Bladeless Hydraulic
Bladeless Hydraulic
Bladeless Hydraulic
Applied Energy
journal homepage: www.elsevier.com/locate/apenergy
Faculty of Civil Engineering, CTU in Prague, Thkurova 7/2077, 166 29 Praha, Czech Republic
Institute of Thermomechanics, ASCR v.v.i., Dolejkova 5, 182 00 Praha, Czech Republic
h i g h l i g h t s
" The rotating motion without using any turbine blades.
" The theoretical explanation of hydraulic principle is rst and unique.
" Low manufacturing turbine costs, especially rotor.
" The turbine is capable of utilizing small water sources, low water gradient.
a r t i c l e
i n f o
Article history:
Received 20 February 2012
Received in revised form 21 November 2012
Accepted 4 December 2012
Available online 18 January 2013
Keywords:
Rolling turbine
Low head hydro power
Stability of ow
Water turbulence
Whirlpool principle
Bladeless hydraulic turbine
a b s t r a c t
A water turbine constructed on the water turbulence or whirlpool principle is capable of utilizing very
small sources even for untapped water, and it is highly suitable for the closed circuit production of electrical energy. The non-monotonic distribution of the radial velocity component is important for the onset
of the driving force of the angular instability. This instability and the existence of the radial uid motion
give rise to the angular volume force. The strong gradient of entropy in the boundary layer of the inner
rotating conical cylinder is a dominant source of vorticity. The solution presented as a result of the theoretical analysis includes discussion and comparison with rough preliminary experimental data. The
rotating uid action is obviously of interest for further research. An improvement in efciency is the genuine motive for further research.
2012 Elsevier Ltd. All rights reserved.
1. Introduction
The process of hydrokinetic energy conversion implies utilization of kinetic energy contained in river streams, tidal currents,
or other man-made waterways for generation of electricity [1]. In
recent years we have tended to encounter some new approach towards energy production, and this is usually found in an effort to
use smaller amounts of renewable resources, in various marginal
sources of water potential (waste-water treatment plant, small
streams and creeks). From this viewpoint we focused on a very
small rolling liquid turbine, which could bring about a certain benet from these non-traditional potentials. It has already been veried in practice that it is technically feasible to sufciently convert
very small water potentials (read low ow capacity and hydraulic
gradient) to an effective output. It can deal with both the case of
renewable energy, for example of a mountain stream, and the case
Corresponding author.
E-mail addresses: beran@fsv.cvut.cz (V. Beran), sedlacek@fsv.cvut.cz (M. Sedlcek), marsik@it.cas.cz (F. Marsk).
0306-2619/$ - see front matter 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.apenergy.2012.12.016
of hydropower, and which has been until now thwarted as a nonutilized potential in various systems of the production process or
within the framework of the operation of higher buildings, etc.
One of the biggest energy consumers in modern society are the
so called statistically average households. A particular effort towards lowering the energy dependence of member states of the
European Community can already be recorded in connection with
Directive No. 93/76/EEC. It has been recently replaced by Directive
2006/32/EC of the European Parliament and of the European Council of 5th April 2006 on energy end-use efciency and energy services. The resulting instrument involves two basic interpretations
leading to the certication or categorization of buildings, but also
to a change of attitude towards energy consumption and usable
renewable resources in their entirety. Energy dependence of the
countries of EU-27, however, continues to grow. EU-27 energy
imports grew within the year 2006 by 2.4% and total energy dependence has grown by 54% that is around 1% per year.
The year 2007 shows a decrease of 0.7% but with the further
years 2008 and 2009 we are witnessing growth of dependency
by +1.7% and in 2009 a small decrease 0.8%. In the long-term
979
Nomenclature
r
u, /
z
t
x
v
w
p
f
L
R1
R2
Re
Q_
ht
s
u
b
Special characters
m
kinematic viscosity (m2 s1)
q
uid density (kg m3)
c
gradient of the channels divergence ()
x
phase frequency (s1)
X
angular velocity of the rotors precessions (rad s1)
X1
angular velocity of a rotor around its axis (rad s1)
When searching for sources of energy it is obvious that hydraulic engines fulll the limits and hydro energy fullls requirements
for the renewable nature of an energy source [4].
Requirements of emission The EU includes among renewable
resources energies that are (a) solar, (b) geothermal, (c) wind, (d)
hydropower see Ref. [25], (e) biomass. The structure of consumption is given in Fig. 3. Hydro-energy is currently the second biggest
commodity of renewable energy. At the same time, however, the
hydro-energy of water ows in Europe is considered to be exhausted, at least in respect of the potential of the bigger energy resources. Energy resources with a low energy potential were in the
last century part of a depleting commodity, see islanding detection,
distributed generators in Ref. [3]. The accessibility of power energy
at relatively low prices pushed to the background its actual
externalities.
2. Description of the machine
Fig. 1. Relative frequency of the concepts of water wheel (upper graph) and water
turbine (lower graph). (Source: Authors processing of the data: Scopus, Web of
Knowledge, and Google)
The rotor and the stator create in a quiescent state a symmetrical coaxial diffuser as shown in Figs. 4 and 5. However, this state is
unstable and as a consequence of the instability of the ow
through the gap between the rotor and the stator it changes to
an asymmetrical one. The shape of the rotor and stator can be variable (i.e., it might be improved or optimized). In practice the most
common rotors are hemispheres as in Fig. 4, but what really matters is the diffusion angle of the gap between the rotor and the stator. One tip of the rotors shaft is xed, so that the rotor can roll
along the inner side of the confuser. When the uid ows along
the rotor, then due to the ow eld instability, the uid starts to
Fig. 2. Average frequency of the terms water energy and water engine and water motor.
980
Fig. 5. Simplied scheme of the turbine. Fluid ows between the inner cone and the
outer cylinder. In practice more complicated shapes of the rotor and stator have
been developed but this gure shows the most important feature of the machine
the diverging non-symmetrical gap crucial for the appearance of volume forces
responsible for the rotation.
Fig. 4. The basic position of the rotor at start and the deviated position of the rotor in motion. This shape of rotor is usual for contemporary turbines in praxis but on the other
hand for theoretical analysis conical shape is more suitable [14].
981
the detail see Eq. (7). The number of precessions can be simply
changed by changing the width of the gap. In the case of a conical
stator this can be done by changing the vertical position of the rotor; see Fig. 4. The rst conception of rolling turbines used a rotor
hanging in the entry part of an outlet nozzle. The diameter of the
rotor for example can be just several centimeters or millimeters.
Water ow rates can change usually from units to tens of liters
per second.
The advantage of such a uid motor lies especially in its simplicity and in the possibility to rotate with a working tool and at
the same time to move it in a precession way. It relies only on
the constructional arrangement of the rotor and outlet nozzle if
the number of shaft rotations or number of precessions is needed
for the technological process [13,14,15,16].
3. Theoretical analysis of rolling turbines performance
The volume forces f fr ; fu ; fz generated in the ow eld
can be easily formulated by Croccos theorem
[17,18,19]. In case the radial component of vorticity is zero the
angular component of the force in the cylindrical coordinates
r; u; z has the following form
v v r ; v u ; v z
@ vu
@hc
@s
T
m
v wu v r wz fu
r@ u
r@ u
@r2
N
;
kg
J
/
kg
2
v2
wz
v z x; u; z b0
qx
bz
0
v r x; u; z b z1 xv z x; u; z
where the function q satises the equation
X21
where
ht u
1 z
a function bz R2 R
which is directly proportional to the width
2R2
of the channel between the cylinders. The approximate solution
can be written as
@r v u @v r
r@ u
r@r
v r 0; v u
X1 rR21
R22 R21
vz 0
v r ; v u ; v z v z max v~ r ; v~ u ; v~ z :
Reynolds number is dened as Re v z max Rm2 R1 z. In order to obtain an approximate analytical solution a new radial coordinate x is
introduced. It is bound with the coordinate r by a linear mapping in
such a way that x = 1 on the surface of the inner cylinder and x = 1
on the surface of the outer cylinder. At the same time we introduce
2
@v z @v r
@v z
@r @z
@z
!2
cb0v z max
2
2b zR2
qq 1 xq0 P 0
in the outer half of such channel is @@rv z < 0, see Fig. 3b. When the
inner cylinder is supported only at the bottom, its position in the
center of the outer channel is unstable and the inner cylinder starts
to roll along the inner side of outer cylinder with the frequency
!
R22
1
;
r2
r @r
in the axial direction. To elucidate better the performance of a rolling turbine we start from the Couette ow between two coaxial cylinders. The most interesting is the viscous ow (with kinematic
viscosity m), when the inner cylinder of radius R1 revolves with
the angular velocity X1 and the outer cylinder of radius R2 is steady.
The ow eld is described as follows
v r @v r
R1 0
X1
R2 R1 0
X1
R1 L R1 0 v z max
Q
R2 R1 0
2L
pqLR22 1 g20
The formula (8) is analogous to the well-known Strouhal relation for the frequency of the periodical disturbances in wakes behind the bluff body, i.e., Sh = X1L/vz max 2 (0.15, 0.4) (see Fig. 5).
Regarding any actual power of the machine it has been properly
measured only for a turbine with a spherical rotor, where the
application of the above theory is limited. Nevertheless, the simplied derivation ts the experimental data in the operating range
satisfactorily, see Fig. 6. The dependence of the power output is
shown in Fig. 7. The theoretical (ideal) mechanical power of owing water at the ux rate Q_ 6:7 kg s1 on hydraulic head
:
H = 3.6 m is Pid Q_ gH219 W. The efciency of the machine was
higher than 55% (losses in the feeding pipes were not included).
Due to a sudden drop of pressure on the rotor, the danger of
cavitation can arise [20]. This problem is now solved in detail both
theoretically and experimentally in our laboratory. The more detailed theoretical analysis and the preliminary experiments supporting this new principle will be presented soon in the full paper.
982
Fig. 6. Velocity proles (a) and corresponding frequency of wave-like disturbance (b) for coaxial cylinders. In the case of a converging gap between the cylinders the product
cRe is negative (dash-dotted lines for cRe = 20), in the case of a diverging gap the product is positive (dotted lines for cRe = 20). The solid line shows zero case cRe = 0, i.e.,
PoiseuilleCouette ow between two coaxial cylinders. The instability may appear only in the area, where x2 > 0.
Fig. 7. Power output dependency on a ow rate for water head H = 3.6 m shows that the maximum efciency of the machine is about 55%.
4. Conclusion
Questions of independent energy resources are not just a theoretical or marginal problem. Independent and substitute resources
are connected with security and with preserving the functionality
of constructions such as tunnels, bridges, the telemetric of highways, civic and housing constructions [11,2123]. A separate question is decreasing energy demand in EU countries [4]. Member
states accepted for the eighth year running the application of the
Directive and the European Parliament and Council 2006/32/ES
aiming at 9% energy reductions [25]. The given aim is achievable
only by increasing energy efciency with the nal user in the public sector. The above named constructions especially at the level of
public demands [24,26] have the possibility to effectively contribute to the fulllment of national aims [1], see also decentralized
energy planning [5]. Besides the described energy application, it
is also possible to use rolling micro-turbines as a motor for the propulsion of various tools. Ecology and sustainability might be im-
based not only being consumer-friendly but in the areas of production and distribution too. The concept of dispersed energy creation
is desirable from many points of view [29]. It was declared as an
independent class of goal-directed research for MIT at the end of
the last decade. It was called micro-electro-mechanical systems
(MEMSs). So far little has changed in the applied energy strategies
of companies producing electric power energy. Such a strategy
probably can be hardly expected, see energy investments [6].
The selected support of small energy sources does exist to a certain extent through the so-called subsidized purchase of energy
from small sources [710,12]. Mini-hydro sources can be one of
those similar initiatives. The contribution of Williamson et al.
[10] presented in their Fig. 1 the range of water turbine efciency,
and in this paper the presented mini-turbine is able to occupy up
to now the southwest part of the remaining vacant working area
of the hydraulic space.
Acknowledgements
This paper originated as part of a CTU in Prague, Faculty of Civil
Engineering research Project on Management of sustainable development of the life cycle of buildings, building enterprises and territories (MSM: 6840770006), nanced by the Ministry of
Education, Youth and Sports of Czech Republic and by the grant
of the Czech Science Foundation No. 201/10/0357 and the pilot
Project 902 121 of the Institute of Thermo mechanics, Czech Academy of Sciences. We also wish to thank Jir Falta for his help with
editing this paper.
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