# Numerical Simulation on Thermodynamics Performance in the Fireproof Sealing by Finite Element Analysis

Authors: Shuai Gao; Guoqing Zhu; Yunji Gao; Guoqiang Chai; Jinju Zhou
Journal: Mathematical Problems in Engineering
 (2019)

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## Abstract

In this paper, the finite element analysis was firstly employed to investigate the thermal analysis on two fireproof sealing models with ANSYS software under HC standard temperature-time condition. The main thermal parameters were analyzed and obtained, including temperature field, thermal flux, and thermal gradient. After comparing the two fireproof sealing models, the major conclusions are summarized as follows: In terms of temperature field, the temperature on the left side of the first model ranges from 60 to 524°C in. In contrast, the highest temperature on the left side of the second model eventually reaches below 151°C. Moreover, the vectors of thermal gradient in the first model are compared with the second model, and the temperature gradient disturbance is more obvious in the second fireproof sealing model, which is better to slow down temperature spreading. The accelerated speed of E1 and G1 is 0.0096°C/s and 0.0619°C/s partly, which are far more than C2 and F2 with values of 0.0028°C/s and 0.0078°C/s, respectively. In a word, the performance of the first fireproof sealing model is inferior to the second fireproof sealing model. The conclusions of the study are meaningful to improve the thermodynamic performance of the fireproof sealing in the converter station.


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## Body

## 1. Introduction

Converter station is an important element in High Voltage Direct Current (HVDC) transmission system, which converts alternating current into direct current or converts direct current into alternating current, and electricity is the blood of industry and daily life. If a fire occurs at a converter station, the converter station will fail in the fire, which will result in loss of business and service and endanger people’s lives. Therefore, the fireproof performance of the fireproof sealing isolated from the converter transformer side and the valve hall side of the converter station is studied.Over the years, a large number of scholars have done a deal of investigations on fire protection with numerical simulation. Raduca et al. [1] used finite element method to present the modeling and simulation of the thermal transfer in the transformers from the high electric voltage stations, and the simulation of an optimal solution was obtained regarding the correct usage of the transformers. Piloto et al. [2] investigated the thermal behavior of the unexposed surface and the nodal internal layers in light steel frame with numerical simulations. Jeyakumar et al. [3] carried out numerical simulations on Ag2SO4/ZnO(ASZ) nanocomposite coating with steady-state thermal analysis using ANSYS to validate the output in the numerical approach, and the results obtained showed that ASZ nanocomposite coating acted as an efficient thermal barrier coating for the exhaust manifold, thus increasing its reliability. Liu et al. [4] carried out some simulations and experiments about welding processes of martensitic steel (RAFM steel) in three-dimensional finite element models by ANSYS software, and the temperature fields and stress fields from simulations were contrasted with that from experiments, respectively. Mittal and Greiner [5] constructed two-dimensional and three-dimensional thermal models of a Nuclear Assurance Corporation Legal Weight Truck (NAC-LWT) cask using the PATRAN commercial finite element package under normal and fire accident conditions. Liu et al. [6] analyzed firstly potential fire scenarios relevant to a cable-stayed bridge crossing the Yangtze River, then the temperature distribution in key elements and the global structural behavior of the bridge under tanker truck fires were calculated by using general purpose finite element analysis software ANSYS. Moreover, numerical simulation results demonstrated that cable-stayed bridge might collapse under some specific fire scenarios. Zhang [7] conducted a comprehensive modal analysis of Z-shaped beam electrothermal microactuators for the first time, and both longitudinal and lateral vibrations were taken into account to obtain the vibration equations of the unique geometric feature: a Z-shaped beam with a shuttle in the middle. Zivkovic et al. [8] investigated the influence of the boiler scale on the thermal stresses and strains of the structure of hot water boilers with the finite elements method by ANSYS software, and maximum thermal stresses appeared in the zone of the pipe-carrying wall of the first reversing chamber. Tomecek [9] studied thermal response of steel columns with lost protection material and varying amounts of missing protection when exposed to the ASTME-119 furnace environment by a finite element analysis of heat transfer. Moreover, some scholars studied the thermodynamic problem and design of fireproof sealing and plugging in building under the fire conditions. In addition, Chung et al. [10] conducted a simulation on the development of a finite element model capable of representing a blast-resistant flexible window (flex-window) system developed by the Air Force Research Laboratory, Airbase Technologies Division (AFRL/RXQ). Hatiegan and Raduca [11] conducted the thermal analysis on the hydrogenerator stator winding and found that the insulation aging is influenced first by the environmental conditions and second by the speed increase of the high temperature chemical reaction in materials. Moreover, Cindea and Hatiegan [12] investigated the influence of the thermal field on X60 carbon steel components during welding in CO2 environment given that the heat source (electric arc) moves.Sun and Zhou [13] studied the thermal properties on new fireproof sealing sheet with the principle of fireproof sealing and plugging in building and proposed the composite applications of fireproof sealing technical measures on the basis of combining the engineering application. Ro [14] investigated the designing of appropriate height of firewalls for toluene and methanol outdoor storage tank’s pool fire accidents with considering input variables, such as thermal radiation, orifice diameter, and elevation, and the result of effect distances was obtained.Fireproof sealing is widely employed to limit the scale of fire in multistory building, commercial building, industrial building, medical building, and other types of public buildings. However, the experiment on fireproof sealing is difficult to conduct to obtain the parameter of thermal and fire resistance. In this paper, the two fireproof sealing models are established by ANSYS, which is the first time to apply finite element analysis to the research of fireproof sealing and improve the effectiveness of the later experiment. Thus, the numerical simulation of finite element analysis is introduced to study the fire protection of firewall sealing wall in this paper. Regarding finite element analysis, mathematical approximation is applied to simulate a real physical system (geometric and load conditions). With simple and interacting elements, a finite number of unknowns can be used to approximate an infinitely unknown real system. In this paper, the finite element analysis was employed to investigate the thermal parameters, such as temperature field, thermal flux, and thermal gradient. When optimum effective combination with different materials was assumed for the model, a good approach was achieved by the simple calculation model, and the fireproof sealing model was made of different material which would enhance fire protection performance.


## 2. Simulation Setup

### 2.1. Geometry Model and Material Parameters

The typical fireproof materials are selected for fireproof sealing models which are widely applied in the market and have the good fireproof performance. Moreover, the combination of various fireproof materials can greatly improve the mechanical and fireproof performance of a high-quality fireproof material. In addition, two typical models are selected for simulation study in combination experiment to explore whether the fire protection performance of various composite materials can be improved using specific research methods. Thus, the main fireproof materials are rock wool, aluminum silicate needle blanket, square steel, fire retardant coating, fire retardant module, ALC board, cement, and fire suppression module. When designing the fireproof sealing, not only fire resistance but also stress and explosion hazard are required, and the thermodynamics should be considered firstly due to the importance of thermal performance. In this paper, two different types of combination of fire sealing were simulated with finite element analysis by ANSYS, and the parameters of thermal were achieved as the evaluation criteria to obtain the optimum effective combination. The finite element analysis can be divided into three procedures. Firstly, the designated model should be built and the materials properties are applied in the models; secondly, the parameters of boundary conditions are given and the forces with different conditions are loaded; lastly, the data are obtained and analyzed to check the desired result after completing the simulation.The fireproof sealing comprising rock wool, aluminum silicate needle blanket, square steel, and ALC board with fire suppression module was selected as the simulative materials of two models. And then thermal parameters, such as density, specific heat capacity, and heat conductivity, were set, respectively, in ANSYS software which could influence the thermal field and the velocity of temperature conduction, and the specific parameters of four materials are shown in Table1 [15]. The apparatus of four material modules were shown separately in Figures 1(a) and 1(b), and the fire surfaces were on the right side of two models. On account of the thermal characteristic changing with fire spread, the type of analysis was selected as transient and three significant thermal parameters were chosen as different characteristics in various temperature fields.Table 1
Different kinds of material properties.
Material category Temperature (°C) Thermal Conductivity (W/(m·K)) Specific Heat (J/(kg·K)) Density (kg/m3) Rock wool 0~300 0.039 150 750 301~500 0.057 501~800 0.134 801~1200 0.197  Aluminum silicate needle-punched blanket 0~400 0.043 96 900 401~800 0.093 801~1200 0.147  Square steel 0~1200 50 460 7850  ALC board 0~1200 0.2 1782.1 500  Fire suppression module 0~1200 0.3 1600 103Figure 1
The designing model of fireproof sealing.
(a) (b)The differences of two fireproof sealing models were the model shape and the initial fire surface. Moreover, the fireproof performance of different materials was exhibited during the simulation in this paper. One fireproof sealing model was shown in Figure1(a) which was made of four kinds of plates with 410 × 500 × 200 mm, and the T-shape was the shape of model in the front side. In contrast to Figure 1(a), the other fireproof sealing model was shown in Figure 1(b) which also consisted of four kinds of plates with 290 × 350 × 200 mm; however, the shape of model was rectangle to ensure protective sealing. A three-dimensional finite element model was built by ANSYS software, and then mesh was compared into 18 and 11 areas, respectively. Furthermore, 10 mm mesh was employed at every different kind and the total number of meshes were 46179 and 26360 partly to meet the accuracy of calculation results, which were exhibited in Figure 3.


### 2.2. Boundary and Temperature Conditions for Thermal Analysis

The fire surface of the first model is on the ALC board and square steel in the right of first model, and the fire surface of the second model is on the rock wool and fire suppression in the right of first model. The fire surface of the fireproof sealing is one side and the two fireproof sealing models have the same initial loads. Thus, when evaluating the fire resistance of building components under liquid hydrocarbon fire conditions, a hydrocarbon (HC) heating curve can be used for fire resistance testing and is suited with the case. For the HC fires, the temperature-time relationship in the fire test furnace is expressed by(1)T=1081-0.325e-0.167t-0.675e-2.5t+T0wheret denotes the time of simulation experiment whose unit is minutes (min) andT is the average temperature at the timet, which is measured in degrees Celsius (°C). Moreover, T0 is the initial average temperature before the start of the test, which is required to be 5°C to 40°C, and the value of T0 is 20°C in this simulation. The standard temperature-time curve of the hydrocarbon (HC) fire is shown in Figure 2. The possible application scenario of the fire temperature rise curve is the oil and gas fire at the converter station.Figure 2
The curve of hydrocarbon (HC) temperature heating.Figure 3
The grid with finite elements of geometrical model.
(a) (b)


### 2.3. Thermal Analysis Model

In the thermal simulation, solid 8-node 70 elements were applied as element types as shown in Figure3. To realize the accuracy of simulation, the initial temperature was set to 20°C as simulation ambient temperature. On account of the temperature of models parameters ranging from 0 to 1200°C, thermodynamic propagations can work after the thermodynamic properties of materials are 20°C. The type of model contact is surface to surface in different materials, and the contact value between the contact surface and the target surface is 1000, which is coordinated with simulation requirement.


## 2.1. Geometry Model and Material Parameters

The typical fireproof materials are selected for fireproof sealing models which are widely applied in the market and have the good fireproof performance. Moreover, the combination of various fireproof materials can greatly improve the mechanical and fireproof performance of a high-quality fireproof material. In addition, two typical models are selected for simulation study in combination experiment to explore whether the fire protection performance of various composite materials can be improved using specific research methods. Thus, the main fireproof materials are rock wool, aluminum silicate needle blanket, square steel, fire retardant coating, fire retardant module, ALC board, cement, and fire suppression module. When designing the fireproof sealing, not only fire resistance but also stress and explosion hazard are required, and the thermodynamics should be considered firstly due to the importance of thermal performance. In this paper, two different types of combination of fire sealing were simulated with finite element analysis by ANSYS, and the parameters of thermal were achieved as the evaluation criteria to obtain the optimum effective combination. The finite element analysis can be divided into three procedures. Firstly, the designated model should be built and the materials properties are applied in the models; secondly, the parameters of boundary conditions are given and the forces with different conditions are loaded; lastly, the data are obtained and analyzed to check the desired result after completing the simulation.The fireproof sealing comprising rock wool, aluminum silicate needle blanket, square steel, and ALC board with fire suppression module was selected as the simulative materials of two models. And then thermal parameters, such as density, specific heat capacity, and heat conductivity, were set, respectively, in ANSYS software which could influence the thermal field and the velocity of temperature conduction, and the specific parameters of four materials are shown in Table1 [15]. The apparatus of four material modules were shown separately in Figures 1(a) and 1(b), and the fire surfaces were on the right side of two models. On account of the thermal characteristic changing with fire spread, the type of analysis was selected as transient and three significant thermal parameters were chosen as different characteristics in various temperature fields.Table 1
Different kinds of material properties.
Material category Temperature (°C) Thermal Conductivity (W/(m·K)) Specific Heat (J/(kg·K)) Density (kg/m3) Rock wool 0~300 0.039 150 750 301~500 0.057 501~800 0.134 801~1200 0.197  Aluminum silicate needle-punched blanket 0~400 0.043 96 900 401~800 0.093 801~1200 0.147  Square steel 0~1200 50 460 7850  ALC board 0~1200 0.2 1782.1 500  Fire suppression module 0~1200 0.3 1600 103Figure 1
The designing model of fireproof sealing.
(a) (b)The differences of two fireproof sealing models were the model shape and the initial fire surface. Moreover, the fireproof performance of different materials was exhibited during the simulation in this paper. One fireproof sealing model was shown in Figure1(a) which was made of four kinds of plates with 410 × 500 × 200 mm, and the T-shape was the shape of model in the front side. In contrast to Figure 1(a), the other fireproof sealing model was shown in Figure 1(b) which also consisted of four kinds of plates with 290 × 350 × 200 mm; however, the shape of model was rectangle to ensure protective sealing. A three-dimensional finite element model was built by ANSYS software, and then mesh was compared into 18 and 11 areas, respectively. Furthermore, 10 mm mesh was employed at every different kind and the total number of meshes were 46179 and 26360 partly to meet the accuracy of calculation results, which were exhibited in Figure 3.


## 2.2. Boundary and Temperature Conditions for Thermal Analysis

The fire surface of the first model is on the ALC board and square steel in the right of first model, and the fire surface of the second model is on the rock wool and fire suppression in the right of first model. The fire surface of the fireproof sealing is one side and the two fireproof sealing models have the same initial loads. Thus, when evaluating the fire resistance of building components under liquid hydrocarbon fire conditions, a hydrocarbon (HC) heating curve can be used for fire resistance testing and is suited with the case. For the HC fires, the temperature-time relationship in the fire test furnace is expressed by(1)T=1081-0.325e-0.167t-0.675e-2.5t+T0wheret denotes the time of simulation experiment whose unit is minutes (min) andT is the average temperature at the timet, which is measured in degrees Celsius (°C). Moreover, T0 is the initial average temperature before the start of the test, which is required to be 5°C to 40°C, and the value of T0 is 20°C in this simulation. The standard temperature-time curve of the hydrocarbon (HC) fire is shown in Figure 2. The possible application scenario of the fire temperature rise curve is the oil and gas fire at the converter station.Figure 2
The curve of hydrocarbon (HC) temperature heating.Figure 3
The grid with finite elements of geometrical model.
(a) (b)


## 2.3. Thermal Analysis Model

In the thermal simulation, solid 8-node 70 elements were applied as element types as shown in Figure3. To realize the accuracy of simulation, the initial temperature was set to 20°C as simulation ambient temperature. On account of the temperature of models parameters ranging from 0 to 1200°C, thermodynamic propagations can work after the thermodynamic properties of materials are 20°C. The type of model contact is surface to surface in different materials, and the contact value between the contact surface and the target surface is 1000, which is coordinated with simulation requirement.


## 3. Results and Discussion

### 3.1. Temperature Field in Fireproof of Different Materials

According to heat transfer, if there is a temperature gradient inside the model, the energy will transfer from the high temperature zone to the low temperature zone, which is transferred in the form of heat conduction.Heat conduction is subject to Fourier law; that is, the heat flow density of a place formed by heat conduction is proportional to the temperature gradient of the same place at the same time in the nonuniform temperature field, and its mathematical expression in the one-dimensional model temperature field is exhibited in [16](2)qx′′=-kdTdxwhereqx′′ is thermal flux, dT/dx is the temperature gradient in the x direction, and k is thermal conductivity.When there is no internal heat source, the unsteady thermal conductivity differential equation of the three-dimensional model temperature field is as follows [17].(3)∂T∂t=α∂2T∂x2+∂2T∂y2+∂2T∂z2It is demonstrated from Figure4 that the distribution of temperature has diverse spread trend in the two fireproof sealing models with different materials. In Figures 4(a) and 4(b), since the right sides of the models are the fire surface, the two models have highest temperature point in common and finally reach to 1100°C. Simultaneously, Figure 4(a) indicates that the temperature conduction to the left is a gradient of heat growth, but the temperature trend irregularly transfers to low energy, which is due to the law of the conservation of energy and the function of two fire surfaces [18]. Ultimately, the temperature on the left side of the first model ranges from 60 to 524°C, and the temperature of rock wool is above 524°C. However, the thermal performance of superstructure is superior to substructures, which demonstrates that the model widths can affect the thermal performance of fireproof sealing. In contrast, Figure 4(b) shows that the regularity of heat conduction is more obvious, and the speed of conduction is apparently slow which could meet the required application requirements. Moreover, the highest temperature on the left side of the second model eventually reaches below 151°C, and the temperature in different material could be fundamentally stabilized in the controlled range.Figure 4
The distribution of the temperature in the fireproof sealing.
(a) (b)By comparing Figure4(a) with Figure 4(b), the first model is inferior to the second model in the temperature field, and the second model is also an optimized choice in terms of heat conduction. In addition, the heat conduction equation employed for the calculation of temperature at various sections of the model is in accord with the law of thermodynamics.


### 3.2. Heat Flux in the Fireproof Sealing

The heat is mainly transmitted by heat conduction for fireproof sealing in a fire scenario, and the heat flux is explained by Fourier’s law. In the one-dimensional model, the relation between heat fluxT(x) and the thermal conductivity k is as follows [19].(4)ϕq=-kdTxdxThe minus sign indicates that the heat flux moves from the higher temperature region to the lower temperature region.In the three-dimensional model, the heat flux vectors are decomposed into several components.(5)ϕq=-ki→∂T∂x+j→∂T∂y+f→∂T∂zSince the thermal field analysis in fireproof sealing is not constant, the analysis of heat flow is critical and thermal flux in the fireproof sealing is shown in Figure5. It is noted from Figure 5 that the minimum value of the heat flux is far less than the maximum value in the fireproof sealing, and the maximum value of heat flux substantially exists in the square steel, which is due to high thermal conductivity in the square steel.Figure 5
Thermal flux in the fireproof sealing.
(a) (b)Thermal flux is a vector parameter, which illustrates the trend of heat flow. To show the best heat flow, the vectors of the thermal flux in the two fireproof sealing models are demonstrated in Figure6. In Figure 6(a), on account of the combination of up and down heat, the vectors of thermal flux accumulate in the connection between square steel and aluminum silicate needle-punched blanket by the fire side, which demonstrates that the heat of bottom right aluminum silicate needle-punched blanket is dominated by the heat flux of the two models. Moreover, the maximum of heat flux vector gathers on square steel commonly in Figures 6(a) and 6(b), which is far more than the other materials. With the heat flowing, the phenomenon of the energy concentration is gradually evident; the values of thermal flux are bigger and bigger with fast speed in the two fireproof sealing models, of which the vector direction is from the high temperature region to the low temperature region.Figure 6
Vectors of the thermal flux in the fireproof sealing.
(a) (b)


### 3.3. Thermal Gradient in Fireproof Sealing

The thermal gradient is a significant thermal parameter in the two fireproof sealing models, which can analyze where and what rate the temperature changes most rapidly under environmental conditions [20].(6)GradT=limΔn→0ΔTΔn=∂T∂nHere,n is the unit vector in the normal direction, and ∂ is the derivative of temperature in the n direction.The thermal gradients are transient in the two fireproof sealing models, and the variation of distribution is demonstrated in Figure7. It is noted from Figure 7(a) that the trend of thermal gradient is not uniform and is changed by the different thermal material properties, and the variation increases rapidly at the junction of square steel and rock wool, which is due to the thermal conductivity with great gap between square and rock wool. In contrast, the minimum value of thermal gradient is on the left of Figure 7 tending toward zero, which keeps away from the fire surface. It is demonstrated from Figure 7(a) that the highest value of thermal gradient is in the aluminum silicate needle blanket and the highest factor intensity of thermal gradient is also in the aluminum silicate needle blanket. However, the highest value of thermal gradient exists in the connection of rock wool and square steel, and the thermal gradient of the second fireproof sealing model is more regular; the increase of temperature gradient shows obvious gradient distribution, as shown in Figure 7(b).Figure 7
Distribution of the thermal gradient in the fireproof sealing.
(a) (b)The vectors of thermal gradient in two fireproof sealing models are exhibited in Figure8. Contrary to thermal flux, the vector direction is from the low temperature region to the high temperature region. Nevertheless, the thermal gradient in different materials has the phenomenon of the regular flow, and the vector direction is in accord with the calculation of the thermal gradient with heat flow. However, the intersection of two heat flows results in the crossing of temperature gradient vectors, which affects the fire prevention effect of the fireproof sealing. Moreover, the vectors of thermal gradient in Figure 8(a) are compared with the vectors of thermal gradient in Figure 8(b), and the temperature gradient disturbance is more obvious in the second fireproof sealing model, which is better to prevent the heat from spreading and slow down the propagation.Figure 8
Vectors of the thermal gradient in the fireproof sealing.
(a) (b)


### 3.4. Temperature Field of Various Materials in Different Nodes

It is noted from Figure1 that the different element points are selected to analyze the temperature field of various materials. Thereby, temperature trend on selected points of various materials is shown in Figure 9. It is noted from Figure 9(a) that the temperature of the other nodes finally reached above 400°C except for the two points D1 and E1, and the F1 point quickly rose to 1100°C at 100s, which is in fire surface to supply the high thermal energy. The temperatures of the A1, G1, B1, and H1 point gradually increase and asymptotically attain the constant values after the rapid rise. However, the temperature at point C1 tends to increase linearly, which demonstrates the stable heat transfer in steel plate. On the contrary, the temperatures at the points of D1 and E rise slowly which are lower than 200°C, due to the protection of the thick protective layer at the two points of D1 and E1. It is demonstrated from Figure 9(a) that the thermal insulation performance in different materials are diverse. The ALC board and aluminum silicate needle-punched blanket are better than square steel in the thermal insulation performance.Figure 9
Temperature distribution of different material element in different nodes, (a) the first “T” shape model, (b) the second rectangle model.
(a) (b)As shown in Figure9(b), the temperature of different nodes in the second model increases slowly. Nevertheless, A2 and D2 increase at a high rate of speed with a power function growth trend. After rapid growth, the temperatures gradually tend to a fixed value, with the highest temperature reaching 1050°C. In contrast, the temperatures of B2, C2, E2, F2, G2, and H2 grow slowly with a linear growth trend. Comparing the temperature trends of A2, D2, and other points, the difference of temperature between them is to 450°C, which indicates that the fire resistance of aluminum silicate needle blanket is better, while the temperatures of C2 and F2 near the left side of the model keep below 100°C all the time.In terms of node temperature, the first model has a maximum temperature of 1050°C and a minimum temperature of 128°C; the second model has a maximum temperature of 908°C and a minimum temperature of 56°C. In contrast, the speed of heat in the first fireproof sealing model is significantly faster than the second model. By comparing the temperature of different nodes of two fireproof sealing models, the overall growth trend of the first model is faster than second model, and the final temperature of the first model is higher than the second model, which shows that the second model has better fire protection performance. Compared with E1/G1 and C2/F2, the temperature of the second model is lower than that of the first model, and the advantage of the second model is obvious. Moreover, the accelerated speed of E1 is 0.0096°C/s and the accelerated speed of G1 is 0.0619°C/s, which is far more than the accelerated speed of C2 and F2 whose values are 0.0028°C/s and 0.0078°C/s, respectively. By comparing the temperatures of different nodes, the second fireproof sealing model is superior to the first fireproof sealing model.The temperatures in various nodes have different trends because of the different energy transfer of the material. The energy formula and energy conversion formula are as follows.Energy conversation formula [21]:(7)Q=cρvΔtwhere c is the specific heat capacity; ρ is density; ν is volume; Δt is temperature change; and Q is the change in energy.


## 3.1. Temperature Field in Fireproof of Different Materials

According to heat transfer, if there is a temperature gradient inside the model, the energy will transfer from the high temperature zone to the low temperature zone, which is transferred in the form of heat conduction.Heat conduction is subject to Fourier law; that is, the heat flow density of a place formed by heat conduction is proportional to the temperature gradient of the same place at the same time in the nonuniform temperature field, and its mathematical expression in the one-dimensional model temperature field is exhibited in [16](2)qx′′=-kdTdxwhereqx′′ is thermal flux, dT/dx is the temperature gradient in the x direction, and k is thermal conductivity.When there is no internal heat source, the unsteady thermal conductivity differential equation of the three-dimensional model temperature field is as follows [17].(3)∂T∂t=α∂2T∂x2+∂2T∂y2+∂2T∂z2It is demonstrated from Figure4 that the distribution of temperature has diverse spread trend in the two fireproof sealing models with different materials. In Figures 4(a) and 4(b), since the right sides of the models are the fire surface, the two models have highest temperature point in common and finally reach to 1100°C. Simultaneously, Figure 4(a) indicates that the temperature conduction to the left is a gradient of heat growth, but the temperature trend irregularly transfers to low energy, which is due to the law of the conservation of energy and the function of two fire surfaces [18]. Ultimately, the temperature on the left side of the first model ranges from 60 to 524°C, and the temperature of rock wool is above 524°C. However, the thermal performance of superstructure is superior to substructures, which demonstrates that the model widths can affect the thermal performance of fireproof sealing. In contrast, Figure 4(b) shows that the regularity of heat conduction is more obvious, and the speed of conduction is apparently slow which could meet the required application requirements. Moreover, the highest temperature on the left side of the second model eventually reaches below 151°C, and the temperature in different material could be fundamentally stabilized in the controlled range.Figure 4
The distribution of the temperature in the fireproof sealing.
(a) (b)By comparing Figure4(a) with Figure 4(b), the first model is inferior to the second model in the temperature field, and the second model is also an optimized choice in terms of heat conduction. In addition, the heat conduction equation employed for the calculation of temperature at various sections of the model is in accord with the law of thermodynamics.


## 3.2. Heat Flux in the Fireproof Sealing

The heat is mainly transmitted by heat conduction for fireproof sealing in a fire scenario, and the heat flux is explained by Fourier’s law. In the one-dimensional model, the relation between heat fluxT(x) and the thermal conductivity k is as follows [19].(4)ϕq=-kdTxdxThe minus sign indicates that the heat flux moves from the higher temperature region to the lower temperature region.In the three-dimensional model, the heat flux vectors are decomposed into several components.(5)ϕq=-ki→∂T∂x+j→∂T∂y+f→∂T∂zSince the thermal field analysis in fireproof sealing is not constant, the analysis of heat flow is critical and thermal flux in the fireproof sealing is shown in Figure5. It is noted from Figure 5 that the minimum value of the heat flux is far less than the maximum value in the fireproof sealing, and the maximum value of heat flux substantially exists in the square steel, which is due to high thermal conductivity in the square steel.Figure 5
Thermal flux in the fireproof sealing.
(a) (b)Thermal flux is a vector parameter, which illustrates the trend of heat flow. To show the best heat flow, the vectors of the thermal flux in the two fireproof sealing models are demonstrated in Figure6. In Figure 6(a), on account of the combination of up and down heat, the vectors of thermal flux accumulate in the connection between square steel and aluminum silicate needle-punched blanket by the fire side, which demonstrates that the heat of bottom right aluminum silicate needle-punched blanket is dominated by the heat flux of the two models. Moreover, the maximum of heat flux vector gathers on square steel commonly in Figures 6(a) and 6(b), which is far more than the other materials. With the heat flowing, the phenomenon of the energy concentration is gradually evident; the values of thermal flux are bigger and bigger with fast speed in the two fireproof sealing models, of which the vector direction is from the high temperature region to the low temperature region.Figure 6
Vectors of the thermal flux in the fireproof sealing.
(a) (b)


## 3.3. Thermal Gradient in Fireproof Sealing

The thermal gradient is a significant thermal parameter in the two fireproof sealing models, which can analyze where and what rate the temperature changes most rapidly under environmental conditions [20].(6)GradT=limΔn→0ΔTΔn=∂T∂nHere,n is the unit vector in the normal direction, and ∂ is the derivative of temperature in the n direction.The thermal gradients are transient in the two fireproof sealing models, and the variation of distribution is demonstrated in Figure7. It is noted from Figure 7(a) that the trend of thermal gradient is not uniform and is changed by the different thermal material properties, and the variation increases rapidly at the junction of square steel and rock wool, which is due to the thermal conductivity with great gap between square and rock wool. In contrast, the minimum value of thermal gradient is on the left of Figure 7 tending toward zero, which keeps away from the fire surface. It is demonstrated from Figure 7(a) that the highest value of thermal gradient is in the aluminum silicate needle blanket and the highest factor intensity of thermal gradient is also in the aluminum silicate needle blanket. However, the highest value of thermal gradient exists in the connection of rock wool and square steel, and the thermal gradient of the second fireproof sealing model is more regular; the increase of temperature gradient shows obvious gradient distribution, as shown in Figure 7(b).Figure 7
Distribution of the thermal gradient in the fireproof sealing.
(a) (b)The vectors of thermal gradient in two fireproof sealing models are exhibited in Figure8. Contrary to thermal flux, the vector direction is from the low temperature region to the high temperature region. Nevertheless, the thermal gradient in different materials has the phenomenon of the regular flow, and the vector direction is in accord with the calculation of the thermal gradient with heat flow. However, the intersection of two heat flows results in the crossing of temperature gradient vectors, which affects the fire prevention effect of the fireproof sealing. Moreover, the vectors of thermal gradient in Figure 8(a) are compared with the vectors of thermal gradient in Figure 8(b), and the temperature gradient disturbance is more obvious in the second fireproof sealing model, which is better to prevent the heat from spreading and slow down the propagation.Figure 8
Vectors of the thermal gradient in the fireproof sealing.
(a) (b)


## 3.4. Temperature Field of Various Materials in Different Nodes

It is noted from Figure1 that the different element points are selected to analyze the temperature field of various materials. Thereby, temperature trend on selected points of various materials is shown in Figure 9. It is noted from Figure 9(a) that the temperature of the other nodes finally reached above 400°C except for the two points D1 and E1, and the F1 point quickly rose to 1100°C at 100s, which is in fire surface to supply the high thermal energy. The temperatures of the A1, G1, B1, and H1 point gradually increase and asymptotically attain the constant values after the rapid rise. However, the temperature at point C1 tends to increase linearly, which demonstrates the stable heat transfer in steel plate. On the contrary, the temperatures at the points of D1 and E rise slowly which are lower than 200°C, due to the protection of the thick protective layer at the two points of D1 and E1. It is demonstrated from Figure 9(a) that the thermal insulation performance in different materials are diverse. The ALC board and aluminum silicate needle-punched blanket are better than square steel in the thermal insulation performance.Figure 9
Temperature distribution of different material element in different nodes, (a) the first “T” shape model, (b) the second rectangle model.
(a) (b)As shown in Figure9(b), the temperature of different nodes in the second model increases slowly. Nevertheless, A2 and D2 increase at a high rate of speed with a power function growth trend. After rapid growth, the temperatures gradually tend to a fixed value, with the highest temperature reaching 1050°C. In contrast, the temperatures of B2, C2, E2, F2, G2, and H2 grow slowly with a linear growth trend. Comparing the temperature trends of A2, D2, and other points, the difference of temperature between them is to 450°C, which indicates that the fire resistance of aluminum silicate needle blanket is better, while the temperatures of C2 and F2 near the left side of the model keep below 100°C all the time.In terms of node temperature, the first model has a maximum temperature of 1050°C and a minimum temperature of 128°C; the second model has a maximum temperature of 908°C and a minimum temperature of 56°C. In contrast, the speed of heat in the first fireproof sealing model is significantly faster than the second model. By comparing the temperature of different nodes of two fireproof sealing models, the overall growth trend of the first model is faster than second model, and the final temperature of the first model is higher than the second model, which shows that the second model has better fire protection performance. Compared with E1/G1 and C2/F2, the temperature of the second model is lower than that of the first model, and the advantage of the second model is obvious. Moreover, the accelerated speed of E1 is 0.0096°C/s and the accelerated speed of G1 is 0.0619°C/s, which is far more than the accelerated speed of C2 and F2 whose values are 0.0028°C/s and 0.0078°C/s, respectively. By comparing the temperatures of different nodes, the second fireproof sealing model is superior to the first fireproof sealing model.The temperatures in various nodes have different trends because of the different energy transfer of the material. The energy formula and energy conversion formula are as follows.Energy conversation formula [21]:(7)Q=cρvΔtwhere c is the specific heat capacity; ρ is density; ν is volume; Δt is temperature change; and Q is the change in energy.


## 4. Conclusion

In this paper, the finite element analysis was employed to investigate the thermal analysis on two fireproof sealing models with ANSYS software under HC standard temperature-time condition. The main thermal parameters, such as temperature field, thermal flux, and thermal gradient, were analyzed and obtained. After comparing two fireproof sealing models, the main conclusions of this paper are summarized as follows:In terms of temperature field, the temperature conduction to the left is a gradient of heat growth, but the temperature trend irregularly transfers from high energy to low energy, which is due to the law of the conservation of energy and the function of two fire surfaces. Moreover, in the first model, the temperature on the left side ranges from 60 to 524°C and the temperature of rock wool is above 524°C. In contrast, the highest temperature on the left side of the second model eventually reaches below 151°C. In a word, the first model is inferior to the second model in the temperature field, and the second model is also an optimized choice in terms of heat conduction.The minimum value of the heat flux is far less than the maximum value in the fireproof sealing. Moreover, with the heat flowing, the vector direction is from the high temperature region to the low temperature region, and the phenomenon of energy concentration is gradually evident. Nevertheless, the vectors of thermal gradient in the first model are compared with the vectors of thermal gradient in the second model, and the temperature gradient disturbance is more obvious in the second fireproof sealing model, which is better to prevent the heat from spreading and slow down the propagationBy comparing the temperature of different nodes of two fireproof sealing models, the overall growth trend of the first model is faster than the second model, which shows that the second model has better fire protection performance. Compared with E1/G1 and C2/F2, the accelerated speed of E1 is 0.0096°C/s and the accelerated speed of G1 is 0.0619°C/s, which is far more than the accelerated speed of C2 and F2 whose values are 0.0028°C/s and 0.0078°C/s, respectively. The temperature of the second model is lower than that of the first model, and the advantage of the second model is obvious.In summary, the finite element analysis is firstly applied in the fireproof sealing as a reference for experiments, and this study is helpful to improve the thermodynamic performance of the fireproof sealing in the converter station. In the next research, it is still necessary to investigate the factors of stress, and the trend of stress and the different combination in different superior materials will be further studied.



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*Source: 9593626-2019-06-19.xml*