Author’s Accepted Manuscript

Numerical simulation of fluid solid coupling heat

Du Cuifeng, Bian Menglong

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PII: S2214-157X(18)30064-9
DOI: https://doi.org/10.1016/j.csite.2018.03.007
Reference: CSITE268
To appear in: Case Studies in Thermal Engineering
Received date: 9 March 2018
Revised date: 16 March 2018
Accepted date: 16 March 2018
Cite this article as: Du Cuifeng and Bian Menglong, Numerical simulation of
fluid solid coupling heat transfer in tunnel, Case Studies in Thermal Engineering,
https://doi.org/10.1016/j.csite.2018.03.007
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 Numerical simulation of fluid solid coupling heat transfer in tunnel

Du Cuifeng, Bian Menglong

School of Civil and Resource Engineering, University of Science and Technology

Beijing, Beijing 100083, China

Abstract

In order to obtain the fluid solid coupling heat transfer law of the roadway, the

coupled heat transfer between rock and air is analyzed through Fluent, Steady-State

Thermal and Static Structural module in ANSYS. The heat flux and thermal strain of

rock and the influence of air which under different wind speed and inlet temperature are

obtained. The heat flux in the rock is approximately uniformly distributed in the circular

ring shape, and the distribution of the heat flux from high to low is as follows: the

roadway wall > rock mass > air. The heat flux of the rock near the wall is greater than

that in the far side wall. The maximum is located at the wall, and the value is 160 W·m-2.

The thermal strain of rock is greatly influenced by local heat source, and the maximum

value is 5.1×10-5m·m-1. Compared with the loader, the hydrothermal water which has

greater influence on the temperature of rock and wind can be regarded as the focus on

the control of heat damage.

Keywords: tunnel; fluid solid coupling; heat transfer; temperature; numerical simulation

1. Introduction

As mining moves deeper, more and more heat problems are faced.[1] Heat damage is

generated by the surrounding rock, mechanical and electrical equipment, hot water or

other heat sources. [2-3] Obtaining heat transfer is the premise of heat treatment, a

1
variety of heat sources will affect each other in ventilation tunnels. [4-5] The rocks

surrounded the roadway are continuously cooled because of heat generating equipment

and hot water, and continuous humidity changes occur in the air, so the heat transfer in

the ventilation tunnel is a complex fluid-solid-coupled heat transfer problem.[6-7]

Fluid-solid coupled heat transfer problem is mainly studied through CFD. There are

many cases in this area, and a variety of CFD software including Multiflux, COMSOL,

LS-DYNA are applied to the heat transfer in mines.[8-10] The heat damage in mines is

mainly caused by hot rock masses. Von et al. simulated the heat flow of rocks under

different conditions by numerical methods.[11] By measuring the rock thermal

conductivity and geothermal gradients, a heat transfer simulation model was developed

to determine the amount of heat needed to heat the intake air in winter. [12] When the

mine rock mass is subjected to high thermal stress, the thermal damage caused by inter-

particle cracks and intra-particle cracks in the rock mass increases, which will affect the

stability of the rock mass. [13-14] Zhang et al. establish differential equations of heat

transfer and seepage to describe the distribution of temperature and seepage fields in

fractured rock masses. Combining the boundary conditions and parameters, a numerical

solution is obtained by numerical solution. [15] Sidney et al. study the geometric

parameters of heat exchange in a complex broken rock combination. [16] The presence

of hot gushing water in the mines causes damage to the walls of the roadway and

increases heat damage. Through the numerical simulation of water inrush from confined

formations in the strata, the change of water pressure and permeability in the formation

can be analyzed to effectively predict the potential water inrush. [17-18] Wang and You

study the influence of multi-parameters such as ventilation parameters, cracks and hot

water in rock mass on thermal conductivity of rock mass from the perspective of fluid-

2
solid coupling heat transfer. [19-20] Gui studied the effect of groundwater flow on the

temperature distribution of karst collapse columns. A method has been proposed to

improve thermal convection by increasing the percolation velocity so that the heat

transfer in porous media is improved. [21] In addition, various physical field coupling

conditions including heat transfer-permeation coupling, seepage-stress coupling,

variable density flow - transport coupling are also numerically simulated in the mine.

[22-24] Simulation studies have shown that underground mine structures can be suitable

systems for heating because of their thermal stability.[25-26] Through the coupled heat

transfer simulation, the change of mine water temperature is relatively small, and the

flooded mine can be used as heat pump water source even in low temperature.[27-28]

More research cases are also related to tunnel heat transfer in cold region, human

thermal comfort, and seasonal climate effects. [29-33]

Under the influence of mixing of rock mass, roadway, vehicle and hot water heat

source, there are few research cases on the distribution of thermal physical field of mine

roadway and rock mass. In this paper, the steady-state heat transfer model of ventilation

tunnel and the surrounding rock is considered, the mathematical model of steady-state

heat transfer of ventilation tunnel is established. Fluent, Steady-State Thermal, and

Static Structural modules in ANSYS are used for thermal-fluid-structure coupled heat

transfer analysis, and the temperature field distribution under different conditions was

obtained.

2. Steady thermal model in ventilation roadway

As the ventilation goes on, the radius of the heating circle of the roadway increases

gradually. When the surrounding rock is homogeneous isotropic, the thermal

conductivity and the surface heat transfer coefficient of the rock are only a function of

3
temperature, and the variation range is small, which can be considered as the fixed value.

After experiencing ventilation for a long enough time, the thermo-physics field of the

surrounding rock heat ring and ventilation tunnel is stable under the same ventilation

parameters. The steady-state thermal conductivity model can solve the problem of fluid-

solid coupling thermal conductivity of the ventilation tunnel. Figure 1 shows the

schematic diagram of ventilation tunnel heat transfer, the dark part of the figure is the

rock heat circle, and the white part is the ventilation tunnel.

Fig. 1. Schematic diagram of heat transfer in ventilation tunnel

In the Figure 1, r1 is the characteristic length; r2 is the radius of the heating circle; t0

is the original rock temperature; tw is the rock wall temperature; tf is the air temperature;

qy and qh are the heat flux. Under the condition of steady heat conduction, the heat

transfer form in the heat transfer circle of the rock mass is heat conduction, and the heat

transfer form of the roadway wall to the air is thermal convection. The heat flux from

the original rock to the rock wall is equal to that produced from the rock wall to the air,

the heat flux density can be expressed as:

4
 (t0  tw )
qy  （1）
r2  r1

qh  h(tw  tf ) （2）

Where: qy and qh are the heat flux density (W·m-2); λ is the thermal conductivity of

rock (W·m-1·K-1); t0, tw and tf are the temperature (℃); r2 and r1 is the radius (m); h is

the convection heat transfer coefficient, W/(m2·K).

The heat flow in the ventilation tunnel is:

Q  hS(tw  tf )  Q J （3）

Where: S is the area of heat transfer (m2); QJ is the heat production from the local

heat source (W).

The formula for h [34] is:

 
h  Nu   0.023  Re0.8  Prn （4）
D D

Where: λ—the thermal conductivity of air, 0.025 W/(M·K); D—the feature length, m;

Nu—Nusselt number; Pr—Prandtl number, 0.7; n—the number is 0.4 when the air is

heated, and the number is 0.3 when the air is cooled.

Under steady-state heat conduction there is a relation: qy=qh, which gives the value of

tw by solving equations (1) and (2), and tw can be substituted into equation (3):

 ht (r  r1 )  t0 
Q  hS  f 2  tf   Q J （5）
 h(r2  r1 )   

Navier-Stokes was used to establish the flow control equations in the numerical

simulation of fluid flow. The standard k-ε two-equation model was used to calculate the

flow characteristics. The fluid is a continuous medium model, and both speed and

5
density are continuous and differentiable functions of spatial coordinates and time. The

continuity equation is a partial differential equation describing the transmission

behavior of conserved quantities. The continuous equation is as follows:


(ui )  0
xi （6）

The momentum theorem states that the magnitude of the external force acting on an

object is equal to the rate of change of momentum of the object in the direction of force.

The momentum equation is as follows：

 p   u j ui 
(uiu j )    (  t )(  )
xi xi xi  x i x j  （7）

The K equation is as follows：

    k 
(ui k )  (  )  G k  
xi xi   k xi  （8）

The ε equation is as follows：

    k  C  1 2
(ui )  (   )  G  C 
 xi 
k 2
xi xi  k k （9）

and：

k2
t  C  
 （10）

u j u j ui
G k  t (  )
xi xi x j （11）

Where: xi and xj are the coordinates of name; ρ is the air density (kg·m-3); P is the

turbulence effective pressure; ui and uj are the fluid velocity (m·s-1); μ is the laminar

viscosity coefficient (Pa·s); μt is the turbulent viscosity coefficient (Pa·s); k is the

6
turbulent kinetic energy (m2·s-2); ε is the turbulent dissipation (m2·s-3); Gk is the

influence coefficient (kg·s-3·m-1); Cε1, Cε2, Cp, Cε, Ck are 1.43, 1.91, 0.09, 1.20, 1,

respectively.

3. Roadway model and parameter setting

3.1 Experimental site and environment

A ventilation tunnel located at Xiadian Gold Mine in Shandong Province of China is

chosen as the experimental subject, and the tunnel is 692 m deep. The cross-sectional

area of the tunnel is 8.34 m2, and the perimeter is 11 m; the experimental lane length is

100 m. The original rock temperature is 31 ℃; the radius of heating circle is 10-20m;

the wind speed is 1 m·s-1; the inlet air temperature is 25 ℃; and the air relative humidity

is 100%. There are a loader whose power is 92KW in the tunnel. Some hydrothermal

water whose area has a length of about 20 m and a depth of about 0.2 m exist in the

middle of the roadway.

The interval between each test point is 10 m, and the point is located at the center of

the roadway. The ventilation multi-parameter detector for each measuring point is used

to monitor parameters such as temperature, wind speed and humidity of section.

3.2 Geometric model and grid

According to the measured tunnel size data, a simplified geometric model is

established by ANSYS as shown in Figure 2.

7
 Fig. 2. Geometric model

In Figure 2, the part (a) is the overall model; the part (b) is the roadway model; the

part (c) is the loader model, and the area designated by the dotted line is the heat

producing area; the part (d) is the hydrothermal model. The loader is located 20-30 m

away from the inlet and the hydrothermal water is located 40-60 m away from the inlet.

Since the tunnel heating circle is 10-20 m, the rock mass within 20 m around the tunnel

is set as the research area.

The grid generation plays a vital role in any analysis. The grid independence test is

executed to obtain the most suitable mesh faces size for particular geometry. In this

paper, the number of grids in the fluid region is tested at 635899, 1040328, 1459987,

2095887, 2568485, respectively. When the number of grids reaches 1040328, the

parameters of the fluid region are basically unchanged. Considering the accuracy and

time of the calculation, the number of grids in the fluid area is set to 1040328. In

addition, the number of grid about the solid region is 58497.

3.3 Parameter setting

In the experiment, Fluent, Steady-State Thermal and Static Structural modules are

8
respectively coupled. After the solution of Fluent is completed, the results of the flow

field are respectively imported into Steady-State Thermal and Static Structural modules

to calculate the temperature field in the solid region and the thermal strain. The Fluent

parameter is set as table 1. The temperature of each surface of the heat generating zone

(Fig. 2. c) is set to 40 ℃. Since the hydrothermal water comes from the interior of the

rock mass and its initial temperature is close to the original rock temperature, so the

surface temperature in Figure 2 (d) is set to 30 ℃.

Table 1 Parameter setting table in Fluent

Parameter Setting information

Solver Pressure-based solver

Time Steady state

Gravity set -9.81 m·s-2

Turbulence model Standard k-ε model

Material Custom granite material properties

Entrance boundary type Velocity-inlet boundary

Entrance speed 0.5 ~ 5 m·s-1

Merry entrance temperature 10 ~ 25 ℃

Turbulence intensity 2.45 % ~ 3.3 %

Hydraulic diameter 3m

Exit boundary type Pressure-outlet boundary

Iteration steps 1000

4. Result and discussion

4.1 Fluid-solid coupling temperature field analysis

After reaching the state of steady heat conduction through ventilation, the

temperature field of rock mass and air is basically stable, but the heat transfer in

9
different areas is different due to the influence of local heat source. The heat flux is the

heat transfer per unit time and unit cross-sectional area, which reflects the strength of

the heat transfer capacity. When the inlet air temperature is 25 ℃ and the wind speed is

1 m·s-1, the heat flux isosurface after solution is shown in Figure 3.

Fig. 3. Isosurface of heat flux

As can be seen from the upper left part of Figure 3, the heat flux in the rock mass is

distributed approximately in a uniform and continuous state. It can be also seen from the

upper right part of the figure that the heat flux in the rock mass is distributed in an

approximately circular ring shape and the heat flux is low at 35 W·m-2 and below. The

heat flux near the wall of the roadway is higher than other locations, with the value

above 71 W·m-2 and the highest value is 160 W·m-2. The isosurface distribution near the

loader is complicated, and the values of heat flux are basically distributed below 35

W·m-2. In summary, the heat flux density near the wall of the roadway is more than

twice that of other areas. As the value of heat flux reflects the strength of heat transfer,

the heat transfer capacity at the wall of the roadway should be weakened in order to

control the heat damage. For example, one of the methods is to install the heat

10
insulation material on the wall of the roadway.

The heat flux distribution of ventilation tunnel is shown in Figure 4.

Fig. 4. Distribution of heat flux in tunnel

Compared with Figure 3 and Figure 4, it can be seen that the overall heat flux values

in the ventilation tunnel are very low, and the heat flux values are mostly distributed

between 0 and 17 W·m-2. In the presence of the loaders and hydrothermal water, the

value of the heat flux is above 17 W·m-2.

Comparing the heat flux density between the rock mass and the tunnel, it can be seen

that the heat flux density in most areas is relatively low in steady-state heat transfer

conditions, and the heat flux density distribution is descending order: wall > rock mass>

air. In addition, the heat flux of the near-wall rock mass is greater than the heat flux

density of the far-wall rock mass, and some higher heat flux values exist at the local

heat source position.

Since the temperature of the rock mass decreases with the continuous ventilation, the

micro-shape or size change of the rock mass is affected by the temperature stress, which

11
is the thermal strain. During the long time ventilation in the roadway, the temperature

stress always exists in the rock mass. Long-term thermal stress will lead to thermal

fatigue of the rock, and even lead to rock cracks and damage. The thermal strain of rock

mass is shown in Figure 5 under the conditions of an inlet air temperature of 25 ℃ and

a wind speed of 1 m·s-1.

Fig. 5. Thermal strain equivalent diagram

It can be seen from the upper left part of Figure 5 that the thermal strain of the rock

mass is at a relatively low value as a whole, and the values are between 4.46×10-5 and

4.57×10-5 m/m. From the upper right part of the figure, it can be seen that the thermal

strain values in the rock mass near the roadway are between 4.57×10-5 and 4.68×10-5

m/m. The thermal strain distribution is affected by the loader and hot water. There is a

significant change about thermal strain in the rock mass surrounding the tunnel and the

area is a continuous thin wall. The maximum value of thermal strain exists on the wall

surface of 5.1×10-5 m/m near the hydrothermal water, and the lowest value is 4.1×10-5

m/m near the loader. The hydrothermal water in the roadway has a natural heat

preservation function, which makes the nearby wall suffer from hot water and cold air at

12
the same time, so that the maximum value of thermal strain is generated. The loader

blocks the wind, which reduced the wind profile and increased the wind speed. The heat

transfer is enhanced so that the wall temperature decreases, and the minimum value of

thermal strain exists on this location.

On the whole, the larger value of thermal strain is on the roadway wall, which is

similar to the heat flux density distribution. This shows that rock mass near the tunnel

wall is not only a strong heat transfer area, but also a thermal damage prone area. The

heat flux and thermal strain near the hydrothermal water are both high, which shows

that the heat transfer capacity in this area is strong and the thermal damage is easy to

occur. From the diagram of the heat flux and the thermal strain, the influence of the

loader in the roadway on the thermal environment is much less than that of the

hydrothermal water, so the hydrothermal water can be used as the focus of thermal

pollution prevention and control. When the inlet air temperature or the wind speed

change, the values of heat flux and thermal strain will change, but the distribution will

have not changed much.

4.2 Effect of different air temperature on the flow field

The temperature distribution of the airflow in the ventilation tunnel is shown in

Figure 6 under different air inlet temperatures.

13
 Fig. 6. Temperature distribution of wind flow at different inlet temperatures

The loader is located 20 to 30 meters from the entrance of the roadway in the figure,

and the hydrothermal water is in the position of 40 to 60 meters. It can be seen from

Figure 6 that the temperature of the airflow remains basically constant at a distance of 0

to 20 m. The temperature of the wind is rapidly increased after a rapid decrease at a

distance of 20 to 40m. At the distance of 40 to 60 m, the airflow temperature affected by

hydrothermal water is low. The temperature is slowly rising at a distance of 60 to 100 m.

Comparing the temperature difference of the different inlet air temperature, the higher

the air temperature, the closer to the temperature of the original rock or the heat source,

the smoother the curve of the air temperature. When the inlet air temperatures are 10 ℃,

15 ℃ , 20 ℃ and 25 ℃ respectively, the airflow at the exit of the roadway is

respectively 14.3 ℃, 18.3 ℃, 22.2 ℃ and 26.2 ℃. The lower the airflow temperature,

the greater the temperature curve changes. From the wind temperature curve in the

figure approximately equidistant longitudinal arrangement, it can be known that

changing the temperature of inlet air can greatly change the temperature field of the

overall airflow, and the heat damage can be effectively prevented by lowering the inlet

14
air temperature.

4.3 Effect of different wind speed on the flow field

The temperature distribution of the air in the roadway under different wind speeds is

shown in Figure 7.

Fig. 7. Temperature distribution of wind flow under different wind speeds

The temperature distribution of the airflow in Figure 7 at different distances is similar

to that in Figure 6 as a whole. When the wind temperature is 25 ℃ and the wind speeds

are 0.5 m/s, 1 m/s, 2 m/s, 3 m/s, 4 m/s and 5 m/s respectively, the outlet airflow

temperatures of the roadway are 26.9 ℃, 26.2 ℃, 25.8 ℃, 25.6 ℃, 25.5 ℃, 25.4 ℃

respectively, the maximum difference in the outlet air temperatures is 1.5 ℃. Compared

the curves in the figure, with the wind speed increases, the vertical difference between

the curves gradually decreases, it can be seen that the way of increasing wind speed

cooling is very limited.

Comparing Figure 6 and Figure 7, the change of air temperature in the hydrothermal

section when the inlet temperature changes is much larger than that when the inlet air

15
velocity changes. Therefore, by reducing the inlet air temperature can get better cooling

effect. The presence of hydrofacies in the roadway has a significant impact on the

temperature field of wind flow, and should be discharged in time.

4.4 Simulation experiment verification

When the air temperature is 25 ℃ and the wind speed is 1m/s, the simulation data

and the measured data are arranged as shown in Figure 8.

Fig. 8. Comparison of simulated and experimental temperature data

The temperature values at the points of the experiment (sorted from the inlet) are

25 ℃, 26.5 ℃, 26 ℃, 26.2℃, 26.5 ℃, 25.8 ℃, 26.5 ℃, 26.5 ℃, 26.8 ℃, 26.9 ℃,

27 ℃, and the simulated temperature values corresponding to the measuring points are

26 ℃, 26.4 ℃, 26.2 ℃, 26 ℃, 26.7 ℃, 25.2 ℃, 26.9 ℃, 26.4 ℃, 26.5 ℃, 26.7 ℃,

26.2 ℃. In addition to the starting point of the temperature difference is 1 ℃ and the

outlet temperature difference is 0.8 ℃, the other points’ difference is between 0.1 ~

0.6 ℃. The experimental data is expressed as fe, the simulated experimental data is

expressed as fs, and the relative error ei is calculated as：

16
 fe  fs
ei   100%
fs （12）

The relative errors are 3.85%, 3.79%, 0.76%, 0.77%, 0.75%, 2.38%, 1.49%, 0.38%,

1.13%, 0.75%, and 3.05%, respectively. All the relative errors are less than 4%. The

difference between the simulated and experimental values are small, so the errors are

within acceptable range.

5. Conclusion

A detailed analysis of thermal fluid solid coupling case is presented in the present

study. The heat transfer analysis of Fluent, Steady-State Thermal and Static Structural

module in ANSYS is conducted, and the interaction relationship between the loader,

hydrothermal water and rock mass in ventilation roadway is analyzed.

According to the simulation results, there is a rule in the rock mass around a

ventilated tunnel. The heat flux is approximately uniformly distributed in a ring shape,

and its values from high to low rankings: wall> rock mass> air. The heat flux of the

rock near the wall is greater than that in the far side wall, and the value of heat flux on

the tunnel wall is twice than other locations.

The thermal strain in the rock mass is a very small change in physical size, which

reflects the possibility of thermal fatigue. From the simulation results, the thermal strain

has a high value in the tunnel wall position, but it is more affected by the local heat

source. The highest value is 5.1×10-5m/m at the wall of the tunnel near the hydrothermal

water and the lowest value is at the wall of the roadway near the loader with a value of

4.1×10-5m/m.

The influence of local heat sources which include the hydrothermal water and loader,

can not be ignored on the environment. The hydrothermal water have a significant

17
impact on the temperature field of rock mass and wind flow, and the influence on the

thermal environment is much greater than that of the loader. Therefore, the

hydrothermal water in tunnels can be the focus of heat damage prevention.

Finally, compared with the increase of wind speed, reducing the inlet temperature has

a better cooling effect to prevent heat damage.

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