In calculations related to modeling the development of a fire in a room, the exact values ​​of the thermophysical parameters of the enclosing structures may not be known. The article compares the dynamics of temperature and the level of thermal radiation during a fire in rooms of the same size with walls made of “inert” material, brick, polished steel and glass by means of field modeling.

It is shown that the dynamics of temperature and radiation in a room with a combustion center is influenced, first of all, by the coefficient of reflection of radiation from the walls. It is also shown that opaque materials practically do not transmit heat to adjacent rooms. The density, heat capacity and thermal conductivity of wall materials have little effect on the dynamics of air temperature and thermal radiation.

The article was first published in the magazine “Pozharnaya bezopasnost'” No. 4-2019 (http://www.vniipo.ru/nt-journal-pozharnaya-bezopasno/).

## Introduction

Integral and zone models are widely used in the study of the dynamics of hazardous fire factors [1]. Although such models do not allow full use of information on the geometry of rooms, wall materials, etc., the results of the calculations are generally acceptable. The increase in the computing power of computers makes it possible to use more advanced field methods for calculating the fire [1]. In general, the field model makes it possible to take into account a large number of parameters of the simulated scene in calculations. Some parameters characterizing the combustion of materials are given in reference books [2]. However, the thermophysical parameters of the walls bounding the premises often cannot be known with high accuracy. It is of interest to assess how strongly these parameters influence the simulation result.

Thermal conductivity, heat capacity, density, emissivity, absorption rate of materials affect the heating rate of walls due to thermal radiation and from hot air. That is, the wall materials affect the heat loss from the room through the walls. Since the thermal energy inside the room is characterized by the air temperature and the intensity of thermal radiation, then at a given combustion intensity, the wall materials affect only the air temperature and thermal radiation, and do not affect the release of soot and toxic reaction products.

This study is devoted to the study of the influence of the properties of wall materials on the dynamics of temperature and thermal radiation inside the room during a fire using a field model. The simulation was carried out in the FDS 6.5.3 environment [3].

## Modeled materials

Heat loss through walls from a room with fire is carried out due to two mechanisms of heat transfer: heat radiation and heat transfer (convective heat exchange between gas flows and the surface of a solid). Both mechanisms are all the more important the higher the temperature inside the room, therefore, it can be expected that at the initial stage of a fire, when the temperature is relatively low [4], wall materials have little effect on the dynamics of temperature and thermal radiation.

It was decided to carry out modeling during combustion of a typical room material “furniture + household products building (I-II degree of fire resistance)” [2].

Wall materials differ mainly in density, thermal conductivity, heat capacity, emissivity (ε) and absorption. For brevity, but meaningfulness of the comparison, the following materials were chosen: “inert”, brick, polished steel, transparent glass. An “inert” material is idealized, always at 20 ° C, opaque, and also has an emissivity of 0.9. Since the temperature of this material does not change, its density, thermal conductivity and heat capacity do not matter. It can be expected that this material will provide the greatest heat loss, since it will act as a “cooler”. The name “inert” will be used below without quotation marks. FDS uses this wall material by default; it can be set explicitly using the “SURF_ID=‘INERT’ property.

In FDS, the Absorption Rate (ABSORPTION_COEFFICIENT) defaults to 50,000 m-1, which means the material is opaque unless otherwise specified.

The material “brick” has the following parameters: density = 1800 kg / m3, thermal conductivity = 0.87 W / (m * K), heat capacity = 0.88 kJ / (kg * K), ε = 0.9. Opaque. In the FDS environment, it is specified by “covering” all walls, partitions, floor and ceiling with a surface with the following properties.

&MATL ID = 'BRICK', EMISSIVITY = 0.9, DENSITY = 1800, CONDUCTIVITY = 0.87, SPECIFIC\_HEAT = 0.88/

SURF ID='BRICK WALL', MATL\_ID='BRICK', BACKING='EXPOSED', THICKNESS=0.25 /

The material “polished steel” has the following parameters: density = 7800 kg / m3, thermal conductivity = 47 W / (m * K), heat capacity = 0.5 kJ / (kg * K), ε = 0.1. Opaque. Considered as an example of a material with a specular surface. In the FDS system, the reflectance is calculated as 1-ε. The material properties in FDS have been defined as follows.

&MATL ID = 'STEEL', EMISSIVITY = 0.1, DENSITY = 7800, CONDUCTIVITY = 47, SPECIFIC\_HEAT = 0.5/

&SURF ID='STEEL WALL', MATL\_ID='STEEL', BACKING='EXPOSED', THICKNESS=0.02 /

The material “transparent glass” has the following parameters: density = 2500 kg / m3, thermal conductivity = 1 W / (m * K), heat capacity = 0.8 kJ / (kg * K), ε = 0.9. Transparent, absorption rate = 0 m-1. The material properties in FDS have been defined as follows.

&MATL ID = 'GLASS', EMISSIVITY = 0.9, DENSITY = 2500, CONDUCTIVITY = 1, SPECIFIC\_HEAT = 0.8, ABSORPTION\_COEFFICIENT = 0/

&SURF ID='GLASS WALL', MATL\_ID='GLASS', BACKING='EXPOSED', THICKNESS=0.02 /

This set of materials includes materials with different thermal conductivity, with fundamentally different emissivity, opaque and transparent, as well as a conventional material that is always at a constant temperature. Note that a material with emissivity ε absorbs exactly the same fraction ε of incident radiation.

## Description of the room

Consider a room with internal dimensions of 5 × 15 m, divided by partitions into three rooms with dimensions of 5 × 4.75 m, 5 × 5 m and 5 × 4.75 m.The thickness of the partitions between the rooms, as well as the thickness of the walls separating the room from the street, is 0.25 m for materials “inert” and “brick”, and 0.02 m for materials “polished steel” and “transparent glass”. In the middle of one of the partitions there is an open doorway 1 m wide and 2 m high. In the outer rooms there are open doorways to the outside. The floor plan is shown at image 1. For further convenience, rooms are numbered from left to right.

In the central room (2), along a solid partition at a height of 0.5 m from the floor, there is a fire center 2 × 1 m in size. In each room, in the middle of each wall, at a height of 1.7 m, there is a temperature meter. Also, in some points of the room, which are marked at image 1 with black dots and signed in small letters, there are temperature and heat radiation meters. All meters are located at a height of 1.7 m. Each thermal radiation meter contains four directional radiation sensors, oriented to the cardinal points.

Let’s simulate burning for 300 seconds.

## The discussion of the results

Wall temperature

Let’s discuss the dynamics of wall temperature for different materials. Recall that in the case of an inert material, the wall temperature was always 20 ° C.

In room 1, we will only be interested in the eastern wall, since it is a partition with room №2, where combustion takes place. The highest temperature of 37 ° C was reached in the case of a steel wall due to the high thermal conductivity of steel.

In the rest of the rooms, all the walls reached their highest temperature when using the “brick” material. This is due to the fact that this material has both low thermal conductivity and high emissivity, and hence a high absorption coefficient. While polished steel predominantly reflects heat radiation, therefore it heats up less - it quickly conducts heat and cools down. The glass in our model does not absorb radiation at all, so it also heats up slowly.

The material of the walls affects their temperature in a fire, but the temperature of the walls is not a dangerous factor. Further, it will be demonstrated that you should not draw a conclusion about the air temperature in the room from the wall temperature.

Air temperature

Consider the graphs of the air temperature at some points. In room 1, the temperature did not deviate in any significant way from 20 ° C for any wall material, that is, an airtight partition, even of a small thickness, reliably protects against high temperatures.

In room 2, the temperature graphs at points a,b,c,d,e,f turned out to be very close to each other. A similar closeness is shown by the temperature dynamics at points a,b,c,d,e,f of room 3. Therefore, further, to reduce the illustrative material in rooms 2 and 3, we will consider the temperature only at the point c.

Image 2 shows the graphs of the temperature at point “c” in room 2 in models with different materials. The hottest air was in the model with polished steel walls. In other cases, the temperatures are almost the same. The temperature threshold of 70 ° C was exceeded in all four cases after approximately the same time ~ 60 sec.

The temperature graphs in the doorway between rooms №2 and №3, as well as at point “c” of room 3, showed similar dynamics. It can be noted that the temperature in the doorway was even slightly higher than at point “c” of room №2. However, at point “c” of room №3, the temperature was already significantly lower than in the doorway.

A significant increase in temperature in the model with polished steel is due to the fact that the mirror surface “locked” the radiation in the room and one of the two heat removal mechanisms almost did not work. The approximate equality of the graphs for other materials is explained by the fact that these materials allowed radiation to escape more efficiently from the room. And, as shown by modeling, it is not so important whether this radiation was absorbed by the wall (inert material and brick), or passed through (glass). And it is not so important whether the wall material heats up a lot. It was mentioned above that the temperature of the walls made of different materials was very different, but it had almost no effect on the air temperature in the rooms.

Moreover, the temperature of the polished steel walls was not the highest, and the air temperature in this model was the highest. The main influence on the room temperature is reflectance from the walls! In the FDS system, the reflectance is calculated as 1-ε, and for polished steel it is 0.9, and for other materials 0.1.

Let’s start examining the graphs of thermal radiation. Noticeably different from the background value the flux of thermal radiation in room №1 at points a and b was only in the case of glass walls (image 3).

This is radiation from a fire source that has passed through the wall. Glass is the only one of the considered materials for which thermal radiation from an ignition source behind a partition can be significant. In the case of other, opaque, materials, the partition did not have time to warm up enough for its own radiation to pose any danger.

In the rest of the rooms, we will consider heat radiation from the western direction, since this is where combustion occurs. The radiation flux at points a,b,c,d,e,f is different. The highest value of the flux is always observed at point “c”, since it is closest to the fire, and the meter in it looks directly at the fire. In image 4 shows for example the graphs of the heat radiation flux at six points of room №2 for a model with brick walls. Further, to reduce the illustrative material, we will compare the flows only at points “c”.

Image 5 shows graphs of the thermal radiation flux in room 2 at point “c” in models with different materials.

The radiation power in the model with mirrored walls is more than twice that of other models. Approximately equal radiation power in models with non-specular materials is mainly determined by the equal reflectivity of the materials. Different temperatures of materials lead to only small differences, since the temperature of the walls, on average, is much lower than the temperature of the ignition source and the combustion area, which produces the “hottest” radiation. That is, the main source of heat radiation in a fire is fire, and the temperature of the walls plays a rather small role. The same cannot be said about the reflectivity of wall materials. They play a huge role.

For the heat radiation flux in the doorway, the same characteristic relationships were observed as in the previous figure. The value of 1.4 kW / m2 in a doorway with steel walls was exceeded after 70 seconds, while in the case of inert, brick and glass walls it was not exceeded at all.

Image 6 shows the graphs of the thermal radiation flux at point “c” of room 3. Here, in the case of steel walls, the radiation is the strongest, as was the case in room №2.

However, the graphs for the other three materials diverge slightly more than in room №2, because in the case of opaque materials, the partition blocks a significant part of the radiation.

The radiation flux in room 3 when using glass walls exceeds the flux when using brick walls by about a third on average. This is due to the transparency of the glass partition between rooms №2 and №3. However, in the case of the polished steel walls, when the radiation was “locked” in the room, the heat flux was much higher than with the glass walls, despite the fact that the partition was opaque and rooms №2 and №3 were connected only by a doorway.

## Conclusion

Comparison of four fundamentally different wall materials for the same room configuration made it possible to conclude that reflection from the walls has the greatest effect on both the temperature and the flux of thermal radiation in a room with an ignition source (and adjacent rooms with open doors). Other parameters of materials practically do not play a role. In the FDS system, the emissivity of a material is set by the EMISSIVITY parameter. And the reflectance is calculated by the system as 1-EMISSIVITY. If the emissivity of the material used in the model matches reality, then it would otherwise not be a big mistake to use the properties of an inert material.

In rooms that are separated from rooms with a source of ignition by an opaque partition of any significant thickness, and do not have open doorways connecting them, the materials of the walls are practically irrelevant.

Transparent walls do not differ much from inert ones in terms of their influence on temperature and radiation inside a room with a source of ignition. However, they strongly affect the radiation in adjacent rooms. Care must be taken to ensure that the transparency of the respective materials is taken into account when simulating. In the FDS system, this is done by setting the material property ABSORPTION_COEFFICIENT = 0 (1 / m). The real value can be specified if known.

In cases where there are no transparent or mirrored walls, it is often possible to assume that the emissivity of the walls is close to 0.9, and use the INERT material. The simulation showed that the difference between the dynamics of temperature and the flux of thermal radiation between the models with the “inert” material and the “brick” material is no more than 20% over the entire simulation time.

In the above study, the combustion of a material with moderate heat release and smoke-generating ability was simulated. In the case of burning high-energy materials, in which the air temperature or the concentration of hazardous substances will obviously exceed the norms permissible for a person in a few seconds after the start of combustion, when the walls do not have time to heat up yet, the issue of the influence of wall materials on temperature and thermal radiation loses its relevance to a large extent.

## Literature

1. Order of the Ministry of Emergency Situations of the Russian Federation of June 30, 2009 No. 382 “On approval of the methodology for determining the calculated values ​​of fire risk in buildings, structures and structures of various classes of functional fire hazard” (as amended on 12.12.2011 No. 749, dated 02.12.2015 No. 632). Appendix No. 6. The procedure for calculating and mathematical models for determining the time of blocking escape routes by hazardous fire factors;
2. Koshmarova YU. A. Prognozirovanie opasnyh faktorov pozhara v pomeshchenii: Textbook. M .: Academy of State Fire Service of the Ministry of Internal Affairs of Russia, 2000, p. 118; (in Russian)
3. https://pages.nist.gov/fds-smv/.
4. Koshmarova YU. A. Matematicheskaya model' nachal’noj stadii pozhara v pomeshchenii pri vosplamenenii goryuchej zhidkosti / Pozharovzryvoopasnost', vol. 10, No. 5, 2004, pp. 70-80. (in Russian)