Turgo Paper
Turgo Paper
Turgo Paper
the end of the sixteenth century (Fig. 1a). The water jet enters
Abstract—The incorporation of computational fluid dynamics in one side of the runner and exits through the other (Fig. 1b).
the design of modern hydraulic turbines appears to be necessary in This allows for a more efficient escape of 'used' water, which
order to improve their efficiency and cost-effectiveness beyond the does not interfere with the incoming jet. Hence, larger jet and
traditional design practices. A numerical optimization methodology
flow rates can be treated compared to a Pelton runner of same
is developed and applied in the present work to a Turgo water
turbine. The fluid is simulated by a Lagrangian mesh-free approach diameter. As a result, a Turgo turbine has higher specific
that can provide detailed information on the energy transfer and speed and smaller size than a Pelton turbine for the same
enhance the understanding of the complex, unsteady flow field, at power. This compensates for its more complex design and
very small computing cost. The runner blades are initially shaped more difficult manufacturing process. Moreover, the smaller
according to hydrodynamics theory, and parameterized using Bezier runner diameter allows to obtain a higher angular velocity, so
polynomials and interpolation techniques. The use of a limited
that the turns multiplier in the coupling with the electrical
number of free design variables allows for various modifications of
the standard blade shape, while stochastic optimization using generator can be avoided, decreasing the costs and increasing
evolutionary algorithms is implemented to find the best blade that the mechanical reliability of the system.
maximizes the attainable hydraulic efficiency of the runner. The
obtained optimal runner design achieves considerably higher
efficiency than the standard one, and its numerically predicted
performance is comparable to a real Turgo turbine, verifying the
reliability and the prospects of the new methodology.
I. INTRODUCTION
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World Academy of Science, Engineering and Technology 28 2007
70-80 o
II. RUNNER DESIGN & PARAMETERIZATION
The mean velocity of the free jet emerging from the nozzle (a)
of the turbine is determined from the net head, by the equation
[5]:
c1=c w1
c = φ ⋅ 2 g H ≈ 0,97 ⋅ 2 g H (1)
β1
β1
u1
where φ is the efficiency of the nozzle, taken here equal to
u
0,97. The corresponding jet diameter, d, can be obtained from
the nominal flow rate:
π 2 β2
QK = ⋅d c (2) w2
4 c2 β2
At the best efficiency point the circumferential speed of the u2
runner is connected with the jet velocity via the relation [5]:
(b)
u1 ≈ (0,46 − 0,47) ⋅ c (3)
Hence the diameter of the runner is (Fig. 2a): Fig. 2 Turgo runner configuration:
(a) Meridian plane (b) Velocity triangles
60 u1
Ds = (4)
πn The mean 3-dimensional surface of the blade is then
generated using the conformal mapping methodology in a
where n is the runner speed in rpm. number of meridian streamlines, and assuming a linear
The runner has a conical shape in the meridian plane (Fig. variation of the blade angle from the leading to the trailing
2a). The inlet blade edge is a straight line and the inlet width edge. An example of the resulting shape is shown in Fig. 3.
is larger than the jet diameter (b1 = 1,2 d), in order to secure The leading edge line is represented by a parabolic function
the entrance of the entire jet even for the highest flow rate. and has adjustable curvature (Fig. 3).
The runner width in the axial direction is taken B ≈ 1,45 d,
and the outlet edge of the blade is drawn with the aid of a
Bezier curve (Fig. 2a). The blade traces on the hub and the
shroud are also generated using corresponding Bezier
polynomials.
The blade inlet and outlet angles, β1 and β2, can be
computed from the corresponding velocity triangles (Fig. 2b).
At a given radial distance r, the runner peripheral velocity is:
u1 = 2πnr, whereas the absolute inlet flow velocity c1 = c, and
its angle relative to the runner disk is: α1 = 25 deg, for the
examined turbine. At the best efficiency point the flow exits
with zero circumferential velocity, hence the outlet velocity Fig. 3 Indicative view of mean blade surface
triangle is orthogonal and can also be constructed (Fig. 2b).
Next, the inner and outer surfaces of the blade are
constructed considering a given blade thickness distribution,
assumed here constant (Fig. 4). The leading edge is rounded
to a semi-elliptic shape.
Finally, the hub and the shroud are easily introduced as
axisymmetric surfaces, and the entire runner can be
reproduced as shown in Fig. 5.
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World Academy of Science, Engineering and Technology 28 2007
0.2
The starting points of the particles are uniformly distributed
within the jet volume, and the time integration starts when the
first particle of the jet impacts on a reference blade. Due to the
0.3
rotation of the runner, the rest particles impact at different
time instants and with different relative angles and velocities
X
(Fig. 6).
0.4
0.5
0.1
Z
0
02
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World Academy of Science, Engineering and Technology 28 2007
independent results for the hydraulic efficiency of the runner, the jet starts to interact with the next coming blade too (not
whereas for the reproduction of the surface flow pattern an shown in Fig. 7), which eventually cuts the jet (Fig. 7c). A
order of magnitude more particles are tracked. remarkable behaviour that can be observed is that the fluid
The mechanical torque Mnum on the runner shaft is leaves the blade from quite different regions during the
computed from the conservation of momentum: interaction period (Figs. 7b,c,d), because of the blade
elevation due to rotation. Therefore the correct design of the
(
M num = ρ Qu ⋅ rin win − rout wout ) (5) entire trailing edge line is decisive in order to achieve high
efficiency.
where Qu is the cumulative flow rate that enters each blade.
The mean angular momentum at the inlet, assuming a
uniform, constant speed jet flow, becomes:
where Vjet is the mean jet flow velocity, Rj-r is the normal
distance between the jet and the runner axis and φjet is the jet
inlet angle relative to the runner disk. The mean angular
momentum at the blade outlet is computed by averaging the
local fluid particle properties there:
(a) (b)
1
rout wout ≅
N
⋅ ∑
i
y out ,i wout ,i (7)
where yout,i and wout,i are the radial distance and the relative
tangential velocity component, respectively, of a particle i at
the moment it flows out of the blade, and N is the total number
of fluid particles that impinge on the inner blade surface. The
overall hydraulic efficiency of the runner is obtained as the
ratio of the developed mechanical power on the shaft, divided
by the corresponding net hydraulic power provided at the
inlet:
(c) (d)
M num ω
ηh = (8)
ρgQH Fig. 7 Selected flow pictures: a) initial jet-blade interaction; b) full
jet impingement; c) end of jet impingement; d) clearance phase
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World Academy of Science, Engineering and Technology 28 2007
remain constant and equal to the blade angle β1 during the jet- diagram drawn in Fig. 11 agrees well with the manufacturer
runner interaction. curves (Fig. 9), at least for high loads, above 500 lt/sec.
80
80
Net head (m)
60
80 84
75
40 70
65
60
20
100 350 600 850 1100
Flow rate (lt/sec)
Fig. 9 Efficiency (%) chart of the real turbine
(b)
Fig. 10 Comparison between the standard (a), and the optimal
IV. OPTIMUM RUNNER DESIGN runner (b)
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World Academy of Science, Engineering and Technology 28 2007
V. CONCLUSION
An effective and fast computational methodology based on
the Lagrangian approach is developed and applied for the
simulation and detailed analysis of the complex, unsteady,
free-surface flow that evolves in the runner of a Turgo turbine.
A standard runner design created by applying the
hydrodynamics theory was found to be reasonable in shape
and performance but not very efficient, while its best
efficiency point is far from the desired operating conditions.
The blade geometry is parameterized using 11 design
variables, and the combination of their values that maximizes
the hydraulic efficiency of the runner is found using a
powerful, stochastic optimization tool. The obtained improved
runner exhibits remarkably higher efficiency than the standard
design, and its characteristic curves are close to the
corresponding ones of a real Turgo turbine.
A more elaborate modeling of the free-surface flow in the
blades and of the jet structure at some complex regions is
required to develop further the present numerical design
optimization methodology, which appears to be very
promising in order to improve the design process and the cost-
effectiveness of this water turbine.
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