On Axial Machines with Counter-Rotating Impellers

Yu. N. Sokolov

1. Features and Advantages

By an axial machine (hydraulic or air-blowing) with counter-rotating impellers we mean one in which the flow of liquid or gas successively passes through two counter-rotating bladed wheels of the axial (propeller) type, entering into energy exchange with them (see the diagram in Fig. 1). Such a machine may be a pump (fan, blower, compressor) if the energy of the flow passing through it increases; it may also be an engine if the flow gives up its energy on the machine’s impellers.

Fig. 1. Diagram of an axial machine with counter-rotating impellers

Assuming that in air-blowing machines we are dealing with small pressure differences, and therefore not taking into account heat exchange of the gas flow with the external medium and the change in its internal energy, the energy of the flow in all the types of machines considered may be determined by the magnitude of the total hydrodynamic head

\[ H = z + \frac{p}{\gamma} + \frac{c^{2}}{2g}. \]

For a pump, fan, or blower the head before the machine is less than after it \((H_1 < H_2)\), and for an engine \(H_1 > H_2\). Accordingly,

the energy exchange between the flow and the impellers of the machine may be expressed by the magnitude of the total head perceived by, or imparted to, the flow:¹)

a) for pumps, fans, and blowers... $H=H_2-H_1$;
b) for motors........................ $H=H_1-H_2$.

As is known from the theory of vane machines, this energy exchange is determined by the angular velocity of the blade element $(\omega)$ and by the change in circulation $(\Delta \Gamma)$ along the contours of the runner; moreover, in the theoretical case (in the absence of hydraulic resistances in the machine) it may be expressed by the relation:

\[ H_t=\frac{\omega}{g}\frac{\Delta \Gamma}{2\pi}, \]

where $g=9.81\ \text{m/sec}^2$ is the acceleration of gravity.

If equality of the vectors of absolute velocities $(c)$ is assumed at all points of the circulation contours (jet theory), for axial machines this leads to the equation:

\[ H_t=\frac{1}{g}u\,\Delta c_u, \]

in which $u$ is the circumferential velocity of the blade element under consideration, and $\Delta c_u$ is the change in the circumferential component of the absolute velocity of the corresponding stream. Denoting these components of the absolute velocities at entry to the runner and at exit from it respectively as $c_{u1}$ and $c_{u2}$, we shall have:

a) for pumps, fans, and blowers................ $\Delta c_u=c_{u2}-c_{u1}$;
b) for motors.................................. $\Delta c_u=c_{u1}-c_{u2}$.

These well-known relations, given here in a generalized form (for pumps and for motors), clearly show that the transfer of energy at the runner of an axial machine of any type is possible only when the circumferential components of the absolute velocities at inlet and outlet change, i.e., when the flow passing through it is swirled or unswirled by the axial-type runner.

In single-stage machines this is possible:

1) either by swirling the outlet flow, if the incoming flow (as is assumed in most cases) is strictly axial, i.e., when $c_{u1}=0$ and the absolute inlet velocity $(c_1)$ coincides with the axial $(c_a)$ component of the mean flow velocity $c_1=c_a$, while $c_{u1}=0$ and $\Delta c_u=c_{u2}$;

2) or by forced swirling of the inlet flow with strictly axial outlet, when $c_2=c_a$ and $\Delta c_u=c_{u1}$;

3) or, finally, in a mixed case, when $c_{u1}\ne0$ and $c_{u2}\ne0$.

In the first case, because of $c_{u2}$, the energy of the outgoing flow increases, which lowers the efficiency (e. p. d.) of both the pump and fan and the motor. The uselessly lost swirl energy can be partially utilized by placing a straightening (guide) apparatus behind the runner, but, as is known, the loss of a considerable part of the energy is nevertheless unavoidable.

In the second case, forced swirling of the flow entering the runner is necessary, i.e., the use of a guide apparatus, and, consequently, the losses associated with this are inevitable.

¹) Here and below (for the purpose of unifying the concept of “head” for gas and liquid machines), by head we mean the quantity measured in meters of liquid (gas) column or in units of specific energy $(\text{kg·m}/\text{kg})$, and it is precisely this quantity that we denote by the symbol $H$. The quantity usually called head in fan theory, $p_2-p_1+\gamma/2\,(c_2^2-c_1^2)$ $(\text{kg}/\text{m}^2)$, we shall call the total pressure rise and denote by $\Delta p$.

The third case, as is evident, is also associated with similar losses in origin.

An increase in the head transmitted on the runner in all these cases requires an increase in the swirl of the flow and entails a corresponding increase in the losses indicated above.

In two-stage machines with axial entry to the first runner, for the head transmitted on this runner we shall have:

\[ H_t'=\frac{1}{g}u'c_{u2}'. \]

If, in this case, the flow leaving the first runner with absolute velocity \(c'=\sqrt{c_a^2+c_{u2}^{\prime 2}}\) is directed onto a second runner rotating in the same direction as the first, then transmission of energy on the second runner in the same direction as on the first (from the wheel to the flow in pumps and fans, or from the flow to the wheel in motors) will be possible only under the following conditions:

a) when the flow, passing through the second runner, becomes still more swirled in the previous direction;

b) when an intermediate—straightening—guide apparatus is placed between the first and second runners, spinning the flow up before its entry to the second runner.

The first is obviously inexpedient, since it will entail increased losses associated with the swirl of the flow leaving the machine, while the second is the usual scheme of two-stage machines, in which, as in single-stage machines, losses of at least part of the swirl energy of the outgoing flow are unavoidable; these losses are the greater, the greater the energy transmitted on the second runner,

\[ H_t''=\frac{1}{g}u''c_{u2}''. \]

In addition, in such two-stage machines losses associated with hydraulic resistances in the intermediate guide apparatus are unavoidable.

The transmission of energy by two axial wheels traversed successively by a flow of liquid or gas, without swirling this flow at the outlet and without the use of an intermediate guide apparatus, becomes possible when these wheels rotate in opposite directions. In this case, the transmission of energy on the first wheel can be ensured by the circumferential component of the outlet velocity \(c_{u2}\), and since the latter is directed opposite to the circumferential velocity of the second wheel, it becomes possible here as well to obtain energy transmission in the required direction owing to the presence of a corresponding difference in the circumferential components of the absolute velocities at inlet and outlet, even in the case when the outlet from the second wheel is axial.

Thus, the fundamental advantage of axial machines with opposite directions of rotation of the runners is the possibility of transmitting energy without the losses associated with swirl of the flow that are unavoidable in single-stage machines or in ordinary two-stage machines.

The basic scheme of an axial two-stage machine with counter-rotation of the runners is not new: the possibility of its realization has been expressed repeatedly over the past decade. Thus, for example, in 1946 Linemann and Heidves [2] published an article on counter-rotating axial fan wheels, in which diagrams of such machines are presented and comparative characteristics are given, confirming the advisability—

the advisability of their use. These characteristics were obtained, unfortunately, only by calculation and are not the result of tests performed on full-scale fans of this type. In foreign journals in recent years, however, proposals have been encountered for the supply of such fans¹.

The use of counter-rotation of aircraft propellers and of blade rows in turbocompressor units for jet aircraft engines is known.

Considering theoretically the working process in the stage of an axial compressor, M. G. Dubinskii [1] points to the possibility of using a pair of cascades moving in opposite directions and acknowledges the expediency of such an arrangement under certain conditions. M. A. Kasparov proposes using counter-rotation of impellers in propeller hydraulic turbines, calling such machines coaxial. In the modern literature there are also other indications of the possibility and expediency of applying counter-rotation of the impellers of axial machines.

It cannot be said, however, that the question of counter-rotation of impellers in axial machines has been sufficiently developed; there is not sufficient clarity even in the very formulation of the question of the expediency of using such machines, and this, apparently, explains the fact that counter-rotation of the impellers of axial machines has not yet found wide application in modern engineering. The wide use of such machines is also hindered by certain design difficulties arising from the need to connect the independent shafts of each of the counter-rotating axial impellers with sources or receivers of energy.

Such difficulties, however, can easily be overcome in certain special cases. Thus, for example, the connection to the motor of counter-rotating axial impellers in fans cannot be difficult when the electric motors can be built into the hub fairings. Counter-rotation of the impellers of an axial fan also proves structurally convenient in the special case when the source of energy is a gas or steam turbine whose blade rows may be arranged on a rim enclosing the blades of the axial impellers of the fan part of the unit. The same structural arrangement may in some cases also be applied to turbopump and turbo-blower units, etc.

A turbofan unit arranged according to the above scheme, with two counter-rotating axial impellers, was proposed and designed in 1951 by a group of workers of the Tomsk Polytechnic Institute and the Tomsk Electromechanical Plant “Glavuglemash,” with the direct participation of the author and under the general direction of Professor V. G. Yurinskii. At present, under the author’s direction, work is being carried out on the investigation of the elements of this unit and on its industrial development as a mine fan for auxiliary ventilation with a pneumatic turbine drive.

The use of axial machines with counter-rotation of the impellers is thus expedient not only from the fundamental considerations set forth above, but also, in a number of concrete cases, for design and technological reasons. The development of these machines requires the elaboration of their theory, the concretization of calculation methods, and the determination of the most successful structural types.

Below are presented some initial results of the author’s work in these directions.

2. Possible Schemes for Energy Transfer

Proceeding from design and technological considerations, it would be desirable for two counter-rotating axial wheels to be symmetrical in the arrangement and profiles of their blades. This requires equality of the blade setting angles \((\theta' = \theta'')\) of the first and second wheels; and, for identical angles of attack, equality of the angles \((\beta)\) between the relative \((w)\) and peripheral \((u)\) velocities will obviously also be necessary—the angles of the corresponding velocity triangles.

Such a symmetrical scheme for constructing the inlet and outlet velocity triangles for the first and for the second counter-rotating axial wheels of a machine that transfers energy to a stream of liquid or gas can be implemented as shown in Fig. 2, where, as below, all

Fig. 2. Combined velocity triangles for a pair of counter-rotating wheels with guide and straightening apparatuses (variant I)

quantities relating to the first wheel are marked with one prime, and those relating to the second with two; the lower indices correspond to the inlet (1) or outlet (2) velocity triangles. As is evident, the transfer of energy by a pair of counter-rotating axial wheels according to this scheme is possible only under the following conditions:

a) supply to the first wheel of a stream already swirled by \(\Delta c_u^1\);

b) exit of the stream from the first wheel and its entry into the second without swirl;

c) exit from the second wheel likewise with swirl.

The magnitude of the energy transferred at each of the wheels according to this scheme will not be large; it is determined only by the swirl of the stream supplied to the first wheel and by the swirl of the stream leaving the second.

A mirror-symmetrical scheme of velocity triangles and corresponding profile cascades for a pair of counter-rotating axial wheels can, however, also be implemented by using the swirl of the stream at the exit from the first wheel for additional transfer of energy both at the first and at the second wheels. The combined velocity triangles for this case are shown in Fig. 3, and the scheme of energy transfer in Fig. 4.

In both the first and the second of the cases considered, symmetry of the blade profiles of the first and second wheels of the axial machine is obtained at the cost of the necessity of swirling the stream supplied to it and unswirling the stream leaving the second wheel (in order to use the swirl energy created by it), that is, at the cost of the necessity of employing guide and straightening apparatuses. This loses (see above) the main advantage of counter-rotation of the working wheels of an axial machine. Since other conditions for energy transfer by a pair of counter-rotating axial wheels in the presence of symmetry in the profiles of their blades and equality of peripheral velo-

it is not possible to represent the velocities simply; one has to abandon the fulfillment of the symmetry condition.

With an asymmetric scheme, the transfer of energy by a pair of counter-rotating axial wheels with equal speeds becomes possible without guide or straightening apparatuses and with axial entry into the first wheel, combined with axial exit from the second. The scheme of energy transfer in this case, with the plotting of velocity and force plans on the blades of two oppositely moving profile cascades (also for the case of transfer of energy to the flow), is given in Fig. 5, and the combined velocity triangles—in Fig. 6.

Fig. 3. Combined velocity triangles of a pair of counter-rotating wheels with guide and straightening apparatuses (variant II)

Fig. 4. Mirror-symmetric scheme of energy transfer by a pair of counter-rotating axial wheels

Fig. 5. Scheme of energy transfer by a pair of counter-rotating axial wheels with axial inlet and axial outlet.

Fig. 6. Combined velocity triangles of a pair of counter-rotating wheels with axial inlet and axial outlet

In this case, the first wheel transfers energy by twisting the flow at the outlet. The magnitude of the theoretical head created by it will be determined by its peripheral velocity and by the peripheral component of the absolute velocity at the outlet:

\[ H_t'=\frac{1}{g}\,u'c_{u2}'. \tag{1} \]

Since the second wheel rotates counter to the swirl created by the first, then, taking the direction of the latter as positive, the circumferential velocity in the second stage (the second wheel) must be taken with the opposite sign. Therefore the theoretical head developed by the second wheel must in this case be expressed as

\[ H_t''=-\frac{1}{g}\,u''(0-c_{u1}'')=\frac{1}{g}\,u''c_{u1}'' \tag{2} \]

and, consequently, the transfer of energy on the second wheel is ensured in the same direction as on the first, but at the expense of the swirl of the flow entering this second wheel (leaving the first).

With identical changes in the circumferential components of the absolute velocities in the first and second wheels,

\[ \Delta c_u'=c_{u2}'-0=\Delta c_u''=0-c_{u1}''=-c_{u1}'' \]

and with equal in magnitude, but opposite in sign, circumferential velocities of these wheels, the transfer of energy to a unit mass flowing through the annular element of the section swept by the blades will also be the same: \(H_t'=H_t''\). It is precisely for this case, which is evidently the most natural and expedient, that the schemes shown in Figs. 5 and 6 have been constructed.

For a pair of counter-rotating axial wheels of a driving machine, the directions of rotation and energy transfer must be changed (now from the flow to the blades); however, the basic schemes of energy transfer and of the velocity triangles remain essentially the same as those considered above.

The scheme of energy transfer and construction of the velocity triangles according to Figs. 5 and 6, as making it possible to make full use of the above-noted advantages of axial machines with counter-rotating runners, should be recognized as the most expedient and should be made the basis for the calculation and design of such machines.

It should be noted, however, that the angles of the velocity triangles of the first and second stages here cannot be the same. This also leads to unequal setting angles of the blades of the first and second runners. Thus, according to our schemes,

\[ \beta''<\beta' \quad \text{and} \quad \Theta''<\Theta'. \]

This does not make it possible to unify the manufacturing technology for each pair of counter-rotating wheels of any particular machine (to use identical patterns or identical dies for manufacturing their blades). The production significance of this circumstance, however, is not so substantial, in view of the advisability—determined by other conditions—of having unequal numbers of blades for these wheels and, consequently, also unequal profiles.

3. Special features of the calculation

The generally accepted method for calculating axial blade machines and selecting the profiles of the sections of their blades, based on the equations of Euler and Zhu-

…of Zhukovskii’s theory¹, can also be applied to the calculation of a pair of counter-rotating axial wheels operating according to the proposed scheme (as in Figs. 5 and 6). The calculation of the first wheel, the inlet to which, as is also assumed for machines of the usual type, remains axial, should not differ in any way from the generally accepted one; in calculating the second wheel, however, it is necessary to take into account the specificity determined by the fact that, in the case of energy transfer to the flow, the head here is created by the circumferential component of the absolute velocity not at the outlet, as is usually the case, but at the inlet.

The theoretical head of the second wheel, as was shown above, is determined by equation (2). From consideration of the velocity triangles of this second wheel (Fig. 6) it follows that the magnitude of the mean relative velocity of flow past its blades \((w'')\) and the angle \((\beta'')\) at which it is directed are determined by the expressions:

\[ w''=\sqrt{c_a^2+\left(u''+\frac{\Delta c_u''}{2}\right)^2}; \tag{3} \]

\[ \operatorname{tg}\beta''=\frac{c_a}{u''+\dfrac{\Delta c_u''}{2}}, \tag{4} \]

that is, instead of the usual difference \(u-\dfrac{\Delta c_u}{2}\), it is now necessary to use the sum of the same quantities.

The magnitudes of the theoretical heads of the first and second counter-rotating axial wheels, determined from expressions (1) and (2), must evidently include the energy imparted to the flow on these wheels,

\[ H'=\left(\frac{p'_2}{\gamma}+\frac{c_a^2}{2g}+\frac{c_{u2}'^{\,2}}{2g}\right) -\left(\frac{p_1}{\gamma}+\frac{c_a^2}{2g}\right) =\frac{p'_2-p_1}{\gamma}+\frac{c_{u2}'^{\,2}}{2g}; \tag{5} \]

\[ H''=\left(\frac{p_2}{\gamma}+\frac{c_a^2}{2g}\right) -\left(\frac{p_1''}{\gamma}+\frac{c_a^2}{2g}+\frac{c_{u1}''^{\,2}}{2g}\right) =\frac{p_2-p_1''}{\gamma}-\frac{c_{u1}''^{\,2}}{2g} \tag{6} \]

and the profile losses arising in them, \(H'_{\mathrm{prf}}\) and \(H''_{\mathrm{prf}}\).

Since losses associated with swirl of the flow do not exist in the case under consideration, the hydraulic efficiencies of each of the counter-rotating axial wheels practically become profile efficiencies:

\[ \eta_c'=\frac{H'}{H_t'}=\frac{H_t'-H'_{\mathrm{prf}}}{H_t'}=\eta_{\mathrm{prf}}'; \tag{7} \]

\[ \eta_c''=\frac{H''}{H_t''}=\frac{H_t''-H''_{\mathrm{prf}}}{H_t''}=\eta_{\mathrm{prf}}''. \tag{8} \]

For the entire machine with a pair of counter-rotating axial wheels, the energy transmitted to the flow is determined as

\[ H=H'+H''=\frac{p_2-p_1}{\gamma}+\frac{c_{u2}'^{\,2}-c_{u1}''^{\,2}}{2g}. \tag{9} \]

In the particular case under consideration, when \(c'_{u2}=c''_{u1}=c_u\),

\[ H=\frac{p_2-p_1}{\gamma}; \tag{10} \]

the theoretical head of the entire machine exceeds the useful head only by the profile losses of both wheels, \(H_{\mathrm{prf}}=H'_{\mathrm{prf}}+H''_{\mathrm{prf}}\), that is:

\[ H_t=H+H_{\mathrm{prf}}. \tag{11} \]

Thus, for the entire machine with a pair of counter-rotating axial wheels, the hydraulic efficiency proves to be equal to the profile efficiency

\[ \eta_h=\frac{H_t-H_{\mathrm{prf}}}{H_t}=\eta_{\mathrm{prf}}, \tag{12} \]

and the swirl coefficient, usually understood as

\[ \eta_{\mathrm{sw}}=\frac{\eta_z}{\eta_{\mathrm{prf}}} = \frac{H-\dfrac{c_u^2}{2g}}{H}, \]

turns into unity.

It is necessary here to take into account that, when the theoretical heads are equal (that is, when equal energy is expended on rotating each of the two counter-rotating axial wheels), the pressure rises produced by the first and second wheels will already differ from one another by twice the “swirl pressure”

\[ \left(\frac{c_u^2}{2g}\gamma\right), \]

produced by the first wheel. Indeed, for \(H''=H'=\dfrac{H}{2}\), it follows from equations (5) and (6) that, whereas

\[ \Delta p'=p'_2-p_1=\frac{H\gamma}{2}-\frac{c_u^2}{2g}\gamma, \tag{13} \]

\[ \Delta p''=p_2-p''_1=\frac{H\gamma}{2}+\frac{c_u^2}{2g}\gamma = \Delta p'+2\left(\frac{c_u^2}{2g}\gamma\right). \tag{14} \]

When using the method developed by TsAGI for the row-by-row calculation of axial fans for the second of a pair of counter-rotating axial wheels operating according to the scheme of Fig. 5, the sign in the expression for the pressure rise produced here through \(u\) and \(c_u\) must likewise be changed. The total pressure rise produced by the second wheel, without taking profile losses into account, is expressed by the difference:

\[ \Delta p''_{t\,\mathrm{tot}} = \left(p''_{2t}+\rho''\frac{c_a^2}{2}\right) - \left(p''_1+\rho''\frac{c_a^2}{2}+\rho''\frac{c_{u1}^{\prime\prime\,2}}{2}\right), \tag{a} \]

where

\[ \begin{aligned} p''_{2t}=p_{2t} &\text{— the pressure downstream of the second wheel (and downstream of the machine as a whole) in the theoretical case;}\\ p''_1 &\text{— the pressure upstream of it;}\\ \rho'' &\text{— the mean density at the second wheel;}\\ c_a &\text{— the axial velocity;}\\ c''_{u1} &\text{— the circumferential component of the velocity at entry to the second wheel.} \end{aligned} \]

At the same time, according to (1),

\[ \Delta p''_{t\,\text{full}} = H_t'' r'' = \rho'' u c''_{u1}. \tag{6} \]

From the last two equations (a) and (6) it follows that the “theoretical static-pressure difference” produced by the second wheel must be expressed as

\[ \Delta p_t'' = p_2 - p_1'' = \rho'' c''_{u1}\left(u + \frac{c''_{u1}}{2}\right). \tag{15} \]

The actual increase in static pressure will then be

\[ \Delta p'' = p_2 - p_1'' = \eta''_{\text{prf}} \rho'' c''_{u1}\left(u + \frac{c''_{u1}}{2}\right), \tag{16} \]

where \(\eta''_{\text{prf}}\) is the profile efficiency of the cascade of the second wheel. The numerical value of the latter, depending on the angles \(\beta''\) and \(\alpha''\), may be established from experimental data (for example, from the corresponding TsAGI graphs).

The fact that, along with equations (15) and (16), for the increase in static pressure on the first wheel one should use the expression of the usual form

\[ \Delta p' = p'_2 - p_1 = \eta'_{\text{prf}}\rho' c'_{u2}\left(u - \frac{c'_{u2}}{2}\right), \tag{17} \]

corresponds to the conclusion derived above concerning the inequality of the pressure increases produced by the wheels operating according to the scheme under consideration, despite the fact that each of them consumes the same energy.

The features given above in the principal calculation relations determine the specificity of the calculation and selection of profiles for an axial machine with counter-rotating impellers when energy is transmitted to the flow in it. For engine-machines, the reverse direction of energy transfer must be taken into account.

4. Experience of application in an axial fan

The fundamental scheme considered above for the most advantageous operating conditions of a pair of counter-rotating axial wheels (according to Fig. 5), and the resulting features in the principal calculation relations, were used by the author in the aerodynamic calculation and profiling of the blades of the fan part of a turbo-fan unit designed in cooperation with the Tomsk Electromechanical Plant (TEMZ) (see above). A prototype of this turbo-fan unit was manufactured in 1952 and tested on the factory stand of TEMZ under the author’s supervision. The abnormal operation of the turbine part of this unit did not ensure the equality, assumed as the basis for the design of the fan part, of the rotational speeds of the impellers; as a result, in the tests mentioned it was not possible to achieve the design operating indices of the unit as a whole.

At present, further work is being carried out on improving and putting into production this mine fan for partial ventilation, with a pneumatic turbine drive and counter-rotation of the impellers.

At the same time, the author set the task of investigating the operating conditions of an axial fan with counter-rotation of the impellers independently of their drive. For this purpose, a special experimental model of such a fan with a drive was designed and manufactured—

rotor blades, “VDV-E,” each of whose impellers was driven by independent direct-current electric motors with a wide possibility of regulating the rotational speeds (up to 5000 rpm).

The longitudinal section of this experimental model of an axial fan with counter-rotating impellers is shown in Fig. 7. The basic dimensions of its impellers, the number and profiles of the blades fully correspond to the fan part of the above-mentioned turbofan unit with pneumatic drive and are therefore made in accordance with the calculation carried out by the author according to the scheme proposed in the present work.

Fig. 7. Experimental model of a fan with a pair of counter-rotating axial impellers, VDV-E.

This experimental model is being subjected to detailed investigations on a stand specially equipped for this purpose in the laboratory of Hydraulic and Air-Duct Machines of the TPI, which is a pressurized chamber for testing TsAGI-type fans with two DC balancing machines, one of which is located behind the screen inside the chamber and is connected to the first impeller of the fan under investigation by a long shaft enclosed in a casing.

The results of one of the series of experiments carried out by the author under these conditions, at the design blade-setting angles and at rotational speeds of the counter-rotating impellers of the experimental fan model \(n' = n'' = 3700\) rpm, are presented in Fig. 8 in dimensionless

\[ \left( H = \frac{\Delta p}{\rho u^2};\quad \overline{Q} = \frac{Q_{\text{ck}}}{F u} \right) \]

and in absolute \((\Delta p\) mm water column; \(Q\) m\(^3\)/min) values of head (total pressure rise) and flow rate. Considering these results, which are not yet limiting with respect to the maximum attainable efficiency of a fan with a pair of counter-rotating axial impellers,\(^1\)

\(^1\) Experiments have established that increasing the rotational speed of each of the investigated pair of counter-rotating impellers, while preserving their equality for the given blade-setting angles (chosen by calculation for rotational speeds of each of the impellers of 4750), increases the maximum efficiency; the rotational speeds of the impellers of 3700, to which the characteristics presented in Fig. 8 refer, were chosen here irrespective of the intention to ensure the maximum efficiency.

it may be stated that the efficiency in the present case is very high and reaches the highest values attained in model tests of the most advanced designs of two-stage axial fans in general. A comparison of the characteristics of the fan under investigation with counter-

Fig. 8. Experimental characteristics of a fan with counter-rotation of the impellers at \(u'=u''=71.1\ \mathrm{m/sec}\).

rotating axial impellers with those for a two-stage fan of the usual type (Fig. 8) at identical peripheral velocities at the blade tip and at approximately the same quality of manufacture

...and radial clearances indicates a significant increase in the overall efficiency of the axial machine due to the use of counter-rotation of the impellers. In the case under consideration, the increase in the maximum values of the total efficiency reaches

\[ \frac{86}{76} \cdot 100 = 113\%. \]

A very substantial advantage of an axial fan with counter-rotating impellers is also the fact that its pressure characteristic, at sufficiently large blade-setting angles, does not have the dip characteristic of most low-pressure fans (Fig. 8), which is highly undesirable under operating conditions. Elimination of such a dip is also possible in axial fans of the ordinary type, but it is achieved at the cost of making them somewhat more complicated and of reducing efficiency.

An unpleasant feature of a pair of counter-rotating impellers in an air stream is the generation by them of a characteristic whistling noise. In tests of the experimental VDV-E model it was established that the intensity of this noise increases greatly with an increase in the rotational speed of the counter-rotating axial impellers, and, at circumferential velocities at the outer blade elements of about 70 m/s and an axial distance between the radial edges of the blades \(A = 13\text{–}14\) mm, reaches 105–106 dB, having a very appreciable effect on the organs of hearing.

Combating this noise is evidently possible by increasing the dimension \(A\); the influence of this on the noise intensity and on the efficiency of a pair of counter-rotating axial impellers is to be the subject of special investigations planned by the author.

Figure 8 also gives the calculated characteristics of the investigated pair of counter-rotating axial fan impellers, obtained by the method of turn-by-turn calculation (see above) using published TsAGI experimental materials on the basis of the above-mentioned changes in the calculation relations for the second impeller. In efficiency and in total head, the calculated indices prove to be noticeably lower than those obtained by direct experiment. The discrepancy should apparently be attributed to the nonconformity of the experimental data used in the calculation with the actual operating conditions of the investigated cascades, and not to any incorrectness of the initial assumptions and the applied calculation relations. This question, however, is subject to further investigation.

As for the power consumed by each of the investigated counter-rotating axial impellers, the results of the tests carried out on the VDV-E model show that, with equal rotational speeds of these impellers, made in accordance with the scheme considered here, each of them requires approximately the same power; moreover, it varies little over the working part of the fan characteristic. The discrepancy between the powers of each of the impellers in individual tests reaches up to 10% of their sum.

A change in the rotational speed of either member of the pair of counter-rotating axial impellers leads, on the contrary, to a sharp redistribution of the power consumed by each of them.

The power characteristics of the pair of counter-rotating axial impellers as a whole thus also confirm the correctness of the propositions set forth above concerning the operating conditions of such a pair.

The experimental investigation of the operating conditions of a pair of counter-rotating axial impellers on the experimental VDV-E fan model must still be expanded and will be continued by the author in the direction of studying the influence of the blade-setting angles and the rotational speeds of each of the impellers on the aerodynamics of the flow passing through them and on the final re-

results of the energy exchange taking place in this process. Nevertheless, already on the basis of the results of the investigations carried out and the data presented in Fig. 8, in particular, the experience of using counter-rotation of axial wheels in fans may confidently be recognized as positive and as opening up broad prospects for increasing the economy and operating qualities of axial machines of various types.

Conclusion

The following are presented in this work:

fundamental substantiations of the features and advantages of axial machines with counter-rotation of the impellers;

an analysis of possible schemes and operating conditions for a pair of counter-rotating axial wheels, and the establishment of the most advantageous ones;

initial substantiations, based on such a most advantageous scheme, of the theory and methods of calculation of the pair under consideration and, finally,

the results of an initial experimental verification of these substantiations of the theory and methods of calculation,—

which testify to the obvious expediency of using machines of this type in all those cases where this does not give rise to difficulties associated with the general structural layout of the machine or with the conditions of its operation.

The use of counter-rotation of impellers in axial machines will, in particular, be expedient in a number of types of axial fans driven by electric motors built into hub fairings. Replacement of the pair of counter-rotating axial wheels of a two-stage axial fan in this case will require, of course, two electric motors instead of one, but since the initial cost of standard electric motors is small, while the reduction in their efficiency (with a decrease in the power of each) is more than compensated by an increase in the efficiency of the fan part, the economic expediency of such a replacement is beyond doubt.

The use of two-stage machines with counter-rotation of axial wheels as mine fans for auxiliary ventilation is all the more expedient because in the initial period of operation, when the ventilated working is not yet great in depth, it is possible, by means of the appropriate structural design of the fan unit with a pair of counter-rotating axial wheels, to ensure its temporary operation with only one of the wheels, with a corresponding reduction in the connected power. The expediency of using counter-rotation of axial wheels in mine fans for main ventilation is not excluded either, but in this direction appropriate design and engineering developments are necessary, as well as the solution, in particular, of the question of reversing the flow produced by a pair of counter-rotating axial wheels.

Axial fans with counter-rotation of impellers may find fairly wide application both in industrial ventilation and in the forced-draft and induced-draft devices of boiler installations. In application to induced-draft installations, however, appropriate design work must also be carried out, connected with the need to protect the drive shafts, electric motors, and bearing assemblies from dusty and hot flue gases; this, if it is necessary to have two counter-rotating wheels, will create certain complications.

Counter-rotation of axial wheels is already finding application in air-duct and compressor installations of a special type; it may, finally, find definite application also in hydraulic machines—in special types of axial pumps and hydraulic turbines. Especially attractive

here is the development of the question of reversible axial machines with a pair of counter-rotating wheels for pumped-storage installations.

The paths outlined here for the application of machines with counter-rotating axial wheels reveal possibilities for increasing the efficiency of blade machines, both those transmitting energy from the runner to the flow and those serving as motors; however, progress along these paths requires further in-depth research and design work. The present work is only the author’s initial contribution to this matter.

References

1. Dubinskii M. G. Theoretical Investigation of Axial Compressors. Moscow, 1947.

2. Linnam F. G., and Hawes S. P. Contra-Rotation Flow Fans. “The Engineer,” July 5, 1946.

1. The author believes that the so-called jet theory of blade machines, based on L. Euler’s equation, and the vortex theory created by N. E. Zhukovskii do not exclude, but supplement, one another. ↩↩