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International Journal of Engineering & Technology, 7 (4.38) (2018) 305-308
International Journal of Engineering & Technology
Experimental Study of Pneumatic Two-Stage Small-Size Radial
Yuri Pavlovich Kuznetsov1*, Lev Anatolevich Zakharov1, Sergey Nikolaevich Khrunkov1, Artem Aleksandrovich
Kraynov1, Aleksandr Evgenevich Zhukov1
1Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Minin Str., 24, Nizhny Novgorod, 603950, Russia
*Corresponding author E-mail: firstname.lastname@example.org
This work is aimed at experimental study of the influence of design variables of the first jet reaction stage on the properties of pneumatic
two-stage small-size radial turbine. Kinematic layout of the considered turbine is presented, operating processes are described, the final
target is formulated to reveal the influence of certain geometrical parameters of the first jet reaction stage which determine overall
turbine efficiency. Criterion of nozzle efficiency is determined, variable parameters of multifactorial experiment are selected;
experimental facility and procedure of data processing are described. The main experimental results are presented. It is established that
the greatest influence on the turbine efficiency is exerted by supersonic nozzle expansion angle. Optimum combination of geometrical
expansion extent and geometrical expansion angle of supersonic nozzle of the first jet reaction stage of two-stage small-size radial
turbine has been experimentally determined.
Keywords: pneumatic drive, turbine drive, jet reaction turbine, Segner wheel, radial turbine, small-size turbine.
Small-size turbines of various kinematic layouts are presently
used in engine manufacturing (superchargers) and in cryogenic
engineering (helium and hydrogen turboexpanders), in aircraft
engineering (cooling turbines, small-size gas turbine engines of
drones) and in power engineering (Zysin turbines, small-size
turbogenerators), in oil and gas industry (ball valve drive) and in
auxiliary mechanisms with pneumatic drive for spacecraft and
submersible vehicles, in commercial pneumatic tools.
Numerous designs of small-size turbines have been developed
according to various requirements but the most advantageous
designs both in terms of manufacturing and efficiency are
multistage radial turbines. Blade system of radial pneumatic
turbine can be manufactured in press mold by die casting of
plastics which significantly reduces its cost upon serial
Aiming at manufacture of competitive pneumatic tool, the Chair
of power plants and thermal engines, Alekseev State Technical
University, Nizhny Novgorod developed and fabricated model
series of experimental manual pneumatic grinding machines.
Their main feature is the use of innovative two-stage radial turbine
where the first stage is comprised of radial jet reaction turbine,
and the second one - of radial centripetal turbine [1, 2, 3]. Both
stages are embodied on a single disk of operating wheel, which is
advantageous in terms of engineering and sizes of the design. This
kinematic layout provides efficient aerodynamic performances,
velocity and economic characteristics as well as possibility to
achieve almost any combination of power and rotation rate.
Kinematic layout of small-size two-stage radial turbine is
illustrated in Fig. 1.
Fig. 1: Kinematic layout of small-size two-stage radial turbine
As illustrated in the figure, working medium (compressed air) is
fed to the first stage (position 1) radially from the rotor center. In
fixed intermediate guiding apparatus (position 2) the flow gets
reversed and reaches the blade system of the second drive stage.
2. Analysis of Operation Processes
Predictions of variables of working medium flow along flowing
part of the two-stage pneumatic small-size turbine performed in
the scope of one-dimension stage theory have demonstrated that
the greatest contribution to the overall turbine efficiency is made
by the first stage: jet reaction rotating nozzle apparatus . In jet
reaction turbine the reaction force is created only by
circumferential projection of outlet velocity [5, 6, 7]. With the
increase in angle between the outlet velocity vector C and
direction of tangent line to operating wheel in the outlet point, the
tangent component of reaction force and, hence, turbine efficiency
sharply drop. Therefore, in order to increase turbine efficiency in
terms of design, it is necessary to provide the minimum angle of
flow outlet. Triangles of velocity vectors at skewed nozzle outlet
are illustrated in Fig. 2.
International Journal of Engineering & Technology
Fig. 2: Schematic view of working medium outlet from turbine nozzle
Contradictory impact of various design nozzle parameters of the
first jet reaction stage (such as the ratio of inlet to outlet nozzle
surface areas, nozzle length, position of nozzle axial line and some
others) on the properties of pneumatic small-size radial turbine
requires for experimental studies. The necessity to study
efficiency of jet reaction turbine is also related with the
dimensions: in small-size turbines, due to high relative roughness
and relative gaps, operation processes can be described
insufficiently using conventional predictions of pneumatic
3. Design of Experiment
Velocity factor of nozzle apparatus of jet reaction turbine (the
ratio of actual flow rate of working medium from nozzle to
isentropic flow rate from the same nozzle) was selected as the
target function. In order to reduce expenses for experiments, the
experimental design theory was applied. Variables (the considered
factors) of jet reaction turbine were selected on the basis of
analysis of a priori information on the influence of factors. Among
all geometric factors affecting turbine efficiency, such as
geometric angle of flow exit, expansion angle of supersonic
nozzle, length of nozzle sub- and supersonic portions, decrease
rate of air pressure in supersonic portion, the most significant ones
were selected. It is known that the variables of supersonic nozzle
have more significant influence on the efficiency of its operation
than the variables of subsonic portion. Hence, two factors were
selected for the experiments: geometrical expansion angle of
and geometrical channel expansion rate in
supersonic portion F/f, which was the ratio of outlet surface area
of the nozzle 1 to its critical surface area 2, Fig. 3. Other assumed
factors had either lower or known influence on the target function,
hence, they were assumed constant in the experiments.
Fig. 3: Factors for studying nozzle efficiency
The next task was determination of domain of the selected factors.
Expansion angle of supersonic portion can vary from γ = 0° to γ =
40°. These limits are of engineering character, since it is required
to install several nozzles on constrained surface of operating
wheel, leaving free segments in order to vary this factor. From the
same considerations, the domain boundaries of geometrical
channel expansion rate in supersonic portion F/f are from 1.0 to
The design of the first series of two-factor experiment, according
to the steepest ascent method, included 5 combinations of factors.
They were comprised of one reference point (point «0») and 4
points in the vicinities, covering all 4 main possible directions of
gradient vector. In order to define correctly parameters of
reference point, a priori information was very important. From the
point of view of gas dynamics, the optimum values of the selected
factors for reference point were as follows: γ=8…12°, F/f=1,53 [8,
9, 10, 11, 12, 13, 14], Fig. 4. In the first experimental series the
step for geometrical expansion rate F/f was set to ΔF/f=0.1, and the
step of geometrical expansion angle of supersonic portion γ was
set to Δγ=2°. According to the experimental design, 5 operating
wheels were developed and manufactured for the first
experimental series. The wheels were manufactured by 3D
printing. Drawings and photos of the experimental operating
wheels are shown in Fig. 5.
Fig. 4: Reference point and region of factor variation
Fig. 5: Experimental operating wheels:
a) – reference point, b, c), d), e) –points 1–4, f) – photograph of operating
4. Experimental Facility
The main properties of experimental turbines were determined on
the experimental facility for stages and blade systems of small-
size turbines  illustrated in Fig. 6. The considered nozzle
apparatus 5 is mounted in the body 4 into the coupling of gas
static suspension 8 which, due to gas layer, prevents mechanical
contact with the fixed rim 7 thus improving the accuracy of
measurements. Air is supplied to the gas static suspension via the
tubes 2. The working medium is supplied to the considered nozzle
apparatus via 3 tubes, position 3, located radially to the receiver in
120° in the plane perpendicular to cylinder axis. The labyrinth
sealings 6 are intended for decrease in air leakage from air supply
system to the nozzle apparatus. The torque created by the nozzle
apparatus is transferred to the moving coupling of the gas static
suspension 8 and is detected by the torque strain sensor 10.
Fig. 6: Experimental facility for studying the nozzle apparatuses: 1 –
receiver; 2 – air inlet tube to gas static suspension; 3 – air inlet tube to the
considered nozzle apparatus; 4 – body for mounting of nozzle apparatus; 5
– the considered nozzle apparatus; 6 – labyrinth sealing;
7 – static rim of gas static suspension; 8 – coupling of gas static
suspension; 9 – flange of gas static suspension; 10 – torque strain sensor.
While measuring torque created by nozzle apparatus, the torque
sensor of the facility detects cumulative flow rate of working
medium (flow rate across the nozzle apparatus and leakages
through labyrinth sealing) at pressure P0. In order to prevent
leakage through labyrinth sealing during measurements of flow
rate across the nozzle apparatus, a special device is used for direct
supply of working medium to the nozzle apparatus bypassing
sealing of gas static suspension and the torque measuring unit
while retaining pressure before the nozzle apparatus.
The layout of supply system and measuring instruments of the
experimental facility are illustrated in Fig. 7, overall view of the
facility – in Fig. 8. The manual tap, the air filter 2, and the
manometer 3 are installed in inlet channel of the supply system.
The supply system is subdivided into 2 lines separated from the
inlet channel by the electropneumatic valves 4 and 5 which protect
the facility against accidental starts with deactivated control
system. The first main line is intended for air supply to gas static
suspension, and the second one – to the experimental facility. The
second pipeline is equipped with the electropneumatic converter 6,
which controls the experiments, and with the instruments to
measure air flow rate and temperature. Therefore, the facility can
International Journal of Engineering & Technology
measure toque created by the nozzle apparatus, as well as
pressure, temperature, and flow rate of working medium.
Fig. 7: Schematic view of supply system and measuring instruments of
1 – manual tap; 2 –K4-10-50 manometer; 3 –EAF6000 filter; 4,5 –
pneumatic valve; 6 –ITV3050-21F4N electropneumatic converter with
pressure indication; 7 –PF2A703H-F10-28N flow meter; 8 – air inlet
collector to torque measuring unit; 9 –DS18B20 temperature sensor.
Fig. 8: Overall view of experimental facility
Integral parameters of the nozzle apparatus were predicted as
follows. The circumferential component of absolute velocity at
outlet from the nozzle apparatus is determined by equation of
flow torque in the nozzle apparatus:
where M is the torque measured on the experimental facility;
is the external radius of the centrifugal nozzle apparatus (in the
experiment: Rext=44 mm); G is the gas mass flow rate.
The radial component of absolute velocity at outlet from the
nozzle apparatus is determined by the continuity equation:
where G is the mass flow rate; F is the surface area of nozzles
determined by outlet cross sections of nozzles; is the real gas
density in outlet cross sections of nozzles.
Since the gas density at outlet from the nozzle apparatus in
actual process is unknown, then the additional interrelations
between the flow variables should be used for determination of
Let us consider the following method of determination of integral
parameters. Since the initial parameters of isentropic and actual
processes coincide, then the loss in nozzles can be determined as
1 1 01
( ) (1 )( )
is p is p is
ii СT T С T T
=−= − = − −
= 1 + (1
is the energy loss during actual expansion in the
is the enthalpy in final cross section of the
nozzle apparatus upon actual expansion ;
is the enthalpy in
final cross section of the nozzle apparatus upon isentropic
is the air mass isobar heat capacity;
temperature in the end of actual air expansion in nozzles;
the temperature in the end of isentropic air expansion in nozzles;
is the velocity factor.
The temperature in the end of isentropic air expansion in nozzles
is determined by the equation of adiabatic expansion:
* is the air braking temperature before the nozzle
apparatus; pa is the air ambient pressure; p0
* is the initial total air
pressure before the nozzle apparatus; k is the adiabatic exponent.
From the equation of state for gas parameters in the nozzle outlet
cross section, let us determine the gas density at outlet from the
where R is the gas constant, for air: R=287 J/kg·K.
Then, with consideration for Eqs. (3), (4), and (5), Eq. (2) is
rewritten as follows:
1 + (1ψ)(
By definition the nozzle velocity factor is:
Finally, we have a set of 2 equations, Eqs. (6) and (7), with 2
unknown variables: ψ and . The set is solved by iterations.
Knowing the velocity projections, it is possible to predict the
angle between the vector of flow outlet velocity and the tangential
line to operating wheel at the flow outlet point.
Taking into consideration the design requirements in the first
experimental series, the following combinations of geometric
variables of operating wheel were used, see Table 1. Table 2
summarizes the main results of the first experimental series. The
surface area of flow cross section of the nozzle apparatus for
various operating wheels was from 13.98 to 15.41 mm2, the air
temperature: +23°C, the ambient pressure: 0.100 MPa`, the
pressure before the nozzle apparatus: 0.321 MPa.
Table 1: F/f and γ factors for the first experimental series
Adopted absolute F/f
Adopted absolute γ
Table 2: Main results of the first experimental series
On the basis of the obtained results, the regression equation of the
first order was derived. The linear response function was adopted
in the first experimental series:
cfFba +⋅+⋅= )/()γ(ψ
International Journal of Engineering & Technology
since such form was required and sufficient for determination of
the function gradient. The obtained regression equation was as
ψ 0.01075 (γ) 0.03075 ( / ) 0.7818Ff= ⋅− ⋅ +
The gradient of response function based on the results of the first
experimental series is illustrated in Fig. 8. In the considered
domain of parameters it is possible to conclude that the velocity
factor depends more on the geometrical expansion extent than on
the geometrical expansion angle of supersonic nozzle of jet
For subsequent specification of optimum geometrical variables of
the nozzle apparatus, it is required to consider the combinations of
variable factors in accordance with direction of the
aforementioned gradient of the response function, see Fig. 9. With
consideration for design requirements in the second experimental
series, the combinations of geometrical variables of operating
wheels in Table 3 were adopted.
Fig. 9: Gradient of factors and experimental points
All experimental lines were positioned on the gradient line, each
subsequent point at higher distance from the reference point "0",
Fig. 9. Surface area of the flow cross section of the nozzle
appratus for various operating wheels was in the range from 14.56
to 15.01 mm2, the air temperature: +20°C, the atmospheric
pressure: 0.101 MPa, the pressure between the nozzle apparatus:
0.320 MPa. The main experimental results of the second series are
summarized in Table 4.
Table 3: F/f and γ for the second experimental series
Adopted absolute F/f
Adopted absolute γ
Table 4: Main results of the second experimental series
Air flow rate
Velocity factor of the nozzle apparatus increased up to point 6 and
then decreased. Therefore, while moving along the gradient
direction, the maximum of target function was passed and the
optimum combination of the considered geometric variables of
nozzle apparatus was determined.
While analyzing experimental data, it should be mentioned that
the greatest influence on the nozzle efficiency is exerted by
geometrical expansion angle of supersonic nozzle of jet reaction
turbine γ, this is indicated by the coefficients of appropriate
variables in regression equation. The obtained results agree with
the data of other researchers [16, 17, 18, 19, 20, 21] and provide
additional information. Herewith, the experimental point 6
provides the greatest efficiency of pneumatic two-stage small-size
radial turbine. Optimum combination of nozzle variables of the
first jet reaction stage of the considered turbine was determined
γ = 12°, F/f = 1.26.
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