EXPERIMENTAL STUDY OF A PAIR OF COUNTER-ROTATING AXIAL WHEELS

Yu. N. Sokolov

(Presented by Prof. Dr. I. N. Butakov)

Until recently, only a few works on axial machines with counter-rotating impellers had been published in the domestic and foreign literature. In this connection, in 1953 and 1954 the author set up and carried out experiments on a specially designed experimental model with a pair of counter-rotating axial wheels (“VDV-E”), intended for operation in an air stream. Some preliminary results of these experiments are given in the author’s previously published works [1] and [2].

Subsequently the author learned of investigations, carried out in 1951 at TsAGI and remaining unpublished, on counter-rotation of the impellers of axial fans; and at the end of 1953 R. Holbeche [4] published material relating to fans with counter-rotating axial wheels of the Canadian firm “Vues,” which also contains corresponding experimental data. Finally, in 1955 a paper by A. P. Artykov [5] was published, containing the results of experimental investigations he had conducted on models of axial fans with one-sided and counter-rotation of the impellers.

Below are presented the results of the author’s experiments, which are compared with the material of the other investigations mentioned above, and some generalizing conclusions are given on the results of applying counter-rotation of axial wheels.

Objectives and arrangement of the experiments

The objective of the experiments conducted by the author was both a general clarification of the technical feasibility of applying counter-rotation of axial wheels, and an investigation of the influence, on the operation of a pair of such counter-rotating wheels, of certain factors determining their design standards. In addition, the objectives of the experiments included an experimental verification of the methods developed by the author for calculating axial machines with counter-rotation of the impellers [3], and the establishment of experimental characteristics of the fan section of the VPD-4 turbofan unit, designed in 1952 with the author’s participation by a group of workers of the Tomsk Polytechnic Institute and the Tomsk Electromechanical Plant.

The experimental model VDV-E, intended for the investigations posed as the task, consisted of two axial wheels with adjustable blades (Fig. 1), whose dimensions and shape, at normal blade setting angles \(\Theta' = 20^\circ\) and \(\Theta'' = 23^\circ\) (at the mean diameter), fully corresponded to those of the above-mentioned VPD-4 turbofan unit. The blades of the first and second wheels were profiled in such a way that their edges facing one another lay in diametral planes, ensuring the same axial distance between them \(a_{1-2}\) along the entire blade length (see the diagram in Fig. 5).

The principal dimensions of the impellers of the VDV-E model, and the parameters of the profiles of their blades and grids, are given in the example of the verification calculation considered in the author’s above-mentioned article [3].

Fig. 1. Experimental model VDV-E.

Each of the impellers of the experimental model had an independent drive from a direct-current electric motor, with the possibility of varying the rotational speed up to 5000 rpm.

The experimental setup consisted of a chamber of diameter \(1700\) mm with a blower, ensuring operation of the investigated pair of counter-rotating wheels in an air flow under all possible regimes, up to negative heads (turbine regime). In order to ensure a uniform and untwisted flow before and after the experimental model, the drive shafts (sufficiently long) were fitted with protective casings, and the balancing machine of the first wheel, located inside the chamber, was separated by a dense screen. Insert rings of the model housing made it possible to move the investigated wheels apart, changing the axial dimension \(a_{1-2}\).

The principal measurements were:

1) the static pressure rise produced by the model under study—by the rarefaction in the chamber \(H_{\text{st}}\);

2) the flow rate of the air passing through the model—by measurements with a tip tube in the calibrated section of the suction pipe \(Q\);

3) the torques \(M'\) and \(M''\), the rotational speeds \(n'\) and \(n''\), and the powers \(N'\) and \(N''\) transmitted by the impellers, from the calibrated deflections of the stators of the balancing machines and from tachometers.

The probable errors of these measurements were: for pressure rise, 0.5%; for flow rate, 0.7%; for shaft torques, rotational speeds, and powers, 1.5%. This corresponds to a maximum probable error in determining the efficiency of no more than 2%.

In view of the relatively small pressure rises produced by the experimental model, the air density in each experiment was assumed constant and the same throughout the entire length of the flow being investigated; it was evaluated from measurements of barometric pressure, temperature, and air humidity in the room.

The dynamic head produced by the pair of wheels was determined from the mean flow velocity downstream of the second wheel in the section constricted by the hub. The total head and the total efficiency of the pair of wheels were thus evaluated without taking into account possible losses in the diffuser, which is also accepted for fan characteristics according to the TsAGI procedure.

In some experiments measurements were also made of the noise produced by the installation and of the mean flow direction between the first and second wheels of the experimental model at the mean diameter—using a miniature cylindrical probe (stem diameter 3.8 mm).

In all, six series of experiments were carried out:

1) with simultaneous variation of the rotational speeds of both wheels—
series \(n\),

2) with variation of the ratio of the rotational speeds of the wheels—
series \(n'' : n'\),

3) with variation of the blade-setting angles of the impellers—
series \(\Theta\)

4) with variation of the axial distance between the blades of the impellers—
series \(a_{1-2}\),

5) with the drive of one of the wheels switched off—
series \(B\),

6) with independent operation of each wheel—
series \(H\).

Results of the Author’s Experiments

Experiments of series \(n\) confirmed the applicability of the usual similarity laws for blade machines also to a pair of counter-rotating axial wheels operating at equal rotational speeds; the experimental characteristics, processed in dimensionless parameters \(\overline{H} = \dfrac{\Delta p}{\rho u^{2}}\) and \(\overline{Q} = \dfrac{Q}{Fu}\), at rotational speeds of both wheels from 1600 to 4200 rpm gave results coinciding within the accuracy of measurement.

Figure 2 shows the pressure characteristic of the investigated pair of counter-rotating wheels, obtained by averaging a whole series*) of experiments carried out at \(n' = n'' = 3700\ \text{rpm}\), and, near it, the experimental points of one such experiment (at 3700 rpm) and of one experiment at \(n' = n'' = 2400\ \text{rpm}\). The position of the points of the latter in the immediate vicinity of the main

*) At \(n' = n'' = 3700\ \text{rpm}\), several basic experiments were carried out, as well as one control experiment in each of the subsequent series.

curve confirms the applicability, noted above, of the laws of similarity.

The head characteristic presented in Fig. 2 corresponds to blade setting angles \((\theta'/\theta'') = 20^\circ/23^\circ\) and to the axial distance between them \(a_{1-2} = 14\ \mathrm{mm}\). In what follows it is taken as the basis for comparison with the results of tests at other values of these quantities, with one of the wheels switched off, or with their independent operation. A characteristic feature of this head characteristic of a pair of counter-rotating axial wheels at moderate blade setting angles

\[ \bar H = \frac{\Delta p}{\rho u^2} \]

Fig. 2. Head characteristic of the experimental model VDV-E.

of their blades is its smooth form: without the “humps” and “breaks” characteristic of gas axial machines of the usual type. This circumstance, confirmed by a whole series of tests, is one of the substantial advantages of counter-rotation, providing broad limits of stable operation for machines of this type.

Figure 3 plots curves of variation of the total $\eta$ and static $\eta_{\mathrm{st}}$ efficiencies of a pair of counter-rotating axial wheels as functions of the reduced flow rate, obtained, again, by averaging a whole series of tests at $n' = n'' = 3700\ \mathrm{rpm}$ and at the same values of $\Theta'$ and $\Theta''$ to which the pressure characteristic in Fig. 2 pertains. To estimate the “scatter” of experimental points near the curve of total efficiency, these points, corresponding to two independent tests carried out under the given conditions, have been plotted. The maximum efficiency achieved in accordance with Fig. 3 is very high—88%, which cannot be obtained in corresponding machines (two-stage axial fans) of one-directional rotation.

The results of the tests of the series $n''/n'$ are presented in Fig. 4. Owing to the unequal numbers of revolutions of each of the impellers in this series of tests, processing their results in dimensionless parameters would not be indicative. Therefore Fig. 4 gives the corresponding curves in terms of the absolute values of the measured quantities.

Fig. 3. Efficiency of the experimental model VDV-E.

The speed of the first wheel in all tests of this series was kept constant ($n' = 3700 = \mathrm{const.}$), while the speed of the second was varied within ratios $n'' : n'$ from 0.7 to 1.15. As the corresponding curves show, increasing the speed of the second wheel considerably increases the total pressure produced by the pair of wheels and leads to a sharp redistribution of the powers consumed by each of the wheels ($N'$ and $N''$).

The largest values of the efficiency of the pair of wheels are ensured under normal conditions of their operation, that is, at $n'' = n'$. In this case the optimum regime (point $c$ on the pressure characteristic) practically corresponds to equality of the powers consumed by each of the wheels (point $K$). With an increase in $n''/n'$, the optimum regime shifts toward larger flow rates (points $d$ and $d'$), but the maximum efficiencies of the pair of wheels decrease when departing from $n'' : n' = 1$

both in one direction and in the other. All this is consistent with the fact that the investigated pair of counter-rotating axial wheels of the experimental model was designed on the basis of the conditions of its normal operation at equal rotational speeds of these wheels and their equal total theoretical head.

In all subsequent experiments (series $\Theta$, $a_{1-2}$, $B$, and $H$), the rotational speeds of both wheels were kept identical and equal to $3700$ rpm.

Fig. 4. Effect of the ratio of the rotational speeds of the first and second counter-rotating wheels on their characteristics.

Experiments of series $\Theta$ were carried out only at the design blade-setting angles and with their increase by $+3^\circ$.* Figure 5 gives the corresponding dimensionless characteristics. As already indicated above, in accordance with the design conditions of the experimental VDV-E model, the design blade-setting angles were small: $\Theta' = 23^\circ$ and $\Theta'' = 20^\circ$ at the mean diameter. The optimum regime in this case also corresponds to small values of the recovered head ($\bar H =$

*) Over a wide range of variation of the blade-setting angles, experiments with a pair of counter-rotating wheels were carried out earlier at TsAGI.

Fig. 5. Influence of changes in the blade angles of a pair of counter-rotating wheels on their characteristics.

\(= \dfrac{\Delta p}{\rho u^2} = 0.140\)) and the dimensionless flow rate \(\left(\bar Q = \dfrac{Q}{Fu} = 0.213\right)\). The pressure characteristic of the pair of wheels at increased blade-setting angles \((\Theta'/\Theta'' = 26^\circ/23^\circ)\) lies, as was to be expected, considerably higher. The optimum values of \(\bar H\) and \(\bar Q\) here are respectively 0.172 and 0.225, but in this case signs of unstable operation already appear in the left-hand part of the characteristic. The efficiency under these conditions, which are off-design for the given pair of wheels, decreases noticeably, but nevertheless remains still sufficiently high.

The experiments of series \(a_{1-2}\) were carried out in order to establish the optimum value of the axial dimension \((a_{1-2})\) between the blades of counter-rotating axial wheels. Increasing this dimension up to a certain limit could improve the operating conditions of the second wheel, ensuring equalization of the flow, whose uniformity is disturbed by passage through the blade lattice of the first wheel. However, friction against the wall in the clearance between the wheels must spin down the flow leaving the first wheel, which entails the loss of part of the swirl energy.

Figure 6 presents the results of the corresponding experiments at axial dimensions \(a_{1-2}\) of 14, 50, 70, and 113 mm. When the wheels were moved apart, the gap between them was kept “closed”: it was filled by an attachment ring \(K\) rotating together with the first wheel (see the diagram in Fig. 6). Examination of the corresponding curves shows that the pressure characteristic of the pair of counter-rotating axial wheels changes insignificantly within the investigated limits of the dimension \(a_{1-2}\); in its working part the curves corresponding to different values of \(a_{1-2}\) practically coincide, while their distortions in the region of small flow rates are not regular and apparently have a random character.

As for the efficiency, the corresponding curves also agree rather closely. Nevertheless, a certain tendency may be noted for the maximum efficiency to increase when \(a_{1-2}\) is increased to 50–70 mm (which in this case corresponds approximately to one chord length of the blade profile of the first wheel at the mean diameter) and to decrease with a further increase in the dimension \(a_{1-2}\).

The dimension \(a_{1-2}\) to a considerable extent determines the noise characteristic of a pair of counter-rotating axial wheels when they operate in an air stream. At \(a_{1-2} = 14\) mm and a speed \(n' = n'' = 3700\) rpm, which corresponds to a peripheral speed at the blade tips of \(u_R = 77.1\) m/s, the intensity of the noise generated by the VDV-E model when installed in a steel chamber (playing the role of a resonator) reached 105–106 dB; moreover, this noise had a high tonality and a whistling character, acting very unpleasantly on the organs of hearing. The sound pressure decreased somewhat with an increase of the dimension \(a_{1-2}\) beyond 50 mm, falling to 102–103 dB at \(a_{1-2} = 70\)–113 mm. Very significant, however, is the circumstance that with an increase in \(a_{1-2}\) the frequency characteristics of the noise are noticeably lowered: the pair of counter-rotating axial wheels at \(a_{1-2} = 50\) mm already produces a low-pitched noise, whose physiological effect is less perceptible.

Figure 7 presents the noise characteristic of the investigated pair of counter-rotating axial wheels when operating in an air stream with axial dimension \(a_{1-2} = 70\) mm. Here also, a separate point marks the sound pressure at \(a_{1-2} = 14\) mm and \(n' = n'' = 3700\) rpm.

Fig. 6. Effect of the axial distance between a pair of counter-rotating axial wheels on their characteristics.

The microphone of the sound-level meter was installed at a distance of 1300 mm from the center of the counter-rotating wheels (see the diagram in Fig. 7).

On the basis of experiments with variation of the clearance between counter-rotating axial wheels in an air flow, it may thus be recommended that this clearance be set no smaller than the chord length of the profiles at the mean diameter, which ensures the highest efficiency and more favorable noise characteristics.

Series B experiments were carried out in order to determine the possibility of regulating the output of the machine by switching off the drive of one of the counter-rotating wheels. The wheel with the disconnected drive then rotated freely in the flow created by the other wheel.

Fig. 7. Noise characteristic of the experimental model VDV-E.

Figure 8 gives the results of such experiments. Disconnecting the drive of the second wheel gives a smaller reduction in the pressure characteristic and efficiency than disconnecting the drive of the first wheel. This is explained by the fact that, when the second wheel rotates freely, the inlet to the first remains normal (axial) for it, which ensures that it generates sufficiently high pressures and operates at a relatively high efficiency under conditions close to the design conditions. Disconnecting the drive of the first wheel, which may then rotate freely, substantially changes the inlet conditions to the second wheel relative to the design conditions, and this significantly reduces the pressure generated by it and the efficiency of the system.

Thus, obtaining three characteristics that differ substantially from one another, as presented in Fig. 8, is not accidental and can be used for the purpose of regulating the output of a machine with a pair of counter-rotating axial wheels. When such a pair operates on some network, it is possible to provide three modes: with normal operation of both wheels, with the drive of the second switched off, and with the drive of the first switched off. If the network characteristic is taken to be quadratic and passing through the point of the optimal operating regime of the pair of wheels, then switching off the drive of the second wheel, as is evident from the characteristics in Fig. 8, ensures a reduction in prod-

capacity to 75% of normal, and switching off the drive of the first—to 61%.

How much more economical such a method of regulation is than ordinary throttling becomes evident if one compares the corresponding energy expenditures, determined in each case by the quantities \(Q\), \(H\), and \(\eta\). Switching off the drive of the second wheel makes it possible to operate at 75% output,

Fig. 8. Switching off the drives of the first and second counter-rotating axial wheels.

reducing the energy consumption by a factor of 2.3 in comparison with that under the corresponding throttling, and switching off the drive of the first wheel (at an output of about 60%)—by a factor of 3.2.

If smooth regulation of capacity is necessary, a combined method may be recommended—with throttling in the intervals between the three operating modes considered above.

Experiments of series \(H\) were carried out with independent operation of each of the counter-rotating wheels, when the second was removed from the flow. The results of these experiments make it possible not only to compare the independent characteristics of each of the wheels with the characteristic of their pair

In-figure notation and labels: \(\bar H=\dfrac{\Delta p}{\rho u^2}\); \(\eta\), \(100\%\); \(88\%\); \(82\%\); “pair of two wheels”; “I wheel”; “pair of two wheels (experiment)”; “recalculation”; “one I wheel”; “one II wheel”; \(\bar Q=\dfrac{Q}{Fu}\).

Fig. 9. Independent and combined operation of a pair of counter-rotating axial wheels according to experimental data and by calculation.

the independent characteristics of each of the wheels with the characteristic of their pair (Fig. 9), but also to verify the possibility of obtaining the latter by recalculation from the former.

The essence of the method developed by the author for such recalculation is as follows. The operating conditions of the first wheel and the pressure rise it produces at a given capacity \(Q\) (and the corresponding axial velocity \(c_a\)) are taken to be the same both in its independent operation and in pair with the second wheel (axial inlet). To estimate the pressure rise produced by the second wheel, similar regimes (at identical \(\beta''\)) are considered:

a) in its independent operation with axial inlet \((Q_0, c_a^0, \Delta p_0'', \Delta c_u^0)\), and
b) in pair with the first wheel \((Q, c_a, \Delta p'' \text{ and } \Delta c_u'')\).

From the corresponding velocity triangles (Fig. 10) we obtain:

\[ x=\frac{Q_0}{Q}=\frac{c_a^0}{c_a}=\frac{u}{u+\Delta c_u}=\frac{\Delta c_u^0}{\Delta c_u''}. \]

Fig. 10. Velocity triangles of the second of the counter-rotating axial wheels during independent operation and operation together with the first wheel.

The pressure rise produced by the second wheel will then be:

in regime a)

\[ \Delta p_0''=\rho u \Delta c_u^0 \eta_i^0; \]

in regime b)

\[ \Delta p''=\rho u \Delta c_u'' \eta_i''. \]

Taking the above into account, for each capacity considered:

1) from the characteristic for independent operation of the first wheel we find \(\Delta p'\) and \(\eta_i'\);

2) assuming, as an approximation, that \(\eta_i \approx \eta_i'\), we calculate

\[ \Delta c_u'=\frac{\Delta p'}{\rho u \eta_i'}; \]

3) we calculate the ratio

\[ x=\frac{u}{u+\Delta c_u'} \]

and find \(Q_0=xQ\);

4) at \(Q_0\), from the characteristic for independent operation of the second wheel, we find \(\Delta p_0''\) and \(\eta_i^0\);

5) assuming that for similar regimes \(\eta_i^0=\eta_i''\), we find

\[ \Delta p''=\frac{\Delta p_0''}{x} \]

and determine the total pressure rise

\[ \Delta p=\Delta p' + \Delta p'', \]

produced by the pair of counter-rotating wheels at the given capacity \(Q\).

The results of such a recalculation, plotted as points in Fig. 9, are compared with the experimental characteristic of a pair of counter-rotating wheels. In the working portion of this characteristic, as can be seen, good agreement is obtained.

In the left-hand portion of the characteristics (with the former blade-setting angles: \(\Theta' = 23^\circ\) and \(\Theta'' = 20^\circ\)), the characteristic feature is the presence of saddle points when the wheels operate independently and the smooth course of the curve \(\overline{H}(\overline{Q})\) when they rotate in opposite directions. This also explains here the noticeable discrepancy between the experimental characteristic of the wheel pair and the results of the above recalculation, which is thus applicable only to the working portion of the characteristics.

Comparison of the Author’s Experimental Material with Other Studies

Comparing the author’s experimental results described here with the material of other experimental studies on a pair of counter-rotating axial fan wheels, it should be considered that they complement and confirm one another.

The extensive experimental material of the TsAGI fan laboratory (1951), which remained unpublished, relates to tests with counter-rotation of standard axial-fan wheels at strictly identical numbers of revolutions and with identical numbers of blades on each wheel. The use precisely of standard wheels (and not wheels specially designed with calculation for counter-rotation) evidently explains the somewhat lower efficiencies obtained here than in the author’s experiments, and the preservation of the region of unstable operation on the pressure characteristic down to smaller blade-setting angles than in the author’s experiments. The reduction of this region of unstable operation owing to the use of counter-rotation, the obtaining, under counter-rotation, of higher, than in single-stage fans, and practically identical to two-stage fans, total efficiencies (but of noticeably higher static efficiencies under counter-rotation), the reduction of noise when the counter-rotating wheels are offset, and, finally, the possibility of stepwise regulation of the output of a pair of counter-rotating wheels are also established by the TsAGI experiments.

The experimental material published in 1955 by A. P. Artsykov [5] also relates only to tests with strictly identical numbers of revolutions of counter-rotating wheels of axial fans when these wheels are mechanically driven from a common shaft. Of particular interest here is the comparison of the characteristics and efficiencies of experimental models with counter-rotation and of those built according to the usual scheme (two stages of one-directional rotation with guide vanes), calculated for practically identical operating conditions. The pressure characteristic under counter-rotation, in its working portion, is steeper than under one-directional rotation (the same explanation of the causes is also noted in the TsAGI experiments). According to A. P. Artsykov’s experiments, the maximum efficiency under counter-rotation is 5–7% higher than under one-directional rotation, and reaches approximately the same values as in the author’s experiments (86–88%). The presence of clearly expressed saddle points on the pressure characteristic of a pair of counter-rotating wheels of an axial fan in A. P. Artsykov’s experiments is explained by the use here of larger blade-setting angles. An increase in the axial distance between the blades of the pair of wheels from 45 to 310 mm, according to A. P. Artsykov’s experiments, leads to a certain decrease in pressure and to a reduction of the maximum efficiency. This also corresponds...

corresponds to the author’s experiments, according to which the maximum efficiency is obtained at an axial distance of about 50 mm, while dimensions considerably smaller than this value were also covered. Analyzing the noise characteristics of axial fans of various types, A. P. Artsykov comes to the conclusion that, for the same head effect, counter-rotation provides more favorable noise qualities.

Conclusions

Summing up all the experimental materials considered above, one may conclude that, with counter-rotation of axial wheels:

a) it is possible to create higher head coefficients

\[ \bar H = \frac{\Delta p}{\rho u^2}; \]

b) the head characteristic is more steeply falling;

c) it is possible to narrow the limits of unstable operation that produce dips in the head characteristic, and, at moderate angles, to obtain smoothly flowing characteristics with no dips at all;

d) higher efficiencies are achieved than in single-stage machines, and efficiencies somewhat higher than in two-stage machines with straightening apparatuses;

e) with independent drive of each of the wheels, by switching off the drive of one of them, it becomes possible to provide stepwise regulation of capacity—three-step regulation for a pair of wheels, with flow rates of 100, 75, and approximately 60 percent of the maximum; this stepwise regulation when operating at reduced flow rates is considerably more economical than throttling;

f) the axial distance between the blades of the impellers is recommended to be set approximately equal to the chord length of the profile of the first wheel at the mean diameter; for medium-sized fans, good results are thereby obtained at a distance of about 50 mm;

g) the frequency characteristic of the noise produced by a pair of axial wheels in an air stream is lowered when they are axially separated; the possibility of using (with counter-rotation) lower peripheral speeds makes it possible also to reduce the overall noise intensity in comparison with fans of the usual type.

All this leads to the conclusion that the use of counter-rotation of axial wheels under certain conditions may be expedient both in fans and in axial machines of other types (air blowers and exhausters, axial compressors, pumps, and some types of hydraulic turbines). The experimental material presented here, with the use of similarity methods, may be applied in the calculation and design of all these axial machines with counter-rotation of the impellers.

References

1. Yu. N. Sokolov. On axial machines with counter-rotation of impellers. Proceedings of the Tomsk Polytechnic Institute, vol. 80, 1955.

2. Yu. N. Sokolov. On the application of counter-rotation of impellers in axial compressor machines. Proceedings of the Conference on Aircraft Blade Machines, Oborongiz, 1958.

3. Yu. N. Sokolov. Calculation of axial machines with counter-rotation of impellers. Proceedings of the Tomsk Polytechnic Institute, vol. 109, 1960.

4. R. R. Holbeche. A New Approach to Axial Flow Fan Production. Modern Power and Engineering, Vol. 47, No. 10—11, October—November 1953.

5. A. P. Artsykov. Operation of a two-stage axial fan with counter-motion of the wheels. Proceedings of the Leningrad Shipbuilding Institute, issue XVII, 1955.