SELECTION OF FANS FOR PARALLEL OPERATION IN DIFFERENT SHAFTS

A. F. KARATAEV

(Presented by the scientific conference of the Mining Operations Faculty).

The development of the simplest and most graphic method for selecting fans for a complex mine ventilation network and for analyzing their operation is of great practical and theoretical importance.

This question acquires exceptional importance under the conditions of Kuzbass, with the ever wider introduction of the flank scheme of mine ventilation, which in all cases, except for the use of the forcing method of ventilation, leads to the joint parallel operation of several fans in different shafts.

Despite the existence of a theoretical treatment of the question of parallel operation of fans [1; 2], up to the present time there has been no simple method for selecting and analyzing the operation of fans connected in parallel. The study of the parallel operation of several fans and their selection by an analytical method is a difficult problem [1,1].

The graphical method of studying fans in their parallel operation [3,335] is not difficult if no more than two fans operate in parallel.

K. S. Borisenko [4,25] recommends that, when selecting fans, the characteristics of the complex ventilation branches of the mine ventilation scheme and the characteristics of the fans be plotted. The point of intersection of these characteristics will determine the required ventilation regime of the fan. The construction of the characteristics of complex ventilation branches, however, is a very complicated and labor-consuming process.

In the present work the task is posed, on the basis of a study of the characteristics of complex ventilation branches of mines and the characteristics of fans, to develop the simplest graphical method for selecting fans for their parallel operation in different shafts.

Study of the equations of the characteristics of complex ventilation branches

In the practice of mine ventilation, two types of equations of the characteristics of ventilation branches are possible:

\[ y = Ax^2, \tag{1} \]

\[ y = Ax^2 + Bx + C. \tag{2} \]

The characteristic of a ventilation branch having an equation of the form (1) passes through the origin of coordinates and intersects the characteristic of the fan, regardless of the form of the fan characteristic, at one point \(A\) (Fig. 1). If point \(A\) lies on the working portion of the fan characteristic, then

This simultaneously indicates that a high efficiency of the fan installation is ensured, as well as the stability of the mine ventilation regime. This proposition is valid only for single or series operation of fans (the pressure–exhaust method of ventilation).

In the parallel operation of fans in different shafts, the characteristics of the ventilation branches are constructed according to equation (2). This equation shows that, in this case, the characteristics of the ventilation branches do not pass through the origin, but intersect the ordinate axis at a certain distance \(A'\) (Fig. 1).

The point \((A')\) at which the characteristic of the ventilation branch intersects the ordinate axis is determined by the magnitude of the constant term \(C\) in equation (2). For \(x = 0\), equation (2) takes the form \(y = C\).

Consequently, depending on the form of the characteristic of the ventilation branch and on the magnitude of the constant term \(C\), as well as on the form of the fan characteristic, in their parallel operation it is possible for the characteristic of the ventilation branch to intersect the fan characteristic at several points (Fig. 1), which indicates the possibility of the occurrence of an unstable mine ventilation regime.

Fig. 1. Characteristic of an axial fan.

To derive the formula for determining the magnitude of the constant term \(C\) in the equation of the characteristic of a complex ventilation branch, we investigate two principal mine-ventilation layouts and fan arrangements (Figs. 2 and 3), to which any computational layouts of mine ventilation and fan arrangements may be reduced.

For the first layout (Fig. 2), according to the indicated directions of air movement, for the ventilation branch \(A—D\) we have:

\[ Q_0 = Q_1 + Q_2 + Q_3 - Q_4 = Q_1 + x_1, \tag{3} \]

where

\[ x_1 = Q_2 + Q_3 - Q_4. \]

The pressure difference between points \(A—D\)

\[ h_{A-D} = h_0 + h_1 = R_0 Q_0^2 + R_1 Q_1^2 = \]

\[ = R_0 (Q_1 + x_1)^2 + R_1 Q_1^2 = R_0 Q_1^2 + 2R_0 Q_1 x_1 + R_0 x_1^2 + R_1 Q_1^2 \]

or

\[ h_{A-D} = (R_0 + R_1) Q_1^2 + 2R_0 Q_1 x_1 + R_0 x_1^2. \tag{4} \]

Expression (4) is the equation of the characteristic of the ventilation branch \(A—D\) (Fig. 2). Taking \(Q_1\) as the variable quantity, and all the remaining terms as constants, we obtain the equation of a parabola of the form

\[ y = Ax^2 + Bx + C, \]

where \(C_{A-D} = R_0 x_1^2\), or, on the basis of equality (3),

\[ C_{A-D} = R_0 (Q_0 - Q_1)^2. \tag{5} \]

For the ventilation branch \(A—E\) (Fig. 2) we have:

\[ Q_0 = Q_1 + Q_2 + Q_3 - Q_4 = Q_2 + x_2, \tag{6} \]

where

\[ x_2 = Q_1 + Q_3 - Q_4; \]

\[ Q_{01}=Q_2+Q_3-Q_4=Q_2+x_3, \tag{7} \]

where

\[ x_3=Q_3-Q_4, \]

\[ Q_{02}=Q_2+Q_3. \tag{8} \]

The pressure difference between points \(A—E\)

\[ h_{A-E}=h_0+h_{01}+h_{02}+h_2 =R_0Q_0^2+R_{01}Q_{01}^2+R_{02}Q_{02}^2+R_2Q_2^2= \]

\[ =R_0(Q_2+x_2)^2+R_{01}(Q_2+x_3)^2+R_{02}(Q_2+Q_3)^2+R_2Q_2^2 \quad \text{or} \]

\[ h_{A-E}=(R_0+R_{01}+R_{02}+R_2)Q_2^2 +(2R_0x_2+2R_{01}x_3+2R_{02}Q_3)Q_2 +R_0x_2^2+R_{01}x_3^2+R_{02}Q_3^2. \tag{9} \]

Fig. 2. Schematic diagram of mine ventilation and fan arrangement.

Expression (9) is also the equation of the characteristic of the ventilation branch \(A—E\) (Fig. 2). Taking \(Q_2\) as the variable quantity, and all the remaining terms as constants, we obtain the equation of a parabola of the form \(y=Ax^2+Bx+C\), where

\[ C_{A-E}=R_0x_2^2+R_{01}x_3^2+R_{02}Q_3^2 \]

or, on the basis of equalities (6), (7), (8),

\[ C_{A-E}=R_0(Q_0-Q_2)^2+R_{01}(Q_{01}-Q_2)^2+R_{02}(Q_{02}-Q_2)^2. \tag{10} \]

Fig. 3. Schematic diagram of mine ventilation and fan arrangement.

The formula for the constant term of the equation of the ventilation branch \(A—K\) (Fig. 2) is analogous to formula (10), but in it \(Q_3\) stands instead of \(Q_2\), i.e.

\[ C_{A-K}=R_0(Q_0-Q_3)^2+R_{01}(Q_{01}-Q_3)^2+R_{02}(Q_{02}-Q_3)^2. \tag{11} \]

For the second scheme (Fig. 3), according to the indicated directions of air movement, for the ventilation branch \(A—f\) we have:

\[ Q_0=Q_1+Q_2+Q_3. \tag{12} \]

\[ Q_{01}=Q_2+x_5. \tag{13} \]

According to (Fig. 3),

\[ x_5=Q_1+Q_3-Q_n, \]

\[ Q_{02}=Q_2+x_6. \tag{14} \]

According to (Fig. 3), \(x_6 = Q_{02} - Q_3\),

\[ Q_{03}=Q_2+Q_3, \tag{15} \]

\[ \begin{aligned} h_{A-f}={}&h_0+h_{01}+h_{02}+h_{03}+h_2 =R_0Q_0^2+R_{01}Q_{01}^2 \\ &+R_{02}Q_{02}^2+R_{03}Q_{03}^2+R_2Q_2^2 =R_0(Q_1+Q_2+Q_3)^2+ \\ &+R_{01}(Q_2+x_5)^2+R_{02}(Q_3+x_6)^2+R_{03}(Q_2+Q_3)^2+R_2Q_2^2 \quad \text{or} \end{aligned} \]

\[ \begin{aligned} h_{A-f}={}&(R_0+R_{01}+R_{02}+R_{03}+R_2)Q_2^2 +(2R_0Q_1+2R_0Q_3+2R_0x_5+ \\ &+2R_{02}x_6+2R_{03}Q_3)Q_2 +R_0Q_1^2+R_0Q_3^2+2R_0Q_1Q_3+ \\ &+R_{01}x_5^2+R_{02}x_6^2+R_{03}Q_3^2 . \end{aligned} \tag{16} \]

Expression (16) is the equation of the characteristic of the ventilation branch \(A-f\) (Fig. 3). Taking \(Q_2\) as the variable quantity, and all the remaining terms as constants, we obtain an equation of a parabola of the form

\[ y=Ax^2+Bx+C,\quad \text{where}\quad C_{A-f}=R_0(Q_1+Q_3)^2+R_{01}x_5^2+ \]

\[ +R_{02}x_6^2+R_{03}Q_3^2 \]

or, on the basis of equalities (12), (13), (14), (15),

\[ C_{A-f}=R_0(Q_0-Q_2)^2+R_{01}(Q_{01}-Q_2)^2+R_{02}(Q_{02}-Q_2)^2+R_{03}(Q_{03}-Q_2)^2 . \tag{17} \]

In an analogous manner one may derive the formula for the magnitude of the constant term for the characteristic of any ventilation branch (Fig. 3).

The formulas for the constant term (5), (10), (11), (17) in the equation of the parabolas, for different calculation schemes of ventilation, arrangements of fans, and their number (Figs. 2 and 3), make it possible to assert that the magnitude of the constant term in the equation (parabola) of any ventilation branch of the mine network is equal to the sum of the products of the resistances of the common sections of the ventilation branches by the square of the difference between the total quantity of air passing through the given common section of the ventilation branch and the quantity of air supplied by the fan of the given branch, i.e.,

\[ C=R_{01}(Q_{01}-Q)^2+R_{02}(Q_{02}-Q)^2+\ldots+R_{0n}(Q_{0n}-Q)^2; \tag{18} \]

where

\[ \begin{aligned} C&\text{—the constant term of the equation (parabola) of the ventilation branch under consideration;}\\ R_{01},\,R_{02},\,R_{0n}&\text{—the aerodynamic resistance of the common sections of the calculation}\\ &\text{\quad scheme of mine ventilation and fan arrangement;}\\ Q_{01},\,Q_{02},\,Q_{0n}&\text{—the quantities of air passing through the common sections of the}\\ &\text{\quad calculation scheme of mine ventilation and fan arrangement;}\\ Q&\text{—the quantity of air supplied by the fan to the ventilation branch under consideration.} \end{aligned} \]

Formula (18) makes it possible to draw the following conclusions:

1. The larger the constant term \(C\), the higher the point \(A'\) (Fig. 1) will be located, and, consequently, the lower the probability of maintaining a stable ventilation regime in the branch.

2. The greater the resistance of the common sections, the more probable the occurrence of an unstable ventilation regime in the ventilation branch.

3. The smaller the quantity of air supplied by the fan to the ventilation branch under consideration in comparison with the total quantity

of air passing through the common sections, the larger the value of the free term \(C\); the lower the probability of maintaining a stable ventilation regime.

1. The more fans are switched on for parallel operation in different shafts, the lower the possibility of maintaining a stable ventilation regime.

Investigation of Fan Characteristics

The characteristic of a fan is the graphically expressed dependence of \(h,\ \eta\) on \(Q\). The \(\eta - Q\) curves make it possible, having specified the limiting efficiency of the fan, to establish the limits of its economical operation. Three types of individual characteristics of mine fans are distinguished:

1) a characteristic having a maximum and a minimum, possessed mainly by axial fans and by some centrifugal fans (Fig. 1);

2) a characteristic having only a maximum, possessed by most centrifugal fans (Fig. 4);

3) a characteristic having neither a maximum nor a minimum, possessed by axial fans with a small blade-setting angle, up to \(20^\circ\), and by some centrifugal fans (Fig. 5) [2,52].

Fig. 4. Characteristic of a centrifugal fan.

Fig. 5. Characteristic of an axial fan with a small blade-setting angle.

The selection of any type of fan is based on two conditions:

1) ensuring economical operation of the fan at the specified parameters;

2) ensuring a stable ventilation regime.

The first condition in selecting fans is achieved when the points of intersection of the characteristics of the mine ventilation branches with the fan characteristics lie on the operating portions of the fan characteristics corresponding to a fan efficiency of not less than 0.5 \((a, б, a', б', a'', б''—Figs. 1, 4, 5)\).

The second condition is achieved by the fact that the characteristic of the mine ventilation branch intersects the fan characteristic at a single point.

Consequently, the stability of the mine ventilation regime depends on the type of fan characteristic, the characteristic of the ventilation branch, and the economy of fan operation on the location of the point of intersection of the fan and ventilation-branch characteristics on the fan characteristic.

The Essence of the Graphical Method for Selecting Fans for Parallel Operation in Different Shafts

The investigation carried out above of the characteristics of complex mine ventilation networks and of the characteristics of mine fans makes it possible to propose the following procedure for selecting fans for parallel operation in different shafts.

1. On tracing paper, on the scale of the available individual fan characteristics, coordinate axes \(h — Q\) are drawn. On these axes a point \(C\) is marked with coordinates \(h, Q\), which characterize the required ventilation regime. These coordinates are obtained on the basis of a calculation of the quantity of air \(Q\) required for delivery into the ventilation branch under consideration, and of the pressure \(h\) required to move the calculated quantity of air \(Q\).

2. On the ordinate axis, the point \(C'\) of intersection of the characteristic of the ventilation branch with the ordinate axis is marked. The value \(C'\) is determined from formula (18).

3. The points \(C\) and \(C'\) are joined by a straight line, which serves for selecting and analyzing the operation of the fan.

4. The tracing paper thus obtained is superimposed on the individual characteristic of the fan (Fig. 4). If the point \(C\) lies on the working part of the fan characteristic, and the straight line \(C — C'\) intersects the fan characteristic only at the point \(C\), this indicates that stable and economical operation of the fan is ensured. Fans for the other ventilation branches of the complex mine network are selected in the same way.

Fig. 6. Schematic diagram of mine ventilation and fan arrangement.

The angle of inclination of the straight line \(C — C'\) to the horizontal characterizes the change in the degree of stability of fan operation. The sharper the angle of inclination of the straight line \(C — C'\) to the horizontal, the lower the stability of fan operation, and vice versa.

By taking the straight line \(C — C'\) as the characteristic of the ventilation branch, we thereby increase the margin of stability (Fig. 1).

An example of the application of the proposed method for selecting fans for their parallel operation in different shafts. The initial data for selecting fans for parallel operation in different shafts are:

1. Compilation of the schematic diagram of mine ventilation and fan arrangement (Fig. 6), indicating the resistances \(R\) of the sections of the ventilation network, the quantity of air \(Q\) passing through them, and their depressions \(h\).

The basic diagram of mine ventilation and the arrangement of fans (Fig. 6) represents ventilation jets with the maximum depression in the direction toward each of the fans.

1. Determination of the design parameters of the fan installations (Fig. 6), i.e., the coordinates of the straight lines \(D—D'\); \(E—E'\); \(K—K'\); \(f—f'\); \(t—t'\). The coordinates of the points \(D, E, K, f, t\) are determined from the basic diagram of ventilation and fan arrangement, and the coordinates of the points \(D', E', K', f', t'\)—by formula (18), in accordance with the basic diagram of mine ventilation and fan arrangement (Fig. 6).

The straight line \(D—D'\) for selecting fan 1 has the following coordinates \(D(Q_D, h_D)\), \(D'(Q_{D'}, h_{D'})\),

where

\[ Q_D = Q_1 = 15\ \text{m}^3/\text{s}\quad (\text{Fig. 6}); \]

\[ h_D = h_0 + h_{01} + h_1 = 50 + 30 + 90 = 170\ \text{mm water gauge}. \]

\[ Q_{D'} = 0; \]

\[ \begin{aligned} h_{D'} &= C_{A-D} = R_0 (Q_0 - Q_1)^2 + R_{01}(Q_{01} - Q_1)^2 = \\ &= 0.00296(130 - 15)^2 + 0.0245(35 - 15)^2 = \\ &= 39.2 + 9.8 = 49\ \text{mm water gauge}. \end{aligned} \]

In the same way we calculate the coordinates of the straight lines for selecting the other fans and enter the results in Table 1.

1. Plotting the straight lines \(D—D'\); \(E—E'\); \(K—K'\); \(f—f'\); \(t—t'\) on tracing paper. At the scale of the available individual characteristics, we plot the coordinate axes \(h—Q\) on the tracing paper, and on these axes, using the coordinates given in Table 1, construct the straight lines \(D—D'\); \(E—E'\); \(K—K'\); \(f—f'\); \(t—t'\) (Fig. 7).

Fig. 7. Characteristic of a two-stage axial fan of series B, \(d = 1.2\), \(n = 1500\) rpm.

By superimposing the resulting tracing paper (Fig. 7) on the individual characteristics of the fans, we select the fans.

For the ventilation branch \(A—D\), with \(Q = 15\ \text{m}^3/\text{s}\) and \(h = 170\ \text{mm water gauge}\), a two-stage fan of series \(B\) with \(D = 1.2\ \text{m}\), at \(n = 1500\) rpm and blade setting angle \(\Theta = 18^\circ\), \(\eta = 0.6\), is suitable [5, 115—119].

For the ventilation branch \(A—E\), an axial two-stage fan of series \(B\) with \(D = 1.2\ \text{m}\), at \(n = 1500\) rpm, with blade setting angle \(\Theta = 27^\circ\), \(\eta = 0.57\) is suitable (Fig. 7).

For the ventilation branch \(A—K\), the same fan is suitable, but with blade setting angle \(\Theta = 38^\circ\), \(\eta = 0.59\), and for branch \(A—f\) with blade setting angle \(\Theta = 47^\circ\).

For the ventilation branch \(A—t\), an axial single-stage fan of series \(B\) with \(D = 1.8\ \text{m}\) at \(n = 1000\) rpm, with blade setting angle \(\Theta = 28^\circ\), \(\eta = 0.61\), is suitable.

Conclusions

The investigation of the characteristics of the ventilation branches and the characteristics of the fans makes it possible to establish:

1. The recommended graphical method for selecting fans for their parallel operation in different shafts provides: simplicity and clarity in the selection of fans, accuracy quite sufficient for practical purposes, and accessibility to any technical worker engaged in mine ventilation.

Table 1

Coordinates of the lines for selecting fans

Therefore, the proposed simplified graphical method for selecting fans is of practical importance.

1. The selection of fans for their parallel operation in different shafts is analogous to the selection of fans operating singly; however, with the characteristic of a fan having only a maximum (Fig. 4), it becomes necessary to check the stability of the ventilation regime in the ventilation branch by the expression \(C<h\) at \(Q=0\), and, with the characteristic of a fan having both a maximum and a minimum (Figs. 1, 4), by the formula

\[ \frac{h_{A-B}-C_{A-B}}{Q_{A-B}} > \operatorname{tg}\alpha, \tag{19} \]

where \(h_{A-B}\) is the depression of ventilation branch \(A-B\);

\(Q_{A-B}\) is the quantity of air supplied by the fan to ventilation branch \(A-B\);

\(C_{A-B}\) is the free term of the equation of the characteristic of ventilation branch \(A-B\), determined by formula (18);

\(\operatorname{tg}\alpha\) is the tangent of the angle of inclination, to the horizontal, of the straight line \(C-C'\) (Fig. 4) used in selecting the fan, when it intersects the fan characteristic at more than one point. Therefore, in the given case it is preferable to apply the simplified graphical method of fan selection described above.

1. The selection of axial fans with a blade-setting angle of up to \(20^\circ\), for their parallel operation in different shafts, is analogous to the selection of fans for single operation.

2. Parallel operation of fans in different shafts may be eliminated by using a forced–suction method, whereby the air will move along the common paths due to the depression of the forcing fan, and subsequently due to the depression of the suction fans. In this case, series operation of the fans is obtained.

3. The magnitude of the free term in the equation of the characteristics of ventilation branches served by centrifugal fans is an indicator of the stability of their operation: at \(C<h\) and \(Q=0\) the operating regime of the fans will be stable if they operate on the right-hand part of the characteristic, while at \(C>h\) and \(Q=0\) it will be unstable.

REFERENCES

1. Pak V. S. Ventilation of Mines by Fans Connected in Parallel. Ugletekhizdat, 1947.

2. Voronin V. N. Mine Fan Installations. Ugletekhizdat, 1953.

3. Skochinskii A. A., Komarov V. B. Mine Ventilation. Ugletekhizdat, 1951.

4. Geier V. G. and Borisenko K. S. Operation of Mine Fan Installations. GONTI, 1939.

5. Khadzhikov R. N. Mine Fan, Pump, and Pneumatic Installations. Ugletekhizdat, 1951.