EXPERIMENTAL STUDY OF FRICTION AND WINDAGE LOSSES IN A TURBINE STAGE

(On the Calculation and Design of a Pneumatic Reversible Turbine)

S. I. SHUBOVICH

Introduction

The use of a pneumatic turbine as a motor for mining machines¹ and, in particular, as a motor for drilling-and-cutting machines has confronted designers with a whole series of new problems.

Alongside questions connected with increasing efficiency under overload conditions, the question of reversing a pneumatic-turbine motor while running also assumes special importance. Reversal of a pneumatic-turbine motor may be achieved by using an additional reverse stage in the turbine, in the same way as is done in marine turbine installations. However, there is concern that, at the comparatively small turbine powers (10–20 hp), the reverse stage may lead to a sharp reduction in the efficiency of the turbine motor because of the additional losses caused by the motion of the reverse blading ring in air, with the blade edges forward.

At present, taking into account the novelty of pneumatic turbine motors, it is hardly possible to find experimental data on the basis of which one could judge the magnitude of the additional losses and the degree of reduction in the efficiency of a low-power pneumatic-turbine motor in the presence of a reverse stage. The proposed experimental study had as its aim the obtaining of such experimental material, which could serve as a basis for resolving the question of the economic advisability of using an additional reverse stage for reversing a pneumatic mine motor.

The present study was carried out in the internal-combustion-engine laboratory of the Tomsk Polytechnic Institute named after S. M. Kirov, in cooperation with the chief designer’s department of the Tomsk Electromechanical Plant named after V. V. Vakhrushev, which provided a DTR-20 pneumatic turbine motor for the tests and assisted in carrying out the work.

Experimental Setup

The present investigation amounted to the experimental determination of friction and windage losses in a low-power turbine motor for the normal direction of motion of the blade ring—with the blade edges backward—and for reverse motion—with the blade edges forward.

As the method for determining the losses sought, the method chosen was spin-up of the pneumatic-turbine engine from an external energy source. For these purposes the DTR-20 engine, whose arrangement is clear from the drawing (Fig. 1), was mounted together with a balanced direct-current electric motor on a special test stand. The layout of the stand is shown in Fig. 2. The basic parameters of the DTR-20 engine are given below. The assembly clearances between the disk and the turbine casing are given in Fig. 3.

Fig. 1. Pneumatic-turbine engine DTR-20.

Basic parameters of the DTR-20 pneumatic-turbine engine

Type of turbine—single-stage, impulse.
Nominal effective power \(N_e = 20\) hp.
Nominal turbine speed \(n = 7500\) rpm.
Working air pressure \(p = 4\) ati.
Gearbox transmission ratio:
    for right-hand rotation of the drive shaft \(\quad i_{\text{right}} = 5.08,\)
    for left-hand rotation of the drive shaft \(\quad i_{\text{left}} = 4.3.\)
Number of working turbine nozzles \(\quad Z_c = 5\)
Degree of partial admission at \(Z_c = 5\) \(\quad \varepsilon = 0.227.\)
Mean diameter of the blade ring \(\quad D = 285\) mm.
Blade height \(\quad L = 13\) mm.
Blade width \(\quad B = 15\) mm.
Blade pitch \(\quad t = 11.2\) mm.
Angles of the inlet and outlet edges \(\quad \beta_{1l} = \beta_2 = 18^\circ.\)

Since the objective of the work undertaken was to determine the friction and windage losses not only in the form of their sum, but also each loss separately, in order to be able to separate them, tests were provided for spinning up the DTR-20 engine with an unbladed disk and with no disk at all. For these tests a disk without blades was prepared in advance (with the groove on the rim soldered over), as well as a spacer bushing corresponding to the length of the disk hub.

Fig. 2. Schematic diagram of the test stand. 1—balancing electric motor; 2—DTR-20 engine; 3—electric tachometer; 4—thermometer for measuring the oil temperature; 5—opening for connecting the turbine chamber with the atmosphere.

In the drawing: “Place for connecting the U-shaped manometer”; “Lithium TT-22”; dimension \(\ell = 0.591\ \mathrm{m}\).

Fig. 3. Schematic section of the turbine chamber. 1—bladed disk; 2—disk without blades.

In the drawing: “nut”; “DTR-20 part”; dimensions \(\varnothing 285\), \(\varnothing 268\), \(\varnothing 305\), \(2\), \(1\), \(5\), \(5\), \(4.5\), \(4.5\), \(11.5\), \(10.5\).

To measure the pressure in the turbine chamber and to connect it with the atmosphere, special holes were drilled in the turbine casing at the points indicated in the diagram (Fig. 2).

To observe the oil temperature in the gearbox of the pneumatic engine, a mercury thermometer was mounted in the gearbox housing.

The balancing electric motor was connected to the direct-current mains according to the usual circuit, as can be seen in Fig. 2. The presence of two rheostats, in the armature circuit and in the excitation circuit, made it possible to vary the number of revolutions of the motor shaft within the range from 600 to 1750 rpm, which corresponded to a variation in the number of revolutions of the turbine disk within the range 2580–7520 rpm at a gear ratio \(i_{\text{left}} = 4.3\), and 3050–8900 rpm at a gear ratio \(i_{\text{right}} = 5.08\).

Connected to the shaft of the electric motor, through a step-up gearbox with a gear ratio \(i = 2\), was the sensor of a TE-22 electric tachometer, whose indicator was brought out to the control panel. The presence of a permanently mounted tachometer made it possible, during the tests, to maintain constant observation of the speed regime of the installation and, at the required time, to take readings of the number of revolutions.

Preliminary and main tests

In order to eliminate possible errors in the measurements, in addition to calibrating and checking the instruments, trial tests were carried out, during which the sensitivity of the balancing device of the electric motor was determined, the influence of individual factors on the measurement results was clarified, and the procedure for subsequent tests was refined.

The sensitivity of the balancing device was evaluated by the magnitude of the friction moment in the balancing supports with the motor operating without load. According to special tests, the friction moment was \(6 \cdot 10^{-3}\ \text{kg m}\), and therefore the errors in measuring the torque, which, as will be seen below, varied within the range from 0.135 to \(1.2\ \text{kg m}\), were within the limits from

\[ \delta_{\max} = \pm \frac{6 \cdot 10^{-3} \cdot 100}{0.135} = \pm 4.5\% \]

to

\[ \delta_{\min} = \pm \frac{6 \cdot 10^{-3} \cdot 100}{1.2} = \pm 0.5\%. \]

The comparatively low accuracy in measuring the moment at small loads could not, however, have a decisive influence on the results of the investigation, since tests with small loads were in most cases carried out for the purpose of determining secondary quantities having little effect on the final result.

To take into account the power expended on driving the electric-motor fan and the friction power in the front balancing suspension (see the schematic section in Fig. 2), the “friction and ventilation” characteristic of the electric motor as a function of speed was taken (Fig. 4), which made it possible, when calculating the results, to introduce the corresponding correction to the measured power.

Preliminary tests established that the results of measuring the power expended on rotating the pneumatic-turbine engine were substantially affected by the viscosity of the oil in the gearbox. In order to eliminate the errors associated with this, all subsequent tests were carried out with one and the same grade of oil (avtol 6) and at practically unchanged oil temperatures.

In the course of preliminary tests it became clear that it was more convenient to change the direction of rotation of the turbine disk not by reversing the electric motor, but by shifting the sliding gear of the pneumatic-turbine-engine reduction gear. This method of changing the direction of rotation was accompanied by a change in the gear ratio (from \(i_{\text{right}}=5.08\) to \(i_{\text{left}}=4.3\)) and by certain changes in the magnitude of the friction losses on the surfaces of the gear teeth, owing to the different degree to which they had been run in.

The change in gear ratio was easily taken into account by reducing the results of the power measurements to the turbine shaft. As for changes in the friction losses on the gear teeth, these changes were taken into account in the calculations, with the exception of one case, which will be discussed below.

As is known, ventilation losses are proportional to the density of the medium in which the turbine disk rotates; therefore, in carrying out the main experiments it was necessary, as far as possible, to create conditions in the turbine chamber under which the density of the medium would remain constant.

Fig. 4. Dependence of the friction and ventilation losses of the balancing electric motor on the speed of the drive shaft.

For this purpose, an opening 8 mm in diameter was drilled in the turbine casing (Fig. 2) to connect the chamber with the atmosphere. To determine the actual pressures in the chamber when this opening was present, pressures were measured by means of a U-shaped manometer with the turbine disk rotating. The point at which the manometer was connected is indicated in the diagram (Fig. 2). The measurements showed that the pressure difference between the chamber (in the region of the rim) and the atmosphere, at a disk speed of \(n=7500\) rpm, does not exceed 30 mm water column; therefore, in the subsequent experiments the air density in the chamber was conventionally taken to be equal to the density of the surrounding air.

The main experiments to determine the power expended in spinning the pneumatic turbine engine were carried out in three stages.

In the first stage, the power expended in spinning the pneumatic turbine engine with the bladed disk was determined. In this stage, five series of experiments were carried out under the following different conditions:

1a. Motion of the blades with their edges forward; the turbine inlet and outlet openings open.

1b. Motion of the blades with their edges forward; the inlet opening closed, the outlet open.

1c. Motion of the blades with their edges forward; the inlet opening open, the outlet closed,

1г. Motion of the blades with their edges forward; the inlet and outlet openings are closed.

1. Motion of the blades with their edges backward; the inlet opening is closed, the outlet is open.

The carrying out of four series of experiments with the blades moving edge-forward was due to the fact that closing the openings mentioned above led to a reduction in the power expended in motoring the engine. With the normal direction of blade motion (edges backward), closing the openings caused such small changes in the power consumed that they practically lay within the limits of insensitivity of the balancing device. In this connection, with the blades moving edge-backward, only one series of experiments was carried out, with the outlet opening open and the inlet opening closed.

Fig. 5. Dependence of the power expended in motoring the DTR-20 engine with a bladed disk on the rotational speed of the turbine shaft.

In the second stage of the experiments, the power expended in motoring the pneumatic-turbine engine with an unbladed disk was determined. Closing the inlet and outlet openings had no effect whatsoever on the magnitude of the power expended, and therefore the experiments were carried out with the openings open in two series: with right-hand and left-hand rotation of the disk. Determination of the power expended in motoring the engine with an unbladed di-

with the disk for the two directions of rotation made it possible, in calculating the windage losses, to eliminate the error caused by the different degree of running-in of the tooth surfaces of the reduction-gear wheels, as was already mentioned above.

The experiments of the third stage had as their purpose the determination of losses in the reduction gear. The experiments were carried out in the usual manner with the turbine disk removed.

In the plot: \(N\), hp; \(n\), rpm. Legend: \(o\)—right-hand rotation, \(i_{\text{right}} = 5.08\); \(x\)—left-hand rotation, \(i_{\text{left}} = 4.3\).

Fig. 6. Dependence of the power expended in motoring the DTR-20 engine with an unbladed disk on the rotational speed of the turbine shaft.

Since in this case the load on the driven shaft of the reduction gear was zero, the power expended in motoring could be regarded as the power of hydraulic losses, that is, as the power expended mainly on friction of the reduction-gear wheels in oil. In the course of conducting the latter experiments, special attention was paid to observations of the constancy of the temperature and oil level in the reduction gear, in order, as far as possible, to eliminate the influence of these factors on the magnitude of the losses being sought.

In the plot: \(N_{\text{hyd}}\), hp; \(n\), rpm. Legend: \(o\)—right-hand rotation, \(i_{\text{right}} = 5.08\); \(x\)—left-hand rotation, \(i_{\text{left}} = 4.3\).

Fig. 7. Dependence of the power expended in motoring the DTR-20 engine with the turbine disk removed on the rotational speed of the turbine shaft.

The results of the experiments of all the series listed are given in processed form in Figs. 5, 6, and 7.

Windage Losses of the Bladed Wheel

The windage losses of the turbine bladed wheel can be found as the difference between the power expended in spinning the pneumatic-turbine motor with a bladed disk and the power expended in spinning the same motor with a disk without blades,

\[ N_\ell = N - N_1 \ \text{hp}, \tag{1} \]

where
\(N_\ell\) is the power of the windage losses, hp,
\(N\) is the power expended in spinning the DTR-20 with a bladed disk, hp,
\(N_1\) is the power expended in spinning the DTR-20 with a disk without blades, hp,

but

\[ N = N_\ell + N_d + N_{\mathrm{red}} \ \text{hp}, \tag{2} \]

where
\(N_d\) is the power expended in disk friction, hp,
\(N_{\mathrm{red}}\) is the power expended on losses in the reduction gear, hp.

In turn, the power expended on losses in the reduction gear may be represented as the sum of the hydraulic losses of the reduction gear and the friction losses on the loaded surfaces of the gear teeth:

\[ N_{\mathrm{red}} = N_{\mathrm{hyd}} + N_{\mathrm{fr}} \ \text{hp}, \tag{3} \]

where
\(N_{\mathrm{hyd}}\) denotes hydraulic losses, hp,
\(N_{\mathrm{fr}}\) denotes friction losses on the surfaces of the gear teeth, hp.

Friction losses vary in proportion to the load, and therefore they can be expressed through the power transmitted by the reduction gear. According to the experiments of M. M. Pischelauri [2], who carried out experimental investigations of a gear transmission similar to the reduction gear of the DTR-20 motor, the friction power may be approximately represented by the following relation:

\[ N_{\mathrm{fr}} = 0.03\,N \ \text{hp}. \tag{4} \]

After substituting expressions (3) and (4) into equation (2), the power expended in rotating the turbine motor with a bladed disk is written in the following form:

\[ N = \frac{N_\ell + N_d + N_{\mathrm{hyd}}}{0.97} \ \text{hp}. \tag{5} \]

In an analogous manner, an expression can be obtained for the power expended in spinning the turbine motor with a disk without blades:

\[ N_1 = \frac{N_d + N_{\mathrm{hyd}}}{0.97}. \tag{6} \]

By subtracting equation (6) from equation (5), the final expression for determining the power of the windage losses of the bladed wheel is obtained:

\[ N_\ell = 0.97\,(N - N_1). \tag{7} \]

The results of calculations of the power \(N_\ell\) by formula (7) are presented in Figs. 8 and 9, respectively, in ordinary and logarithmic coordinates; the values of \(N\) and \(N_1\) needed for these calculations were taken from the graphs (Figs. 5 and 6). As Fig. 9 shows, the windage losses are proportional to the number of revolutions to the power \(2.88\)—\(2.92\).

The dependences of the power of windage losses on the number of revolutions, presented in Fig. 8, may be written in the following form:

\[ N_{\lambda}=a\left(\frac{n}{1000}\right)^m, \tag{8} \]

where
\(a\) is the proportionality coefficient;
\(n\) is the number of revolutions of the wheel, rpm;
\(m\) is a constant exponent.

Fig. 8. Dependence of the power of the windage losses of the blade wheel on the number of revolutions.

In the figure:

1. Motion of the blades with their edges backward; outlet opening open, inlet opening closed.
2. Motion of the blades with their edges forward; outlet and inlet openings closed.
3. Motion of the blades with their edges forward; outlet opening open, inlet opening closed.

Axis labels: \(N_{\lambda}\), hp; \(n/1000\), rpm.

Determination of the coefficient \(a\) by the method of least squares [1] for the curves presented in Fig. 8, with the mean value of the exponent \(m = 2.9\), gives the following results:

\[ a = 0.823 \cdot 10^{-3} \]

for motion of the blades with their edges backward, with the outlet opening open and the inlet opening closed;

\[ a = 1.78 \cdot 10^{-3} \]

for motion of the blades with their edges forward and with the inlet and outlet openings closed;

\[ a = 3.22 \cdot 10^{-3} \]

for motion of the blades with their edges forward and with the openings open.

And now the expressions for the power of the windage losses, respectively, will be written as:

\[ N_{\ell}=0.823\cdot 10^{-3}\left(\frac{n}{1000}\right)^{2.9}\ \text{hp}, \]

\[ N_{\ell}=1.78\cdot 10^{-3}\left(\frac{n}{1000}\right)^{2.9}\ \text{hp}, \tag{9} \]

\[ N_{\ell}=3.22\cdot 10^{-3}\left(\frac{n}{1000}\right)^{2.9}\ \text{hp}. \]

The maximum relative errors of these equations, as the calculations show, are respectively equal to 6.5, 2.5, and 3.9%; moreover, these errors occur no more than once and at disk speeds below 5000 rpm.

Fig. 9. Dependence of the power of the windage losses of the blade ring on the number of revolutions in logarithmic coordinates.

Calculations show that the experimental curves (Fig. 8) are satisfied, with a sufficient degree of accuracy, by more convenient cubic equations, namely:

\[ N_{\ell}=0.7\cdot 10^{-3}\left(\frac{n}{1000}\right)^{3}\ \text{hp}. \tag{10} \]

when the blades move with their edges backward and with the discharge opening open and the inlet opening closed;

\[ N_{\lambda}=1.46\cdot 10^{-3}\left(\frac{n}{1000}\right)^3 \text{ hp.} \tag{11} \]

when the blades move with their edges forward and with the inlet and discharge openings closed;

\[ N_{\lambda}=2.7\cdot 10^{-3}\left(\frac{n}{1000}\right)^3 \text{ hp.} \tag{12} \]

when the blades move with their edges forward and with the inlet and discharge openings open.

The maximum relative errors of the cubic equations with respect to the experimental curves are (at individual points), respectively, 7.3, 5.0, and 6.5%. Consequently, without appreciable errors, the windage losses may henceforth be considered proportional to the cube of the number of revolutions.

Usually, in calculating windage losses, equations of the following form [3] are used:

\[ N_{\lambda}=KLD^4\gamma\left(\frac{n}{1000}\right)^3 \text{ hp.,} \tag{13} \]

where \(K\) is an empirical coefficient depending on the direction of motion of the wheel, the degree of shielding of the wheel, the magnitude of the radial and axial clearances between the wheel and the casing walls, the dimensions of the wheel, etc.;
\(L\) — blade height, m;
\(D\) — mean diameter of the wheel, m;
\(\gamma\) — specific weight of the air (steam) medium surrounding the wheel, kg/m\(^3\).

The coefficient \(K\) for the experiments carried out can be found from equations (10), (11), (12), and (13) after substituting into equation (13) the values of \(D\), \(L\), and \(\gamma\)

\[ D=0.285\text{ m},\quad L=0.013\text{ m},\quad \gamma=1.17\frac{\text{kg}}{\text{m}^3}. \]

The calculations give the following values of the coefficient \(K\):
\(K=7.0\) when the blades move with their edges backward and with the discharge opening open and the inlet opening closed;
\(K=14.6\) when the blades move with their edges forward and with the inlet and discharge openings closed;
\(K=27.0\) when the blades move with their edges forward and with the openings open.

Now, for the three listed cases of rotation of the wheel, the windage losses (at a degree of partial admission \(\varepsilon=0\)) of DTR-20 type turbines may be expressed by the following empirical equations:

\[ N_{\lambda}=7.0\,LD^4\gamma\left(\frac{n}{1000}\right)^3 \text{ hp.,} \tag{14} \]

\[ N_{\lambda}=14.6\,LD^4\gamma\left(\frac{n}{1000}\right)^3 \text{ hp.,} \tag{15} \]

\[ N_{\lambda}=27.0\,LD^4\gamma\left(\frac{n}{1000}\right)^3 \text{ hp.} \tag{16} \]

Calculations of windage losses, carried out by the author for the DTR-20 turbine using formula (14) and the well-known formula of Prof. Stodola 1) [5], showed that Stodola’s formula gives windage-loss values 2.5 times greater than formula (14).

Such a discrepancy in the calculation results can be explained by the fact that Stodola’s formula is given for uncovered wheels 2), whereas formula (14) was obtained from experiments with a shrouded rim and with small axial and radial clearances. In confirmation of this explanation, it may be noted that analogous comparative calculations by formula (14) and by the BBC company formula for shrouded wheels [4] showed good agreement of the results.

Thus, formula (14) can be applied only to a well-shrouded blade rim. The range of application of formula (14) becomes still more limited if one takes into account that the coefficient \(K\) is not a constant quantity and depends in a complicated manner on the dimensions of the rim.

Comparison of formulas (15), (16) with formula (14) shows that the windage losses when the rim moves in the reverse direction (with the blade edges forward) are almost four times greater than the losses in the normal direction of motion (with the blade edges backward), and are approximately twice as great under the condition that the inlet and outlet ports are closed.

From what has been said it follows that the windage losses in the reverse-running stage of a reversible turbine may turn out to be quite considerable if measures are not taken to reduce them, for example by using devices for closing the inlet and outlet ports.

Friction Losses of the Turbine Disk

The power of disk friction in air may evidently be determined from experimental data by a formula which, analogously to (7), is written in the following form:

\[ N_d = 0.97\,(N_1 - N_{wd})\ \text{hp}. \tag{17} \]

The results of calculations by formula (17) are given below, in Figs. 10 and 11, for right-hand rotation of the turbine disk \((i_{\text{right}} = 5.08)\). For left-hand rotation of the disk

Fig. 10. Dependence of disk-friction power on the number of revolutions,

1) In these calculations by A. Stodola’s formula

\[ N_r = [1.46\,D^2 + 0.83\,(1-\varepsilon)\,DL\,1.5]\,\gamma\,U^3 \cdot 10^{-6}\ \text{hp}, \]

the first term, which accounts for disk friction, was discarded, and the degree of partial admission \(\varepsilon\) was taken equal to zero.

2) A. Stodola, in giving his formula for calculating friction and windage losses, indicates that with shrouded wheels the magnitudes of the losses decrease by a factor of 2–4 [6].

(\(i_{\mathrm{red}} = 4.3\)) such calculations were not carried out, since in this case the power \(N_1\), expended on turning the motor with the unbladed disk, also includes additional losses in the reduction gear associated with the increased friction of poorly run-in surfaces of the gear teeth, which it does not appear possible to take into account.

Fig. 11. Dependence of the disk-friction power on the number of revolutions in logarithmic coordinates.

From the graph (Fig. 11) it can be seen that the dependence of the disk-friction power on the number of revolutions is a parabola of the following form:

\[ N_d = a_1 \left(\frac{n}{1000}\right)^3 \text{ hp}, \tag{18} \]

where \(a_1\) is a constant coefficient.

According to calculations by the method of least squares, from the data of the tests carried out,

\[ a_1 = 0.348 \cdot 10^{-3}. \]

Consequently, equation (19) will now be written in the following form:

\[ N_d = 0.348 \cdot 10^{-3} \left(\frac{n}{1000}\right)^3 \text{ hp}. \tag{19} \]

The disk-friction losses in air may be represented by the well-known relation [4]:

\[ N_d=K_1 D_d^{5}\gamma\left(\frac{n}{1000}\right)^3\ \text{hp}, \tag{20} \]

where \(K_1\) is an empirical coefficient,
\(D_d\) is the outside diameter of the disk, m.

From equations (20) and (21), after substituting the value of \(D_d\) for the disk of the turbine subjected to testing \((D_d=0.268\ \text{m})\) and the value \(\gamma=1.17\), the coefficient \(K_1\) is found to be

\[ K_1=\frac{0.348\cdot 10^{-3}}{0.268\cdot 1.17}=0.215. \]

Equation (20) may now be written in the following form:

\[ N_d=0.215D_d^{5}\gamma\left(\frac{n}{1000}\right)^3\ \text{hp}. \tag{21} \]

As calculations show, the deviations of the experimental points (Fig. 11) from the curve constructed according to equation (21) reach 15%. Such deviations were to be expected because of the relatively large errors that occurred in measuring the power expended on rotating the shaft of the pneumatic motor with the disk removed and with a disk without blades installed.

Formula (21), in comparison with the formulas of Prof. Stodola and other investigators, gives disk-friction losses that are 5–10% too high, despite the fact that the formulas of Stodola and others were obtained from experiments with uncovered disks, that is, under conditions in which disk friction should be greater. This apparent contradiction is explained by the fact that the coefficient \(K_1\) is not a constant quantity. According to data from a number of investigators, the coefficient \(K_1\) is a function of the Reynolds number, which, in particular according to Prandtl’s experiments [7], has the following form:

\[ K_1=\frac{A}{\sqrt[5]{R_e}}, \tag{22} \]

where \(A\) is a constant quantity,
\(R_e\) is the Reynolds number.

The Reynolds number, all other conditions being equal, is proportional to the linear dimension; therefore, with a decrease in the disk diameter, according to expression (22), the value of the coefficient \(K_1\) will increase.

Since the experiments of Stodola and other investigators were carried out with disks whose diameter was approximately twice the diameter of the DTR-20 disk, the disk-friction losses had relatively smaller values.

From what has been said it follows that formula (21), like formula (22), may be applied to well-covered disks and provided that the disk diameter differs little from the diameter of the DTR-20 disk with which the experiments described above were performed.

Calculation of the Performance of a Pneumatic-Turbine Motor Equipped with a Reversing Stage

The values of windage losses obtained as a result of the experimental investigation, under various conditions of rotation of the bladed wheel, make it possible to determine by calculation the performance of a pneumatic motor equipped with a reversing stage.

Below is an approximate calculation of the principal indicators of a pneumatic turbine engine whose runner is provided with doubled (“two-tier”) blades, forming the forward- and reverse-running rims of the turbine. A schematic view of such a reversible turbine and the shape of the doubled blade are shown in Fig. 12.

As initial data for the calculation it is assumed that the reverse-running stage, made according to the scheme described, is built into the turbine of a DTR-20 engine, and that, in order to reduce additional ventilation losses, the forward- and reverse-running stages have devices for closing the inlet and outlet openings.

Labels in Fig. 12: doubled blade; reverse-running rim; forward-running rim; \(z_1 = 32\); \(z_2 = 33\); \(z_3 = 16\); \(z_4 = 13\).

Fig. 12. Schematic of a pneumatic turbine engine with a reversible turbine.

According to the report on tests of the DTR-20 engine [3], the latter possesses the power and economic characteristics presented in Fig. 13. The presence of a reverse-running stage will evidently cause these characteristics to change in the direction of deterioration. The effective power, owing to the presence of additional losses in the reverse-running stage, will decrease somewhat, and the specific air consumption will correspondingly increase.

It should be noted, however, that when a reversible turbine is present, the need for one pair of gears in the reduction gear is eliminated; in the DTR-20 engine this pair was intended to change the direction of rotation of the driven shaft. With a smaller number of gears in the reduction gear, the hydraulic losses will also be smaller, which will to some extent compensate for the drop in power caused by the additional ventilation losses of the reverse-running stage.

The effective power of the DTR-20 engine with a reversible turbine can evidently be found from the following expression:

\[ N_e^{p} = N_e - N_l + \Delta N_{\text{hyd}} \ \text{h.p.}, \tag{23} \]

where \(N_e^{p}\) is the effective power of a DTR-20 type engine with a reversible turbine, h.p.;

\(N_e\) is the effective power of the DTR-20 engine in the normal version, h.p.;

\(N_{\ell}\) — ventilation losses of the reverse-run row with the exhaust and inlet openings closed, hp;

\(\Delta N_{\text{hyd}}\) — increase in the power of the DTR-20 engine due to the reduction of hydraulic losses in the reducer, hp.

The effective power of the DTR-20 engine in the standard version may be taken for the calculations from the characteristics (Fig. 13).

Fig. 13. Dependence of the effective power, specific air consumption, and adiabatic efficiency of the DTR-20 engine on the rotational speed of the turbine shaft.

Graph labels: \(N_e\), hp; \(q\), \(\text{m}^3/\text{hp}\cdot\text{min}\); \(\eta_{ad}\); \(n\), rpm; “2 nozzles,” “3 nozzles,” “4 nozzles,” “5 nozzles.”

The ventilation losses of the reverse-run row are found from the empirical relation (16)

\[ N_{\ell} = 14.6\, L D^{4}\gamma \left(\frac{n}{1000}\right)^{3}\ \text{hp}. \]

The blade height of the reverse-run row, as a first approximation, may be taken equal to \(L = 13\) mm, and the mean diameter of the reverse-run row, for design reasons, may be taken equal to \(D_1 = 255\) mm.

The specific weight of the air medium may be determined from the condition that the pressure and temperature in the chamber of the additional row are equal to the pressure and temperature in the chamber of the DTR-20 engine in the standard version.

According to the data of report [3], the mean excess pressure in the chamber of the DTR-20 turbine is \(\Delta p = 30\) mm Hg, and the mean temperature is \(t \simeq 0^\circ\text{C}\); consequently, the specific weight of the air medium will be

\[ \gamma = \gamma_0 \frac{760+\Delta p}{760}\cdot \frac{T_0}{T} = 1.293\,\frac{760+30}{760} = 1.34\ \text{kg}/\text{m}^3. \]

After substituting the numerical values of \(D_1\), \(L\), and \(\gamma\) into (16), the calculation formula for the windage losses of the reverse-running blade row may be written, for the given specific conditions, as

\[ N_\lambda = 1.08\cdot 10^{-3}\left(\frac{n}{1000}\right)^3\ \text{hp}. \tag{24} \]

The increase in the power of a DTR-20 engine when a reversing turbine is present, owing to a reduction in the hydraulic losses of the reduction gear, may be estimated approximately from the following elementary considerations. In the DTR-20 reduction gear, in its lower part, there are two intermediate shafts with gears immersed in an oil bath (Fig. 1), which, when rotating, must be assumed to produce hydraulic losses. If it is assumed that the intermediate shafts with gears produce losses equal to 70% of the idling losses of the reduction gear, then, with only one intermediate shaft present (which will be the case when a reversing turbine is used), these losses will amount to only 35% of the idling losses of the reduction gear, and the engine power will therefore increase by the same amount. Consequently,

\[ \Delta N_{\text{gid}} = 0.35\,N_{\text{gid}}\ \text{hp}. \tag{25} \]

With the aid of formulas (23), (24), (25) and the test data for the DTR-20 engine (Fig. 13), the characteristics of the engine with a reversing turbine can readily be determined when the forward-running blade row is operating.

To determine the characteristics in the case of the opposite direction of rotation of the turbine, i.e., when the reverse-running blade row is operating, it is obviously necessary, in equation (23), to take into account the reduction in effective power due to the decrease in relative internal efficiency (because of the smaller diameter of the reverse-running blade row) and the increase in additional losses in connection with the increased windage losses of the forward-running blade row.

Taking the above into account, equation (23) may be written in the following form:

\[ N_e^{p} = N_e\cdot K_\eta - N_\lambda\cdot K_d + \Delta N_{\text{gid}}\ \text{hp}. \tag{26} \]

Here

\[ K_\eta = \frac{\eta'_{oi}}{\eta_{oi}} \]

is the ratio of the relative internal efficiency of the reverse-running blade row to the relative internal efficiency of the forward-running blade row,

\[ K_d = \frac{N_\lambda'}{N_\lambda} \]

is the ratio of the windage losses of the forward-running blade row to the windage losses of the reverse-running blade row.

For the given specific conditions, the values of the coefficients \(K_\eta\) and \(K_d\) will be:

\[ K_\eta = \frac{0.58}{0.56} = 0.95^{1)} \]

\[ K_d = \left(\frac{D}{D_1}\right)^4 = \left(\frac{285}{255}\right)^4 = 1.56. \]

\(^{1)}\) The ratio of the relative internal efficiencies was calculated for the nominal speed regime \((n = 7500\ \text{rpm})\) and is conventionally accepted below as a constant quantity.

Now equation (26) can be written in a form convenient for calculations

\[ N_e^{p}=0.95\,N_e-1.56\,N_u+0.35\,N_{\mathrm{iw}}\ \text{hp}. \tag{27} \]

The results of calculations of the effective power of the DTR-20 engine with a reversible turbine, according to formulas (23) and (27), are summarized in Table 1 and presented in Figs. 14, 15. Also given there are the values of the specific air consumption and the adiabatic efficiency\(^1\), which were determined from the following relations:

\[ \frac{\eta_{ad}^{p}}{\eta_{ad}}=\frac{N_e^{p}}{N_e}\qquad \frac{q^{p}}{q}=\frac{N_e}{N_e^{p}}, \]

where \(\eta_{ad}^{p}\) is the adiabatic efficiency of the reversible turbine,
\(\eta_{ad}\) is the adiabatic efficiency of the DTR-20 engine,
\(q^{p}\) is the specific air consumption of the engine with the reversible turbine, \(\mathrm{Nm^3/(hp\cdot min)}\),
\(q\) is the specific air consumption of the DTR-20 engine, \(\mathrm{Nm^3/(hp\cdot min)}\).

Table 1

\(^1\) According to the general theory of steam turbines, the adiabatic efficiency \((\eta_{ad})\) corresponds to the effective efficiency \((\eta_e)\).

From a comparison of the calculated characteristics (Figs. 14 and 15) with the characteristics of the DTR-20, it can be seen that the presence of a reverse-running blade row in the reversible turbine, during forward running of the turbine and at a rated power of 20 hp (five working nozzles), leads to a relative reduction in effective power and adiabatic efficiency of 1.4%. As the rated power of the turbine decreases, i.e., as the number of working nozzles decreases, the relative reduction of the indices becomes greater and reaches, with two working nozzles ($N_e = 8$ hp), 3.7%. In the case of reverse running of the turbine, when the reverse-running blade row is in operation, the reduction in power and efficiency proves to be more substantial and reaches, respectively, 3 and 12% relative to the indices of the DTR-20 engine with a nonreversible turbine.

Fig. 14. Calculated characteristics of a pneumatic-turbine engine with a reversible turbine (forward running).

If it is taken into account that, under the operating conditions of mining machines, reverse running is used to a considerably lesser extent than forward running, one may conclude that the economic indices of an engine with a reversible turbine under operating conditions will be only slightly inferior to those of the DTR-20 engine with a nonreversible turbine.

From a comparison of the characteristics mentioned above it can also be seen that, as the turbine speed decreases, the indices of the engine with a reversible turbine approach those of an engine with an ordinary non-

with a reversible turbine and become practically identical at a speed equal to approximately one-half of the rated speed. Thus, the shortcoming of turbine motors in the sense of reduced economy under overload conditions is not aggravated when a reversible turbine is used instead of an ordinary, nonreversible turbine.

It follows from all that has been said that the use of reversible turbines in mine motors of 10–20 hp is possible and economically expedient. The indisputable advantages of pneumatic reversing of a mine turbine motor provide great convenience in the operation of mining machines and thereby offset a certain reduction in economy caused by the presence of the reversible turbine.

Fig. 15. Calculated characteristics of a pneumatic-turbine motor with a reversible turbine (reverse running).

In designing reversible turbines for mine motors, one should take into account the stronger influence of the turbine-disk diameter on the windage losses of the reverse- and forward-running stages, as compared with the influence of the rotational speed (see formulas 14, 16, 21); therefore, in order to attain high efficiencies, it is necessary to strive to reduce the diameter and increase the rotational speed of the working disk. Reducing the disk diameter is useful in a low-power turbine also because in this case the turbine will have greater partial admission and smaller windage losses in the forward-running stage.

References

1. Blokh L. S. Basic Graphical Methods for Processing Experimental Data. Mashgiz, 1951.

2. Mechanical Engineering: Encyclopedic Handbook, vol. 11. Mashgiz, 1948.

3. Flugel M. Steam Turbines. Gosenergoizdat, 1939.

4. Stodola K. Calculation and Design of Steam Turbines. Energoizdat, 1933.

5. Stodola A., Dampf-und Gasturbinen, 1922.

6. Balje O. E., A. Contribution to the Problem of Designing Radial Turbomachines, Trans., ASME vol. 74, May 1952.

1. The idea of using a pneumatic turbine as a motor for mining mechanisms was put forward in 1950 by Professor V. T. Yurinskii of the Tomsk Polytechnic Institute named after S. M. Kirov. Under the direction of Prof. Yurinskii, teams of TPI and the TEMZ plant created the first models of mine turbine motors. ↩