Mathematical modelling of non-isothermal flow in buildings

Numerical simulations are used in many areas of science and technology. In last time are numerical methods used not only in small scale applications, in fluid mechanics, but are also used in civil engineering for simulation of air flow, for simulation of heat transfer. This paper deals with simulation of air flow in building for municipal use. The core of the paper is the calculation of the input parameters for the creation of numerical model and description of the model itself. The conclusion provides an analysis and comparison of simulation results with calculated values for the building.


Introduction
The numerical model is defined on the basis of various physical phenomena in complex differential equations.In this case, we will observe the flow of air in a rather complex geometry.In view of the fact that this is the 3D model of flow which can be described as a system of partial differential equations that can be solved by numerical methods.The calculation of the following equations are typically designed for a number of cells.
For the solution of ventilation can be used Fluent program, part of the software ANSYS package.When creating a numerical model it must be determined in the applicable geometry created with mesh computing.It is necessary to know all the input data and set them as boundary conditions that are necessary for correct calculation.After performing the calculation, it can be a graphical displayed of results.
In the numerical solution we choose a general model of the building.Another criterion was the choice of the ventilation system, the selected building should be ventilated with air to circulate.The layout of the proposed construction building is in Fig. 1.Numerical simulation is performed in order to determine if it is possible to achieve the natural air flow and the natural exchange of different combinations of open and closed windows and doors [1,13] in the building.

Modeling and mesh computing
3D model of the building was made up from drawings for construction of the building.The model has been adapted and simplified to the need to perform CFD simulations.
Network is a systemic breakdown of computational domain into sub interlinked cells in 2D space or in 3D space [2].
For numerical simulation have been chosen, these mesh computing: -hexagonal, -tetragonal, -polyhedral.Because it is a very complex model geometry the mesh must be created quickly.Of course computational mesh had to be of sufficient quality to get the best results from CFD simulations.[13]

Hexagonal mesh
The mesh is made up of mostly by hexagonal elements Fig. 2. Model building has a complex geometry, the mesh is made up of a quadrilateral and by triangonal elements.Given the complexity of the geometry was aggravation elements toward the center of the volume of the model and to create a network composed of the elements of hexagonal and tetragonal.

Tetragonal mesh
Fig. 3 shows a network element tetragonal and was allowed automatically in the whole volume.

Polyhedral mesh
Polyhedral mesh was made up of a mesh consisting of elements of tetragonal, as a command converting polyhedral fig. 4. Hexagonal mesh showed the worst quality mesh.Tetragonal mesh did not meet the quality or number of elements, but after converting to mesh polyhedral significantly decreased the number of elements and improve the quality of the mesh.For simulation was chosen polyhedral mesh.

Boundary conditions
Building has heated bench with a constant temperature at 36 °C and heated floor temperature at 25 °C.Outdoor design temperature is set to 15 °C.Design temperature for the walls is 5 °C.In the building will be simulated airflow with closed windows and doors at first.Based on simulation results, will be decided on whether the natural flow will be sufficient for air exchange in the building or installation of ventilation elements will be required [1].
In the programming environment of FLUENT have been set initial and boundary conditions.Among the software simulations, Ansys Fluent software allows, the simulation of physical and thermophysical effects to the greatest interface.Modeling airflow simulations were transferred by employing three models: -Laminar, -k -İ model, -k -Ȧ model.
The procedure for entering the initial and boundary conditions were as follows: 1) input of material parameters, 2) enter the input and output values of the flowing medium, 3) set points, 4) adjusting the calculation, 5) initialization calculation, 6) start of calculation.

CFD simulation results
CFD simulation result is achieved by making the natural flow (Tab.5) of air in the building.The resulting rates were compared with closed and open windows and doors using three calculation models.

The results of numerical simulation model Laminar (open windows and doors)
Fig. 5 shows the temperature fields in laminar model.After completion of iterations can see the method and direction of mixing cold outside air with warmer air inside.Air distribution through building can be seen by streamlines and vectors of the air in the premises through the low-lying inlet openings (doors and windows) and exit through the skylight.
Fig. 5 Temperature ratio in laminar building model Fig. 4 shows the different temperatures that range between -14.8 °C to 25 °C in a church building section.Low visible mainly at the door and at the window 2, 5. Air temperature 25 °C is accumulated in the heated benches and rises to the ceiling..17m.s -1 .In the middle of the building can be seen mixing of air at lower speeds than the speed of the air inlet and outlet openings in each.

The results of numerical simulation model k-İ
Fig. 7 are shown the temperature fields in the model k-İ.In this model, the expiration of iterations was cold air entering through the lower area of the door and set down in the upper part of the door and the window and the window 1, 5. Also, you can see the temperature conditions through the headroom space.The movement of the nozzle and direction vectors is shown in Figure 8.

The results of the numerical simulation model k -Ȧ
The model k -Ȧ was undesirable chimney effectfacing the flow of air inside the building, to a greater extent taking place thereto, and the skylight window of 3, and to a lesser extent through the open doors 2. The numerical simulation with closed windows and doors have been selected sections to display the contours of temperature and air velocity.

The results of numerical simulation model Laminar
Fig. 10 shows the internal temperature status with doors and windows closed as there is for heating the surrounding air from the benches on the ground floor and first floor and the air cooling of the walls.

Conclusion
Three types of meshes was created and compared after simulations.
The results of the comparison: -A hexagonal network, increase magnification cell towards its center (the worst network).When reducing the number of components quality of network decreased.
-Tetragonal network was due to poor quality converted to grid "polyhedral", thereby reducing the number of components and quality of the network increased.
The result of the comparison network was chosen for simulation hexagonal grid and three models of turbulence "laminar", "k-İ", "realizable" of a wall with an extended feature "enhanced wall treatments" a model "for İ-standard".The simulations were carried out with closed and then opened selected windows and doors.
The main goal was to handle numerical simulation of flow in the building and pointing out that it is possible to perform such analyzes even before the position of the object itself.
Laminar model was best to simulate natural air flow through building.

Fig. 1
Fig. 1 Building model geometry before treatment

Fig. 4
Fig. 4 Cut polyhedral meshTable 4. Parameters of a polyhedral mesh and quality

Fig. 6
Fig.6 Shows streamlines and the vectors in laminar model Fig.6are shown the ventilation velocity laminar model; max.air velocity reaches 25.17 m.s -1 .In the middle of the building can be seen mixing of air at lower speeds than the speed of the air inlet and outlet openings in each.

Fig. 9
Fig. 9 Temperature ratio in the k -Ȧ model

Fig. 10 Fig. 11
Fig. 10 Temperature conditions in the model Laminar

Table 1 .
Parameters of the building.

Table 2 .
Parameters of a hexagonal mesh and quality

Mesh Number of elements Orthogonal Quality Ortho Skew Hexagonal mesh
1,536,370 1.005.10 -1 0.999

Table 5 .
Scores air speed of CFD simulations