.V. Prorokova, Vestnik IGEU 4 (2015) [in Russian]

2. B. Gebkhart, Y. Dzhaluriya, R. Mekhadzhan, B. Sammakiya, Svobodnokonvektivnye

techeniya, teplo- i massoobmen (Mir, Moscow, 1991) [in Russian]

3. Yu.A. Tabunshchikov, M.A. Brodach, AVOK, 2002 [in Russian]

4. A.M. Grimitlin, T.A. Datsyuk, D.M. Denisikhina, AVOK Severo-Zapad, 2013 [in

Russian]

5. I.A. Belov, S.A. Isaev, Modelirovanie turbulentnykh techeniy (Balt. gos. tekhn. un-t,

2001) [in Russian]

6. I. Weinhold, J. Parry, The Three Waves of Commercial CFD. URL: www.mentor.com

**[12.07.2016]**
7. GOST 30494-2011 Zdaniya zhilye i obshchestvennye. Parametry mikroklimata v

pomeshchenii (2011)

DOI: 10.1051/, (2017) 7920100792 matecconf/201MATEC Web of Conferences 01007

Thermophysical Basis of Energy Technologies - 2016

**5**