Chapter 8

SIMULATION OF THE HEAT AND MOISTURE TRANSFER

BETWEEN AIRWAY WALLS AND MINE AIR AT A HEADING FACE

WITH FORCING AUXILIARY VENTILATION SYSTEM

Jianliang Gao Dept. of Earth Resources Engineering	Kenichi Uchino Masahiro Inoue
Kyushu University Fukuoka, Japan	Dept. of Earth Resources Engineering Kyushu University Fukuoka, Japan

ABSTRACT

It is of paramount importance that thermal environment is effectively and properly controlled in mines which suffer from heat problem. Up to now numerous studies have been made to control the climatic conditions in underground mines, but most of the researches are made on a single roadway with through airflow. However those on climatic conditions in developing drivages are very few. In the present study Computational Fluid Dynamics has been introduced to analyze the simultaneous transfer of heat and mass in this problem. The 3-dimension
turbulent flow model was used to simulate the transfer of heat and moisture between rock surface and the airflow at a heading face with auxiliary forcing ventilation system. Based on the results of simulation, the distributions of temperature and moisture content at a heading face with forcing auxiliary ventilation were obtained, and the distributions of the local heat transfer coefficient at roadway surface were also investigated. The present study provides an important basis for establishing a proper method for the prediction of the thermal environment conditions in locally ventilated working places.

KEYWORDS

Workplace, working face, heat-transfer, mass-transfer, heat-transfer coefficient

INTRODUCTION

Complicated processes of heat exchange and water evaporation lead to changes in the temperature and humidity of the ventilation airflow during the driving of headings. In the case when virgin rock temperature is high, the increase in air temperature and humidity is significant, causing a deterioration of climatic conditions in the working place. It is of paramount importance in these places that the thermal environment is effectively and properly controlled. There is therefore a great need to have reliable prediction techniques in order to support decisions that will have a significant influence on the level of production cost.

The study on the prediction of heat flow and the consequent psychrometric conditions in mine workings has been undertaken by a number of researchers for a wide range of mining conditions (Yanagimoto, et al., 1974, 1980; Uchino, et al., 1982; Inoue, et al., 1986; McPherson, 1993). Many techniques have been developed over the years to predict the heat flow and the resultant psychrometric conditions in mine workings. But most of the researches are concentrated on a single roadway with through airflow. The researches on the simulation of the thermal conditions of airflow flowing in duct and in developing drivages with auxiliary ventilation were very few.

Because the pattern of the airflow in a workplace with auxiliary ventilation is very different from that in a roadway with through airflow, the method of calculation of the heat and moisture transfer between the surrounding rock and the airflow would be considerably different. In the working face with auxiliary ventilation the velocity of air near the wall surface changes greatly with the location, and the heat transfer coefficients at different parts of the wall surface can not be treated as constant. Therefore, in order to determine thermal environmental conditions it is essential to know the distributions of heat-transfer coefficient on airway surface so that the heat and mass flow into the ventilation air can be calculated accurately.

Some researches had been done on the prediction of the thermal environment of the working face with auxiliary ventilation (Shimada, et al., 1990; Fiala, et al., 1991; Ross, et al., 1997; Kertikov, 1997), but their studies were concentrated on the temperature and humidity calculation in the section of the roadway where the duct is set, and there are few researches on the simulation of thermal environment of the airflow in a workplace with auxiliary ventilation. There are also some commercial software packages that can be used to solve the airflow, temperature field in the working face, but they can only be used to solve the problem at steady state because the wall temperature is usually set at a given value. The effect of evaporation of water on the airway surface has not been coded into the packages. Also the distribution of heat transfer coefficient on the surface of the roadway of the working face, which is an important factor in the determination of environmental conditions in a direct or indirect manner, has not been studied yet.

The aim of the work presented here is to investigate the distribution of air velocity, distribution of airflow temperature and moisture content, and to determine how the local heat-transfer coefficient distributes on the surface of the airway, as well as how it changes with airflow rate in a working face with forcing auxiliary ventilation.

MATHEMATICAL MODEL

Governing Equations

Many equations have been proposed for modeling and computation of turbulent flow, which can be classified as: zero-equation models, one-equation models, two-equation models, Reynolds stress models and direct numerical simulation models. High-Reynolds-number
model is one of the most widely used “two-equation models”. The
model introduces the equations of turbulent energy
and dissipation rate
in the formulation, and had been very successful in computing the turbulent flows under various conditions.

In high-Reynolds-number
model the governing equations for the turbulent airflow in the working face with auxiliary ventilation include: mass conservation or continuity equation, three Navier-Stocks equations for velocity u, v, and w, respectively, and two equations for turbulence energy
and dissipation rate
, which combined with the energy equation governing the temperature, and mass transfer equation for the transportation of water-vapor, provide sufficient information for the determination of the interested variables.

All the dependent variables of interest here obey a generalized conservation principle. If the dependent variable is denoted by
, the general differential equation is:

(1)

where
is the diffusion coefficient,
the density of the fluid, t time and S the source term representing volumetric rate of generation, respectively.

The quantity
and S are specific to a particular meaning of
, which is listed in table 1.

Table 1. values of
and S for different

		S
u
v
w
k
T		0
D		0

Where

P = pressure

C_pa = thermal capacity of air at constant pressure

= kinematic viscosity

= turbulent kinematic viscosity,

= turbulent dynamic viscosity

(1.1)

B_x, B_y B_z, = components of body force per unit volume

= density of airflow

Pr = Prandtl number of air

Pr_t = turbulent Prandtl number of air

Sc = Schmidt number

Sc_t = turbulent Schmidt number

G_k = rate of generation of turbulence energy

(1.2)

C_D, C₁, C₂,
,
= experimental constant, the values are listed in table 2.

Table 2. Experimental constant

CD			C1	C2	Prt	Sct
0.09	1.0	1.3	1.44	1.92	0.9	1.0

Boundary Conditions

On the cross section of duct outlet where the air is discharged out of the forcing auxiliary ventilation duct, u=u_in, v=0, w=0, T=constant, D=constant. Therefore,

(1.3)

(1.4)

where R is the radius of the duct.

On the roof, floor, side-wall and the head of the working face, u=0, v=0, w=0,
=0,
=0, wetness fraction
=constant.

Initial Conditions

For transient simulation the initial rock temperature is set at a given value T₀, the initial airflow temperature and moisture content are supposed to be equal to those of discharged air at the outlet of the duct, respectively.

CALCULATION METHOD

Algorithm

The fundamental principles can be expressed in terms of a set of coupled partial differential equations known as the governing equations of fluid flow. CFD is a popular technique for determining a numerical solution for these equations. This is typically done by dividing the flow region into a large number of cells that form a series of grids. In each of the cells, the governing equations are simplified and a solution process produces values of pressure, velocity, turbulence-kinetic-energy and kinematic rate of dissipation, temperature and moisture content at the centers of these cells. It is thus possible to obtain a continuous solution throughout the domain by interpolating between these cell values.

Control Volume Method, in which the SIMPLE algorithm is applied, is used to derive the required discretization equations from above governing equations. The basic idea of the method is that the calculation domain is divided into a number of nonoverlapping control volumes such that there is one control volume surrounding each grid point. The fundamental physical principles are applied to the control volume, and to the fluid crossing the control surface. Therefore, instead of looking at the whole flow field at once, with the control volume model we limit our attention to just the fluid flow equations that we directly obtain by applying the fundamental physical principles to a finite volume (figure 1) in integral form. The integral forms of the governing equations can be manipulated to obtain partial differential equations indirectly. The differential equation is integrated over each control volume. The result is the discretization equations containing the values of
for a group of control volumes in the form of equation (2).

(2)

where

a_P = center point coefficient

a_E, a_W, a_N, a_S, a_T, a_B = coefficient related to east, west, north, south, top and bottom neighbour, respectively

Figure 1. Control volume

The combination of TDMA (Tri Diagonal-Matrix Algorithm) and Gauss-Seidel method is formed to solve the discretization equations line by line. Under-relaxation device is adopted to avoid divergence in the iterative solution of nonlinear equations.

Treatment Near the Wall

Unlike that in a solid, the transfer of heat and mass in a fluid can occur through conduction as well as convection through the movement of the fluid. The critical elements in the process are the boundary layer and the distributions of the temperature and moisture content in the airflow. Once the heat and mass have penetrated into the flow the energy and mass transport occurs mainly through the convection by moving media. Therefore the buffer region, or boundary layer, plays a very critical role in heat- and mass-transfer process. The condition and property of this layer determine the rate at which the heat and mass are transferred.

Diffusion coefficient on wall
: The high-Reynolds-number model fails near the wall where the Reynolds number is low. One of the successful modifications due to this effect is the low-Reynolds-number model that is applicable in the vicinity of a solid wall. When the low-Reynolds-number model is used, large number of grid points with small interval are needed near the wall. This leads to the increase of the total number of the grid points, therefore calculation will be time-consuming. “The law of wall” is often applied to solve the problem. In other words, the logarithmic velocity distribution is valid for all Reynolds numbers for which turbulent flow near a wall exists .

From the logarithmic velocity distribution for a near wall flow we can set up simple formulae to calculate the diffusion coefficient on the wall
which is an important parameter to calculate the heat-transfer coefficient.

Sensible heat flux from wall surface into airflow : From
the heat transfer coefficient at a point on airway surface can be calculated. Suppose that in figure 1 the bottom of the control volume is the wall of the airway, the heat transfer coefficient
at point b on the surface of roadway is:

(3)

Therefore, the sensible heat flux from the wall surface at the point b into the ventilation air can be known as:

(4)

where

q_s = sensible heat flux per unit area from wall at point b

T_wall = rock surface temperature at point b

T_p = air temperature at point p

Latent heat flux from wall surface into airflow: The mass transfer flux from the wall, which is covered by water into the airflow, is presented by equation (5)

(5 )

where

m_s = mass transfer flux per unit area from point b into airflow, i.e. the mass of vaporized water from per unit area of wall surface in a second

m_wall = moisture content at point b of the wall surface

m_p = moisture content at point p

= mass-transfer coefficient at point b

The mass-transfer coefficient,
, can be calculated from the heat-transfer coefficient,
, by use of Lewis' formula.

(6)

If the wall surface is completely covered or coated with liquid water, it is reasonable to assume that, immediately adjacent to the liquid surface, the space will be saturated. The moisture content is equal to the saturated vapor concentration at surface temperature T_wall.

Usually the wall surface is not completely covered or coated with liquid water. For the partially wet rock surfaces wetness fraction,
, is defined as that fraction of the total surface area that is covered or coated with liquid water. The mass-transfer flux per unit area from partially wet rock surface into the airflow is:

(7)

The latent heat flux from per unit area of wet surface q_L is

(8)

where L_v = latent heat of water evaporation

Sensible heat transfer will take place on both the dry and wet surfaces while latent heat forms at wet surface only. The total strata heat flows can be calculated by adding the latent heat and sensible heat together.

SIMULATION RESULTS

Based on the above theory and algorithm, a program has been developed to simulate the heat- and mass-transfer process at a working face with forcing auxiliary ventilation system in Fortran code. The air velocity in the working face, heat- and mass-transfer process between roadway surface and airflow, heat- and mass-transfer process in the airflow, and the heat conduction process in the surrounding rock of the working face can be calculated with the program.

Because the heat and mass in the airflow are transported mainly through the convection by moving air, the magnitude and distribution of air velocity play a decisive role in the process of heat- and mass-transfer. In order to test the reliability of the coded algorithm, the distribution of the velocity in the heading face with forcing auxiliary ventilation is obtained by simulation, and compared with the experimental data measured in a model roadway (Tomita, 1997) at first. It has shown that the simulation results are in close agreement with the experimental data. It is thus concluded the CFD method and coded program can be used to simulate the heat- and mass-transfer process at the working face with forcing auxiliary ventilation.

Temperature and Humidity Distribution

A square roadway with a width of 4.0 m is taken as an example to show the results of the simulation. The outlet of duct is also supposed to be square with a width of 0.7 m. The air is discharged at a velocity of 15.0 m/s from outlet which is 10.0 m away from the working face. The temperature and humidity of delivered air from the outlet of the duct are 25°C and 10 g/(kg dry air), respectively. The virgin rock temperature is 50°C. The roadway surface is supposed to be smooth.

In general, the temperature, water vapor and velocity fields are coupled and interact strongly. Thus the velocity field affects the distributions of temperature and moisture content, and vice versa. In many situations, when the velocity is high and temperature differences are small in the space, the temperature is influenced by the velocity field, and the velocity field is mildly affected by the temperature differences. The velocity is also influenced by the variation in density of air which is created by the non-uniform distributions of the temperature and the moisture content.

The influence of temperature on the velocity field has been studied firstly in steady state with the roadway surface temperatures being set at 50°C and 25°C respectively. Because an auxiliary fan is normally used in the working face, the heat- and mass-transfer is a process of forced convection, the influence of air temperature on the distribution of velocity is negligible. The following study is based on the calculated results of heat- and mass-transfer in the presence of a given flow field, i.e. the velocity components and the density of the airflow are not dependent on the variations of the temperature and moisture content.

The distributions of temperature and moisture content on the cross section that is six meters away from the outlet of the duct, and on the longitudinal vertical section across the axis of the roadway are shown in figure 2 and figure 3, respectively.

As it is conceived from the similarity between the governing equations for heat-transfer and mass-transfer, the distributions of air temperature are similar to those of water vapor. Both the air temperature and moisture content on the vertical section along the axis of the roadway are lowest (figure 2B and figure 3B). The temperature of air and the moisture content in the airflow increase as the air flows toward the head of the working face and in the reversed airflow, as well as it dissipates toward the side-walls. Generally, the air temperature and moisture content are lower in the upper level of the cross section than in the lower ones.

Distribution and Variation of Local Heat-transfer Coefficient

In a straight round pipe with fully developed turbulent through airflow, the heat-transfer coefficients on the inner surface of the pipe are uniform theoretically. In a straight roadway which is not round, the heat-transfer coefficient varies with the location. Specially in the corner the heat-transfer coefficient is lower than in other part, because the airflow velocity there is lower. In the case of through airflow the average heat-transfer coefficient may be used to simulate the heat- and mass-transfer process. In the working face with auxiliary ventilation, however, the local heat-transfer coefficient would vary in a wide range because the air velocities near the wall surface are position-dependent and vary widely. Considering the young age of developing roadway, it is not suitable to employ the average heat transfer coefficient for simulating the heat- and mass-transfer. It is thus necessary to pay attention to the distributions of the local heat-transfer coefficient on the roadway surface.

Figure 2. Distribution of the air temperature

Figure 3. Distribution of the moisture content

The local heat-transfer coefficient
　is defined by the following equation:

(9)

where

q_s = sensible heat flux calculated from formulae (4)

T_wall = surface temperature of roadway

T_ave = average air temperature in the working face

(10)

where

T_in = the temperature of the air discharged from

the outlet of the duct

T_out = average air temperature in the roadway

at the cross section x=0

The local heat-transfer is predominantly dependent on the distribution of velocity of the airflow which depends on the shape of the roadway, the size and position of the duct outlet and the airflow rate. When the geometrical conditions are given, it only depends on the airflow rate. Many studies have been carried out on the correlation between heat-transfer coefficient and Reynolds number in a straight pipe with through airflow. The relationship can be expressed by following equation:

(11)

where

= heat-transfer coefficient in a smooth straight

pipe with through airflow

R_e = Reynolds number

= thermal conductivity of air

D = hydraulic equivalent diameter of the pipe

The results of the simulation with CFD elucidate the relationship between heat-transfer coefficient and characteristics of airflow and geometry of the roadway. Firstly, the ratio of local heat-transfer coefficient
to
　does not change with the airflow rates in the working face. The distributions of the dimensionless heat-transfer coefficient
on the roof, floor, side-wall, and head are shown in figure 4.

The local heat-transfer coefficient greatly depends on the magnitude of the airflow velocity near and parallel to the roadway surface. It can be seen from the figures that the local heat-transfer coefficient varies with location in a wide range. On the roof near the outlet of the duct where the airflow is discharged from the air duct, the local heat-transfer coefficient is the highest. As the air flows toward the working face and dissipates toward the two side-walls, the velocity decreases, the local heat-transfer coefficient decreases. On the roof and the floor, the local heat-transfer coefficients are higher near the center line and decreases towards the walls. On the head of the working face, the highest local heat-transfer coefficients appear above the roadway axis. The average value of
at roof, floor, side-wall, and head are 9.7, 5.0, 3.5 and 6.7, respectively. The overall average dimensionless heat-transfer coefficient
is 5.6. It means that the overall heat-transfer coefficient in the working face with forcing auxiliary ventilation is 5.6 times of that in an airway with same amount of through airflow.

Figure 4. Distribution of dimensionless local

heat-transfer coefficient

SUMMARY

In order to simulate the heat- and mass-transfer in a working face with auxiliary ventilation, CFD method was employed and the governing equations were solved by the use of SIMPLE algorithm. The results of the calculation of airflow have shown a close agreement with the experimental data, and it is concluded that the model can be used to simulate the heat- and mass-transfer process in the working face with forcing auxiliary ventilation.

The results are summarized as follows:

1. Fundamental airflow patterns in a working face with forcing auxiliary ventilation were elucidated.

2. Distributions of air temperature and moisture content in a working face were revealed theoretically in detail for the first time, providing practically important information for the proper control of the thermal environment in the face.

(3) Local heat-transfer coefficients at the wall of the roadway were first obtained theoretically and correlated with the characteristics of airflow and the geometry of the roadway.

The present study in this project is a preliminary step towards the improved prediction of the thermal environment at a working face with forcing auxiliary ventilation. But the results furnish the basis of next program that is used to simulate the thermal environment in a developing roadway. The improved program is to be able to deal with the air leakage through the ventilation duct, the heat- and mass-transfer between the airflow in the developing roadway with surrounding stratum rock, and the heat exchange between the air stream flowing in airway and in the auxiliary ventilation duct with the advancing of the heading face.

REFERENCES

Fiala, J., and Kohut, J., 1991, “Airflow Temperature and Humidity Changes in Auxiliary Ventilated Airways,” Proceedings, 5th U.S. Mine Vent. Symp., Y. J. Wang, ed., SME, Littleton, CO, pp273-279

Kertikov, V., 1997, “Air Temperature and Humidity in Dead-end Headings with Auxiliary Ventilation,” Proceedings, 6th Int. Mine Vent. Cong., Rama V. Ramani, ed., SMME, Littleton, CO, pp269-275

Ross, A.J., Tuck, M. A. Stokes, M.R. and Lowndes, I.S., 1997, “Computer Simulation of Climatic Conditions in Rapid Development Drivages,” Proceedings, 6th Int. Mine Vent. Cong., Rama V. Ramani, ed., SMME, Littleton, CO, pp283-288

Inoue, M. and Uchino, K., 1986, “New Practical Method for Calculation of Air Temperature and Humidity along Wet Roadway,” Journal of the Mining and Metallurgical Institute of Japan, Vol.102, N0. 6, pp.353-357

Shimada, S. and Ohmura, S., 1990, “Experimental Study on Cooling of Heading Face by Local Ventilation,” Journal of the Mining and Materials Processing Institute of Japan, Vol.106, No.12, pp.725-729

Uchino, K, Inoue, M., and Yanagimoto T., 1982, “Theoretical Calculation of Temperature of Ventilation Air with Varying Air Temperature at the Entrance,” Journal of the Mining and Metallurgical Institute of Japan,, Vol.98, No.5, pp.1123-1128

Yanagimoto, T. and Uchino, K., 1974, “Applications of Finite Difference Method to Calculation of Temperature of Mine Air,” Journal of the Mining and Metallurgical Institute of Japan, Vol.90, No.9, pp.583-597

Yanagimoto, T. and Uchino, K., 1980, “Problems of Temperature Distribution and Heat Flow in Rocks around Roadways,” Journal of the Mining and Metallurgical Institute of Japan, Vol.96, No.2,
pp.71-77

McPherson, M. J., 1993, Subsurface Ventilation and Environmental Engineering. Chapman & Hall, London

Tomita, S., 1997, “Study on the airflow in a driving face with auxiliary ventilation,” master dissertation, Kyushu University

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54

PROCEEDINGS OF THE 7^TH INTERNATIONAL MINE VENTILATION CONGRESS

55

SIMULATION OF THE HEAT AND MOISTURE TRANSFER

P

Δz

Δx

Δy

e

s

n

b

t

w

W

E

N

S

T

B

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