Ejection effect in a low-head hydropower plant: turbine power and efficiency

Abstract

The aim of this research is to complement and improve the results about ejection effect in a low-head hydropower plant from a previous study in physical models and to evaluate the effect of ejection on the turbine power and efficiency, in the model alternative with the best performance. The study covers four additional geometric alternatives, aside from the original design and the six already tested alternatives in that study, using 1:70 scale model tests. Three approaches were considered: (1) The development of a theoretical equation for the ejection effect, based on the equations of conservation of momentum and energy, (2) An assessment of an empirical relationship for the effective ejection using dimensionless flow parameters from 521 flow scenarios and (3) The development of two empirical relationships between the effective ejection and the power and efficiency increments of the HPP turbines (63 flow scenarios).

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Ejection effect in a low-head hydropower plant:
turbine power and efficiency
Mauricio Romero, José Junji Ota, Tobias Bleninger, Paulo Henrique Cabral
Dettmer, Marcelo Luiz Noriller & Guilherme Moreira Grossi
To cite this article: Mauricio Romero, José Junji Ota, Tobias Bleninger, Paulo Henrique Cabral
Dettmer, Marcelo Luiz Noriller & Guilherme Moreira Grossi (2023): Ejection effect in a low-head
hydropower plant: turbine power and efficiency, Journal of Applied Water Engineering and
Research, DOI: 10.1080/23249676.2023.2201476
To link to this article: https://doi.org/10.1080/23249676.2023.2201476
© 2023 The Author(s). Published by Informa
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Journal of Applied Water Engineering and Research, 2023
https://doi.org/10.1080/23249676.2023.2201476
Ejection effect in a low-head hydropower plant: turbine power and efficiency
Mauricio Romero a∗†, José Junji Ota b, Tobias Bleninger c, Paulo Henrique Cabral Dettmer d, Marcelo Luiz
Noriller dand Guilherme Moreira Grossi e
aPostgraduate Program in Water Resources and Environmental Engineering PPGERHA, Federal University of Paraná, Curitiba, Brazil
bDepartment of Hydraulics and Sanitation, Federal University of Paraná, Curitiba, Brazil cDepartment of Environmental Engineering,
Federal University of Paraná, Curitiba, Brazil dInstitute of Technology and Development (LACTEC-CEHPAR), Curitiba, Brazil
eIberdrola Renovables Energía, S.A.U, Rio de Janeiro, Brazil
(Received 10 December 2021; accepted 4 April 2023)
The aim of this research is to complement and improve the results about ejection effect in a low-head hydropower plant
from a previous study in physical models and to evaluate the effect of ejection on the turbine power and efficiency, in the
model alternative with the best performance. The study covers four additional geometric alternatives, aside from the original
design and the six already tested alternatives in that study, using 1:70 scale model tests. Three approaches were considered:
(1) The development of a theoretical equation for the ejection effect, based on the equations of conservation of momentum
and energy, (2) An assessment of an empirical relationship for the effective ejection using dimensionless flow parameters
from 521 flow scenarios and (3) The development of two empirical relationships between the effective ejection and the
power and efficiency increments of the HPP turbines (63 flow scenarios).
Keywords: Ejection effect; ejection characteristics curves; hydraulic models; low-head hydropower plant; turbine power
and efficiency
1. Introduction
A currently accepted view indicates that, the exploration of
small hydropower plants (HPP), from 100 to 1000 kW with
very small hydraulic head differences, (such as 0.80 m), is
an attractive hydraulic resource from an economic and eco-
logical point of view (Butera et al. 2020). As an example,
for Amazonian rivers, low head hydro plants are practi-
cally the only option, since larger facilities will create also
larger reservoirs and flooded areas with adverse ecological
and socioeconomical effects (Lees et al. 2016).
However, there are still problems, often related to the
inefficiency of small plants with turbines and negative eco-
logical effects (Wiemann et al. 2007). Besides, compared
with larger units, low-head hydropower plants are less eco-
nomic, and the efficiency level of the hydro power unit
decreases with the deceasing size.
In addition, low-head HPPs do not have a reservoir
to store water, thus, their electricity production varies
according to the hydrological characteristics of the river.
Therefore, usually large amounts of water pass through the
spillway during high flow events, without being used to
generate energy (Majumder and Ghosh 2013).
Schiffer et al. (2015) show the possibility of increas-
ing the available hydraulic head at the draft tube outlets by
applying the ejection effect in low-head HPP, with power
∗Corresponding author. Email: mauricioromero.m@fcyt.umss.edu.bo
†Currently at San Simon University (UMSS) as staff researcher, Hydraulics Laboratory (LHUMSS), Cochabamba, Bolivia.
This article has been corrected with minor changes. These changes do not impact the academic content of the article.
increments up to 25% compared to a conventional HPP
during flood events (Romero et al. 2019).
The first studies of that type were produced by Soviet
researchers, back in the earliest decades from the twentieth
Century. Romero et al. (2019) indicate that the most impor-
tant research works, through the use of physical models,
are the ones of Veits (1947), Kachanovskii (1947), Egorov
(1948), Ermakov (1949), Serkov (1967), Mustafin (1951),
Slisskii (1953), Borayev (1979) and Schiffer et al. (2015).
Another interesting study was performed by Fritsch
et al. (2015) on real prototype turbines at hydropower
plants of Mühltalwehr and Stadtwehr in Austria, where a
special type of ejector power plant (run-of-river type) was
equipped with a vertical Kaplan turbine and a bent draft
tube. The results of field measurements were compared to
the ones of tests in a laboratory and with empirical formu-
las. A significant increase of power and further operational
advances were achieved by means of an implemented
ejector gate.
In Brazil, studies on hydropower gain using the ejection
effect were initiated by Yamakawa and Terabe (2016)using
a physical model (1:70). Romero et al. (2019) described an
early stage of the present research in 1:70 physical scale
models, considering six variants from an initial low-head
HPP design. In addition, Cabral Dettmer et al. (2019)used
© 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/
by-nc- nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed,
or built upon in any way. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.

2M. Romero et al.
a CFD-model, through the open-source software Open-
FOAM, to assess the ejection effect in the same HPP initial
design, comparing their results to the corresponding mea-
sured values in the physical model and to the theoretical
results from the model of Slisskii (1953).
The ejection effect, applied to a low-head HPP is the
application of the Venturi Effect to a channel with free sur-
face flow (Wiemann et al. 2007). The flow acceleration
hereby is caused by the injection of high-speed jets through
an ejector structure (a spillway or lateral or bottom con-
duits), which consequently reduces the downstream water
level, thus increasing the head difference (Sheaua 2016;
Tukimin et al. 2016; Zhang 2017). This difference results in
an additional gain in head at the draft tube outlet, increas-
ing the energy production. The downside of the ejection
effect is that it is only applicable when an excess of water
passing through the HPP is available.
Ejection in a low-head HPP is a rather difficult prob-
lem to address, due to the 3D field flow characteristics
caused by the mixing of hydraulically unequal jets, exiting
from both the turbine draft tubes and the bottom or lateral
conduit outlets.
More important, studies about the ejection effect con-
cerning submerged conditions (backwater effect) at the
ejector structure outlet are rather scarce and not readily
available, and to date, no research work has taken into con-
sideration a series of wall-jets exiting from outlets having
different aspect ratios (ζ), ζ=height/width, in relation to
the draft tubes.
In this sense, the aim of this research is to complement
and improve the results illustrated in Romero et al. (2019)
and to evaluate the effect of the ejection effect on the tur-
bine power and efficiency, in a model alternative with the
best performance.
The study covers four additional geometrical alterna-
tives, aside from the original design and the six already
tested alternatives in Romero et al. (2019), using 1:70 scale
model tests. Three approaches were considered:
(1) The development of a theoretical equation for the
ejection effect, based on the equations of conserva-
tion of momentum and energy,
(2) An assessment of an empirical relationship for the
effective ejection using dimensionless flow param-
eters and
(3) The development of empirical relationships
between the effective ejection and the power and
efficiency increments of the HPP turbines.
2. Ejection effect
The ejection effect, or simply ejection, is caused by the
mixture of the excess flow coming out from an ejector
structure (either a spillway or a lateral conduit) and the flow
exiting the draft tube of the turbine.
Figure 1. HPP scheme of functioning (a) conventional
(Qb=0) (b) hydro-combined (Qb>0); elevation of main chan-
nel: zmc; datum elevation: zd; elevation of the conduit bottom end
at the exit of the HPP: zb; elevation of the channel ground level at
the outlet of the HPP: zgl (modified from Romero et al. 2019).
The high-speed outlet jet from the ejector transmits part
of its kinetic energy and momentum to the lower speed jet
from the turbine, causing in turn, drops in the static head
at the draft tube and the tailrace level in the surroundings
of the facility, thus, increasing the effective turbine head
(Schiffer et al. 2015).
For a total turbine discharge (Qt), Figure 1shows two
HPP functioning schemes (Romero et al. 2019): (a) a con-
ventional scheme, where the total discharge exiting the
bottom conduits (Qb) is zero, Qb=CdAb√2gHst, and (b)
a hydrocombined scheme where Qb>0. Cd=discharge
coefficient of lateral conduits, Ab=b×h1=total cross-
section area of the exiting jet through the lateral conduits,
b=total bottom width of conduits, h1=opening height
at the bottom discharge gates, Hst =existing head between
the water level upstream the HPP and the tailrace.
The total piezometric effect of the ejection (hej ,tot) can
be assessed by the expression hej ,tot =z2–z1, where (z2)is
the water level of the tailrace (see Figure 1(a)) for a hydro-
combined scheme, z1=zgl +htis the piezometric level
measured at the bottom of the draft tube outlet, (ht)isthe
piezometric head below the water, measured from the bot-
tom end of the conduit outlet and, (zgl) is elevation of the
ground level at the outlet of the HPP.
For a conventional scheme, the gain of head of the
turbines (h) is assessed through a formula proposed by
Slisskii (1953) and described in detail in Romero et al.
(2019). Ead and Rajaratnam (2002) showed that, in plane
turbulent wall-jets with finite tailwater depths, the momen-
tum flux of the forward flow at the wall-jet presents a
noticeable decay with distance from the issuing nozzle.
This decay is due to the entrainment of the induced reverse
flow, which has a negative momentum, thus, requiring
a reduction hof the water surface near the slot exit
(pressure gradient).
Other expressions to evaluate hwere proposed by
Ead and Rajaratnam (2002) for turbulent wall-jets with

Journal of Applied Water Engineering and Research 3
Table 1. Information in prototype values of the total lateral
conduits discharge: Qb; overflow discharge from a spillway of
the HPP: Qsp ; turbinate discharge: Qt; water level at cross–
section II-II (tailrace): z2; efficiency coefficient for h:ηcand
number of conventional and hydrocombined tests; normal pool
level upstream the HPP: zo=60.00 m; Alternative 01.
QbQtQsp z2
(m3s−1)(m
3s−1)(m
3s−1)(m)
Min 0 1920 0 35.22
Max 1812 1994 3200 40.73
ηc0.70
Conventional
tests 9
Hydrocombined
tests 8
very simple geometries and Bhuiyan et al. (2011), with a
second order equation for hfor an offset-jet. Dey et al.
(2017) pointed out that his created due to flow sub-
mergence and Oskouie et al. (2019) indicate a correlation
between the increase of jet discharge and h.
Therefore, the so-called effective ejection effect (hej ,ef ),
hej ,ef =hej ,tot –h–Htis calculated from both the con-
ventional and hydro-combined schemes, where (Ht)are
the head losses along the HPP (intake of the spiral case,
central vortex structure and the related wall shear, along the
draft tube). For practical purposes, it is commonly assumed
that Ht=0 (Slisskii 1953; Boži´
c2016).
To assess hej ,tot for submerged conduits (Figure 1),
Slisskii (1953) used the conservation equations of linear
momentum and energy (Energy – Momentum Equations)
to calculate htfor a control volume between cross-sections
I and II. The method consists of two sequential steps
(Romero et al. 2019): (a) the initial assessment of hej ,tot for
h=0 and (b) the calculation of hej ,ef by the expression
hej ,ef =hej ,tot –h–Ht, letting Ht=0.
3. Methodology
3.1. The physical model implementation
The physical model of the pilot HPP (Alternative 01;
Romero et al. 2019, p. 5789) was implemented in a flume
at the Institute of Technology for Development (CEHPAR-
LACTEC) in Curitiba, Brazil. It was designed based on
Froude’s law of similarity. The geometric scale of 1:70 was
adopted. The dimensions of the experimental channel are
2.92 m wide, 1.70 m high and 32 m long.
As illustration, the basic data from the prototype used
for the project design is presented in Table 1.
The aspect ratio of the turbine draft tubes is ζ=0.93
and variable for the lateral conduits cross-sections, con-
trolled by the gates depicted in Figure 2. The model charac-
teristics, the calibration processes and the obtained results
from the first six variants (Alternatives 02–07) concerning
the curves of Ejection Characteristics are well documented
Table 2. Geometric dimensions in prototype values and num-
ber of lateral conduits; the aspect ratio ζ=height/width; Alter-
natives 08–11.
Alternatives
Lateral Conduits 08 09 10 11
at both side
ends of
HPP
height (m) 12.40 6.00 12.40 –
width (m) 1.60 3.00 2.90 –
ζmax (m) 7.75 2.00 4.28 –
number 2 2 2 –
central height (m) 12.40 6.00 12.40 12.40
width (m) 2.90 6.00 5.50 5.50
ζmax (m) 4.28 1.00 2.25 2.25
number 2 2 2 2
in Romero et al. (2019) and therefore will not be discussed
here.
3.2. Implementation of Alternatives 08–11
Alternatives 08–11 are depicted in Figure 3and Table 2.
For Alternative 08, the cross-section variations in the con-
duits aimed to increasing the interaction surface between
both jets exiting the lateral conduits and draft tubes.
Alternative 09 had as main goal to evaluate the influ-
ence of the elevation of the initial bottom conduits (Alter-
native 01) on the ejection effect, where, according to Slis-
skii (1953), an improvement on hej ,ef should be observed
if the exiting jets of the lateral conduits reached the main
channel after the sloping part of the apron.
The total lateral conduits discharge (Qb) was doubled
for Alternative 10, in relation to the original design. Alter-
native 11 was implemented to assess the ejection effect
produced by only two central dischargers. This alterna-
tive aimed to lower the construction costs of the HPP,
by removing both conduits at the extremes of the chan-
nel, in addition to reducing the width of the main channel,
immediately downstream of the HPP.
For each alternative, both equations of conservation
of linear momentum, for an adopted control volume, and
energy (Equation of Bernoulli for lateral conduits) were
applied, in a procedure similar to that implemented for
Alternatives 01–07 (Romero et al. 2019, p. 5791).
The equation used to assess the value of the water depth
(ht) at the HPP outlet was obtained by applying the equa-
tions of conservation of linear momentum and Bernoulli’s
for a submerged conduit to a control volume, between
cross-sections I-I and II-II (Appendix 1), as:
h2
t=[2(h2−e)+d]d−1
B1
[2h2
2Blp −(h2−e)2B]
−2
gB1
[VtQt−V2Q2+CvQb
×2gHst +V2
o
2g+h2−e+d+ht(1)

4M. Romero et al.
Figure 2. Plan and lateral views of the powerhouse and one hydropower unit (modified from Romero et al. 2019).
Figure 3. Lateral views of studied alternatives (08–11), maximum aspect ratio: ζmax; height of the sloping part of the apron: d;widthof
both the channel and ramp near the HPP: B1; width of the lateral piers: Blp ; total channel width at section II-II: B.
where h2=water depth at section II-II (m), e=height
of the step in Alternatives 06 and 07 (m), d=height of
the sloping part of the apron (m), B1=width of both the
channel and ramp near the HPP (m), B=total channel
width at section II-II (m), Blp =width of the lateral piers
(m), Vt=average flow velocity at the draft tube outlets (m
s−1), V2=average flow velocity in the channel at cross-
section II-II (m s−1), Vo=average flow velocity upstream
the HPP (m s−1), Qt=total turbine discharge (m3s−1),
Q2=total discharge in the channel downstream the HPP
(m3s−1), Qb=total lateral conduits discharge (m3s−1),
Hst =existing head between the water level upstream the
HPP and the tailrace (m), Cv=velocity coefficient (–),
g=acceleration of gravity (m s−2).
Equation (1) is a fourth-order polynomial, in which, by
the Descartes’ rule of sign, the function f(ht4) presents
two negative and two positive zeroes. The value of ht(the
third real positive zero) in which z2>z1or hej ,ef >0is
considered the physically correct solution. Hence, for a
given ht, values of z1=zgl +htand (hej ,ef )tm =z2−z1
are also known. The subscript (tm) denotes ‘theoretical
model’. A corrected and final value of the theoretical
value of the effective ejection is given by the expression
hej ,ef =ϕc(hej ,ef )tm.
A correction factor ϕc=(hej ,ef )pm/(hej ,ef )tm =
f(Qt/QTot ), as a function of Qtand the total discharge in the
system QTot =Q2+Qsp (Appendix 2), was implemented
again for each new alternative (see Figure 4). The subscript
(pm) denotes ‘physical model’. The overflow discharge
from a HPP spillway (Qsp ) was not included in the physi-
cal model (Romero et al. 2019, p. 5790), but it is essential
to set the downstream elevation z2through the known
rating curve h2vs QTot at section II-II downstream the
HPP.

Journal of Applied Water Engineering and Research 5
Figure 4. Diagrams ϕcvs. Qt/QTot for studied alternatives, cor-
rection factor: ϕc; total turbine discharge: Qt; total discharge
in the system: QTot ; effective ejection measured in the physical
model; (hej ,ef )pm.
The theoretical calibration of hej ,ef for Alternatives 08–
11 was performed using information of Qb,Q
t,z2and the
correction coefficient (ηc)forhfrom Slisskii (Romero
et al. 2019, p. 5788) from 27 and 13 hydrocombined and
conventional tests in the physical model respectively. The
normal pool level upstream the HPP (zo)wassetto60m
and Qsp varied from 0 to 3189 m3s−1in prototype values.
As illustration, Figure 5presents the flow chart of the
methodology to obtain the effective ejection hej ,ef .
3.3. Turbine power and efficiency related to effective
ejection
A lot of research has been done in recent years concerning
aspects about Kaplan turbines, by means of experimental
data from hydraulic models, combined with CFD studies
like, for instance, hydraulic losses (Höfler et al. 2011;Jošt
et al. 2014; Lipej 2015; Boži´
c2016), efficiency and power
(Gajic et al. 2004; Motycak et al. 2010; Ko and Kurosawa
2014).
Power (P) and efficiency (ef) of a turbine are related
as P=efγQt(Hst –Ht) (Agrawal 1997; Williamson
et al. 2011), where (γ) is the specific weight of water. The
difference between Hst –Htis referred as the net head of
the turbine (Hsn) (Agrawal 1997). The subscript (s)inHsn
is referred to whether Step 1 or 2is considered for Hst (see
Figure 5).
An expression for Ht=CpQK2is presented in
Austergard and Schumacher (2010) and Isaksson (2015),
where (Cp) is a pressure drop coefficient and (QK)is
the discharge on each Kaplan turbine. In the present
research QK=Qt/3 and Cp=4.86 ×10−6s2m−5.The
value of Cpwas provided by the Kaplan turbine manu-
facturer for the prototype, for a vertical axis turbine of
diameter =9380 mm and revolution =76 rpm.
Figure 6(a,b) illustrates the Kaplan turbine hill charts
for Pand ef, both provided by the turbine manufacturer,
Figure 5. Methodology flow chart to obtain the effective ejec-
tion: hej ,ef .
as a function of Qtand Hn. The following regression
models were calibrated, with multiple determination coef-
ficients (R2) of 0.9974 and 0.9876 for Equations (2) and (3)
respectively:
P=1543.298 −204.595Hn−2.461Qt+0.343HnQt
−3.837 ×10−3(H2
nQt)−5.789 ×10−5(HnQ2
t)
+0.067H3
n+1.604 ×10−7(Q3
t)(2)
ef=33.125 +1.270Hn+3.482 ×10−2(Qt)
+1.134 ×10−3(HnQt)
−6.320 ×10−2(H2
n)−1.410 ×10−5(Q2
t)(3)
Line 7–6 from Figure 6(a) depicts the operational limit
showing the maximum total turbinate discharge Qt=1950
m3s−1, whereas line 8–7 shows the operational limit
of the turbine distributor (100% open), where 1843 m3
s−1≤Qt≤1950 m3s−1and 19.0 m ≤Hsn ≤21.0 m (see
Equation (4)). Along this later line, increments of power P
and efficiency efare expected to occur, both as functions
of the effective ejection hej ,ef .
Qt=832.77 +52.02Hsn (4)

6M. Romero et al.
Figure 6. Provided hill charts from the turbine manufacturer of (a) power P(b) efficiency ef,depicting operational limit conditions for
turbines operation and ejection effect (lines 8–7–6), total turbine discharge: Qt; net head available for the turbines: Hn; turbine distributor
opening (%): ao. Blue lines in both hill charts illustrate other operational limits.
Table 3. Information in prototype values of the total lateral conduits discharge: Qb; overflow discharge from a spillway of the HPP:
Qsp ; turbinate discharge: Qt=1500 m3s−1; water level at cross-section II-II (tailrace): z2; efficiency coefficient for h:ηcand number
of simulated hypothetical flow scenarios for the effective ejection: hej ,ef ; normal pool level upstream the HPP: zo=60.00 m; Alternatives
08–11.
Alternative 08 Alternative 09
QbQsp z2QbQsp z2
(m3s−1)(m
3s−1)(m)(m
3s−1)(m
3s−1)(m)
min 1212 0 37.71 1212 0 37.71
max 1812 3700 43.29 1812 3700 43.29
Calibrated ηc1.41 0.70
Hydrocombined simulations 40 40
Alternative 10 Alternative 11
QbQsp z2QbQsp z2
(m3s−1)(m
3s−1)(m)(m
3s−1)(m
3s−1)(m)
min 1800 0 38.73 1800 0 38.73
max 3540 1800 41.32 2400 3700 41.27
Calibrated ηc1.20 1.57
Hydrocombined simulations 57 40
To assess the increments of power (P∗), P∗=[(P2
–P1)/P1]×100% and efficiency (e∗
f), e∗
f=[(e1f–
e2f)/e1f]×100% for any given alternative, the iterative
procedure to obtain hef ,ej ,Qt,Qb,Hst and Hsn shown in
Figure 5is repeated until Qtsatisfy Equation (4). Sub-
scripts 1and 2denote ‘Step 1’ and ‘Step 2’ respectively
(see Figure 5). Once this procedure is completed for
each flow scenario, the above expressions can be used to
calculate P1,P2,e1f,e2fand hence P∗and e∗
f.
4. Results and discussion
4.1. Best alternative found
Values of hej,ef were produced for Alternatives 08–11 from
177 hypothetical flow scenarios (see Table 3) following
the described procedure in item 3.2. The total maximum
turbinate discharge Qt=1500 m3s−1was set as constant
for both step calculations depicted in Figure 5.
The curves of Ejection Characteristics of the submer-
gence (Z∗) and the dimensionless effective ejection (h∗),
Z∗=z2/zovs. h∗=hej ,ef /h2, are presented in Figure 7for
several values of the discharge ratio (Q∗), Q∗=Qt/Qb.
In addition, Table 4shows the regression models for
the maximum Ejection Characteristics Z∗=f(h∗max) and
Q∗=f(h∗max).
A general plot of curves Z∗=f(h∗max) is presented
in Figure 8for all alternatives studied, including the
results depicted in Romero et al. (2019). Alternative 08
shows a remarkable variation in the trajectory of curve
Z∗=f(h∗max) related to Alternatives 01–07, due to the
change in the dimensions of the cross-sections of the lateral
bottom conduits.
In Alternative 09, elevating the bottom outlets of the
lateral conduits from zgl =zb=8.80 m (Figure 1, Alter-
native 01) to zb=15.41 m (Figure 3), increased h∗max in
relation to Alternative 08, providing that the off-set jets

Journal of Applied Water Engineering and Research 7
Figure 7. Curves of Ejection Characteristics Z∗=z2/zovs. h∗=hej,ef /h2for different values of the discharge ratio parameter:
Q∗=Qt/Qb; alternatives (a) 08 (b) 09 (c) 10 and (d) 11; total turbine discharge: Qt=1950 m3s−1(prototype); normal pool level
upstream the HPP: zo=60.0 m (prototype); submergence parameter: Z∗; dimensionless effective ejection parameter: h∗.
Table 4. Functions of ejection characteristics Z∗=a(hmax∗)b,Q∗=a(hmax∗)b; submergence parameter: Z∗=zo/z2; discharge ratio
parameter: Q∗=Qt/Qb; dimensionless effective ejection parameter: h∗=hej ,ef /h2; turbinate discharge: Qt=1.950 m3s−1; normal
pool level upstream the HPP: zo=60 m (prototype).
Z∗=a(hmax∗)bQ∗=a(hmax ∗)b
Alternative abR
2abR
2
08 0.913 0.1383 0.9971 0.006 −2.1027 0.9996
09 0.877 0.1307 0.9916 0.011 −1.9692 0.9972
10 1.143 0.2490 0.9592 0.031 −2.5399 0.9790
11 0.985 0.1896 0.9845 0.006 −2.3266 0.9888
impinge beyond the sloping part of the apron, as observed
during the experimental tests (Slisskii 1953; Serkov 1967).
Significant improvements in the hej ,ef magnitude were
accomplished through Alternatives 10 and 11, due to the
rather different geometric dimensions of the bottom con-
duits. From Figure 8, it is observed that Alternative 11 is
the best among all the cases studied, including the initial
results achieved in Romero et al. (2019).
In addition, the geometric configuration of the HPP
in Alternative 11 favours a better interaction and mix-
ing between both wall-jets exiting the lateral conduits and
the draft tubes, contributing in turn to a more efficient
exchange of kinetic energy, linear momentum and flow
entrainment between the higher and lower velocity jets
(Schiffer et al. 2015; Craske 2016). A shorter channel at
the HPP outlet in this alternative (B1=129.05 m in Figure
3), has an additional influence on the average velocities in
the main channel, compared to the other alternatives.
Additionally, Alternative 11 presents the following
advantages: (a) lateral conduits with enhanced con-
veyance; (b) simplified HPP operational issues; and (c)
the lowest implementation costs. However, some aspects
should also be considered as drawbacks: (a) reversal flow
regions, which are still present and might cause horizon-
tal oscillations on the submerged jump, and, in return, an
ejection effect reduction (Slisskii 1953; Borayev 1979) and
(b) scouring processes are likely to occur in the sloping
part of the apron, due to high flow velocities exiting the

8M. Romero et al.
Figure 8. Curves of maximum Ejection Characteristics,
Z∗=z2/zovs. h∗max =(hej ,ef )max/h2; total turbine discharge:
Qt=1950 m3s−1(prototype); normal pool level upstream the
HPP: zo=60.0 m (prototype); submergence parameter: Z∗;max-
imum dimensionless effective ejection parameter: h∗max. Alterna-
tives 01–07 are extracted from Romero et al. (2019).
lateral conduits (Hassan and Narayanan 1985; Chatterjee
et al. 1994; Dey and Sarkar 2006; Hamidifar et al. 2011;
Aamir and Ahmad 2019).
4.2. Empirical model relating effective ejection to
hydrodynamic variables
A power function hej ,ef =a(Q∗)b(Z∗)c(Fo)dwas explored,
where the Froude number (Fo) at the outlets of the lateral
conduits, Fo=Vb/(gh1)0.5, it is an important factor in jet
studies (Ead and Rajaratnam 2002; Dey and Sarkar 2008;
Dey et al. 2017,2019).
The regression was performed using 521 (hej ,ef ,Q∗,
Z∗,F
o) available data from Alternatives 01–11 (physi-
cal model and theoretical simulation results). A random
number of 419 data (80%) were used for the model
calibration, leaving the remaining 102 (20%) for val-
idation. The correlation analysis considered the Proba-
bility Values (P-values) for the regression coefficients
(a, b,cand d), the Absolute Mean Error (AME) and
the Nash-Sutcliffe Coefficient (NS) (Equations 5 and 6;
Romero 2013).
AME =N
i=1|(hej ,ef )data−(hej ,ef )rm |
(hej ,ef )data
N×100% (5)
NS =1−N
i=1[(hej ,ef )data −(hej .ef )rm]2
N
i=1[(hej ,ef )data −(hej ,ef )data]2(6)
where the subscript rm denotes ‘regression model’ and
N=total amount of data.
Figure 9presents both the diagrams of h∗data vs. h∗rm
for calibration and validation of the regression model and
Table 5illustrates the statistics of the regression results for
Equation (7). Values of AME =12.96% and NS =0.8541
Table 5. Regression statistics for Equation
(7); adjusted R2=0.7430; a=0.0040; stan-
dard error: SE.
Variable Value P-Value SE
log(a)−2.3957 1.32E-164 0.052
b−1.0634 3.51E-82 0.044
c−7.9521 1.216E-91 0.299
d−0.4148 1.37E-11 0.060
were obtained for the calibration stage and AME =8.16%
and NS =0.9222 for the validation stage.
h∗=0.0040(Q∗)−1.0634(Z∗)−7.9521 (Fo)−0.4148 (7)
Equation (7) shows that h∗is inversely proportional
to Q∗,Z∗and Foat the exit of the gates from the lateral
conduits. The magnitude of the exponents is an indicator
of the order of importance of the hydrodynamic variables
considered in relation to the effective ejection.
From that, it is clear that the flow submergence plays
a preponderant role on the effective ejection, followed
by the turbine/ejector discharge rate (Kachanovskii 1947;
Slisskii 1953; Dey et al. 2017; Romero et al. 2019) and
the flow regime at the exit of the gates of the lateral
conduits.
Ead and Rajaratnam (2002) and Bhuiyan et al. (2011)
illustrate direct relationships between the water level drops
at the submerged outlet from a single slot or gate, issuing
reattached wall and offset jets respectively into a qui-
escent pool, and the corresponding Froude numbers Fo.
The present case is much more complex, involving joint
interactive jets at different speeds in a highly turbulent
environment (Hoch and Jiji 1981; Karimpour et al. 2011;
Ball et al. 2012; Ferraro et al. 2016; Oskouie et al. 2019),
with important variations of the lateral conduit’s aspect
ratio ζ. As illustration, Figure 10 presents a plot of the
effective ejection h∗vs. Fofor all available data, depict-
ing an inverse relationship between both variables and
somehow confirming the physical meaning of the negative
exponent for Foin Equation (7).
4.3. Empirical models for effective ejection and turbine
power and efficiency
To find the empirical relationships between the effective
dimensionless ejection (h+), h+=hej ,ef /Hsn as a function
of the increments P∗and ef∗, data from the experimen-
tal tests and theoretical simulations of Alternative 10 were
used, which has the widest range of flow rates observed
among all the other alternatives (see Figure 7(c)).
The procedure shown in point 3.3 was applied to the
data from 6 experimental tests in the physical model
(hydrocombined scheme) and 57 simulated hypothet-
ical scenarios. The range of the initial applied dis-
charges for Step 1 (s=1, Figure 5) were: 1921 m3

Journal of Applied Water Engineering and Research 9
Figure 9. Regression (a) and validation (b) diagrams of h∗data vs. h∗rm from Alternatives 01–11. Subscripts data and rm: ‘experimental
and theoretical data’ and ‘regression model’ respectively.
Figure 10. Diagram Fovs. h∗from Alternatives 01–11; Froude
number at the exit gate of the lateral conduits: Fo; dimensionless
effective ejection parameter: h∗.
s−1<Qt<1950 m3s−1;630 m3s−1<Qb<3560 m3
s−1;0<Qsp <1800 m3s−1and the considered water
levels were: zo=60.0 m; 36.53 m <z2<41.13 m.
As illustration, Figure 11 presents the charts of h+
vs. Q∗as a function of P∗and ef∗. Figure 11(a) shows
that, along line 8–7 (1843 m3s−1≤Qt≤1950 m3s−1),
for decreasing values of Q∗(Qt<Qb), the effective
ejection h+increases as well as P∗, within a range of
1% <P∗<26%, which is in agreement to the range
of 18–25% reported by Schiffer et al. (2015)forP∗.
The effective ejection h+also increases with ef∗when
Q∗decreases. The observed range of the increment is
0.16 <ef∗<1.54% (see Figure 11(b)).
As a final step, Equations (8) and (9) present the regres-
sion equations for the turbine power P∗and efficiency ef∗
increments as functions of the effective ejection h+, both
equations are valid for the boundary line 8–7 (1843 m3
s−1≤Qt≤1500 m3s−1and 19.0 m ≤Hsn ≤21.0 m) and
have determination coefficients R2of 0.9113 and 0.9859
respectively.
P∗=2870.637(h+)2.1888 (8)
e∗
f=33.962(h+)1.4262 (9)
5. Conclusions
In the present research work, the ejection effect in a low-
head hydropower pilot plant with lateral conduits was stud-
ied. The research included four geometrical alternatives to
the original design and six already tested alternatives from
a previous study, under submerged downstream condition,
using 1:70 scale models tests. As an initial approach, a
theoretical equation was proposed to assess the water ele-
vation at the exit of HPP and, therefore the ejection effect
under submerged conditions. This equation is based on
the equations of conservation of linear momentum and
energy. As a second approach, an empirical regression
model was obtained and validated from 521 flow scenarios.
The proposed model related the measured and theoretically
obtained effective ejection to relevant flow variables.
Finally, an analysis of the turbine power and efficiency
was performed for the alternative with the widest range of
tested discharges (Alternative 10) in relation to the effec-
tive ejection, along a borderline imposing the operational
limit of the turbine distributor (100% open).
Hence, from the above stages, the following conclu-
sions are obtained:
•For all the four studied alternatives, the maximum
Ejection Characteristics Z∗=f(h∗max) and Q∗=f
(h∗max) were found.
•The best model alternative was identified, within a
number of variants, tested both in the physical and
theoretical models. In this alternative, the geomet-
ric dimensions of the conduits (high-aspect ratio ζ)
contributed to a better interaction and mixing of the
exiting wall-jets from both the lateral conduits and
the draft tubes, thus, increasing more efficiently an

10 M. Romero et al.
Figure 11. Charts of (a) h+vs. Q∗as a function of the power increment: P∗and (b) h+vs Q∗as a function of efficiency increment:
ef∗for boundary line 8–7; dimensionless effective ejection: h+=hej .ef /Hn; neat head: Hn; discharge ratio parameter: Q∗=Qt/Qb;total
turbine discharge: Qt; total lateral conduits discharge: Qb.
exchange of kinetic energy, linear momentum and
flow entrainment, between the jets of higher and
lower speed.
•The best alternative presented additional advantages
like enhanced conveyance of the bottom conduits
and simplified HPP operational and maintenance
costs. However, hydrodynamic processes that could
reduce the effective ejection and cause local scour-
ing at the HPP afterbay should be addressed, like for
instance the streamwise submerged jump horizontal
flow oscillations, flow turbulence and the interaction
between the high-speed wall-jets exiting the bottom
conduits and the sloping part of the apron.
•The order of importance, from highest to lowest, of
the studied variables in the prediction of the effective
ejection is given by the relative flow submergence
Z∗, the ratio of the turbine and lateral conduits dis-
charges Q∗and the Froude number Foat the outlets
of the lateral bottom conduits gates.
•Two empirical relationships between the effective
ejection effect hej ,ef and the Kaplan turbine’s power
P∗and efficiency ef∗increments were found from
63 flow scenarios for the model alternative with
the widest discharge range for the lateral conduits,
which are valid for the operational limit of the
turbine distributor (100% open).
•This one-dimensional approach needs to be cali-
brated in a physical model or prototype taking into
account the geometric modifications of the studied
case (1D or 2D). This leads to obtaining a cor-
rection function of ϕcvs. Qt/QTot (see Figure 4),
which is specific to each case studied, such that
hej ,ef =ϕc(hej ,ef )tm
The present research dealt with very complex and chal-
lenging issues, mostly on the matter of addressing the
ejection effect under drowned conditions, complex flow
fields characteristics due to the HPP and downstream chan-
nel geometries, jets of different velocities issuing from
outlets of very different aspect-ratios ζin relation to the
corresponding ones from the draft tubes, all of them placed
side by side and interacting in a way that was not studied
previously.
Unfortunately, the tested physical models did not allow
to verify experimentally generated turbine power and effi-
ciency, especially when talking about a real operation
range in the real turbine hill chart. But as a first attempt
to get some results from a very complex research work and
technical restrictions, it is believed that the obtained results
are reasonable and of course, they can be improved in the
future.
An interesting continuation of the present study would
be to additionally consider the modification of the aspect
ratio ζof the draft tube outlets, in order to improve the
results achieved so far. Special emphasis should be given
on considering the situation where width is larger than
height.
In this sense, this paper expects to encourage further
research on this promising technique, that may contribute
to provide an extra amount of energy and power to the
beneficiaries, taking advantage of flood discharges, that
otherwise would go through the HPP wasted.
Acknowledgements
The first author wants to gratefully acknowledge the Post-
graduate Programme in Water Resources and Environmental
Engineering (PPGERHA) at the Federal University of Paraná
UFPR, the Institute of Technology for Development (LACTEC-
CEHPAR) in Curitiba, Brazil and San Simon University UMSS
in Cochabamba, Bolivia, for the continuous support during his
studies and research at UFPR.

Journal of Applied Water Engineering and Research 11
Disclosure statement
No potential conflict of interest was reported by the author(s).
Funding
This research was supported by the CAPES Foundation of the
Brazilian Ministry of Education −MEC, through a scholarship
fund for doctoral studies No. 88882.461738/2019-01 at the Fed-
eral University of Paraná −UFPR, in the framework of the
PPGERHA Programme (code 40001016021P0). The experimen-
tal part was funded by GERAÇÃO CIII S.A, ITAPEBI S.A. and
C. H. TELES PIRES S.A., through a Research and Develop-
ment Programme regulated by Brazilian Electricity Regulatory
Agency – ANEEL (Agência Nacional de Energia Elétrica) reg-
istered as P&D-6559-0001/2017, executed by the Institute of
Technology and Development −LACTEC. Tobias Bleninger
acknowledges the productivity stipend from the National Council
for Scientific and Technological Development – CNPq, grant no.
312211/2020-1, call No. 09/2020.
Notes on contributors
Mauricio Romero Civil Engineering (1992) at the Universidad
Mayor de San Simon (UMSS, Cochabamba, Bolivia). Master’s
degree at the Vrije Universiteit Brussel (Belgium, 1997), Doc-
toral studies in Water Resources and Environmental Engineering
from PPGERHA Programme of the Federal University of Paraná
UFPR (Curitiba, Brazil) (2020). Professor at the Civil Engineer-
ing Department of the UMSS and former director of the Hydraulic
Laboratory of UMSS (LHUMSS, 2005, 2007–2016). Areas of
specialization: fluid mechanics, physical and numerical mod-
elling, groundwater hydrology, sediment transport, erosion and
scour in high mountain rivers, water resources and environmental
engineering.
José Junji Ota Graduated in Electronic Engineering from
Federal Technological University of Paraná (1981), Gradu-
ated in Civil Engineering from Federal University of Paraná
UFPR (1975), Master’s in Civil Engineering from University of
Kanazawa (1983) and Ph.D. in Engineering at Newcastle Upon
Tyne (1999). He is currently an Adjunct Professor at the Federal
University of Paraná and a researcher at the Institute of Technol-
ogy for Development LACTEC-CEHPAR. He has experience in
Civil Engineering, with an emphasis on Hydraulics, acting on the
following topics: hydraulic works, sediment transport, spillways,
SHPs, reduced physical models and mathematical models.
Tobias Bleninger Professor (2011) for Environmental Fluid
Mechanics, and Applied Mathematics at the Department of
Environmental Engineering of the Federal University of Paraná
(UFPR) in Curitiba, Brazil. He is a Civil Engineer (2000) from the
Karlsruhe Institute of Technology (KIT), Germany, where he did
his Doctor in Environmental Fluid Mechanics (2006) and lead the
research group of Environmental Fluid Mechanics of the Institute
for Hydromechanics (2007–2011). Tobias Bleninger has experi-
ence in Hydraulics and Fluid Mechanics, with focus on physical
and numerical modelling of Mixing and Transport Processes of
Environmental Fluid Systems.
Paulo Henrique Cabral Dettmer Civil engineer with master’s
degree in Water Resources Engineering from the Federal Univer-
sity of Paraná (UFPR). He works as a researcher at the Institute of
Technology for Development (LACTEC-CEHPAR), developing
hydraulic model studies for more than 9 HPP´s.
Marcelo Luiz Noriller Graduated in Environmental Engineering
at the Federal University of Paraná UFPR (2014) and Master’s
student at the Postgraduate Program in Water and Environmental
Resources PPGERHA at UFPR. He is a researcher engineer at
Institute of Technology for Development (LACTEC-CEHPAR),
where he works in the area of Hydraulic Engineering in reduced
hydraulic models of hydropower plants.
Guilherme Moreira Grossi Civil Engineer (1998–2002) from
the Federal University of Minas Gerais (Belo Horizonte, Minas
Gerais, Brazil), postgraduate in Project Management (2012) from
the Getúlio Vargas Foundation (Curitiba, Paraná, Brazil), spe-
cialist engineer in eolic-photovoltaic, hydroelectric and thermo-
electric projects at Neoenergia Renewables Board (2018–2021);
coordinator of hydroelectric projects (2010–2013) at VLB Engen-
haria; civil technical manager of hydroelectric projects (2009–
2010) by ERSA Energias Renováveis SA.
ORCID
Mauricio Romero http://orcid.org/0000-0002-4523-5079
José Junji Ota http://orcid.org/0000-0001-9653-1495
Tobias Bleninger http://orcid.org/0000-0002-8376-3710
Paulo Henrique Cabral Dettmer http://orcid.org/0000-0002-
9489-2286
Marcelo Luiz Noriller http://orcid.org/0000-0001-8424-8553
Guilherme Moreira Grossi http://orcid.org/0000-0001-6492-
1368
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Appendices
A. Appendix 1
A.1. Assessment of the value of the water depth (ht)at
the HPP outlet
This appendix presents the model used to directly estimate the
water depth (ht) at the exit of the HPP and then, the water
elevation (z1) for submerged condition. Equations of conserva-
tion of both linear momentum and energy (Bernoulli equation)
were applied to obtain an expression for htfor a control volume
depicted in the scheme in Figure A1.1.
The linear momentum conservation equation for a control
volume between the exit cross-section of the HPP and Section
II-II downstream the structure is (Henderson 1966):
F=∫ρV(V·dA)(A1)
where (F) is a force acting on a control surface of the control vol-
ume, ρis the water density, Vis the flow velocity into or out of
Figure A1.1. Lateral and plan schemes of variables, discharges
and pressure distribution for the theoretical assessment of the
piezometric head below the water, at the exit of the HPP: ht.
the control volume through a control surface and (dA) is the dif-
ferential area through which the flow enters or leaves the control
volume.
Applying Equation (A1) for the variables represented in
Figure A1, for hydrostatic forces and uniform flow, downstream
the HPP:
1
2γh2
tB1+γh2
2Blp +1
2γ(2h2−e)eB1−1
2γh2
2B
−1
2γ[2(h2−e)+d]dB1=−ρ(VtQt+VbQb)+ρ(V2Q2)
(A2)
where (γ) is the specific weight of water and (Vb) is the aver-
age velocity of flow exiting the bottom conduits. Applying the
Bernoulli equation for Vband including a velocity coefficient
Cv=0.996 (Slisskii 1953):
Vb=Cv2gV2
o
2g+Hst +h2−e+d−ht(A3)
By combining and rearranging Equations (A2) and (A3),
Equation (1) is obtained for ht.
A. Appendix 2
A.1. Operational scheme for physical models
As illustration, Figure A2.1 from Romero et al. (2019)presents
the operational scheme of the studied models for downstream
boundary conditions at the tilting gate (rating curve h2vs QTot ).
A. Appendix 3
Notation
Avector of area (m2);
Attotal cross-sectional area of the turbine draft tubes
(m2);
aoturbine distributor opening (%);
Btotal channel width at section II-II (m);
Blp width of the lateral piers (m);
B1width of both the channel and ramp near the HPP
(m);
btotal width of the submerged conduits (m);
Cddischarge coefficient of lateral conduits (–);
Cppressure fall coefficient (s2m–5);
Cvvelocity coefficient (–);
dheight of the sloping part of the apron (m);
eheight of the step in Alternatives 06 and 07 (m);
efturbine efficiency (%);
ef∗increment of turbine efficiency (%);
Fvector of force (N);
FoFroude number at the exit gate of the lateral conduits
(–);
gacceleration of gravity (m s–2);
Hsn neat head available for the turbines (m);
Hst existing head between the water level upstream the
HPP and the tailrace (m);
h1gate opening height of lateral conduits (m);
h2water depth at section II-II (m);
hej ,ef effective ejection (m);
hej ,tot total ejection (m);
htpiezometric head below the water, at the exit of the
HPP (m);
h∗dimensionless effective ejection parameter, includ-
ing h2(–);

14 M. Romero et al.
h+dimensionless effective ejection including the neat
head Hsn (–);
Pturbine power (MW);
P∗increment of turbine power (%);
Q2the total discharge in the channel downstream the
HPP (m3s–1);
Qbtotal lateral conduits discharge (m3s–1);
QKthe turbine discharge on each Kaplan turbine
(=Qt/3) (m3s–1);
Qsp overflow discharge from a spillway of the HPP
(m3s–1);
QTot total discharge in the system (m3s–1);
Qttotal turbine discharge (m3s–1);
Q∗discharge ratio parameter (–);
R2determination coefficient;
ssubscript, 1 or 2 (for first or second calculation
Step);
t,bsubscripts for ‘turbine’and‘lateral or bottom con-
duits’;
tm,pm,rm subscripts for ‘theoretical model’, ‘physical model’
and ‘regression model’;
Vvector of flow velocity (m s–1);
V2average flow velocity in the channel at cross-section
II-II (m);
Vttotal average flow velocity at the draft tube outlets
(m s–1);
Vbtotal average flow velocity at the conduit outlets
(m s–1);
Z∗submergence parameter (–);
zonormal pool level upstream the HPP (reservoir) (m);
z1piezometric level measured at the bottom of the
draft tube outlet (m);
z2water level at cross-section II-II (tailrace) (m);
zbelevation of the conduit bottom end at the exit of the
HPP (m);
zddatum elevation ( =0.0 m);
zgl elevation of the channel ground level at the outlet of
the HPP;
hgain of head of the turbine (m);
Hthead losses along the HPP (m);
ρwater density (kg m–3);
ϕccorrection factor as a function of the total discharge
in the system QTot (–);
γspecific weight of water (N m–3);
ηcefficiency coefficient ranging from 0.5 to 0.9 (–);
ζaspect ratio of issuing nozzle or orifice (–).
Figure A2.1. Operational scheme of physical model for water levels assessments, based upon the rating curve h2vs. QTot at the tilting
gate (Romero et al. 2019); total discharge in the channel downstream the HPP: Q2; total turbine discharge: Qt; total lateral conduits
discharge: Qb; overflow discharge from a spillway of the HPP: Qsp ; total discharge in the system: QTot ; water depth at section II-II (tilting
gate): h2.